- This Week

- News in Focus

- Books & Arts

- Opinion

- Work

- Research

- Amendments & Corrections

- Innovations In

This Week

- Bring us your LLMs: why peer review is good for AI models

- Make trains great again — for the sake of people and the planet

- Equity in science is a beautiful lie — and I’m done pretending

EDITORIAL 17 September 2025

Bring us your LLMs: why peer review is good for AI models

Deepseek’s R1 model has been peer reviewed. Others should follow the firm’s example.

You have full access to this article via your institution.

Download PDF

Some of the risks of large language models can be mitigated if the tools are subjected to peer review.Credit: Matteo Della Torre/NurPhoto/Getty

None of the most widely used large language models (LLMs) that are rapidly upending how humanity is acquiring knowledge has faced independent peer review in a research journal. It’s a notable absence. Peer-reviewed publication aids clarity about how LLMs work, and helps to assess whether they do what they purport to do.

That changes with the publication[1] in Nature of details regarding R1, a model produced by DeepSeek, a technology firm based in Hangzhou, China. R1 is an open-weight model, meaning that, although researchers and the public do not get all of its source code and training data, they can freely download, use, test and build on it without restriction. The value of open-weight artificial intelligence (AI) is becoming more widely recognized. In July, US President Donald Trump’s administration said that such models are “essential for academic research”. More firms are releasing their own versions.

Since R1’s release in January on Hugging Face, an AI community platform, it has become the platform’s most-downloaded model for complex problem-solving. Now, the model has been reviewed by eight specialists to assess the originality, methodology and robustness of the work. The paper is being published alongside the reviewer reports and author responses. All of this is a welcome step towards transparency and reproducibility in an industry in which unverified claims and hype are all too often the norm.

DeepSeek’s paper focuses on the technique that the firm used to train R1 to ‘reason’. The researchers applied an efficient and automated version of a ‘trial, error and reward’ process called reinforcement learning. In this, the model learns reasoning strategies, such as verifying its own working out, without being influenced by human ideas about how to do so.

In January, DeepSeek also published a preprint that outlined the researchers’ approach and the model’s performance on an array of benchmarks[2]. Such technical documents, which are often called model or system cards, can vary wildly in the information they contain.

In peer review, by contrast, rather than receive a one-way flow of information, external experts can ask questions and request more information in a collaborative process overseen and managed by an independent third party: the editor. That process improves a paper’s clarity, ensuring that authors justify their claims. It won’t always lead to major changes, but it improves trust in a study. For AI developers, this means that their work is strengthened and therefore more credible to different communities.

Peer review also provides a counterbalance to the practice of AI developers marking their own homework by choosing benchmarks that show their models in the best light. Benchmarks can be gamed to overestimate a model’s capabilities, for instance, by training on data that includes example questions and answers, allowing the model to learn the correct response[3].

In DeepSeek’s case, referees raised the question of whether this practice might have occurred. The firm provided details of its attempts to mitigate data contamination and included extra evaluations using benchmarks published only after the model had been released.

Peer review led to other important changes to the paper. One was to ensure that the authors had addressed the model’s safety. Safety in AI means avoiding unintended harmful consequences, from mitigating inbuilt biases in outputs to adding guardrails that prevent AIs from enabling cyberattacks. Some see open models as less secure than proprietary models, because, once downloaded by users, they are outside of the developers’ control (that said, open models also allow a wider community to understand and fix flaws).

Reviewers of R1 pointed out a lack of information about safety tests: for example, there were no estimates of how easy it would be to build on R1 to create an unsafe model. In response, DeepSeek’s researchers added important details to the paper, including a section outlining how they evaluated the model’s safety and compared it with rival models.

Firms are starting to recognize the value of external scrutiny. Last month, OpenAI and Anthropic, both based in San Francisco, California, tested each other’s models using their own internal evaluation processes. Both found issues that had been missed by their developers. In July, Paris-based Mistral AI released results of an environmental assessment of its model, in collaboration with external consultants. Mistral hopes that this will improve transparency of reporting standards across the industry.

Given the rapid pace at which AI is developing and being unleashed on society, these efforts are important steps. But most lack the independence of peer-reviewed research, which, despite its limitations, represents a gold standard for validation.

Some companies worry that publishing could give away intellectual property — a risk, given the huge financial investment that such models have received. But, as shown with Nature’s publication of Google’s medical LLM Med-PaLM, peer review is possible for proprietary models[4].

Peer reviews relying on independent researchers is a way to dial back hype in the AI industry. Claims that cannot be verified are a real risk for society, given how ubiquitous this technology has become. We hope, for this reason, that more AI firms will submit their models to the scrutiny of publication. Review doesn’t mean giving outsiders access to company secrets. But it does mean being prepared to back up statements with evidence and ensuring that claims are validated and clarified.

Nature 645, 559 (2025)

doi: https://doi.org/10.1038/d41586-025-02979-9

References

1. Guo, D. et al. Nature 645, 633–638 (2025).

2. DeepSeek–AI et al. Preprint at arXiv https://doi.org/10.48550/arXiv.2501.12948 (2025).

3. Eriksson, M. et al. Preprint at arXiv https://doi.org/10.48550/arXiv.2502.06559 (2025).

4. Singhal, K. et al. Nature 620, 172–180 (2023).

Reprints and permissions

EDITORIAL 16 September 2025

Make trains great again — for the sake of people and the planet

As railways enter their third century of service, research must support their renaissance for more-sustainable travel that supports human development.

China leads the world in the scale of its expansion of high-speed rail, but there’s no settled view on the benefits of such networks. Credit: Wenpu Wang/Getty

You have full access to this article via your institution.

Download PDF

What if there were a technology that could help to reduce greenhouse-gas emissions, air pollution and environmental degradation, while improving health, reducing social inequality and boosting economic growth? There is, and this month it turns 200. The opening of the Stockton and Darlington Railway in northeast England on 27 September 1825 is generally considered to be the birth of the modern railway — an event that set in motion a revolution in human mobility and social organization.

Initially, the railways enjoyed breakneck expansion, but since the mid-twentieth century, railway development in most countries has hit the buffers, and been overtaken by growth in road and air travel. A study by the Paris-based International Transport Forum (ITF) of 51 mainly high- income countries found that rail’s share of freight transport had fallen from 38% in 1980 to 24% in 2017 (see go.nature.com/3vpckhd). In the European Union in 2022, just 8.4% of passenger kilometres were travelled by rail, compared with 9% by air and 73% by car.

Despite prominent investments in high-speed rail in Japan, China and parts of Europe, the overall length of networks in many countries has declined as conventional lines deemed unprofitable have been cut. Meanwhile, rail transport is a low priority in many low- and middle-income countries, where networks are sparse or non-existent. The entire African continent, for example, has just 87,000 kilometres of rail. By contrast, India has at least 65,000 kilometres, and a land surface area just one-tenth of the size.

It’s time to turn the tables, and acknowledge the vast benefits of railways as a cornerstone of a sustainable transport system that can support human development and economic growth. Research from across disciplines can inform policy in preparation for a much-needed renaissance, as railways travel into their third century.

According to the International Energy Agency, transport currently accounts for around one-quarter of global carbon dioxide emissions. Between 1990 and 2022, those emissions grew by 1.7% a year — an increase greater than that of any sector besides industry — as more people in more parts of the world became more mobile. Over 90% of the energy used to power transport comes from fossil fuels.

Those figures alone justify a renewed focus on rail transport. Per passenger kilometre, it produces one-fifth of the emissions of car transport, and less than one-quarter of those of flying. Direct emissions can be cut to zero if trains are powered by fully renewable electricity.

Rail transport also contributes little in the way of air-fouling particulate emissions, which are a health hazard. This is particularly important in a rapidly urbanizing world. Better rail-based mass-transit options could help to reduce urban sprawl, as well as the land needed for roads, car parks and other car-related infrastructure. Less-congested cities with fewer motor vehicles are more liveable places where people are more inclined to walk and cycle, reaping the health benefits of these activities. They are also more inclusive, particularly for younger and older people who are less likely to own a vehicle. As both urbanization and average population density grow, research shows that the economic benefits of investment in rail outstrip those of investment in roads[1].

But it is not just cities. The United Kingdom will be celebrating its role in birthing the railways later this month, but the country also offers an example of the effects disinvestment in railways can have. A 2024 study[2] examined a sustained programme of cuts made to the nation’s railway network from the 1950s to the 1980s. It found that the predominantly rural areas most affected by the cuts saw population declines, job losses and drops in the number of skilled workers, relative to areas that were unaffected.

One way research can help to get things back on track is by broadening the criteria governments use to assess railway investment, says Christian Wolmar, an independent transport consultant and author based in London. All too often, these are based on narrow metrics of profitability or ‘time saved’ by potential users, with insufficient consideration of the wider social and environmental impacts. Economists, other social scientists and sustainability researchers can all contribute to developing more-robust assessments of these indirect benefits.

Such initiatives can feed into broader regulatory and policy frameworks. Only one-third of countries have fully incorporated the transport sector into their ‘nationally determined contributions’ — their ongoing commitments to reduce greenhouse-gas emissions under the 2015 Paris climate agreement — according to an ITF tracker (see go.nature.com/4nxdiju). To meet net-zero targets, emissions from transport need to decline by 3% a year from now on.

Research can also illuminate the winners and losers created by investment decisions. China, for example, is set to continue the breakneck expansion of its high-speed rail, aiming to reach 60,000 kilometres by 2030. But scholars are debating the wisdom of the speed and scale of this expansion, with uncertainty remaining about how widely the economic benefits of high-speed links are distributed[3].

At its zenith, immediately before the First World War, the US rail network extended to more than 400,000 kilometres — greater than the distance from Earth to the Moon. Today, it covers little more than half of that. The extent of this decline underscores the need to turn around the neglect of a technology that has not only changed the world, but could also save the planet.

Nature 645, 560 (2025)

doi: https://doi.org/10.1038/d41586-025-02980-2

References

1. Zheng, Q. Y., Law, T. H., Wong, S. V. & Ng, C. P. Transp. Pol. 153, 87–96 (2024).

2. Gibbons, S., Heblich, S. & Pinchbeck, E. W. J. Urban Econ. 143, 103691 (2024).

3. Blanquart, C. & Koning, M. Eur. Transp. Res. Rev. 9, 12 (2017).

Reprints and permissions

WORLD VIEW 16 September 2025

Equity in science is a beautiful lie — and I’m done pretending

Science isn’t really moving towards equity; institutions are just perfecting the appearance of equity. We need to build an alternative system.

By

Dolors Armenteras

For years, I thought equity in science was possible. I believed it in meeting rooms to which I had been invited to speak, until I realized that I had not been invited to shape the discussion. I believed it in working groups that applauded diversity, until I noticed that my ideas only landed when echoed by someone else. And international organizations regularly sought me out, but it was hardly ever for a leadership role.

In 2021, I proposed ways to build healthier collaborations between countries with unequal resources: currently they benefit mainly the wealthier partner (D. Armenteras Nature Ecol. Evol. 5, 1193–1194; 2021). The article resonated with scientists across Latin America, Africa and Asia, who thanked me for exposing these skewed partnerships. But what also stood out to me was that none of the committees and organizations that had so often solicited my input got in touch.

Many scholars from historically overexploited countries (often referred to as the global south) expected that exposing the problem would trigger change. Four years on, I see it clearly: the scientific system was never designed for equity. For people whose privilege stems from geography, institutional reputation and inherited networks, the system works perfectly the way it is. That’s why institutions focus only on improved access and optics. They look like they are changing, but the same people retain control.

I still believe in science and in justice. But I no longer think that power can be shared equitably in the current system. In 2023, I was invited to contribute to a global map charting the use of controlled fire in ecosystem management. This meant condensing 25 years of research into a 40-minute questionnaire for a chance to win an artwork made by an Indigenous artisan and, perhaps, be invited to a workshop. It was written in Spanish and framed as inclusive. But it exposed how the system works: extract specialist knowledge at low cost and mostly without giving credit, repackage it into global claims and call it collaboration. I declined.

In 2025, I was invited to contribute to a project developing a global standard for gathering fire data. It used all the right words: co-production, inclusion and diversity. It cited my work. But I wasn’t being invited to co-design or co-lead the project, or even as a peer — only to “contribute regional input”. Time commitment: less than 20 hours. Visibility: none. Influence: symbolic. When I declined, explaining my reasons, I received two replies. One was defensive: “You know I’d never reach out with a symbolic request,” sidestepping my actual concerns. The other was polite, affirming the project’s importance but failing to address its asymmetry. Neither academic offered co-authorship or fresh terms. Nothing changed. These weren’t bad people. That’s the hardest part. They were playing by the rules of a system that rewards extractive collaboration — especially when it’s wrapped in the language of equity.

The system doesn’t thrive just because of the people at the top. It holds strong because many scientists in less-privileged positions want to be included. Sometimes we are chosen — not for our ideas or our leadership, but because we tick the right box. A woman from Latin America, visible and qualified. But we don’t become a peer. Our work is not cited as often. Our students become local guides instead of co-authors. Grants continue to be written without us.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 561 (2025)

doi: https://doi.org/10.1038/d41586-025-02916-w

Reprints and permissions

Competing Interests

The author declares no competing interests.

News in Focus

- First CRISPR horses spark controversy: what’s next for gene-edited animals?

- Air pollution directly linked to increased dementia risk

- These nations are wooing PhD students amid US funding uncertainties

- Can researchers stop AI making up citations?

- Chemists cram record nine metals into trendy 2D material

- ‘Amazing feat’: US man still alive six months after pig kidney transplant

- Newfound immune cell in mice hints at why inflammation spikes with old age

- ‘Brain dial’ turns food consumption on or off in mice

- AI is helping to decode animals’ speech. Will it also let us talk with them?

- How billions of hacked mosquitoes and a vaccine could beat the deadly dengue virus

NEWS 05 September 2025

First CRISPR horses spark controversy: what’s next for gene-edited animals?

Horses with genomic edits to make them run faster have been banned from polo, but a zoo of CRISPR-edited animals is gaining acceptance in agriculture.

By

Katie Kavanagh

Scientists have bred the world’s first horses with CRISPR-mediated genomic edits to enhance their muscle power and speed.Credit: Agustin Marcarian/Reuters

These horses might look like ordinary horses, but there is something highly unusual about their genomes. They are the first of their species to have their DNA edited using CRISPR–Cas9, a technique that cuts the genome at a specific location to change gene expression and achieve a desired trait.

The horses are clones of the prize-winning steed Polo Pureza, but they have a tweak to myostatin — a gene involved in regulating muscle development — that is designed to quicken their pace. CRISPR was used in fetal fibroblasts (connective tissue cells) to generate embryos through cloning, and then the embryos were implanted into mares.

The development of these five CRISPR-edited horses ten months ago, by the non-profit research organization Kheiron Biotech in Buenos Aires, is proving controversial among horse breeders in Argentina, where polo is extremely popular, Reuters reported on 30 August.

Critics are concerned that the technology threatens people’s livelihoods and that it will compromise the tradition of using selective breeding to generate elite horses. The Argentine Polo Association has now banned the use of gene-edited horses in the sport, following the lead of similar organizations such as the International Federation for Equestrian Sports[1], which banned the practice in 2019.

Some scientists, however, welcome the CRISPR horses. “It’s cool to show that CRISPR works and you can create CRISPR-altered horses,” says Molly McCue, a veterinary clinician scientist at the University of Minnesota in Minneapolis. “Horse[riders] often feel very strongly about breeding as an art and not a science, but really it is both together,” she adds.

The CRISPR horses join a menagerie of gene-edited animals that have wide-ranging applications — mostly with the goal of improving agriculture. Such efforts have now transformed from a research promise into a commercial reality, says Tad Sonstegard, chief scientific officer at Acceligen, a company in Eagan, Minnesota, that specializes in the precision breeding of livestock. Biological engineering ethicist Jeantine Lunshof, at Harvard Medical School in Boston, Massachusetts, puts the rise of the technology in animals down to improvements in CRISPR techniques and “a broader acceptance of gene editing”.

CRISPR in agriculture

Acceligen is one of a handful of companies that are using CRISPR to alter the genomes of livestock, with the goal of making animal products such as meat and milk in a more efficient manner. Its ‘PRLR-SLICK’ cattle have an edit in the prolactin receptor gene that gives them shorter, slicker hair, providing tolerance to heat stress. Sonstegard says that the short-haired PRLR-SLICK cows should be able to adapt to hotter climates and to tolerate the rising temperatures associated with climate change, increasing the accessibility of meat and dairy products to people around the world. In 2022, the US Food and Drug Administration (FDA) approved the PRLR-SLICK cattle for meat production and human consumption, deeming them a low risk to safety, but it’s unclear when the meat will hit the US market.

With a similar goal, researchers in India announced the first CRISPR-edited sheep earlier this year. As with the Argentine horses, the scientists edited the myostatin gene of the sheep to increase muscle mass — but in this case, the goal was to increase meat production rather than to speed the sheep up.

Scientists have used CRISPR to make pigs more resistant to porcine reproductive and respiratory syndrome, and to make their meat hypoallergenic.Credit: Acceligen

Disease resistance is another reason that scientists are producing CRISPR animals. Genus, a company based in Basingstoke, UK, has used CRISPR to generate pigs that contain a mutation in the CD163 gene. This makes them resistant to a virus that causes porcine reproductive and respiratory syndrome (PRRS), which can be deadly for suckling pigs. In 2020, the FDA approved the gene-edited pigs for sale in the United States, and they are expected to go on the market there in 2026.

Researchers are also using CRISPR to make animal products that are safer for human consumption. GalSafe pigs, made by Revivicor in Blacksburg, Virginia, are designed to be a source of hypoallergenic meat. Researchers use CRISPR to inactivate the GGTA1 gene, which produces alpha-gal, a sugar molecule found in most mammals that can cause allergic reactions in humans who eat red meat. Revivicor is also investigating whether organs from the pigs could be transplanted into people: the company says that the same gene edits might reduce the risk of pig organs being rejected from human bodies. The FDA approved GalSafe pigs for use in biomedical therapeutics and for human consumption in 2020.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 565-566 (2025)

doi: https://doi.org/10.1038/d41586-025-02800-7

References

1. Campbell, M. L. H. & McNamee, M. J. Sport Ethics Phil. 15, 227–250 (2020).

2. Epstein, L. R., Lee, S. S., Miller, M. F. & Lombardi, H. A. Proc. Natl Acad. Sci. USA 118, e2004831117 (2021).

3. Landel, C. & Pritchett-Corning, K. R. Appl. Biosaf. 23, 168–179 (2018).

4. Pozzebon, M., Guldbrandtsen, B. & Sandøe, P. Nanoethics 18, 6 (2024).

Reprints and permissions

NEWS 04 September 2025

Air pollution directly linked to increased dementia risk

Long-term exposure accelerates the development of Lewy body dementia and Parkinson’s disease with dementia in people who are predisposed to the conditions.

By

Rachel Fieldhouse

A study has found that exposure to air pollution can increase the risk of developing Lewy body dementia.Credit: Sonu Mehta/Hindustan Times/Shutterstock

An analysis of 56 million people has shown that exposure to air pollution increases the risk of developing a particular form of dementia, the third most common type after Alzheimer’s disease and vascular dementia.

The study, published in Science on 4 September[1], suggests that there is a clear link between long-term exposure to PM2.5 — airborne particles that are smaller than 2.5 micrometres in diameter — and the development of dementia in people with Lewy body dementia or Parkinson’s disease.

The study found that PM2.5 exposure does not necessarily induce Lewy body dementia, but “accelerates the development” in people who are already genetically predisposed to it, says Hui Chen, a clinician–neuroscientist at the University of Technology Sydney in Australia.

PM2.5 exposure

Lewy body dementia is an umbrella term for two different types of dementia: Parkinson’s disease with dementia, and dementia with Lewy bodies. In both cases, dementia is caused by the build-up of α-synuclein (αSyn) proteins into clumps, called Lewy bodies, in the brain’s nerve cells, which cause the cells to stop working and eventually die. Studies have suggested that long-term exposure to air pollution from car exhausts, wildfires and factory fumes is linked with increased risks of developing neurodegenerative illnesses, including Parkinson’s disease with dementia[2].

Study co-author Xiaobo Mao, who researches neurodegenerative conditions at Johns Hopkins University in Baltimore, Maryland, says he and his colleagues wanted to determine whether PM2.5 exposure also influenced the risk of developing Lewy body dementia. They analysed 2000–14 hospital-admissions data from 56.5 million people with Lewy body dementia and Parkinson’s disease with or without dementia. The data served to identify people with severe neurological diseases.

They found that long-term PM2.5 exposure was associated with an increased risk of hospitalization for all three neurodegenerative conditions, including a 12% increased risk for severe dementia with Lewy bodies that required hospitalization. They noted that living in areas of higher PM2.5 exposure was linked with a higher relative risk of Lewy body dementia — including dementia with Lewy bodies and Parkinson’s disease with dementia — than of Parkinson’s without dementia (see ‘Air pollution and Parkinson’s disease’).

Source: Ref. 1

The team then performed experiments in mice to investigate why exposure to air pollution affected dementia risk. Mice were exposed to PM2.5 pollution through their nostrils, then the researchers tested for behaviours linked with dementia-like problems. After ten months of PM2.5 exposure, mice showed behavioural challenges in maze exploration tests for spatial memory, and tasks that tested their recognition of new objects. At ten months, the team also observed a substantial increase in the build-up of αSyn in the animals’ brains.

Exposure to PM2.5 for ten months also caused shrinkage of the medial temporal lobe in mice — a brain region that is responsible for memory formation and retrieval. In comparison, there were no changes to the brains of genetically modified mice lacking αSyn, suggesting that the protein is required for neurodegenerative pathology.

The team also found clumps of αSyn in the gut and lungs of mice exposed to PM2.5, but not in the control or genetically modified mice. Mao says that αSyn acts like a seed, which can propagate and spread from the gut to the brain by way of the gut–brain axis, and eventually cause Alzheimer’s disease or Lewy body dementia. PM2.5 also accumulates in the lungs, causing inflammation before entering the bloodstream and crossing the blood–brain barrier.

Predisposition needed

The researchers next investigated gene-expression changes caused by PM2.5 exposure in mice and compared them with gene-expression changes observed in people with Lewy body dementia. They focused on the anterior cingulate cortex — a brain region linked with cognitive deficits in people with dementia. They found a strong correlation of gene-expression changes between PM2.5-exposed mice and people with Lewy body dementia and Parkinson’s disease with dementia, but no correlation with Parkinson’s disease without dementia.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 566-567 (2025)

doi: https://doi.org/10.1038/d41586-025-02844-9

References

1. Zhang, X. et al. Science 389, eadu4132 (2025).

2. Best Rogowski, C. B. et al. Lancet Planet. Health 9, 101266 (2025).

Reprints and permissions

NEWS 09 September 2025

These nations are wooing PhD students amid US funding uncertainties

Pauses to some US graduate programmes have led universities in several countries to launch initiatives to entice would-be PhD students.

By

Rachel Fieldhouse

The University of Paris-Saclay in Orsay, France, is one European university trying to attract future PhD students from the United States. Credit: neirfy/Getty

The United States has long been one of the most popular destinations for international students pursuing graduate studies. But pauses to some of the country’s university PhD programmes and the imposition of visa restrictions for students from certain countries have prompted other nations to try to attract those students who have been affected by the changes or who no longer want to study in the United States.

US President Donald Trump’s administration has proposed slashing budgets at some of the country’s top scientific agencies and has frozen funds for grants and contracts for universities.

Chris Tisdell, a researcher in education and mathematics at the University of New South Wales (UNSW) in Sydney, Australia, says he has heard reports of international students already shifting away from the United States because of uncertainties surrounding funding. International student arrivals dropped by 30% in June this year compared with June 2024, according to data reported by the US International Trade Administration.

Gwilym Croucher, a researcher in higher education at the University of Melbourne, Australia, says he expects talented PhD candidates to look elsewhere. “The beneficiaries of that may be established places like Canada, Australia, the UK, a lot of Europe, but they may also be China and India,” he says.

So, which countries have stepped up efforts to woo PhD students? And what are they offering?

Canada

Several universities in Canada have set up programmes to attract students from the United States.

In July, Western University in London launched a Doctoral Excellence Award, targeting current and prospective students of US universities, including those who have had an offer rescinded in the past six months, at US universities ranked in the top 100 globally. Initially, 25 students will be supported, receiving a PhD stipend for up to four years of study, as well as “fast-tracked admissions and help finding a supervisor”, says Florentine Strzelczyk, Western University’s provost. PhD stipends increased across Canada, after the government set a blanket rate of Can$40,000 annually last year.

Earlier this year, the University of British Columbia in Vancouver also extended the deadline to allow for late applications from US citizens to be considered for certain graduate programmes starting in January 2026.

Alicia Piazza is in her third year of a PhD at Brock University in St. Catharine’s and recommends Canada for graduate studies, particularly because of the quality of training on offer. “I’m three years in and I’m still learning,” she says. The classes she has attended, including one on grant writing and another on presenting and analysing research papers, have prepared her to work in academia or industry. Students at the university are also encouraged to apply for external funding, and she successfully applied for a scholarship from the Natural Sciences and Engineering Research Council of Canada.

Piazza receives a stipend from the university that covers her tuition fees, and was also guaranteed a position as a teaching assistant, which helps to cover living expenses, she says. “The rent is not too bad, so it’s pretty affordable,” she adds.

Europe

France, Germany and Spain are among other countries that have introduced new programmes to attract students, particularly those from the United States, alongside initiatives to attract scientists further on in their careers.

The University of Paris-Saclay in Orsay, France, is offering eight spots for students to pursue a PhD in subjects spanning climate and environmental science, global health, humanities, social sciences and energy transition. Students who have already started a PhD in the United States are also eligible. International students can apply for several scholarships that cover accommodation and living costs, and in some cases health insurance. Students supported by funding from their university, institution or the national research agency receive between €16,800 (US$19,400) and €18,000 per year.

Meanwhile, the Max Planck Society in Germany has launched a Transatlantic Program and encouraged prospective students to apply to programmes at its international research schools and graduate centres. Doctoral students are under contract with the society, with set working hours of 39 hours per week and a minimum pay of €32,400 per year.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 568-569 (2025)

doi: https://doi.org/10.1038/d41586-025-02416-x

Reprints and permissions

NEWS 08 September 2025 Clarification 09 September 2025

Can researchers stop AI making up citations?

OpenAI’s GPT-5 hallucinates less than previous models do, but cutting hallucination completely might prove impossible.

By

Elizabeth Gibney

OpenAI says GPT-5 has reduced the frequency of fake citations and other kinds of hallucination.Credit: Kirill Kudryavtsev/AFP via Getty

Artificial intelligence (AI) models are known to confidently conjure up fake citations. When the company OpenAI released GPT-5, a suite of large language models (LLMs), last month, it said it had reduced the frequency of fake citations and other kinds of ‘hallucination’, as well as ‘deceptions’, whereby an AI claims to have performed a task it hasn’t.

With GPT-5, OpenAI, based in San Francisco, California, is bucking an industry-wide trend, because newer AI models designed to mimic human reasoning tend to generate more hallucinations than do their predecessors. On a benchmark that tests a model’s ability to produce citation-based responses, GPT-5 beat its predecessors. But hallucinations remain inevitable, because of how LLMs function.

“For most cases of hallucination, the rate has dropped to a level” that seems to be “acceptable to users”, says Tianyang Xu, an AI researcher at Purdue University in West Lafayette, Indiana. But in particularly technical fields, such as law and mathematics, GPT-5 is still likely to struggle, she says. And despite the improvements in hallucination rate, users quickly found that the model errs in basic tasks, such as creating an illustrated timeline of US presidents.

OpenAI is making “small steps that are good, but I don’t think we’re anywhere near where we need to be”, says Mark Steyvers, a cognitive science and AI researcher at the University of California, Irvine. “It’s not frequent enough that GPT says ‘I don’t know’.”

A feature, not a bug

Hallucinations are a result of the fundamental way in which LLMs work. As statistical machines, the models make predictions by generalizing on the basis of learnt associations, leading them to produce answers that are plausible, but sometimes wrong. Another issue is that, similar to a student scoring points for guessing on a multiple-choice exam, during training, LLMs get rewarded for having a go rather than acknowledging their uncertainty, according to a preprint published by OpenAI on 4 September[1].

Improvements have come from scaling up the size of LLMs — in terms of both the richness of their internal associations and the amount of data they are trained on, says Xu. But hallucinations are particularly prevalent in topics for which the model has scant training data or its underlying information is wrong, she says. Hallucinations can also happen when an AI tries to summarize or analyse papers that are too long for that model to process.

Eliminating hallucinations entirely is likely to prove impossible, says Mushtaq Bilal, a researcher at Silvi, a Copenhagen-based firm that makes an AI app to aid the creation of systematic reviews in science. “I think if it was possible, AI labs would have done it already.”

But reducing errors and getting a model to admit that it doesn’t know an answer have been “a pretty heavy focus” for OpenAI, says Saachi Jain, who manages the firm’s AI safety training team. According to technical documents released with GPT-5, OpenAI concentrated on “training our models to browse effectively for up-to-date information”, as well as cutting hallucinations. The firm focused on reducing hallucinations in lengthy, open-ended responses to queries, because this best represents real-life use of ChatGPT, says Jain.

In one literature-review benchmark known as ScholarQA-CS, GPT-5 “performs well” when it is allowed to access the web, says Akari Asai, an AI researcher at the Allen Institute for Artificial Intelligence, based in Seattle, Washington, who ran the tests for Nature. In producing answers to open-ended computer-science questions, for example, the model performed marginally better than human experts did, with a correctness score of 55% (based on measures such as how well its statements are supported by citations) compared with 54% for scientists, but just behind a version of the institute’s own LLM-based system for literature review, OpenScholar, which achieved 57%.

However, GPT-5 suffered when the model was unable to get online, says Asai. The ability to cross-check with academic databases is a key feature of most AI-powered systems designed to help with literature reviews. Without Internet access, GPT-5 fabricated or muddled half the number of citations that one of its predecessors, GPT-4o, did. But it still got them wrong 39% of the time, she says.

On the LongFact benchmark, which tests accuracy in long-form responses to prompts, OpenAI reported that GPT-5 hallucinated 0.8% of claims in responses about people or places when it was allowed to browse the web, compared with 5.1% for OpenAI’s reasoning model o3. Performance dropped when browsing was not permitted, with GPT-5’s error rate climbing to 1.4% compared with 7.9% for o3. Both models showed worse performance than did the non-reasoning model GPT-4o, which had an error rate of 1.1% when offline.

On other independent evaluations — such as the Hughes Hallucination Evaluation Model, which is run by the AI platform Vectara in Palo Alto, California, and looks at how often an LLM makes false claims when summarizing a document — rival models such as Google’s Gemini 2.0 slightly outperformed GPT-5, although both erred less than 1.5% of the time.

Learning to admit defeat

OpenAI also reported that the model was more honest in its responses than the company’s previous models were. When given a coding task that was impossible to complete — for example, owing to a lack of access to necessary hardware — GPT-5 claimed to have done the task 17% of the time, compared with 47% for o3. Although Jain wouldn’t give details of the firm’s methods, she hinted that, in later stages of the model’s training, OpenAI worked on rewarding it for answering honestly.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 569-570 (2025)

doi: https://doi.org/10.1038/d41586-025-02853-8

Updates & Corrections

- Clarification 09 September 2025: This article has been amended to clarify that Saachi Jain manages OpenAI's AI safety training team.

References

1. Kalai, A. T., Nachum, O., Vempala, S. S. & Zhang, E. Preprint at arXiv https://doi.org/10.48550/arXiv.2509.04664 (2025).

Reprints and permissions

NEWS 04 September 2025

Chemists cram record nine metals into trendy 2D material

MXenes, distant cousins of graphene, reach new heights of complexity — opening the way for use in advanced batteries and more.

By

Katherine Bourzac

2D materials called MXenes (coloured particle shown here in scanning electron micrograph) contain several layers of metals and carbons or nitrogen atoms. Credit: Devynn Leatherman-May, Brian C. Wyatt, and Babak Anasori, Purdue University

Chemists have doubled the members of a family of buzzy 2D materials, and even jammed a record nine metals into one of them. The feat, published today in Science[1], has excited researchers because it opens the door to designing a multitude of weird but useful substances.

The materials are so complex that, at this point, it’s impossible to simulate them with computer models, says Max Hamedi, a physicist at the KTH Royal Institute of Technology in Stockholm. Scientists will need to test their properties in the laboratory, he adds — a tantalizing prospect. “Maybe we will get some properties that are very surprising and that we couldn’t predict.”

The newly expanded family of materials, called MXenes (pronounced ‘max-eens’), has previously caused a stir because their high electrical conductivity and other characteristics suggest that they might one day be used in technologies such as next-generation batteries and coatings that protect against electromagnetic interference. Not only that, but these materials can be dispersed in water, so they can be sprayed or painted onto surfaces.

Snazzy sandwiches

The first MXene ever synthesized, a 2D sheet of titanium carbide, was reported in 2011[2] by a team co-led by Yury Gogotsi, a nanomaterials scientist at Drexel University in Philadelphia, Pennsylvania. Unlike the iconic 2D material graphene, which is a single layer of carbon atoms, MXenes contain several layers of metal and carbon or nitrogen atoms. In the case of titanium carbide, for instance, there are two ‘bread’ layers of titanium atoms that sandwich a sheet of carbon.

But scientists don’t have tight control over which metals end up in which layers when more are added. Certain metals ‘like’ to be in a particular layer owing to atomic properties, such as the size of each atom and its hunger for electrons, says Babak Anasori, a materials engineer at Purdue University in West Lafayette, Indiana, and co-author of the latest study.

So although a person making a sandwich can stack up layers of cheese, lettuce, pickles and other ingredients in the order of their choosing, chemists making MXenes yield control to nature. To create these materials, scientists start by heating ingredients in a furnace to make crystals. In the resulting materials, certain metals always choose to be in the inner layers, whereas others are drawn to the outside.

Owing to these constraints, some metals, including tungsten, zirconium and hafnium, have been challenging to incorporate, Anasori says. And scientists have not been able to make MXenes with certain metals on the inner or outer layers: for instance, molybdenum likes to go on the outside of the sandwich, whereas titanium likes to be enveloped. Materials prefer to adopt an atomic configuration that minimizes the energy — or enthalpy — needed to create it.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 570-571 (2025)

doi: https://doi.org/10.1038/d41586-025-02839-6

References

1. Wyatt, B. C. et al. Science https://doi.org/10.1126/science.adv4415 (2025).

2. Naguib, M. et al. Adv. Mater. 23, 4248–4253 (2011).

3. Nemani, S. K. et al. ACS Nano 15, 12815–12825 (2021).

Reprints and permissions

NEWS 08 September 2025

‘Amazing feat’: US man still alive six months after pig kidney transplant

The first six months after an organ transplant are the riskiest for recipients.

By

Rachel Fieldhouse

Tim Andrews leaving hospital in January after he received a genetically modified pig kidney.Credit: Kate Flock/Massachusetts General Hospital

A 67-year-old US man is still alive more than six months after receiving a kidney from a genetically modified pig. This is the longest a pig organ has survived in a living person. Researchers say the outcome is a landmark case of successful xenotransplantation — the process of transplanting organs from animals to humans.

The recipient, Tim Andrews, had end-stage kidney disease and had been receiving dialysis for more than two years before he underwent the surgery in January. He has been dialysis-free since receiving the kidney. Andrews was one of three patients to receive genetically modified pig kidneys supplied by the biotechnology company eGenesis in Cambridge, Massachusetts, on compassionate grounds.

Reaching six months’ survival is an amazing feat, says Wayne Hawthorne, a transplant surgeon at the University of Sydney in Australia. The first six months is the period of “highest risk for the patient and also the transplant”, he adds. Possible complications include anaemia and graft rejection, when the immune system attacks the new organ. “The six-month time point marks that things have gone extremely well,” Hawthorne says. Reaching 12 months would be another milestone and a “fantastic long-term outcome”, he adds.

Previously, the recipient with longest-surviving genetically modified pig organ was a 53-year-old US woman, Towana Looney, who had a functioning pig kidney for four months and nine days. However, the organ was removed earlier this year because her immune system began to reject it.

Genetically modified

Andrews received a kidney from a pig with three types of genetic modification. One involved the elimination of three antigens to prevent organ rejection; another the addition of seven human genes that reduce inflammation and the risk of bleeding complications. Retroviruses that are found in the pig genome were also deactivated.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 571-572 (2025)

doi: https://doi.org/10.1038/d41586-025-02851-w

References

1. Starzl, T. E et al. Lancet 341, 65–71 (1993).

Reprints and permissions

NEWS 04 September 2025

Newfound immune cell in mice hints at why inflammation spikes with old age

Pathogen-consuming cells found in fat tissue also play a part in lipid balance.

By

Gemma Conroy

Macrophages, which hoover up pathogens, have been implicated in the chronic inflammation that sets in with the march of time.Credit: SPL

A newly discovered type of immune cell found in fat tissue seems to contribute to the chronic inflammation associated with ageing, according to preliminary data from mice — but other immune cells in fat help to keep inflammation at bay[1].

The inflammation-promoting cells emerge only in older mice, researchers found. Although the cells’ precise role is unclear, they display several signatures associated with ‘inflammageing’ — the persistent inflammation that develops as people grow older. The findings were published on 2 September in Nature Aging.

“We did not anticipate that there would be a completely new cell type,” says study co-author Vishwa Deep Dixit, an immunobiologist at Yale University in New Haven, Connecticut.

Inflammation age

When injuries or infections occur, the immune system mounts a protective response by releasing cells and proteins to affected tissues. This complex cascade is called inflammation. But as we age, inflammation gradually increases and becomes persistent instead of being a state that occurs only when things go wrong.

Among the cells that help to regulate this inflammageing are a variety of macrophages — white blood cells that hoover up pathogens and cellular debris — that reside in fat tissue. But the exact roles of each type of macrophage and how these cells change throughout the ageing process remain a mystery, says study co-author Elsie Gonzalez-Hurtado, also an immunobiologist at Yale University. “There wasn’t really a good characterization of these cells.”

To build a clearer picture, Gonzalez-Hurtado and her colleagues imaged macrophages in the visceral fat, the deep fat that wraps around the organs, of young and aged mice. The researchers sorted the macrophages into categories on the basis of the cells’ RNA molecules. These molecules indicate which genes in a cell are active, and therefore offer a guide to the cell’s function.

Multitude of macrophages

The results revealed 13 distinct types of visceral-fat macrophage, some of which varied in abundance with age. A previously known type of macrophage that resides near nerves, for example, became less numerous in female mice as they grew older — but its numbers remained constant in males. Another previously known type of macrophage, which congregates near fat-tissue blood vessels, was less numerous in older male mice than in younger ones, but its levels did not vary with age in female mice.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 572-573 (2025)

doi: https://doi.org/10.1038/d41586-025-02788-0

References

1. Gonzalez-Hurtado, E. et al. Nature Aging https://doi.org/10.1038/s43587-025-00952-9 (2025).

Reprints and permissions

NEWS 10 September 2025

‘Brain dial’ turns food consumption on or off in mice

Master-control area integrates information about hunger, a food’s tastiness and more — and can even drive intake of plastic pellets.

By

Amanda Heidt

Food consumption can be turned off in mice by silencing neurons in a particular brain area. Credit: Ricardo Ribas/SOPA Images/LightRocket/Getty

Scientists have identified a ‘brain dial’ that can turn food consumption on or off, at least in mice. The effect of this brain region is so powerful that when scientists manipulated it, mice that were already full kept eating — and even gobbled inedible plastic pellets.

The region receives and coordinates multiple streams of information, such as hunger levels, nutritional deficits and whether a food is pleasurable to eat. It is a “key hub” linking the sensory traits of food to weight control — a finding with implications for human health, according to a paper published on 10 September in Cell[1].

“I am deeply impressed by this study,” says Matthew Carter, a neuroscientist at Williams College in Williamstown, Massachusetts. The work is unusual in separating out how hunger and a food’s sensory qualities affect food consumption, he says, and demonstrates that a single brain region integrates a range of signals to drive consumption.

The bitter with the sweet

Food intake is influenced by roughly a dozen brain regions. These areas gather information on various factors that together drive our appetite for something and how likely we are to consume it. A person with low salt levels might crave a salty snack, for example, but decline something bitter. In 2019, researchers suggested that all of these stimuli might be funnelled into a brain region called the bed nucleus of the stria terminalis (BNST)[2], but it remained unclear what exactly was happening inside.

Charles Zuker, a neuroscientist at Columbia University in New York City, and his team wanted to trace the brain circuits involved in an animal’s response to tastes. The researchers began by characterizing neurons that become active when a mouse tastes something sweet. In the central amygdala and hypothalamus, they found sweet-detection neurons with branches that link to neurons in the BNST.

When the scientists silenced those BNST neurons, the animals lost their interest in sugar even when hungry, and largely ceased to eat. The researchers also activated those BNST neurons in mice that had recently been fed and so shouldn’t seek out food. Nevertheless, the activation prompted the mice to ingest all kinds of things: water (a neutral substance they would typically ignore unless thirsty), salt, fat, bitter substances and even plastic pellets.

Collectively, these and other results “tell us that the BNST is functioning as something of a master ‘dial’ with bidirectional control”, Zuker says. “If we can figure out how to turn that dial, it would give us some influence over things like body weight.”

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 573 (2025)

doi: https://doi.org/10.1038/d41586-025-02871-6

References

1. Canovas, J. A., Wang, L., Mohamed, A. A. M., Abbott, L. F. & Zuker, C. S. Cell https://doi.org/10.1016/j.cell.2025.08.021 (2025).

2. Wang, Y. et al. Nature Commun. 10, 2769 (2019).

Reprints and permissions

NEWS FEATURE 17 September 2025

AI is helping to decode animals’ speech. Will it also let us talk with them?

The complexity of vocal communication in some primates, whales and birds might approach that of human language.

By

Rachel Fieldhouse

Illustration: David Parkins

Deep in the rainforests of the Democratic Republic of the Congo, Mélissa Berthet found bonobos doing something thought to be uniquely human.

During the six months that Berthet observed the primates, they combined calls in several ways to make complex phrases[1]. In one example, bonobos (Pan paniscus) that were building nests together added a yelp, meaning ‘let’s do this’, to a grunt that says ‘look at me’. “It’s really a way to say: ‘Look at what I’m doing, and let’s do this all together’,” says Berthet, who studies primates and linguistics at the University of Rennes, France.

In another case, a peep that means ‘I would like to do this’ was followed by a whistle signalling ‘let’s stay together’. The bonobos combine the two calls in sensitive social contexts, says Berthet. “I think it’s to bring peace.”

The study, reported in April, is one of several examples from the past few years that highlight just how sophisticated vocal communication in non-human animals can be. In some species of primate, whale[2] and bird, researchers have identified features and patterns of vocalization that have long been considered defining characteristics of human language. These results challenge ideas about what makes human language special — and even how ‘language’ should be defined.

Perhaps unsurprisingly, many scientists turn to artificial intelligence (AI) tools to speed up the detection and interpretation of animal sounds, and to probe aspects of communication that human listeners might miss. “It’s doing something that just wasn’t possible through traditional means,” says David Robinson, an AI researcher at the Earth Species Project, a non-profit organization based in Berkeley, California, that is developing AI systems to decode communication across the animal kingdom.

As the research advances, there is increasing interest in using AI tools not only to listen in on animal speech, but also to potentially talk back.

Combining calls

Researchers studying animal communication ask some of the same types of question that linguists do. How are speech sounds physically produced (phonetics)? How are sounds combined to make meaningful units (morphology)? What rules determine how phrases and sentences are structured (syntax)?

Until about a decade ago, researchers thought that only humans used a feature known in linguistics as compositionality. This is the combining of meaningful words, calls or other noises into expressions that have a meaning derived from those of their parts.

But in 2016, a study of Japanese tits (Parus minor) changed how scientists thought about compositionality. The birds looked for predators when they heard an ‘alert’ call and approached a sound’s source after hearing a ‘recruitment’ call. When they heard the calls in that order, they performed both behaviours[3]. But they didn’t do so when the order was reversed, suggesting compositionality: the combination of calls had its own meaning.

A study in 2023 extended that work. By presenting chimpanzees (Pan troglodytes) with fake snakes in the wild, scientists showed that the primates similarly combine ‘alarm’ and ‘recruitment’ vocalizations into a message that prompts others to gather around the caller to respond to a threat[4].

However, humans remained the only species known to use compositionality in more than one way. For instance, by ordering words differently to change the meaning of the phrase, adding endings to words to modify meaning and creating metaphors and idioms to produce a figurative expression.

Bonobos in the Democratic Republic of the Congo combine calls into phrases in several ways.Credit: Christian Ziegler/Nature Picture Library

But the study by Berthet and her colleagues softened that distinction between humans and other animals. They recorded 700 calls by 30 adult bonobos and found that the animals combined a finite number of calls in four ways[1]. One — a yelp–grunt combination — the authors considered to have ‘trivial’ compositionality, because the meaning of the individual calls had merely been combined. (For instance, ‘the red car’ describes an object that is both red and a car.) In the three other cases, one call modified the other, resulting in ‘non-trivial’ compositionality. (‘A terrible actor’ describes a person who is bad at acting, not someone who is terrible and an actor.)

Evolutionary biologist Cédric Girard-Buttoz at the Lyon Neuroscience Research Center, France, and his colleagues reported in May that chimpanzees also combine a finite number of calls in several ways[5]. For some vocalizations, the meaning of the combined phrase can’t be determined from the meaning of the individual calls, as is the case for some idioms in human languages. For example, a hoot, used when resting on the ground, followed by a pant, which signifies playing and affiliation, prompted the chimpanzees to climb a tree, make a nest and rest together, even though neither call is typically associated with tree climbing, says Girard-Buttoz. Generating meaning in several ways is a building block of language, he adds.

Whales, too, have some notable features of human language. Researchers at Project CETI, a non-profit organization in New York City, have been tracking and recording sperm whales (Physeter macrocephalus) off the coast of the Caribbean island of Dominica to compile a large data set of movements and sounds. By finding patterns that link whale sounds and behaviours, the scientists hope to translate ‘whale speak’.

CETI linguist Gašper Beguš has been training generative-AI models to produce sounds and sequences of sounds that mimic those made by sperm whales. Whereas humans create distinct sounds by sending air through vocal folds in the throat, which vibrate at different frequencies, these whales send air through a lip-like structure in their nasal passage, which vibrates and creates clicks. The clicks are grouped into units called codas.

Scientists attach sensors that can gather bioacoustic and other data to sperm whales using drones.Credit: Jaime Rojo

CETI scientists reported last year that sperm whales have their own ‘phonetic alphabet’, with codas varying in characteristics such as tempo and rhythm[6]. Beguš and his colleagues have since found that whale codas can differ in ways analogous to vowels and diphthongs in human language. Vowels in human speech differ on the basis of the tongue’s position and the shape of the lips, such as for the ‘ee’ in cheese versus the ‘o’ in hot. Diphthongs, or gliding vowels, are created by combining two vowels in a single syllable, such as in ‘pout’, resulting in a frequency change as the lips and tongue move.

Beguš’s team identified two codas with distinct sound patterns that the researchers called an a-vowel and i-vowel. They also found that these vowels changed frequency in four ways: they can rise, they can fall, they can fall then rise or they can rise then fall[7]. The frequency changes could be indicative of diphthongs.

What’s in a language

Whether the sophistication of animal communication is enough to qualify it as language depends on how a person defines the term and what they think about how animals think. There are two prevailing views, Beguš says. “One world view says that language and complex thought are intrinsically connected.” According to this view, complex thought came first and language is a way to externalize thoughts. If so, animals can’t have a language unless they are capable of complex thought.

The other view holds that language is just one kind of communication, like gestures or facial expressions, and complex thought isn’t required. In this case, animals could have a language with or without complex thought. Experiments that train animals to communicate with humans, such as those with the bonobo Kanzi, who died earlier this year, have hinted that animals might be capable of having a language. But that’s a different question from whether they use language on their own in the wild.

“The word is still out on whether we’ll find a full-on language,” says Robinson.

For one, some aspects of human language haven’t been found in other species yet. Three of the 16 features — displacement, productivity and duality — on a language checklist created by linguist Charles Hockett haven’t been identified in non-human animals.

Displacement is the ability to talk about abstract concepts, such as the past, the future or things that are distant. This feature hasn’t been seen convincingly in animal communication, although there is anecdotal evidence in some instances, such as dolphins calling the names of other dolphins that had disappeared years ago, and orangutans (Pongo spp.) telling others about a predator that was previously in an area, Berthet says.

Productivity is the ability to say things that have never been said or heard before, and be understood by another individual.

And duality describes meaningful messages made up of smaller meaningful units, which consist of even smaller, meaningless sounds. Although whales use clicks to create longer codas, scientists haven’t yet shown that clicks are meaningless and codas are meaningful.

Recursion is another feature that might be unique to human language. This is when sentences or phrases are embedded in each other to create deeper levels of meaning. By training crows (Corvus corone) to peck at open and closed brackets in the appropriate sequence on a touch screen, Diana Liao, who studies vocal communication and cognition at the University of Tübingen in Germany, and her colleagues found evidence that the animals are mentally capable of recursion[8]. “They do this even better than macaque monkeys and on par with human toddlers”, Liao says. However, it’s not clear whether crows use it in their communication.

It’s also unclear whether animals have grammatical rules that define how vocal communication is structured. And, although primates have been shown to mix and match calls to generate meaning, the number of meanings that they can produce is “really far from what humans can do”, says Girard-Buttoz.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 574-576 (2025)

doi: https://doi.org/10.1038/d41586-025-02917-9

References

1. Berthet, M., Surbeck, M. & Townsend, S. W. Science 388, 104–108 (2025).

2. Arnon, I. et al. Science 387, 649–653 (2025).

3. Suzuki, T. N., Wheatcroft, D. & Griesser, M. Nature Commun. 7, 10986 (2016).

4. Leroux, M. et al. Nature Commun. 14, 2225 (2023).

5. Girard-Buttoz, C. et al. Sci. Adv. 11, eadq2879 (2025).

6. Sharma, P. et al. Nature Commun. 15, 3617 (2024).

7. Beguš, G., Sprouse, R. L., Leban, A., Silva, M. & Gero, S. Preprint at OSF https://doi.org/10.31219/osf.io/285cs (2023).

8. Liao, D. A., Brecht, K. F., Johnston, M. & Nieder, A. Sci. Adv. 8, eabq3356 (2022).

9. Rutz, C. et al. Science 381, 152–155 (2023).

10. Pardo, M. A. et al. Nature Ecol. Evol. 8, 1353–1364 (2024).

11. Oren, G. et al. Science 385, 996–1003 (2024).

12. Kobayashi, K. et al. Preprint at arXiv https://doi.org/10.48550/arXiv.2502.00344 (2025).

Reprints and permissions

NEWS FEATURE 16 September 2025

How billions of hacked mosquitoes and a vaccine could beat the deadly dengue virus

Outbreaks of dengue are killing thousands of people in South America each year and getting worse. Brazil hopes to turn the tide with a home-grown vaccine and an army of mosquitoes infected with Wolbachia bacteria.

By

Lucila Pinto

The mosquito Aedes aegypti transmits dengue and other viruses. Credit: Cadu Rolim/Fotoarena via ZUMA

Support for this article was provided by the Pulitzer Center.

Last month, a parade of vehicles wound its way through three cities in Brazil, releasing clouds of mosquitoes into the air. The insects all carry a secret weapon — a bacterium called Wolbachia that lowers the odds that the mosquitoes can transmit the dreaded dengue virus to humans.

These infected mosquitoes are the latest weapon in Brazil’s fight against dengue, which infects millions of people in the country each year and can be fatal. A biofactory that opened in the town of Curitiba in July can produce 100 million mosquito eggs per week — making it the largest such facility in the world. The company that runs it, Wolbito do Brasil, aims to protect about 14 million Brazilians per year through its Wolbachia-infected mosquitoes.

That will come as welcome news for the Brazilian health officials battling the rapidly growing threat of dengue. In 2024, the country experienced its worst outbreak yet: with 6.6 million probable cases and more than 6,300 related deaths. This year’s outbreak, although less severe, is also one of the highest on record, with 1.6 million probable cases so far (see ‘Dangerous outbreaks’). And the problem is spreading. Argentina, Colombia and Peru also experienced record-breaking outbreaks in 2024 and have seen a sustained increase in cases in recent years. Across Latin America and the Caribbean, deaths from dengue last year totalled more than 8,400 and the global figure reached more than 12,000 — the highest ever recorded for this disease.

SOURCE: Brazilian Ministry of Health

As outbreaks grow larger and the crisis becomes more urgent, the Wolbachia method isn’t Brazil’s only bet. A locally produced dengue vaccine is now awaiting approval by the country’s drug-regulatory agency, and its health ministry expects to start administering tens of millions of doses by next year.

These twin advances offer some hope to other countries — in the region and beyond. Driven by forces such as climate change, mosquito adaptation, globalized trade and movements of people, dengue is becoming a crisis worldwide, with an estimated 3.9 billion people at risk of infection. As Brazil rolls out its armies of infected mosquitoes and a vaccine in the coming year, the rest of the world will be watching closely.

The local approach

Currently, there is one main dengue vaccine in use around the world: Qdenga, licensed by the Japanese pharmaceutical company Takeda. The vaccine has been approved in many countries, including Brazil, which was the first nation to include it in its public-health system.

However, Qdenga’s roll-out in Brazil is limited. The country bought nine million doses of the two-dose vaccine this year: enough to vaccinate 4.5 million of its population of more than 210 million. So far, Qdenga has been administered to children between the ages of 10 and 14, one of the groups most likely to end up in hospital after contracting dengue, together with older people. Its safety and efficacy have not yet been tested in adults aged over 60.

The main reasons for such a limited roll-out in Brazil are availability and cost. Even though Brazil secured Qdenga from Takeda at one of the cheapest prices in the world —around US$19 per dose — the cost is still high compared with other vaccines. And even in the most optimistic scenario, the maximum number of doses Takeda could provide by 2028 is 50 million — enough to vaccinate 25 million people. What’s more, for people who have not had dengue before, clinical trials did not show Qdenga to be effective against all four variants — or serotypes — of the dengue virus.

Brazil is trying to address all of those limitations with its one-dose vaccine candidate, developed at the Butantan Institute, a public biomedical research centre in São Paulo. “Having local production capacity gives us independence on decisions — how many doses we need, and at what speed to vaccinate,” says Esper Kallás, Butantan’s director. “You can practise prices that are more suitable and absorbable by a public-health system such as Brazil’s.”

Butantan is also optimistic that its vaccine will be effective against all four forms of dengue. Severe disease usually occurs when a person is infected by a different serotype to their first infection. That means that a successful vaccine needs to generate antibodies for all four serotypes without triggering severe reactions, which makes it a difficult vaccine to develop. “It was indeed a challenge, as each serotype behaves differently,” says Neuza Frazatti Gallina, manager of the viral vaccine development laboratory at Butantan.

The vaccine’s development began at the US National Institutes of Health in the late 1990s, where scientists transformed dengue viruses they had isolated from patients into weakened vaccine strains that could trigger the production of protective antibodies without causing disease. In 2009, Butantan extended that research by working to solve the challenges of combining the four strains into a vaccine.

Eggs of mosquitoes infected with Wolbachia bacteria. After hatching, the mosquitoes will be released to prevent the spread of dengue.Credit: Xinhua/Shutterstock

After testing 30 formulations, Butantan arrived at one that proved highly effective in preventing infections, according to the preliminary results of a phase III trial involving more than 16,000 volunteers in Brazil. The study reported that two years after vaccinations, the formulation was 89% effective in preventing infections in people who had previously been infected with dengue, and 74% effective in those with no previous exposure[1].

“It was a well-designed trial,” says Annelies Wilder-Smith, who is team lead for vaccine development at the World Health Organization (WHO). But she says one limitation of the trial is that it was conducted in a single country, and therefore runs a risk that all four serotypes were not circulating at the time.

In fact, serotypes 3 and 4 were not prevalent during the data-collection period of the clinical trial, although they are now circulating in Brazil. Butantan researchers suggest that the vaccine will be effective against serotypes 3 and 4, pointing to data from a phase II trial[2] in 300 adults that showed participants produced neutralizing antibodies to each of the serotypes. That study evaluated safety and immunological response in the short term, rather than looking at the vaccine’s long-term efficacy in preventing infections. The full results of the Brazilian phase III trial — which will provide data on long-term effectiveness — are not yet public and are undergoing peer review.

The vaccine is already moving through the country’s regulatory process. And although there’s still no certainty about when Anvisa, Brazil’s regulatory agency, will approve the vaccine, the government is counting on it. In February, President Luiz Inácio Lula da Silva announced that, starting in 2026, the Ministry of Health would be buying 60 million doses annually.

To meet that demand, Butantan is now producing the vaccine at its São Paulo facility. On its lush campus, an entire building is dedicated to churning out doses.

Regarding the vaccine’s approval, “We are very confident,” says Kallás. “We also anticipate that there is a very prominent need to have this product in the arms of people. So we hit the road running and started producing vaccines late last year.”

Although Butantan’s production efforts will focus initially on meeting Brazil’s need for millions of doses, Kallás expects that the vaccine could reach other countries. Butantan has been discussing with its development partner — the pharmaceutical giant Merck — and the Pan American Health Organization (PAHO) how to make the vaccine accessible to other countries. The logical first step, he says, would be to roll it out through PAHO to Latin America and the Caribbean, and then to other regions.

In the meantime, Merck is developing a potential vaccine for Asia with an almost identical formulation, which builds on the knowledge that Butantan has developed. In a statement, the drug firm said that Butantan is “sharing clinical data and other learnings”. In June, Merck started enrolling participants for its own phase III trial. “All the data, experiences and insights they have collected with the Butantan vaccine will be helpful,” says Wilder-Smith.

Infecting mosquitoes

While Butantan awaits news about the vaccine’s approval, the Wolbachia method to control dengue is gaining momentum. The World Mosquito Program (WMP) — a non-profit group of companies owned by Monash University in Melbourne, Australia, where the strategy was developed — has operations in 14 countries, including Vietnam, Indonesia, Mexico and Colombia, but Brazil leads the way in terms of the scale of its expansion.

The method’s arrival in the Americas is tied to Brazilian researcher Luciano Moreira, now the chief executive of Wolbito do Brazil. Wolbachia is naturally present in around 50% of insects, but not in the mosquito species Aedes aegypti, which is the main transmitter of dengue and many other viruses.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 578-580 (2025)

doi: https://doi.org/10.1038/d41586-025-02918-8

References

1. Kallás, E. G. et al. N. Engl. J. Med. 390, 397–408 (2024).

2. Kallás, E. G. et al. Lancet Infect. Dis. 20, 839–850 (2020).

3. Moreira, L. A. et al. Cell 139, 1268–1278 (2009).

4. Pinto, S. B. et al. PLoS Negl. Trop. Dis. 15, e0009556 (2021).

5. Anders, K. L. et al. Preprint at medRxiv https://doi.org/10.1101/2025.04.06.25325319 (2025).

6. Utarini, A. et al. N. Engl. J. Med. 384, 2177–2186 (2021).

Reprints and permissions

Books & Arts

- Heroes or hoarders? The strange brains of people who collect

- How did assaults on science become the norm — and what can we do?

BOOK REVIEW 15 September 2025

Heroes or hoarders? The strange brains of people who collect

Public museums and private collections are stuffed with scientific artefacts gathered by individuals — often with highly questionable obsessions and motivations.

By

Andrew Robinson

Parts of Hans Sloane’s extensive collection are held in the British Museum and the Natural History Museum in London. Credit: Alamy

A Noble Madness: The Dark Side of Collecting from Antiquity to Now James Delbourgo Riverrun (2025)

The Galileo Museum, a science museum in Florence, Italy, has astronomer Galileo Galilei’s preserved middle finger on display. Encased in a gilded glass egg, the digit is exhibited “as if it were the relic of a Christian saint”, remarks historian of science James Delbourgo in his illuminating and entertaining history of the ‘dark side’ of humanity’s obsession with collecting things. The finger was severed from Galileo’s corpse in 1737 — long after his death in 1642 — along with an index finger also displayed at the museum and a vertebra held at the University of Padua, Italy. According to a witness to the dismemberment, the Italian nobleman who took the fingers desired them “because Galileo wrote so many beautiful things with them”.

It is an unusual story, but perhaps not entirely atypical. As Delbourgo shows in A Noble Madness, a large driver of the desire to collect artefacts is curiosity — whether scientific, historical, religious or otherwise. But perhaps even more often, it is obsession. Delbourgo focuses on this compulsive aspect, and the varying ways in which society has regarded people who are driven to amass stuff. He offers “a grand portrait gallery that charts the changing image of the collector from the ancient looter and medieval idolater to the decadent of the fin de siècle and the modern-day hoarder”.

Dark desires

A compelling example of such obsession is Henry Wellcome. He is known today through the biomedical research-funding organization Wellcome, and the Wellcome Collection museum and library in London. Born in 1853 to an itinerant missionary father in a log cabin in Wisconsin, by his death in 1936, Wellcome had become a highly successful pharmaceutical entrepreneur in the United Kingdom. He also owned a grotesquely overwhelming collection of objects, the variety and sheer number of which the world had never seen — mainly because few were on display.

Wellcome obtained many of these objects through highly dubious means, notes Frances Larson in her disturbing 2009 history of his collection, An Infinity of Things. In 1912, for example, Wellcome’s right-hand man wrote to an agent in India, a doctor, that the country must be “completely ransacked as far as we possibly can for literature and other objects of interest connected with ancient medicine”. The agent duly did his best — but there is little evidence that Wellcome ever studied or ‘enjoyed’ what had been collected. He was always too busy acquiring new things, right up to his death. His obsession was rooted in possession.

The Wellcome Museum deliberately avoids displaying information about its founder, notes Delbourgo. He regards this stance as “myopic: the Wellcome’s abdication of its duty to educate visitors about its origins denies the public the chance to make up its own mind about its past”.

The British Museum, just down the road in London, is less coy about the man who provided its founding collection in 1753. Physician and naturalist Hans Sloane — the subject of Delbourgo’s 2017 book Collecting the World — was an avid collector of curiosities and animal and plant specimens. His motivations were multifarious. He collected manuscripts from astrologers and alchemists to document their ascientific convictions as “disorders of the mind”, delusions that he felt might be cured by bloodletting, his specialism. But when it came to collecting from the natural world, he was explicit about a financial incentive: to “figure out what species were good for, what they cost, and how to make money off them”, in Delbourgo’s words. To his critics, Sloane was an “ignorant arriviste”. Today, his financial links to the slave plantations in Jamaica that part-funded his collecting are openly acknowledged in an exhibit showing a bust of Sloane.

Galileo’s elegantly preserved middle finger.Credit: Eric Vandeville/Gamma-Rapho/Getty

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 581-582 (2025)

doi: https://doi.org/10.1038/d41586-025-02919-7

Competing Interests

The author declares no competing interests.

BOOK REVIEW 16 September 2025

How did assaults on science become the norm — and what can we do?

An insightful book explores attacks on science from a historical and a personal perspective.

By

Gretchen T. Goldman

Anti-vaccine groups protested against the actions of Anthony Fauci, who served as chief medical adviser to the US president in 2021–22. Credit: Dave Decker/Zuma Press/eyevine

Science under Siege: How to Fight the Five Most Powerful Forces that Threaten Our World Michael E. Mann & Peter J. Hotez PublicAffairs (2025)

Months into President Trump’s second term, science and scientists are under attack as never before in the United States. The administration is forcing devastating cuts to previously stable US research investments, dismantling federal science agencies and programmes, ousting independent scientific officials and blatantly disregarding evidence on issues that affect us all, including vaccines, air pollution and fossil fuels.

The scientific community needs to recognize these trends and fight back in every way possible. The timely release of Science under Siege by paediatrician and vaccine specialist Peter Hotez and climate scientist Michael Mann is a welcome addition to the scientific community’s arsenal. Both authors work to dispel misinformation in the public and political arenas, and both have experienced personal attacks because of it.

Mann, known for his ‘hockey stick’ visual representation of soaring global average temperatures owing to climate change, has faced years of public disparagement and threats to his physical safety. Hotez found himself in the crosshairs of the politicization of public-health guidance, on vaccines in particular, during the COVID-19 pandemic — and had to hire private security. Together, they explore the forces that undermine science in the United States and beyond.

Five forces to contend with

The duo skilfully establishes parallels in the attacks on climate scientists and on public-health professionals. The two fields might seem disparate, but specialists in both share a responsibility to inform the public about the “one-two punch of climate change and pandemics” — the effects of which are mutually reinforcing to “threaten massive loss in human life” — and find solutions.

In some cases, Mann and Hotez note, the same tactics are used in attempts to discredit their work in both fields — sometimes even by the same people. For example, climate-disinformation messaging morphed over several years from ‘it’s not real’ to ‘it’s actually good for us’. These same tactics were adopted by peddlers of COVID-19 misinformation, who claimed that widespread infection could lead to herd immunity, and caught on much faster, mere months after the virus began spreading.

But who’s behind the lies, propaganda and attacks? Mann and Hotez identify five forces — the ‘five Ps’ — that drive threats to science and scientists: plutocrats, petrostates, pros (that is, academics and specialists who use their credentials to promote disingenuous, and lucrative, contrarian views), propagandists and the press. Mann and Hotez detail how bad actors continue to propagate misinformation, persecute scientists, undermine science-based decisions from policymakers and the public and threaten global health and safety.

Fighting back

As the president of the Union of Concerned Scientists — a science-advocacy non-profit organization that spends its time fighting these known enemies — I found this thorough naming and shaming resonant and indeed cathartic. I imagine that this exploration of just how pervasive and well-funded these forces are might also bring relief to scientists wondering why their commitment to truth-telling isn’t enough.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 583-584 (2025)

doi: https://doi.org/10.1038/d41586-025-02920-0

Competing Interests

The author declares no competing interests.

Opinion

- GPS timekeeping is increasingly vulnerable: here’s how to deliver future-proofed time

- Mirror of the unknown: should research on mirror-image molecular biology be stopped?

COMMENT 15 September 2025

GPS timekeeping is increasingly vulnerable: here’s how to deliver future-proofed time

With crucial infrastructure increasingly dependent on accurate, resilient clocks, outages in the dominant system for global positioning highlight the need for other ways of distributing time information.

By

Leon Lobo,

Douglas Paul &

Chander Velu

Aviation and road transport are among the sectors that currently depend on increasingly vulnerable GPS timekeeping. Credit: Kevin Carter/Getty

It might not be apparent, but almost everything people do in this digitally connected world, from sending a text or e-mail to doing an Internet search or paying for something online, depends on accurate, resilient timing. Most electronic communications rely on digital infrastructure that is synchronized to a common time reference, enabling information to flow at a known rate. Accurate timing is also crucial for synchronizing and stabilizing infrastructure such as electricity grids, for helping to ensure the integrity of financial transactions, for steering machinery for precision agriculture, and for managing transport, logistics and postal delivery systems, among a host of other essential functions.

Today, the necessary timing signals come overwhelmingly from Global Navigation Satellite Systems (GNSS). These deliver signals from space, with only a radio receiver needed to receive and interpret them. Chief among them is the US-developed Global Positioning System (GPS). GPS is free to use, and the technology is mature: miniature GPS receivers are now embedded in every smartphone, at a cost of a few dollars per unit. This is an easy, low-cost way to reliably synchronize time, certainly compared with the old method of physically calibrating your clock to a reference clock at a national standards agency.

But this success has bred complacency — and led to underappreciated risk. GNSS are far from fail-safe. In many parts of the world, organized-crime syndicates and military authorities are among those increasingly jamming GNSS signals (blocking them entirely) or spoofing them (transmitting false signals to provide misleading time and position coordinates). Disruptions to the signal due to extreme weather events are also on the rise. In some sectors, such as aviation, a multitude of systems would potentially be affected in the event of more-widespread outages. But there is low awareness of the risks — and protections are hugely variable between sectors.

The increasing vulnerability of time signals from space necessitates the development of alternative ways of accessing accurate, resilient and secure time. We (the authors) have been involved in varying capacities in technology and economic measures to deliver a nationwide, resilient terrestrial timing solution that is independent of GNSS in the United Kingdom. Here we set out three key steps that we think would help to facilitate the development of alternative time sources worldwide: increasing buy-in from business; linking up existing, heterogeneous local timing systems; and creating entirely new uses for time.

Getting buy-in from business

Constellations of GNSS satellites disseminate time from the national-standards laboratories that contribute to the formulation of the global time scale, Coordinated Universal Time (UTC). The GPS system was developed by the US Department of Defense during the cold war, initially for the exclusive use of the US military. Each GPS satellite carries multiple atomic clocks, which are ultimately synchronized with a representation of the UTC, known as UTC(USNO), generated by an ensemble of atomic clocks at the US Naval Observatory in Washington DC. The signals these satellites beam down to Earth enable users to determine the time to within an accuracy of 10–7 seconds, or 100 billionths of a second.

Recognition in the 1980s of the wider potential societal benefits of GNSS led the United States to make an intentionally degraded, ‘selectively available’ version of the GPS signal accessible to everyone globally, free of charge. The full version was made public in 2000, since when its use has ballooned in a plethora of civilian applications. Other GNSS systems exist, such as GLONASS (operated by Russia), Galileo (the European Union) and BeiDou (China). But GPS remains dominant owing to widespread public confidence in a US-provided infrastructure and to the system’s earlier availability for general use, which means a large number of older receivers are only GPS-compliant. Some 5.6 billion end-user GNSS receiver units were in use in 2023, a number predicted to increase to almost 9 billion units in 2033 (see ‘Sky-high demand’). The economic benefits of using GNSS have been estimated to be around US$300 billion annually for the United States, $81 billion across Europe and from $9 billion to about $18 billion for the United Kingdom (see ‘Productivity plus’).

Source: EU Agency for the Space Programme (https://go.nature.com/42AQKJL)

The potential costs of disruption to GNSS are similarly considerable: across all sectors, a report for the UK government in 2023 estimated these costs, per day, to be almost $1.9 billion for the United Kingdom alone. But whereas the economic benefits of using GNSS often accrue to individual firms, the economic cost of disturbances to the GPS signal — for example, the failure of the electricity grid due to a GPS outage that might affect transport, financial and communication systems — tends to be borne by all of society.

More onus needs to be put on firms and utilities that provide services through GNSS to invest in timing resilience. Regulation to increase the liability of individual firms, and personal accountability of senior managers for ensuring resilience of time, is one way to make this happen. There is also a need to support the development of alternative assured ‘holdover time’ capabilities: accurate, locally based clocks that can continue to provide time for a while if the main GNSS signals are lost.

Source: London Economics (https://go.nature.com/4G5NDYM)

The cumulative investment costs across every organization in every sector to provide such a holdover system are likely to be significant. Developing national public infrastructures for delivering resilient timekeeping directly from national representations of UTC — in effect, recreating timekeeping as a national public utility — is a way to reduce direct costs for businesses. Such a public utility could instil trust and confidence in users, and cover its costs by offering tiered, paid-for levels of assurance of time. In the United Kingdom, a supporting terrestrial clock system is being designed and developed as a nationwide time infrastructure through the National Timing Centre research and development programme (of which one of us, L.L., is head) at the National Physical Laboratory (NPL) at Teddington. This system is linked to UTC(NPL), the United Kingdom’s real-time realization of UTC.

But limited understanding of the need for alternative assured-time capabilities is a barrier to achieving business and political buy-in. A programme of public awareness about the use and importance of GNSS should be rolled out globally, emphasizing both the risks inherent in the current systems and the benefits of alternative timing systems for increased resilience and enhanced performance.

Linking up time systems

Crucial infrastructures, from financial services to transport and energy systems, are often interdependent. Yet they tend to operate as independent ecosystems, subject to their own legislation and with their own regulatory standards, policies, supply chains and digital ecosystems.

Little thought tends to be given to the security of timekeeping in the design and maintenance of the digital systems underpinning this infrastructure. Time’s intangible nature means that it often falls in the gap between cybersecurity and physical-security measures designed to protect digital and physical assets, respectively. When mitigating GNSS loss or disruption is considered at all, it tends to be by individual firms on an ad hoc basis. For example, telecommunications network providers often have atomic clocks distributed across their fibre exchanges to enable synchronization to be maintained for the Internet backbone even if GNSS signals are disrupted. Such mitigation measures are rarely tested robustly for the possibility of GNSS outages across all interconnected sectors.

The increasingly interlinked nature of timing infrastructure implies that terrestrial clocks need to be integrated and able to coordinate time in the case of disruption to GNSS. This underlines the desirability of government intervention to provide a base capability that is accessible to all users wherever and whenever they need it. This might take the form of new legislation or regulation and standards to allow interoperability between essential infrastructures. It is part of the rationale behind the UK National Timing Centre’s research programme.

A further consideration is that the global supply chain for timing systems — from atomic clocks, time distribution and monitoring systems to user equipment — is currently sparse and lacks diversity. The ubiquity and utility of GNSS for time has resulted in industry investing in and developing receivers that are low in size, weight, power and cost, proliferating dependency on this single solution. (One of us, D.P., is head of the UK Hub for Quantum Enabled Position, Navigation and Timing, led by the University of Glasgow, UK, which runs a programme developing cheaper timing technologies.) A more diverse supply chain needs to be built to provide the enabling technologies to support a national timing infrastructure that can enhance the resilience of time. This needs to be complemented by an upgrade of the skills pipeline.

Private-sector investments in building such a resilient supply chain to provide reliable timing will depend on effective, long-term commitment from governments[1]. Policy initiatives such as direct public investment, or incentives such as tax credits, interest deferrals and loans, must be immune to political winds of change to truly de-risk such investments. This could be achieved by regulating the minimum holdover time — the length of time any backup system can provide accurate timekeeping — across industries to ensure commitment to build and develop such time-based resilience. Such regulation needs to define the requirements for specific clocks with the accuracy needed to enable each national infrastructure to operate effectively.

Creating new uses for time

The extra revenue-generating opportunity of new timing systems is, on the face of it, limited when compared with the extra costs. A focus solely on managing risk and enhancing the resilience of time systems might not, therefore, be enough to convince firms of the need to invest in supporting the development of terrestrial holdover timing systems.

Financial markets require precise, trustable time for transactions to be recorded accurately.Caption: Michael M. Santiago/Getty

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 585-588 (2025)

doi: https://doi.org/10.1038/d41586-025-02921-z

References

1. Dubey, R. et al. Int. J. Product. Econ. 258, 108790 (2023).

2. Chandler, A. D. Jr The Visible Hand (Harvard Univ. Press, 1977).

3. Panagariya, A. Asia Glob. Econ. 2, 100027 (2022).

Reprints and permissions

Competing Interests

D.P. received funding for research aligned to this article from the Royal Academy of Engineering Chair in Emerging Technologies (Grant number CiET2021/123), EPSRC (Grant numbers EP/Y00485X/1, EP/X012689/1 and EP/Z533178/1) and Innovate UK (Grant number 10142512). D.P. is also a senior adviser to Serendipity Capital, a venture-capital investment firm in critical technologies.

COMMENT 15 September 2025

Mirror of the unknown: should research on mirror-image molecular biology be stopped?

Amid growing debates about the benefits and risks of studying looking-glass versions of life’s building blocks, there is an urgent need to bridge divergent views.

By

Ting Zhu

In theory, all biological structures, functions and even organisms could be recreated in their mirror image, leading to endless possibilities.Credit: Getty

This week, experts in synthetic biology and microbiology, among other fields, are gathering in Manchester, UK, to explore the benefits and risks of building synthetic life. One of the topics that will be discussed is how research might be restricted to prevent the creation of organisms made of components that are the mirror image of those that make up life on Earth. Days after the Manchester meeting, the issue will be examined at a workshop organized by the US National Academies of Sciences, Engineering, and Medicine. And other meetings are planned.

Most of the biological molecules known to make up life on Earth have a specific handedness, or chirality. Amino acids have left-handed chirality, for example, whereas DNA is right-handed. Because mirror-image bacteria or other synthetic life forms would be made of molecules of opposite handedness (so with right-handed amino acids and left-handed DNA), the concern is that such organisms might represent a hazard to known life[1]–[3] (see also go.nature.com/3hshyst and go.nature.com/3vwuytw). For example, some of them might be capable of evading immune systems, confounding medicines, resisting predation and causing harms to humans, non-human animals, plants and ecosystems[2],[3].

Prohibiting the creation of molecules or biological entities of either chirality that could endanger human health or environmental stability should be uncontroversial. And discussions early in the development of a field — as well as efforts to engage the public — can be constructive when it comes to ensuring that research is conducted responsibly and ethically.

But in the face of vast unknowns, the noble path of pre-emptively protecting humanity from potential risks in the distant future can be slippery. And we should tread cautiously.

The concept of a mirror-image biological world is not new. It was first proposed in 1860 by French chemist and microbiologist Louis Pasteur[4]. And the potential benefits and risks of mirror-image organisms have been discussed by the research community for more than 30 years[1]–[3] (see also go.nature.com/3hshyst and go.nature.com/3vwuytw). However, in the past few months, the conversation has abruptly shifted to calls for hard limits on basic research and funding[2].

At this point, there are divergent views (see go.nature.com/46tgjvf and eLetters by R. Derda et al. and D. Perrin in ref. 2) on how soon it might be possible to create mirror-image organisms; the potential benefits and risks of generating mirror-image life and of developing precursor technologies; whether moratoria on research should be imposed; and, if so, what areas of study should be restricted.

Given the countless unanswered questions, careful consideration of the scientific facts learnt so far — regarding what it would take to create a mirror-image life form, and the pros and cons of research on mirror-image molecular biology more broadly — is crucial for bridging divergent views and fostering rational and informed debate.

On the distant horizon

In December 2024, nearly 40 experts, including in synthetic biology, ecology and immunology, co-authored a Policy Forum article in Science[2] and released a separate 299-page technical report[3]. In both, the authors argued that were mirror-image life created, it would be very likely to present unprecedented risks to humans, animals, plants and ecosystems.

Multiple meetings have followed the Science publication, including in the United Kingdom, the United States, France and the Netherlands.

But how close are scientists to being able to create a mirror-image life form?

Scientists have been pondering the idea of a mirror-image world of biology for more than a century.Credit: Jorg Greuel/Getty

Dozens of research groups, including those at pharmaceutical companies, have been synthesizing and investigating mirror-image proteins, DNA and RNA for the past three decades to understand fundamental biology and develop therapeutics[5]–[14]. My colleagues and I have been exploring various mirror-image molecular processes, too. These include the replication of mirror-image DNA, the transcription of mirror-image DNA into mirror-image RNA and the translation of mirror-image RNA into mirror-image proteins — in other words, a mirror-image version of the central dogma of molecular biology[7]–[11].

Research in mirror-image molecular biology is still in its infancy. But scientists working in this field have been humbled by the tremendous challenges of exploring this unknown world[5]–[14]. The creation of mirror-image organisms, if it ever became feasible, would face monumental conceptual and technical barriers.

Hundreds to thousands of cellular components — including proteins, nucleic acids, membranes, metabolites and complex carbohydrates called glycans — would need to be synthesized chemically or enzymatically in their chirally inverted forms. Some of these are encoded directly by DNA. But many are synthesized or modified by other complex biological machinery, meaning their compositions and structures cannot simply be derived from DNA sequences. And many have not yet been characterized.

It took our group nearly four years to chemically synthesize a mirror-image protein fragment of up to around 470 amino acids[9] — the longest single-chain mirror-image polypeptide reported so far. Synthesizing longer polypeptides and membrane proteins that are rich in water-repelling (hydrophobic) domains would be even harder.

Likewise, we have been trying to chemically synthesize a highly simplified version of a mirror-image ribosome since 2016, and are still years away from achieving it. Should we succeed, this ribosome will lack protein and RNA modifications and will not have aminoacyl-tRNA synthetases (the enzymes responsible for attaching specific amino acids to their corresponding transfer RNAs during protein biosynthesis)[8],[11]. This means it will be able to produce only short peptides and small proteins (say, of about 300 amino acids)[8].

Even if all the constituent molecules of the simplest bacterium could be synthesized in their mirror-image forms, these would need to be folded correctly and assembled with spatio-temporal precision to create a mirror-image bacterium that functions as a complex, autonomously replicating cell.

Many laboratories have built non-living membrane-bound compartments, in which copies of DNA and RNA molecules can be made or in which RNA molecules can be translated into proteins. Although researchers have been able to isolate biologically derived ribosomes and other cellular machinery with natural chirality for decades, no lab has been able to use this machinery to produce all the essential cellular components in vitro.

Researchers don’t yet know how to assemble a natural-chirality self-replicating cell from biologically derived building blocks — let alone how to chemically synthesize a mirror-image one from the ground up. And although other strategies for the creation of mirror-image life have been proposed (such as the stepwise conversion of a natural-chirality cell into a mirror-image cell[2],[3]), there is insufficient evidence to support their feasibility.

In short, it is crucial to distinguish mirror-image molecular biology from the creation of mirror-image organisms. A self-replicating cell has molecular diversity, metabolic complexity and structural intricacy that are orders of magnitude greater than what’s found in any currently synthesizable biomolecular system. And the creation of a mirror-image organism lies well beyond the reach of present-day science.

Endless possibilities

Because all biological structures, functions and even organisms could be recreated in their mirror image, the possibilities — good and bad — in a looking-glass world are endless. As well as considering the risks of hypothetical scenarios, such as the creation of mirror-image life, it is important to keep in mind the realized and potential benefits of the mirror-image molecular biology research that is already under way[5]–[14].

When given to animals or humans, mirror-image peptides and nucleic-acid drugs can trigger a much milder immune response compared with their natural-chirality counterparts[13]. They are also more resistant to biodegradation, which means a dose can stay in the body for much longer. The implications for drug discovery are profound.

Dozens of mirror-image peptides, DNA and RNA molecules are already being developed as drug candidates for cancer, metabolic diseases, infectious diseases and inflammatory disorders[10],[13]. Indeed, a synthesized mirror-image ribosome would probably drastically accelerate pharmaceutical discovery by enabling the high-throughput production of mirror-image peptides[8],[11].

All sorts of other possible applications of mirror-image molecules or biological entities can be imagined, particularly in medicine and sustainability.

Mirror-image glucose tastes as sweet as its natural-chirality counterpart, but does not provide calories because it is not metabolized by the enzymes found in natural-chirality organisms[15]. This means that mirror-image glucose and other mirror-image sugars could serve as non-caloric sweeteners or other food additives.

Mirror-image DNA molecules have the same capacity to hold information as their natural-chirality counterparts do, but they are more resistant to biodegradation and easier to distinguish from contaminant (natural-chirality) DNA. As such, mirror-image DNA molecules can serve as robust information repositories[9].

Nanoparticles or nanocapsules, built using mirror-image proteins, could enable the safe delivery of drugs by shielding them from the immune system. Mirror-image DNA or RNA molecules designed to detect the presence of certain human proteins and metabolites, such as thrombin[10] and guanine[11], could be used as diagnostic biosensors in clinical settings.

Meanwhile, mirror-image versions of enzymes that are capable of degrading plastics that have no chirality could offer a solution to plastic pollution[12]. Like their natural-chirality counterparts, such enzymes can break down plastics but are more resistant to biodegradation themselves. In principle, mirror-image versions of enzymes that can capture carbon might similarly be used to help address climate change.

Plastic-consuming bacteria, shown in this artist’s impression, contain enzymes that degrade plastics. Biostable mirror-image versions of these proteins could offer a solution to plastic pollution.Credit: Thomas Parsons/Science Photo Library

As well as providing solutions for all sorts of practical problems, basic research on biology through the looking glass could offer insights into the structures and functions of biomolecules. It could shed light on the origin of homochirality (the dominance of one set of chiral molecules in known forms of life), and even on the origin of life[11]. It could guide searches for new life forms, for instance, on Earth as well as on other planets.

Of course, the very properties that promise to make mirror-image proteins and nucleic acids so useful in so many contexts — their biostability and tendency to induce only a mild immune response in humans and other organisms — could also make certain mirror-image organisms harmful[1]–[3] (see also go.nature.com/3hshyst and go.nature.com/3vwuytw).

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 588-591 (2025)

doi: https://doi.org/10.1038/d41586-025-02912-0

References

1. Brewster, J. H. & Laskowski, M. Jr Science 258, 1289; author reply 1290 (1992).

2. Adamala, K. P. et al. Science https://doi.org/10.1126/science.ads9158 (2024).

3. Adamala, K. P. et al. Technical Report on Mirror Bacteria: Feasibility and Risks (Stanford Digital Repository, 2024); available at https://doi.org/10.25740/cv716pj4036

4. Pasteur, L. Researches on the Molecular Asymmetry of Natural Organic Products (1860). Alembic Club Reprint No. 14 (Alembic Club, 1905).

5. Milton, R. C., Milton, S. C. & Kent, S. B. Science 256, 1445–1448 (1992).

6. Zawadzke, L. E. & Berg, J. M. J. Am. Chem. Soc. 114, 4002–4003 (1992).

7. Wang, Z., Xu, W., Liu, L. & Zhu, T. F. Nature Chem. 8, 698–704 (2016).

8. Chen, J., Chen, M. & Zhu, T. F. Chem 7, 786–798 (2021).

9. Fan, C., Deng, Q. & Zhu, T. F. Nature Biotechnol. 39, 1548–1555 (2021).

10. Chen, J., Chen, M. & Zhu, T. F. Nature Biotechnol. 40, 1601–1609 (2022).

11. Xu, Y. & Zhu, T. F. Science 378, 405–412 (2022).

12. Guo, C., Zhang, L.-Q. & Jiang, W. Chem 9, 363–376 (2023).

13. Harrison, K., Mackay, A. S., Kambanis, L., Maxwell, J. W. C. & Payne, R. J. Nature Rev. Chem. 7, 383–404 (2023).

14. Zhang, G. & Zhu, T. F. Nature Chem. 16, 592–598 (2024).

15. Dubovski, N., Ben Shoshan-Galeczki, Y., Malach, E. & Niv, M. Y. Food Chem. 373, 131393 (2022).

Reprints and permissions

Competing Interests

T.Z. has applied with his colleagues for patents related to some of the beneficial applications mentioned in the Comment article.

Work

- ‘Lipstick on a pig’: how to fight back against a peer-review bully

- Sweet like chocolate: researching in the shade of a cacao tree

CAREER FEATURE 15 September 2025

‘Lipstick on a pig’: how to fight back against a peer-review bully

Scientific societies, journals, editors and researchers are pushing back against mean-spirited peer reviews.

By

Katarina Zimmer

Find a new job

Illustration: David Parkins

Nyssa Silbiger still recalls the rude remark that reviewer three made in 2014 about her first paper describing her PhD research. “The phrases I have so far avoided using in this review are, ‘lipstick on a pig’, and ‘bullshit baffles brains’,” they wrote.

To Silbiger, a marine biologist at the University of Hawai‘i at Mānoa, the words cut deep. The critique not only made it difficult to work out how she should revise her manuscript on the bioerosion of coral reefs, but also led her to question her abilities and whether she belonged in science at all. “As a twenty-something student, that can have a really big impact on your ability not only to conduct science, but your whole future career,” says Silbiger, who now leads her own marine-ecology group at the university.

Peer review is supposed to be critical. But too often, Silbiger says, reviewer feedback crosses the line into an unprofessional realm. Such unacceptable behaviours range from outright bullying of other scientists and personal comments about the authors to mean-spirited or unhelpful remarks without constructive, evidence-based criticism. In 2019, Silbiger and Amber Stubler, a marine ecologist at Occidental College in Los Angeles, California, conducted a survey of roughly 1,100 scientists. Some 58% of respondents reported that they had encountered unprofessional peer-review comments[1]. In particular, women, non-binary scientists and people of colour said that the experience had harmed their confidence and productivity and delayed their career advancement.

Attention to the issue has grown ever since and, fortunately, so have ways to address it. Journals, editors and scientific organizations have begun to explore a range of solutions to prevent bullying during the peer-review process and to hold mean-spirited reviewers accountable. Many scientists are also taking matters into their own hands by pushing back on unprofessional reviews.

“There is progress being made, just in small increments and in different flavours,” says Emma Dunne, a palaeobiologist at the Friedrich Alexander University of Erlangen–Nuremberg in Germany, and the ethics editor of the journal Historical Biology. “I would like to think that things can only get better.”

Why do nasty peer reviews happen?

However negatively a referee views a study, there’s always a polite, evidence-based way to express criticism, says Sally Thomas, the Palaeontological Association’s publications officer. During the organization’s peer-review workshop for early-career researchers, she stresses the importance of being careful with language (see ‘Don’t do it’). “Always put yourself in the shoes of the author,” says Thomas, who is based in Cambridge, UK. Start by writing something positive, she says, “and then lay out what is not so good about the work in a totally unemotional and logical way”.

Don’t do it

As a peer reviewer, avoid harmful and unhelpful comments such as these real examples.

• “The writing of this paper was atrocious.”4

• “The result of attending university in a developing country.”4

• “You should look closely at a career outside of science.”1

• “This young lady is lucky to have been mentored by the leading men in the field.”4

• “Utterly disappointed in this submission, it achieves nothing, and was a waste of funding.”4

• “The author’s last name sounds Spanish. I didn’t read the manuscript because I’m sure it’s full of bad English.”1

• “This manuscript was not worth my time so I did not read it and recommend rejection.”4

• “I have rewritten so much of this troubled paper that I should be included as an author.”4

• “The first author is a woman. She should be in the kitchen, not writing papers.”1

• “This paper is, simply, manure.”1

• “What the authors have done is an insult to science.”1

• “The author’s status as a trans person has distorted his view of sex beyond the biological reality.”1

• “The English is not good enough; please have it reviewed by a native speaker.”

• “The authors provide us with a nice example [of] what they can, and cannot do, and how they (wrongly) understand nature and ecology.”4

• “This person works for an NGO [non-governmental organization], you shouldn’t believe anything they say.”1

Yet research indicates that some scientists worry that being too nice will allow poor-quality studies to be published or think that authors deserve harsh comments for submitting substandard work[2]. Other times, overly harsh reviews might be intended to hinder or delay the publication of papers by competing laboratory groups. Personal snipes at study authors are also widespread, including ones targeting early-career scientists, women and people of colour, notes palaeontologist Farid Saleh at the University of Lausanne in Switzerland. He recalls how a reviewer once singled him and a female co-author out on a paper with 12 other authors, “calling us disingenuous, not real scientists, and making other personal attacks”. Remarks that disparage the authors’ English-language skills without constructive feedback are unprofessional and can exacerbate the existing challenges that individuals whose primary language is not English face in scientific publishing, adds Valeria Ramírez Castañeda, a biologist at the University of California, Berkeley, who has studied such challenges[3].

Not all rude-seeming reviews are intentional, because cultural attitudes to directness vary. A blunt comment from one scientist might be perceived as rude by researchers who are used to more diplomatic language, Ramírez Castañeda says. Reviews by scientists who lack the skills or experience to give nuanced feedback, senior researchers accustomed to the more-adversarial academic cultures of the past and scientists who don’t have the time to thoughtfully consider a paper might seem harsher than intended.

What authors can do

Avoiding problematic peer reviews starts by considering which journal to submit to and what its peer-review practices are. Specialists agree that the most common form of peer review — single-anonymous, in which referee identities are concealed from the authors but not vice versa — can promote unprofessional comments by giving reviewers anonymity.

Valeria Ramírez Castañeda says peer reviewers shouldn’t penalize a lack of English fluency.Credit: Valeria Ramírez Castañeda

Fortunately, many journals have begun to offer other kinds of peer review — such as double-anonymous review, in which both author and reviewer identities are concealed. This can help to prevent problematic comments and review-related rejections when reviewers are biased against authors from some demographics or nations. IOP Publishing (IOPP), a publisher of physical-science journals in Bristol, UK, has found few differences in overall rejection rates for papers with double-anonymous reviews compared with single-anonymous ones. However, an internal analysis of 2024 data covering around 28,000 papers suggests that some groups might benefit from double-anonymous reviews. Scientists in Africa were 4% more likely to have their paper accepted when the authors chose to be anonymous during the peer-review stage. But there is no clear trend for women and non-binary authors, says Laura Feetham-Walker, IOPP’s reviewer-engagement manager. And, in some scientific fields, “it’s not that challenging [for a reviewer] to identify who the senior authors are on any paper”, even if they are anonymized, notes Simon Harold, chief editor of Nature Ecology & Evolution in London. (Nature’s Careers team is independent of the journal’s publisher, Springer Nature, which also publishes Nature Ecology & Evolution and other Nature Portfolio journals.)

Many journals, including the BMJ, Nature and some of the other Nature Portfolio journals (see go.nature.com/4nvd9zs), also offer open, or transparent, peer review. In this case, the reviews — and sometimes the referees’ identities — are published with the paper. Although this practice can encourage more-considerate behaviour, early-career scientists often worry about retaliation when critically reviewing papers from more-senior or influential authors. The sense of being able to speak freely with anonymity “is why I think the anonymous peer-review system is the default”, Harold adds.

When biologist Mayank Chugh was pursuing a master’s degree, members of his lab group in India received harsh feedback and demoralizing comments about their written English in some of their papers. So, they decided to submit his first paper to the journal eLife. The journal has both a consultative review process — in which editors and reviewers discuss the manuscript together and share consolidated feedback with the authors — and a policy to publish reviews and encourage reviewers to disclose their names. “We trusted that process over what we had experienced before,” says Chugh, who is now at the University of Maryland, Baltimore County, and a member of eLife’s early-career advisory group. Morteza Mahmoudi, a nanoscientist and anti-bullying researcher at Michigan State University in East Lansing, takes further steps when he anticipates an unproductive peer-review process — something he has often experienced with papers that challenge commercially important assumptions in his field. He now asks editors to exclude certain researchers from reviewing — an option that many journals provide. In these cases, “I don’t get those unnecessary delays in the process or harsh comments”, says Mahmoudi.

After receiving a reviewer’s report, if authors aren’t sure whether the language is problematic, Feetham-Walker recommends that the authors ask themselves: “Has this comment helped me to improve my paper, or has it just undermined my confidence?” Importantly, peer review should critique only the science, she adds. “The main defining factor of unprofessional comments is that they are personal.” If still in doubt, Mahmoudi advises authors to consult their colleagues.

It’s important to remember that harsh reviews can help authors to improve their paper, notes Mirvat Alasnag, an interventional cardiologist at King Fahad Armed Forces Hospital in Jeddah, Saudi Arabia. “If it’s not what you wanted to hear, leave the noise behind, but try as hard as you can to look at the comments and see if they’re valuable,” she says.

However, in the case of especially egregious comments, she and others recommend flagging the problematic behaviour to the manuscript-handling editor (see ‘How to avoid — and push back on — peer review bullying’). Silbiger suggests that authors write an e-mail thanking the editor and reviewer for the critical appraisal and noting that they will take the suggestions into consideration. Then, they should detail the comments they felt were unethical and unprofessional and ask that those comments be removed from the review process — and possibly flagged to the reviewer as being unhelpful.

How to avoid — and push back on — peer-review bullying

Researchers advise on how to avoid and address problematic comments from reviewers.

Choose the right journal. Consider journals that have transparent, open review processes in which reviews are made public, for instance, or that give authors the option to veto certain reviewers.

Focus on the science. Try to isolate the scientific critiques in problematic reviews, and if they’re valuable, focus on addressing them. If in doubt, get a second opinion from colleagues on whether a comment is worth addressing.

Write to the editor. Thank the editor for their time and politely point out the specific comments you found discriminatory or rude.

Consider appealing. If you think that a problematic review has unduly influenced the review process and led to a rejection, consider appealing the editor’s decision.

After Silbiger revised her manuscript in 2014 — and reviewer three responded with further unprofessional comments — her PhD supervisor wrote to the journal’s chief editor. After explaining how the team had addressed the valid criticisms and pointing out the unprofessional remarks that couldn’t be addressed, she asked the chief editor to decide whether to accept or reject the paper. The paper was ultimately published and has been cited 88 times. “If you’re junior, sometimes it helps to have your senior author be the one to write the letter,” Silbiger says.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 809-812 (2025)

doi: https://doi.org/10.1038/d41586-025-02922-y

References

1. Silbiger, N. J. & Stubler, A. D. PeerJ 7, e8247 (2019).

2. Gerwing, T. G. et al. Res. Integr. Peer Rev. 6, 4 (2021).

3. Ramírez-Castañeda, V. PLoS ONE 15, e0238372 (2020).

4. Gerwing, T. G. et al. Res. Integr. Peer Rev. 5, 9 (2020).

WHERE I WORK 15 September 2025

Sweet like chocolate: researching in the shade of a cacao tree

Naailah Ali aims to support cacao farmers in the West Indies by improving the bean-fermentation process.

By

Rachel Brazil

Naailah Ali is a food technologist at the University of the West Indies’ Cocoa Research Centre in St Augustine, Trinidad and Tobago. Credit: Kelly-Ann Bobb for Nature

“The seven-year-old cacao tree (Theobroma cacao) that I’m inspecting in this photo is part of the Model Cocoa Orchard established by the University of the West Indies’ Cocoa Research Centre (CRC), where I work as a food-technology researcher. My colleagues and I use this 1,500-tree orchard in Valsayn, a town in the north of the island of Trinidad, to better understand cocoa production.

My research focuses on the fermentation of cacao beans, a process that is carried out mainly at a small scale on local farms. Cacao trees produce fruit pods, which are harvested and broken open to release the pulp-covered beans. I’m holding one here. The acidity, sweetness and floral flavour vary from pod to pod. It’s the pulp that acts as the fuel for the microorganisms that drive the beans’ fermentation.

The chemical changes that occur over about a week remove the beans’ bitterness and turn them red-brown, but only after roasting do they gain their chocolate flavour. The success of the fermentation process is dependent on climate. And with weather patterns becoming less predictable, the quality of the beans has started to decline. We have started to experiment with manipulating sucrose and water levels at the start of fermentation, and we are also using other techniques to tweak the process.

Enjoying our latest content?

Login or create an account to continue

- Access the most recent journalism from Nature's award-winning team

- Explore the latest features & opinion covering groundbreaking research

Access through your institution

or

Sign in or create an account

Continue with Google

Continue with ORCiD

Nature 645, 814 (2025)

doi: https://doi.org/10.1038/d41586-025-02923-x

This Interview has been edited for length and clarity.

Research

- Scaling and logic in the colour code on a superconducting quantum processor

- Topological prethermal strong zero modes on superconducting processors

- DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning

- Supervised learning in DNA neural networks

- Long-range PM2.5 pollution and health impacts from the 2023 Canadian wildfires

- Flourishing chemosynthetic life at the greatest depths of hadal trenches

- Whole-genome sequencing of 490,640 UK Biobank participants

- A generic non-invasive neuromotor interface for human-computer interaction

- Lithium deficiency and the onset of Alzheimer’s disease

- Mitochondrial origins of the pressure to sleep

- A gut sense for a microbial pattern regulates feeding

- Driving a protective allele of the mosquito FREP1 gene to combat malaria

- Fluctuating DNA methylation tracks cancer evolution at clinical scale

- Excised DNA circles from V(D)J recombination promote relapsed leukaemia

- Programmable protein ligation on cell surfaces

Article Open access Published: 26 May 2025

Scaling and logic in the colour code on a superconducting quantum processor

N. Lacroix,

A. Bourassa,

F. J. H. Heras,

L. M. Zhang,

J. Bausch,

A. W. Senior,

T. Edlich,

N. Shutty,

V. Sivak,

A. Bengtsson,

M. McEwen,

O. Higgott,

D. Kafri,

J. Claes,

A. Morvan,

Z. Chen,

A. Zalcman,

S. Madhuk,

R. Acharya,

L. Aghababaie Beni,

G. Aigeldinger,

R. Alcaraz,

T. I. Andersen,

M. Ansmann,

F. Arute,

K. Arya,

A. Asfaw,

J. Atalaya,

R. Babbush,

B. Ballard,

J. C. Bardin,

A. Bilmes,

S. Blackwell,

J. Bovaird,

D. Bowers,

L. Brill,

M. Broughton,

D. A. Browne,

B. Buchea,

B. B. Buckley,

T. Burger,

B. Burkett,

N. Bushnell,

A. Cabrera,

J. Campero,

H.-S. Chang,

B. Chiaro,

L.-Y. Chih,

A. Y. Cleland,

J. Cogan,

R. Collins,

P. Conner,

W. Courtney,

A. L. Crook,

B. Curtin,

S. Das,

S. Demura,

L. De Lorenzo,

A. Di Paolo,

P. Donohoe,

I. Drozdov,

A. Dunsworth,

A. Eickbusch,

A. Moshe Elbag,

M. Elzouka,

C. Erickson,

V. S. Ferreira,

L. Flores Burgos,

E. Forati,

A. G. Fowler,

B. Foxen,

S. Ganjam,

G. Garcia,

R. Gasca,

É. Genois,

W. Giang,

D. Gilboa,

R. Gosula,

A. Grajales Dau,

D. Graumann,

A. Greene,

J. A. Gross,

T. Ha,

S. Habegger,

M. Hansen,

M. P. Harrigan,

S. D. Harrington,

S. Heslin,

P. Heu,

R. Hiltermann,

J. Hilton,

S. Hong,

H.-Y. Huang,

A. Huff,

W. J. Huggins,

E. Jeffrey,

Z. Jiang,

X. Jin,

C. Joshi,

P. Juhas,

A. Kabel,

H. Kang,

A. H. Karamlou,

K. Kechedzhi,

T. Khaire,

T. Khattar,

M. Khezri,

S. Kim,

P. V. Klimov,

B. Kobrin,

A. N. Korotkov,

F. Kostritsa,

J. Mark Kreikebaum,

V. D. Kurilovich,

D. Landhuis,

T. Lange-Dei,

B. W. Langley,

P. Laptev,

K.-M. Lau,

J. Ledford,

K. Lee,

B. J. Lester,

L. Le Guevel,

W. Yan Li,

Y. Li,

A. T. Lill,

W. P. Livingston,

A. Locharla,

E. Lucero,

D. Lundahl,

A. Lunt,

A. Maloney,

S. Mandrà,

L. S. Martin,

O. Martin,

C. Maxfield,

J. R. McClean,

S. Meeks,

A. Megrant,

K. C. Miao,

R. Molavi,

S. Molina,

S. Montazeri,

R. Movassagh,

C. Neill,

M. Newman,

A. Nguyen,

M. Nguyen,

C.-H. Ni,

M. Y. Niu,

L. Oas,

W. D. Oliver,

R. Orosco,

K. Ottosson,

A. Pizzuto,

R. Potter,

O. Pritchard,

C. Quintana,

G. Ramachandran,

M. J. Reagor,

R. Resnick,

D. M. Rhodes,

G. Roberts,

E. Rosenberg,

E. Rosenfeld,

E. Rossi,

P. Roushan,

K. Sankaragomathi,

H. F. Schurkus,

M. J. Shearn,

A. Shorter,

V. Shvarts,

S. Small,

W. Clarke Smith,

S. Springer,

G. Sterling,

J. Suchard,

A. Szasz,

A. Sztein,

D. Thor,

E. Tomita,

A. Torres,

M. Mert Torunbalci,

A. Vaishnav,

J. Vargas,

S. Vdovichev,

G. Vidal,

C. Vollgraff Heidweiller,

S. Waltman,

J. Waltz,

S. X. Wang,

B. Ware,

T. Weidel,

T. White,

K. Wong,

B. W. K. Woo,

M. Woodson,

C. Xing,

Z. Jamie Yao,

P. Yeh,

B. Ying,

J. Yoo,

N. Yosri,

G. Young,

Y. Zhang,

N. Zhu,

N. Zobrist,

H. Neven,

P. Kohli,

A. Davies,

S. Boixo,

J. Kelly,

C. Jones,

C. Gidney &

…

K. J. Satzinger

Nature volume 645, pages 614–619 (2025)

Abstract

Quantum error correction1,2,3,4 is essential for bridging the gap between the error rates of physical devices and the extremely low error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors5,6,7,8 have focused primarily on the surface code[9], which offers a high error threshold but poses limitations for logical operations. The colour code[10] enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and realizations of colour codes11,12,13,14,15,16,17,18,19 have not addressed performance scaling with code size on any platform. Here we present a comprehensive demonstration of the colour code on a superconducting processor[8]. Scaling the code distance from three to five suppresses logical errors by a factor of Λ3/5 = 1.56(4). Simulations indicate this performance is below the threshold of the colour code, and the colour code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking[20] and inject magic states[21], a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. Finally, we teleport logical states between colour codes using lattice surgery[22]. This work establishes the colour code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

Similar content being viewed by others

Main

Quantum computing holds immense potential for solving complex problems beyond the reach of classical computers23,24. However, most practical quantum computing applications require gate error rates far below what current physical devices can achieve[25]. Quantum error correction (QEC) offers a solution to bridge this gap by encoding logical qubits across multiple physical qubits1,2. This encoding can exponentially suppress errors, provided the physical error rates are below a critical threshold[26].

Realizing scalable, fault-tolerant quantum computation in practice requires overcoming several core challenges, including achieving low logical error rates with reasonable qubit overhead and performing logical operations efficiently. Considerable experimental progress has been made in recent years to address these challenges. Notably, scalable error suppression was recently demonstrated by increasing the size of a logical qubit encoded in the surface code[8] using superconducting circuits[27]. QEC implementations with superconducting qubits5,6,7,28,29 have predominantly focused on the surface code[9] or variants thereof30,31, although alternative approaches such as bosonic encodings are also being explored32,33. The surface code offers a high error threshold and is compatible with planar, four-nearest-neighbour architectures. However, it demands substantial qubit overhead and has limitations for certain logical operations[34], motivating the investigation of alternative planar codes.

Colour codes10,35 allow for more efficient logical operations and require fewer qubits than the surface code to encode a logical qubit at a fixed code distance[36]. The smallest instance of the colour code, the Steane code[37], has been implemented with trapped ions11,12 and neutral atoms[18], demonstrating logical operations and logical circuits13,14,15,16,17,18,19. Colour codes can perform all Clifford gates[38] within a single error correction cycle and support resource-efficient magic state injection protocols required to implement non-Clifford gates21,39,40. A recent breakthrough harnessed these features to reduce the overhead required for non-Clifford gate implementation in surface code architectures41,42. Colour codes also enable multi-qubit entangling operations with less space-time overhead because of their ability for simultaneous fault-tolerant multi-qubit Pauli measurements[43].

However, colour codes have a stricter error threshold than surface codes because of their higher weight stabilizer measurements[35]. Moreover, these colour codes require more elaborate decoding strategies, and conventional colour code syndrome extraction circuits require higher connectivity than four-nearest-neighbour architectures35,44, which is difficult to realize on superconducting devices. As a result, error suppression by increasing the colour code size has not yet been demonstrated, to our knowledge, on any experimental platform.

Nevertheless, recent advances in superconducting qubit performance[8], improvements in decoding algorithms39,40,45,46,47 and optimized error-syndrome extraction circuits44,47 now open new possibilities for implementing the colour code on existing hardware. Here we demonstrate building blocks of fault-tolerant quantum computation using the colour code on a superconducting processor. Specifically, we suppress logical errors by increasing code distance, characterize single-qubit logical Clifford gates, inject magic states and perform lattice surgery[22] to demonstrate multi-logical-qubit operations. This comprehensive demonstration establishes the colour code as a promising approach for resource-efficient, fault-tolerant quantum computation on superconducting circuits.

Colour codes with superconducting qubits

Triangular colour codes10,48 are two-dimensional topological stabilizer codes[2]. In these constructions, three tiles meet at each vertex of the lattice, and the tiles can be coloured (red, green and blue in this work) such that no two adjacent tiles share the same colour. Data qubits are located at each vertex of the lattice, and each tile has an X-type and a Z-type stabilizer.

Several such lattices exist, each with potentially different syndrome extraction circuits for stabilizer measurements[47]. Here we choose to implement a code based on a hexagonal lattice embedded in a square grid of qubits with a superdense syndrome extraction circuit[47] (Fig. 1a,b). This choice is particularly attractive for superconducting qubits because it requires only nearest-neighbour connectivity on a square grid of qubits. Moreover, this choice enables simultaneous measurement of X- and Z-type stabilizers of each tile using two auxiliary qubits labelled X and Z in Fig. 1a, located at the centre of each tile. Conceptually, the two auxiliary qubits are prepared in a Bell pair, and each interact with the three nearest data qubits of the tile using the controlled-NOT (CNOT) gates to accumulate first the Z-type, then the X-type stabilizer, as shown in Fig. 1b. A Bell-basis measurement of the auxiliary qubits follows, allowing both stabilizers of the hexagon to be measured simultaneously up to Pauli corrections dealt with by a frame update[47].

Fig. 1: Superdense colour code.

a, Example tile in the bulk of a red, green and blue hexagonal lattice used for the superdense colour code. The lattice is embedded on a square grid of data qubits (golden circles labelled D1–D6) and X/Z auxiliary qubits (red, green and blue circles), with their connectivity indicated by solid grey lines. b, Superdense syndrome extraction circuit for the tile shown in a (see the main text). c, Distance-5 colour code qubit, with one of the distance-3 qubit subsets outlined in purple. Data qubits included in the logical operators XL and ZL are circled and connected by a solid black line. Red arrows indicate qubit pairs interchanged for the implementation of the colour code on our quantum device. d, Deformed code layout after interchanging the qubits to ensure that each readout line contains only data or auxiliary qubits. The readout lines are oriented diagonally from top left to bottom right (two dashed grey lines).

This construction allows the encoding of a single distance-5 logical qubit using 19 data qubits and 18 auxiliary qubits (Fig. 1c). It consists of six weight-6 stabilizers (two per hexagonal tile) and 12 boundary weight-4 stabilizers (two per quadrilateral tile). The logical operators XL and ZL are defined as the product of the individual Pauli X and Z operators, respectively, of data qubits along a boundary of the triangle.

We implement this logical qubit on the 72-qubit Willow processor first introduced in ref. [8]; see Supplementary Information section A for a summary of the device performance. The design of this processor favours the simultaneous readout of all qubits sharing a readout line to minimize measurement-induced dephasing. To accommodate this constraint, we swap the roles of auxiliary and data qubits for certain pairs of qubits, as indicated by the red arrows in Fig. 1c. This adjustment results in the code layout shown in Fig. 1d, in which each readout line contains only data qubits or auxiliary qubits, but no mixture of both. This ensures that all qubits on each readout line are measured either in each QEC cycle (auxiliary qubit readout line) or at the end of the protocol only (data qubit readout line). To avoid the use of costly swap gate decompositions, we use circuit transformations that add no additional operations and preserve the fault tolerance of the circuit, as detailed in Supplementary Information section B. Apart from these circuit transformations, the CNOT gates are compiled to a combination of native Hadamard gates and CZ gates; see Supplementary Information section B.3 for a full circuit diagram of a QEC cycle on the distance-5 logical qubit.

Distance scaling

First, we demonstrate that the colour code is a viable candidate for encoding logical qubits by testing its memory performance and scaling. Specifically, we preserve logical states in the X and Z bases through repeated cycles of error correction and suppress the logical error per cycle by increasing the code distance d from three to five. Here, the distance of the code corresponds to the minimum number of physical qubit errors required to cause an undetectable logical error. A distance d code can correct any (d − 1)/2 independent errors. We compare the performance of the distance-5 code to the average performance of three distance-3 colour code subsets. An example subset is shown with a purple outline in Fig. 1c,d, and a visual representation of all d = 3 subsets is presented in Supplementary Information section C. For each experimental run, we initialize the data qubits in a product state of the Z and X bases, project the logical qubit into the target logical state using a single cycle of stabilizer measurements, perform n − 1 additional cycles of error correction, and finally measure all data qubits in the Z and X bases. We obtain the logical operator value from the product of the relevant data qubits in this final measurement, and the run succeeds if the corrected logical measurement after decoding coincides with the target logical state; otherwise, a logical error has occurred.

For each error correction cycle, the auxiliary qubit readout outcomes correspond to the stabilizer values and indicate the parity of the involved data qubits (0 for even parity, 1 for odd parity). We construct the error syndrome, in which each element is obtained by comparing stabilizer values in two consecutive cycles and takes a value of 1 if a change of parity is detected and 0 otherwise. By averaging each syndrome element over 50,000 experimental runs, we obtain the average error detection probability Pd for each stabilizer in each cycle, see Fig. 2a for the error detection probabilities of the distance-5 X-basis state-preservation experiment and Supplementary Information section C.4 for others. We find that Pd remains nearly constant in the bulk of the error correction cycles, suggesting a stable error rate throughout the experiment. As expected, weight-6 stabilizers exhibit a higher error detection probability (Pd,6 = 0.149 when averaging over all cycles and stabilizers), compared with boundary weight-4 stabilizers (Pd,4 = 0.112), which involve fewer gates and are thus less susceptible to errors, as shown in Fig. 2b.

Fig. 2: Distance scaling experiment.

a, Detection probability Pd as a function of QEC cycle n for individual stabilizers (faded lines) and their average (solid line) for an X-basis state-preservation experiment in a distance-5 colour code. Weight-6 stabilizers are coloured in red and weight-4 stabilizers are coloured in gold. b, Detection probability for each tile of the distance-5 colour code, averaged over cycles and bases. c, Measured logical error PL for distance-3 (green triangles) and distance-5 (blue pentagons) codes averaged over the X and Z bases. Faded symbols correspond to individual distance-3 subsets. The solid lines, shown for the averaged distance-3 code and the distance-5 code, are fits to \({P}_{{\rm{L}}}={\varepsilon }_{0}\times {(1-2\times {\varepsilon }_{d})}^{n}+1/2\), with fitting parameters ε_0 and εd. d, Logical error per cycle, εd, compared with code distance, d. Same symbols as in c. e, Relative contributions of different error sources to the error budget for the colour code: CZ errors (CZ); errors from spurious interactions during two-qubit gates (CZ stray int.); leakage errors during two-qubit gates (CZ leakage); measurement errors (Meas.); single-qubit gate error (1Q); data-qubit idle error during measurement and reset of auxiliary qubits (Data idle); reset error (Reset); leakage due to incoherent heating from |1⟩ to |2⟩ (Heating). The relative contributions of the different error channels are indicated.

Because each data qubit in the bulk participates in three stabilizers per basis (compared with two for the surface code), efficient matching-based decoders49,50 cannot be used directly[47]. Therefore, we use new decoding strategies35,44,47,51 to infer whether logical errors have occurred; see Supplementary Information section D for an overview of the different decoders used in this work.

To assess the performance of our colour code, we initialize the logical qubit, measure up to n = 29 cycles of error correction, and compute the logical error probability PL as a function of n. We then fit PL to obtain the logical error per cycle εd (ref. [5]). We average the error per cycle of the three different distance-3 subsets to obtain \({\overline{\varepsilon }}_{3}\) and compute the error suppression factor \({\varLambda }_{3/5}={\overline{\varepsilon }}_{3}/{\varepsilon }_{5}\). With a neural-network decoder (AlphaQubit)[51], we obtain Λ3/5 = 1.56(4) and ε_5 = 0.0110(2).

This significant reduction in logical error with increasing distance suggests performance below the error correction threshold of the colour code, corroborated by Pauli simulations extrapolating to larger distances and varying noise strengths (see Supplementary Information section E). The observed error suppression factor is in reasonable agreement with the simulated error suppression factor \({\varLambda }_{3/5}^{{\rm{sim}}}=1.680(4)\). By varying the strength of individual error sources in simulations, we estimate their relative contributions to \(1/{\varLambda }_{3/5}^{{\rm{sim}}}\) (ref. [8]). This analysis suggests that CZ gates are the primary contributors, accounting for about 39% of the error budget (including CZ-gate-induced leakage and stray interactions during CZ gates). The remaining contributions are approximately equally distributed among measurement errors, single-qubit gate errors, and data-qubit idle errors during the measurement and reset of auxiliary qubits.

Logical randomized benchmarking

Achieving fault-tolerant quantum computation requires not only correcting errors in idle logical qubits but also applying logical gates that do not spread errors. Transversal single-qubit logical gates[52] achieve this by applying the desired gate independently to each physical data qubit, keeping potential errors isolated. They are inherently fault-tolerant, simple to implement and efficient, as they require only a single time step of physical gates.

An important advantage of the colour code over the surface code is its ability to perform all single-qubit logical Clifford gates transversely. Here, we implement all 24 gates of the Clifford group using a combination of Hadamard gates H, phase gates S, and Pauli operators, see Supplementary Information section F. We characterize the average error of transversal Clifford operations using logical randomized benchmarking[20]. In analogy to interleaved randomized benchmarking at the physical qubit level[53], the protocol consists of applying multiple sequences of m randomly chosen logical Clifford gates, each followed by a final Clifford gate C−1 that inverts the sequence. The logical qubit is subsequently measured and compared with the initial logical state, |0L⟩. This process is repeated for various Clifford sequence lengths m, with a cycle of error correction between each Clifford gate. To obtain an estimate of the average error per logical Clifford gate, we compare these sequences with the reference sequences in which no Clifford gates are applied, that is, a standard |0L⟩ state-preservation experiment (Fig. 3a).

Fig. 3: Logical randomized benchmarking.

a, Logical-qubit-level reference (Ref.; green) and interleaved randomized benchmarking (IRB; blue) circuit diagrams, consisting of error correction cycles (QEC), randomly selected Clifford gates (C_1, …, Cm), a Clifford recovery gate C−1 and a Z basis measurement (MZ). b–d, Simplified circuit diagrams for a tile of the colour code indicating measurements included in an X-stabilizer error-detecting region spanning across two consecutive cycles without logical gate (b), and how it changes on the application of a logical Hadamard gate H (c), or a logical phase gate S (d) between two error correction cycles, see text for details. The green, blue and purple highlighted sections correspond to regions in which the detecting region is sensitive to Z, X and both X and Z errors, respectively. A CNOT gate symbol spanning three qubit wires indicates three consecutive CNOTs between the auxiliary qubit and its neighbouring data qubits. e, Measured fidelity (symbols) and exponential fits (solid lines) for the interleaved (blue) and reference (green) sequences compared with the number of logical Clifford gates m. The data are decoded using the neural-network decoder. Error bars represent the standard deviation of fidelity over 25 random Clifford sequences, each repeated 20,000 times.

In a state-preservation experiment (no logical gates), subsequent measurements of the same auxiliary qubits are used to construct error syndrome elements. Applying a logical gate between error correction cycles transforms the stabilizers, changing how syndrome elements are constructed, as shown in Fig. 3b–d and explained in more detail in Supplementary Information section F.

We realize logical randomized benchmarking in a distance-3 colour code, varying the number of randomly chosen Clifford gates m = 0–10, with 25 random sequences for each m. When compiling these circuits to native physical operations available on our hardware, single-qubit gates implementing the transversal gate are potentially merged with those from adjacent error correction cycles to minimize the total number of operations per qubit. We observe an exponentially decaying randomized benchmarking fidelity, with the sequence, including transversal Clifford gates, decaying slightly faster than the reference idling experiment (Fig. 3e). We extract an average logical Clifford gate error εC, which quantifies the additional error introduced by the logical Clifford gate in each cycle. Using the neural-network decoder, we obtain εC = 0.0027(3). This is significantly lower than the logical error per cycle, \({\overline{\varepsilon }}_{3}=0.0171(3)\), underscoring the efficiency of implementing transversal single-qubit gates.

Magic state injection

Despite their efficient implementation, transversal gates cannot form a universal gate set[52] required for arbitrary error-corrected quantum computation. For the colour code, extending the transversal gate set with a non-Clifford single-qubit T-gate (π/4 rotation around the z-axis) suffices to perform all single-qubit logical operations necessary for universal quantum computation. This gate can be implemented by preparing a high-fidelity resource magic state[21] on an auxiliary logical qubit and consuming it in a gate teleportation protocol4,21. Preparing the high-fidelity magic state consists of two steps: first, injecting a magic state prepared on a physical qubit into a logical qubit, and second, distilling very high-fidelity magic states from an ensemble of faulty ones through magic state distillation[21]. Here, we focus on the state injection step.

We begin by preparing an arbitrary state |ψ⟩ on a single data qubit using Y- and Z-rotations, parameterized by the polar angle θ and azimuthal angle ϕ, respectively. We then grow into a distance-3 colour code by initializing the new data qubits pairwise into Bell states (Fig. 4a, purple ellipses), ensuring the X and Z operators of the injection qubit (indicated with a black arrow) deterministically extend to \({X}_{{\rm{L}}}\) and \({Z}_{{\rm{L}}}\) (ref. [39]). Executing a single cycle of error correction thereafter projects the distance-3 colour code into |ψL⟩ (see Fig. 4b for a simplified circuit diagram and Supplementary Information section G for details). Because the protocol is applicable to arbitrary states and starts with a single physical qubit, an error on the injection data qubit cannot be detected. However, it has been shown to achieve lower error rates than other injection protocols for CSS codes[39].

Fig. 4: Arbitrary state injection in a distance-3 colour code.

a, Schematic of a distance-3 colour code. The arbitrary state |ψ⟩ is prepared on the data qubit indicated by a black arrow. The black line indicates the logical operators of the colour code, and the purple ellipses indicate Bell pairs, see the main text. b, Simplified circuit diagram for the state injection. Each line corresponds to one of the data qubits, on which we apply single-qubit Y- and Z-rotations (yellow boxes), Bell pair preparation circuits (purple boxes), a QEC cycle and a measurement in the X, Y or Z basis (MXYZ) for logical state tomography. c, Decoded (semi-transparent circles) and post-selected (solid dots) expectation value of the logical Pauli operators XL (blue), YL (red) and ZL (green) when sweeping the polar angle θ. The solid lines correspond to ideal expectation values. d, Decoded (semi-transparent circles) and post-selected (solid dots) infidelities for the prepared logical state |ψL⟩. e, Magic state |mL⟩ infidelity as a function of rejected data fraction for |AL⟩ (green squares), |HL⟩ (blue diamonds) and |TL⟩ (red triangles), see the main text and Supplementary Information section G. The dashed lines serve as a guide to the eye, and the error bars indicate a 95% bootstrapped confidence interval. Each state is shown on the Bloch sphere by an arrow of the corresponding colour.

We characterize the injection of arbitrary states by sweeping the polar angle θ from 0 to 2π while keeping ϕ = 0 and performing logical tomography, measuring the expectation values of XL, YL and ZL. As expected for a rotation around the y-axis of the logical Bloch sphere, \(\langle {Z}_{{\rm{L}}}\rangle \) and \(\langle {X}_{{\rm{L}}}\rangle \) oscillate with sinusoidal shapes, whereas \(\langle {Y}_{{\rm{L}}}\rangle \) remains close to zero (Fig. 4c). From the measured values, we compute the state infidelity across the sweep, obtaining an average infidelity of 0.039(3) using the Möbius decoder (Chromobius)[47] and 0.009(4) when post-selecting for runs without detectable errors (keeping on average 74.8% of the runs) (Fig. 4d). Note that post-selection is acceptable in this context because state injection protocols can be repeated until a high-fidelity resource state is achieved with high confidence[54].

We perform a similar analysis for the azimuthal angle sweep and then focus on preparing specific magic states (see Supplementary Information section G). We examine |AL⟩, |HL⟩ and |TL⟩, corresponding to the +1 eigenstate of the XL + YL, XL + ZL, and XL + YL + ZL, operators, respectively. We achieve post-selection infidelities of \(0.000{8}_{-3}^{+15}\), \(0.004{1}_{-38}^{+37}\) and \(0.008{6}_{-65}^{+67}\) with retained data fractions of 75.2%, 74.6% and 75.7%, respectively. Here, the uncertainty represents a 95% confidence interval calculated using bootstrapping. We also explore partial post-selection, balancing data rejection with infidelity (Fig. 4e). These high-fidelity magic states surpass the threshold required for magic state distillation21,55, exceed the fidelities previously achieved in superconducting circuits and are on par with the best state injection implementations on other platforms (Supplementary Information section G).

State teleportation using lattice surgery

Lattice surgery22,39,43,56 enables the efficient realization of multi-qubit fault-tolerant operations, such as the CNOT gate, with only nearest-neighbour interactions. It performs these operations using fault-tolerant measurements of multi-qubit logical Pauli operators, combined with conditional operations based on the measurement outcomes.

Here, we showcase the lattice surgery framework using an MXX parity measurement, which measures the two-qubit Pauli operator XL1XL2, along with a classical Pauli frame update to teleport16,57 a logical state, |ψL⟩, from one logical qubit (L1) to another (L2), represented schematically in Fig. 5a. The protocol consists of simultaneously initializing L1 in |ψL⟩ and L2 in |0L⟩, measuring MXX by merging the two logical qubits for three cycles, followed by splitting them for one cycle (see Fig. 5b for a space-time visualization of the code evolution and Fig. 5c–e for spatial cuts at the key stages). The parity outcome m_1 is determined from the product of the X-basis stabilizers introduced during the merge (Fig. 5d, hatched tiles) and the Bell measurement of two additional data qubits that are also introduced during the merge to extend the boundary stabilizers. Finally, L1 is measured in the Z basis and logical state tomography is performed on L2 to reconstruct the teleported state density matrix. The parity measurement outcome m_1 and Z basis measurement outcome m_2 of L1 are used in post-processing to apply a conditional Pauli frame update \({Z}_{{\rm{L}}}^{{m}_{1}}{X}_{{\rm{L}}}^{{m}_{2}}\) to the state of L2, effectively completing the teleportation of the logical operators indicated in Fig. 5c (black line) from L1 to L2. Further details and circuit-level diagrams are provided in Supplementary Information section H.

Fig. 5: State teleportation in the colour code using lattice surgery.

a, Simplified circuit diagram to teleport a state |ψL⟩ from logical qubit L1 to a logical qubit L2 using an XX-parity measurement (MXX) realized by lattice surgery, and Pauli frame updates conditioned on the measurement outcomes m_1 and m_2 performed in post-processing (dashed boxes). b, Space-time block diagram showing the MXX lattice surgery operation, with horizontal cuts displaying the evolution of the stabilizers as a function of the QEC cycles, as detailed in c–e. c–e, Representation of the active qubits (coloured) and stabilizers before (c) and after (d) the merge operation, and after the split operation (e). The hatched tiles indicate stabilizers in the X basis only, whereas filled tiles indicate both X and Z stabilizers with support on its vertices. The black line indicates the teleported logical operator from L1 to L2, after the Pauli frame update. f–i, Measured (colour), simulated (black wireframe) and ideal (dotted grey wireframe) expectation values of the Pauli logical operators of L2 after teleporting state |0L⟩, |1L⟩, |+L⟩ and |−L⟩, respectively. j, Measured (gold bars) and simulated (black wireframe) teleported state fidelity F of the four logical X and Z eigenstates.

We experimentally realize the teleportation protocol for four input states (|0L⟩, |1L⟩, |+L⟩ and |−L⟩) and measure the expectation value of the logical Pauli operators XL, YL and ZL of the output state. For each state, only the expectation value in its corresponding eigenbasis (Z basis for |0L⟩ and |1L⟩, X basis for |+L⟩ and |−L⟩) shows a large deviation from zero after decoding (Fig. 5f–i). The decoded eigenvalues are in general agreement with the ideal expectations (dotted grey wireframe) and reasonably match Pauli noise simulations based on device benchmarks (black wireframe), except for \(\langle {Y}_{{\rm{L}}}\rangle \) in the X-basis states, which we discuss in Supplementary Information section H.3. Calculating fidelity with the ideal logical states yields fidelities between 86.5(1)% and 90.7(1)% when decoded with the neural-network decoder (Fig. 5j). These measurements enable us to bound the average fidelity of the single-qubit teleportation channel, \({\mathcal{T}}\), at \(\overline{F}({\mathcal{T}}\,)\ge 84.7(1) \% \) (see Supplementary Information section H for details).

Discussion and outlook

In this work, we demonstrate key building blocks of fault-tolerant quantum computation using the colour code on a superconducting processor. Combining improved device performance, compact syndrome extraction circuits, and new decoding strategies, we achieve clear error suppression with Λ3/5 = 1.56(4) when scaling the code from distance-3 to distance-5. We characterize transversal single-qubit logical Clifford gates using randomized benchmarking. Furthermore, we demonstrate high-fidelity magic state injection and successfully teleport logical Pauli states between distance-3 qubits using lattice surgery.

These results highlight that QEC with superconducting qubits has reached a pivotal stage at which the noise threshold may no longer be the main driver of code choice, and efficient logical operations are a crucial factor. At present, the surface code achieves better logical error suppression (on the same processor, \({\varLambda }_{3/5}^{{\rm{surface}}}=2.31(2)\); ref. [8]), but simulations suggest that improving physical error rates by about a factor of four could render the colour code more qubit-efficient than the surface code (Supplementary Information section I). Importantly, the efficient transversal Clifford gates of the colour code and more flexible lattice surgery would simplify algorithm implementations[43]. Colour codes also underpin the most efficient methods to generate high-fidelity magic states41,42, which could be used alongside surface code computation58,59,60. Quantifying the practical impact of these advantages for large-scale algorithms requires detailed resource estimation studies.

The key goals for future research with colour codes include increasing device performance and size, improving decoding speed and accuracy, demonstrating logical gate error suppression with growing code size, and characterizing more of the unique abilities of the colour code for logical gates. As hardware continues to improve, other quantum-error-correcting codes may also become available for practical implementation. Together, we expect these developments to accelerate progress towards scalable and resource-efficient fault-tolerant quantum computation.

Data availability

Data are available from the corresponding authors upon request or at Zenodo (https://doi.org/10.5281/zenodo.14238944)[61].

References

1. Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995).

2. Gottesman, D. Stabilizer Codes and Quantum Error Correction. PhD thesis (California Institute of Technology, 1997).

3. Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

4. Terhal, B. M. Quantum error correction for quantum memories. Rev. Mod. Phys. 87, 307–346 (2015).

5. Krinner, S. et al. Realizing repeated quantum error correction in a distance-three surface code. Nature 605, 669–674 (2022).

6. Ye, Y. et al. Logical magic state preparation with fidelity beyond the distillation threshold on a superconducting quantum processor. Phys. Rev. Lett. 131, 210603 (2023).

7. Sundaresan, N. et al. Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders. Nat. Commun. 14, 28521 (2023).

8. Google Quantum AI. Quantum error correction below the surface code threshold. Nature 638, 920–926 (2025).

9. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).

10. Bombin, H. & Martin-Delgado, M. A. Topological quantum distillation. Phys. Rev. Lett. 97, 180501 (2006).

11. Nigg, D. et al. Quantum computations on a topologically encoded qubit. Science 345, 302–305 (2014).

12. Ryan-Anderson, C. et al. Realization of real-time fault-tolerant quantum error correction. Phys. Rev. X 11, 041058 (2021).

13. Postler, L. et al. Demonstration of fault-tolerant universal quantum gate operations. Nature 605, 675–680 (2022).

14. Ryan-Anderson, C. et al. Implementing fault-tolerant entangling gates on the five-qubit code and the color code. Preprint at https://arxiv.org/abs/2208.01863 (2022).

15. Paetznick, A. et al. Demonstration of logical qubits and repeated error correction with better-than-physical error rates. Preprint at https://arxiv.org/abs/2404.02280 (2024).

16. Ryan-Anderson, C. et al. High-fidelity teleportation of a logical qubit using transversal gates and lattice surgery. Science 385, 1327–1331 (2024).

17. Mayer, K. et al. Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer. Preprint at https://arxiv.org/abs/2404.08616 (2024).

18. Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626, 58–65 (2024).

19. Postler, L. et al. Demonstration of fault-tolerant Steane quantum error correction. PRX Quantum 5, 030326 (2024).

20. Combes, J., Granade, C., Ferrie, C. & Flammia, S. T. Logical randomized benchmarking. Preprint at https://arxiv.org/abs/1702.03688 (2017).

21. Bravyi, S. & Kitaev, A. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A 71, 022316 (2005).

22. Horsman, D., Fowler, A. G., Devitt, S. & Van Meter, R. Surface code quantum computing by lattice surgery. New J. Phys. 14, 123011 (2012).

23. Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).

24. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41, 303 (1999).

25. Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).

26. Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279, 342–345 (1998).

27. Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021).

28. Marques, J. F. et al. Logical-qubit operations in an error-detecting surface code. Nat. Phys. 18, 80–86 (2022).

29. Hetényi, B. & Wootton, J. R. Creating entangled logical qubits in the heavy-hex lattice with topological codes. PRX Quantum 5, 040334 (2024).

30. Bonilla Ataides, J. P., Tuckett, D. K., Bartlett, S. D., Flammia, S. T. & Brown, B. J. The XZZX surface code. Nat. Commun. 12, 2172 (2021).

31. Chamberland, C., Zhu, G., Yoder, T. J., Hertzberg, J. B. & Cross, A. W. Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits. Phys. Rev. X 10, 011022 (2020).

32. Sivak, V. V. et al. Real-time quantum error correction beyond break-even. Nature 616, 50–55 (2023).

33. Putterman, H. et al. Hardware-efficient quantum error correction via concatenated bosonic qubits. Nature 638, 927–934 (2025).

34. Campbell, E. T., Terhal, B. M. & Vuillot, C. Roads towards fault-tolerant universal quantum computation. Nature 549, 172–179 (2017).

35. Landahl, A. J., Anderson, J. T. & Rice, P. R. Fault-tolerant quantum computing with color codes. Preprint at https://arxiv.org/abs/1108.5738 (2011).

36. Bombin, H. & Martin-Delgado, M. A. Optimal resources for topological two-dimensional stabilizer codes: comparative study. Phys. Rev. A 76, 012305 (2007).

37. Steane, A. Multiple-particle interference and quantum error correction. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 452, 2551–2577 (1996).

38. Gottesman, D. The Heisenberg representation of quantum computers. Preprint at https://arxiv.org/abs/quant-ph/9807006 (1998).

39. Zhang, J., Wu, Y.-C. & Guo, G.-P. Facilitating practical fault-tolerant quantum computing based on color codes. Phys. Rev. Res. 6, 033086 (2024).

40. Lee, S.-H., Li, A. & Bartlett, S. D. Color code decoder with improved scaling for correcting circuit-level noise. Quantum 9, 1609 (2025).

41. Itogawa, T., Takada, Y., Hirano, Y. & Fujii, K.Efficient magic state distillation by zero-level distillation. PRX Quantum 6, 020356 (2025).

42. Gidney, C., Shutty, N. & Jones, C. Magic state cultivation: growing T states as cheap as CNOT gates. Preprint at https://arxiv.org/abs/2409.17595 (2024).

43. Thomsen, F., Kesselring, M. S., Bartlett, S. D. & Brown, B. J. Low-overhead quantum computing with the color code. Phys. Rev. Res. 6, 043125 (2024).

44. Takada, Y. & Fujii, K. Improving threshold for fault-tolerant color-code quantum computing by flagged weight optimization. PRX Quantum 5, 030352 (2024).

45. Baireuther, P., Caio, M. D., Criger, B., Beenakker, C. W. J. & O’Brien, T. E. Neural network decoder for topological color codes with circuit level noise. New J. Phys. 21, 013003 (2019).

46. Sahay, K. & Brown, B. J. Decoder for the triangular color code by matching on a möbius strip. PRX Quantum 3, 010310 (2022).

47. Gidney, C. & Jones, C. New circuits and an open source decoder for the color code. Preprint at https://arxiv.org/abs/2312.08813 (2023).

48. Bombin, H. An introduction to topological quantum codes. Preprint at https://arxiv.org/abs/1311.0277 (2013).

49. Edmonds, J. Paths, trees, and flowers. Can. J. Math, 17, 449–467 (1965).

50. Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. Topological quantum memory. J. Math. Phys. 43, 4452–4505 (2002).

51. Bausch, J. et al. Learning high-accuracy error decoding for quantum processors. Nature 635, 834–840 (2024).

52. Eastin, B. & Knill, E. Restrictions on transversal encoded quantum gate sets. Phys. Rev. Lett. 102, 110502 (2009).

53. Magesan, E. et al. Efficient measurement of quantum gate error by interleaved randomized benchmarking. Phys. Rev. Lett. 109, 080505 (2012).

54. Li, Y. A magic state’s fidelity can be superior to the operations that created it. New J. Phys. 17, 023037 (2015).

55. Reichardt, B. W. Quantum universality from magic states distillation applied to CSS codes. Quantum Inf. Process. 4, 251–264 (2005).

56. Landahl, A. J. & Ryan-Anderson, C. Quantum computing by color-code lattice surgery. Preprint at https://arxiv.org/abs/1407.5103 (2014).

57. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993).

58. Litinski, D. & von Oppen, F. Braiding by Majorana tracking and long-range CNOT gates with color codes. Phys. Rev. B 96, 205413 (2017).

59. Poulsen Nautrup, H., Friis, N. & Briegel, H. J. Fault-tolerant interface between quantum memories and quantum processors. Nat. Commun. 8, 1321 (2017).

60. Shutty, N. & Chamberland, C. Decoding merged color-surface codes and finding fault-tolerant Clifford circuits using solvers for satisfiability modulo theories. Phys. Rev. Appl. 18, 014072 (2022).

61. Google Quantum AI. Data for “Scaling and logic in the color code on a superconducting quantum processor” (1.0.0). Zenodo https://doi.org/10.5281/zenodo.14238944 (2024).

Acknowledgements

N.L. thanks A. Wallraff for enabling the research stay at Google Quantum AI. The Google DeepMind team thanks G. Holland, C. Beattie and T. Sargeant for their support. We thank the broader Google Quantum AI team for supporting and enabling this work.

Author information

Author notes

1. These authors contributed equally: N. Lacroix, A. Bourassa

Authors and Affiliations

1. Google Research, Mountain View, CA, USA

N. Lacroix, A. Bourassa, N. Shutty, V. Sivak, A. Bengtsson, M. McEwen, O. Higgott, D. Kafri, J. Claes, A. Morvan, Z. Chen, A. Zalcman, S. Madhuk, R. Acharya, L. Aghababaie Beni, G. Aigeldinger, R. Alcaraz, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Babbush, B. Ballard, J. C. Bardin, A. Bilmes, J. Bovaird, D. Bowers, L. Brill, M. Broughton, D. A. Browne, B. Buchea, B. B. Buckley, T. Burger, B. Burkett, N. Bushnell, A. Cabrera, J. Campero, H.-S. Chang, B. Chiaro, L.-Y. Chih, A. Y. Cleland, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, S. Das, S. Demura, L. De Lorenzo, A. Di Paolo, P. Donohoe, I. Drozdov, A. Dunsworth, A. Eickbusch, A. Moshe Elbag, M. Elzouka, C. Erickson, V. S. Ferreira, L. Flores Burgos, E. Forati, A. G. Fowler, B. Foxen, S. Ganjam, G. Garcia, R. Gasca, É. Genois, W. Giang, D. Gilboa, R. Gosula, A. Grajales Dau, D. Graumann, A. Greene, J. A. Gross, T. Ha, S. Habegger, M. Hansen, M. P. Harrigan, S. D. Harrington, S. Heslin, P. Heu, R. Hiltermann, J. Hilton, S. Hong, H.-Y. Huang, A. Huff, W. J. Huggins, E. Jeffrey, Z. Jiang, X. Jin, C. Joshi, P. Juhas, A. Kabel, H. Kang, A. H. Karamlou, K. Kechedzhi, T. Khaire, T. Khattar, M. Khezri, S. Kim, P. V. Klimov, B. Kobrin, A. N. Korotkov, F. Kostritsa, J. Mark Kreikebaum, V. D. Kurilovich, D. Landhuis, T. Lange-Dei, B. W. Langley, P. Laptev, K.-M. Lau, J. Ledford, K. Lee, B. J. Lester, L. Le Guevel, W. Yan Li, A. T. Lill, W. P. Livingston, A. Locharla, E. Lucero, D. Lundahl, A. Lunt, A. Maloney, S. Mandrà, L. S. Martin, O. Martin, C. Maxfield, J. R. McClean, S. Meeks, A. Megrant, K. C. Miao, R. Molavi, S. Molina, S. Montazeri, R. Movassagh, C. Neill, M. Newman, A. Nguyen, M. Nguyen, C.-H. Ni, M. Y. Niu, L. Oas, W. D. Oliver, R. Orosco, K. Ottosson, A. Pizzuto, R. Potter, O. Pritchard, C. Quintana, G. Ramachandran, M. J. Reagor, R. Resnick, D. M. Rhodes, G. Roberts, E. Rosenberg, E. Rosenfeld, E. Rossi, P. Roushan, K. Sankaragomathi, H. F. Schurkus, M. J. Shearn, A. Shorter, V. Shvarts, S. Small, W. Clarke Smith, S. Springer, G. Sterling, J. Suchard, A. Szasz, A. Sztein, D. Thor, E. Tomita, A. Torres, M. Mert Torunbalci, A. Vaishnav, J. Vargas, S. Vdovichev, G. Vidal, C. Vollgraff Heidweiller, S. Waltman, J. Waltz, S. X. Wang, B. Ware, T. Weidel, T. White, K. Wong, B. W. K. Woo, M. Woodson, C. Xing, Z. Jamie Yao, P. Yeh, B. Ying, J. Yoo, N. Yosri, G. Young, Y. Zhang, N. Zhu, N. Zobrist, H. Neven, S. Boixo, J. Kelly, C. Jones, C. Gidney & K. J. Satzinger

2. Department of Physics, ETH Zurich, Zurich, Switzerland

N. Lacroix

3. Google DeepMind, London, UK

F. J. H. Heras, L. M. Zhang, J. Bausch, A. W. Senior, T. Edlich, S. Blackwell, Y. Li, P. Kohli & A. Davies

4. Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA

J. C. Bardin

5. Department of Physics, University of Connecticut, Storrs, CT, USA

I. Drozdov

6. Department of Computer Science, University of California, Santa Barbara, CA, USA

M. Y. Niu

7. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

W. D. Oliver

8. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA

W. D. Oliver

9. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

W. D. Oliver

Contributions

N.L., A. Bourassa, C.G. and K.J.S. designed the experiments with input from M.M. and C. Jones. N.L. and A. Bourassa calibrated the device and performed the experiments with the support of A. Bengtsson, Z.C., M.M., A. Morvan and K.J.S. N.L. analysed the data with support from A. Bourassa. N.L., J. Bausch, F.J.H.H., L.M.Z., A. Bourassa and N.S. decoded the data with support from V. Sivak and O.H. A.Z. provided input regarding average fidelity of the teleportation channel. N.S., O.H., N.L., J. Claes and D.K. performed the numerical simulations. N.L., A. Bourassa and K.J.S. wrote the manuscript. J.K., C. Jones, C.G. and K.J.S. supervised the work. L.A.B., J. Bausch, S. Blackwell, S. Boixo, A. Bourassa, P.C., A. Davies, T.E., C.G., A.G.F., O.H., C. Jones, F.J.H.H., K.J.S., P.K., J.L., N.L., Y.L., S. Madhuk, L.S.M., M. Newman, V. Sivak, N.S., A.W.S. and A.Z. jointly developed the decoders used in this work. R. Acharya, R. Alcaraz, A.A., F.A., G.A., J.A., K.A., M.A., D.A.B., L.A.B., J.A.G., B. Ballard, J. Bausch, A. Bengtsson, A. Bilmes, S. Blackwell, S. Boixo, A. Bourassa, J. Bovaird, B. Buchea, B. Burkett, D.B., L.B., M.B., N.B., R.B., T.B., B.B.B., J. Campero, B. Chiaro, J. Claes, J. Cogan, B. Curtin, A.C., H.-S.C., L.-Y.C., P.C., R.C., W.C., Z.C., J.C.B., K.C.M., W.C.S., S. Das, A. Davies, S. Demura, A. Dunsworth, I.D., P.D., S.D.H., V.D.K., L.D.L., W.D.O., A.D.P., A.E., C.E., M.E., T.E., B.F., E.F., L.F.B., H.F.S., R. Gasca, D. Gilboa, R. Gosula, D. Graumann, A.G., C.G., G.G., S.G., W.G., É.G., A.G.D., A.G.F., S. Habegger, S. Heslin, S. Hong, A.H., H.-Y.H., J.H., M.H., O.H., P.H., R.H., T.H., A.H.K., T.I.A., C. Jones, C. Joshi, E.J., P.J., X.J., Z.J., F.J.H.H., W.J.H., B.J.L., M.J.R., K.J.S., M.J.S., Z.J.Y., T. Khaire, T. Khattar, P.K., A.K., B.K., D.K., F.K., H.K., J.K., K.K., M.K., S.K., D. Landhuis, K.L., A. Locharla, D. Lundahl, A. Lunt, K.-M.L., E.L., J.L., N.L., P.L., T.L.-D., Y.L., A.L.C., L.L.G., S. Madhuk, A. Maloney, S. Mandrà, S. Meeks, A. Megrant, R. Molavi, S. Molina, S. Montazeri, A. Morvan, A.M.E., R. Movassagh, C.M., J.M.K., L.S.M., M.M., O.M., D.M.R., M.M.T., C.N., M. Newman, M. Nguyen, C.-H. Ni, A.N., H.N., A.N.K., K.O., L.O., R.O., A.P., O.P., R.P., M.P.H., W.P.L., C.Q., G. Ramachandran, G. Roberts, E. Rosenberg, E. Rosenfeld, E. Rossi, P.R., R.R., J.R.M., A. Shorter, V. Shvarts, V. Sivak, S. Small, S. Springer, A. Szasz, A. Sztein, G.S., J.S., K.S., N.S., V.S.F., L.S.M., A.T., D.T., E.T., A.T.L., A.V., G.V., J.V., S.V., C.V.H., P.V.K., T. Weidel, T. White, B.W., J.W., K.W., M.W., S.W., B.W.K.W., B.W.L., A.W.S., C.X., S.X.W., B.Y., G.Y., J.Y., N.Y., P.Y., W.Y.L., A.Y.C., M.Y.N., N. Zhu, N. Zobrist, A.Z. and Y.Z. sponsored the project, designed and fabricated the device, built and maintained the cryogenic and control systems, provided software infrastructure, performed the initial bring-up of the device and provided relevant guidance.

Corresponding authors

Correspondence to N. Lacroix, A. Bourassa or K. J. Satzinger.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Michael Vasmer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Information, including Supplementary Figs. 1–15 and additional references.

Peer Review File

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Lacroix, N., Bourassa, A., Heras, F.J.H. et al. Scaling and logic in the colour code on a superconducting quantum processor. Nature 645, 614–619 (2025). https://doi.org/10.1038/s41586-025-09061-4

- Received: 18 December 2024

- Accepted: 23 April 2025

- Published: 26 May 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09061-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Logical quantum processor based on reconfigurable atom arrays

Article Open access 06 December 2023

Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders

Article Open access 18 May 2023

Logical-qubit operations in an error-detecting surface code

Article 16 December 2021

Experimental demonstration of logical magic state distillation

- Pedro Sales Rodriguez

- John M. Robinson

- Sergio H. Cantú

Nature Article 14 Jul 2025

Article Open access Published: 27 August 2025

Topological prethermal strong zero modes on superconducting processors

Feitong Jin,

Si Jiang,

Xuhao Zhu,

Zehang Bao,

Fanhao Shen,

Ke Wang,

Zitian Zhu,

Shibo Xu,

Zixuan Song,

Jiachen Chen,

Ziqi Tan,

Yaozu Wu,

Chuanyu Zhang,

Yu Gao,

Ning Wang,

Yiren Zou,

Aosai Zhang,

Tingting Li,

Jiarun Zhong,

Zhengyi Cui,

Yihang Han,

Yiyang He,

Han Wang,

Jia-Nan Yang,

Yanzhe Wang,

Jiayuan Shen,

Gongyu Liu,

Jinfeng Deng,

Hang Dong,

Pengfei Zhang,

Weikang Li,

Dong Yuan,

Zhide Lu,

Zheng-Zhi Sun,

Hekang Li,

Junxiang Zhang,

Chao Song,

Zhen Wang,

Qiujiang Guo,

Francisco Machado,

Jack Kemp,

Thomas Iadecola,

Norman Y. Yao,

H. Wang &

…

Dong-Ling Deng

Nature volume 645, pages 626–632 (2025)

Abstract

Symmetry-protected topological phases1,2,3,4 cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model[5]. They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations1,2,3,4,6,7,8. In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay9,10,11. Here we report the observation of a distinct type of topological edge mode12,13,14, which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach15,16,17,18 to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems.

Similar content being viewed by others

Main

Symmetry and topology are fundamental to characterizing quantum phases of matter1,2. Their interplay gives rise to a rich variety of exotic phases1,2,3,4 that cannot be described by the traditional Landau–Ginzburg symmetry-breaking model[5]. A prominent example is symmetry-protected topological (SPT) phases, which feature nonlocal order parameters and topological boundary modes that are robust against local perturbations respecting the protected symmetry1,2,3,4,6,7,8. These robust boundary modes provide an opportunity to store and process quantum information in a perturbation-resilient fashion[19]. In a clean, gapped system without disorder, these edge modes are typically restricted to the zero-temperature manifold9,10,11. At finite temperature, these edge modes would interact strongly with thermal excitations in the bulk and decohere rapidly. Realizing robust topological edge modes at finite temperatures is crucial to understanding hot SPT phases of matter and has potential applications in building a noise-resilient quantum memory[9].

A popular strategy to stabilize topological edge modes at finite temperature involves adding strong disorder so as to make the system many-body localized20,21,22. In such a scenario, bulk thermal excitations become localized, preventing them from scattering with and decohering the topological edge modes23,24,25. Despite exciting progress along this direction26,27,28, the stability of many-body localization is still under active debate29,30,31,32, which limits our understanding of the long-time behaviour of localization-based SPT phases at finite temperature. Moreover, the presence of strong disorder slows down equilibration, making it difficult to unambiguously distinguish genuine late-time dynamics from early-time transient behaviours in experiments26,27,28. An alternative strategy is to suppress the interactions between bulk excitations and edge modes by emergent symmetries, rather than localization12,13,14. In this case, the system can be disorder-free and bulk excitations remain mobile, but the additional symmetry constraints give rise to approximately conserved edge states that remain, effectively, decoupled from the bulk. These topological edge states form so-called prethermal strong zero modes, which feature nearly exponentially long coherence times even at infinite temperature12,13,14,33,34,35,36. Pioneering experiments have observed signatures of topological edge modes at up to infinite temperature in periodically driven systems with strong disorder37,38,39. Yet, the observation of long-lived finite-temperature topological edge modes protected in disorder-free systems remains a notable challenge and has evaded experiments so far.

Here we report such an observation with a newly developed high-performance 125-qubit superconducting quantum processor (Fig. 1). We select 100 neighbouring qubits arranged in a one-dimensional (1D) chain (Fig. 1a), featuring median fidelities of simultaneous single- and two-qubit gates of about 0.9995 and 0.995, respectively. This enables us to successfully implement the dynamics of a prototypical SPT Hamiltonian (Fig. 1b) in different regimes. We prepare the system in different initial states with different energies, which correspond to different effective temperatures, and then evolve it under the SPT Hamiltonian with varying parameters. We observe that, in the presence of thermal excitations, the lifetime of edge states is greatly enhanced in the dimerized regime with spatially periodically modulated couplings, in stark contrast to the fast decay in the homogeneous case. This distinction also manifests in the spatial profiles of edge modes, which become more localized as the couplings deviate from the homogeneous regime. To reveal the underlying mechanism, we measure the site-resolved dynamics of mobile excitations. Although the thermal excitations are mobile, an approximate U(1) × U(1) symmetry emerges in the dimerized case that suppresses the bulk–edge interactions. This stands in sharp contrast to the many-body localized scenario in which the interactions are suppressed because of the localization of bulk excitations (Fig. 1c). We further confirm this prethermal suppression mechanism by measuring the energy spectrum, in which an extra gap gradually opens as the chain dimerizes, explaining the origin of the emergent symmetry. Furthermore, we prepare a logical Bell state encoded within these topological edge modes and demonstrate its substantially prolonged coherence time at finite temperature in the dimerized and off-resonant regime. This shows that the edge modes have potential applications towards building a noise-resilient finite-temperature quantum memory.

Fig. 1: The 125-qubit quantum processor and the theoretical model.

a, Photograph of the superconducting quantum processor. The 100 qubits used to construct the 1D chain are highlighted with circles, with two edge qubits marked in dark blue and the other qubits in pink. The couplers actively used are highlighted with light blue lines. b, Schematic of the 1D Hamiltonian in equation (1) and its representation in the Majorana fermion picture. Three-body stabilizers \(\{{\sigma }_{i-1}^{z}{\sigma }_{i}^{x}{\sigma }_{i+1}^{z}\}\) at even and odd sites, shown as blue and orange dashed frames, can have different strengths denoted by Je and Jo, respectively. Two spin-1/2 edge modes are situated at the two ends of the chain, characterized by \({\mathop{Z}\limits^{ \sim }}_{{\rm{L}}},{\mathop{X}\limits^{ \sim }}_{{\rm{L}}}\) for the left edge and \({\mathop{Z}\limits^{ \sim }}_{{\rm{R}}},{\mathop{X}\limits^{ \sim }}_{{\rm{R}}}\) for the right edge. At finite temperatures, thermal excitations (yellow wave packets) emerge in the bulk, flipping the values of stabilizers. After the Jordan–Wigner (JW) transformation, the 1D qubit chain is mapped into two Kitaev chains, in which the upper chain inherits the even-site interaction strength Je (blue lines) and the lower chain inherits the odd-site interaction strength Jo (orange lines). Two edge modes are transformed into four Majorana fermions at the ends of two chains. Single-qubit \({\sigma }_{i}^{x}\) terms (black dashed lines) become couplings of onsite Majorana pairs, and two-qubit \({\sigma }_{i}^{x}{\sigma }_{i+1}^{x}\) interactions (grey lines) bridge the two chains. c, Schematic of thermal excitation dynamics and their interactions with edge modes. Thermal excitations (yellow wave packets) can propagate through the chain under perturbations. In the homogeneous regime (left, Jo = Je), edge–bulk interactions at the boundaries decohere and ruin the edge modes. Whereas in the (off-resonant) dimerized regime (middle, Jo ≠ Je), these interactions are markedly suppressed, resulting in long-lived robust edge modes at up to infinite temperature. In the many-body localized scenario (right), transport is forbidden and thermal excitations remain localized without influencing the boundaries. Scale bar, 10 mm (a).

SPT Hamiltonian and its implementation

We consider a 1D Hamiltonian with an even number of qubits denoted by N (Fig. 1b):

$$\begin{array}{l}H\,=\,{H}_{0}+{H}_{1},\\ {H}_{0}\,=\,{J}_{{\rm{e}}}\mathop{\sum }\limits_{i=1}^{\frac{N}{2}-1}{\sigma }_{2i-1}^{z}{\sigma }_{2i}^{x}{\sigma }_{2i+1}^{z}+{J}_{{\rm{o}}}\mathop{\sum }\limits_{i=1}^{\frac{N}{2}-1}{\sigma }_{2i}^{z}{\sigma }_{2i+1}^{x}{\sigma }_{2i+2}^{z},\\ {H}_{1}\,=\,{h}_{x}\mathop{\sum }\limits_{i=1}^{N}{\sigma }_{i}^{x}+{V}_{xx}\mathop{\sum }\limits_{i=1}^{N-1}{\sigma }_{i}^{x}{\sigma }_{i+1}^{x},\end{array}$$

(1)

where ħ is set to 1, \({\sigma }_{i}^{x,z}\) are Pauli operators acting on the ith qubit, Je denotes the strength of three-body stabilizer terms centred around even sites, Jo denotes the strength of three-body stabilizer terms centred around odd sites and hx and Vxx are parameters characterizing the transverse field and interaction strength, respectively. In the limit of hx, Vxx → 0, H = H_0 and its eigenstates are the 1D cluster stabilizer eigenstates[40]. The two manifolds at the bottom and top of the spectrum, in which the expectation values of stabilizers \(\{{\sigma }_{i-1}^{z}{\sigma }_{i}^{x}{\sigma }_{i+1}^{z}\}\) all equal to −1 or +1, both correspond to zero temperature. In our experiments, we choose the states with all stabilizers equal to +1 in the top manifold (denoted as {|Ψ_0⟩}) as the zero-temperature states. Within {|Ψ_0⟩}, the degeneracy is fourfold, hosting two nontrivial spin-1/2 topological edge modes protected by a \({{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{2}\) symmetry, where each \({{\mathbb{Z}}}_{2}\) is generated by the products of \({\sigma }_{i}^{x}\) over even or odd sites. These SPT edge modes are characterized by logical operators \({\widetilde{X}}_{{\rm{L}}}={\sigma }_{1}^{x}{\sigma }_{2}^{z},{\widetilde{Z}}_{{\rm{L}}}={\sigma }_{1}^{z}\) for the left edge and \({\widetilde{X}}_{{\rm{R}}}={\sigma }_{N-1}^{z}{\sigma }_{N}^{x},{\widetilde{Z}}_{{\rm{R}}}={\sigma }_{N}^{z}\) for the right edge (Fig. 1b and Supplementary Information section 1C). In the presence of interactions H_1, the edge modes hybridize, leading to a finite lifetime that scales exponentially with the system size N. As the temperature increases, the system approaches the centre of the spectrum, occupying more excited states in which some of the stabilizers are flipped. The interactions H_1 allow these excitations to propagate through the system, reach the boundaries and decohere the edge states, resulting in a notably shorter lifetime than the hybridization time (Supplementary Information section 1A).

We emulate many-body dynamics under the Hamiltonian in equation (1) with N = 100 superconducting qubits using first-order Trotter decomposition U(δt) = U_1(δt)U_0(δt), where \({U}_{1}(\delta t)={{\rm{e}}}^{-{\rm{i}}{H}_{1}\delta t}\) and \({U}_{0}(\delta t)={{\rm{e}}}^{-{\rm{i}}{H}_{0}\delta t}\). Implementing U(δt) is challenging because three-body interactions do not arise naturally in superconducting platforms, leading to large circuit depths. As shown in Fig. 2a, even a single time step U(δt) demands a deep circuit with six layers of two-qubit gates and three layers of single-qubit gates, corresponding to a 288-ns running time (Supplementary Information sections 2B and 2C). Therefore, the high performance of the quantum processor (Supplementary Information section 2A) is crucial for observing coherent dynamics under U before the accumulated experimental errors dominate. In our experiments, we achieve low-error quantum gates at the 100-qubit scale, with median simultaneous single- and two-qubit gate fidelities of about 0.9995 and 0.995, respectively (Extended Data Fig. 1). We set δt = 0.5, Je = π/5, hx = 0.11 and Vxx = 0.2 and tune the odd-site stabilizer strength Jo to observe distinct dynamical regimes. We note that the heating induced by Trotterization errors is suppressed within our experimental timescale because of Floquet prethermalization41,42,43 (Methods and Supplementary Information section 1B).

Fig. 2: Robust topological edge modes at up to infinite temperature.

a, Quantum circuit for implementing U(δt), which emulates a single-step evolution (288 ns) under the Hamiltonian in equation (1). The system is initialized in either the manifold {|Ψ_0⟩} (excitation number n = 0, corresponding to zero temperature), the manifold {|Ψe⟩} (n ≠ 0, finite temperature), or the product states \(| \bullet 00\ldots 0\bullet \rangle \) (effectively infinite temperature), and evolved with U(δt) for t cycles. Here, Jo, Je and hx are parameterized into the rotation angle θ around the x axis of the Bloch sphere [X(θ)]. Vxx is encoded in a combination of controlled-phase gates [CPhase(−2Vxx)] and Z phase gates [Z(Vxx)]. b, Measured time dynamics for the left edge operators in the homogeneous case (Jo = Je = π/5). Black lines show the results of echo circuits, which estimate the decay caused by circuit errors (see Supplementary Information section 2G for more data and discussions). c, Measured site-resolved dynamics of normalized expectation value \(\overline{\langle {K}_{i}\rangle }\) for bulk stabilizers \(\{{\sigma }_{i-1}^{z}{\sigma }_{i}^{x}{\sigma }_{i+1}^{z}\}\) and edge operator \({\mathop{X}\limits^{ \sim }}_{{\rm{L}}}\) in the homogeneous case (Jo = Je = π/5) near the left edge. The nearest excitations to the left edge are initialized at {Q_3, Q_5} (top) and {Q_5, Q_7} (bottom). d, Measured time dynamics of the left edge operators with fixed Je = π/5 and varying Jo. Resonant processes lead to enhanced decay rates at Jo/Je = 1 for \({\widetilde{Z}}_{{\rm{L}}}\) and Jo/Je = 1, 2 for \({\widetilde{X}}_{{\rm{L}}}\). Error bars in b and d represent the standard deviation over five rounds of measurements, with each taking 10,000 shots. The time dynamics of the right-edge operators are shown in Extended Data Fig. 3. e, Spatial profile of the prethermal strong zero mode \({\varPsi }_{{\rm{L}}}^{z}\). The solid boxes denote theoretical predictions, with black frames highlighting the positive values and red frames highlighting the negative values. The coefficients are obtained by averaging the late-time dynamics over cycles from t = 25–40, with the sum of their squares normalized to unity.

Robust edge modes at infinite temperature

We first explore the influence of bulk excitations on edge modes in the homogeneous regime (Je = Jo). We start by contrasting the experimentally measured time dependence of the edge modes when the system is initialized in the manifold {|Ψ_0⟩} versus product states \(| \bullet 00\ldots 0\bullet \rangle \) in Fig. 2b (see Methods and Extended Data Fig. 2 for initial state preparation). The latter, manifesting as an effectively infinite-temperature state with poorly protected edge modes, decays much faster. Although {|Ψ_0⟩} is not the exact zero-temperature state of the system in the presence of an interaction term H_1, it resides in the low-temperature regime, leading to limited effects of excitations on the edge modes. As such, the observed decay is attributed to external experimental imperfections, especially circuit errors. This is verified by the agreement between the dynamics of {|Ψ_0⟩} and the echo circuit \({U}_{{\rm{echo}}}(t)={({U}^{\dagger })}^{t}{U}^{t}\) (ref. [44]).

To expose the origin of faster decoherence for edge modes at finite temperatures, we introduce excitations into the bulk in a controlled way by initializing the system in the manifold {|Ψe⟩} with n = 16 excitations. Notably, we observe that |Ψe⟩ with excitations near each end can show an even faster decay of the edge modes than the product state (Fig. 2b). To illustrate the effect of excitation positions, we further probe time-dependent expectation values of bulk stabilizers \({\{{K}_{i}={\sigma }_{i-1}^{z}{\sigma }_{i}^{x}{\sigma }_{i+1}^{z}\}}_{i=2}^{N-1}\), and edge operators \(\{{K}_{1},{K}_{N}\}=\{{\widetilde{X}}_{{\rm{L}}},{\widetilde{X}}_{{\rm{R}}}\}\). We define the normalized expectation value as \(\overline{\langle {K}_{i}\rangle }=\langle {\varPsi }_{{\rm{e}}}| {K}_{i}(t)| {\varPsi }_{{\rm{e}}}\rangle /\langle {\varPsi }_{{\rm{0}}}| {K}_{i}(t)| {\varPsi }_{{\rm{0}}}\rangle \) to underscore the decay caused by excitations. In Fig. 2c, we show the measured \(\overline{\langle {K}_{i}\rangle }\) dynamics near the left edge with two different initial excitation positions and observe that the edge mode is maintained until excitations propagate to the edge, demonstrating that its rapid decay is due to the edge–bulk interactions.

In the dimerized regime (Je ≠ Jo), the edge modes show distinct behaviours (Fig. 2d). Starting with |Ψe⟩, we measure the time dependence of edge operators for Jo/Je ranging from 0.8 to 3.2. It is evident from Fig. 2d that the lifetime of the edge modes is prolonged as Jo/Je deviates from 1. Theoretically, the edge operators in the dimerized regime can be described as prethermal strong zero modes (Supplementary Information section 1D), which induce almost exact fourfold degeneracy throughout the entire spectrum, leading to enhanced resilience against thermal excitations14,35,45. Taking the left edge as an example, this zero mode, to first order in hx and Vxx, is given by[14]

$${\varPsi }_{{\rm{L}}}^{z}={\widetilde{Z}}_{{\rm{L}}}+\frac{{h}_{x}}{{J}_{{\rm{e}}}}{\sigma }_{1}^{x}{\sigma }_{2}^{x}{\sigma }_{3}^{z}-\frac{{V}_{xx}}{{J}_{{\rm{o}}}^{2}-{J}_{{\rm{e}}}^{2}}(\,{J}_{{\rm{e}}}{\sigma }_{1}^{x}{\sigma }_{3}^{z}+{J}_{{\rm{o}}}{\sigma }_{1}^{y}{\sigma }_{2}^{y}{\sigma }_{3}^{x}{\sigma }_{4}^{z}).$$

(2)

Note the divergence of the third term when Jo/Je = 1, where the edge mode has a larger overlap with bulk terms, leading to a shortened lifetime for \({\widetilde{Z}}_{{\rm{L}}}\). By measuring the late-time average of each operator in \({\varPsi }_{{\rm{L}}}^{z}\), we experimentally reconstruct[39] the corresponding coefficients and quantitatively verify the theoretical prediction. As shown in Fig. 2e, the measured bulk contribution gradually increases as Jo/Je decreases from 3.17 to 1.5, signifying that \({\varPsi }_{{\rm{L}}}^{z}\) extends into the bulk. Moreover, as Jo/Je decreases further to 0.6, the coefficients of \({\sigma }_{1}^{x}{\sigma }_{3}^{z}\) and \({\sigma }_{1}^{y}{\sigma }_{2}^{y}{\sigma }_{3}^{x}{\sigma }_{4}^{z}\) change sign, as predicted by the analytical expression in equation (2) when crossing the resonance at Jo/Je = 1. Similar divergences arise for \({\varPsi }_{{\rm{L}}}^{x}\), but with two resonant points (Jo/Je = 1, 2), corresponding to two lifetime dips (Fig. 2d) and two sign changes (Extended Data Fig. 4). This non-monotonicity in the edge mode lifetime and the divergence of coefficients illustrate the intricacy of edge–bulk interactions, providing a distinction between the dimerization mechanism and the suppression of interaction strength.

Excitation dynamics and emergent symmetry

To understand the dimerization mechanism for enhancing the lifetime of edge modes at finite temperatures, we examine site-resolved excitation dynamics and bulk–edge interactions for the whole chain. We plot the measured dynamics of \(\overline{\langle {K}_{i}\rangle }\) for Jo/Je = 1.0 (homogeneous), 2.0 (dimerized but resonant) and 3.17 (dimerized and off-resonant) in Fig. 3 (see also Extended Data Fig. 5 for the raw data). The excitation dynamics are distinct in the three cases. First, in the homogeneous case, excitations deep in the bulk propagate diffusely across even and odd sites (Fig. 3a). By contrast, in the two dimerized cases, excitations initially located at even (or odd) sites are constrained to move along sites of the same parity (Fig. 3b,c). Neighbouring excitation pairs with different parities propagate freely without interacting with each other, whereas pairs with the same parity collide. Second, excitations near the boundaries in the homogeneous case are absorbed by the edge states, whereas for the dimerized and off-resonant case (Fig. 3c), they are reflected at the boundaries without affecting the edge states (see also Extended Data Fig. 6). Third, for the dimerized but resonant case (Fig. 3b), despite similar dynamics observed near the right boundary as in the off-resonant case, the excitations interact strongly with the left edge because of the resonance (Supplementary Information section 1D).

Fig. 3: Excitation dynamics and the emergent U(1) × U(1) symmetry.

a–c, Measured site-resolved dynamics of normalized expectation value \(\overline{\langle {K}_{i}\rangle }\) for the homogeneous (Jo = Je = π/5) (a), the dimerized but resonant (Jo = 2Je = 2π/5) (b) and the dimerized and off-resonant (Jo = 3.17Je = 3.17π/5) (c) cases. For \(\overline{\langle {K}_{i}\rangle }\) at odd (even) sites, colour bars are chosen to be red (blue) for a better visualization of the excitation dynamics. d–f, Measured time dynamics of the total excitation number n, and of the excitation number at even (ne) and odd (no) sites, which are extracted from a to c. In the homogeneous case (d), the values of ne and no gradually converge, yet their sum remains approximately constant, reflecting the U(1) symmetry on the total excitation number n in the bulk. In the dimerized but resonant case (e), the exchange of excitations between two Kitaev chains, which happens near the left edge, can be observed through the decrease of no and increase of ne. By contrast, in the dimerized and off-resonant case (f), ne and no are conserved independently, indicating an emergent U(1) × U(1) symmetry. The grey dashed lines represent the initial values of no = 6, ne = 10, n = 16 and ne + 2no = 22 in e. Error bars represent the standard deviation over five rounds of measurements, with each taking 20,000 shots.

The distinct behaviours of the three cases above can be better understood in the Majorana fermion picture (Fig. 1b and Methods). Through Jordan–Wigner transformation, the cluster Hamiltonian H_0 is transformed into two Kitaev chains composed of Majorana fermions on even and odd sites, respectively. The stabilizers centred at even sites are mapped to inter-site coupling terms with strength Je in the upper chain, and odd sites are mapped to inter-site coupling terms with strength Jo in the lower chain. The edge mode is mapped to two Majorana fermions at the end of each Kitaev chain, and the single- and two-body terms in H_1 are mapped to onsite and inter-chain coupling terms. With Jo = Je, the two Kitaev chains share the same coupling strength and can exchange excitations resonantly through Vxx terms both in the bulk and at the boundaries, in which the latter couple to the edge Majorana fermions and lead to the decay of the edge modes. In the small-perturbation regime (hx, Vxx ≪ Jo, Je), the system exhibits long-lived prethermal behaviour with an approximate U(1) symmetry of the total excitation number n in the bulk. However, despite the conserved n, the number of bulk excitations on even sites ne and odd sites no rapidly equilibrate in the homogeneous case (Fig. 3d), showing the effect of the resonant inter-chain interactions. Dimerizing the coupling strengths makes the excitation exchange in the bulk off-resonant, but resonances can still arise at the boundaries for certain values of Jo/Je. For example, when Jo/Je = 2.0, the exchange of one excitation in the lower chain and two excitations in the upper chain through the \({\sigma }_{2}^{x}{\sigma }_{3}^{x}\) term in H_1 becomes resonant. This results in the observed rapid decay of \({\widetilde{X}}_{{\rm{L}}}\), and all ne, no and n are no longer conserved (Fig. 3e). This resonance can be eliminated by choosing Jo and Je to be incommensurable. Consequently, the excitation exchanges become off-resonant both in the bulk and at the boundaries, leading to two Kitaev chains effectively decoupled and exhibiting two separate approximate U(1) conservation laws for ne and no (Fig. 3f). This U(1) × U(1) symmetry emerges in the prethermal regime in which Je, Jo ≫ hx, Vxx and Jo/Je is off-resonant, which is also confirmed in our numerical simulations with matrix product states (Supplementary Information section 1H). The lifetime of this regime scales exponentially with the ratio of the energy scale of H_0 to that of the perturbation H_1 (Supplementary Information section 1E). Up to this timescale, the U(1) × U(1) symmetry, combined with the inherent \({{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{2}\) symmetry of the system, gives rise to robust edge modes persisting up to infinite temperature.

Energy spectrum

Recent theoretical progress suggests that prethermalization is a generic phenomenon in gapped local many-body systems, in which quantum dynamics is restricted to each symmetry sector protected by the energy gaps[46]. This prediction also applies to our experiments, as the emergent U(1) × U(1) symmetry and the robust edge modes are manifestations of energy gaps in the spectrum. Using the energy spectroscopy technique39,47, we measure the spectrum of smaller SPT chains in the integrable limit (Vxx = 0) on another processor[48] in parallel, which has a similar design but better coherence performance. To enhance the experimental visibility of the energy spectrum, we measure the time-domain dynamics of a set of operators \({O}_{{\rm{L}},i}=({\prod }_{k=1}^{2i}{\sigma }_{k}^{x}){\sigma }_{2i+1}^{z},{O}_{{\rm{R}},i}=({\prod }_{k=1}^{2i}{\sigma }_{2N+1-k}^{x}){\sigma }_{2(N-i)}^{z}\) and average their spectra after Fourier transformation, which enables a faithful detection of energy gaps in our experiments for system sizes up to N = 16 qubits (Supplementary Information sections 1G and 2D).

For the 16-qubit chain, we measure the dynamics of OL/R,i(t) up to i = 3, where OL/R,3 are 7-body operators (Supplementary Fig. 5). The averaged frequency-domain signals are shown in Fig. 4a. The results provide substantial information to understand the origin of the emergent symmetries. First, as the two Kitaev chains are decoupled at Vxx = 0, \(\overline{{O}_{{\rm{L}}}(\omega )}\) gives access to the spectrum for the upper chain and \(\overline{{O}_{{\rm{R}}}(\omega )}\) gives access to the spectrum for the lower chain. The peaks correspond to Bogoliubov fermionic modes in each chain, in which peaks near ω = 0 are attributed to the edge modes, and the remaining peaks characterize the bulk excitation modes. In our finite-sized system, the edge modes are hybridized by gaps ζ induced by the \({h}_{x}{\sigma }_{i}^{x}\) terms in H_1. As we increase Jo, thereby decreasing the correlation length in the lower Kitaev chain (Fig. 1b), one such gap ζo in \(\overline{{O}_{{\rm{R}}}(\omega )}\) closes. Furthermore, in Extended Data Fig. 7, we observe that ζe, ζo gradually close as the system size increases. Second, we observe gaps Δo ∝ Jo (Δe ∝ Je) separating the edge mode from the bulk excitation modes, impeding transitions between edge and bulk caused by onsite interactions. When the two chains are decoupled, Δe, Δo give rise to an approximate U(1) symmetry in each chain. However, these U(1) symmetries can be destroyed when inter-chain interactions are present. In the full spectrum of the entire system (Fig. 4b) obtained from combining \(\overline{{O}_{{\rm{L}}}(\omega )}\) and \(\overline{{O}_{{\rm{R}}}(\omega )}\), we observe that the bulk energy spectra of the two Kitaev chains become exactly equal when Jo/Je = 1. This explains the strongly resonant excitation exchange process observed in the homogeneous case. When the system is dimerized (Jo ≠ Je), an extra gap δ ∝ |Je − Jo| appears, signifying the energy required to exchange one pair of excitations between the chains. This gap bolsters the emergent U(1) × U(1) symmetry and suppresses the excitation exchange process at boundaries, resulting in robust long-lived edge modes up to infinite temperature. Notably, we find that these gaps, Δe, Δo and δ, persist as the system size increases (Extended Data Fig. 7).

Fig. 4: Spectroscopy of energy spectrum.

a, Averaged Fourier transforms of \({\mathop{Z}\limits^{ \sim }}_{{\rm{L}}}\) and bulk terms OL,1, OL,2, OL,3 dynamics as a function of ω and Jo/Je, revealing the spectrum of the upper Kitaev chain in Fig. 1b (top). Similar Fourier results on the right, revealing the spectrum of the lower Kitaev chain (bottom). The gap ζo indicates the hybridization between edge modes. The gaps Δo and Δe separate the edge modes from the bulk excitation mode. b, The complete spectrum obtained from combining \(\overline{{O}_{{\rm{L}}}(\omega )}\) and \(\overline{{O}_{{\rm{R}}}(\omega )}\), where δ represents the gap between the bulk modes on different Kitaev chains. The results are obtained from a chain with N = 16 qubits.

Protection of logical Bell state

The long-lived topological edge modes observed in experiments offer a potential application to store quantum information at finite temperatures. Compared with physical qubits, our approach protects the edge modes from local, symmetry-preserving noises (Supplementary Information section 2F). These edge modes also contrast with the Ising chains, in which a classical bit might be preserved by edge spin polarization35,39. To this end, we prepare a logical Bell state encoded by these edge states and show its robustness to thermal excitations. Owing to the geometrically adjacent two edges on the processor (Fig. 1a, blue circles), we can initialize the system with edge modes being a logical Bell state \({| \mathop{0}\limits^{ \sim }\rangle }_{{\rm{L}}}{| \mathop{0}\limits^{ \sim }\rangle }_{{\rm{R}}}+{\rm{i}}{| \widetilde{1}\rangle }_{{\rm{L}}}{| \widetilde{1}\rangle }_{{\rm{R}}}\) by local two-qubit gates (see Extended Data Fig. 8 for the details of the preparation circuit and logical Bell state fidelity).

The solid lines in Fig. 5a show the measured fidelity dynamics of the logical Bell state for initial states being within {|Ψe⟩} with Jo/Je = 1.0, 2.0 and 3.17, respectively. As expected, the fidelity in the homogeneous scenario decays the most rapidly to the lower bound of 0.25, followed by the dimerized but resonant system. The lifetime of the logical Bell state in the dimerized and off-resonant system is largely prolonged, almost reaching that of the zero-temperature case (dashed line). Furthermore, we carry out state tomography (Supplementary Information section 2E) on the logical space of each system after a time evolution of t = 10. As shown in Fig. 5b, the logical Bell state in the homogeneous case is completely decohered, corresponding to an identity matrix of a maximally mixed state. In the dimerized but resonant case, it also exhibits rapid decoherence with vanishing off-diagonal terms. By contrast, it is largely preserved for the dimerized and off-resonant case, showing notable robustness against thermal excitations at finite temperature.

Fig. 5: Fidelity dynamics of the logical Bell state at finite temperature.

a, Measured fidelity dynamics of logical Bell state in the homogeneous (Jo = Je = π/5), the dimerized but resonant (Jo = 2Je = 2π/5), and the dimerized and off-resonant (Jo = 3.17Je = 3.17π/5) cases. The data shown in the solid lines are obtained with initial states being within {|Ψe⟩} and the dashed lines are obtained with initial states being within {|Ψ_0⟩}. The initial state preparation circuit is shown in Extended Data Fig. 8a. Error bars represent the standard deviation over five rounds of measurements, with each round taking 10,000 shots for each operator. b, Measured density matrices (green bars) of logical Bell state after a time evolution of t = 10 in the three different cases with initial states being within {|Ψe⟩}. The ideal Bell state density matrix is shown with the hollow frame.

Discussion

The robust edge modes observed in our experiments are attributed to emergent symmetries within the prethermal regime, thereby eliminating the necessity for strong disorder. We established that these symmetries arise from distinct gaps in the energy spectrum, a common phenomenon in quantum many-body systems. This dimerization-induced prethermalization mechanism is neither restricted to 1D systems nor SPT phases. Recent works predict the robust storage of quantum information at finite temperatures using boundary modes at interfaces between distinct phases[49], nonlocal operators in toric codes[12] and 2D subsystem codes[50], and local corner modes in higher-order SPT phases[51]. The quantum processor developed in this work would also be exploited in these scenarios. In particular, it would be interesting and important to implement boundary modes at phase interfaces and corner modes in higher dimensions. Our work opens new possibilities for quantum information storage resilient to thermal excitations on noisy intermediate-scale quantum devices. Furthermore, it has been shown that periodically and quasi-periodically driven systems possess additional dynamical symmetries, which can supplement or even replace the intrinsic symmetries of the Hamiltonian38,52,53. It could be possible to extend our study to realize new dynamical SPT phases that possess edge modes resilient against both perturbations and thermal excitations, without relying on any intrinsic symmetry or localization.

Methods

Experimental setup

Our experiments are performed on a 2D flip-chip superconducting quantum processor, which possesses 125 frequency-tunable transmon qubits[54] and 218 tunable couplers[55] between the adjacent qubits (Fig. 1a). In our experiments, we actively use 100 qubits and 100 couplers of them to simulate the many-body dynamics of 1D disorder-free cluster Hamiltonian H in equation (1). Each time step of its evolution unitary U(δt) is decomposed into combinations of single-qubit rotations and two-qubit gates. For each qubit, a single-qubit rotation is implemented by applying a microwave pulse or a fast flux pulse, which are combined by a combiner at room temperature and then transmitted to the qubit at low temperature (20 mK) to rotate the qubit state along longitudinal or latitudinal lines of the Bloch sphere. Two-qubit interaction between the nearest-neighbour two qubits can be dynamically controlled by applying a fast flux pulse to the corresponding coupler, which also enables the implementation of high-fidelity two-qubit controlled-phase (CPhase) gates[56]. Each qubit is capacitively coupled to a readout resonator for dispersive readout, which is designed at a frequency of around 6.4 GHz. The processor is integrated into a printed circuit board package using the wire bonding technique. This package is further protected by magnetic shields before being mounted on the mixing chamber plate of a dilution refrigerator. See Supplementary Fig. 7 for the wiring information of the dilution refrigerator and room-temperature control electronics.

Initial state preparation

In our experiments, the system is initialized to the manifold {|Ψ_0⟩} with no excitation, the manifold {|Ψe⟩} with 16 excitations, or the product states \(| \bullet 00\ldots 0\bullet \rangle \), each with a predetermined bulk state and varying edge modes. To measure the temporal dependence of the logical operators \(\widetilde{Z}\) and \(\widetilde{X}\), we prepare the edge modes into their eigenstates, which are denoted as \(| \widetilde{0}\rangle ,| \widetilde{1}\rangle \) for \(\widetilde{Z}\), and \(| \widetilde{+}\rangle ,| \widetilde{-}\rangle \) for \(\widetilde{X}\). For the zero-temperature case, these states are defined as

$${| \widetilde{0}\rangle }_{{\rm{L}}}{| \widetilde{0}\rangle }_{{\rm{R}}}=\mathop{\prod }\limits_{i=1}^{99}{{\rm{C}}Z}_{i,i+1}\,[{| 0\rangle }_{1}\,(\underset{i=2}{\overset{99}{\bigotimes }}{| +\rangle }_{i}){| 0\rangle }_{100}],$$

(3)

$${| \widetilde{+}\rangle }_{{\rm{L}}}{| \widetilde{+}\rangle }_{{\rm{R}}}=\mathop{\prod }\limits_{i=1}^{99}{{\rm{C}}Z}_{i,i+1}\,(\underset{i=1}{\overset{100}{\bigotimes }}{| +\rangle }_{i}),$$

(4)

and the circuits for preparing these states are shown in Extended Data Fig. 2a,b. For {|Ψe⟩}, excitations are induced into the bulk by applying Xi(π) (Zi(π) in Extended Data Fig. 6) gates on the qubit i. For the product-state case, we prepare the \(| 000\ldots 00\rangle \) state for measuring \(\{{\mathop{Z}\limits^{ \sim }}_{{\rm{L}}},{\mathop{Z}\limits^{ \sim }}_{{\rm{R}}}\}\) and the \(| +00\ldots 0+\rangle \) state for measuring \(\{{\mathop{X}\limits^{ \sim }}_{{\rm{L}}},{\mathop{X}\limits^{ \sim }}_{{\rm{R}}}\}\).

The preparation for the logical Bell state \({| \mathop{0}\limits^{ \sim }\rangle }_{{\rm{L}}}{| \mathop{0}\limits^{ \sim }\rangle }_{{\rm{R}}}+{\rm{i}}{| \widetilde{1}\rangle }_{{\rm{L}}}{| \widetilde{1}\rangle }_{{\rm{R}}}\) is more involved. This is done by first applying a logical \(\widetilde{X}(-{\rm{\pi }}/2)\) rotation on \({| \widetilde{0}\rangle }_{{\rm{L}}}{| \widetilde{0}\rangle }_{{\rm{R}}}\), and then a combination of two-qubit gates and single-qubit gates on two edge modes to effectively implement the logical controlled-NOT gate. The total circuit for preparing the logical Bell state is shown in Extended Data Fig. 8a.

Characterization of Trotter errors

Quantum simulation of continuous-time many-body dynamics with a discretized evolution circuit U is prone to an accumulation of Trotter errors, which tends to heat the system to infinite temperature. However, with a small Trotter step, the heating is suppressed by the Floquet prethermalization, leading to an exponentially long heating time t*. For t < t*, the stroboscopic dynamics of system are governed by an effective Hamiltonian HF, defined by \(\exp (-{\rm{i}}{H}_{{\rm{F}}}T)\equiv U\). Although HF, in general, is difficult to analyse, it can be constructed order by order by the Floquet–Magnus expansion57,58, in which the lower-order terms are sufficient to describe the short-term evolution on current noisy intermediate-scale quantum devices. The zeroth-order term gives H_0 + H_1, and the first-order terms present many other many-body terms (Supplementary Information section 1B). Hence, these additional terms can be considered as extra interactions and make the edge–bulk interaction in our model more general.

Transformation to Majorana fermions

The spin Hamiltonian H = H_0 + H_1 can be transformed into two Kitaev chains of Majorana fermions. This is done by first applying the Jordan–Wigner transformation, which maps Pauli spin operators into fermionic creation and annihilation operators, and then transforming the latter into Majorana operators αi, βi (Supplementary Information section 1F). The total transformation reads

$${\sigma }_{i}^{x}=-\,{\rm{i}}{\alpha }_{i}{\beta }_{i},\quad {\sigma }_{i}^{z}=-\left[\mathop{\prod }\limits_{j=1}^{i-1}(-{\rm{i}}{\alpha }_{j}{\beta }_{j})\right]{\alpha }_{i}.$$

(5)

Besides \({\sigma }_{i}^{x}\), the three-body stabilizers and two-body interactions in H are mapped into the following forms:

$${\sigma }_{i-1}^{z}{\sigma }_{i}^{x}{\sigma }_{i+1}^{z}=-\,{\rm{i}}{\beta }_{i-1}{\alpha }_{i+1},{\sigma }_{i}^{x}{\sigma }_{i+1}^{x}=-\,{\alpha }_{i}\,{\beta }_{i}{\alpha }_{i+1}\,{\beta }_{i+1}.$$

(6)

Notably, the three-body stabilizers at even sites are mapped into coupling terms involving Majorana operators only at odd sites and those at odd sites are mapped into coupling terms involving Majorana operators only at even sites, giving rise to two Kitaev chains. Moreover, the logical operators for edge modes become

$${\widetilde{Z}}_{{\rm{L}}}=-\,{\alpha }_{1},{\widetilde{X}}_{{\rm{L}}}=-\,{\alpha }_{2},{\widetilde{Z}}_{{\rm{R}}}=-\,{\rm{i}}G{\beta }_{N},{\widetilde{X}}_{{\rm{R}}}=-\,{\rm{i}}G{\beta }_{N-1},$$

(7)

where \(G={\prod }_{j=1}^{N}(-{\rm{i}}{\alpha }_{j}{\beta }_{j})={\prod }_{j=1}^{N}{\sigma }_{i}^{x}\), is the generator for the total \({{\mathbb{Z}}}_{2}\) symmetry. As H preserves the \({{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{2}\) symmetry generated by \({\prod }_{i=1}^{\frac{N}{2}}{\sigma }_{2i}^{x}\) and \({\prod }_{i=1}^{\frac{N}{2}}{\sigma }_{2i-1}^{x},G\) is also preserved during the evolution. Therefore, the logical operators \({\widetilde{Z}}_{{\rm{L}}},{\widetilde{X}}_{{\rm{L}}},{\widetilde{Z}}_{{\rm{R}}}\), and \({\widetilde{X}}_{{\rm{R}}}\) are determined by Majorana edge modes α_1, α_2, βN−1, and βN, respectively.

Data availability

The data that support the findings in this study are available on Code Ocean[59].

Code availability

The code used in this study is available on Code Ocean[59].

References

1. Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P. & Ryu, S. Classification of topological quantum matter with symmetries. Rev. Mod. Phys. 88, 035005 (2016).

2. Wen, X.-G. Colloquium: zoo of quantum-topological phases of matter. Rev. Mod. Phys. 89, 041004 (2017).

3. Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604–1606 (2012).

4. Senthil, T. Symmetry-protected topological phases of quantum matter. Annu. Rev. Condens. Matter Phys. 6, 299–324 (2015).

5. Landau, L. D. & Lifshitz, E. M. Statistical Physics 3rd edn, Vol. 5 (Elsevier, 2013).

6. Pollmann, F., Berg, E., Turner, A. M. & Oshikawa, M. Symmetry protection of topological phases in one-dimensional quantum spin systems. Phys. Rev. B 85, 075125 (2012).

7. Fidkowski, L. & Kitaev, A. Topological phases of fermions in one dimension. Phys. Rev. B 83, 075103 (2011).

8. Ma, R. & Wang, C. Average symmetry-protected topological phases. Phys. Rev. X 13, 031016 (2023).

9. Brown, B. J., Loss, D., Pachos, J. K., Self, C. N. & Wootton, J. R. Quantum memories at finite temperature. Rev. Mod. Phys. 88, 045005 (2016).

10. Hastings, M. B. Topological order at nonzero temperature. Phys. Rev. Lett. 107, 210501 (2011).

11. Roberts, S., Yoshida, B., Kubica, A. & Bartlett, S. D. Symmetry-protected topological order at nonzero temperature. Phys. Rev. A 96, 022306 (2017).

12. Else, D. V., Fendley, P., Kemp, J. & Nayak, C. Prethermal strong zero modes and topological qubits. Phys. Rev. X 7, 041062 (2017).

13. Parker, D. E., Vasseur, R. & Scaffidi, T. Topologically protected long edge coherence times in symmetry-broken phases. Phys. Rev. Lett. 122, 240605 (2019).

14. Kemp, J., Yao, N. Y. & Laumann, C. R. Symmetry-enhanced boundary qubits at infinite temperature. Phys. Rev. Lett. 125, 200506 (2020).

15. Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

16. Tacchino, F., Chiesa, A., Carretta, S. & Gerace, D. Quantum computers as universal quantum simulators: state-of-the-art and perspectives. Adv. Quantum Technol. 3, 1900052 (2020).

17. Daley, A. J. et al. Practical quantum advantage in quantum simulation. Nature 607, 667–676 (2022).

18. Fauseweh, B. Quantum many-body simulations on digital quantum computers: state-of-the-art and future challenges. Nat. Commun. 15, 2123 (2024).

19. Bravyi, S., Hastings, M. B. & Michalakis, S. Topological quantum order: stability under local perturbations. J. Math. Phys. 51, 093512 (2010).

20. Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015).

21. Kjäll, J. A., Bardarson, J. H. & Pollmann, F. Many-body localization in a disordered quantum Ising chain. Phys. Rev. Lett. 113, 107204 (2014).

22. Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).

23. Huse, D. A., Nandkishore, R., Oganesyan, V., Pal, A. & Sondhi, S. L. Localization-protected quantum order. Phys. Rev. B 88, 014206 (2013).

24. Chandran, A., Khemani, V., Laumann, C. R. & Sondhi, S. L. Many-body localization and symmetry-protected topological order. Phys. Rev. B 89, 144201 (2014).

25. Bahri, Y., Vosk, R., Altman, E. & Vishwanath, A. Localization and topology protected quantum coherence at the edge of hot matter. Nat. Commun. 6, 7341 (2015).

26. Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).

27. Choi, J.-Y. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016).

28. Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016).

29. Morningstar, A., Colmenarez, L., Khemani, V., Luitz, D. J. & Huse, D. A. Avalanches and many-body resonances in many-body localized systems. Phys. Rev. B 105, 174205 (2022).

30. Ha, H., Morningstar, A. & Huse, D. A. Many-body resonances in the avalanche instability of many-body localization. Phys. Rev. Lett. 130, 250405 (2023).

31. Long, D. M., Crowley, P. J. D., Khemani, V. & Chandran, A. Phenomenology of the prethermal many-body localized regime. Phys. Rev. Lett. 131, 106301 (2023).

32. Léonard, J. et al. Probing the onset of quantum avalanches in a many-body localized system. Nat. Phys. 19, 481–485 (2023).

33. Fendley, P. Parafermionic edge zero modes in Zn-invariant spin chains. J. Stat. Mech. 2012, P11020 (2012).

34. Fendley, P. Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain. J. Phys. A Math. Theor. 49, 30LT01 (2016).

35. Kemp, J., Yao, N. Y., Laumann, C. R. & Fendley, P. Long coherence times for edge spins. J. Stat. Mech. 2017, 063105 (2017).

36. Yates, D. J., Abanov, A. G. & Mitra, A. Dynamics of almost strong edge modes in spin chains away from integrability. Phys. Rev. B 102, 195419 (2020).

37. Zhang, X. et al. Digital quantum simulation of Floquet symmetry-protected topological phases. Nature 607, 468–473 (2022).

38. Dumitrescu, P. T. et al. Dynamical topological phase realized in a trapped-ion quantum simulator. Nature 607, 463–467 (2022).

39. Mi, X. et al. Noise-resilient edge modes on a chain of superconducting qubits. Science 378, 785–790 (2022).

40. Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001).

41. Abanin, D. A., De Roeck, W. & Huveneers, F. Exponentially slow heating in periodically driven many-body systems. Phys. Rev. Lett. 115, 256803 (2015).

42. Mori, T., Kuwahara, T. & Saito, K. Rigorous bound on energy absorption and generic relaxation in periodically driven quantum systems. Phys. Rev. Lett. 116, 120401 (2016).

43. Abanin, D., De Roeck, W., Ho, W. W. & Huveneers, F. A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems. Commun. Math. Phys. 354, 809–827 (2017).

44. Mi, X. et al. Time-crystalline eigenstate order on a quantum processor. Nature 601, 531–536 (2022).

45. Else, D. V., Bauer, B. & Nayak, C. Prethermal phases of matter protected by time-translation symmetry. Phys. Rev. X 7, 011026 (2017).

46. Yin, C. & Lucas, A. Prethermalization and the local robustness of gapped systems. Phys. Rev. Lett. 131, 050402 (2023).

47. Roushan, P. et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017).

48. Xu, S. et al. Digital simulation of projective non-Abelian anyons with 68 superconducting qubits. Chin. Phys. Lett. 40, 060301 (2023).

49. Olund, C. T., Yao, N. Y. & Kemp, J. Boundary strong zero modes. Phys. Rev. B 111, L201114 (2025).

50. Wildeboer, J., Iadecola, T. & Williamson, D. J. Symmetry-protected infinite-temperature quantum memory from subsystem codes. PRX Quantum 3, 020330 (2022).

51. Jiang, S., Yuan, D., Jiang, W., Deng, D.-L. & Machado, F. Prethermal time-crystalline corner modes. Phys. Rev. Lett. https://doi.org/10.1103/np9w-jsf9 (2025).

52. Else, D. V., Ho, W. W. & Dumitrescu, P. T. Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically driven systems. Phys. Rev. X 10, 021032 (2020).

53. Friedman, A. J., Ware, B., Vasseur, R. & Potter, A. C. Topological edge modes without symmetry in quasiperiodically driven spin chains. Phys. Rev. B 105, 115117 (2022).

54. Koch, J. et al. Charge-insensitive qubit design derived from the cooper pair box. Phys. Rev. A 76, 042319 (2007).

55. Yan, F. et al. Tunable coupling scheme for implementing high-fidelity two-qubit gates. Phys. Rev. Appl. 10, 054062 (2018).

56. Foxen, B. et al. Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms. Phys. Rev. Lett. 125, 120504 (2020).

57. Magnus, W. On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math. 7, 649–673 (1954).

58. Blanes, S., Casas, F., Oteo, J. A. & Ros, J. The magnus expansion and some of its applications. Phys. Rep. 470, 151–238 (2009).

59. Jin, F. et al. Topological prethermal strong zero modes on superconducting processors. Code Ocean https://codeocean.com/capsule/8397511/tree (2025).

Acknowledgements

We thank A. Gorshkov, F. L. Liu and Z. X. Gong for discussions. The device was fabricated at the Micro-Nano Fabrication Center of Zhejiang University. The electronics for controlling the superconducting quantum processors were developed by Hangzhou Logical Qubit Technology. We acknowledge the support from the National Natural Science Foundation of China (grant nos. T2225008, 92365301, 12274368, 12274367, 12174342, 12322414, 12404570, 12404574, U20A2076, 12075128 and 123B2072), the Innovation Program for Quantum Science and Technology (grant nos. 2021ZD0300200 and 2021ZD0302203), the Zhejiang Provincial Natural Science Foundation of China (grant nos. LR24A040002 and LDQ23A040001) and the National Key Research and Development Program of China (grant no. 2023YFB4502600). H. Wang is also supported by the New Cornerstone Science Foundation through the XPLORER PRIZE. T.I. acknowledges support from the National Science Foundation (grant no. DMR-2143635). F.M. acknowledges support from the NSF through a grant for ITAMP (award no. 2116679) at Harvard University. J.K. acknowledges support from the Army Research Office (grant no. W911NF-24-1-0079) and from EPSRC (grant no. EP/V062654/1). N.Y.Y. acknowledges support from the US Department of Energy by the QuantISED 2.0 program and from a Simons Investigator award. S.J., W.L., Z.L., Z.-Z.S. and D.-L.D. acknowledge in addition support from the Tsinghua University Dushi Program and the Shanghai Qi Zhi Institute Innovation Program SQZ202318.

Author information

Author notes

1. These authors contributed equally: Feitong Jin, Si Jiang, Xuhao Zhu

Authors and Affiliations

1. School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Zhejiang University, Hangzhou, China

Feitong Jin, Xuhao Zhu, Zehang Bao, Fanhao Shen, Ke Wang, Zitian Zhu, Shibo Xu, Zixuan Song, Jiachen Chen, Ziqi Tan, Yaozu Wu, Chuanyu Zhang, Yu Gao, Ning Wang, Yiren Zou, Aosai Zhang, Tingting Li, Jiarun Zhong, Zhengyi Cui, Yihang Han, Yiyang He, Han Wang, Jia-Nan Yang, Yanzhe Wang, Jiayuan Shen, Gongyu Liu, Jinfeng Deng, Hang Dong, Pengfei Zhang, Hekang Li, Junxiang Zhang, Chao Song, Zhen Wang, Qiujiang Guo & H. Wang

2. Center for Quantum Information, IIIS, Tsinghua University, Beijing, China

Si Jiang, Weikang Li, Dong Yuan, Zheng-Zhi Sun & Dong-Ling Deng

3. Shanghai Qi Zhi Institute, Shanghai, China

Si Jiang, Zhide Lu & Dong-Ling Deng

4. Instituut-Lorentz, Universiteit Leiden, Leiden, The Netherlands

Weikang Li

5. Hefei National Laboratory, Hefei, China

Zheng-Zhi Sun, Zhen Wang, Qiujiang Guo, H. Wang & Dong-Ling Deng

6. ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA

Francisco Machado

7. Department of Physics, Harvard University, Cambridge, MA, USA

Francisco Machado, Jack Kemp & Norman Y. Yao

8. TCM Group, Cavendish Laboratory, Ray Dolby Centre, University of Cambridge, Cambridge, UK

Jack Kemp

9. Department of Physics and Astronomy, Iowa State University, Ames, IA, USA

Thomas Iadecola

10. Ames National Laboratory, Ames, IA, USA

Thomas Iadecola

Contributions

F.J., X.Z. and Z.B. carried out the experiments and analysed the experimental data under the supervision of Q.G. and H. Wang; S.J., J.K., N.Y.Y., T.I., F.M., W.L., Z.L., Z.-Z.S., D.Y. and D.-L.D. conducted the theoretical analysis; H.L. and J.C. fabricated the device supervised by H. Wang; D.-L.D., Q.G., S.J., F.J., X.Z., H. Wang, J.K., N.Y.Y., T.I. and F.M. co-wrote the paper; H. Wang, Q.G., Z.W., C.S, J. Zhang, F.J., X.Z., Z.B., F.S., K.W., Z.Z., S.X., Z.S., J.C., Z.T., Y. Wu, C.Z., Y.G., N.W., Y.Z., A.Z., T.L., J. Zhong, Z.C., Y. Han, Y. He, Han Wang, J.-N.Y., Y. Wang, J.S., G.L., J.D., H.D. and P.Z. contributed to the experimental setup. All authors contributed to the discussion of the results.

Corresponding authors

Correspondence to Qiujiang Guo, H. Wang or Dong-Ling Deng.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Xiao Mi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Pauli errors of single-qubit and two-qubit gates.

Gate errors are benchmarked with simultaneous cross-entropy benchmarking (XEB). Errors of single-qubit gates (blue circles) are obtained by running single-qubit XEB sequences for all 100 qubits simultaneously, while errors of two-qubit gates [red bars, including CZ and CPhase (−0.4)] are averaged over the two-qubit layers used in our experiments. For each two-qubit layer, we run two-qubit XEB sequences simultaneously for all the two-qubit gates in this layer. The maximum number of parallel two-qubit gates in our experiments is 50. The inset shows the cumulative distribution of gate errors, with the dashed lines indicating the median values.

Extended Data Fig. 2 Initial state preparation.

a, Quantum circuit for preparing the initial cluster state for measuring \(\langle \mathop{Z}\limits^{ \sim }(t)\rangle \) in Fig. 2b,d and Extended Data Fig. 3a,c. The first three layers, including one layer of Hadamard gates and two layers of CZ gates, prepare the zero-temperature state in \(\{| {\Psi }_{0}\rangle \}\) with all stabilizers and \({\widetilde{Z}}_{{\rm{L}}},{\widetilde{Z}}_{{\rm{R}}}\) taking values +1. The last layer applies single-qubit π rotations around the x-axis of the Bloch sphere [X(π) gates] on the bulk qubits, each flipping two stabilizers and hence inducing two bulk excitations. The initial states in the manifold \(\{| {\Psi }_{{\rm{e}}}\rangle \}\) are obtained from applying the X(π) gates on qubits {Q_4, Q_19, Q_34, Q_39, Q_63, Q_69, Q_82, Q_97}, which induces 16 excitations in the bulk. In the bottom panel of Fig. 2c and Extended Data Fig. 3b, the X(π) gates are applied to {Q_6, Q_19, Q_34, Q_39, Q_63, Q_69, Q_82, Q_95} to observe the effect of varying excitation positions on the edge modes. b, Quantum circuit for preparing the initial state for measuring \(\langle \mathop{X}\limits^{ \sim }(t)\rangle \) in Fig. 2, Fig. 3 and Extended Data Fig. 3, with \({\widetilde{X}}_{{\rm{L}}},{\widetilde{X}}_{{\rm{R}}}\) taking values + 1. c, Expectation values of the stabilizers Ki (\({\sigma }_{i-1}^{z}{\sigma }_{i}^{x}{\sigma }_{i+1}^{z}\) in the bulk and \({\mathop{X}\limits^{ \sim }}_{{\rm{L}}},{\mathop{X}\limits^{ \sim }}_{{\rm{R}}}\) at the edges) for initial states in \(\{| {\Psi }_{0}\rangle \}\) (top panel) and in \(\{| {\Psi }_{{\rm{e}}}\rangle \}\) (bottom panel). The data are extracted from Extended Data Fig. 5 at t = 0. Error bars represent the standard deviation over fifteen rounds of measurements (five for the homogeneous case, five for the dimerized but resonant case, and five for the dimerized and off-resonant case), with each taking 20,000 shots. Grey dashed lines indicate the values of ±1.

Extended Data Fig. 3 Measured time dynamics of the right edge operators.

a, \(\langle {\mathop{Z}\limits^{ \sim }}_{{\rm{R}}}(t)\rangle \) and \(\langle {\mathop{X}\limits^{ \sim }}_{{\rm{R}}}(t)\rangle \) in the homogeneous case (Jo = Je = π/5). b, Measured site-resolved dynamics of normalized expectation value \(\overline{\langle {K}_{i}\rangle }\) near the right edge. The nearest excitations to the right edge are initialized at {Q_96, Q_98} (top panel) and {Q_94, Q_96} (bottom panel). c, Measured \(\langle {\mathop{Z}\limits^{ \sim }}_{{\rm{R}}}(t)\rangle \) and \(\langle {\mathop{X}\limits^{ \sim }}_{{\rm{R}}}(t)\rangle \) with fixed Je = π/5 and varying Jo. Error bars in a and c represent the standard deviation over five rounds of measurements, with each taking 10,000 shots.

Extended Data Fig. 4 Prethermal strong zero mode \({{\boldsymbol{\Psi }}}_{{\bf{L}}}^{{\boldsymbol{x}}}\) and its spatial profile.

\({\Psi }_{{\rm{L}}}^{x}\) diverges at both Jo/Je = 1 and 2, where we observe the changes of signs for operators when crossing these two points. The solid boxes denote theoretical predictions, where black and red frames mark positive and negative values, respectively. The coefficients are obtained by averaging the late-time dynamics over cycles from t = 25 to 40, with the sum of their squares normalized to unity.

Extended Data Fig. 5 Raw data of excitation dynamics.

a, Measured site-resolved dynamics \(\langle {\Psi }_{0}| {K}_{i}(t)| {\Psi }_{0}\rangle \) with the initial state being within \(\{| {\Psi }_{0}\rangle \}\) with no excitation (n = 0). The top, middle, and bottom panels show the data obtained from the system in the homogeneous, dimerized but resonant, and dimerized and off-resonant regimes, respectively. b, Measured site-resolved dynamics \(\langle {\Psi }_{{\rm{e}}}| {K}_{i}(t)| {\Psi }_{{\rm{e}}}\rangle \) with the initial state being within \(\{| {\Psi }_{{\rm{e}}}\rangle \}\) with n = 16 excitations. The excitation dynamics in Fig. 3 are normalized by \(\overline{\langle {K}_{i}\rangle }=\langle {\Psi }_{{\rm{e}}}| {K}_{i}(t)| {\Psi }_{{\rm{e}}}\rangle /\langle {\Psi }_{0}| {K}_{i}(t)| {\Psi }_{0}\rangle \) to reveal the effect caused by the bulk excitations.

Extended Data Fig. 6 Excitation dynamics with only two Vxx interaction terms \({{\boldsymbol{\sigma }}}_{{\bf{1}}}^{{\boldsymbol{x}}}{{\boldsymbol{\sigma }}}_{{\bf{2}}}^{{\boldsymbol{x}}}\) and \({{\boldsymbol{\sigma }}}_{{\bf{99}}}^{{\boldsymbol{x}}}{{\boldsymbol{\sigma }}}_{{\bf{100}}}^{{\boldsymbol{x}}}\) at the two edges.

a-c, Measured site-resolved dynamics of normalized expectation value \(\overline{\langle {K}_{i}\rangle }\) for bulk stabilizers \(\{{\sigma }_{i-1}^{z}{\sigma }_{i}^{x}{\sigma }_{i+1}^{z}\}\) and edge operators \(\{{\mathop{Z}\limits^{ \sim }}_{{\rm{L}}},{\mathop{Z}\limits^{ \sim }}_{{\rm{R}}}\}\) in the homogeneous (top panel, Jo = Je = π/2), dimerized (middle panel, Jo = 0.5Je = π/4), and many-body localized regimes (bottom panel). The bulk excitations are induced by applying Z(π) gates on sites {Q_5, Q_7, Q_21, Q_42, Q_60, Q_80, Q_95, Q_97}. For the system in the homogeneous and dimerized regimes, we set hx = 0.23, Vxx = 0.2. For the system in the many-body localized regimes, we fix Vxx = 0.2 and randomly choose Jo, Je, hx from [π/6, 5π/6], [π/6, 5π/6], and [0.18, 0.28], respectively for 10 random instances. d-f, Measured time dynamics of the total excitation number n, excitation number at even (ne) and odd (no) sites, which are calculated from a-c. Error bars in d and e represent the standard deviation over five rounds of measurements, with each taking 20,000 shots. Error bars in f are the standard error of the statistical mean for the 10 instances, with each taking 100,000 shots. Grey dashed lines represent the initial values of no = 5, ne = 3, n = 8 and ne + 0.5no = 5.5 in e.

Extended Data Fig. 7 Spectroscopy of energy spectra for different system sizes.

Experimental results for system sizes from N = 8 to N = 16 are displayed from top to bottom. The first two columns show the averaged spectra of the upper and lower Kitaev chains as functions of ω and Jo/Je. The third column shows their combination as the spectra of the entire system. The presented spectra are obtained by averaging the Fourier spectra of different operators Oi, where the averaged sets are chosen to be i ∈ {0} (which are \({\widetilde{Z}}_{{\rm{L}}},{\widetilde{Z}}_{{\rm{R}}}\)) for N = 8, i ∈ {0, 1, 2} for N = 10, 12, and i ∈ {0, 1, 2, 3} for N = 14, 16.

Extended Data Fig. 8 Preparation of logical Bell state.

a, Quantum circuit for preparing the logical Bell state \({| \mathop{0}\limits^{ \sim }\rangle }_{{\rm{L}}}{| \mathop{0}\limits^{ \sim }\rangle }_{{\rm{R}}}+{\rm{i}}{| \mathop{1}\limits^{ \sim }\rangle }_{{\rm{L}}}{| \mathop{1}\limits^{ \sim }\rangle }_{{\rm{R}}}\). The CZ gate applied on two edge qubits Q_1 and Q_100 is local as the two edge qubits are geometrically near to each other on our processor (see Fig. 1 of the main text). b, Measured density matrix of the prepared logical Bell state, which is extracted from logical state tomography. Its fidelity is about 0.975. c, Measured density matrix in full computational space of Q_1, Q_2, Q_99, Q_100, with fidelity of 0.971 to the ideal density matrix. In b and c, solid bars are experimental data and hollow frames are the ideal density matrix.

Supplementary information

Supplementary Information

Peer Review File

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Jin, F., Jiang, S., Zhu, X. et al. Topological prethermal strong zero modes on superconducting processors. Nature 645, 626–632 (2025). https://doi.org/10.1038/s41586-025-09476-z

- Received: 08 July 2025

- Accepted: 29 July 2025

- Published: 27 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09476-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Thermoelectric properties of topological chains coupled to a quantum dot

Article Open access 27 January 2023

Digital quantum simulation of Floquet symmetry-protected topological phases

Article Open access 20 July 2022

Long-lived topological time-crystalline order on a quantum processor

Article Open access 17 October 2024

Article Open access Published: 17 September 2025

DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning

Daya Guo,

Dejian Yang,

Haowei Zhang,

Junxiao Song,

Peiyi Wang,

Qihao Zhu,

Runxin Xu,

Ruoyu Zhang,

Shirong Ma,

Xiao Bi,

Xiaokang Zhang,

Xingkai Yu,

Yu Wu,

Z. F. Wu,

Zhibin Gou,

Zhihong Shao,

Zhuoshu Li,

Ziyi Gao,

Aixin Liu,

Bing Xue,

Bingxuan Wang,

Bochao Wu,

Bei Feng,

Chengda Lu,

Chenggang Zhao,

Chengqi Deng,

Chong Ruan,

Damai Dai,

Deli Chen,

Dongjie Ji,

Erhang Li,

Fangyun Lin,

Fucong Dai,

Fuli Luo,

Guangbo Hao,

Guanting Chen,

Guowei Li,

H. Zhang,

Hanwei Xu,

Honghui Ding,

Huazuo Gao,

Hui Qu,

Hui Li,

Jianzhong Guo,

Jiashi Li,

Jingchang Chen,

Jingyang Yuan,

Jinhao Tu,

Junjie Qiu,

Junlong Li,

J. L. Cai,

Jiaqi Ni,

Jian Liang,

Jin Chen,

Kai Dong,

Kai Hu,

Kaichao You,

Kaige Gao,

Kang Guan,

Kexin Huang,

Kuai Yu,

Lean Wang,

Lecong Zhang,

Liang Zhao,

Litong Wang,

Liyue Zhang,

Lei Xu,

Leyi Xia,

Mingchuan Zhang,

Minghua Zhang,

Minghui Tang,

Mingxu Zhou,

Meng Li,

Miaojun Wang,

Mingming Li,

Ning Tian,

Panpan Huang,

Peng Zhang,

Qiancheng Wang,

Qinyu Chen,

Qiushi Du,

Ruiqi Ge,

Ruisong Zhang,

Ruizhe Pan,

Runji Wang,

R. J. Chen,

R. L. Jin,

Ruyi Chen,

Shanghao Lu,

Shangyan Zhou,

Shanhuang Chen,

Shengfeng Ye,

Shiyu Wang,

Shuiping Yu,

Shunfeng Zhou,

Shuting Pan,

S. S. Li,

Shuang Zhou,

Shaoqing Wu,

Tao Yun,

Tian Pei,

Tianyu Sun,

T. Wang,

Wangding Zeng,

Wen Liu,

Wenfeng Liang,

Wenjun Gao,

Wenqin Yu,

Wentao Zhang,

W. L. Xiao,

Wei An,

Xiaodong Liu,

Xiaohan Wang,

Xiaokang Chen,

Xiaotao Nie,

Xin Cheng,

Xin Liu,

Xin Xie,

Xingchao Liu,

Xinyu Yang,

Xinyuan Li,

Xuecheng Su,

Xuheng Lin,

X. Q. Li,

Xiangyue Jin,

Xiaojin Shen,

Xiaosha Chen,

Xiaowen Sun,

Xiaoxiang Wang,

Xinnan Song,

Xinyi Zhou,

Xianzu Wang,

Xinxia Shan,

Y. K. Li,

Y. Q. Wang,

Y. X. Wei,

Yang Zhang,

Yanhong Xu,

Yao Li,

Yao Zhao,

Yaofeng Sun,

Yaohui Wang,

Yi Yu,

Yichao Zhang,

Yifan Shi,

Yiliang Xiong,

Ying He,

Yishi Piao,

Yisong Wang,

Yixuan Tan,

Yiyang Ma,

Yiyuan Liu,

Yongqiang Guo,

Yuan Ou,

Yuduan Wang,

Yue Gong,

Yuheng Zou,

Yujia He,

Yunfan Xiong,

Yuxiang Luo,

Yuxiang You,

Yuxuan Liu,

Yuyang Zhou,

Y. X. Zhu,

Yanping Huang,

Yaohui Li,

Yi Zheng,

Yuchen Zhu,

Yunxian Ma,

Ying Tang,

Yukun Zha,

Yuting Yan,

Z. Z. Ren,

Zehui Ren,

Zhangli Sha,

Zhe Fu,

Zhean Xu,

Zhenda Xie,

Zhengyan Zhang,

Zhewen Hao,

Zhicheng Ma,

Zhigang Yan,

Zhiyu Wu,

Zihui Gu,

Zijia Zhu,

Zijun Liu,

Zilin Li,

Ziwei Xie,

Ziyang Song,

Zizheng Pan,

Zhen Huang,

Zhipeng Xu,

Zhongyu Zhang &

…

Zhen Zhang

Nature volume 645, pages 633–638 (2025)

Abstract

General reasoning represents a long-standing and formidable challenge in artificial intelligence (AI). Recent breakthroughs, exemplified by large language models (LLMs)1,2 and chain-of-thought (CoT) prompting[3], have achieved considerable success on foundational reasoning tasks. However, this success is heavily contingent on extensive human-annotated demonstrations and the capabilities of models are still insufficient for more complex problems. Here we show that the reasoning abilities of LLMs can be incentivized through pure reinforcement learning (RL), obviating the need for human-labelled reasoning trajectories. The proposed RL framework facilitates the emergent development of advanced reasoning patterns, such as self-reflection, verification and dynamic strategy adaptation. Consequently, the trained model achieves superior performance on verifiable tasks such as mathematics, coding competitions and STEM fields, surpassing its counterparts trained through conventional supervised learning on human demonstrations. Moreover, the emergent reasoning patterns exhibited by these large-scale models can be systematically used to guide and enhance the reasoning capabilities of smaller models.

Main

Reasoning capability, the cornerstone of human intelligence, enables complex cognitive tasks ranging from mathematical problem-solving to logical deduction and programming. Recent advances in AI have demonstrated that LLMs can exhibit emergent behaviours, including reasoning abilities, when scaled to a sufficient size4,5. However, achieving such capabilities in pre-training typically demands substantial computational resources. In parallel, a complementary line of research has demonstrated that LLMs can be effectively augmented through CoT prompting. This technique, which involves either providing carefully designed few-shot examples or using minimalistic prompts such as “Let’s think step by step”3,6, enables models to produce intermediate reasoning steps, thereby substantially enhancing their performance on complex tasks. Similarly, further performance gains have been observed when models learn high-quality, multistep reasoning trajectories during the post-training phase2,7. Despite their effectiveness, these approaches exhibit notable limitations. Their dependence on human-annotated reasoning traces slows scalability and introduces cognitive biases. Furthermore, by constraining models to replicate human thought processes, their performance is inherently capped by the human-provided exemplars, which prevents the exploration of superior, non-human-like reasoning pathways.

To tackle these issues, we aim to explore the potential of LLMs for developing reasoning abilities through self-evolution in a RL framework, with minimal reliance on human labelling efforts. Specifically, we build on DeepSeek-V3 Base[8] and use Group Relative Policy Optimization (GRPO)[9] as our RL framework. The reward signal is only based on the correctness of final predictions against ground-truth answers, without imposing constraints on the reasoning process itself. Notably, we bypass the conventional supervised fine-tuning (SFT) phase before RL training. This design choice originates from our hypothesis that human-defined reasoning patterns may limit model exploration, whereas unrestricted RL training can better incentivize the emergence of new reasoning capabilities in LLMs. Through this process, detailed in the next section, our model (referred to as DeepSeek-R1-Zero) naturally developed diverse and sophisticated reasoning behaviours. To solve reasoning problems, the model exhibits a tendency to generate longer responses, incorporating verification, reflection and the exploration of alternative approaches within each response. Although we do not explicitly teach the model how to reason, it successfully learns improved reasoning strategies through RL.

Although DeepSeek-R1-Zero demonstrates excellent reasoning capabilities, it faces challenges such as poor readability and language mixing, occasionally combining English and Chinese in a single CoT response. Furthermore, the rule-based RL training stage of DeepSeek-R1-Zero is narrowly focused on reasoning tasks, resulting in limited performance in broader areas such as writing and open-domain question answering. To address these challenges, we introduce DeepSeek-R1, a model trained through a multistage learning framework that integrates rejection sampling, RL and supervised fine-tuning, detailed in the ‘DeepSeek-R1’ section. This training pipeline enables DeepSeek-R1 to inherit the reasoning capabilities of its predecessor, DeepSeek-R1-Zero, while aligning model behaviour with human preferences through further non-reasoning data.

To enable broader access to powerful AI at a lower energy cost, we have distilled several smaller models and made them publicly available. These distilled models exhibit strong reasoning capabilities, surpassing the performance of their original instruction-tuned counterparts. We believe that these instruction-tuned versions will also greatly contribute to the research community by providing a valuable resource for understanding the mechanisms underlying long CoT reasoning models and for promoting the development of more powerful reasoning models. We release DeepSeek-R1-Zero, DeepSeek-R1, data samples and distilled models to the public as described in the ‘Code availability’ section.

DeepSeek-R1-Zero

To implement large-scale RL of DeepSeek-R1-Zero, we use a highly efficient RL pipeline. Specifically, we use GRPO[9] as our RL algorithm, described in Methods section ‘GRPO’. Furthermore, we use a rule-based reward system to compute accuracy and format rewards, with detailed methodologies outlined in Methods section ‘Reward design’. Furthermore, our high-performance RL infrastructure is described in Supplementary Information, section 2.1, ensuring scalable and efficient training.

Specifically, we apply the RL technique on the DeepSeek-V3 Base to train DeepSeek-R1-Zero. During training, we design a straightforward template to require DeepSeek-R1-Zero to first produce a reasoning process, followed by the final answer. The prompt template is written as below.

“A conversation between User and Assistant. The User asks a question and the Assistant solves it. The Assistant first thinks about the reasoning process in the mind and then provides the User with the answer. The reasoning process and answer are enclosed within <think>...</think> and <answer>...</answer> tags, respectively, that is, <think> reasoning process here </think><answer> answer here </answer>. User: prompt. Assistant:”, in which the prompt is replaced with the specific reasoning question during training. We intentionally limit our constraints to this structural format, avoiding any content-specific biases to ensure that we can accurately observe the natural progression of the model during the RL process.

Figure 1a shows the performance trajectory of DeepSeek-R1-Zero on the American Invitational Mathematics Examination (AIME) 2024 benchmark throughout the RL training process, in which the average pass@1 score on AIME 2024 shows a marked increase, jumping from an initial value of 15.6% to 77.9%. Also, by using the self-consistency decoding[10], the performance of the model can be further improved, achieving an accuracy of 86.7%. This performance greatly surpasses the average performance across all human competitors of the AIME. Besides the maths competitions, as shown in Supplementary Fig. 8, DeepSeek-R1-Zero also achieves remarkable performance in coding competitions and graduate-level biology, physics and chemistry problems. These results underscore the effectiveness of RL in enhancing the reasoning capabilities of LLMs.

Fig. 1: Accuracy and output length of DeepSeek-R1-Zero throughout the training process.

a, AIME accuracy of DeepSeek-R1-Zero during training. AIME takes a mathematical problem as input and a number as output, illustrated in Extended Data Table 1. pass@1 and cons@16 are described in Supplementary Information, section 4.1. The baseline is the average score achieved by human participants in the AIME competition. b, The average response length of DeepSeek-R1-Zero on the training set during the RL process. DeepSeek-R1-Zero naturally learns to solve reasoning tasks with more thinking time. Note that a training step refers to a single policy update operation.

As well as the progressive enhancement of reasoning capabilities during training, DeepSeek-R1-Zero also demonstrates self-evolutionary behaviour with RL training. As shown in Fig. 1b, DeepSeek-R1-Zero exhibits a steady increase in thinking time throughout training, driven only by intrinsic adaptation rather than external modifications. Making use of long CoT, the model progressively refines its reasoning, generating hundreds to thousands of tokens to explore and improve its problem-solving strategies.

The increase in thinking time helps with the autonomous development of sophisticated behaviours. Specifically, DeepSeek-R1-Zero increasingly exhibits advanced reasoning strategies such as reflective reasoning and systematic exploration of alternative solutions provided in Extended Data Fig. 1a, substantially boosting its performance on verifiable tasks such as maths and coding. Notably, during training, DeepSeek-R1-Zero exhibits an ‘aha moment’, shown in Table 1, characterized by a sudden increase in the use of the word ‘wait’ during reflections, provided in Extended Data Fig. 1b. This moment marks a distinct change in reasoning patterns and clearly shows the self-evolution process of DeepSeek-R1-Zero.

Table 1 An interesting ‘aha moment’ of an intermediate version of DeepSeek-R1-Zero

The self-evolution of DeepSeek-R1-Zero underscores the power and beauty of RL: rather than explicitly teaching the model how to solve a problem, we simply provide it with the right incentives and it autonomously develops advanced problem-solving strategies. This serves as a reminder of the potential of RL to unlock higher levels of capabilities in LLMs, paving the way for more autonomous and adaptive models in the future.

DeepSeek-R1

Although DeepSeek-R1-Zero exhibits strong reasoning capabilities, it faces several issues. DeepSeek-R1-Zero struggles with challenges such as poor readability and language mixing, as DeepSeek-V3 Base is trained on several languages, especially English and Chinese. To address these issues, we develop DeepSeek-R1, whose pipeline is illustrated in Fig. 2. In the initial stage, we collect thousands of cold-start data that exhibit a conversational, human-aligned thinking process, as detailed in Supplementary Information, section 2.3.2. RL training is then applied with hyperparameters in Methods section ‘Training details of the first RL stage’, data details in Supplementary Information, section 2.3.1, to improve the model performance with the conversational thinking process and language consistency. Subsequently, we apply rejection sampling and SFT once more. This stage incorporates both reasoning and non-reasoning datasets into the SFT process, as detailed in Supplementary Information, section 2.3.3, enabling the model to not only excel in reasoning tasks but also demonstrate advanced writing capabilities. To further align the model with human preferences, we implement a secondary RL stage designed to enhance the helpfulness and harmlessness of the model while simultaneously refining its reasoning capabilities. The reward model is described in Methods section ‘Reward design’ and RL hyperparameters are in Methods section ‘Training details of the second RL stage’. The total training cost is listed in Supplementary Information, section 2.4.4.

Fig. 2: The multistage pipeline of DeepSeek-R1.

A detailed background on DeepSeek-V3 Base and DeepSeek-V3 is provided in Supplementary Information, section 1.1. The models DeepSeek-R1 Dev1, Dev2 and Dev3 represent intermediate checkpoints in this pipeline.

We evaluate our models on MMLU[11], MMLU-Redux[12], MMLU-Pro[13], DROP[14], C-Eval[15], IFEval[16], FRAMES[17], GPQA Diamond[18], SimpleQA[19], C-SimpleQA[20], CLUEWSC[21], AlpacaEval 2.0 (ref. [22]), Arena-Hard[23], SWE-bench Verified[24], Aider-Polyglot[25], LiveCodeBench[26] (2024-08–2025-01), Codeforces[27], Chinese National High School Mathematics Olympiad (CNMO 2024)[28] and AIME 2024 (ref. [29]). The details of these benchmarks are provided in Supplementary Tables 15–29.

Table 2 summarizes the performance of DeepSeek-R1 across several developmental stages, as outlined in Fig. 2. A comparison between DeepSeek-R1-Zero and DeepSeek-R1 Dev1 reveals substantial improvements in instruction-following, as evidenced by higher scores on the IF-Eval and Arena-Hard benchmarks. However, owing to the limited size of the cold-start dataset, Dev1 exhibits a partial degradation in reasoning performance compared with DeepSeek-R1-Zero, most notably on the AIME benchmark. By contrast, DeepSeek-R1 Dev2 demonstrates marked performance enhancements on benchmarks that require advanced reasoning skills, including those focused on code generation, mathematical problem solving and STEM-related tasks. Benchmarks targeting general-purpose tasks, such as AlpacaEval 2.0, show marginal improvement. These results indicate that reasoning-oriented RL considerably enhances reasoning capabilities while exerting limited influence on user-preference-oriented benchmarks.

Table 2 Experimental results at each stage of DeepSeek-R1

DeepSeek-R1 Dev3 integrates both reasoning and non-reasoning datasets into the SFT pipeline, thereby enhancing the proficiency of the model in both reasoning and general language-generation tasks. Compared with Dev2, DeepSeek-R1 Dev3 achieves notable performance improvements on AlpacaEval 2.0 and Aider-Polyglot, attributable to the inclusion of large-scale non-reasoning corpora and code-engineering datasets. Finally, comprehensive RL training on DeepSeek-R1 Dev3 using mixed reasoning-focused and general-purpose data produced the final DeepSeek-R1. Marginal improvements occurred in code and mathematics benchmarks, as substantial reasoning-specific RL was done in previous stages. The primary advancements in the final DeepSeek-R1 were in general instruction-following and user-preference benchmarks, with AlpacaEval 2.0 improving by 25% and Arena-Hard by 17%.

We also compare DeepSeek-R1 with other models in Supplementary Information, section 4.2. Model safety evaluations are provided in Supplementary Information, section 4.3. A comprehensive analysis of evaluation is provided in Supplementary Information, section 5, including a comparison with DeepSeek-V3, performance evaluations on both fresh test sets, a breakdown of mathematical capabilities by category and an investigation of test-time scaling behaviour. Supplementary Information, section 6 shows that the strong reasoning capability can be transferred to smaller models.

Ethics and safety statement

With the advancement in the reasoning capabilities of DeepSeek-R1, we deeply recognize the potential ethical risks. For example, R1 can be subject to jailbreak attacks, leading to the generation of dangerous content such as explosive manufacturing plans, whereas the enhanced reasoning capabilities enable the model to provide plans with better operational feasibility and executability. Besides, a public model is also vulnerable to further fine-tuning that could compromise inherent safety protections.

In Supplementary Information, section 4.3, we present a comprehensive safety report from several perspectives, including performance on open-source and in-house safety evaluation benchmarks, and safety levels across several languages and against jailbreak attacks. These comprehensive safety analyses conclude that the inherent safety level of the DeepSeek-R1 model, compared with other state-of-the-art models, is generally at a moderate level (comparable with GPT-4o (2024-05-13)[30]). Besides, when coupled with the risk control system, the safety level of the model is increased to a superior standard.

Conclusion, limitation and future work

We present DeepSeek-R1-Zero and DeepSeek-R1, which rely on large-scale RL to incentivize model reasoning behaviours. Our results demonstrate that pre-trained checkpoints inherently have substantial potential for complex reasoning tasks. We believe that the key to unlocking this potential lies not in large-scale human annotation but in the provision of hard reasoning questions, a reliable verifier and sufficient computational resources for RL. Sophisticated reasoning behaviours, such as self-verification and reflection, seemed to emerge organically during the RL process.

Even if DeepSeek-R1 achieves frontier results on reasoning benchmarks, it still faces several capability limitations, as outlined below.

Structure output and tool use

At present, the structural output capabilities of DeepSeek-R1 remain suboptimal compared with existing models. Moreover, DeepSeek-R1 cannot make use of tools, such as search engines and calculators, to improve the performance of output. However, as it is not hard to build a RL environment for structure output and tool use, we believe that the issue will be addressed in the next version.

Token efficiency

Unlike conventional test-time computation scaling approaches, such as majority voting or Monte Carlo tree search (MCTS), DeepSeek-R1 dynamically allocates computational resources during inference according to the complexity of the problem at hand. Specifically, it uses fewer tokens to solve simple tasks but generating more tokens for complex tasks. Nevertheless, there remains room for further optimization in terms of token efficiency, as instances of excessive reasoning—manifested as overthinking—are still observed in response to simpler questions.

Language mixing

DeepSeek-R1 is at present optimized for Chinese and English, which may result in language-mixing issues when handling queries in other languages. For instance, DeepSeek-R1 might use English for reasoning and responses, even if the query is in a language other than English or Chinese. We aim to address this limitation in future updates. The limitation may be related to the base checkpoint, DeepSeek-V3 Base, which mainly uses Chinese and English, so that it can achieve better results with the two languages in reasoning.

Prompting engineering

When evaluating DeepSeek-R1, we observe that it is sensitive to prompts. Few-shot prompting consistently degrades its performance. Therefore, we recommend that users directly describe the problem and specify the output format using a zero-shot setting for optimal results.

Software-engineering tasks

Owing to the long evaluation times, which affect the efficiency of the RL process, large-scale RL has not been applied extensively in software-engineering tasks. As a result, DeepSeek-R1 has not demonstrated a huge improvement over DeepSeek-V3 on software-engineering benchmarks. Future versions will address this by implementing rejection sampling on software-engineering data or incorporating asynchronous evaluations during the RL process to improve efficiency.

Beyond specific capability limitations, the pure RL methodology itself also presents inherent challenges:

Reward hacking

The success of pure RL depends on reliable reward signals. In this study, we ensure reward reliability through a reasoning-domain rule-based reward model. However, such dependable reward models are difficult to construct for certain tasks, such as writing. If the reward signal is assigned by a model instead of predefined rules, it becomes more susceptible to exploitation as training progresses, which means that the policy model may find shortcuts to hack the reward model. Consequently, for complex tasks that cannot be effectively evaluated by a reliable reward model, scaling up pure RL methods remains an open challenge.

In this work, for tasks that cannot obtain a reliable signal, DeepSeek-R1 uses human annotation to create supervised data and only conducts RL for hundreds of steps. We hope that, in the future, a robust reward model can be obtained to address such issues.

With the advent of pure RL methods such as DeepSeek-R1, the future holds immense potential for solving any task that can be effectively evaluated by a verifier, regardless of its complexity for humans. Machines equipped with such advanced RL techniques are poised to surpass human capabilities in these domains, driven by their ability to optimize performance iteratively through trial and error. However, challenges remain for tasks for which constructing a reliable reward model is inherently difficult. In such cases, the lack of a robust feedback mechanism may slow progress, suggesting that future research should focus on developing innovative approaches to define and refine reward structures for these complex, less verifiable problems.

Furthermore, making use of tools during the reasoning process holds notable promise. Whether it is using tools such as compilers or search engines to retrieve or compute necessary information or using external tools such as biological or chemical reagents to validate final results in the real world, this integration of tool-augmented reasoning could greatly enhance the scope and accuracy of machine-driven solutions.

Methods

GRPO

GRPO[9] is the RL algorithm that we use to train DeepSeek-R1-Zero and DeepSeek-R1. It was originally proposed to simplify the training process and reduce the resource consumption of proximal policy optimization (PPO)[31], which is widely used in the RL stage of LLMs[32]. The pipeline of GRPO is shown in Extended Data Fig. 2.

For each question q, GRPO samples a group of outputs {o_1, o_2,…, oG} from the old policy \({\pi }_{{\theta }_{{\rm{old}}}}\) and then optimizes the policy model πθ by maximizing the following objective:

$$\begin{array}{ll} & {{\mathcal{J}}}_{{\rm{GRPO}}}(\theta )={\mathbb{E}}[q \sim P(Q),{\{{o}_{i}\}}_{i=1}^{G} \sim {\pi }_{{\theta }_{{\rm{old}}}}(O| q)]\\ & \frac{1}{G}\mathop{\sum }\limits_{i=1}^{G}\left(\min \left(\frac{{\pi }_{\theta }({o}_{i}| q)}{{\pi }_{{\theta }_{{\rm{old}}}}({o}_{i}| q)}{A}_{i},\,\text{clip}\left(\frac{{\pi }_{\theta }({o}_{i}| q)}{{\pi }_{{\theta }_{{\rm{old}}}}({o}_{i}| q)},1-{\epsilon },1+{\epsilon }\right){A}_{i}\right)-\beta {{\mathbb{D}}}_{KL}({\pi }_{\theta }| | {\pi }_{{\rm{ref}}})\right),\end{array}$$

(1)

$${{\mathbb{D}}}_{{\rm{KL}}}({\pi }_{\theta }| | {\pi }_{{\rm{ref}}})=\frac{{\pi }_{{\rm{ref}}}({o}_{i}| q)}{{\pi }_{\theta }({o}_{i}| q)}-\log \frac{{\pi }_{{\rm{ref}}}({o}_{i}| q)}{{\pi }_{\theta }({o}_{i}| q)}-1,$$

(2)

in which πref is a reference policy, ϵ and β are hyperparameters and Ai is the advantage, computed using a group of rewards {r_1, r_2,…, rG} corresponding to the outputs in each group:

$${A}_{i}=\frac{{r}_{i}-{\rm{mean}}(\{{r}_{1},{r}_{2},\cdots \,,{r}_{G}\})}{{\rm{std}}(\{{r}_{1},{r}_{2},\cdots \,,{r}_{G}\})}.$$

(3)

We give a comparison of GRPO and PPO in Supplementary Information, section 1.3.

Reward design

The reward is the source of the training signal, which decides the direction of RL optimization. For DeepSeek-R1-Zero, we use rule-based rewards to deliver precise feedback for data in mathematical, coding and logical reasoning domains. For DeepSeek-R1, we extend this approach by incorporating both rule-based rewards for reasoning-oriented data and model-based rewards for general data, thereby enhancing the adaptability of the learning process across diverse domains.

Rule-based rewards

Our rule-based reward system mainly consists of two types of reward: accuracy rewards and format rewards.

Accuracy rewards evaluate whether the response is correct. For example, in the case of maths problems with deterministic results, the model is required to provide the final answer in a specified format (for example, within a box), enabling reliable rule-based verification of correctness. Similarly, for code competition prompts, a compiler can be used to evaluate the responses of the model against a suite of predefined test cases, thereby generating objective feedback on correctness.

Format rewards complement the accuracy reward model by enforcing specific formatting requirements. In particular, the model is incentivized to encapsulate its reasoning process within designated tags, specifically <think> and </think>. This ensures that the thought process of the model is explicitly delineated, enhancing interpretability and facilitating subsequent analysis.

$${{\rm{Reward}}}_{{\rm{rule}}}={{\rm{Reward}}}_{{\rm{acc}}}+{{\rm{Reward}}}_{{\rm{format}}}$$

(4)

The accuracy, reward and format reward are combined with the same weight. Notably, we abstain from applying neural reward models—whether outcome-based or process-based-to reasoning tasks. This decision is predicated on our observation that neural reward models are susceptible to reward hacking during large-scale RL. Moreover, retraining such models necessitates substantial computational resources and introduces further complexity into the training pipeline, thereby complicating the overall optimization process.

Model-based rewards

For general data, we resort to reward models to capture human preferences in complex and nuanced scenarios. We build on the DeepSeek-V3 pipeline and use a similar distribution of preference pairs and training prompts. For helpfulness, we focus exclusively on the final summary, ensuring that the assessment emphasizes the use and relevance of the response to the user while minimizing interference with the underlying reasoning process. For harmlessness, we evaluate the entire response of the model, including both the reasoning process and the summary, to identify and mitigate any potential risks, biases or harmful content that may arise during the generation process.

Helpful reward model

For helpful reward model training, we first generate preference pairs by prompting DeepSeek-V3 using the Arena-Hard prompt format, listed in Supplementary Information, section 2.2, for which each pair consists of a user query along with two candidate responses. For each preference pair, we query DeepSeek-V3 four times, randomly assigning the responses as either Response A or Response B to mitigate positional bias. The final preference score is determined by averaging the four independent judgments, retaining only those pairs for which the score difference (Δ) exceeds 1 to ensure meaningful distinctions. Furthermore, to minimize length-related biases, we ensure that the chosen and rejected responses of the whole dataset have comparable lengths. In total, we curated 66,000 data pairs for training the reward model. The prompts used in this dataset are all non-reasoning questions and are sourced either from publicly available open-source datasets or from users who have explicitly consented to share their data for the purpose of model improvement. The architecture of our reward model is consistent with that of DeepSeek-R1, with the addition of a reward head designed to predict scalar preference scores.

$${{\rm{Reward}}}_{{\rm{helpful}}}={{\rm{RM}}}_{{\rm{helpful}}}({{\rm{Response}}}_{{\rm{A}}},{{\rm{Response}}}_{{\rm{B}}})$$

(5)

The helpful reward models were trained with a batch size of 256, a learning rate of 6 × 10−6 and for a single epoch over the training dataset. The maximum sequence length during training is set to 8,192 tokens, whereas no explicit limit is imposed during reward model inference.

Safety reward model

To assess and improve model safety, we curated a dataset of 106,000 prompts with model-generated responses annotated as ‘safe’ or ‘unsafe’ according to predefined safety guidelines. Unlike the pairwise loss used in the helpfulness reward model, the safety reward model was trained using a pointwise methodology to distinguish between safe and unsafe responses. The training hyperparameters are the same as the helpful reward model.

$${{\rm{Reward}}}_{\text{safety}}={{\rm{RM}}}_{\text{safety}}({\rm{Response}})$$

(6)

For general queries, each instance is categorized as belonging to either the safety dataset or the helpfulness dataset. The general reward, Rewardgeneral, assigned to each query corresponds to the respective reward defined in the associated dataset.

Training details

Training details of DeepSeek-R1-Zero

To train DeepSeek-R1-Zero, we set the learning rate to 3 × 10−6, the Kullback–Leibler (KL) coefficient to 0.001 and the sampling temperature to 1 for rollout. For each question, we sample 16 outputs with a maximum length of 32,768 tokens before the 8.2k step and 65,536 tokens afterward. As a result, both the performance and response length of DeepSeek-R1-Zero exhibit a substantial jump at the 8.2k step, with training continuing for a total of 10,400 steps, corresponding to 1.6 training epochs. Each training step consists of 32 unique questions, resulting in a training batch size of 512 per step. Every 400 steps, we replace the reference model with the latest policy model. To accelerate training, each rollout generates 8,192 outputs, which are randomly split into 16 minibatches and trained for only a single inner epoch.

Training details of the first RL stage

In the first stage of RL, we set the learning rate to 3 × 10−6, the KL coefficient to 0.001, the GRPO clip ratio ϵ to 10 and the sampling temperature to 1 for rollout. For each question, we sample 16 outputs with a maximum length of 32,768. Each training step consists of 32 unique questions, resulting in a training batch size of 512 per step. Every 400 steps, we replace the reference model with the latest policy model. To accelerate training, each rollout generates 8,192 outputs, which are randomly split into 16 minibatches and trained for only a single inner epoch. However, to mitigate the issue of language mixing, we introduce a language consistency reward during RL training, which is calculated as the proportion of target language words in the CoT.

$${{\rm{Reward}}}_{{\rm{language}}}=\frac{{\rm{Num}}({{\rm{Words}}}_{{\rm{target}}})}{{\rm{Num}}({\rm{Words}})}$$

(7)

Although ablation experiments in Supplementary Information, sction 2.6 show that such alignment results in a slight degradation in the performance of the model, this reward aligns with human preferences, making it more readable. We apply the language consistency reward to both reasoning and non-reasoning data by directly adding it to the final reward.

Note that the clip ratio plays a crucial role in training. A lower value can lead to the truncation of gradients for a large number of tokens, thereby degrading the performance of the model, whereas a higher value may cause instability during training. Details of RL data used in this stage are provided in Supplementary Information, section 2.3.

Training details of the second RL stage

Specifically, we train the model using a combination of reward signals and diverse prompt distributions. For reasoning data, we follow the methodology outlined in DeepSeek-R1-Zero, which uses rule-based rewards to guide learning in mathematical, coding and logical reasoning domains. During the training process, we observe that CoT often exhibits language mixing, particularly when RL prompts involve several languages. For general data, we use reward models to guide training. Ultimately, the integration of reward signals with diverse data distributions enables us to develop a model that not only excels in reasoning but also assigns priority to helpfulness and harmlessness. Given a batch of data, the reward can be formulated as

$${\rm{Reward}}={{\rm{Reward}}}_{{\rm{reasoning}}}+{{\rm{Reward}}}_{{\rm{general}}}+{{\rm{Reward}}}_{{\rm{language}}}$$

(8)

in which

$${{\rm{Reward}}}_{{\rm{reasoning}}}={{\rm{Reward}}}_{{\rm{rule}}}$$

(9)

$${{\rm{Reward}}}_{{\rm{general}}}={{\rm{Reward}}}_{\text{reward\_model}}+{{\rm{Reward}}}_{\text{format}}$$

(10)

The second stage of RL retains most of the parameters from the first stage, with the key difference being a reduced temperature of 0.7, as we find that higher temperatures in this stage lead to incoherent generation. The stage comprises a total of 1,700 training steps, during which general instruction data and preference-based rewards are incorporated exclusively in the final 400 steps. We find that more training steps with the model-based preference reward signal may lead to reward hacking, which is documented in Supplementary Information, section 2.5.

Data availability

We provide the data samples used in our rejection sampling and RL prompts at https://github.com/deepseek-ai/DeepSeek-R1 (https://doi.org/10.5281/zenodo.15753193)[33]. Comprehensive statistics and details of our complete data-generation methodology are presented in Supplementary Information, section 2.3.

Code availability

Trained weights of DeepSeek-R1-Zero and DeepSeek-R1 are available under an MIT license at https://github.com/deepseek-ai/DeepSeek-R1 (https://doi.org/10.5281/zenodo.15753193)[33]. The inference script is released at https://github.com/deepseek-ai/DeepSeek-V3 (https://doi.org/10.5281/zenodo.15753347)[34]. Neural networks were developed with PyTorch[35] and the distributed framework is based on our internal framework HAI-LLM (https://www.high-flyer.cn/en/blog/hai-llm). The inference framework is based on vLLM[36]. Data analysis used Python v.3.8 (https://www.python.org/), NumPy v.1.23.1 (https://github.com/numpy/numpy), Matplotlib v.3.5.2 (https://github.com/matplotlib/matplotlib) and TensorBoard v.2.9.1 (https://github.com/tensorflow/tensorboard).

References

1. Brown, T. B. et al. Language models are few-shot learners. In Advances in Neural Information Processing Systems 33 (eds Larochelle, H. et al.) (ACM, 2020).

2. OpenAI et al. GPT4 technical report. Preprint at https://doi.org/10.48550/arXiv.2303.08774 (2024).

3. Wei, J. et al. Chain-of-thought prompting elicits reasoning in large language models. In Advances in Neural Information Processing Systems 35 (eds Koyejo, S. et al.) 24824–24837 (ACM, 2022).

4. Wei, J. et al. Emergent abilities of large language models. In Transactions on Machine Learning Research (eds Kamath, G. et al.) (2022).

5. Kaplan, J. et al. Scaling laws for neural language models. Preprint at https://doi.org/10.48550/arXiv.2001.08361 (2020).

6. Kojima, T., Gu, S. S., Reid, M., Matsuo, Y. & Iwasawa, Y. Large language models are zero-shot reasoners. In Advances in Neural Information Processing Systems 35 (eds Oh, A. H. et al.) 22199–22213 (ACM, 2022).

7. Chung, H. W. et al. Scaling instruction-finetuned language models. J. Mach. Learn. Res. 25, 1–53 (2024).

8. DeepSeek-AI et al. DeepSeek-V3 technical report. Preprint at https://doi.org/10.48550/arXiv.2412.19437 (2025).

9. Shao, Z. et al. DeepSeekMath: pushing the limits of mathematical reasoning in open language models. Preprint at https://doi.org/10.48550/arXiv.2402.03300 (2024).

10. Wang, X. et al. Self-consistency improves chain of thought reasoning in language models. In 11th International Conference on Learning Representations (ICLR, 2023).

11. Hendrycks, D. et al. Measuring massive multitask language understanding. In 9th International Conference on Learning Representations (ICLR, 2021).

12. Gema, A. P. et al. Are we done with MMLU? In Proc. 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (eds Chiruzzo, L. et al.) Vol. 1 (Long Papers), 5069–5096 (ACL, 2025).

13. Wang, Y. et al. MMLU-Pro: a more robust and challenging multi-task language understanding benchmark. In Advances in Neural Information Processing Systems 37 (eds Globersons, A. et al.) 95266–95290 (ACM, 2024).

14. Dua, D. et al. DROP: a reading comprehension benchmark requiring discrete reasoning over paragraphs. In Proc. 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies Vol. 1 (Long and Short Papers) (eds Burstein, J. et al.) 2368–2378 (ACL, 2019).

15. Huang, Y. et al. C-EVAL: a multi-level multi-discipline Chinese evaluation suite for foundation models. In Advances in Neural Information Processing Systems 36 (eds Oh, A. et al.) 62991–63010 (ACM, 2023).

16. Zhou, J. et al. Instruction-following evaluation for large language models. Preprint at https://doi.org/10.48550/arXiv.2311.07911 (2023).

17. Krishna, S. et al. Fact, fetch, and reason: a unified evaluation of retrieval-augmented generation. In Proc. 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies Vol. 1 (Long Papers) 4745–4759 (ACL, 2025).

18. Rein, D. et al. GPQA: a graduate-level Google-proof Q&A benchmark. Preprint at https://doi.org/10.48550/arXiv.2311.12022 (2023).

19. OpenAI. Introducing SimpleQA; https://openai.com/index/introducing-simpleqa/ (2024).

20. He, Y. et al. Chinese SimpleQA: a Chinese factuality evaluation for large language models. In Proc. 63rd Annual Meeting of the Association for Computational Linguistics Vol. 1 (Long Papers), 19182–19208 (ACL, 2025).

21. Xu, L. et al. CLUE: a Chinese Language Understanding Evaluation benchmark. In Proc. 28th International Conference on Computational Linguistics (eds Scott, D. et al.) 4762–4772 (International Committee on Computational Linguistics, 2020).

22. Dubois, Y., Galambosi, B., Liang, P. & Hashimoto, T. B. Length-controlled AlpacaEval: a simple way to debias automatic evaluators. Preprint at https://doi.org/10.48550/arXiv.2404.04475 (2025).

23. Li, T. et al. From crowdsourced data to high-quality benchmarks: Arena-Hard and BenchBuilder pipeline. Preprint at https://doi.org/10.48550/arXiv.2406.11939 (2024).

24. OpenAI. Introducing SWE-bench verified; https://openai.com/index/introducing-swe-bench-verified/ (2024).

25. Aider. Aider LLM leaderboards; https://aider.chat/docs/leaderboards/ (2024).

26. Jain, N. et al. LiveCodeBench: holistic and contamination free evaluation of large language models for code. In 13th International Conference on Learning Representations (ICLR, 2024).

27. Mirzayanov, M. Codeforces; https://codeforces.com/ (2025).

28. Chinese Mathematical Society (CMS). Chinese National High School Mathematics Olympiad; https://www.cms.org.cn/Home/comp/comp/cid/12.html (2024).

29. Mathematical Association of America. American Invitational Mathematics Examination; https://maa.org/maa-invitational-competitions (2024).

30. OpenAI. Hello GPT-4o; https://openai.com/index/hello-gpt-4o/ (2024).

31. Schulman, J., Wolski, F., Dhariwal, P., Radford, A. & Klimov, O. Proximal policy optimization algorithms. Preprint at https://doi.org/10.48550/arXiv.1707.06347 (2017).

32. Ouyang, L. et al. Training language models to follow instructions with human feedback. In Advances in Neural Information Processing Systems 35 (eds Koyejo, S. et al.) 27730–27744 (ACM, 2022).

33. Nano et al. deepseek-ai/DeepSeek-R1: v1.0.0. Zenodo https://doi.org/10.5281/zenodo.15753192 (2025).

34. Yu, X. et al. deepseek-ai/DeepSeek-V3: v1.0.0. Zenodo https://doi.org/10.5281/zenodo.15753346 (2025).

35. Paszke, A. et al. PyTorch: an imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32 (eds Wallach, H. M. et al.) 8026–8037 (ACM, 2019).

36. Kwon, W. et al. Efficient memory management for large language model serving with PagedAttention. In Proc. ACM SIGOPS 29th Symposium on Operating Systems Principles 611–626 (ACM, 2023).

Acknowledgements

The research is supported by DeepSeek-AI.

Author information

Author notes

1. Fuli Luo

Present address: Individual Researcher, Beijing, China

2. Jinhao Tu

Present address: Jianping High School, Shanghai, China

3. Kai Hu

Present address: University of Science and Technology of China, Hefei, China

4. Kexin Huang, Wenqin Yu, Xinyuan Li, Yue Gong & Yujia He

Present address: Peking University, Beijing, China

5. Zijun Liu

Present address: Tsinghua University, Beijing, China

6. Ziyang Song

Present address: Citadel Securities, Hong Kong SAR, China

Authors and Affiliations

1. DeepSeek-AI Team, Hangzhou, China

Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Peiyi Wang, Qihao Zhu, Runxin Xu, Ruoyu Zhang, Shirong Ma, Xiao Bi, Xiaokang Zhang, Xingkai Yu, Yu Wu, Z. F. Wu, Zhibin Gou, Zhihong Shao, Zhuoshu Li, Ziyi Gao, Aixin Liu, Bing Xue, Bingxuan Wang, Bochao Wu, Bei Feng, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chong Ruan, Damai Dai, Deli Chen, Dongjie Ji, Erhang Li, Fangyun Lin, Fucong Dai, Fuli Luo, Guangbo Hao, Guanting Chen, Guowei Li, H. Zhang, Hanwei Xu, Honghui Ding, Huazuo Gao, Hui Qu, Hui Li, Jianzhong Guo, Jiashi Li, Jingchang Chen, Jingyang Yuan, Jinhao Tu, Junjie Qiu, Junlong Li, J. L. Cai, Jiaqi Ni, Jian Liang, Jin Chen, Kai Dong, Kai Hu, Kaichao You, Kaige Gao, Kang Guan, Kexin Huang, Kuai Yu, Lean Wang, Lecong Zhang, Liang Zhao, Litong Wang, Liyue Zhang, Lei Xu, Leyi Xia, Mingchuan Zhang, Minghua Zhang, Minghui Tang, Mingxu Zhou, Meng Li, Miaojun Wang, Mingming Li, Ning Tian, Panpan Huang, Peng Zhang, Qiancheng Wang, Qinyu Chen, Qiushi Du, Ruiqi Ge, Ruisong Zhang, Ruizhe Pan, Runji Wang, R. J. Chen, R. L. Jin, Ruyi Chen, Shanghao Lu, Shangyan Zhou, Shanhuang Chen, Shengfeng Ye, Shiyu Wang, Shuiping Yu, Shunfeng Zhou, Shuting Pan, S. S. Li, Shuang Zhou, Shaoqing Wu, Tao Yun, Tian Pei, Tianyu Sun, T. Wang, Wangding Zeng, Wen Liu, Wenfeng Liang, Wenjun Gao, Wenqin Yu, Wentao Zhang, W. L. Xiao, Wei An, Xiaodong Liu, Xiaohan Wang, Xiaokang Chen, Xiaotao Nie, Xin Cheng, Xin Liu, Xin Xie, Xingchao Liu, Xinyu Yang, Xinyuan Li, Xuecheng Su, Xuheng Lin, X. Q. Li, Xiangyue Jin, Xiaojin Shen, Xiaosha Chen, Xiaowen Sun, Xiaoxiang Wang, Xinnan Song, Xinyi Zhou, Xianzu Wang, Xinxia Shan, Y. K. Li, Y. Q. Wang, Y. X. Wei, Yang Zhang, Yanhong Xu, Yao Li, Yao Zhao, Yaofeng Sun, Yaohui Wang, Yi Yu, Yichao Zhang, Yifan Shi, Yiliang Xiong, Ying He, Yishi Piao, Yisong Wang, Yixuan Tan, Yiyang Ma, Yiyuan Liu, Yongqiang Guo, Yuan Ou, Yuduan Wang, Yue Gong, Yuheng Zou, Yujia He, Yunfan Xiong, Yuxiang Luo, Yuxiang You, Yuxuan Liu, Yuyang Zhou, Y. X. Zhu, Yanping Huang, Yaohui Li, Yi Zheng, Yuchen Zhu, Yunxian Ma, Ying Tang, Yukun Zha, Yuting Yan, Z. Z. Ren, Zehui Ren, Zhangli Sha, Zhe Fu, Zhean Xu, Zhenda Xie, Zhengyan Zhang, Zhewen Hao, Zhicheng Ma, Zhigang Yan, Zhiyu Wu, Zihui Gu, Zijia Zhu, Zijun Liu, Zilin Li, Ziwei Xie, Ziyang Song, Zizheng Pan, Zhen Huang, Zhipeng Xu, Zhongyu Zhang & Zhen Zhang

Contributions

All authors have contributed to the publication, being variously involved in collecting and curating data, designing the experiments and building the LLM training framework. The authors also participated in implementing and testing the experimental set-up, refining the RL process and performing the analysis of results. The scientific findings were discussed and approved by all contributors. This article was written by a subgroup of authors designated by the collaboration and it underwent an internal collective review process. All authors reviewed and approved the final version of the manuscript. Core contributors: D.G., D.Y., H.Z., J.S., R.Z., R.X., Q.Z., S.M., P.W., X.B., X.Z., X.Y., Y.W., Z.F.W., Z.G., Z.S., Z.L., Z.G. These authors, designated as core contributors, contributed equally to this work, and are presented in alphabetical order. The remaining authors have also contributed meaningfully to the study, and their names are likewise presented in alphabetical order.

Corresponding author

Correspondence to Wenfeng Liang.

Ethics declarations

Competing interests

The authors declare no competing interests and will not file patents related to the content of this manuscript.

Peer review

Peer review information

Nature thanks Edward Beeching, Yarin Gal, José Hernández-Orallo, Daphne Ippolito, Subbarao Kambhampati, Lewis Tunstall, Yiming Zhang and Lexin Zhou for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Evolution of reasoning-related linguistic features in model outputs across training steps.

a, Frequency of representative reflective terms in model-generated outputs throughout the training process. Reflective terms—including ‘wait’, ‘mistake’, ‘however’, ‘but’, ‘retry’, ‘error’, ‘verify’, ‘wrong’, ‘evaluate’ and ‘check’—were identified and curated by a panel of three human experts. Each expert independently proposed a set of words indicative of reflective reasoning, which were subsequently consolidated through consensus into a final vocabulary list. b, Frequency of the term ‘wait’ in model outputs over the course of training. This term was virtually absent during the initial training stages, appeared sporadically between steps 4,000 and 7,000 and exhibited a marked increase in frequency after step 8,000. These trends suggest the emergence of temporal reasoning or self-monitoring behaviour as training progresses.

Extended Data Fig. 2 Illustration of the proposed GRPO for RL-based training.

In the proposed framework, a LLM is used as a policy model to generate responses {o_1, o_2,…, oG} conditioned on a given query q. Each response within the group is evaluated by a reward model—either learned (model-based) or manually specified (rule-based)—to assign a scalar reward signal. Subsequently, GRPO computes the relative advantages of each group member based on their assigned rewards. Rather than relying on an explicit value function, as in PPO, GRPO directly estimates advantages from the intra-group reward distribution. The policy parameters are then updated to maximize the expected reward while simultaneously minimizing divergence from a reference policy, typically quantified through the KL divergence. By eliminating the need for a separate value network, GRPO offers a simplified yet effective alternative to traditional actor-critic methods such as PPO.

Extended Data Table 1 An illustrative example from the AIME dataset

Supplementary information

Supplementary Information

Supplementary Sections 1–11, including Supplementary Tables 1–29 and Supplementary Figs. 1–16 – see Contents for details.

Peer Review file

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Guo, D., Yang, D., Zhang, H. et al. DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning. Nature 645, 633–638 (2025). https://doi.org/10.1038/s41586-025-09422-z

- Received: 14 February 2025

- Accepted: 17 July 2025

- Published: 17 September 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09422-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

AI can learn to show its workings through trial and error

- Daphne Ippolito

- Yiming Zhang

Nature News & Views 17 Sept 2025

Article Open access Published: 03 September 2025

Supervised learning in DNA neural networks

Kevin M. Cherry &

Lulu Qian

Nature volume 645, pages 639–647 (2025)

Abstract

Learning enables biological organisms to begin life simple yet develop immensely diverse and complex behaviours. Understanding learning principles in engineered molecular systems could enable us to endow non-living physical systems with similar capabilities. Inspired by how the brain processes information, the principles of neural computation have been developed over the past 80 years[1], forming the foundation of modern machine learning. More than four decades ago, connections between neural computation and physical systems were established[2]. More recently, synthetic molecular systems, including nucleic acid and protein circuits, have been investigated for their abilities to implement neural computation3,4,5,6,7. However, in these systems, learning of molecular parameters such as concentrations and reaction rates was performed in silico to generate desired input–output functions. Here we show that DNA molecules can be programmed to autonomously carry out supervised learning in vitro, with the system learning to perform pattern classification from molecular examples of inputs and desired responses. We demonstrate a DNA neural network trained to classify three different sets of 100-bit patterns, integrating training data directly into memories of molecular concentrations and using these memories to process subsequent test data. Our work suggests that molecular circuits can learn tasks more complex than simple adaptive behaviours. This opens the door to molecular machines capable of embedded learning and decision-making in a wide range of physical systems, from biomedicine to soft materials.

Similar content being viewed by others

Main

Learning is a fundamental process driving adaptability and survival across biological scales. At the organismal level, neural rewiring and synaptic plasticity enable the brain to learn and form memories, essential for behavioural adaptation and decision-making[8]. At the cellular level and in a simpler form, the immune system learns from pathogen encounters, enhancing future responses[9]. At the molecular level and in the simplest form, biochemical circuits in bacteria learn about their environment, forming short-term memories to optimize survival[10].

Inspired by these natural processes, researchers have explored the deep connections between biological learning algorithms and engineered cellular and molecular networks in numerous theoretical and experimental studies11,12,13. These studies span a diverse range of systems, including abstract chemical reaction networks14,15,16, genetic regulatory networks17,18,19, protein circuits7,20 and metabolic circuits[21]. Notably, DNA-based systems such as cell-free transcriptional and translational circuits22,23, polymerase-exonuclease-nickase DNA circuits6,24, DNA strand-displacement circuits3,4,5,24,25 and DNA tile self-assembly[26] have been developed to perform molecular pattern recognition and classification.

Despite three decades of engineering research, experimental demonstrations have been limited to simple adaptive behaviours in systems with no more than a dozen signals27,28,29. The goal of this work is to implement a molecular system that can autonomously learn to perform complex information-processing tasks. To distinguish learning from simple adaptation, consider a future artificial cell that learns from a more advanced entity, such as a biological cell. It observes the teacher’s behaviour, remembers how the teacher responds to a stimuli, learns from multiple examples over time, and generalizes this knowledge to respond independently to similar stimuli. Developing such a system requires several features. First, the artificial cell must interpret molecular inputs on its own, without relying on an instructor to translate between formats—so training and test data must share the same molecular ‘language’ (independence). Second, it must remember new examples without overwriting past memories, integrating all training data presented sequentially (integration). Third, it must generalize from examples, processing test data that differ from training data using a general-purpose architecture for complex and noisy information (generality). Fourth, it must retain long-term memories, making appropriate decisions even days or months after training data are removed (stability). Fifth, its success should be judged by its ability to correctly classify test data given sufficient training examples (accuracy). Sixth, its performance should be enhanced by its ability to process sequential test data and update its decisions over time (reusability). Finally, its power depends on the type of information that it can store and process (flexibility).

We demonstrate a DNA-based molecular system with learning capabilities that satisfy four key features—independence, integration, generality and stability. Stability arises naturally from the DNA implementation, and generality builds on previous work[4], whereas independence and integration require substantial engineering, as we will discuss in this paper. The remaining features—accuracy, reusability and flexibility—are not fully met and represent goals for future work (Extended Data Fig. 1).

Concept and design

In silico learning produces a DNA neural network with fixed memories—acting like a hardwired processor. In contrast, in vitro learning enables the liquid system itself to form memories in response to example molecular inputs during a training phase—acting like an adaptive memory device. When composed together with a processor, this integrated system provides learned input–output functions applied to a subsequent testing phase (Extended Data Fig. 2). In previous work, we introduced a simple in silico learning algorithm using averaged training patterns as weights for winner-take-all computation[4]. Here we implement a variant for in vitro learning by molecules within a DNA neural network (Fig. 1a). Initially, all weights are zero, representing a blank memory. During training, input patterns and class labels collectively activate specific weights, adding the input to the corresponding memory. After all examples are presented, the resulting weights—encoded in the concentrations of activator molecules—passively store aggregated training data. Learning transitions to testing by connecting the memory device to the processor, transferring information from activators to weight molecules. These now-active weights interact with test inputs, compute weighted sums for each output and trigger a winner-take-all competition. The output with the largest sum is amplified, producing binary signals that classify the input based on its similarity to the learned memories (Fig. 1b).

Fig. 1: Concept and design of supervised learning in DNA neural networks.

a, Abstract training and testing process. b, Example of learning two 9-bit patterns ‘L’ and ‘T’ followed by classification of two corrupted tests. x_1 to xn and y_1 to y_2 are binary inputs and outputs, respectively, represented by coloured and greyscale nodes. Black and white nodes represent outputs that are computed as ON and OFF, respectively. xv = {x_1, x_2, …, xn} can be either a training or test pattern, shown as a mixture of molecules in a droplet (actual form in an experiment) or arranged in a \(\sqrt{n}\)-by-\(\sqrt{n}\) array for visual clarity. A total of q and p patterns are used for training and testing, respectively. qj is the total number of training patterns in class j. l_1 and l_2 are binary class labels represented by polygon shapes. aj = {a1,j, a2,j, …, an,j} is a learned memory associated with output yj, which equals the average of all training patterns in class j. After training, the value of aj can then be transferred to wj for classification of test patterns. Light grey and black wires indicate inhibited and activated weights with zero and learned values, respectively. sj is the weighted sum of inputs for comparing a test pattern with memory j, represented by a polygon-shaped node matching the class label. c, Chemical reaction network implementation. d, Seesaw DNA circuit implementation. Black species indicate molecules whose concentrations correspond to variable values in the abstract mathematical function. Grey species indicate molecules designed to facilitate the desired reactions; their concentrations are typically in excess. Threshold thi is used to clean up noise in xi so that the input is only considered ON if xi > thi. For implementation reasons, the computation of weighted sum is split into weight multiplication pi,j = wi,jxi and summation \({s}_{j}={\sum }_{i=1}^{n}{p}_{i,j}\). The ON value of the output is set by the restoration gate concentration gj. kf and ks are reaction rate constants that must satisfy kf ≫ ks in a pair of reactions with shared reactants; separate reactions labelled with kf or ks do not need to have identical rates. Label inhibitor Inhj is not initially present during training but added after each training event to clean up leftover label. Notations for the seesaw circuit diagram are explained in Extended Data Fig. 2 caption.

The training process resembles ‘learning by memorizing’, conceptually akin to Hebbian learning[30] and k-means clustering[31] (‘Learning algorithm’ in Methods). Unlike modern machine learning, which relies on loss functions and optimization, our approach is simpler yet effective for molecular systems. Although it does not extend naturally to deeper neural networks, it provides an initial step for exploring more advanced architectures.

To implement the learning and testing algorithm with molecules, we first translate the abstract mathematical function into a set of chemical reactions, where each variable is represented by the concentration of a chemical species (Fig. 1c). These reactions are then realized using DNA strand displacement[32]. Although arbitrary chemical reaction networks can be implemented in principle[33], experimental demonstrations have been limited to small systems with a few reactions34,35. Simpler schemes such as the seesaw motif[36] have enabled larger systems with hundreds of reactions3,4,37,38. Here, inspired by activatable species used in adaptive DNA circuits25,27,39, we extend the seesaw architecture with two new activatable gate motifs (Extended Data Fig. 3) to implement the learning chemical neural network (Fig. 1d and ‘Implementation of learning and testing’ in Methods).

Motif characterization

The first motif is an activatable amplification gate (Extended Data Fig. 3). Using this motif, we developed a weight gate that catalytically produces a weighted input signal Pi,j, consisting of a toehold ‘T’ flanked by two long domains Xi and Pj (Fig. 2a). To activate a specific weight Wi,j, the activator Acti,j must carry both input bit (i) and memory class (j) information. Although this could be encoded using two consecutive toeholds via the allosteric toehold mechanism[40], that design has drawbacks (‘Alternative activatable weight design’ in Methods). Instead, we encode class information in toehold Tj and bit information in branch migration domain Ai (Fig. 2a). An activator with matching Tj and Ai binds to the inhibited weight \({W}_{i,j}^{* }\), exposing a universal toehold U* for input binding. To embed a hidden thermodynamic drive[41], we introduce a bulge loop B between U and Xi in the weight gate’s top strand, with the activator carrying B*. Bulge elimination in branch migration lowers the reverse rate and prolongs U* exposure, enhancing input binding.

Fig. 2: Characterization of key motifs.

a, DNA strand-displacement implementation of weight activation followed by weight multiplication. Arrows with black-filled and white-filled arrowheads indicate the forwards and backwards directions of a reversible reaction step, respectively. White-filled arrowheads are omitted if a reaction is considered to be approximately irreversible. b,c, Fluorescence kinetics experiments of the activatable weight gate with varying activator (b) and input (c) concentrations. A reporter molecule shown in Extended Data Fig. 4a reacts with the output of this reaction, resulting in an increased fluorescence signal, which is then normalized to concentration based on control experiments. Experimental data (dotted trajectories) are overlaid with mass-action simulations of chemical kinetics obtained by solving ordinary differential equations (solid trajectories). Relative concentrations of the inhibited weight, fuel and reporter are 1.5× , 3× and 2×, respectively. Standard concentration (1×) is 50 nM here and in all other figures. Endpoint measurements of output concentrations are plotted against activator or input concentrations to reveal their relationship. The solid line indicates a linear fit to the experimental data. The dotted line indicates equal input–output concentration, used as a comparison for the experimental data, highlighting the effect of signal amplification. d, Crosstalk evaluation with 18 weight gates and activators. e,f, DNA strand-displacement implementation of supervised learning (e) and label inhibition (f). g,h, Fluorescence kinetics experiments of the learning gate with varying label (g) and input (h) concentrations. The bottom strand in the inhibited activator and the inputs are modified with a fluorophore and a quencher, respectively (Extended Data Fig. 5a). i, Crosstalk evaluation with eight learning gates and input–label pairs. Excess label at 5× was used. The coloured trajectories in d and i indicate output concentrations over 2 h for distinct activators, or activator concentrations over 8 h for distinct input–label pairs, with each colour representing a specific activator or input–label pair.

Source data

We characterized the weight gate using fluorescence kinetics experiments (Supplementary Note 1). With fixed input and varying activator concentrations, the output reached the activator level within 2 h, demonstrating accurate 1-bit information transfer from passive to active memory (Fig. 2b and Extended Data Fig. 4d). With fixed activator and varying input concentrations, the output exceeded the input by over 4-fold in 20 h, saturating at the activator level—showing robust weight multiplication and signal amplification (Fig. 2c and Extended Data Fig. 4d).

We assessed weight-activation specificity using crosstalk experiments involving 18 inhibited weights and activators (Fig. 2d and Extended Data Fig. 4f). All matching pairs (diagonal) yielded ≥88% of the target signal, whereas mismatched pairs (306 off-diagonal cases) produced ≤20%, with 287 cases below 10%—indicating excellent specificity. These experiments were performed without competition—each tube contained one weight and one activator. In the actual memory transfer, all weights and activators are present together, and mismatches must compete with matches. We expect real-scenario crosstalk to be at least an order of magnitude better.

The second motif is an activatable transformation gate (Extended Data Fig. 3). Using this motif, we developed a learning gate that stoichiometrically produces an activator signal (Fig. 2e). A key requirement is irreversible consumption of input and label strands to prevent errors in future learning events. A simple allosteric toehold design is reversible, and although a drain molecule could enforce irreversibility, it introduces complications (‘Alternative learning gate design’ in Methods). Instead, we embed irreversibility into the learning gate itself (Fig. 2e). A Tj bulge loop in the Xi domain slows reverse branch migration, and upon top-strand release, the Tj domain forms a hairpin with Tj*, further inhibiting the reverse reaction. We experimentally confirmed irreversibility (Supplementary Fig. 20 and Supplementary Note 5.2) and optimized Xi length to balance strand quality and intermediate-state stability. This minimizes spurious activation during interaction with weight gates (Supplementary Fig. 21 and Supplementary Note 5.3).

Although learning is irreversible when both label and input are present, the label alone must interact reversibly with the learning gate. Otherwise, all gates in a memory would be locked on by one training pattern and respond incorrectly to patterns in the other class. This reversibility is built into a transient intermediate activator (Fig. 2e), which is less stable than the activated weight (Fig. 2a). Consequently, the produced activator followed the expected linear dependence on label and input concentrations, but slightly below ideal values (Fig. 2g,h). To improve kinetics and reaction completion (Extended Data Fig. 5d), we used excess label and added an inhibitor to remove leftover label between training events (Fig. 2f).

We evaluated the learning motif’s specificity using crosstalk experiments with eight learning gates and input–label pairs (Fig. 2i and Extended Data Fig. 5e). Unlike the weight motif, which uses a standard fluorescence reporter, these experiments required distinct fluorophore–quencher strands for each reaction (Extended Data Fig. 5a), limiting the experiment scale owing to cost. All matching pairs produced ≥94% of the target signal, whereas all 56 mismatched cases yielded ≤10%, demonstrating high specificity. As with weight crosstalk tests, these were done without competition; actual learning scenarios are expected to show even lower crosstalk.

Activatable memories

The activatable weight motif enables a DNA neural network to receive memories encoded in activators for performing different tasks. In this section, the activators represent weights from in silico training, allowing us to separately evaluate the function of the programmable processor before integrating it with the memory device. We constructed a network with two 100-bit activatable memories and provided 3 distinct sets of activator strands, each encoding 2 classes of handwritten digits from the Modified National Institute of Standards and Technology (MNIST) database[42] (Fig. 3). In previous work, we averaged 100 training patterns per class and selected the top-20 bits to form the weight matrix[4]. Here, lacking a molecular mechanism for bit selection, classification accuracy declines (Supplementary Fig. 31a). To compensate, we developed a ‘good teacher’ strategy: rank and filter above-average training patterns, then randomly select ten per class (Supplementary Note 5.12)—used here for setting activator concentrations and for training in the next section.

Fig. 3: Pattern classification with activatable memories.

a–c, Test patterns selected based on their positions in the weighted sum space for three distinct pairs of MNIST handwritten digits: 0 and 1 (a), 3 and 4 (b), and 6 and 7 (c). Weights are determined as the average of ten training patterns per class. The entire test dataset is shown in light grey. Test patterns within a 20% margin to the diagonal line (s_1 = s_2) are excluded for experimental feasibility. d,e, Fluorescence kinetics experiments with 12 test patterns per class on activated memories of 0 and 1 in memory 1 and 2 (d), respectively, or swapped in memory 2 and 1 (e). The difference between two output concentrations (Y_1 − Y_2) at the end of the experiments is shown for all test patterns sorted according to their distance to the diagonal line in the weighted sum space. For the left set of patterns, the distance decreases from left to right; for the right set of patterns, the distance increases. f–i, Endpoint data for testing activated memories of 3 and 4 in memory 1 and 2 (f), respectively, or swapped in memory 2 and 1 (g) or 6 and 7 in memory 1 and 2 (h), respectively, or swapped in memory 2 and 1 (i).

Source data

Test patterns were selected based on their positions in the weighted sum space, reflecting classification difficulty. For each class, 12 representative tests were chosen via k-means clustering (k = 12), selecting 1 example per cluster (Fig. 3a–c). To ensure experimental feasibility, we excluded examples within 20% of the diagonal, retaining 53% of zeros and 83% of ones from the dataset. Outside this margin, the network is expected to classify all test patterns correctly with clear binary outputs. Within the margin, classifications are still possible but less binary. Similarly, the expected lower bounds of classification accuracy—determined by the fraction of test patterns outside the 20% margin—for the full MNIST dataset were 56% for threes, 46% for fours, 56% for sixes and 71% for sevens (Supplementary Fig. 31d). Fluorescence kinetics experiments confirmed correct outputs for all test patterns, showing clear on–off separation (Fig. 3d–i). Separation quality correlated with distance from the diagonal: greater distance yielded larger separations. To assess DNA sequence dependence, we encoded digit pairs with swapped memory molecules. Experimental results showed minor differences, consistent with simulations using reaction rates from the motif characterization (Extended Data Fig. 6).

The ability to receive memories enables the DNA neural network to function as a field-programmable device, performing different classification tasks based on the activators provided. Although it is still following instructions rather than learning, this demonstration is powerful—it can execute any combination of commands from a library of hundreds to classify complex and noisy inputs.

Learned weights

The learning motif enables a DNA neural network to develop memories encoded in activators for later computation. In this section, the activators represent weights learned from in vitro training, allowing us to separately evaluate the function of the adaptive memory device before integrating it with the processor. We constructed a network of learning gates that received 100-bit training data from 2 classes of handwritten digits and monitored the produced activators. A robust learning system should handle arbitrary training patterns in any order. To test this, we used a ‘batch training’ procedure, simultaneously presenting all patterns from the same class—analogous to batch training in machine learning. In molecular terms, mixing pre-prepared patterns yields a training mixture where each input strand’s quantity reflects the combined signal from all patterns. Although this method lacks intra-class order variation, it still tests robustness by presenting the two classes in different orders (Fig. 4a). Training with individual patterns would slow learning owing to lower input concentrations and require label inhibition between patterns of different classes, complicating the experiments.

Fig. 4: Learned weights.

a, Abstract training process of learning two classes of 100-bit handwritten digits in two distinct orders. Grey and black wires indicate inhibited and learned weights, respectively. b, Fluorescence kinetics experiments that read out the learned weights. Learning was performed as follows: present all 10 training patterns from one class together with the class label, wait for 24 h, add the label inhibitor, wait for 2 h, and then repeat with the second class. After learning was completed, 100 aliquots of the learned memories were each mixed with a unique pair of activatable weight molecules (\({W}_{i,1}^{* }\) and \({W}_{i,2}^{* }\)), a fuel strand (XFi), all 100 input strands (X_1 to X_100), and a pair of standard reporters that each converts one of the two possible output signals to fluorescence. The two reporters were modified with fluorophores ATTO590 and ATTO488, respectively, allowing for simultaneous readout in two fluorescence channels. Eight hours of kinetics data are shown in two 10-by-10 arrays. Each position in both arrays corresponds to the same sample. Each array corresponds to one of the two fluorescence channels. c, Measured weight concentrations at 4 h and error statistics for learning handwritten digits 0 and 1 in two distinct orders. d,e, Overlaid training patterns (10 per class), representing target weights, and learned weights (measured weight concentrations at 4 h) for learning handwritten digits 3 and 4 (d) or 6 and 7 (e). f, Distribution of errors from experiments shown in c–e. Ø indicates a blank memory. w_1 and w_2 indicate the weight matrix for memory 1 and 2, respectively.

Source data

We performed fluorescence kinetics experiments to read out learned weights after training with digits 0 and 1 (Fig. 4b). Each plot in the data array shows signal increase for one activated weight in the two 100-bit memories. Visually, the digit shapes emerged, confirming successful learning. Quantitatively, pixels with 0 values in all 10 training patterns showed low signals—0.5 ± 0.3% of the total signal for 1 and 1.1 ± 0.4% for 0—whereas other pixels showed up to 13-fold signal increases over background (see endpoint values in Extended Data Fig. 7).

To investigate background noise, we captured snapshots of the training process at the start, midpoint, and end (Fig. 4c). Before training, background signals in memories 1 and 2 were 0.4 ± 0.4% and 0.7 ± 0.3% of the total signal, respectively (Fig. 4c, left column). Memory 2’s higher background persisted post-training (Fig. 4c, middle and right columns), probably owing to sequence variations and synthesis errors causing spurious weight activation. Still, this noise was minimal compared with earlier versions of the learning and activatable weight motifs (Supplementary Note 4.7).

Introducing the first batch of training patterns with their label led to correct storage in the target memory, whereas the other remained largely unaffected (Fig. 4c), demonstrating strong label specificity. The second batch was similarly stored without disrupting the earlier memory. Learned weights were consistent across two training orders, confirming robust learning regardless of which class was presented first or which memory stored each class.

Further robustness was demonstrated using two additional pairs of distinct training patterns (Fig. 4d,e and Extended Data Fig. 8), showing the system’s ability to learn arbitrary information from two classes of 100-bit patterns. Error analysis revealed that memory 2 consistently had more noise than memory 1, regardless of training patterns (Fig. 4f). In addition, a few bits showed lower-than-expected values across training patterns and in both memories, probably owing to secondary structures in the learning intermediates (‘Errors in learned weights’ in Methods).

The ability to develop memories enables the DNA neural network to learn from examples. As shown, it can store arbitrary patterns within a given complexity, integrating them into two memories in any order. Learning is powered solely by the training patterns and labels. After training, the system reaches thermodynamic equilibrium, stably storing learned weights until testing begins.

Testing after training

The true effectiveness of the DNA neural network’s learning ability lies in its classification performance after connecting the memory device to the processor, where learned information is transferred from activators to weights for downstream computation. This step is the most challenging in building a functional learning system. In earlier designs, we achieved 4-bit learning and 4-bit activatable memories separately but not integrated (Supplementary Note 4). With a revised design, we successfully demonstrated integrated 9-bit learning and testing (Supplementary Fig. 21), but failed to scale to 100-bit (Supplementary Fig. 22 and Supplementary Note 5.4). Investigations revealed that unused molecules—more prevalent in larger systems—were the primary issue. For instance, unused learning gates can cause label occlusion, weakening the production of activator signals. They may also leak with weight gates or test inputs, creating spurious memories. We addressed these challenges through design revisions and fabrication techniques (Supplementary Figs. 23–28 and Supplementary Notes 5.5–5.10). Solutions included adding clamps to suppress toeless strand displacement37,43, adjusting annealing ratios, and using clean-up strands to promote competition between full-length and truncated strands, improving gate purity.

To test the scalability of our final design (Fig. 2), we created training and test patterns of increasing complexity (Fig. 5a). We predicted that the performance depends on the ratio of unused-to-used memory bits—that is, inhibited-to-activated weights post-training. Experiments with increasing memory size and varying fractions of activated bits confirmed this (Fig. 5b–d and Extended Data Fig. 9). Overall, performance declined with increasing complexity. However, as long as the total-to-activated bit ratio remained constant, increasing the number of activated bits had minimal impact (Fig. 5e). Performance worsened as this ratio increased (Fig. 5f). These results validated our hypothesis and highlighted a key trade-off: to learn complex patterns, training inputs must not activate too many bits—for example, there is only 1 binary pattern that can be learned if it has 100 ones. Paradoxically, unused bits become the dominant factor degrading testing performance. Scaling beyond two memories introduces further challenges, such as a quadratic increase in annihilator species and biased winner-take-all competition from imperfect reaction rates[4].

Fig. 5: Scalability of pattern classification using learned weights.

a, Learned weights (top) and test patterns (bottom) with increasing complexity from 4 bits to 100 bits. In learned weights, grey pixels indicate unused memory bits with no associated molecules. White pixels indicate activatable but not activated memory bits with inhibited activator and inhibited weights that are present throughout training and testing. Coloured pixels indicate memory bits activated by training patterns and their labels. In test patterns, each white and black pixel indicates the absence and presence of an input strand, respectively. n is the total number of activable bits in a memory, b is the number of activated bits in a memory and number of ones in an input, and p is an input’s position (s_1, s_2) in the weighted sum space. b–d, Fluorescence kinetics experiments for testing after learning with three representative cases: b = 4 and n = 4 (b), b = 12 and n = 36 (c), and b = 20 and n = 100 (d). Fluorescence kinetics data for eight test patterns of two classes are shown in two separate plots. The difference between the 2 outputs at 8 h is shown in the bar chart, next to the learned weights. e,f, Performance analysis based on the complexity of activated bits (e) and total bits (f). Error bars represent standard deviation of eight test patterns for each combination of b and n.

Source data

The DNA neural network with learning capabilities is far more complex than the previous one using weights trained in silico[4]. Our 100-bit, 2-memory network involved over 700 distinct species in a single test tube and more than 1,200 unique strands across learning and testing (Fig. 6b). Depending on the number of training patterns, up to 80% of activators and weights must remain inhibited post-training (Fig. 6c). Despite these challenges, we demonstrated successful classification in 72 representative tests after 3 distinct training processes (Fig. 6d and Extended Data Fig. 10), proving that engineered molecular systems can learn complex information-processing tasks.

Fig. 6: A 100-bit pattern classification using learned weights.

a, Abstract testing process. b, Comparing the number of initial species in a DNA neural network without[4] and with learning capability. c, Comparing the number of inhibited and activated species before and after training. The total numbers are calculated based on a single training pattern where b = 20. d, Simulations (solid trajectories) and fluorescence kinetics experiments (dotted trajectories) of pattern classification for 18 representative cases after 3 distinct training processes. Weight matrices before and after training were taken from the experiments shown in Fig. 4.

Source data

Discussion and conclusion

The DNA neural network developed here autonomously performs pattern classification after learning, processing test patterns composed of the same types of molecule as in training, but in new combinations. This demonstrates independence beyond field-programmable devices that rely on instructors to translate environmental signals. It also shows generality, enabling classification beyond simple lookup of previous examples. The system received training patterns over time and stored them into two distinct memories based on label information, demonstrating integration beyond simple memorization. After training, the memories remained passive and isolated from computation until testing began, providing stability beyond short-term memories. Together, these features bring us closer to realizing the future artificial cell envisioned at the beginning of this paper (Extended Data Fig. 1).

The DNA neural network with learning capabilities is remarkably robust given its complexity. Aside from fluorescence reporters, the entire system was constructed using unpurified strands, yet performance remained uncompromised—indicating strong tolerance to impurity-induced molecular noise. Double-stranded complexes were purified using a one-pot procedure to correct stoichiometry errors (for example, all 100 learning gates per memory in one mixture). The robustness, combined with low cost and simple fabrication, makes the system readily accessible for future applications.

Learning has been proposed to accelerate evolution through the Baldwin effect, which reshapes the fitness landscape44,45. Our work explores how chemical systems can learn from an unknown environment, forming memories from past inputs to process future signals. However, supervised learning requires labelled examples—a ‘teacher’—which is incompatible with early life. The next challenge is enabling unsupervised learning, where systems enhance their capabilities through unguided exposure to a molecular environment. In such a regime, the system constantly learns and refines its classification decisions. Achieving this requires overcoming a major limitation: the use-once nature of current DNA neural networks. Computation consumes stored energy, driving the system towards equilibrium. Once used, outputs cannot be reversed without added energy. Although various approaches to reusable enzyme-free DNA circuits have been explored46,47,48,49,50, none are yet scalable. Advancing sustainable computation will be essential to realizing unsupervised learning in molecular systems.

Truly impressive learning behaviours depend on the complexity of neural networks. Although scaling DNA neural networks to the level of the human brain or advanced artificial intelligence models remains infeasible, there is substantial room for increasing their complexity. A current limitation is the absence of spatial organization, which is essential for efficient information encoding in both biological neural networks and electronic computers[51]. Phase-separated DNA condensates offer a promising solution[52]. These micrometre-sized droplets, containing billions of branched DNA monomers, could provide the spatial organization needed to scale up learning DNA neural networks by at least an order of magnitude. Alternatively, reaction–diffusion DNA systems[53] offer another spatial paradigm for sophisticated pattern formation and classification behaviours54,55.

The potential of learning molecular systems extends far beyond current demonstrations. DNA-based classifiers have been used in disease diagnostics56,57; with learning, they could enable therapeutics that remember previous encounters with disease biomarkers, improving future responses. DNA circuits can also control soft materials, allowing them to expand or contract in response to stimuli58,59. With learning, these materials could adapt based on past experiences. Our work addresses the long-standing challenge of molecular learning, opening paths for intelligent molecular systems. These advances could endow non-living physical systems with adaptive decision-making abilities, transforming fields from molecular therapeutics to programmable active materials[60].

Methods

Learning algorithm

The learning algorithm adds each binary training pattern to memory j if binary label lj = 1 (Fig. 1a,b), resulting in weights that are averaged training patterns for each class. Conceptually, this approach is similar to Hebbian learning[30], often summarized by the phrase ‘cells that fire together wire together’. Although classical Hebbian learning is an unsupervised learning rule in recurrent neural networks, it can be generalized to feedforward winner-take-all neural networks[61]. In our case, weight wi,j representing the wire between input node xi and weighted sum node sj is turned on when training data containing input xi and label lj are simultaneously present (Fig. 1a). The training process is also conceptually similar to the widely used clustering algorithm k-means[31], but used in a supervised setting[62]. In our case, k = 2 clusters correspond to the two memories and the means correspond to the averaged training patterns.

Implementation of learning and testing

As the testing phase directly builds on our previous work of DNA-based winner-take-all neural networks[4], we first describe this phase as follows before explaining the learning phase. The weighted sum function is divided into weight multiplication and summation (Fig. 1c,d), owing to an architectural constraint that catalytic reactions in the seesaw motif support fan-out but not fan-in[37]. Weight multiplication and summation are then translated into a catalytic and stoichiometric reaction, respectively. The fan-out of each input multiplied by weights in two or more memories is implemented using an amplification gate motif, whereas the fan-in of weighted sums from all inputs is implemented using an integration gate motif (Extended Data Fig. 3). The catalytic property of the weight multiplication reaction allows for arbitrary analogue weights, including greater than one. The thresholding reaction (with a threshold species Thi representing thi = 0.5) is not explicitly translated from the mathematical function, but enables the clean-up of noisy input signals. The combination of thresholding and catalysis implements a signal restoration function that converts mildly corrupted inputs (high background or signal decay) to ideal binary signals. The winner-take-all function is implemented using pairwise annihilation (facilitated by annihilator Anhi,j) that enables a competition between any two signals, allowing them to turn each other off, and signal restoration (facilitated by restoration gate RGj and fuel YFj) that amplifies the winner species to an ideal on signal. A reporting reaction (facilitated by reporter Repj) is used to stoichiometrically convert an output signal to fluorescence for readout in experiments.

The training phase cannot be implemented with the previously developed reaction mechanisms in the seesaw motif. The key function here is the summed multiplication of binary input and label signals (Fig. 1b), which could be implemented with Xi + Lj → Wi,j, where the total concentration of Wi,j is accumulated over all training patterns that have the same label. However, a problem is that, unlike the product species for all reactions in the testing phase, Wi,j is not a signal species but a double-stranded gate species. To translate a signal species into a gate species, we developed an activatable amplification gate motif where the presence and absence of an activator signal determines the on and off states of the gate, respectively (Extended Data Fig. 3). Using this motif, we can then separate the training process into two reactions: supervised learning Xi + Lj → Acti,j, where an input and label strand collectively produce an activator, and weight activation \({{\rm{Act}}}_{i,j}+{W}_{i,j}^{* }\to {W}_{i,j}\), where the activator turns on a specific weight gate.

The supervised learning reaction can be implemented with an activatable transformation gate motif (Extended Data Fig. 3), using the label as an activator for a learning gate that is initially off (\({{\rm{Act}}}_{i,j}^{* }\)) but can be turned on to react with an input in a training pattern and produce the weight activator (Acti,j). To focus on the essential concept of learning while simplifying other aspects of the algorithm, the scaling of 1/qj (Fig. 1b) is implicitly achieved by using a lower amount of the input strand per training pattern when more patterns are used. Lastly, similar to the thresholding reaction, although not explicitly needed, a label inhibition reaction (facilitated by inhibitor Inhj) is introduced to clean up excess label between training events, facilitating accurate learning.

Combining the training phase and testing phase (Extended Data Fig. 2c), the resulting DNA neural network has five layers (Fig. 1d). The first two layers each utilize the two types of activatable gate motif discussed above, the output of one is an activator signal (Acti,j) and the other is a regular signal (product Pi,j of weight multiplication). This difference in output format may seem insignificant, but along with other desired properties of the two motifs, it led to many important details within the molecular design that will be discussed in the section on motif characterization.

Compared with the DNA neural network without learning capabilities[4], this neural network may seem only mildly more complicated with one additional layer, but the network topology has advanced in a non-trivial fashion. The same set of input signals can participate in both the learning and testing phase, reacting with the activatable gates in both of the first two layers. When all gates are present, the only information that determines which gate the input actually reacts with is whether the gate is on or off. When the label is present, it turns on the learning gate; when the activator produced from learning is present, it turns on the weight gate. Undesired spurious activation within these two types of gate will alter the interpretation of the input, for example, confusing a test pattern as a training pattern. Moreover, the DNA neural network without learning capabilities[4] used sparse weight matrices to efficiently perform pattern classification tasks, where zero weights corresponded to eliminated weight and fuel species. Here, to learn to perform arbitrary pattern classification tasks within a given pattern complexity and class number, the neural network must have the ability to turn on every element in the weight matrices, requiring the presence of all species in the first two layers. These conditions put more stringent requirements on the molecular design, which cannot be addressed at the individual molecule level, but all interlinked issues such as leak, occlusion, crosstalk and reaction reversibility must be considered as a whole at the system level. We discuss all of these issues in an earlier design (Supplementary Note 4) and summarize a set of system-level design criteria that is applied to the final design (Supplementary Note 3).

During the training phase, all species within the first layer of the DNA neural network will be present, creating passive memories represented by the activator species. These species store the full learned information in a one-to-one fashion (Acti,j encodes Wi,j) but they do not react with any input signals. Transition from training to testing is enabled by combining all species in the remaining four layers with the resulting learning mixture into a single test tube. The added species represent a processor with blank memories. Once the activators and weight gates are mixed together, information transfers from the passive memories to the activated memories, allowing the processor to perform pattern classification tasks using the learned memories (Extended Data Fig. 2b).

Implementation of arbitrary chemical reaction networks

Although not fully verified by theory, we speculate that the extended seesaw motifs now lead to a general-purpose implementation of arbitrary chemical reaction networks (Supplementary Note 4.3). Like the original seesaw motif[36], every species in the additional motifs remains one- or two-stranded.

Alternative activatable weight design

To turn on a weight Wi,j, the activator Acti,j could be implemented with two consecutive toeholds using an allosteric toehold mechanism[40] that allows for the control of toehold availability via a short regulator strand (Supplementary Fig. 10a). Toehold Xit* encodes the input bit information i and toehold Tj* encodes the memory class information j. However, there are several problems with this design. First, encoding the bit information in a short toehold lacks sufficient specificity for 100-bit patterns, giving rise to crosstalk in weight activation (Supplementary Fig. 17 and Supplementary Note 4.8). Second, all input strands have distinct toehold sequences and react with the weight gates at different rates, leading to the lack of synchronization in the production of weighted sum signals. This asynchrony creates the possibility that a fraction of one weighted sum signal might arrive before the other and become amplified without being annihilated, resulting in biased classification decisions. Third, the activator strand violates the system-level three-letter code (Supplementary Fig. 9 and Supplementary Note 3.3), allowing it to occlude and be occluded by other signal strands. Lastly, like the activator, the label must have a complementary toehold to the input (Supplementary Fig. 11a). Because all input strands have distinct toeholds, 100 label strands per class would be necessary to activate the learning gates for 100-bit training patterns. This is both wasteful, given that the label only needs to encode the class information but not the bit information, and problematic, allowing for increased spurious interactions that reduce the performance of learning and testing.

Design considerations for the weight gate

We investigated the impact of the bulge size and the possibility of replacing the bulge with a nick (Supplementary Fig. 19 and Supplementary Note 5.1). As expected, experiments suggested that a larger bulge drove weight activation more effectively but also increased undesired leak between the input or fuel and the weight gate. Replacing the bulge with a nick results in shorter strands but more strands per complex, reducing synthesis errors at the cost of increased stoichiometry errors (Supplementary Note 3.1). Experiments suggested that the nick provided a higher reaction completion but also more leak. A key difference in the leak mechanism comparing the bulge and the nick design is that although the forward reaction is always bimolecular, the reverse reaction is either unimolecular or bimolecular depending on the design. At a relatively low concentration (for example, 50 nM in our experiments), unimolecular reactions are faster than bimolecular reactions, and thus leak in the bulge design is both kinetically slow and thermodynamically unfavoured. For similar reasons, the nick design not only showed worse leak but also more crosstalk in weight activation, as well as worse leak between the learning gate and the weight gate. On the basis of these observations, we chose the weight gate design with a 2-nt bulge. In addition, a clamp cj is necessary to mitigate leak between the learning gate and the weight gate, preventing spontaneous activation without training. In this design, the system-level three-letter code is satisfied by using non-star domains (As, Cs and Ts) of Tj and Ai on the activator and a two-letter code (As and Ts only) for the universal toehold U and bulge B.

Alternative learning gate design

The desired irreversibility of learning could be provided by a double-stranded drain molecule that converts an intermediate waste to inert wastes with no open toeholds (Supplementary Fig. 11a). This design may seem straightforward, but we discovered several problems upon experimental investigation. First, all drains must be available for learning but most of them will not be consumed depending on the training patterns. Unreacted drains will severely occlude the weight gates in testing, preventing them from being effectively activated (Supplementary Fig. 14 and Supplementary Note 4.5). Second, shortening the toehold on the drain improves the occlusion but sacrifices the robustness of irreversibility, especially when fluorophore and quencher modifications are used to monitor the learning process (Supplementary Fig. 15 and Supplementary Note 4.6). Lastly, mismatches can be introduced to improve irreversibility, but they lead to substantial leak between the learning gates and weight gates, causing spurious memories without training (Supplementary Fig. 16 and Supplementary Note 4.7).

Errors in learned weights

Interestingly, error analysis identified a few bits (27, 85 and 86) that consistently had lower values than expected across all training patterns and both memories (Fig. 4c and Extended Data Fig. 8). Simulations suggested some signal loss during training (Supplementary Fig. 5) but did not explain why certain bits performed worse. We hypothesized that the issue lay in the DNA sequences of the learning gates associated with these bits—our sequence design criteria did not account for intermediate structures in the learning reaction, such as the intermediate activator in which the label is bound to the gate before the input has reacted (Fig. 2e). To investigate further, we used NUPACK63,64 to analyse the secondary structures of all 100 intermediate activators in each memory (Supplementary Fig. 6c). A well-formed structure should have the toehold U* available for binding to the input strand. However, in problematic structures, the toehold partially binds to the Xib* domain owing to the destabilizing effect of the Tj bulge loop. NUPACK analysis predicted that the intermediate activators for bits 27, 85 and 86 were among the worst malformed structures, supporting our hypothesis. Simulations with adjusted reaction rates based on toehold availability showed better agreement with experimental observations (Supplementary Fig. 6d–f). In future work, more stringent sequence design criteria could be applied to avoid malformation in all intermediate structures.

Lessons for engineering complex molecular systems

Two important lessons that we learned for engineering complex molecular systems are as follows. First, a failure mode of the debugging strategy is to focus on individual challenges. A solution for one problem may give rise to another problem somewhere else in the system. With further cascading, in the worst-case scenario, this debugging strategy may form a deadlock in a cycle. After understanding the failure mode, we arrived at an alternative strategy where all challenges are considered as a whole and solutions are devised to address the entire body of challenges simultaneously (Supplementary Note 4.9). Second, a waste of energy may occur if there is no approach to differentiate fabrication problems from design problems. For example, we discovered severe and uneven sample evaporation in source plates for a liquid handler, resulting in wildly inaccurate concentrations that directly affect the computation of the molecular system. Instead of just relying on a better sample storage method, we established a systematic approach to regularly evaluate the sample quality and reorder new strands whenever needed (Supplementary Note 5.13).

Data availability

All data supporting the findings of this study are available within the paper and its Supplementary Information. Source data files are available at CaltechDATA (https://doi.org/10.22002/5bvkt-r7y16)[65]. Source data are provided with this paper.

Code availability

The code for simulation and data analysis is available at CaltechDATA (https://doi.org/10.22002/5bvkt-r7y16)[65].

References

1. McCulloch, W. S. & Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133 (1943).

2. Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).

3. Qian, L., Winfree, E. & Bruck, J. Neural network computation with DNA strand displacement cascades. Nature 475, 368–372 (2011).

4. Cherry, K. M. & Qian, L. Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks. Nature 559, 370–376 (2018).

5. Xiong, X. et al. Molecular convolutional neural networks with DNA regulatory circuits. Nat. Mach. Intell. 4, 625–635 (2022).

6. Okumura, S. et al. Nonlinear decision-making with enzymatic neural networks. Nature 610, 496–501 (2022).

7. Chen, Z. et al. A synthetic protein-level neural network in mammalian cells. Science 386, 1243–1250 (2024).

8. Churchland, P. S. & Sejnowski, T. J. The Computational Brain (MIT Press, 2016).

9. Farmer, J. D., Packard, N. H. & Perelson, A. S. The immune system, adaptation, and machine learning. Physica D 22, 187–204 (1986).

10. Vladimirov, N. & Sourjik, V. Chemotaxis: how bacteria use memory. Biol. Chem. 390, 1097–1104 (2009).

11. Kieffer, C., Genot, A. J., Rondelez, Y. & Gines, G. Molecular computation for molecular classification. Adv. Biol. 7, 2200203 (2023).

12. Nagipogu, R. T., Fu, D. & Reif, J. H. A survey on molecular-scale learning systems with relevance to DNA computing. Nanoscale 15, 7676–7694 (2023).

13. Vasle, A. H. & Moškon, M. Synthetic biological neural networks: from current implementations to future perspectives. Biosystems 237, 105164 (2024).

14. Hjelmfelt, A., Weinberger, E. D. & Ross, J. Chemical implementation of neural networks and Turing machines. Proc. Natl Acad. Sci. USA 88, 10983–10987 (1991).

15. Poole, W. et al. Chemical Boltzmann Machines. In 23rd International Conference on DNA Computing and Molecular Programming (DNA 23) (eds Brijder, R. & Qian, L.) 210–231 (Springer, 2017).

16. Vasić, M., Chalk, C., Luchsinger, A., Khurshid, S. & Soloveichik, D. Programming and training rate-independent chemical reaction networks. Proc. Natl Acad. Sci. USA 119, e2111552119 (2022).

17. Buchler, N. E., Gerland, U. & Hwa, T. On schemes of combinatorial transcription logic. Proc. Natl Acad. Sci. USA 100, 5136–5141 (2003).

18. Fernando, C. T. et al. Molecular circuits for associative learning in single-celled organisms. J. R. Soc. Interface 6, 463–469 (2009).

19. Rizik, L., Danial, L., Habib, M., Weiss, R. & Daniel, R. Synthetic neuromorphic computing in living cells. Nat. Commun. 13, 5602 (2022).

20. Bray, D. Protein molecules as computational elements in living cells. Nature 376, 307–312 (1995).

21. Pandi, A. et al. Metabolic perceptrons for neural computing in biological systems. Nat. Commun. 10, 3880 (2019).

22. Kim, J., Hopfield, J. & Winfree, E. Neural network computation by in vitro transcriptional circuits. Adv. Neural Inf. Process. Syst. 17, 681–688 (2004).

23. van der Linden, A. J. et al. DNA input classification by a riboregulator-based cell-free perceptron. ACS Synth. Biol. 11, 1510–1520 (2022).

24. Genot, A. J., Fujii, T. & Rondelez, Y. Scaling down DNA circuits with competitive neural networks. J. R. Soc. Interface 10, 20130212 (2013).

25. Lakin, M. R. & Stefanovic, D. Supervised learning in adaptive DNA strand displacement networks. ACS Synth. Biol. 5, 885–897 (2016).

26. Evans, C. G., O’Brien, J., Winfree, E. & Murugan, A. Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly. Nature 625, 500–507 (2024).

27. Pei, R., Matamoros, E., Liu, M., Stefanovic, D. & Stojanovic, M. N. Training a molecular automaton to play a game. Nat. Nanotechnol. 5, 773–777 (2010).

28. Kim, J., Khetarpal, I., Sen, S. & Murray, R. M. Synthetic circuit for exact adaptation and fold-change detection. Nucleic Acids Res. 42, 6078–6089 (2014).

29. Nakakuki, T. et al. DNA reaction system that acquires classical conditioning. ACS Synth. Biol. 13, 521–529 (2024).

30. Rojas, R. Neural Networks: A Systematic Introduction (Springer, 2013).

31. MacQueen, J. Some methods for classification and analysis of multivariate observations. In Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability (eds Le Cam, L. M. & Neyman, J.) Vol. 1, 281–297 (University of California Press, 1967).

32. Yurke, B., Turberfield, A. J., Mills Jr, A. P., Simmel, F. C. & Neumann, J. L. A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000).

33. Soloveichik, D., Seelig, G. & Winfree, E. DNA as a universal substrate for chemical kinetics. Proc. Natl Acad. Sci. USA 107, 5393–5398 (2010).

34. Chen, Y.-J. et al. Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8, 755–762 (2013).

35. Srinivas, N., Parkin, J., Seelig, G., Winfree, E. & Soloveichik, D. Enzyme-free nucleic acid dynamical systems. Science 358, eaal2052 (2017).

36. Qian, L. & Winfree, E. A simple DNA gate motif for synthesizing large-scale circuits. J. R. Soc. Interface 8, 1281–1297 (2011).

37. Qian, L. & Winfree, E. Scaling up digital circuit computation with DNA strand displacement cascades. Science 332, 1196–1201 (2011).

38. Thubagere, A. J. et al. Compiler-aided systematic construction of large-scale DNA strand displacement circuits using unpurified components. Nat. Commun. 8, 14373 (2017).

39. Johnson, H. A. & Condon, A. A coupled reconfiguration mechanism for single-stranded DNA strand displacement systems. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (eds Ouldridge, T. E. & Wickham, S. F. J.) Vol. 238, 3:1–3:19 (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2022).

40. Yang, X., Tang, Y., Traynor, S. M. & Li, F. Regulation of DNA strand displacement using an allosteric DNA toehold. J. Am. Chem. Soc. 138, 14076–14082 (2016).

41. Haley, N. E. et al. Design of hidden thermodynamic driving for non-equilibrium systems via mismatch elimination during DNA strand displacement. Nat. Commun. 11, 2562 (2020).

42. Deng, L. The MNIST database of handwritten digit images for machine learning research [best of the web]. IEEE Signal Process. Mag. 29, 141–142 (2012).

43. Seelig, G., Soloveichik, D., Zhang, D. Y. & Winfree, E. Enzyme-free nucleic acid logic circuits. Science 314, 1585–1588 (2006).

44. Baldwin, J. M. A new factor in evolution. Am. Nat. 30, 441–451 (1896).

45. Hinton, G. E. & Nowlan, S. J. How learning can guide evolution. Complex Syst. 1, 495–502 (1987).

46. Genot, A. J., Bath, J. & Turberfield, A. J. Reversible logic circuits made of DNA. J. Am. Chem. Soc. 133, 20080–20083 (2011).

47. DelRosso, N. V., Hews, S., Spector, L. & Derr, N. D. A molecular circuit regenerator to implement iterative strand displacement operations. Angew. Chem. Int. Ed. 56, 4443–4446 (2017).

48. Scalise, D., Dutta, N. & Schulman, R. DNA strand buffers. J. Am. Chem. Soc. 140, 12069–12076 (2018).

49. Garg, S. et al. Renewable time-responsive DNA circuits. Small 14, 1801470 (2018).

50. Hahn, J. & Shih, W. M. Thermal cycling of DNA devices via associative strand displacement. Nucleic Acids Res. 47, 10968–10975 (2019).

51. Clamons, S., Qian, L. & Winfree, E. Programming and simulating chemical reaction networks on a surface. J. R. Soc. Interface 17, 20190790 (2020).

52. Takinoue, M. DNA droplets for intelligent and dynamical artificial cells: from the viewpoint of computation and non-equilibrium systems. Interface Focus 13, 20230021 (2023).

53. Wang, S. S. & Ellington, A. D. Pattern generation with nucleic acid chemical reaction networks. Chem. Rev. 119, 6370–6383 (2019).

54. Mordvintsev, A., Randazzo, E., Niklasson, E. & Levin, M. Growing neural cellular automata. Distill 5, e23 (2020).

55. Randazzo, E., Mordvintsev, A., Niklasson, E., Levin, M. & Greydanus, S. Self-classifying MNIST digits. Distill 5, e00027–002 (2020).

56. Lopez, R., Wang, R. & Seelig, G. A molecular multi-gene classifier for disease diagnostics. Nat. Chem. 10, 746–754 (2018).

57. Zhang, C. et al. Cancer diagnosis with DNA molecular computation. Nat. Nanotechnol. 15, 709–715 (2020).

58. Cangialosi, A. et al. DNA sequence-directed shape change of photopatterned hydrogels via high-degree swelling. Science 357, 1126–1130 (2017).

59. Fern, J. & Schulman, R. Modular DNA strand-displacement controllers for directing material expansion. Nat. Commun. 9, 3766 (2018).

60. Stern, M. & Murugan, A. Learning without neurons in physical systems. Annu. Rev. Condensed Matter Phys. 14, 417–441 (2023).

61. Sanger, T. D. Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Netw. 2, 459–473 (1989).

62. Al-Harbi, S. H. & Rayward-Smith, V. J. Adapting k-means for supervised clustering. Appl. Intell. 24, 219–226 (2006).

63. Dirks, R. M., Bois, J. S., Schaeffer, J. M., Winfree, E. & Pierce, N. A. Thermodynamic analysis of interacting nucleic acid strands. SIAM Rev. 49, 65–88 (2007).

64. Fornace, M. E. et al. NUPACK: analysis and design of nucleic acid structures, devices, and systems. Preprint at https://doi.org/10.26434/chemrxiv-2022-xv98l (2022).

65. Cherry, K. M. & Qian, L. Supervised learning in DNA neural networks [Data set]. CaltechDATA https://doi.org/10.22002/5bvkt-r7y16 (2025).

Acknowledgements

We thank G. Gowri for preliminary investigation of an activatable gate motif; S. Badelt and E. Winfree for evaluation of a chemical reaction network to DNA strand-displacement implementation scheme using Peppercorn; C. Evans for providing information on how to install and use StickyDesign; D. Scalise, T. Song and E. Winfree for discussions and suggestions; and R. M. Murray for sharing an acoustic liquid handler. This research received support through Schmidt Sciences, LLC. K.M.C. and L.Q. were also supported by an NSF grant (1908643).

Author information

Authors and Affiliations

1. Bioengineering, California Institute of Technology, Pasadena, CA, USA

Kevin M. Cherry & Lulu Qian

2. Computer Science, California Institute of Technology, Pasadena, CA, USA

Lulu Qian

3. Computation and Neural Systems, California Institute of Technology, Pasadena, CA, USA

Lulu Qian

Contributions

K.M.C. and L.Q. initiated the project and came up with the key mechanisms. K.M.C. designed and performed the experiments. K.M.C. and L.Q. developed the model, performed the simulations, analysed the data and wrote the paper. L.Q. guided the project.

Corresponding author

Correspondence to Lulu Qian.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Anne Condon and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Criteria of learning.

Independence: the same set of 100 input strands were used for training and testing, satisfying the independence criteria. Integration: training patterns presented in any desired order were stored into two 100-bit memories, satisfying the integration criteria. Generality: while above-average examples of handwritten digits were used for training, a wider range of digits were correctly classified for testing, satisfying the generality criteria. Stability: some testing experiments were performed days after training, satisfying the stability criteria. The wait time is mainly limited by DNA degradation in magnesium, and in principle could be extended to at least weeks, or months if stored in a sodium buffer, and years if the molecules are lyophilized. Accuracy: handwritten digits outside of a 20% margin in the weighted sum space were used for testing, indicating a lower bound of 53% classification accuracy for ‘0’ and 83% for ‘1’ (same as the top plots in Fig. S31d, with more details explained in Supplementary Note 5.12). Reusability: each trained DNA neural network was distributed into 24 aliquots for distinct tests (12 per class) in parallel. Flexility: training and testing inputs were all binary signals with high and low concentrations representing ON and OFF states, respectively. Learned memories were composed of analog signals representing the average of all training patterns, but could only be used to classify binary tests.

Extended Data Fig. 2 Components of learning.

a, DNA neural network that uses fixed memories to process information, like a hardwired processor. b, DNA neural network composed of a memory device and a processor, capable of developing memories based on training data and using the memories to process subsequent test data. The four highlighted contents—motif characterization, activatable memories, learned weights, and testing after training—correspond to four sections in this paper. c, Seesaw DNA circuit implementation of the memory device and the processor. Each two-sided circle is a node representing a seesaw motif, with the black number above it indicating the identity of the node. A total of 2n + 6 nodes are required for implementing a learning neural network with 2 memories that each has n bits. The location and absolute value of each red number (e.g. 1.5) or variable (e.g. x_1) indicate the identity and initial concentration of a DNA species, respectively. A red number on a wire connected to a node indicates a free signal species, which can be an input Xi, label Lj, or fuel strand XFi or YFj. A negative red number inside a node indicates a threshold species Thi. A positive red number inside a node indicates a gate species, which can be an inhibited activator \(Ac{t}_{i,j}^{* }\), inhibited weight \({W}_{i,j}^{* }\), summation gate SGj, or restoration gate RGj. A red number on a wire that stops perpendicularly at two wires indicates an annihilator species Anhj,k. A negative red number inside a half node with a zigzag arrow indicates a reporter species Repj. A black arrowhead pointing to the center of a node indicates a set of activators that each activates a specific gate species within the node; the order of the wires joining at the arrowhead corresponds to the order of the gates that each wire activates (e.g. the top wire activates the top gate). Initial concentrations of all species in the supervised learning layer and weight activation and multiplication layer are shown for the situation where a single bit in the training or test pattern is on (xi = 1). For patterns with b out of n bits being on, the initial concentrations will be divided by b. For example, with 100-bit training and testing patterns that have 20 1s, the initial concentration of each inhibited activator and inhibited weight is 1.5/20 = 0.075×, that of each threshold is 0.5/20 = 0.025×, and that of each fuel is 3/20 = 0.15×. Species concentrations in other layers do not change with b. Standard concentration (1×) is 50 nanomolar (nM) here and in all other figures.

Extended Data Fig. 3 Collection of motifs.

Integration gate motif produces an output with a steady-state concentration expected to be the total initial concentration of all inputs. The ideal reaction is stoichiometric and irreversible, implemented with an reversible reaction facilitated by an excess gate. Amplification gate motif produces multiple outputs, each of which has a steady-state concentration expected to be the initial concentration of the gate that produces the output if and only if the input exceeds the threshold. A pair of ideal reactions includes a faster thresholding reaction and a slower catalytic reaction, enabling the input to be consumed before any leftover input can effectively produce the outputs. The catalytic reaction is implemented with a pair of reversible reactions facilitated by an excess fuel. Activatable amplification gate motif has all gates initially inhibited and only become functional if an activator is present. The steady-state output concentration is expected to be the initial concentration of the activator if and only if the input exceeds the threshold. The ideal reactions include an additional activation reaction facilitated by an excess inhibited gate. The activator is also considered a free signal species. To contrast with activator signals, the input and output can be referred to as regular signals. Activatable transformation gate motif produces an output in the form of an activator for a downstream gate when an input and activator are both present. Only one of all activators will be on, selectively turning on a gate and producing a specific output whose steady-state concentration is expected to be the initial input concentration. A reporter converts an output to fluorescence for readout. An annihilator facilitates the competition between two signals, with whichever has a larger initial concentration remains.

Extended Data Fig. 4 Characterization of the activatable weight motif.

a, Sequence-level diagrams of inhibited weight \({W}_{1,1}^{* }\), activator Act1,1 (renamed as ssAct1,1 for single-stranded activator, to contrast with double-stranded activator dsAct1,1 produced from learning), input X_1, fuel XF_1, and reporter. The reporter containing a fluorophore and a quencher modified strand reacts with the output of this reaction (P1,1), resulting in creased fluorescence signal, which is then normalized to concentration based on control experiments. For simplicity, instead of using a distinct Pj domain for each output Pi,j, a single P domain was used for all experiments in this figure, allowing for fluorescence readout using the same reporter. b, Sequence-level diagrams of inhibited weight \({W}_{1,2}^{* }\) and single-stranded activator ssAct1,2. The input, fuel, and reporter are the same as shown in panel a. c, Sequence-level diagrams of double-stranded activators dsAct1,1 and dsAct1,2. d,e, Fluorescence kinetics experiments and simulations with distinct activatable weight gates and single-stranded (d) or double-stranded (e) activators. Fluorescence kinetics data (dotted trajectories) are overlaid with mass-action simulations of chemical kinetics by solving ordinary differential equations (solid trajectories). Details of modeling see Supplementary Note 2.1. Double-stranded activators produced during training (Fig. 2e) exhibited faster kinetics than single-stranded activators (Fig. 2a) due to the additional stacking bond between Xi and Tj domains. The small variations of reaction kinetics across distinct inhibited weights and activators can be explained by the sequence of the Tj domain and the minor secondary structure within the Ai and U* domains. 1 × indicates a standard concentration of 50 nM. Relative concentrations of the inhibited weight \({W}_{i,j}^{* }\), fuel XFi, and reporter are 1.5×, 3×, and 2×, respectively. f, Crosstalk evaluation. The first two hours of the fluorescence kinetics data are shown in Fig. 2d whereas endpoint data of output concentrations (relative to the standard concentration) at 10 hours are shown here.

Source data

Extended Data Fig. 5 Characterization of the learning motif.

a, Sequence-level diagrams of inhibited activator \(Ac{t}_{1,1}^{* }\), input X_1, and label L_1. The \({5}^{{\prime} }\) end of the bottom strand in the inhibited activator is modified with a fluorophore, and the \({3}^{{\prime} }\) end of the input strand is modified with a quencher. The double-stranded activator produced from this reaction has the quencher adjacent to the fluorophore, resulting in decreased fluorescence, which is then normalized to increased activator concentration based on control experiments. b, Sequence-level diagrams of inhibited activator \(Ac{t}_{1,2}^{* }\), input X_1, and label L_2. c, Sequence-level diagrams of inhibited activators \(Ac{t}_{5,1}^{* }\) and \(Ac{t}_{5,2}^{* }\), along with input X_5. Label strands are the same as shown in panels a and b. d, Fluorescence kinetics experiments and simulations with distinct learning gates and input-label pairs. Fluorescence kinetics data (dotted trajectories) are overlaid with mass-action simulations of chemical kinetics by solving ordinary differential equations (solid trajectories). Details of modeling see Supplementary Note 2.2. The small variations of reaction kinetics across distinct learning gates can be explained by the sequence of the Lj domain and the minor secondary structure within the U* and Xib* domains. 1 × indicates a standard concentration of 50 nM. e, Crosstalk evaluation. Excess label (5×) was used. Four distinct fluorophores, ATTO488, ATTO550, ATTO590, and ATTO647 were used on \(Ac{t}_{1,1}^{* }\), \(Ac{t}_{3,1}^{* }\), \(Ac{t}_{5,1}^{* }\), and \(Ac{t}_{7,1}^{* }\), respectively. The same set of fluorophores with a different order were used on the other four inhibited activators. Eight hours of fluorescence kinetics data are shown in Fig. 2i whereas endpoint data of activator concentrations (relative to the standard concentration) at 8 hours are shown here. f, Reversibility evaluation. Before 16 hours, all fluorescence kinetics trajectories are repeats of the same sample with 1.5 × learning gate (\(Ac{t}_{5,1}^{* }\) or \(Ac{t}_{5,2}^{* }\)), 0.5 × input (X_5), and 5 × label (L_1 or L_2). Label inhibitor (Inh_1 or Inh_2) with varying concentrations was added at 16 hours and fluorescence data was collected until 32 hours. No fluorescence decrease was observed with increased inhibitor concentration, suggesting robust irreversibility of the learning gate.

Source data

Extended Data Fig. 6 Activatable memories.

a-f, Simulations and fluorescence kinetics experiments with 12 test patterns per class on activated memories of 0 and 1 (a,b), 3 and 4 (c,d), or 6 and 7 (e,f) in memory 1 and 2 (a,c,e), respectively, or swapped in memory 2 and 1 (b,d,f). Difference between two output concentrations (Y_1 − Y_2) at the end of the experiments are shown for all test patterns sorted according to their distance to the diagonal line in the weighted sum space. For the left set of patterns, the distance decreases from left to right; for the right set of patterns, the distance increases.

Source data

Extended Data Fig. 7 Learned weights with training patterns 0 and 1.

a, Overlaid training patterns (10 per class) for learning handwritten digits 0 and 1. b,c, Fluorescence kinetics data, endpoint signal values at 4 hours, and error statistics for learning 1 first into memory 2 and then 0 into memory 1 (b) or learning 0 first into memory 2 and then 1 into memory 1.

Source data

Extended Data Fig. 8 Learned weights with training patterns 3 and 4 or 6 and 7.

a, Overlaid training patterns (10 per class) for learning handwritten digits 3, 4, 6 and 7. b,c, Fluorescence kinetics data, endpoint signal values at 4 hours, and error statistics for learning 3 first into memory 2 and then 4 into memory 1 (b) or learning 6 first into memory 2 and then 7 into memory 1.

Source data

Extended Data Fig. 9 Evaluating the scalability of pattern classification with learned weights.

Fluorescence kinetics data for 8 test patterns of two classes are shown in two separate plots. Difference between two outputs at the end of the 8-hour experiments are shown in the bar chart, next to the learned weights. In learned weights, gray pixels indicate unused memory bits with no associated molecules. White pixels indicate activatable but not activated memory bits with inhibited activator and inhibited weights that are present throughout training and testing. Colored pixels indicate memory bits activated by training patterns and their labels.

Source data

Extended Data Fig. 10 100-bit pattern classification with learned weights.

a-c, Simulations (solid trajectories) and fluorescence kinetics experiments (dotted trajectories) of pattern classification for 72 representative cases after three distinct training processes with MNIST digits 0 and 1 (a), 3 and 4 (b), and 6 and 7 (c).

Source data

Supplementary information

Supplementary Information

Supplementary Methods, Notes, Figs. 1–33, Tables 1–19 and References.

Source data

Source Data Figs. 2–6 and Extended Data Figs. 4–10.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Cherry, K.M., Qian, L. Supervised learning in DNA neural networks. Nature 645, 639–647 (2025). https://doi.org/10.1038/s41586-025-09479-w

- Received: 06 January 2025

- Accepted: 30 July 2025

- Published: 03 September 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09479-w

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Nonlinear decision-making with enzymatic neural networks

Article 19 October 2022

Molecular convolutional neural networks with DNA regulatory circuits

Article 04 July 2022

Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly

Article Open access 17 January 2024

Article Open access Published: 10 September 2025

Long-range PM2.5 pollution and health impacts from the 2023 Canadian wildfires

Qiang Zhang,

Yuexuanzi Wang,

Qingyang Xiao,

Guannan Geng,

Steven J. Davis,

Xiaodong Liu,

Jin Yang,

Jiajun Liu,

Wenyu Huang,

Changpei He,

Binhe Luo,

Randall V. Martin,

Michael Brauer,

James T. Randerson &

…

Kebin He

Nature volume 645, pages 672–678 (2025)

Abstract

Smoke from extreme wildfires in Canada adversely affected air quality in many regions in 20231,2. Here we use satellite observations, machine learning and a chemical transport model to quantify global and regional PM2.5 (particulate matter less than 2.5 μm in diameter) exposure and human health impacts related to the 2023 Canadian wildfires. We find that the fires increased annual PM2.5 exposure worldwide by 0.17 μg m–3 (95% confidence interval, 0.09–0.26 μg m–3). North America had the largest increase in annual mean exposure (1.08 μg m–3; 0.82–1.34 μg m–3), but there were also increases in Europe (0.41 μg m–3; 0.32–0.50 μg m–3) owing to long-range transport. Annual mean PM2.5 exposure in Canada increased by 3.82 μg m–3 (3.00–4.64 μg m–3). In the USA, the contribution of the Canadian fires to increased PM2.5 was 1.49 μg m–3 (1.22–1.77 μg m–3), four times as large as the contribution from the 2023 wildfires originating in the USA. We find that 354 million (277–421 million) people in North America and Europe were exposed to daily PM2.5 air pollution caused by Canadian wildfires in 2023. We estimate that 5,400 (3,400–7,400) acute deaths in North America and 64,300 (37,800–90,900) chronic deaths in North America and Europe were attributable to PM2.5 exposure to the 2023 Canadian wildfires. Our results highlight the far-reaching PM2.5 pollution and health burden that large wildfires can have in a single year.

Similar content being viewed by others

Main

Wildfires impact the global carbon cycle3,4, ecosystems5,6, air quality7,8,9,10,11 and human health12,13,14,15. Among these impacts, the contribution of wildfires to global PM2.5 pollution has been steadily increasing in recent years, with the largest increase in North America8,9,10,11. Between May and September of 2023, severe wildfires in Canada burned a total of 15 million ha of forest (about 4% of the total forest area in Canada and more than 7 times the annual mean burned area for 1983–2022) and resulted in vast carbon emissions (647 TgC)16,17. Smoke generated from the Canadian wildfires was not only transported across North America and led to air-quality alerts in many regions of the USA[1] but also transported across the North Atlantic to reach Europe and Asia[2], which underscored that severe wildfires do not have only local consequences. Although PM2.5 exposure from wildfires has been investigated in different ways8,9,10,11,18,19,20 and transboundary fire pollution episodes have been identified in previous studies21,22,23,24,25,26,27,28,29, the impacts of such extreme wildfires on global air quality and human health remain underexplored30,31,32. Given the potential continued impact from projected increase in future wildfires33,34,35, quantifying exposure to this air pollution and the level of health impact at a global extent can inform responses, including fire monitoring and forecasting, fire suppression, land management and landscape-scale fuel treatments, and climate mitigation more broadly.

Here we combine several global models and observation datasets to develop a near-real-time framework to estimate global and regional PM2.5 exposure (that is, population-weighted mean PM2.5 concentration) and deaths attributable to the 2023 Canadian wildfires (Extended Data Fig. 1). Details of our analytic approach are in Methods. In summary, we first use the GEOS-Chem chemical transport model (a global three-dimensional model of atmospheric chemistry driven by meteorological input from the Goddard Earth Observing System)[36] and three near-real-time global fire emission inventories (the Global Fire Emissions Database (GFED)[37], the Quick Fire Emissions Dataset (QFED)[38] and the Global Fire Assimilation System (GFAS)[39]) to derive global daily PM2.5 concentrations and the fractional share of these concentrations related to wildfires. We then use a machine-learning approach to retrieve the global daily PM2.5 concentration from a range of data, including ground-monitoring measurements, satellite retrievals, reanalysis data and GEOS-Chem model simulations (Supplementary Fig. 1), and attribute the share of retrieved total PM2.5 concentration to wildfires using the previously simulated fractional contribution. By performing a series of evaluation and sensitivity tests to the three inventories (Supplementary Table 1), the results presented hereafter correspond to estimates with the GFED as a priori input and the impacts of using different inventories on our conclusions are discussed (‘Discussion’). We further attribute fire-related PM2.5 concentrations to wildfires in different source regions (that is, Eastern Canada, Western Canada, Western USA, Eastern USA and other global regions) by using a zero-out approach with the GFED inventory (Supplementary Table 2). Finally, we use previously established exposure–response functions15,40 to estimate acute and chronic deaths attributable to PM2.5 exposure from Canadian wildfires. It should be noted that various exposure–response functions are available and that the mortality estimates are highly dependent on the function used (‘Discussion’). Unless otherwise specified, ranges of results reported reflect the 95% confidence interval (CI) and numbers of deaths reported reflect the median rounded to the nearest hundred.

Primary emissions of carbon dioxide (CO_2) and air pollutants from the 2023 Canadian wildfires are substaintially different in three bottom-up fire emission inventories (that is, GFED, QFED and GFAS), ranging from 139 TgC to 658 TgC, from 0.55 Tg to 0.76 Tg black carbon, and from 8.9 Tg to 15.0 Tg organic carbon (Extended Data Fig. 2a). Despite differences in the magnitude of emissions, there is consensus among the three bottom-up inventories that the 2023 Canadian fire emissions were the highest in at least 20 years. Emissions of CO_2 and primary aerosols in 2023 were 4.9–10.7-times higher than the annual average for 2003–2022 and 2.9–5.1-times higher than in 2021 (the year with the next highest emissions; Extended Data Fig. 2b).

Transboundary smoke exposure

We estimate that wildfires worldwide accounted for a global annual mean PM2.5 exposure of 1.32 μg m–3 (95% CI, 0.66–1.98 μg m–3) in 2023. Of this total, the Canadian fires account for 0.17 μg PM2.5  m–3 (95% CI, 0.09–0.26 μg PM2.5 m–3), or 13% of the total fire-related PM2.5 exposure. Despite this relatively small global impact, PM2.5 smoke from Canadian fires spread across the North American continent and was transported to Europe (Fig. 1a; global region definition presented in Extended Data Fig. 3a). Indeed, the Canadian fires account for more than half of fire-related PM2.5 exposure along the western coasts of Europe (Fig. 1e,h), and increased annual mean PM2.5 exposure of 1.08 μg m–3 (95% CI, 0.82–1.34 μg m–3) and 0.41 μg m–3 (95% CI, 0.32–0.50 μg m–3) in North America and Europe, respectively (Extended Data Table 1). In Europe, 90% of the total population (620 million) were exposed to more than 0.32 μg m–3 of increased annual mean PM2.5 concentrations owing to the 2023 Canadian wildfires. The contribution of the 2023 Canadian wildfires to the annual mean PM2.5 exposure in other world regions was comparatively small and statistically insignificant when compared with the interannual variability (Methods).

Fig. 1: Global and regional PM2.5 pollution from the 2023 Canadian wildfires.

a, Global annual mean PM2.5 concentrations from Canadian fires in 2023. b–d, Regional annual mean PM2.5 exposure (population-weighted mean) in Canada (b), the USA (c) and Europe (d) from Canadian fires in 2023. e, Global fraction of annual mean PM2.5 concentration from the 2023 Canadian fires in total fire-related PM2.5 concentration. f–h, Regional fraction of annual mean PM2.5 exposure in Canada (f), the USA (g) and Europe (h) from the 2023 Canadian fires in total fire-related PM2.5 exposure.

Source Data

Nearer to and directly downwind of the wildfires, impacts were much more substantial. Because wildfires in the USA and elsewhere affected PM2.5 pollution at the same time as the Canadian fires, we separately analyse PM2.5 exposure in Canada and the USA related to fire emissions from five different regions: Eastern Canada, Western Canada, the Eastern USA, the Western USA and fires in all other regions (see source region definitions and the Environmental Protection Agency’s delineation of North American ecological regions in Extended Data Fig. 3b and Supplementary Fig. 2).

Extended Data Fig. 4 shows the annual mean PM2.5 concentrations in Canada and the USA that are related to the fires in each country. Although smoke from US fires affected pollution concentrations along the southern boundary of Western Canada, fire-related PM2.5 across Canada as a whole was dominated by its own fires. Annual mean PM2.5 exposure in Canada itself increased by 3.82 μg m–3 (95% CI, 3.00–4.64 μg m–3) owing to its own fires (maximum monthly mean exposure of 16.07 μg m–3 in June; Extended Data Fig. 5). PM2.5 hotspots in Canada include the James Bay region of Quebec and large areas of Alberta, Saskatchewan and the Northwest Territories (Extended Data Fig. 4a), which is consistent with the distribution of burned area and sources of primary emissions (Extended Data Fig. 6). Although wildfires in Western Canada and Eastern Canada had comparable impacts on PM2.5 concentrations in Eastern Canada, the wildfires in Eastern Canada had only a small effect on pollution in Western Canada (Fig. 2; see impacted region definitions in Extended Data Fig. 3c).

Fig. 2: The 2023 annual mean PM2.5 exposure in Canada and the USA owing to fires from different source regions.

Each cell in the grid shows population-weighted mean PM2.5 concentrations in each impacted region of Canada and the USA (indicated by the column) by fire source regions (indicated by the row). The definition of wildfire source regions in Canada and the USA are presented in Extended Data Fig. 3b, and the impacted regions are defined in Extended Data Fig. 3c. ‘Other fires’ means fires from other global regions apart from Canada and the USA.

Source Data

In the USA, the 2023 Canadian fires accounted for 1.49 μg m–3 (95% CI, 1.22–1.77 μg m–3) of the annual mean PM2.5 exposure (maximum monthly mean exposure of 8.04 μg m–3 in June; Extended Data Fig. 5), which is four times as large as the 0.35 μg m–3 (95% CI, 0.29–0.42 μg m–3) exposure related to fires in the USA in the same year. As shown in Extended Data Fig. 4c, PM2.5 concentrations in the USA were impacted by smoke plumes from Canada that extended over large areas of the Rocky Mountains, the Midwest, Ohio Valley and the Northeast regions. The US Midwest was especially affected: the annual mean PM2.5 exposure in the region increased by 3.13 μg m–3 (95% CI, 2.82–3.44 μg m–3; Fig. 2). In comparison, the annual mean PM2.5 exposures increased by 2.35 μg m–3 (95% CI, 2.11–2.59 μg m–3) in Ohio Valley, 2.52 μg m–3 (95% CI, 2.27–2.78 μg m–3) in the Northeast, and 1.92 μg m–3 (95% CI, 1.69–2.15 μg m–3) in the Rocky Mountains. At the state level, the largest PM2.5 impacts were in North Dakota (3.85 μg m–3; 95% CI, 3.39–4.31 μg m–3). Meanwhile, the impacts of the Canadian fires on the Southwest and West regions of the USA were modest. Nonetheless, in 7 of the 9 regions of the continental USA analysed, the Canadian fires increased the annual PM2.5 exposure by more than 0.5 μg m–3, and increased the annual PM2.5 exposure by more than 1 μg m–3 for 187 million Americans (57% of total; Extended Data Fig. 7). As in Canada, the downwind effects of the 2023 fires in Western Canada affected US air quality more than the fires in Eastern Canada: 60% of the annual exposure in the USA related to Canadian fires was from Western Canada.

Figure 3 shows the daily and cumulative PM2.5 exposure in Canada, the USA and Europe related to different sources of fire emissions. In Canada, there were frequent large spikes of air pollution throughout the spring, summer and autumn of 2023 related in particular to persistent fires in Western Canada (Fig. 3a). The magnitude of pollution episodes was mostly lower in the USA, but fires in Eastern Canada caused two spikes in June that led to the national daily average PM2.5 exposure exceeding 30 μg m–3 (Fig. 3b and Supplementary Table 3). During these two episodes, a low-pressure system over the Canadian Maritime Provinces coupled with a high-pressure ridge to the west channelled a plume of pollution into population centres of the Eastern USA (Supplementary Figs. 3–5). In contrast, wildfires in Western Canada had a persistent and overall larger impact on US air quality throughout the fire season (Fig. 3e). Smoke from these western fires was transported eastwards along the northern margin of the Rocky Mountains and then spread first southeastwards into the Great Plains and then back up into the northeast owing to the greatly developed subpolar low pressure (Supplementary Fig. 6).

Fig. 3: Daily and cumulative PM2.5 exposures from different sources in 2023.

a–c, Daily PM2.5 exposure in Canada (a), the USA (b) and Europe (c) from fire sources in different source regions, anthropogenic sources and other sources (for example, biogenic, dust and sea salt). d–f, Cumulative fire-related PM2.5 exposures in Canada (d), the USA (e) and Europe (f) from different source regions. The definitions of wildfire source regions in Canada and the USA are presented in Extended Data Fig. 3b. ‘Other fires’ means fires from other global regions apart from Canada and the USA.

Source Data

As shown in Fig. 1d, the 2023 Canadian fires also had broad impacts on PM2.5 exposure in Western Europe, especially in Mediterranean countries such as Spain, Italy and France (also see Methods and Supplementary Figs. 7–12). The smoke plumes from Canada were transmitted eastwards into Europe by a westerly airflow situated over the mid-latitudes and crossed the North Atlantic (Supplementary Fig. 7). The largest episodes of trans-Atlantic pollution occurred in late June owing to the large polewards pressure gradient between the Azores high and the Icelandic low, leading to widespread air pollution in Europe (Supplementary Fig. 8). As in the USA, though, the Western Canadian fires led to greater cumulative exposure in Europe (Fig. 3f).

Health impacts

We further quantify the extent of the Canadian fires’ impacts on global health by the number of ‘Canada smoke days’ in which both (1) the daily mean PM2.5 concentrations exceeded 15 μg m−3 (the recommended 24-hour guideline levels of the World Health Organization (WHO)) and (2) the Canadian fires accounted for at least 50% of the total 24-hour average PM2.5 concentration. With these criteria, 354 million (95% CI, 277–421 million) people in North America and Europe were exposed to at least 1 Canada smoke days in 2023, with a total of 4.84 billion person-days of exposure in that year (Extended Data Table 1). In the USA alone, 267 million (95% CI, 222–273 million) people (79% of total) were exposed to at least 1 Canada smoke days—3.69 billion person-days of exposure. In addition, 98% of the Canadian population (38.1 million people; 95% CI, 37.0–38.1 million) experienced such Canada smoke days, with an average of 27.1 days per person. Although the annual mean PM2.5 exposure from Canadian fires was larger in Canada than in the USA, total person-days exposure to Canada smoke days was three-times greater in the USA owing to the much larger population in downwind areas of the USA. Similarly, 47.7 million (95% CI, 17.0–104.7 million) people in Europe were exposed to Canada smoke days (more people than in Canada itself), with an average of 1.0 days per person, mostly during the period between 26 June and 7 July. In turn, we estimate 5,400 (95% CI, 3,400–7,400) acute deaths attributable to exposure on those Canada smoke days, including 4,100 (95% CI, 2,600–5,600) in the USA and 1,300 (95% CI, 800–1,800) in Canada (Fig. 4a).

Fig. 4: Global acute and chronic deaths attributable to the 2023 Canadian wildfires.

a, Acute deaths. b, Chronic deaths. Errors bars denote the 95% CI of the estimates. The asterisk indicates regions where the Canadian-wildfire-related annual mean PM2.5 concentration is not statistically significant compared with the interannual variation of PM2.5 concentration.

Source Data

With 5 months of continuous exposure to smoke from the 2023 Canadian wildfires (Fig. 3), the chronic health impacts of the 2023 Canadian wildfires were also substantial and widespread (Fig. 4b). Worldwide, we estimate that 82,100 (95% CI, 47,700–116,500) people died prematurely attributable to chronic smoke exposure from the 2023 Canadian wildfires (or 0.9% of the total PM2.5-related deaths and 0.1% of total all-cause deaths worldwide in 2023), with 64,300 (95% CI, 37,800–90,900) deaths occurring in North America and Europe. Of these deaths, 41,900 (95% CI, 28,400–55,400) occurred in North America, including 33,000 (95% CI, 22,500–43,500) in the USA and 8,300 (95% CI, 5,800–10,800) in Canada (accounting for about 17% and 39% of total PM2.5 attributable deaths or 1.2% and 2.9% of total all-cause deaths in those countries in 2023, respectively). Longer-range health impacts were also substantial. In Europe, we estimate 22,400 (95% CI, 14,900–29,900) attributable chronic deaths in Europe related to the intercontinental transport of smoke from the Canadian fires (Fig. 4b), accounting for 3.8% of total PM2.5 attributable deaths and 0.3% of total all-cause deaths in 2023.

Discussion

Our results quantify the magnitude and extent of smoke pollution and health impacts related to the 2023 Canadian wildfires. Although our analysis is focused on the year 2023, we also compare the results with 2021 and 2017, which had the second- and third-greatest wildfire emissions from Canada since 2000 (Extended Data Fig. 2b). The 2023 Canadian wildfires induced 2.6-times and 5.3-times higher global annual PM2.5 exposure than that of 2021 and 2017, respectively, demonstrating the large impacts on global air pollution. Previous studies have argued that wildfire-related PM2.5 has influenced trends in annual PM2.5 concentration in the USA since 2016[9]. With increasing PM2.5 exposure from Canadian wildfires from 2017 to 2023 (2017, 0.26 μg m–3; 2021, 0.55 μg m–3; 2023, 1.49 μg m–3), our results show that transboundary smoke pollution may have remarkably contributed to the reversed PM2.5 trend in the USA.

Our model can be evaluated in multiple ways. First, the station-based 20-fold cross-validation shows that the global daily PM2.5 concentrations we model agree well with surface observations (R^2 = 0.84, root-mean-squared error (RMSE) = 8.62 μg m–3; Extended Data Fig. 8) and are comparable to other recent studies10,41. Second, following a similar approach to ref. [10], modelled daily PM2.5 concentrations are compared with surface observations during fire events in Canada and the USA (Methods). During 20 such fire events in Canada and the USA (which together account for >80% of fire-related PM2.5 exposure in 2023), our results agree well with daily PM2.5 observations in both Canada (R^2 = 0.59, RMSE = 16.50 μg m–3) and the USA (R^2 = 0.78, RMSE = 12.50 μg m–3) (Extended Data Fig. 9 and Supplementary Table 4).

More importantly, to investigate the impact of different emission estimates in fire inventories42,43, we conduct two additional sensitivity analyses to derive global daily PM2.5 concentrations by using the QFED and the GFAS as the a priori inventory. In general, we found that the performances of the three inventories are comparable. Machine-learning-based global daily PM2.5 concentrations with the three fire inventories (that is, GFED, QFED and GFAS) show similar accuracy when comparing with surface observations in the sample-based cross-validation (R^2 = 0.87–0.88, RMSE = 7.46–7.92 μg m–3; Supplementary Fig. 13 and Supplementary Tables 5 and 6). During 20 selected fire events, modelled daily PM2.5 concentrations with the different fire inventories show consistent performance against surface observations in the USA (R^2 = 0.78–0.80, RMSE = 11.70–12.50 μg m–3) but moderate differences in Canada (R^2 = 0.59–0.75, RMSE = 12.83–16.50 μg m–3). Global fire-related annual PM2.5 exposure in 2023 estimated with the GFED and the GFAS are very close (1.32 μg m–3 and 1.30 μg m–3, respectively), whereas the QFED-based estimates (2.36 μg m–3) are 79% higher than the other two. In Canada, fire-related annual PM2.5 exposure estimated with the 3 inventories shows better agreement (3.75–4.49 μg m–3) than the global average. In the USA, GFED- and GFAS-based estimates on fire-related annual PM2.5 exposure in 2023 are close to each other, whereas the QFED-based estimates are 59–70% higher, as does the comparison with other recent studies (Supplementary Fig. 14). To put our results in context with recent analyses using a similar approach9,10,11,44, we present the GFED-based estimates in this work, and we believe that the impacts of fire inventory choice on our conclusions are minor given their similar fire-related PM2.5 exposure estimates in Canada.

Various exposure–response functions have been used in previous studies (Supplementary Tables 7–9) when estimating acute and chronic deaths attributable to wildfire PM2.5 exposure, including functions derived from global15,40,45,46 or regional47,48,49 meta-analysis and derived for all-cause mortality15,40,46,47,48,49,50 or cause-specific mortality[45]. Here we use widely used global pooled functions derived for all-cause mortality15,40 to estimate acute and chronic deaths given the global nature of this study. The estimated global acute and chronic deaths attributable to the 2023 Canadian wildfires varied by a factor of 4 (1,300–5,400) and 5 (31,000–152,000), respectively, when different exposure–response functions were used (Supplementary Tables 7 and 8; see Methods for details), indicating large variations in wildfire PM2.5 exposure–response functions and the urgent need for well-designed epidemiological studies. Even still, the overall conclusion of this study, that is, the enormous and far-reaching PM2.5 pollution and health burden from a single large wildfire, remain robust.

Our findings are subject to several important uncertainties and limitations. Fire emissions have large uncertainties in general owing to errors in emission factors and estimates of fuel burned[37], which are then propagated within chemical transport models such as the GEOS-Chem model we use, leading to uncertainties in both simulated PM2.5 concentrations and estimates of the contribution of fire emissions (Supplementary Figs. 15 and 16). Smoke-injection height is not considered in the GEOS-Chem simulation, which may lead to overestimates and underestimates of fire-related PM2.5 concentration in the fire source region and the downwind region, respectively[51]. The all-source estimates of PM2.5 exposure we develop are also subject to uncertainties derived from errors in input data and the machine-learning model itself (Supplementary Figs. 13 and 17). Finally, there are uncertainties in our estimates of attributable mortality owing to statistical methods and the limited epidemiology evidence on which exposure–response functions are based. In each case, we have assessed and quantified uncertainties by comprehensive analysis and sensitivity testing, integrating and aggregating errors in all steps through Monte Carlo, and we report 95% CIs for all of our main results. Further details about the calculation of uncertainties are in Methods.

Beyond these quantified uncertainties, we are cognizant of several limitations in our approach that might be improved by future studies. For example, the relatively coarse resolution of the GEOS-Chem model (2° × 2.5°) may underestimate or overestimate fire-related pollution exposure52,53 (it is noted that the baseline exposures are resolved at 0.1° × 0.1° resolution). Simulating long-range transport of wildfire-related PM2.5 and quantifying its contribution to total PM2.5 exposure are subject to uncertainties. After long-range transport, pollution from local sources may outweigh the contribution of the Canadian wildfires to the annual mean PM2.5 concentration. The contribution of the 2023 Canadian wildfires was statistically significant over North America and Europe when compared with the interannual variability in PM2.5 concentrations but statistically insignificant over other downwind regions (Methods and Supplementary Fig. 18).

The health impacts we estimate assume a uniform toxicity of different PM2.5 species, which may underestimate the health impacts of wildfire emissions that have a higher proportion of carbonaceous aerosols whose toxicity tends to be greater than that of other species54,55. Wildfire-related PM2.5 may also contain more oxidative and proinflammatory components that could increase oxidative potential during long-range transport, and thereby affect health effects in downwind regions56,57. These factors are not accounted for in current PM2.5 exposure–response functions and deserve further investigation. Although increased toxicity of wildfire-related PM2.5 compared with all-source PM2.5 has been observed, evidence of the health effects of wildfire-related PM2.5 is still limited13,58,59,60. In particular, some studies have reported mixed effects on acute health impacts in regions with limited sample size or varying analytic approaches15,59,60,61. Our estimates of chronic mortality are also estimated using an exposure–response function for all-source PM2.5 rather than for wildfire PM2.5 given the lack of epidemiological evidence. Further well-designed epidemiological studies on this topic are urgently needed. In addition, we limit our analysis of fire-related health impacts to attributable mortality; numerous studies have reported non-fatal impacts of acute wildfire smoke exposure13,58. Lastly, although we use ambient outdoor PM2.5 concentrations as the indicator of PM2.5 exposure during fire events, successfully limiting infiltration of PM2.5 into indoor environments can substantially reduce such exposure and related health impacts. Further investigation of the changes in human behaviour and related PM2.5 exposure during fire events will thus help to improve the accuracy of estimated health impacts in the future.

Nonetheless, our results robustly reveal that the 2023 Canadian wildfires led to substantial and extensive long-range PM2.5 pollution and health impacts. Given recent trends in the frequency and severity of boreal and temperate wildfires[62] and further projected increases in extreme fires under climate change33,34,35, the global health impacts of the wildfires we assess can be expected to continue and grow in the future. Although many places are investing in efforts to manage wildfire risks via landscape-scale fuels management and early suppression, the vast extent and remoteness of many fire-prone forests presents a daunting and long-term task. In the meantime, accurate air-quality forecasting and pollution alert systems may be quick and cost-effective options for reducing human exposure to wildfire smoke63,64. Given the relatively large differences among current fire emission inventories42,43, such forecast and alert systems could benefit from improved fire emission estimates based on advanced satellite observations. Moreover, the transboundary wildfire impacts we demonstrate suggest the potential value of international cooperation to monitor and prevent extreme wildfires.

Methods

Model framework

This study combines multiple datasets and models, as presented in Extended Data Fig. 1, to estimate the contribution of the 2023 Canadian wildfires to global PM2.5 exposure and health impacts under a near-real-time framework (http://tapdata.org.cn). We also analyse two additional years, 2021 and 2017, which were reported as the years with the second- and third-largest wildfire emissions in Canada since 2000 (Extended Data Fig. 2b), for comparison. We first used the GEOS-Chem chemical transport model[36] at a spatial resolution of 2° × 2.5° and 3 near-real-time global fire emission inventories, that is, the Global Fire Emissions Database version 4 with small fires (GFEDv4.1s)37,65, the Quick Fire Emissions Dataset version 2.5 (QFEDv2.5r1)[38] and the Global Fire Assimilation System version 1.2 (GFASv1.2)[39], to simulate the global daily PM2.5 concentrations and the fractional shares in total PM2.5 concentrations contributed by wildfire emissions using a zero-out approach. Second, to improve the spatial resolution and accuracy of the global daily PM2.5 estimation, we developed a machine-learning-based PM2.5 retrieval model that combines data from multiple sources, including ground-monitoring measurements, satellite retrievals, reanalysis data and GEOS-Chem simulations, to estimate the global daily PM2.5 concentrations at a spatial resolution of 0.1° × 0.1°. The PM2.5 retrieval model was trained using GEOS-Chem simulations with the GFED, the QFED and the GFAS as a priori fire emissions, respectively, and three sets of global daily PM2.5 estimates were derived. Then the retrieved total PM2.5 concentrations based on the GFED, the QFED and the GFAS were multiplied by previously simulated fractional contributions with corresponding fire emissions, to obtain the PM2.5 exposure attributable to wildfires. The performance of the three fire emission inventories in estimating fire-related PM2.5 exposures was evaluated, and the GFED-based results were selected for presentation and further analysis to facilitate comparisons with other recent studies that use similar approaches9,10,11,44. To investigate the transboundary impact of Canadian wildfires globally and in North America, we further quantified the contributions of five regions’ wildfires (that is, Eastern Canada, Western Canada, Eastern USA, Western USA and other global regions; Extended Data Fig. 3b) to PM2.5 concentrations by conducting additional zero-out scenarios using the GFED emission inventory. Finally, we assessed the acute and chronic deaths attributable to PM2.5 pollution from Canadian wildfires using previously established exposure–response functions15,40. Further details of each analytical step are provided below.

Global fire emissions

A fire emission inventory is an essential input dataset for our analyses. We separately examined the impacts of fire emissions using three near-real-time fire emission inventories available for the year 2023, the GFED37,65, the QFED[38] and the GFAS[39]. The model results and fire-related PM2.5 estimates using each of the three fire emissions datasets are discussed in ‘Model evaluation’.

GFEDv4.1s

The GFED inventory was developed for use in large-scale modelling studies. The latest GFEDv4.1s used in this study is archived at https://surfdrive.surf.nl/files/index.php/s/5y7TdE6ufwpkAW1. It is based on 500-m Moderate Resolution Imaging Spectroradiometer (MODIS) burned area maps[66] supplemented with MODIS active fires converted to burned area[67]. After 2016, emissions are derived from MODIS active fires scaled to emissions based on the 2001–2016 period when both datasets overlapped. Emission factors, mostly from ref. [68], are used to convert fire carbon emissions to trace gases and aerosols. The emissions, including carbon, dry matter, CO_2, CO, NOx, organic carbon, black carbon, PM2.5, total particulate matter and SO_2 among others, are available from 1997 to 2023 at 0.25° × 0.25° globally37,65.

QFEDv2.5r1

The QFED inventory was developed by the National Aeronautics and Space Administration (NASA) and serves as the standard fire emissions in the GEOS data assimilation system and the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) reanalysis data products[69]. In this study, QFEDv2.5r1 is used, which is available at https://portal.nccs.nasa.gov/datashare/gmao/qfed/. On the basis of a top-down approach, QFED obtains the fire radiative power (FRP) and location from satellite observations from MODIS Level 2 fire products and MODIS Geolocation products and calculates the open combustion of non-fossilized vegetative or organic fuel[38]. It provides high spatiotemporal resolution and near-real-time global biomass burning emissions, including the 0.1° × 0.1° daily emissions of black carbon, organic carbon, SO_2, CO, CO_2, PM2.5, NH_3, NOx and so on, from 2001 to present.

GFASv1.2

The GFASv1.2 data are used for the Copernicus Atmosphere Monitoring Service (CAMS) global atmospheric composition and regional air-quality forecasts, which can be found at https://ads.atmosphere.copernicus.eu/cdsapp#!/dataset/cams-global-fire-emissions-gfas?tab=overview/. Fire emissions are calculated based on FRP measurements from two MODIS instruments onboard NASA’s Terra and Aqua satellite that are first converted to estimates of the dry matter consumed by fire and then to emissions using biome-specific emission factors. The GFAS provides daily averaged biomass burning and vegetation fire emissions for 40 pyrogenic species (aerosols, reactive gases and greenhouse gases) from 2003 to the present, with a spatial resolution of 0.1° × 0.1° (ref. [39]).

GEOS-Chem simulation

Using each of the three fire emission inventories (that is, the GFED, the QFED and the GFAS), we estimated the global PM2.5 concentrations using the three-dimensional global chemical transport model GEOS-Chem[36]. These concentrations are an important input to our PM2.5 retrieval model (‘Retrieval of global PM2.5 based on multi-source data fusion’) and are used to quantify the fractional contributions of wildfire emissions to total PM2.5 concentrations (‘Estimation of fire-specific PM2.5 exposure’ and ‘Fire source attribution’). GEOS-Chem has been used by numerous previous studies to simulate smoke pollution from wildfires8,43,70,71,72,73,74,75,76.

GEOS-Chem v.14.0.1 (https://zenodo.org/records/7271974/) is used in this study. The near-real-time meteorological data from the Goddard Earth Observation System-Forward Processing (GEOS-FP)[77] of the NASA Global Modeling and Assimilation Office (GMAO) was used to drive the GEOS-Chem model. The GEOS-FP data span the time period from 2011 to the present, with a native resolution of 0.25° × 0.3125° and 72 vertical levels. We reduce the vertical levels to 47 and the spatial resolution to 2.0° × 2.5° to support the global chemical transport simulations. GEOS-Chem uses standard full chemistry with detailed oxidant–aerosol chemistry. Sulfate–nitrate–ammonium aerosol thermodynamics are computed with ISORROPIAv2.2[78].

All emissions in GEOS-Chem are configured by HEMCO (Harmonized Emissions Component) 3.0[79], to combine and regrid the different emissions. The global anthropogenic emissions (including shipping) of NOx, SO_2, CO, NH_3, black carbon, organic carbon and volatile organic compounds are provided by the Community Emissions Data System (CEDS) v2 inventory (https://data.pnnl.gov/dataset/CEDS-4-21-21/)[80]. Aircraft emissions are from the Aviation Emissions Inventory Code (AEIC)[81] inventory. For global fire emissions, GFEDv4.1s, QFEDv2.5r1 and GFASv1.2 are used respectively. Dust[82], sea salt[83], lighting NOx (ref. [84]), soil NOx (ref. [85]) and biogenic volatile organic compounds (MEGAN v2.1[86]) are calculated online in HEMCO. We use the non-local scheme implemented in ref. [87] for the boundary-layer mixing in GEOS-Chem, which emits all emissions into the atmospheric boundary layer, including wildfire emissions.

Retrieval of global PM2.5 based on multi-source data fusion

We estimate the global daily PM2.5 exposures from all sources at a 0.1° × 0.1° horizon resolution using a multilayer machine-learning retrieval model that fuses data from ground-monitoring measurements, satellite retrievals, GEOS-Chem model simulations, meteorological fields, reanalysis data and population distribution. The structure of the PM2.5 retrieval model is illustrated in Supplementary Fig. 1. We separately train our retrieval model with GEOS-Chem simulations based on the GFED, the QFED and the GFAS emissions (but with the same model structure) to derive three sets of global PM2.5 concentration estimates. Further details about the data sources and the model structure are provided below.

Ground measurements

We collected PM2.5 surface monitoring data from different global regions as model input. We obtained surface PM2.5 measurements in Canada from Environmental Canada (https://data-donnees.az.ec.gc.ca/data/air/monitor/national-air-pollution-surveillance-naps-program/Data-Donnees/). We obtained PM2.5 measurements in the USA from the US Environmental Protection Agency (US EPA) AirNow (https://www.epa.gov/outdoor-air-quality-data/download-daily-data) and from the Interagency Monitoring of Protected Visual Environments (IMPROVE) (https://views.cira.colostate.edu/fed/QueryWizard/Default.aspx). To improve the representation of air pollution, we also collected PM2.5 monitoring data from: the AirFire programme of the US Forest Service (https://info.airfire.org/airmonitor-package) for the USA; the European Air Quality Portal (https://eeadmz1-cws-wp-air02.azurewebsites.net/) for Europe; the China National Environmental Monitoring Center (CNEMC; http://www.cnemc.cn/) for China; and the OpenAQ (https://openaq.org/) for other regions around the world. Hourly measurements were averaged as daily records and only daily records generated from at least 16 hourly data points were included. In summary, we collected approximately 453,000 valid daily records from about 1,610 monitors in North America, approximately 567,000 valid daily records from about 2,010 stations in Europe, approximately 612,000 valid daily records from about 1,720 stations in China, as well as approximately 68,000 valid daily records from about 850 stations in other regions for the year 2023.

Aerosol optical depth

Satellite aerosol optical depth (AOD) retrievals were extracted from the MODIS Level 2 aerosol products (MOD04 and MYD04) at a 0.1° spatial resolution[88]. To improve the data coverage and better reflect the aerosol loading during the day, we first fused the AOD retrievals from the Dark Target algorithm and the Deep Blue algorithm with daily linear regressions, and then fused the AOD from the Aqua and Terra satellites with daily linear regressions. As considerable gaps in the AOD data still existed after this data fusion, we used the CAMS modelling and reanalysis data (https://ads.atmosphere.copernicus.eu)[89] with complete coverage to provide information on the spatial distribution of aerosols. CAMS parameters, including the AOD at 550 nm, black carbon AOD, organic carbon AOD, wildfire combustion rate, FRP and total column carbon monoxide, were adopted in the model. The MODIS AOD and various CAMS AODs were treated as separate predictors in the retrieval model.

GEOS-Chem simulations

The PM2.5 simulations from GEOS-Chem were used in this model. As three fire emission inventories were used in GEOS-Chem to simulate surface PM2.5 concentrations, we constructed three model training datasets with different GEOS-Chem simulations using the GFED, the QFED and the GFAS, respectively.

Other ancillary data

Smoke plume information in North America was collected from the Hazard Mapping System (HMS; https://www.ospo.noaa.gov/Products/land/hms.html#about)[90], provided by the National Oceanic and Atmospheric Administration/National Environmental Satellite, Data, and Information Service (NOAA/NESDIS). The density-assigned and time-marked plumes polygons were manually generated from GOES-16 and GOES-17 ABI true-colour imagery. We assigned the time-specific plume data to daily plume density and included it in the model to provide valuable information on smoke plume distributions in North America. Meteorological fields, including daily average air temperature at 2 m, specific humidity at 2 m, relative humidity, surface pressure, boundary-layer height, total latent energy flux, evaporation from turbulence, U and V wind components at 10 m, and total precipitation, were extracted from GEOS-FP reanalysis data at a spatial resolution of 0.25° × 0.3125° and downscaled to the 0.1° modelling grid by the inverse distance weighting algorithm. The gridded population distribution data for 2020 were obtained from WorldPop (https://www.worldpop.org/) at a resolution of 30 arcseconds91,92 and we assumed a constant population distribution in 2017, 2021 and 2023. We constrained the gridded WorldPop population data with national total population for each year from the United Nations (https://population.un.org/wpp/)[93], US Census Bureau, Population Division (https://www.census.gov/data/tables/time-series/demo/popest/2020s-state-total.html)[94] and Statistics Canada (https://www150.statcan.gc.ca/)[16].

Model structure

The total PM2.5 retrieval model was designed with a three-layer random forest structure following our previous work[95] (Supplementary Fig. 1). The first-layer model predicts the high-pollution index, which is a binary variable indicating whether the station-day concentration is higher than the mean plus two standard deviations of PM2.5 concentrations of the corresponding station and month. In our previous work[96], we found that a two-layer model including the high-pollution indicator and the Synthetic Minority Over-sampling Technique (SMOTE) resampling algorithm can correct the low- bias from the unbalanced training sample of high-pollution events. Following the approach, we applied the SMOTE resampling algorithm to increase the representation of high-pollution events in the model training samples. The second-layer model uses the prediction of high-pollution index as a predictor to predict the total PM2.5 concentrations. Previous studies have shown that the model trained with the residual can correct the systematic bias and improve the model prediction accuracy97,98. The third-layer model then predicts the residual between PM2.5 predictions and measurements and was trained by with-fire samples and no-fire samples separately, to highlight the potential differences in PM2.5 characteristics during fire events. Here the with-fire samples were defined as samples with CAMS combustion rate >0 or the HMS plume density >0 (refs. 8,9). The final PM2.5 concentration estimation is the prediction from the second-layer model plus the prediction from the third-layer model. The model was trained separately with data for 2023, 2021 and 2017 as well as with GEOS-Chem simulations with the GFED, the QFED and the GFAS emissions.

Estimation of fire-specific PM2.5 exposure

PM2.5 exposure attributable to wildfire emissions was then estimated using three fire emissions, respectively. In detail, the wildfire-related PM2.5 was quantified by multiplying the GEOS-Chem simulated fire contributions to total PM2.5 by the retrieved all-source PM2.5 concentrations. Supplementary Table 1 summarizes the GEOS-Chem simulations used in this study. We conducted the GEOS-Chem simulations with the GFED, the QFED and the GFAS inventories separately (that is, ‘base’ in Supplementary Table 1) as well as the no-fire GEOS-Chem simulation that turned off global fire emissions (that is, ‘nofire’ in Supplementary Table 1). All other emissions mentioned in ‘GEOS-Chem simulation’ are the same in the base and nofire simulations. Then the fraction of PM2.5 concentrations attributable to wildfires was calculated by equation (1) on a 2° × 2.5° grid, as determined by the GEOS-Chem model. We constructed three sets of wildfire-fraction data from the GEOS-Chem simulations driven by the three fire emissions. Likewise, the anthropogenic-related PM2.5 was calculated using equation (2) with similar model runs (turning off anthropogenic emissions, that is, ‘noanthro’ in Supplementary Table 1). The contributions from sources other than wildfires and anthropogenic activities were then obtained by subtracting their contributions from the total as in equation (3):

$${F}_{{\rm{f}}{\rm{i}}{\rm{r}}{\rm{e}},k}={{\rm{G}}{\rm{C}}}_{{\rm{f}}{\rm{i}}{\rm{r}}{\rm{e}},k}/{{\rm{G}}{\rm{C}}}_{{\rm{b}}{\rm{a}}{\rm{s}}{\rm{e}},k}=({{\rm{G}}{\rm{C}}}_{{\rm{b}}{\rm{a}}{\rm{s}}{\rm{e}},k}-{{\rm{G}}{\rm{C}}}_{{\rm{n}}{\rm{o}}{\rm{f}}{\rm{i}}{\rm{r}}{\rm{e}}})/{{\rm{G}}{\rm{C}}}_{{\rm{b}}{\rm{a}}{\rm{s}}{\rm{e}},k}$$

(1)

$${F}_{{\rm{a}}{\rm{n}}{\rm{t}}{\rm{h}}{\rm{r}}{\rm{o}},k}={{\rm{G}}{\rm{C}}}_{{\rm{a}}{\rm{n}}{\rm{t}}{\rm{h}}{\rm{r}}{\rm{o}},k}/{{\rm{G}}{\rm{C}}}_{{\rm{b}}{\rm{a}}{\rm{s}}{\rm{e}},k}=({{\rm{G}}{\rm{C}}}_{{\rm{b}}{\rm{a}}{\rm{s}}{\rm{e}},k}-{{\rm{G}}{\rm{C}}}_{{\rm{n}}{\rm{o}}{\rm{a}}{\rm{n}}{\rm{t}}{\rm{h}}{\rm{r}}{\rm{o}},k})/{{\rm{G}}{\rm{C}}}_{{\rm{b}}{\rm{a}}{\rm{s}}{\rm{e}},k}$$

(2)

$${F}_{{\rm{other}},k}=1-{F}_{{\rm{fire}},k}-{F}_{{\rm{anthro}},k}$$

(3)

where the subscript k represents the three fire emissions, that is, GFED, QFED and GFAS. GCbase,k and GCnoanthro,k represent the GEOS-Chem-simulated PM2.5 concentrations from the base and noanthro scenarios using fire emissions k, respectively. GCnofire represents the simulation with fire emissions turned off. Ffire,k, Fanthro,k and Fother,k represent the fractional contribution of wildfires, anthropogenic and other emissions to PM2.5 estimated from fire emissions k, respectively.

Then we spatially match the PM2.5 fractions from GEOS-Chem simulations (2° × 2.5°) with the 0.1° PM2.5 retrievals through bilinear interpolation. The PM2.5 retrievals were multiplied by the corresponding fractions to get the fire-related, anthropogenic-related and other-source-related PM2.5, as shown in equations (4)–(6):

$${C}_{{\rm{fire}},k}={C}_{{\rm{PM}},k}\times {F}_{{\rm{fire}},k}={C}_{{\rm{PM}},k}\times ({{\rm{GC}}}_{{\rm{fire}},k}/{{\rm{GC}}}_{{\rm{base}},k})$$

(4)

$${C}_{{\rm{anthro}},k}={C}_{{\rm{PM}},k}\times {F}_{{\rm{anthro}},k}={C}_{{\rm{PM}},k}\times ({{\rm{GC}}}_{{\rm{anthro}},k}/{{\rm{GC}}}_{{\rm{base}},k})$$

(5)

$${C}_{{\rm{other}},k}={C}_{{\rm{PM}},k}\times {F}_{{\rm{other}},k}$$

(6)

where CPM,k represents the total PM2.5 concentrations estimated from the machine-learning-based model using fire emissions k (k = GFED, QFED, GFAS) in ‘Retrieval of global PM2.5 based on multi-source data fusion’, Cfire,k, Canthro,k and Cother,k represent the fire-, anthropogenic- and other-source-related PM2.5 concentrations based on fire emissions k.

Model evaluation

Our models were fully evaluated at each step of the construction of fire-related PM2.5 concentrations (Extended Data Fig. 1): the performance of the GEOS-Chem PM2.5 simulations, the performance of the PM2.5 retrieval model and the performance of PM2.5 retrievals during fire events. Models based on the three fire emissions (GFED, QFED and GFAS) were compared in all the evaluations to understand the impacts of fire emissions on model performance. Total and fire-related PM2.5 concentrations estimated using the three fire emissions were compared with each other. We also quantified the wildfire-related PM2.5 estimates in previous years (2017 and 2021) and compared them with other studies as an additional evaluation of our methods.

Evaluation of GEOS-Chem PM2.5 simulations

The annual average GEOS-Chem PM2.5 concentrations driven by three fire emission inventories (GFED, QFED and GFAS) were evaluated against PM2.5 ground observations in Canada and the USA (Supplementary Fig. 15). In Canada, the modelled PM2.5 correlated reasonably well with ground observations, with R ranging between 0.41 and 0.69 and normalized model bias (NMB) between 0.01 and 0.72 for the three fire emissions. We noticed one outlier with unrealistically high PM2.5 simulations in Canada resulted from high fire emission estimates; therefore, we also reported evaluation statistics without this data point to avoid the effects of an outlier (Supplementary Fig. 15). After removing the outlier, R between modelled and observed PM2.5 increased from 0.41–0.69 to 0.66–0.82 and NMB was reduced from 0.01–0.72 to −0.04–0.30 in Canada. In the USA, simulations based on the three fire emissions had comparable performance against ground observations, with R between 0.46 and 0.47. As the only differences in these simulations are the underlying fire emission inventories, the differences in model performance can be solely attributed to the inventories. Compared with the GEOS-Chem simulation with the GFED inventory, using the QFED inventory helps to reduce both the overestimates of PM2.5 concentration in Canada (NMB from 0.30 to 0.16) and the underestimates in the USA (NMB from −0.22 to −0.06), whereas using the GFAS inventory reduces the overestimates of PM2.5 concentration in Canada (NMB from 0.30 to −0.04) but gives similar results to GFED in the USA (NMB from −0.22 to −0.27). By comparing estimates of fire-related PM2.5 exposure from different fire emission inventories in this way, we can evaluate the effects of GEOS-Chem model performance on the results (‘Comparisons of fire-related PM2.5 among three fire emissions and with previous studies’).

Evaluation of PM2.5 retrieval model

The PM2.5 retrieval model was evaluated by both station-based and sample-based 20-fold cross-validation. The model training dataset was randomly divided into 20 equal folds according to air-quality monitoring stations and station-day observations, separately. Then the model was trained on 19 of these folds and tested on the remaining fold. This process was repeated 20 times until each fold of the data was used for testing once. The model performance was quantified by the comparisons between cross-validation predictions and ground measurements at the daily, monthly and yearly levels to reflect model uncertainties at different temporal scales (Extended Data Fig. 8 and Supplementary Fig. 13). In addition, to highlight the model’s ability in retrieving daily variations in PM2.5 when controlling the seasonal and spatial variations, we included month-intercept (fix-month R^2) as well as month and station intercepts (fix-month-and-station R^2) when computing R^2 (within R^2) of the 20-fold cross-validation predictions following a previous study[10] (Supplementary Table 5). We also calculated the station-specific R^2 to show the variations in model performance in space. Evaluation results of the retrieval models trained with GEOS-Chem simulations using the three fire emissions in 2023 are listed in Extended Data Fig. 8, Supplementary Fig. 13 and Supplementary Table 5. As the HMS data are available for only North America, we assessed the impact of including HMS data on global PM2.5 retrievals. As shown in Supplementary Fig. 17, inclusion of the HMS data in the model led to substantial differences in PM2.5 retrievals over North America whereas it had minor impacts in other regions. Therefore, we incorporated the HMS data as a predictor to improve the accuracy of wildfire-related PM2.5 estimates in North America.

Globally, the retrieval model characterizes variations in PM2.5 well, and models based on the GFED, the QFED and the GFAS performed similarly well under both the station-based and sample-based 20-fold cross-validation. The station-based 20-fold cross-validation R^2 ranged between 0.84 and 0.85 (RMSE between 8.55 μg m−3 and 8.62 μg m−3) at the daily scale, all equal to 0.88 (RMSE between 5.80 μg m−3 and 5.95 μg m−3) at the monthly scale, and ranged between 0.87 and 0.88 (RMSE between 4.80 μg m−3 and 5.00 μg m−3), in the year 2023. The sample-based cross-validation results are comparable to the station-based cross-validation results, indicating robust model performance in regions with limited observations. All models trained with the three fire emission inventories showed only a slight decrease in R^2 when controlling the seasonal and spatial variations (that is, fix-month R^2 between 0.86 and 0.88, and fix-month-and-station R^2 between 0.80 and 0.82), indicating the model’s ability to capture daily variations in PM2.5 (Supplementary Table 5). Spatially, the global median station-specific R^2 was 0.79, 0.79 and 0.79 with 90% of station-specific R^2 above 0.37, 0.36 and 0.37 for models based on the GFED, the QFED and the GFAS, respectively. Our model performances are comparable to previous studies developing a global PM2.5 retrieval model, in that the cross-validation R^2 of daily retrievals is around 0.91 and the RMSE ranges between 8.4 μg m−3 and 9.2 μg m−3 (refs. 10,41).

Regionally we found a lower R^2 in Canada, which is mainly caused by several outliers in Canada resulting from unrealistically high GEOS-Chem simulations mentioned in ‘Evaluation of GEOS-Chem PM2.5 simulations’. To avoid the influence of these occasional outliers on model evaluation, we reported the model performance after removing data points outside 2σ of the Cook’s distance of linear regression (Supplementary Table 5). Models based on the three fire emissions performed comparably well after removing the outliers. As these outliers of the retrieved PM2.5 concentration occurred in a few days and in remote regions with sparse population, they do not considerably affect our exposure assessment and health burden quantification.

Evaluation of PM2.5 retrievals during fire events

To assess the model’s performance in capturing fire-related PM2.5 variations, we further evaluated the model performance during fire events (Extended Data Fig. 9 and Supplementary Table 4)—when the PM2.5 is dominated by wildfires. We first identified several major fire events and then compared the station-day observations during these fire events with the sample-based 20-fold cross-validation predictions. Thus, the station-day observations selected for evaluations were excluded from the model training to reveal the model performance in regions and periods without observations. We identified fire events with a similar protocol reported by an earlier work[10], mainly according to the variations in PM2.5 observations. A station-day is labelled as affected by wildfires when (1) it is during one of the manually identified fire events that showed a substantial increase in national daily average PM2.5 monitoring time series data in Canada and the USA, separately. (2) The daily average PM2.5 concentration is higher than the median of all the station-day records during this fire event. Here we used the median as cut-off number rather than selecting one station with the largest increase because one station’s data were not sufficient to support the validation. (3) The PM2.5 concentration is higher than twice the background PM2.5 concentration before the fire season (first 2 months in 2023) at the corresponding station. (4) The PM2.5 concentration is higher than 15 μg m−3, the WHO air-quality guidelines level. In total, 11 and 9 fire events were identified in Canada and the USA, respectively. The events lasted between 3 days and 23 days. The national fire-related PM2.5 exposure during these fire events accounted for 83% and 81% of the annual fire-related PM2.5 exposure in Canada and the USA, respectively, indicating that most significant fire events were identified by this method.

In North America, the three retrieval models with different fire emissions correctly reflected PM2.5 variations during the fire events, with similar cross-validation R^2 ranging between 0.78 and 0.80 in the USA, but moderately different R^2 between 0.59 and 0.75 in Canada (Supplementary Table 4). We also noticed that as previously reported41,99, our model still slightly underestimated PM2.5 levels during extreme fire events with NMB ranging between −0.14 and −0.09 and between −0.13 and −0.10 for Canada and the USA, respectively.

Comparisons of fire-related PM2.5 among the three fire emissions and with previous studies

To further understand the impacts of different fire emissions on total and fire-related PM2.5 estimates, we compared the spatial and temporal distributions of our results among the three fire emissions (Supplementary Table 6). The spatial correlation was calculated using 3-year averaged gridded PM2.5 data among models based on the 3 fire emissions, whereas the temporal correlation was calculated using daily population-weighted mean PM2.5 concentrations for 3 years among models based on the 3 fire emissions. Some previous studies9,10,11,44 have investigated the impact of wildfires on PM2.5 exposure other than the 2023 Canadian extreme wildfires. We also compared our fire-related PM2.5 estimates with those previous studies as additional evaluations.

For spatial comparisons, the all-source PM2.5 estimates based on the three fire emission inventories showed similar spatial distributions to high correlations globally (all pairwise Pearson correlation coefficients r were 0.99). The spatial distributions of fire-related PM2.5 were also highly correlated between different emissions at the global scale, with pairwise r ranging between 0.88 and 0.95. The spatial patterns between the QFED-based and the GFAS-based estimates were more similar in specific regions than the GFED-base results, as fire emissions from the QFED and the GFAS were estimated using a similar approach based on FRP from the MODIS instrument. For temporal comparisons, the population-weighted daily mean all-source PM2.5 estimates showed high correlations at both the global scale (all pairwise Pearson correlation coefficients r were 0.99) and the regional scale. The fire-related PM2.5 estimates had some temporal differences globally among the 3 inventories, but showed even higher correlations in Canada and the USA, with pairwise r of fire-related PM2.5 ranging between 0.94 and 0.99 in Canada and between 0.94 and 0.97 in the USA.

Supplementary Fig. 14 shows the comparisons of estimated population-weighted fire-related PM2.5 in Canada and the USA based on the three inventories, as well as their comparisons with previous studies9,10,11,44. The fire-related PM2.5 in Canada and the USA based on the three inventories showed consistent increasing trends in 2017, 2021 and 2023; however, the magnitudes of the estimated fire-related PM2.5 varied between inventories, with the GFAS showing the lowest and the QFED showing the highest. In Canada, fire-related annual PM2.5 exposure estimated with the 3 inventories showed good agreement (3.75–4.49 μg m−3, relative difference within 20%). Given their similar fire-related PM2.5 exposure estimates in Canada, the choice of fire inventory has a relatively minor effect on our overall conclusions. In the USA, the GFED-based and the GFAS-based estimates on fire-related annual PM2.5 exposure in 2023 are also similar (1.96 μg m−3 and 1.83 μg m−3, respectively), whereas the QFED-based estimates (3.11 μg m−3) are 59–70% higher, consistent with several other recent studies (Supplementary Fig. 14). Because the GEOS-Chem PM2.5 simulations with the QFED inventory show better agreement with surface observations in the USA, our estimates of fire-related contributions to PM2.5 may be underestimated in the USA when using the GFED inventory.

Our population-weighted estimates of fire-related PM2.5 based on GFED emissions in 2017 (1.62 μg m−3 in Canada and 1.16 μg m−3 in the USA) are nearly identical to estimates by a previous study that used GFED emissions from 2000–2019[10] (1.50 μg m−3 in Canada and 1.21 μg m−3 in the USA). Another study[44] estimated the source contribution to ambient PM2.5 in 2017 globally using GFED fire emissions and reported that the population-weighted fire-related PM2.5 in Canada and the USA was 1.35 μg m−3 and 0.90 μg m−3, respectively, again similar to the GFED-based and the GFAS-based estimates. In addition, ref. [11] developed a data fusion model to divide the fire-source and other-source PM2.5 in the USA and estimated that the mean fire-source PM2.5 concentrations inside and outside the vicinity of an EPA air-quality monitoring station (defined by a 5-km radius) in 2017 are 0.97 μg m−3 and 0.92 μg m−3, respectively, also close to our GFED-based and GFAS-based estimates.

In summary, although the GFED, the QFED and the GFAS inventories show varied air-pollutant emissions and led to different fire-related PM2.5 concentrations in GEOS-Chem simulations, the total PM2.5 retrieval models with different fire emission inventories showed generally consistent performance. For the fire-related PM2.5 concentrations, the GFED-based and the GFAS-based estimates are similar and more comparable to previous studies9,10,11,44. We understand that each fire inventory has its own advantages and disadvantages; therefore, we cannot justify which one is the best. Given that the GFED has frequently been used in recent analyses8,10,12,43, to put our results in the context with the literature, we choose to present the GFED-based estimates in the main text.

Fire source attribution

To further quantify the contributions of fires from different regions in North America, we divided Canada and the USA into four regions, Eastern Canada (CE), Western Canada (CW), Eastern USA (UE) and Western USA (UW) (Extended Data Fig. 3b). According to the EPA’s delineation of North American ecological regions (Supplementary Fig. 2; https://www.epa.gov/eco-research/ecoregions-north-america/), the Level I ecoregions divide North America into 15 broads. It can be seen that the majority of Canada is covered by forests, whereas the eastern and western parts of the USA are separated by plains and deserts. Therefore, we defined the above four regions according to administrative divisions in combination with the ecological regions in this study.

We then implemented simulations with regional wildfire emissions turned off using the GFED emissions (Supplementary Table 2). In addition, given that the zero-out approach may lead to additional bias owing to the nonlinear relationship between emissions and modelled PM2.5 concentrations, the case of ‘offNA’ is used to evaluate this impact and constrain the results. The regional contributions can be calculated using equations (7)–(11):

$$\begin{array}{l}{\rm{Scale}}=({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offNA}},{\rm{GFED}}})/[({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offCE}},{\rm{GFED}}})\\ \,\,+\,({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offCW}},{\rm{GFED}}})\\ \,\,+\,({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offUE}},{\rm{GFED}}})\\ \,\,+\,({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offUW}},{\rm{GFED}}})]\end{array}$$

(7)

$${F}_{{\rm{fireCE}},{\rm{GFED}}}={\rm{Scale}}\times ({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offCE}},{\rm{GFED}}})/{{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}$$

(8)

$${F}_{{\rm{fireCW}},{\rm{GFED}}}={\rm{Scale}}\times ({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offCW}},{\rm{GFED}}})/{{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}$$

(9)

$${F}_{{\rm{fireUE}},{\rm{GFED}}}={\rm{Scale}}\times ({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offUE}},{\rm{GFED}}})/{{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}$$

(10)

$${F}_{{\rm{fireUW}},{\rm{GFED}}}={\rm{Scale}}\times ({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offUW}},{\rm{GFED}}})/{{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}$$

(11)

where GCoffCE,GFED, GCoffCW,GFED, GCoffUE,GFED, GCoffUW,GFED and GCoffNA,GFED are the GEOS-Chem-simulated PM2.5 concentrations using the GFED emissions under the offCE, offCW, offUE, offUW and offNA scenarios, respectively. FfireCE,GFED, FfireCW,GFED, FfireUE,GFED and FfireUW,GFED are the fractional contributions to the PM2.5 concentrations from fire emissions in CE, CW, UE and UW, respectively.

The zero-out approach used here may introduce additional bias due to the nonlinear relationship between emissions and modelled PM2.5 concentrations. The bias can be calculated as equation (12):

$$\begin{array}{l}{\rm{Bias}}=({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offNA}},{\rm{GFED}}})-[({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offCE}},{\rm{GFED}}})\\ \,\,\,+\,({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offCW}},{\rm{GFED}}})\\ \,\,\,+\,({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offUE}},{\rm{GFED}}})\\ \,\,\,+\,({{\rm{GC}}}_{{\rm{base}},{\rm{GFED}}}-{{\rm{GC}}}_{{\rm{offUW}},{\rm{GFED}}})]\end{array}$$

(12)

The absolute and relative biases due to nonlinearity are presented in Supplementary Fig. 16. Over the four regions, the absolute biases range from −0.009 μg m−3 to 0.012 μg m−3, and the relative biases range from −1.35% to −0.09%, indicating that the biases related to nonlinear effects are relatively small.

To investigate the significance of the Canadian wildfire impact on the interannual variability in PM2.5 concentrations in downwind regions, we compared the estimated annual mean PM2.5 concentrations from the 2023 Canadian wildfires with 2000–2023 satellite-derived annual PM2.5 concentrations (https://sites.wustl.edu/acag/datasets/surface-pm2-5/#V6.GL.02.03/)[100] and 2014–2023 annual mean PM2.5 observations over the USA and Europe (Supplementary Fig. 18). When comparing with the interannual variability in PM2.5 concentrations, the contribution of the 2023 Canadian wildfires was statistically significant in North America and Europe whereas it was statistically insignificant over other downwind regions. In the USA, the 2023 Canadian wildfires contributed to an average of 1.50 μg m−3 annual mean PM2.5 over the locations of the EPA sites, larger than the differences in observed the PM2.5 concentration between 2022 and 2023 (0.99 μg m−3) as well as the mean interannual variabilities in the observed PM2.5 concentration during 2014–2023 (0.59 μg m−3, P < 0.01). In Europe, the 2023 Canadian wildfires contributed to an average of 0.43 μg m−3 annual mean PM2.5 over the locations of European Environment Agency (EEA) sites, accounting for 20% of the differences in observed PM2.5 concentration between 2022 and 2023 (2.10 μg m−3) and 14% of the mean interannual variabilities in observed PM2.5 concentration during 2014–2023 (3.02 μg m−3, P < 0.05).

Long-range transport of the 2023 Canadian wildfire plumes to Europe

The Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model has been widely used to track the back trajectories for air parcels arriving at the receptor101,102,103,104. To track the transports and sources of PM2.5 pollution in Europe related to the 2023 Canadian wildfires, we used the HYSPLIT model to calculate the 7-day back trajectories for the entire European region (excluding Russia) on a 0.1° × 0.1° grid basis from May to September in 2023 at an hourly resolution. The HYSPLIT model version 5.3.0 (https://www.ready.noaa.gov/ready2-bin/getlinuxtrial.pl/) was used for the analysis. Each backward trajectory was run for 7 days with 1-hour time steps, initialized at 0:00, 6:00, 12:00 and 18:00 coordinated universal time (UTC) daily. The arrival height was 500 m above ground, approximately within the planetary boundary layer. The HYSPLIT model was driven by three-dimensional meteorological fields from the Global Data Assimilation System of National Centers for Environmental Prediction (GDAS NCEP), with a time resolution of 3 hours, a horizontal resolution of 1° × 1° and a vertical resolution of 23 levels.

We then defined the transport trajectory density (TTD) to represent the capability of pollutant transport from source regions to the receptor region (Europe), which is the total number of trajectories passing through the 0.1° × 0.1° grid box of source regions during the study period. The TTD of each grid box during the study period can be calculated by equation (13):

$${{\rm{TTD}}}_{i}=\mathop{\sum }\limits_{j=1}^{m}{F}_{i,j}$$

(13)

where i is the index of each grid box and m is the total number of trajectories that passed through all receptor grid boxes (81,052 in this study). For each trajectory j (ranging from 1 to m), Fi,j is defined as 1 if trajectory j passes through grid box i; otherwise, Fi,j is defined as 0. Therefore, TTDi is the total number of trajectories that passed through the grid box i during the study period. Supplementary Fig. 9 shows the spatial distribution of TTD sums from May to September in 2023. High TTD values were observed over the majority of Canada between May and September 2023, indicating the frequent trans-Atlantic plumes that prompt pollution transported from the wildfire source regions to downwind regions, and finally reached Europe.

Supplementary Fig. 10 further illustrates the vertical transport process that brought the Canadian wildfire plumes to the surface of Europe during the late-June trans-Atlantic episode. High PM2.5 concentrations are observed on 29 June and 2 July over the large areas in Northern France and Belgium (Supplementary Fig. 8 and Supplementary Fig. 10a). During the pollution episode, the GEOS-Chem simulation shows that the enhancement of surface PM2.5 concentration from Canadian wildfires was accompanied by a high PM2.5 concentration at high altitude (Supplementary Fig. 10b). The modelled PM2.5 enhancement from Canadian wildfires corresponds well with the observed peak of PM2.5 concentration, demonstrating the vertical transport process during the episode. Meanwhile, 7-day back trajectories with 500-m arrival height indicate that the airflows originating from the Canadian wildfire source regions were transported into the boundary layer above the site location on 29 June and 2 July (Supplementary Fig. 10c), providing compelling evidence of long-range transport of wildfire-related PM2.5 from Canada to Europe.

Health impacts

Acute mortality attributable to exposure to Canadian wildfires

The acute and chronic mortality attributable to 2023-Canadian-wildfires-related PM2.5 exposure were estimated separately. The acute mortality was estimated for all grids ‘Canada smoke days’ in which both (1) grid daily mean PM2.5 concentrations exceeded 15 μg m−3 (the recommended 24-hour average guideline levels of the WHO) and (2) Canadian-wildfires-related PM2.5 accounted for at least half of the total daily PM2.5 (ref. [10]). Details on the estimation of fire-specific PM2.5 concentrations are described above. Following previous studies[50], the acute mortality attributable to Canadian wildfires PM2.5 exposure was assessed using equation (14):

$${D}_{i,j}=\mathop{\sum }\limits_{j=1}^{365}\{[({\rm{RR}}({C}_{i,j})-1)/{\rm{RR}}({C}_{i,j})]\times {P}_{i}\times ({I}_{i}({{\rm{Country}}}_{a})/365)\}$$

(14)

where Di,j represents the all-cause acute premature mortality attributable to Canadian-wildfires-related PM2.5 exposure in grid i on day j. RR(Ci,j) represents the relative risk at exposure level C in grid i on day j and the exposure level was assessed as the daily average Canadian-wildfires-related PM2.5 concentrations. A global RR estimates of 1.021 (95% CI, 1.018, 1.024)[15] per 10 μg m−3 increase of wildfire PM2.5 exposure was used for all regions. Pi represents the population in grid i that was constructed as described in ‘Estimation of fire-specific PM2.5 exposure’. Ii represents the baseline all-cause death rate in grid i that belong to Country a, which was collected from the Global Burden of Disease (GBD) 2019 study (https://ghdx.healthdata.org/gbd-2019)[45].

Compelling evidence for the increased toxicity of wildfire-related PM2.5 relative to all-source PM2.5 have been reported13,58, and various exposure–response functions for acute exposure to wildfire PM2.5 have been developed by recent studies15,46,48,49. Here we use a widely used global pooled relative risk of wildfire PM2.5 exposure[15] to estimate the acute premature mortality considering the global nature of this study and the comparability across different regions. To investigate the impacts of the choice of relative risks on the acute premature mortality estimates, we further assess the acute premature mortality attributable to the 2023 Canadian wildfires by using the relative risks for wildfire PM2.5 from newly developed global meta-analysis[46], two studies in North America48,49 and relative risk from a meta-analysis on all-source PM2.5 (ref. [50]). The results of comparison are presented in Supplementary Table 7. The estimated global acute premature mortality attributable to Canada smoke day exposure varied by a factor of four when different RR estimates were used. Among the different functions derived for wildfire PM2.5, mortality estimates using global pooled relative risks15,46 (ranging from 2,800 to 5,400) were higher than those using regional relative risks48,49 (1,300–2,600). Estimates using relative risks derived for wildfire PM2.5 exposure15,46,48,49 generally yield higher mortality estimates (1,300–5,400) than those using all-source relative risk[50] (1,800), implying increased toxicity of wildfire-related PM2.5 compared with all-source PM2.5.

Chronic premature mortality attributable to exposure to Canadian wildfires

All-cause premature mortality attributable to chronic smoke exposure from the 2023 Canadian wildfires was estimated with a meta-analysis relative risk estimate of 1.08 (95% CI, 1.06, 1.09) per 10 μg m−3 increase in PM2.5 exposure[40].

The health burden attributable to chronic PM2.5 exposure was assessed using equation (15):

$${D}_{i}=[({\rm{RR}}({C}_{i})-1)/{\rm{RR}}({C}_{i})]\times {P}_{i}\times {I}_{i}({{\rm{Country}}}_{a})$$

(15)

where Dy,i,n represents the chronic premature mortality attributable to Canadian-wildfires-related PM2.5 exposure in grid i. RR(Ci) represents the relative risk at exposure level C in grid i. Ci represents the annual average PM2.5 concentration in grid i. Pi represents the population in grid i, and Ii represented the baseline all-cause death rate in grid i in Country a of year 2019, which was collected from the GBD 2019 study (https://ghdx.healthdata.org/gbd-2019)[45]. The theoretical minimum risk exposure level (TMREL) for the chronic health effects attributable to PM2.5 ranged between 2.4 μg m−3 and 5.9 μg m−3, as reported in the GBD 2019 study.

The chronic exposure mortality attributable to Canadian wildfires was assessed with the direct proportion approach105,106, which assumes that the increase in mortality is in proportion to the increases in PM2.5 exposure. Thus, the chronic exposure mortality attributable to all-source ambient PM2.5 exposure was assessed first and the Canadian-wildfires-associated chronic mortality was quantified by calculating the proportion of Canadian-wildfire-derived PM2.5 within all-source ambient PM2.5.

It should be noted that the RR used here is derived for all-source PM2.5 rather than wildfire PM2.5, owing to the limited epidemiological evidence of chronic health effects from wildfire-related PM2.5 exposure. We use the exposure–response function for all-cause mortality rather than the cause-specific exposure–response function (that is, the widely used GBD approach[45]) as this study aims to estimate the total mortality burden whereas the cause-specific may underestimate the total chronic mortality of ambient PM2.5 (ref. [107]). Relative risk derived from regional meta-analysis47,49 may differ from those derived from global pooled analysis[40]. Given the global nature of this study, we choose the all-cause global pooled relative risk in our analysis[40]. We further conducted a sensitivity analysis to evaluate the impact of exposure–response functions on the chronic premature mortality45,47,49, as shown in Supplementary Table 8. Using cause-specific exposure–response function[45] yields 31,000 global chronic premature mortality, lower than estimates using all-cause functions40,47,49 (ranging from 82,100 to 152,000). For all-cause premature mortality estimates with 3 different relative risks, mortalities estimated by global relative risk[40] (82,100) are remarkably lower than those estimated by regional relative risks47,49 (that is, the USA, 117,500–152,000), indicating large variation of relative risks across different global regions.

We also reviewed the approaches of estimating chronic health burden from wildfire-related PM2.5 exposure used in different global and regional studies12,31,44,46,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123, as shown in Supplementary Table 9. Although annual average exposure is widely used in those studies, it may not reflect the population experience of sporadic wildfire PM2.5 exposure owing to the different nature of wildfire smoke exposure and the urban and background pollution exposure. Substantial differences in chronic health burden assessment approaches were observed, which varied in mortality endpoints (cause-specific versus all-cause), the relative risk and the definition of exposed population. Many of those studies quantified PM2.5-related health impacts of landscape fires on populations that are annually impacted by fire-related air pollution from local or nearby fires, whereas our study investigated the transboundary air pollution and the health burden of a single extreme wildfire event. Specifically, ref. [31] quantified the transboundary PM2.5 health impact of wildfires in the Arctic Council, which is most comparable to the purpose of our study. In their analysis, areas where the increase in carbonaceous PM2.5 from wildfires was statistically insignificant were excluded from the health impact assessment. A previous study[46] estimated global, regional, and national mortality burden attributable to fire-related PM2.5 exposure, which is estimated for all population with the same exposure–response function used in our study[40]. We then followed the widely accepted approach in our analysis and conducted significance tests for the estimated contribution of the annual mean PM2.5 concentration from the 2023 Canadian wildfires.

Uncertainty analysis

Our results are subject to a number of uncertainties and limitations. The uncertainty ranges (95% CI) in different steps of our analysis are discussed below.

First, the emission inventories used in this study bear large uncertainties. For example, the uncertainties in the GFED emissions mainly come from the inadequate representation of the natural variation of the emission factors during fire events, and the high uncertainties in the amount of fuel burned estimated from burned area. It is reported that a best-guess uncertainty assessment for GFEDv4.1s at regional scales could be a 1σ of about 50% in general but higher in areas where small fires burned area is important or where there is notable fuel consumption in organic soils[37].

Second, the PM2.5 concentrations simulated by the global chemical transport model are affected by errors in emission inventories and the model’s representation of physical and chemical processes such as vertical transport[51] and secondary organic aerosols[124]. Specifically, the smoke-injection height is not considered in the GEOS-Chem simulation, which may lead to overestimates and underestimates of fire-related PM2.5 concentrations in fire source regions and downwind regions, respectively[51]. Given the huge computational cost for model sensitivity simulations considering the uncertainties in emissions, we use the normalized root-mean-square deviation (NRMSD) between the modelled and the observed PM2.5 concentrations to represent the overall model errors in total PM2.5, and use the NRMSD between the modelled and the observed PM2.5 concentrations over fire events to represent the model errors in fire-related PM2.5. The NRMSD for GEOS-Chem-based total PM2.5 and fire-related PM2.5 ranged between 42.8% and 62.0% and between 44.3% and 53.0%, respectively, among Canada, the USA and Europe, but a bit higher in other regions globally (for example, close to 100.0%). Although the absolute errors in GEOS-Chem-based simulations are large, some errors are common between the total and fire-related PM2.5 and have limited impacts on their ratios.

Third, the multi-source fused PM2.5 data obtained from our retrieval model are influenced by errors in all the input data and the multilayer machine-learning model itself. We have fully evaluated the model’s performance using a cross-validation approach and the performance was comparable to previous studies10,41. We use the NRMSD between PM2.5 retrieval and observed PM2.5 concentrations to represent its uncertainties (2.0–7.1% among different regions).

As presented in equation (4), the overall uncertainties involved in fire-related PM2.5 exposures are determined by uncertainties in GEOS-Chem simulated fractional contributions of fire emissions (GCfire/GCbase) and in total PM2.5 exposures based on the retrieval model (CPM). The errors in GCbase, GCfire and CPM are defined above. The errors in the ratio (GCfire/GCbase) were then quantified by 10,000 trials of Monte Carlo simulation. Finally, the overall uncertainties of fire-related PM2.5 (Cfire) were derived from the aggregations of errors above.

The overall uncertainties (presented as 95% CI) of acute and chronic mortality attributable to Canadian wildfires were then assessed by Monte Carlo simulations with 1,000 iterations[45]. Uncertainties embedded in all input parameters of the risk assessment model were considered. The uncertainties in exposure levels are described above. The uncertainties in baseline mortality, exposure–response functions and TMREL were collected from the GBD 2019 study. The uncertainty in national total population was provided by United Nations data (high-fertility and low-fertility scenarios). All the parameters, except TMREL, which was simulated by a uniform distribution, were simulated by normal distributions.

Comparison with other relevant studies

The impacts of the 2023 Canadian wildfires on surface PM2.5 air quality have been reported in a few recent studies. By proposing a multidimensional air pollution correlation network framework, ref. [28] argued that the 2023 Canadian wildfires significantly impact the air pollution behaviour in the Northeastern USA region. Reference [29] estimated the PM2.5 concentration in the Northeastern USA in June 2023 by combining chemical transport model results and surface PM2.5 measurements. They identified two ‘smoke wake’ events in June 2023 (6–8 June and 28–30 June) with significant PM2.5 enhancement caused by the transport of Canadian wildfire plumes. Our results also capture these two events in the same region, although our estimates of PM2.5 concentrations are lower than those of ref. [29] during the first ‘smoke wave’ event (6–8 June), which might be attributed to the coarse model resolution in our analysis (Supplementary Table 3). By using a global chemical transport model, ref. [2] found that the Canadian wildfires significantly impacted air quality in the Northern Hemisphere, which was consistent with our findings. They identified six widespread air pollution episodes due to the Canadian wildfires from May to August, which are also captured in our GESO-Chem simulation (Supplementary Fig. 11) and retrieved PM2.5 concentration (Supplementary Fig. 12).

Canadian wildfire-related chronic PM2.5 exposure is associated with approximately 22, 10 and 3 deaths per 100,000 people in 2023 in Canada, the USA and Europe, respectively. For comparison, chronic mortalities from all-source PM2.5 exposure are 55, 57 and 80 per 100,000 people in 2023 in the three regions, respectively, underscoring the non-negligible contribution of wildfire smoke to public health burdens. Our estimates on Canadian wildfire-related per capita mortality rates in the USA and Canada are notably higher than wildfire-related per capita mortality rates reported in refs. 46,125, owing to high PM2.5 exposure levels attributable to the record-breaking Canadian wildfires in 2023 as well as the all-cause exposure–response function used in our analysis.

We estimated that the 2023 Canadian fires accounted for 3.82 μg m−3 (3.00–4.64 μg m−3) of annual mean PM2.5 exposure in Canada in 2023, which is lower than 2000–2019 annual mean fire-related PM2.5 exposure in typical wildfire hotspot regions[10] such as sub-Saharan Africa (6.99 μg m−3), mainland Southeast Asia (5.77 μg m−3), Indonesia (6.28 μg m−3) and Brazil (5.68 μg m−3). In another study[44], annual mean fire-related PM2.5 exposure in typical wildfire hotspot regions were estimated to be 0.72 μg m−3 in Indonesia, 1.26 μg m−3 in Brazil and 1.26 μg m−3 in Southeast Asia in 2017, indicating the large interannual variabilities in wildfire activities. Reference [109] estimated that global landscape fires alone result in 44 million and 4 million people annually being exposed to air quality considered ‘unhealthy’ and ‘hazardous’, respectively. In comparison, we estimated that the 2023 Canadian wildfires caused 139.3 million and 0.25 million people to be exposed to ‘unhealthy’ (PM2.5 > 55 μg m−3) and ‘hazardous’ (PM2.5 > 250.5 μg m−3) air quality. Large health impacts from wildfire-related air pollution have been reported in these hotspot regions46,109,110,111,112,114,115,116,118. For instance, wildfires-induced chronic mortality was estimated to be 160,200 in Africa in 2017[110], 59,000 in Southeast Asia in 2014[118], 13,700–44,000 in equatorial Asia during 2004–2015[116], and 16,800 in South America in 2012[111]. In recent study[46], it was estimated that 384,600, 144,300 and 79,300 people died annually in sub-Saharan Africa, Southeast Asia, and Latin American and the Caribbean, respectively, owing to chronic wildfire smoke exposure during 2000–2019. In contrast, we estimated that the 2023 Canadian fires resulted in 8,300 (95% CI, 5,800–10,800) PM2.5-attributable chronic premature deaths in Canada given the low population density close to fire regions. Globally, we estimated 82,100 (95% CI, 47,700–116,500) PM2.5-attributable chronic premature deaths owing to smoke exposure from the 2023 Canadian wildfires, indicating the large health impacts from long-range transported PM2.5 pollution.

Although notable impacts of the 2023 Canadian wildfires on surface PM2.5 concentration in Europe are observed, those impacts are remarkably low compared with the impact of smoke from local fires that are not diluted by long-range transport. For instance, ref. [126] estimated that 2.1 million people were exposed to concentrations above 36 μg m−3 for at least 1 day between 23 and 30 June owing to the Saddleworth Moor and Winter Hill fires in northern England. In comparison, our estimates shows that 0.81 million people in Europe were exposed to the same level of PM2.5 pollution for at least 1 day between 26 June and 7 July 2023 owing to the trans-Atlantic pollution of Canadian wildfires.

Dust has been recognized as another important natural source of air pollution44,127. A study[127] estimated that Sahara dust contributed 5–20 μg m−3 of surface PM_10 concentration in South Europe and 0.5–1.0 μg m−3 in North Europe during 2016–2017. Another study[44] estimated that windblown dust increased the annual mean PM2.5 exposure in 2017 by 1.72 μg m−3, 1.50 μg m−3, 1.18 μg m−3, 0.07 μg m−3 and 0.19 μg m−3 in Central Europe, Eastern Europe, Western Europe, Canada and the USA, respectively. PM2.5 exposure was lower than dust-related PM2.5 exposure in Europe but higher than that in Canada and the USA. In turn, windblown dust contributed to 34,972, 33 and 1,126 annual chronic premature deaths in Europe, Canada and the USA, respectively[44]. Our estimates for Canadian-wildfire-related deaths are substantially lower than dust-related deaths in Europe, but much higher than that in Canada and the USA. It should be noted that both dust and fire activities have large interannual variabilities so the comparison could be different for other years.

Data availability

GFEDv4.1s emission data are available at https://surfdrive.surf.nl/files/index.php/s/5y7TdE6ufwpkAW1. QFEDv2.5r1 emission data are available at https://portal.nccs.nasa.gov/datashare/gmao/qfed/. GFASv1.2 data are available at https://ads.atmosphere.copernicus.eu/cdsapp#!/dataset/cams-global-fire-emissions-gfas?tab=overview/. PM2.5 surface monitoring data for different regions are available from Environmental Canada (https://data-donnees.az.ec.gc.ca/data/air/monitor/national-air-pollution-surveillance-naps-program/Data-Donnees/), the US Environmental Protection Agency (US EPA) AirNow (https://www.epa.gov/outdoor-air-quality-data/download-daily-data), US EPA Interagency Monitoring of Protected Visual Environments (IMPROVE) (https://views.cira.colostate.edu/fed/QueryWizard/Default.aspx), the US Forest Service (https://info.airfire.org/airmonitor-package), the European Air Quality Portal (https://eeadmz1-cws-wp-air02.azurewebsites.net/), the China National Environmental Monitoring Center (CNEMC, http://www.cnemc.cn/), and OpenAQ (https://openaq.org/). Satellite AOD retrievals from the MODIS Level 2 aerosol products (MOD04 and MYD04) are available at https://ladsweb.modaps.eosdis.nasa.gov/search/. The CAMS modelling and reanalysis data are available at https://ads.atmosphere.copernicus.eu. The smoke plume information from the Hazard Mapping System (HMS) is available at https://www.ospo.noaa.gov/Products/land/hms.html. The GEOS-FP reanalysis data are available at https://portal.nccs.nasa.gov/datashare/gmao/geos-fp/. The WorldPop gridded global population distribution data can be obtained from https://www.worldpop.org/. The national total population data of each year are from United Nations (https://population.un.org/wpp/), US Census Bureau, Population Division (https://www.census.gov/data/tables/time-series/demo/popest/2020s-state-total.html) and Statistics Canada (https://www150.statcan.gc.ca/). The baseline national all-cause death rate, cause-specific death rate, and 5-year age-specified population structure from the GBD study can be obtained from https://vizhub.healthdata.org/gbd-results/. Global fire-related PM2.5 concentration in 2023 generated from this study is available from the figshare repository at https://doi.org/10.6084/m9.figshare.25736643.v1 and http://tapdata.org.cn. All maps were created based on freely available shapefiles from the Database of Global Administrative Boundaries (https://gadm.org/), using NCAR Command Language (NCL) v6.4.0 (http://www.ncl.ucar.edu/) and R v4.1.3 (https://www.r-project.org/) with the ggplot2 v.3.5.1 (https://ggplot2.tidyverse.org) library. All data presented in the paper are provided with this paper. Source data are provided with this paper.

Code availability

GEOS-Chem 14.0.1 used in this study is available at https://zenodo.org/records/7271974 (ref. [128]). The code developed for this study is available from https://github.com/QingyangXiao/Code-for-calculating-global-fire-related-PM2.5-and-health-impacts.

References

1. Canadian wildfire smoke puts around 70 million US residents under air quality alerts. Cable News Network https://edition.cnn.com/2023/07/16/weather/canada-wildfires-us-air-quality-alerts-sunday/index.html (2023).

2. Wang, Z. et al. Severe global environmental issues caused by Canada’s record-breaking wildfires in 2023. Adv. Atmos. Sci. 41, 565–571 (2024).

3. Schimel, D. & Baker, D. The wildfire factor. Nature 420, 29–30 (2002).

4. Friedlingstein, P. et al. Global Carbon Budget 2023. Earth Syst. Sci. Data 15, 5301–5369 (2023).

5. Bond, W. J., Woodward, F. I. & Midgley, G. F. The global distribution of ecosystems in a world without fire. New Phytol. 165, 525–537 (2005).

6. Kelly, L. T. et al. Fire and biodiversity in the Anthropocene. Science 370, eabb0355 (2020).

7. McClure, C. D. & Jaffe, D. A. US particulate matter air quality improves except in wildfire-prone areas. Proc. Natl Acad. Sci. USA 115, 7901–7906 (2018).

8. O’Dell, K., Ford, B., Fischer, E. V. & Pierce, J. R. Contribution of wildland-fire smoke to US PM2.5 and its influence on recent trends. Environ. Sci. Technol. 53, 1797–1804 (2019).

9. Burke, M. et al. The contribution of wildfire to PM2.5 trends in the USA. Nature 622, 761–766 (2023).

10. Xu, R. B. et al. Global population exposure to landscape fire air pollution from 2000 to 2019. Nature 621, 521–529 (2023).

11. Zhang, D. L. et al. Wildland fires worsened population exposure to PM2.5 pollution in the contiguous United States. Environ. Sci. Technol. 57, 19990–19998 (2023).

12. Johnston, F. H. et al. Estimated global mortality attributable to smoke from landscape fires. Environ. Health Perspect. 120, 695–701 (2012).

13. Reid, C. E. et al. Critical review of health impacts of wildfire smoke exposure. Environ. Health Perspect. 124, 1334–1343 (2016).

14. Cascio, W. E. Wildland fire smoke and human health. Sci. Total Environ. 624, 586–595 (2018).

15. Chen, G. B. et al. Mortality risk attributable to wildfire-related PM2.5 pollution: a global time series study in 749 locations. Lancet Planet. Health 5, e579–e587 (2021).

16. Canadian Interagency Forest Fire Centre. Wildfire graphs. CIFFC https://ciffc.net/statistics (2023).

17. Byrne, B. et al. Carbon emissions from the 2023 Canadian wildfires. Nature 633, 835–839 (2024).

18. Meng, J. et al. Source contributions to ambient fine particulate matter for Canada. Environ. Sci. Technol. 53, 10269–10278 (2019).

19. Childs, M. L. et al. Daily local-level estimates of ambient wildfire smoke PM2.5 for the contiguous US. Environ. Sci. Technol. 56, 13607–13621 (2022).

20. Wei, J. et al. Long-term mortality burden trends attributed to black carbon and PM2.5 from wildfire emissions across the continental USA from 2000 to 2020: a deep learning modelling study. Lancet Planet. Health 7, e963–e975 (2023).

21. Wotawa, G. & Trainer, M. The influence of Canadian forest fires on pollutant concentrations in the United States. Science 288, 324–328 (2000).

22. Forster, C. et al. Transport of boreal forest fire emissions from Canada to Europe. J. Geophys. Res. Atmos. 106, 22887–22906 (2001).

23. Colarco, P. R. et al. Transport of smoke from Canadian forest fires to the surface near Washington, DC: injection height, entrainment, and optical properties. J. Geophys. Res. Atmos. 109, D06203 (2004).

24. DeBell, L. J. et al. A major regional air pollution event in the northeastern United States caused by extensive forest fires in Quebec, Canada. J. Geophys. Res. Atmos. 109, D19305 (2004).

25. Vaughan, G. et al. Transport of Canadian forest fire smoke over the UK as observed by lidar. Atmos. Chem. Phys. 18, 11375–11388 (2018).

26. Hung, W. T. et al. The impacts of transported wildfire smoke aerosols on surface air quality in New York State: a case study in summer 2018. Atmos. Environ. 227, 117415 (2020).

27. Yang, Z. F. et al. Influence of the transported Canadian wildfire smoke on the ozone and particle pollution over the mid-Atlantic United States. Atmos. Environ. 273, 118940 (2022).

28. McCracken, T., Chen, P., Metcalf, A. & Fan, C. Quantifying the impacts of Canadian wildfires on regional air pollution networks. Sci. Total Environ. 928, 172461 (2024).

29. Yu, M. Z., Zhang, S. Y., Ning, H., Li, Z. L. & Zhang, K. Assessing the 2023 Canadian wildfire smoke impact in northeastern US: air quality, exposure and environmental justice. Sci. Total Environ. 926, 171853 (2024).

30. Wen, J. F. et al. Quantifying fire-specific smoke exposure and health impacts. Proc. Natl Acad. Sci. USA 120, e2309325120 (2023).

31. Silver, B., Arnold, S. R., Reddington, C. L., Emmons, L. K. & Conibear, L. Large transboundary health impact of Arctic wildfire smoke. Commun. Earth Environ. 5, 199 (2024).

32. Stevens, R., Poterlot, C., Trieu, N., Rodriguez, H. A. & Hayes, P. L. Transboundary transport of air pollution in eastern Canada. Environ. Sci. Adv. 3, 448–469 (2024).

33. Xie, Y. Y. et al. Tripling of western US particulate pollution from wildfires in a warming climate. Proc. Natl Acad. Sci. USA 119, e2111372119 (2022).

34. Brown, P. T. et al. Climate warming increases extreme daily wildfire growth risk in California. Nature 621, 760–766 (2023).

35. Wang, S. S. C., Leung, L. R. & Qian, Y. Projection of future fire emissions over the contiguous US using explainable artificial intelligence and CMIP6 models. J. Geophys. Res. Atmos. 128, e2023JD039154 (2023).

36. Bey, I. et al. Global modeling of tropospheric chemistry with assimilated meteorology: model description and evaluation. J. Geophys. Res. Atmos. 106, 23073–23095 (2001).

37. Van Der Werf, G. R. et al. Global fire emissions estimates during 1997–2016. Earth Syst. Sci. Data 9, 697–720 (2017).

38. Koster, R. D., Darmenov, A. S. & da Silva, A. M. The Quick Fire Emissions Dataset (QFED): Documentation of Versions 2.1, 2.2 and 2.4. Report No. NASA/TM-2015-104606 (NASA, 2015).

39. Kaiser, J. W. et al. Biomass burning emissions estimated with a global fire assimilation system based on observed fire radiative power. Biogeosciences 9, 527–554 (2012).

40. Chen, J. & Hoek, G. Long-term exposure to PM and all-cause and cause-specific mortality: a systematic review and meta-analysis. Environ. Int. 143, 105974 (2020).

41. Wei, J. et al. First close insight into global daily gapless 1 km PM2.5 pollution, variability, and health impact. Nat. Commun. 14, 8349 (2023).

42. Pan, X. H. et al. Six global biomass burning emission datasets: intercomparison and application in one global aerosol model. Atmos. Chem. Phys. 20, 969–994 (2020).

43. Carter, T. S. et al. How emissions uncertainty influences the distribution and radiative impacts of smoke from fires in North America. Atmos. Chem. Phys. 20, 2073–2097 (2020).

44. McDuffie, E. E. et al. Source sector and fuel contributions to ambient PM2.5 and attributable mortality across multiple spatial scales. Nat. Commun. 12, 3594 (2021).

45. Murray, C. J. L. et al. Global burden of 87 risk factors in 204 countries and territories, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019. Lancet 396, 1223–1249 (2020).

46. Xu, R. et al. Global, regional, and national mortality burden attributable to air pollution from landscape fires: a health impact assessment study. Lancet 404, 2447–2459 (2024).

47. Pope, I. I. I. et al. Mortality risk and fine particulate air pollution in a large, representative cohort of US adults. Environ. Health Perspect. 127, 077007 (2019).

48. Doubleday, A. et al. Mortality associated with wildfire smoke exposure in Washington state, 2006–2017: a case-crossover study. Environ. Health 19, 4 (2020).

49. Connolly, R. et al. Mortality attributable to PM2.5 from wildland fires in California from 2008 to 2018. Sci. Adv. 10, eadl1252 (2024).

50. Orellano, P., Reynoso, J., Quaranta, N., Bardach, A. & Ciapponi, A. Short-term exposure to particulate matter (PM_10 and PM2.5), nitrogen dioxide (NO_2), and ozone (O_3) and all-cause and cause-specific mortality: systematic review and meta-analysis. Environ. Int. 142, 105876 (2020).

51. Kahn, R. A. et al. Wildfire smoke injection heights: two perspectives from space. Geophys. Res. Lett. 35, L04809 (2008).

52. Fenech, S. et al. The influence of model spatial resolution on simulated ozone and fine particulate matter for Europe: implications for health impact assessments. Atmos. Chem. Phys. 18, 5765–5784 (2018).

53. Zhao, X. et al. Improving assessment of population exposure and health impacts to PM2.5 with high spatial and temporal data. GISci. Remote Sens. 61, 2388921 (2024).

54. Xu, R. B. et al. Wildfires, global climate change, and human health. N. Engl. J. Med. 383, 2173–2181 (2020).

55. Aguilera, R., Corringham, T., Gershunov, A. & Benmarhnia, T. Wildfire smoke impacts respiratory health more than fine particles from other sources: observational evidence from Southern California. Nat. Commun. 12, 1493 (2021).

56. Wong, J. P. S. et al. Effects of atmospheric processing on the oxidative potential of biomass burning organic aerosols. Environ. Sci. Technol. 53, 6747–6756 (2019).

57. Zhou, S., Xu, R. B., Chen, G. B., Yu, P. & Guo, Y. M. Where is the boundary of wildfire smoke? Innov. Med. 1, 100024 (2023).

58. Liu, J. C., Pereira, G., Uhl, S. A., Bravo, M. A. & Bell, M. L. A systematic review of the physical health impacts from non-occupational exposure to wildfire smoke. Environ. Res. 136, 120–132 (2015).

59. Grant, E. & Runkle, J. D. Long-term health effects of wildfire exposure: a scoping review. J. Clim. Change Health 6, 100110 (2022).

60. Gao, Y. et al. Long-term impacts of non-occupational wildfire exposure on human health: a systematic review. Environ. Pollut. 320, 121041 (2023).

61. Magzamen, S. et al. Differential cardiopulmonary health impacts of local and long‐range transport of wildfire smoke. GeoHealth 5, e2020GH000330 (2021).

62. Senande-Rivera, M., Insua-Costa, D. & Miguez-Macho, G. Spatial and temporal expansion of global wildland fire activity in response to climate change. Nat. Commun. 13, 1208 (2022).

63. Pavlovic, R. et al. The FireWork air quality forecast system with near-real-time biomass burning emissions: recent developments and evaluation of performance for the 2015 North American wildfire season. J. Air Waste Manage. Assoc. 66, 819–841 (2016).

64. Kim, H. C., Chai, T. F., Stein, A. & Kondragunta, S. Inverse modeling of fire emissions constrained by smoke plume transport using HYSPLIT dispersion model and geostationary satellite observations. Atmos. Chem. Phys. 20, 10259–10277 (2020).

65. Randerson, J. T., Van Der Werf, G. R., Giglio, L., Collatz, G. J. & Kasibhatla, P. S. Global Fire Emissions Database, Version 4.1 (GFEDv4) (ORNL DAAC, 2018).

66. Giglio, L., Randerson, J. T. & Van Der Werf, G. R. Analysis of daily, monthly, and annual burned area using the fourth-generation Global Fire Emissions Database (GFED4). J. Geophys. Res. Biogeosci. 118, 317–328 (2013).

67. Randerson, J. T., Chen, Y., van der Werf, G. R., Rogers, B. M. & Morton, D. C. Global burned area and biomass burning emissions from small fires. J. Geophys. Res. Biogeosci. 117, G04012 (2012).

68. Akagi, S. K. et al. Emission factors for open and domestic biomass burning for use in atmospheric models. Atmos. Chem. Phys. 11, 4039–4072 (2011).

69. Randles, C. A. et al. The MERRA-2 aerosol reanalysis, 1980 onward. Part I: System description and data assimilation evaluation. J. Clim. 30, 6823–6850 (2017).

70. Lu, X. et al. Wildfire influences on the variability and trend of summer surface ozone in the mountainous western United States. Atmos. Chem. Phys. 16, 14687–14702 (2016).

71. Liu, J. C. et al. Wildfire-specific fine particulate matter and risk of hospital admissions in urban and rural counties. Epidemiology 28, 77–85 (2017).

72. Wang, S. C. et al. Transport of Central American fire emissions to the U.S. Gulf Coast: climatological pathways and impacts on ozone and PM2.5. J. Geophys. Res. Atmos. 123, 8344–8361 (2018).

73. Lutsch, E. et al. Detection and attribution of wildfire pollution in the Arctic and northern midlatitudes using a network of Fourier-transform infrared spectrometers and GEOS-Chem. Atmos. Chem. Phys. 20, 12813–12851 (2020).

74. Xue, T. et al. Open fire exposure increases the risk of pregnancy loss in South Asia. Nat. Commun. 12, 3205 (2021).

75. Wizenberg, T. et al. Exceptional wildfire enhancements of PAN, C_2H_4, CH_3OH, and HCOOH over the Canadian High Arctic during August 2017. J. Geophys. Res. Atmos. 128, e2022JD038052 (2023).

76. Wu, Y. et al. Wildfire-related PM2.5 and health economic loss of mortality in Brazil. Environ. Int. 174, 107906 (2023).

77. Rienecker, M. M. et al. The GEOS-5 Data Assimilation System-Documentation of Versions 5.0.1, 5.1.0, and 5.2.0. Report No. NASA/TM-2008-104606 (NASA, 2008).

78. Fountoukis, C. & Nenes, A. ISORROPIA II: a computationally efficient thermodynamic equilibrium model for K+–Ca2+–Mg2+–NH_4+–Na+–SO_42––NO_3––Cl––H_2O aerosols. Atmos. Chem. Phys. 7, 4639–4659 (2007).

79. Lin, H. P. et al. Harmonized Emissions Component (HEMCO) 3.0 as a versatile emissions component for atmospheric models: application in the GEOS-Chem, NASA GEOS, WRF-GC, CESM2, NOAA GEFS-Aerosol, and NOAA UFS models. Geosci. Model Dev. 14, 5487–5506 (2021).

80. McDuffie, E. E. et al. A global anthropogenic emission inventory of atmospheric pollutants from sector-and fuel-specific sources (1970–2017): an application of the Community Emissions Data System (CEDS). Earth Syst. Sci. Data 12, 3413–3442 (2020).

81. Simone, N. W., Stettler, M. E. J. & Barrett, S. R. H. Rapid estimation of global civil aviation emissions with uncertainty quantification. Transp. Res Part D 25, 33–41 (2013).

82. Fairlie, T. D., Jacob, D. J. & Park, R. J. The impact of transpacific transport of mineral dust in the United States. Atmos. Environ. 41, 1251–1266 (2007).

83. Jaeglé, L., Quinn, P. K., Bates, T. S., Alexander, B. & Lin, J. T. Global distribution of sea salt aerosols: new constraints from in situ and remote sensing observations. Atmos. Chem. Phys. 11, 3137–3157 (2011).

84. Murray, L. T., Jacob, D. J., Logan, J. A., Hudman, R. C. & Koshak, W. J. Optimized regional and interannual variability of lightning in a global chemical transport model constrained by LIS/OTD satellite data. J. Geophys. Res. Atmos. 117, D20307 (2012).

85. Hudman, R. C. et al. Steps towards a mechanistic model of global soil nitric oxide emissions: implementation and space based-constraints. Atmos. Chem. Phys. 12, 7779–7795 (2012).

86. Guenther, A. B. et al. The Model of Emissions of Gases and Aerosols from Nature version 2.1 (MEGAN2.1): an extended and updated framework for modeling biogenic emissions. Geosci. Model Dev. 5, 1471–1492 (2012).

87. Lin, J. T. & McElroy, M. B. Impacts of boundary layer mixing on pollutant vertical profiles in the lower troposphere: implications to satellite remote sensing. Atmos. Environ. 44, 1726–1739 (2010).

88. Levy, R. C. et al. The Collection 6 MODIS aerosol products over land and ocean. Atmos. Meas. Tech. 6, 2989–3034 (2013).

89. Inness, A. et al. The CAMS reanalysis of atmospheric composition. Atmos. Chem. Phys. 19, 3515–3556 (2019).

90. Schroeder, W. et al. Validation analyses of an operational fire monitoring product: the Hazard Mapping System. Int. J. Remote Sens. 29, 6059–6066 (2008).

91. Wardrop, N. A. et al. Spatially disaggregated population estimates in the absence of national population and housing census data. Proc. Natl Acad. Sci. USA 115, 3529–3537 (2018).

92. Reed, F. J. et al. Gridded population maps informed by different built settlement products. Data 3, 33 (2018).

93. United Nations, Department of Economic and Social Affairs, Population Division. World Population Prospects 2022: Methodology of the United Nations Population Estimates and Projections. Report No. UN DESA/POP/2022/TR/NO. 4 (United Nations, 2022).

94. US Census Bureau, Population Division. Annual Estimates of the Resident Population for the United States, Regions, States, District of Columbia, and Puerto Rico: April 1, 2020 to July 1, 2023. NST-EST2023-POP (US Census Bureau, 2023).

95. Geng, G. N. et al. Tracking air pollution in China: near real-time PM2.5 retrievals from multisource data fusion. Environ. Sci. Technol. 55, 12106–12115 (2021).

96. Xiao, Q. Y. et al. Separating emission and meteorological contributions to long-term PM2.5 trends over eastern China during 2000–2018. Atmos. Chem. Phys. 21, 9475–9496 (2021).

97. Ma, Z. W. et al. Satellite-based spatiotemporal trends in PM2.5 concentrations: China, 2004–2013. Environ. Health Perspect. 124, 184–192 (2016).

98. Bai, K. X., Li, K., Guo, J. P. & Chang, N. B. Multiscale and multisource data fusion for full-coverage PM2.5 concentration mapping: can spatial pattern recognition come with modeling accuracy? ISPRS J. Photogramm. Remote Sens. 184, 31–44 (2022).

99. Xue, T. et al. Spatiotemporal continuous estimates of PM2.5 concentrations in China, 2000–2016: a machine learning method with inputs from satellites, chemical transport model, and ground observations. Environ. Int. 123, 345–357 (2019).

100. Shen, S. et al. Enhancing global estimation of fine particulate matter concentrations by including geophysical a priori information in deep learning. ACS ES&T Air 1, 332–345 (2024).

101. Draxler, R. R. & Hess, G. D. An overview of the HYSPLIT_4 modelling system for trajectories. Aust. Meteorol. Mag. 47, 295–308 (1998).

102. Lu, Z. F., Streets, D. G., Zhang, Q. & Wang, S. W. A novel back‐trajectory analysis of the origin of black carbon transported to the Himalayas and Tibetan Plateau during 1996–2010. Geophys. Res. Lett. 39, L01809 (2012).

103. Tang, W. Y. et al. Widespread phytoplankton blooms triggered by 2019–2020 Australian wildfires. Nature 597, 370–375 (2021).

104. Cedeño Laurent, J. G. et al. Physicochemical characterization of the particulate matter in New Jersey/New York City area, resulting from the Canadian Quebec wildfires in June 2023. Environ. Sci. Technol. https://doi.org/10.1021/acs.est.4c02016 (2024).

105. Zhang, Q. et al. Transboundary health impacts of transported global air pollution and international trade. Nature 543, 705–709 (2017).

106. Zhao, H. Y. et al. Reduction of global life expectancy driven by trade-related transboundary air pollution. Environ. Sci. Technol. Lett. 9, 212–218 (2022).

107. Burnett, R. et al. Global estimates of mortality associated with long-term exposure to outdoor fine particulate matter. Proc. Natl Acad. Sci. USA 115, 9592–9597 (2018).

108. Lelieveld, J., Evans, J. S., Fnais, M., Giannadaki, D. & Pozzer, A. The contribution of outdoor air pollution sources to premature mortality on a global scale. Nature 525, 367–371 (2015).

109. Roberts, G. & Wooster, M. J. Global impact of landscape fire emissions on surface level PM2.5 concentrations, air quality exposure and population mortality. Atmos. Environ. 252, 118210 (2021).

110. Gordon, J. N. D. et al. The effects of trash, residential biofuel, and open biomass burning emissions on local and transported PM2.5 and its attributed mortality in Africa. GeoHealth 7, e2022GH000673 (2023).

111. Butt, E. W. et al. Large air quality and human health impacts due to Amazon forest and vegetation fires. Environ. Res. Commun. 2, 095001 (2020).

112. Nawaz, M. O. & Henze, D. K. Premature deaths in Brazil associated with long-term exposure to PM2.5 from Amazon fires between 2016 and 2019. GeoHealth 4, e2020GH000268 (2020).

113. Matz, C. J. et al. Health impact analysis of PM2.5 from wildfire smoke in Canada (2013–2015, 2017–2018). Sci. Total Environ. 725, 138506 (2020).

114. Koplitz, S. N. et al. Public health impacts of the severe haze in equatorial Asia in September–October 2015: demonstration of a new framework for informing fire management strategies to reduce downwind smoke exposure. Environ. Res. Lett. 11, 094023 (2016).

115. Crippa, P. et al. Population exposure to hazardous air quality due to the 2015 fires in equatorial Asia. Sci. Rep. 6, 37074 (2016).

116. Kiely, L. et al. Air quality and health impacts of vegetation and peat fires in equatorial Asia during 2004–2015. Environ. Res. Lett. 15, 094054 (2020).

117. Barbosa, J. V., Nunes, R. A. O., Alvim-Ferraz, M. C. M., Martins, F. G. & Sousa, S. I. V. Health and economic burden of wildland fires PM2.5-related pollution in Portugal—a longitudinal study. Environ. Res. 240, 117490 (2024).

118. Reddington, C. L. et al. Air pollution from forest and vegetation fires in Southeast Asia disproportionately impacts the poor. GeoHealth 5, e2021GH000418 (2021).

119. Fann, N. et al. The health impacts and economic value of wildland fire episodes in the U.S.: 2008–2012. Sci. Total Environ. 610–611, 802–809 (2018).

120. Ford, B. et al. Future fire impacts on smoke concentrations, visibility, and health in the contiguous United States. GeoHealth 2, 229–247 (2018).

121. O’Dell, K. et al. Estimated mortality and morbidity attributable to smoke plumes in the United States: not just a western US problem. GeoHealth 5, e2021GH000457 (2021).

122. Liu, Y. et al. Health Impact Assessment of the 2020 Washington State wildfire smoke episode: excess health burden attributable to increased PM2.5 exposures and potential exposure reductions. GeoHealth 5, e2020GH000359 (2021).

123. Neumann, J. E. et al. Estimating PM2.5-related premature mortality and morbidity associated with future wildfire emissions in the western US. Environ. Res. Lett. 16, 035019 (2021).

124. Liao, H., Henze, D. K., Seinfeld, J. H., Wu, S. L. & Mickley, L. J. Biogenic secondary organic aerosol over the United States: comparison of climatological simulations with observations. J. Geophys. Res. Atmos. 112, D06201 (2007).

125. Ma, Y. et al. Long-term exposure to wildland fire smoke PM2.5 and mortality in the contiguous United States. Proc. Natl Acad. Sci. USA 121, e2403960121 (2024).

126. Graham, A. M. et al. Impact on air quality and health due to the Saddleworth Moor fire in northern England. Environ. Res. Lett. 15, 074018 (2020).

127. Wang, Q. Q., Gu, J. W. & Wang, X. R. The impact of Sahara dust on air quality and public health in European countries. Atmos. Environ. 241, 117771 (2020).

128. The International GEOS-Chem User Community. geoschem/GCClassic: GEOS-Chem Classic 14.0.1. Zenodo https://doi.org/10.5281/zenodo.7271974 (2022).

Acknowledgements

This work is supported by the National Natural Science Foundation of China (41921005 and 42222507) and the New Cornerstone Science Foundation through the XPLORER PRIZE. We thank G. van der Werf for providing near-real-time GFED4s data and for discussions. We also acknowledge the free use of QFED and GFAS near-real-time fire emission data.

Author information

Author notes

1. These authors contributed equally: Qiang Zhang, Yuexuanzi Wang, Qingyang Xiao

Authors and Affiliations

1. Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing, China

Qiang Zhang, Yuexuanzi Wang, Jin Yang, Wenyu Huang & Changpei He

2. State Key Joint Laboratory of Environmental Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing, China

Qingyang Xiao, Guannan Geng, Xiaodong Liu, Jiajun Liu & Kebin He

3. Department of Earth System Science, Stanford University, Stanford, CA, USA

Steven J. Davis

4. State Key Laboratory of Earth Surface Processes and Disaster Risk Reduction, Beijing Normal University, Beijing, China

Binhe Luo

5. Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, MO, USA

Randall V. Martin

6. School of Population and Public Health, University of British Columbia, Vancouver, British Columbia, Canada

Michael Brauer

7. Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA, USA

Michael Brauer

8. Department of Earth System Science, University of California, Irvine, Irvine, CA, USA

James T. Randerson

Contributions

Q.Z. conceived of and led the study. Y.W. and Q.Z. conducted the GEOS-Chem simulations and the calculated wildfire-related PM2.5. Q.X., Y.W., Q.Z. and X.L. developed the PM2.5 retrieval model and estimated the health impacts. Q.X. and C.H. performed the model evaluation. G.G. and Y.W. conducted the uncertainty analysis. J.Y. performed the back-trajectory analysis. J.L., W.H., B.L., R.V.M., M.B. and J.T.R. provided the analytical tools and data. Q.Z., Y.W., Q.X., G.G., S.J.D. and K.H. interpreted the results. Q.Z., Y.W., Q.X., G.G. and S.J.D. wrote the paper with input from all authors.

Corresponding author

Correspondence to Qiang Zhang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Methodology framework to estimate PM2.5 exposure and mortality attributable to wildfire emissions and from different source regions.

The framework comprises six steps: simulation of total PM2.5 concentration and fractional contribution from wildfires, retrieval of total PM2.5 concentration, retrieval of fire-related PM2.5 concentration, simulation of fractional contribution of the 2023 Canadian wildfires to PM2.5 concentration, retrieval of PM2.5 concentration caused by the 2023 Canadian wildfires, and estimation of premature deaths attributable to PM2.5 exposure from the 2023 Canadian wildfires.

Extended Data Fig. 2 Canadian wildfire emissions from 2000 to 2023.

a, Emissions of CO_2 and air pollutants (PM2.5, BC, OC) in 2023. b, Annual Canadian wildfire CO_2 emissions from 2000–2023. The bars in (a) show the 2023 Canadian wildfire emissions of CO_2 and air pollutants (PM2.5, BC, OC) from GFEDv4.1 s (blue), QFEDv2.5r1 (orange) and GFASv1.2 (yellow). The lines in (b) show annual Canadian wildfire CO_2 emissions from GFEDv4.1 s (blue, 2000–2023), QFEDv2.5r1 (orange, 2001–2023) and GFASv1.2 (yellow, 2003–2023).

Source Data

Extended Data Fig. 3 Region definitions used in this study.

a, The definitions of the global regions. b, The definitions of the wildfire source regions. c, The definitions of the impacted regions in North America.

Extended Data Fig. 4 PM2.5 concentration in Canada and U.S. attributable to wildfires in each region.

a,b, The 2023 annual mean PM2.5 concentrations (μg m–3) over Canada related to Canadian fires (a) and the U.S. fires (b). c,d, The 2023 annual mean PM2.5 concentrations (μg m–3) over the U.S. related to Canadian fires (c) and the U.S. fires (d).

Extended Data Fig. 5 Monthly PM2.5 exposures from different sources in 2023.

a,b,c, Monthly PM2.5 exposure (μg m–3) from wildfires in five source regions (i.e., Eastern Canadian fires, Western Canadian fires, Western U.S. fires, Eastern U.S. fires, and other fires), anthropogenic source, and other sources (including biogenic, dust, and sea salt) in Canada (a), the U.S. (b) and Europe (c) in 2023. In a,b,c, the colors of the stacked bars denote the contribution of the different sources.

Source Data

Extended Data Fig. 6 Spatial distribution of annual primary PM2.5 emissions from wildfires over North America in 2023 in different emission inventories.

a, in GFEDv4.1 s. b, in QFEDv2.5r1. c, in GFAS v1.2.

Extended Data Fig. 7 The cumulative population PM2.5 exposure in the U.S. in 2023 attributable to different wild fire source regions.

The colors of the dash lines denote Canadian fires, U.S. fires and other fires.

Source Data

Extended Data Fig. 8 Station-based cross-validation performance for estimating all-source PM2.5 concentrations.

a,b,c, Station-based twenty-fold cross-validation results for estimating all-source PM2.5 using GFED as a prior fire emission at daily (a), monthly (b), and yearly (c) scale in the year 2023, respectively. RMSE, root mean squared error. NMB, normalized mean bias. d,e,f, Station-based twenty-fold cross-validation results for estimating all-source PM2.5 using QFED as a prior fire emission at daily (d), monthly (e), and yearly (f) scale in the year 2023, respectively. g,h,i, Station-based twenty-fold cross-validation results for estimating all-source PM2.5 using GFAS as a prior fire emission at daily (g), monthly (h), and yearly (i) scale in the year 2023, respectively. Ground-based PM2.5 measurements collected globally, including data from North America (Environmental Canada: https://data-donnees.az.ec.gc.ca/data/air/monitor/national-air-pollution-surveillance-naps-program/Data-Donnees/, US Environmental Protection Agency: https://www.epa.gov/outdoor-air-quality-data/download-daily-data, Interagency Monitoring of Protected Visual Environments: https://views.cira.colostate.edu/fed/QueryWizard/Default.aspx, and AirFire program of the US Forest Service: https://info.airfire.org/airmonitor-package), Europe (European Air Quality Portal: https://eeadmz1-cws-wp-air02.azurewebsites.net/), China (China National Environmental Monitoring Center: http://www.cnemc.cn/), and other regions (OpenAQ: https://openaq.org/).

Extended Data Fig. 9 Cross-validation performance for estimating PM2.5 during fire events.

a,b,c, Twenty-fold cross-validation results for estimating PM2.5 during fire events over Canada using GFED (a), QFED (b) and GFAS (c) as a prior fire emission in the year 2023. RMSE, root mean squared error. NMB, normalized mean bias. d,e,f, Twenty-fold cross-validation results for estimating PM2.5 during fire events over U.S. using GFED (d), QFED (e) and GFAS (f) as a prior fire emission in the year 2023.

Extended Data Table 1 Annual mean PM2.5 exposure attributable to different sources in 2023 and acute exposure metrics of 2023 Canadian wildfires in global regions

Supplementary information

Supplementary Information

The file contains Supplementary Figs. 1–18 and Tables 1–9.

Supplementary Data

nc files for source data for Fig. 1, and Extended Data Figs. 4 and 6.

Source data

Source Data Figs. 1–4 and Extended Data Fig. 2, 5 and 7.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Zhang, Q., Wang, Y., Xiao, Q. et al. Long-range PM2.5 pollution and health impacts from the 2023 Canadian wildfires. Nature 645, 672–678 (2025). https://doi.org/10.1038/s41586-025-09482-1

- Received: 31 March 2024

- Accepted: 31 July 2025

- Published: 10 September 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09482-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Drivers and Impacts of the Record-Breaking 2023 Wildfire Season in Canada

Article Open access 20 August 2024

The contribution of wildfire to PM2.5 trends in the USA

Article 20 September 2023

Human driven climate change increased the likelihood of the 2023 record area burned in Canada

Article Open access 20 December 2024

Article Open access Published: 30 July 2025

Flourishing chemosynthetic life at the greatest depths of hadal trenches

Xiaotong Peng,

Mengran Du,

Andrey Gebruk,

Shuangquan Liu,

Zhaoming Gao,

Ronnie N. Glud,

Peng Zhou,

Ruoheng Wang,

Ashley A. Rowden,

Gennady M. Kamenev,

Anastassya S. Maiorova,

Dominic Papineau,

Shun Chen,

Jinwei Gao,

Helu Liu,

Yuan He,

Inna L. Alalykina,

Igor Yu. Dolmatov,

Hanyu Zhang,

Xuegong Li,

Marina V. Malyutina,

Shamik Dasgupta,

Anastasiia A. Saulenko,

Vladimir A. Shilov,

Shuting Liu,

Tongtong Xie,

Yuangao Qu,

Xikun Song,

Haibin Zhang,

Hao Liu,

Weijia Zhang,

Xiaoxia Huang,

Hongzhou Xu,

Wenjing Xu,

Vladimir V. Mordukhovich &

…

Andrey V. Adrianov

Nature volume 645, pages 679–685 (2025)

Abstract

Hadal trenches, some of the Earth’s least explored and understood environments, have long been proposed to harbour chemosynthesis-based communities1,2. Despite increasing attention, actual documentation of such communities has been exceptionally rare3,4. Here we report the discovery of the deepest and the most extensive chemosynthesis-based communities known to exist on Earth during an expedition to the Kuril–Kamchatka Trench and the western Aleutian Trench using the manned submersible Fendouzhe. The communities dominated by siboglinid Polychaeta and Bivalvia span a distance of 2,500 km at depths from 5,800 m to 9,533 m. These communities are sustained by hydrogen sulfide-rich and methane-rich fluids that are transported along faults traversing deep sediment layers in trenches, where methane is produced microbially from deposited organic matter, as indicated by isotopic analysis. Given geological similarities with other hadal trenches, such chemosynthesis-based communities might be more widespread than previously anticipated. These findings challenge current models of life at extreme limits and carbon cycling in the deep ocean.

Similar content being viewed by others

Main

Chemosynthesis-based communities represent a remarkable example of life’s ability to adapt and thrive in some of the most extreme conditions on Earth5,6,7,8. Since the initial discovery of these communities at hydrothermal vents[9], the detection of chemosynthesis-based communities at cold seeps, supporting highly diverse and abundant chemosymbiotic biota1,3,4,5,6,7,8, has increased and expanded our understanding of deep-sea ecological systems and the biogeochemical processes that underpin them. The communities, typically dominated by Bivalvia and Siboglinidae, and sustained by microbial chemosynthesis, are confined to areas where fluids rich in hydrogen sulfide and/or methane are released through geological fractures6,7.

Despite being found on passive and active margins across a wide range of ocean depths5,6,7,8, cold-seep communities have remained largely unexplored in hadal trenches with depths exceeding 6,000 m. Only two small seep communities at hadal depths have been discovered by submersible and remotely operated vehicle, one dominated by vesicomyid clams at nearly 6,437 m depth and another dominated by thyasirid clams at 7,326–7,434 m in the Japan Trench3,4,10. In addition, probable chemosynthetic mats have been observed at a depth of 10,677 m at the bottom of the Mariana Trench[11]; however, they are not associated with any seep animal communities. The biogeographical distribution of chemosynthesis-based communities in the deepest parts of the world’s oceans, their potential roles in shaping the deep-sea ecosystem and the mechanisms behind the formation of methane seeps at such great depths remain elusive.

The Kuril–Kamchatka Trench and the Aleutian Trench are formed by the tectonic interactions between the Pacific Plate and the North American Plate, and meet at the Kamchatka Aleutian Transition connection[12]. This area is geologically highly active with many seismically and volcanically active sites. The Kuril–Kamchatka Trench is formed by the northwestward subduction of the Pacific Plate beneath the Okhotsk Plate and extends around 2,100 km from Hokkaido in the south to Kamchatka Peninsula in the north[13]. The maximum depth of the trench bottom reaches 9,578 m, based on our submersible conductivity–temperature–depth data. Previous research conducted by expeditions aboard research vessel (RV) Vityaz and RV Sonne in the Kuril–Kamchatka Trench shows that the trench is characterized by predominantly heterotrophic benthic fauna14,15. However, some specimens of chemosymbiotrophic taxa15,16, in particular frenulate siboglinids, were also recovered using a trawl, indicating that methane seeps may exist on the trench bottom. The Aleutian Trench is about 2,900 km long, extends from the Alaska and Kenai peninsulas in North America to Kamchatka[13] and marks a boundary where the Pacific Plate has been subducting northwestwards beneath the Bering Sea Plate. Both trenches underlie a highly productive boreal region of the North Pacific Ocean and are characterized by distinct spring blooms and high annual primary production[17].

Chemosynthetic community distribution and diversity

Investigations of the trench bottom of the Kuril–Kamchatka Trench and the western Aleutian Trench from 8 July to 17 August 2024, using RV Tansuoyihao with the full-ocean-depth manned submersible Fendouzhe capable of reaching the deepest part of the ocean at nearly 11,000 m, resulted in the discovery of widespread cold-seep chemosynthesis-based communities in both trenches (Fig. 1). During dive FDZ 271 in the Kuril–Kamchatka Trench, we first encountered dense chemosynthetic communities dominated by frenulate siboglinids at a depth of 9,533 m, situated atop black muds at the boundary between the trench bottom and the basement of the accretionary prism. This boundary corresponds to the outcrop of a geological normal fault, a feature formed by bending of the incoming plate, as indicated by regional seismic data[18]. We have designated this seep site as The Deepest because of its unparalleled depth, marking it as the deepest known seepage location discovered so far (Fig. 2a). Subsequent to this initial discovery, we executed a comprehensive series of 23 dives in geologically analogous settings to determine the spatial distribution, scale and biodiversity of the chemosynthetic communities inhabiting the trench floors. During 19 of these dives (Supplementary Table 1), we observed, recorded and sampled chemosynthesis-based communities, revealing their proliferation in a distinct zone along the basement of the accretionary prism. This zone stretches 2,500 km along the bottom of the trenches, representing a notable ecological feature of these two hadal trenches that has not been recognized or reported despite previous sediment and fauna investigations in these areas.

Fig. 1: Map showing the Kuril–Kamchatka Trench and western Aleutian Trench.

The study area, situated in the northwest Pacific, is demarcated by a white rectangle in the inset. Orange dots represent dive sites where chemosynthesis-based communities were observed and sampled and crosses indicate dive sites lacking such communities. Open orange circles delineate potential seep sites characterized by black sediments. White arrows illustrate the direction of subduction for the Pacific Plate beneath the Okhotsk Plate and the Bering Sea Plate. The dashed white lines indicate the transitional connection zones between the Kuril–Kamchatka Trench and the Aleutian Trench. Bathymetric data were acquired using the KM-EM122 multi-beam bathymetric system during the research expedition. Scale bar, 200 km. Credit: map created using Global Mapper 14 software, with background data sourced from GeoMapApp (http://www.geomapapp.org), under a CC BY 4.0 licence.

Fig. 2: Representative fauna of cold-seep sites in the Kuril–Kamchatka Trench and western Aleutian Trench.

a, Free-moving polychaetes Macellicephaloides grandicirra (white; reaching 6.5 cm in size) navigate among dense colonies of frenulate siboglinids, with tubes 20–30 cm in length and approximately 1 mm in diameter, at 9,532 m at The Deepest. b, Clusters of frenulate siboglinids extending red haemoglobin-filled tentacles, with small Gastropoda (white spots) on tops of the tubes near the tentacles, at 9,320 m at Wintersweet Valley. c, Tightly packed frenulate siboglinids are home to abundant free-moving polychaetes M. grandicirra (white) at 9,332 m at Cotton Field. d, Dense aggregation of vesicomyid bivalves A. phaseoliformis (reaching 23 cm in size) in the sediment, with approximately 6–8 cm of valves exposed and often hosting Actiniaria, at 5,743 m at Clam Bed. e, Tube-dwelling polychaetes Anobothrus sp. and Actiniaria are dominant at 6,870 m at Aleutian Deepest, with spots of white microbial mats. f, Dense aggregation of vesicomyid bivalves I. fossajaponicum (reaching 3 cm in size) associated with black sediments and accompanied by tube-dwelling polychaetes Anobothrus sp. at 6,928 m at Aleutian Deepest. g, Dark blue muds surrounded by clusters of frenulate siboglinids, mark methane seeps at 6,800 m at Blue Marsh. h, Large patches of white, snow-like microbial mats stretch tens of metres, accompanied by frenulate siboglinid tubeworms at 6,700 m at Icy River. The images were taken by the manned submersible equipped with a high-definition camera system. The name of each cold seep indicated in the lower left corner. The distance between laser beams is 10 cm. An expanded showcase of cold-seep fauna is given in Supplementary Video 1.

The species composition and structure of chemosynthesis-based communities in the Kuril–Kamchatka Trench, with depths ranging from nearly 7,000 m to 9,533 m, is distinct from those observed in the Kamchatka Aleutian Transition and the western Aleutian Trench where depths are predominantly less than 7,000 m. In the Kuril–Kamchatka Trench, most communities are dominated by frenulate siboglinids (Extended Data Fig. 1). The composition of siboglinid species among communities in the Kuril–Kamchatka Trench seems to differ considerably. The most abundant species are representatives of Lamellisabella, Polybrachia, Spirobrachia and Zenkevitchiana. A notable discovery in the central Kuril–Kamchatka Trench at a depth of 9,120 m (dive FDZ 274) is the Wintersweet Valley site, which is predominantly inhabited by two species of frenulate siboglinids (Lamellisabella and Polybrachia) (Fig. 2b). These frenulate siboglinids were found in great abundance along a substantial portion of a seep field, around 2 km in length, which was explored during a single dive. The colonies consist of thousands of individuals with tubes extending out of the sediment. Associated with the frenulate siboglinids is a suite of species obligate to this particular habitat, including tube-dwelling polychaetes Terebelliformia and numerous Gastropoda that settled on the siboglinid tubes, as well as a variety of heterotrophic benthic fauna including free-moving polychaetes Macellicephaloides, crinoids Bathycrinus, holothurians Elpidia hanseni and amphipods сf. Princaxelia.

In addition, two other large cold-seep fields, the Dead Valley and Cotton Field sites, were observed at depths of 9,522 and 9,566 m during dive FDZ 275. These fields are located roughly 120 km southwest of Wintersweet Field and extend at least 2.2 km along the 9,520 m contour line. In Dead Valley, dense clusters of frenulate siboglinids occur, with tubes covered by white flocculent material and lying almost horizontally (Extended Data Fig. 2). Siboglinids seem to be dead, suggesting cessation of fluid activity in this part of the field. By contrast, Cotton Field (Fig. 2c), situated 50 m southwest of Dead Valley, supports dense populations of living frenulate siboglinids in association with numerous free-moving polychaetes (Macellicephalinae) and Gastropoda. It is noteworthy that frenulate siboglinids were encountered in nine of eleven dives conducted at the base of the accretionary prisms in the Kuril–Kamchatka Trench, albeit with varying densities of occurrence. During dive FDZ 278, frenulate siboglinids with a relatively high abundance of thyasirid bivalves (Tartarothyasira cf. hadalis) and tube-dwelling polychaetes (Anobothrus sp.) were discovered at a depth of 8,764 m. Tartarothyasira hadalis (initially described as Maorithyas hadalis[10]) has been documented in the hadal zone of the Japan Trench at a depth of 7,326–7,434 m (refs. 3,11). The presence of these chemosymbiotrophic bivalves in the Kuril–Kamchatka Trench marks the deepest occurrence of such organisms ever discovered in hadal zones.

In contrast to the Kuril–Kamchatka Trench, the chemosynthesis-based communities located in the Kamchatka Aleutian Transition are characterized by a high abundance of two species of chemosymbiotrophic vesicomyid clams Abyssogena phaseoliformis and Isorropodon fossajaponicum (Extended Data Table 1 and Extended Data Fig. 3). Fields of siboglinids and clusters of bivalves in the Kamchatka Aleutian Transition were located next to each other, but did not overlap. During dive FDZ 284, dense aggregations of bivalves were initially identified in muddy sediments at a depth of 5,988 m. The communities in this field are largely dominated by I. fossajaponicum and tube-dwelling ampharetid polychaetes (Anobothrus sp.). On the subsequent dive, FDZ 297, an expansive seep field termed Clam Bed (Fig. 2d) was discovered, extending roughly 2 km along a steep fault at a depth of 5,800 m. The dominant species in this community is A. phaseoliformis. In addition to clams, the seep field supports a diverse array of fauna, including gastropods Peltospiridae and Provanidae, tube-dwelling polychaetes Ampharetidae and Maldanidae, free-moving polychaetes Polynoidae and Dorvilleidae, amphipods cf. Abyssododecas and actiniarians Sagartiidae. Similar A. phaseoliformis dominated communities have previously been described for the Japan Trench and the eastern Aleutian Trench19,20.

The cold-seep communities in the western Aleutian Trench are dominated by Bivalvia, Siboglinidae or Ampharetidae. During dives FDZ 285 and FDZ 296, we documented the presence of thyasirid (Tartarothyasira cf. hadalis and Axinus sp.) and vesicomyid (I. fossajaponicum) bivalve aggregations (Extended Data Table 1), as well as tube-dwelling polychaetes Anobothrus sp. (Fig. 2e,f), distributed discontinuously along a 5-km stretch of a subducting normal fault between depths of 6,900 and 6,930 m. In addition, during dive FDZ 286, a large field of Tartarothyasira cf. hadalis more than 500 m across was observed at a depth of 6,756 m (Extended Data Fig. 2). Frenulate siboglinids are primarily located around the periphery of areas with aggregations of bivalves. During dives FDZ 294 and FDZ 295, a seep field designated as Blue Marsh (Fig. 2g) extending over at least 2 km, was discovered at a depth of 6,635 m. The central regions of these seeps are commonly dominated by tube-dwelling Ampharetidae, whereas the margins are predominantly inhabited by frenulate siboglinids, Polybrachia, Spirobrachia and Zenkevitchiana. Furthermore, a seep field named Icy River (Fig. 2h) was noted east of the Blue Marsh field at a depth of 6,630 m. This field is characterized by white microbial mats surrounded by frenulate siboglonids. In comparison with the Kuril–Kamchatka Trench, the abundance of bivalves and tube-dwelling polychaetes in the western Aleutian Trench is notably higher.

The seep communities identified in this study, akin to those documented in the hadal zone and at shallower depths3,4,20,21,22, are distinguished by their exceptionally high abundance and density of specialized species. We found maximum densities of up to 5,813 ± 1,335 (mean ± s.d.) Siboglinidae and 293 ± 69 Bivalvia per square metre in two trenches (Supplementary Table 1). The composition and structure of the investigated communities exhibit a marked patchiness across various spatial scales. This variability is observed not only in individual trenches and across depth ranges, but also between different trenches. Furthermore, certain species are distributed across a broad latitudinal and bathymetric gradient. The consistent presence of the same chemosymbiotrophic species across the Japan, Kuril–Kamchatka and Aleutian trenches suggests the presence of a connected system of reducing habitats in the hadal zone of the northern Pacific. Connections among the trench-hosted seep communities may extend even farther south to the Japan and Mariana trenches, as suggested by the presence of similar looking clam taxa20,21,22.

Pore-water and carbonate geochemistry

The molecular and isotopic compositions of gases associated with cold seeps in the seep sediments provide compelling evidence for a microbial origin of methane (Extended Data Table 2). Analysis of hydrocarbon in head gases and sediments of pushcores showed that methane constitutes 100% of the total hydrocarbons, suggesting a microbial origin for the methane23,24. Analysis of carbon (C) and deuterium (D) stable isotope showed that methane samples exhibited δ^13CVPDB (Vienna Pee Dee Belemnite) values ranging from −78.1‰ to −95.7‰ and δDVSMOW (Vienna Standard Mean Ocean Water) values ranging from −142.2‰ to −188.8‰. These findings further indicate that the methane is derived from microbial carbonate reduction rather than from methyl-based methanogenesis25,26,27,28 (Fig. 3a). These geochemical data collectively indicate that the methane present in the seep sediments is the result of microbial reduction of CO_2 derived from sedimentary organic matter.

Fig. 3: Origins and phases of methane in hadal cold seeps.

a, δ^13CVPDB and δDVSMOW diagram classifying the source of methane. The base diagram is adapted from previous studies25,26,28, which used field measurements of stable carbon and hydrogen isotopes of methane (CH_4) from diverse sedimentary environments to distinguish between different types of microbial and thermogenic methanogenesis. Yellow dots in the CO_2 reduction (CR) category represent data from the methane samples analysed in this study. b, Schematic phase diagram of methane hydrate–sea water system. Solid black lines represent the phase boundaries between H+I – H+L and H+L – L+V ; the shaded (grey blue) H+L phase zone and grey lines therein indicate the methane hydrate solubilities in sea water (mCH_4, in ppm). Red diamonds represent the temperature and pressure conditions at stations where seeps are present. H + I, methane hydrate + ice; H + L, methane hydrate + liquid; L + V, liquid + vapour; M, methyl-based methanogenesis.

The sediments associated with cold seeps are typically dark grey to black, coloration attributed to the high iron sulfide content present in the sediment matrix. Upon retrieval, sediment cores from these seeps exhibited a distinct hydrogen sulfide odour. The vertical profiles of methane, ammonia \(({{\rm{NH}}}_{4}^{+})\), dissolved organic carbon, dissolved inorganic carbon (DIC), δ^13C-DIC, sulfate \(({{\rm{SO}}}_{4}^{2-})\), hydrogen sulfide and salinity in two pushcores showed typical distribution patterns associated with cold-seep environments (Extended Data Fig. 4). These patterns indicate the processes of anaerobic methane oxidation coupled with sulfate reduction5,29,30, organic matter diagenesis5,30 and hydrate decomposition[31]. In addition, metastable hexahydrate calcium carbonate (ikaite, CaCO_3·6H_2O), with clusters of euhedral spear-like crystals (Extended Data Fig. 5), are found in association with the black sediments of cold seeps. Ikaite δ^13C values range from −17.29‰ to −26.89‰ (Extended Data Table 3), suggesting that they are probably authigenic precipitates from \({{\rm{CO}}}_{3}^{2-}\) supplied from the early diagenetic decomposition of sedimentary organic matter[32], preceding microbial methane oxidation.

The modelling of methane phases under hadal zone conditions (Fig. 3b) indicates that at all observed seep sites at depths ranging from 5,662 m to 9,533 m, methane occurs in a dissolved form in pore water and as hydrate, with the absence of a vapour phase. This finding aligns with in situ observations conducted by submersible, which have noted the absence of bubbling and any associated gas phase during dives. Methane concentrations measured in the headspace of sediment pushcore reached 118,882 ppm, substantially exceeding the methane solubility in equilibrium with hydrate at these depths (545 ppm at 9,500 m). Calculation of the hydrate stability zone (Extended Data Fig. 6) indicates the potential presence of hydrates at these profound depths in sedimentary layers. A focused coring and drilling campaign is needed to revisit these seeps to validate this hypothesis.

Formation of hadal cold seeps

The formation processes of cold seeps on trench bottoms differ markedly from those located on accretionary prisms at shallower depths. Cold seeps on accretionary prisms are characterized by the ejection of fluids through thrust faults33,34,35, with these fluids originating from subducted sediments and migrating upwards over distances often exceeding 1,000 m (ref. [36]). By contrast, this study indicates that the fluids associated with trench-bottom seeps are sourced from trench sediments that have not been subducted. This hypothesis is bolstered by the composition of the fluids, primarily biogenic methane—typically produced through microbial carbonate reduction a few to several hundred metres beneath the seabed[37]. We propose that these fluids from the deep sediment layers of the trench migrate upwards along bending-related faults or other major fractures that occur at the leading edge of the accretionary prisms.

Figure 4 illustrates a geological model of cold-seep formation in the Kuril–Kamchatka and Aleutian trenches. In these trenches, the V-shaped topography serves as a natural trap, facilitating the rapid accumulation of substantial quantities of organic matter on the trench bottom38,39. This organic matter is introduced from the highly productive ocean surface where phytoplanktonic blooms frequently occur and from the trench slope by means of gravity flows triggered by earthquakes and landslides40,41. Under the anoxic conditions prevalent in the deep sediment layers, microbial reduction of carbon dioxide derived from sedimentary organic material can sustain methanogenesis25,26,27,28. We argue that, over time, this methane accumulates beneath impermeable sediment layers in the form of dissolved methane fluid and methane hydrate. The compression forces associated with incoming plate subduction[42] then facilitate the lateral migration of methane fluids in the deep sediment layers at the trench bottom, directing them towards the accretionary prism. Ultimately, methane fluids migrate upwards through large fault zones (for instance, bending-related normal faults) that occur at the basement of the accretionary prism. Upon reaching the sea floor, methane fluids escape as a hadal cold seep and support the observed chemosynthesis-based ecosystems.

Fig. 4: Formation of hadal trench cold seeps.

a, Schematic geological model presenting the cross-section view of the subducting plate and the overriding plate along the trench, as indicated by seismic survey data[18] from these areas. The light green arrows depict the migration of organic matter into the trench, encompassing both downward and lateral movements. The white arrow denotes the direction of subduction, and the dashed line signifies the trench axis, which is nearly parallel to the striped zone of cold seeps. Black triangles point to the trench’s axis. Note the prevalence of normal faults developed in the subducting plate. b, Detailed view of the area outlined by the black rectangle in a showing the formation of gas hydrates in deep sediment layers. Methane-rich fluids migrate horizontally towards the accretionary wedge as a result of the compression forces associated with subduction. Normal faults at the leading edge of the accretionary wedge create a pathway that facilitates the upward migration of seep fluids. Figure created using previously published location data[18] of subducting bending faults.

Implications

Although hadal seeps have been documented before, the depths probed here, coupled with the thriving communities discovered and distribution ranges observed, significantly expand the known habitat, depth and biogeographical distributions for a great many species. Moreover, studies of organisms thriving in these communities can provide clues about physiological boundaries, adaptive strategies and previously unknown animal–microbe interactions shaped by high-pressure conditions[1]. Our findings also challenge the traditional perspective on the energy sources sustaining hadal fauna, which were predominantly believed to be derived from surface-derived particulate organic matter and carrion fall[43]. The widespread occurrence of chemosynthesis-based communities suggests an underappreciated role of chemical energy in shaping the hadal ecosystem. The co-existence of chemosynthesis-based organisms with a substantial number of heterotrophic benthic fauna, such as Actiniaria, Echiura, Holothuroidea and Amphipoda (Extended Data Fig. 7), suggests that methane seep production in the trench extends its influence to the broader benthic community[44]. If such a trophic subsidy for heterotrophic benthic fauna is demonstrated and quantified by follow-up research, this study would have served to highlight a previously unrecognized contribution of chemosynthetic processes to the overall functioning of hadal ecosystems.

The detection of anomalously high methane concentrations and the potential for gas hydrate formation in the hadal zone provide new insights into deep carbon cycling. The widespread methane-rich environments in two hadal trenches, where microbial reduction of CO_2 from sedimentary organic matter presumably results in methane production, suggest a vibrant and active microbial community in the hadal sediments. This indicates that the deep-subsurface biosphere may exert a more important influence on biogeochemical processes in subduction zones, representing a previously unrecognized energy supply45,46. The accumulation of methane in sedimentary layers generated by this deep-subsurface biosphere could potentially sequester considerable amounts of sedimentary organic carbon, suggesting a portion of subducting organic carbon can be stored in the trench sediments in a form of methane for prolonged geological time, rather than being subducted to the deep lithosphere. It remains unknown whether the current findings can be extrapolated to other trench systems, but given the geological similarities hadal methane reservoirs may be more widespread, irrespective of the presence of fault zones that could serve as conduits for the release of methane-rich fluids. This hypothesis is supported by the recovery of gas hydrates from drilling sediments in the Middle America Trench[47] and the Peru–Chile Trench at depths surpassing 5,000 m (ref. [48]), and the presence of similar seep communities in the Japan Trench3,4. These findings underscore the complex nature of carbon cycling in the deep sea and highlight the critical need to integrate hadal processes into global carbon models49,50 to improve the accuracy of predictions about carbon dynamics and climate change responses on geological timescale. Furthermore, the potential presence of methane hydrates at great depths in hadal trenches may enhance global inventory of methane gas hydrate resources.

Methods

The investigation was carried out during TS42 cruise between 7 July and 18 August 2024 by RV Tan Suo Yi Hao with the full-ocean-depth human-occupied vehicle Fendouzhe, which was fitted with hydraulically powered manipulators on two swing arms. Under the guidance of operators in the human-occupied vehicle, the arms efficiently acquired the samples and stored them safely in a biological box and a geological box of the vehicle.

Processing of benthic fauna and sea floor video footage

Upon retrieval of the submersible, all collected specimens were promptly transferred from the biological collection box and slurp sampler to the shipboard laboratory. The specimens were then sorted into main taxonomic groups of different levels using visual inspection or under stereomicroscopes. Each organism was counted and preserved in pre-cooled, non-denatured 95% ethanol or in a 4% buffered formaldehyde solution depending on the taxon. Following initial preservation, certain taxonomic groups were further transferred to 70% ethanol for long-term storage.

Visual assessment of species identification, density and spatial structure of the macro-epifauna and mega-epifauna of the seep communities was carried out on the basis of the analysis of video footage recorded by two  high-definition cameras mounted on the human-occupied vehicle. For each dive, between three and ten representative screenshots showing the densest cold-seep communities were selected from the video footage. The area of each image was estimated using the submersible’s laser scale, which projects two parallel laser points 10 cm apart onto the sea floor. This provided a reliable spatial reference for calculating the area of the sea floor captured in each image. A standardized quadrat (for example, 50 × 50 cm) was drawn near the laser dots by using this laser scale as a reference in the image. The calculated area was then converted into square metres for standardized density calculations. Animals visible in each quadrat were manually counted, and faunal density was expressed as the number of individuals per square metre. For each dive, density values from the selected images were used to calculate the mean faunal density, and the standard deviation was computed to quantify the variability among replicate images.

Phylogenetic analyses of the coxI gene sequences

Up to 0.5 cm^3 of fauna tissue was cut into tiny pieces and subjected to DNA extraction using the PowerSoil DNA Isolation kit (MoBio Laboratories). The extracted DNA was quantified using a Qubit dsDNA HS Assay Kit with Qubit 2.0 fluorometer (Invitrogen). A metagenomic library was constructed using the VAHTS Universal DNA Library Prep Kit for Illumina v.4 and sequenced on the NovaSeq X Plus platform (Illumina) to generate 2 × 150 bp pair-ended reads. Raw sequencing reads were qualified using Fastp v.0.23.2 and assembly into contigs using MEGAHIT v.1.2.9. The coxI gene encoding cytochrome c oxidase subunit I of the fauna was retrieved from metagenomic contigs. The retrieved coxI was searched against the National Center for Biotechnology Information GenBank database for preliminary taxonomy identification.

Gas and pore-water sampling

During each dive, 6–12 sediment pushcores were collected using the manipulators of the submersible. Upon recovery, these pushcores were immediately transported to the ship’s cold room, which is kept at around 4 °C, to facilitate subsequent processing. Among them, one or two pushcores were allocated for gas concentration analysis onboard, with only subsamples exhibiting high methane concentrations being prepared for further carbon and deuterium isotope analysis. In addition, one or two pushcores were used to extract pore water samples for geochemical analysis.

Pore-water sampling was conducted using Rhizon samplers (as described in ref. [51]). These samplers were inserted into the cores at 2-cm intervals and connected to 50-ml evacuated disposable syringes fitted with three-way Luer-lock stopcocks. The first approximately 1 ml of extracted pore water was discarded to remove any contaminants. Subsequently, around 15 ml of pore water was collected within a 2-h time frame. One portion of the pore water was preserved with a 20% zinc acetate solution for subsequent hydrogen sulfide analysis. The remaining pore water samples were transferred to 15-ml centrifuge tubes and frozen for subsequent ion analysis.

For the analysis of gas composition and isotopes, sediment samples were collected using a 2.5-ml cutoff plastic syringe, which was inserted through pre-drilled holes in the pushcore tube at depth intervals of 4 cm. A 2.5-ml sediment sample was then transferred to a 20-ml gas-tight glass vial, which was filled with 2 M NaOH solution and sealed with a crimp cap containing butyl rubber stoppers. The vials were vigorously shaken and stored in an upside-down position at 4 °C until analysis, which was conducted onboard in a single day. Before analysis, the vials were shaken again, and 2 ml of the NaOH solution was replaced with helium gas to create a headspace. The headspace gas from the push core was also directly extracted using a 20-ml syringe equipped with a three-way stopcock and was immediately transferred to a 12-ml vacuum Labco vial for further analysis.

Gas concentration and isotope

The concentration of dissolved gases was determined using a gas chromatograph (Trace GC1310; Thermo Scientific) installed onboard the research vessel. Headspace volumes ranging from 100 to 500 μl were sampled and injected into a gas chromatograph equipped with a flame ionization detector. The analytical precision achieved in these measurements is consistently lower than 5%.

The δ^13C and δD isotopic compositions of methane were analysed using a gas chromatography–isotope ratio mass spectrometer system, which consisted of a Trace GC1310 connected to a Delta V Advantage Isotope Ratio MS (Thermo Scientific). The analysis was conducted at the Institute of Deep-Sea Science and Engineering (IDSSE), Chinese Academy of Sciences.

Methane was selectively separated from the gas matrix using a gas chromatography column (27 m × 0.3  mm × 20.00 μm; PoraPLOT Q). The separated methane was then combusted in a combustion oven at a temperature of 1,000 °C, which was interfaced with the isotope ratio mass spectrometer (IRMS) for subsequent analysis. The resulting CO_2 was directly introduced into the IRMS for measurement.

The precision of the repeated analyses, expressed as the standard deviation (1σ), was ±0.5‰ for δ^13C and ±2‰ for δD. The isotopic compositions of individual carbon compounds were reported as δ-values (‰) relative to the international standards Vienna Peedee Belemnite (VPDB) for δ^13C and Vienna Standard Mean Ocean Water (VSMOW) for δD.

Pore-water geochemistry

Hydrogen sulfide concentrations were determined colorimetrically using the methylene blue method (with a limit of detection of approximately 0.5 μM). The concentration of \({{\rm{SO}}}_{4}^{2-}\) in pore water was quantified by ion chromatography using a Dionex ICS-900 system, which was equipped with an AS50 AutoSampler. To ensure that the \({{\rm{SO}}}_{4}^{2-}\) concentrations fell in the optimal analytical range for the ion chromatograph, the anion samples were diluted 70-fold with Milli-Q water. The analytical precision for the determination of \({{\rm{SO}}}_{4}^{2-}\) was ±3.0%. \({{\rm{NH}}}_{4}^{+}\) concentrations were measured using a fluorescence spectrometer (LS55, PE) following the procedure reported in ref. [52], with a relative deviation of 0.5%. DIC concentrations and δ^13C-DIC values were analysed using a Gas Bench II IRMS at IDSSE. The samples were pretreated with an acid solution on the Gas Bench II; the resulting carbon dioxide, carried by helium, was separated by a constant-temperature chromatographic column and subsequently analysed for isotope abundance using a MAT253 gas stable IRMS. The analytical precision for DIC was ±0.15% and that for δ^13C-DIC was ±0.5‰. Dissolved organic carbon concentrations were measured by a high-temperature catalytic oxidation method using a Multi N/C 3100 (CLD) analyser at IDSSE. Samples were thawed at room temperature and acidified to pH 2 with 2 mol l−1 hydrochloric acid before injection. Salinity was measured in the laboratory using a handheld digital salinity meter (ATAGO PAL-SALT) after the samples were thawed to room temperature.

Methane phase modelling

The phase boundaries and methane hydrate solubility in the methane hydrate–sea water system were calculated using thermodynamic models53,54. The chemical potential of the hydrate phase was determined through the application of the Van der Waals–Platteeuw hydrate model, in conjunction with angle-dependent ab initio intermolecular potentials, as previously described in ref. [55]. The Gibbs–Thomson equation, incorporating appropriately parameterized hydrate–water interface values, was used to account for the capillary effects of porous sediments on the hydrate–liquid–vapour equilibrium and the hydrate–liquid equilibrium. The influence of surface textures and mineral components was neglected in this analysis.

The activity coefficients for water and methane in the methane–sea water system were calculated using the Pitzer model. By applying the Poynting correction to the fugacity of methane dissolved in aqueous solution at the hydrate–liquid equilibrium, where methane gas is absent, the extended model for three-phase equilibrium was adapted to predict the solubility of methane in aqueous solution at the hydrate–liquid equilibrium.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

The coxI gene sequences of six chemosynthetic invertebrates have been deposited in the GenBase database under accession numbers C_AA106802 to C_AA106807 and are publicly accessible at https://ngdc.cncb.ac.cn/genbase.

References

1. Boulègue, J., Benedetti, E. L., Dron, D., Mariotti, A. & Létolle, R. Geochemical and biogeochemical observations on the biological communities associated with fluid venting in Nankai Trough and Japan Trench subduction zones. Earth Planet. Sci. Lett. 83, 343–355 (1987).

2. Blankenship-Williams, L. E. & Levin, L. A. Living deep: a synopsis of hadal trench ecology. Mar. Technol. Soc. J. 43, 137–143 (2016).

3. Fujikura, K. et al. The deepest chemosynthesis-based community yet discovered from the hadal zone, 7326 m deep, in the Japan Trench. Mar. Ecol. Prog. Ser. 190, 17–26 (1999).

4. Ogawa, Y., Fujioka, K., Fujikura, K. & Iwabuchi, Y. En echelon patterns of Calyptogena colonies in the Japan Trench. Geology 24, 807–810 (1996).

5. Levin, L. A. in Oceanography and Marine Biology Vol. 43 (eds Gibson, R. N., Atkinson, R. J. A. & Gordon, J. D. M) 1–46 (CRC, 2005).

6. Sibuet, M. & Olu, K. Biogeography, biodiversity and fluid dependence of deep-sea cold-seep communities at active and passive margins. Deep Sea Res. II 45, 517–567 (1998).

7. Aguilar Pérez, M. I., Zapata-Ramírez, P. A. & Micallef, A. A review of cold seeps in the Western Atlantic, focusing on Colombia and the Caribbean. Front. Mar. Sci. 11, 1430377 (2024).

8. Cordes, E. E. et al. The influence of geological, geochemical, and biogenic habitat heterogeneity on seep biodiversity. Mar. Ecol. 31, 51–65 (2010).

9. Lonsdale, P. Clustering of suspension-feeding macrobenthos near abyssal hydrothermal vents at oceanic spreading centers. Deep Sea Res. 24, 857–863 (1977).

10. Oliver, P. G. & Chen, C. Revision of the generic placement of two hadal bivalves (Bivalvia: Thyasiridae) from the Japan Trench, with the introduction of a new genus Tartarothyas. J. Conchol. 45, 35–50 (2024).

11. Hand, K. P. et al. Discovery of novel structures at 10.7 km depth in the Mariana Trench may reveal chemolithosutotrophic microbial communities. Deep Sea Res. I 160, 103238 (2020).

12. Davaille, A. & Lees, J. M. Thermal modeling of subducted plates: tear and hot spot at the Kamchatka corner. Geophys. Res. Lett. 27, 3663–3666 (2000).

13. Jamieson, A. J. & Stewart, H. A. Hadal zones of the Northwest Pacific Ocean. Prog. Oceanogr. 190, 102477 (2021).

14. Brandt, A., Brix, S., Riehl, T. & Malyutina, M. Biodiversity and biogeography of the abyssal and hadal Kuril–Kamchatka trench and adjacent NW Pacific deep-sea regions. Prog. Oceanogr. 181, 102232 (2020).

15. Kamenev, G. M. et al. Macrofauna and nematode abundance in the abyssal and hadal zones of interconnected deep-sea ecosystems in the Kuril Basin (Sea of Okhotsk) and the Kuril–Kamchatka Trench (Pacific Ocean). Front. Mar. Sci. 9, 812464 (2022).

16. Mironov, A. N., Krylova, E. M. & Drozdov, A. L. Specific taxonomic and trophic structure of hadal benthic communities. In Abstracts of the 9th Deep-Sea Biology Symposium (National Univ. of Ireland, 2000).

17. Shuntov, V. P. Biology of Far-Eastern Seas of Russia Vol. 1 (TINRO-Center, 2001).

18. Klaeschen, D., Belykh, I., Gnibidenko, H., Patrikeyev, S. & von Huene, R. Structure of the Kuril Trench from seismic reflection records. J. Geophys. Res. Solid Earth 99, 24173–24188 (1994).

19. Suess, E. et al. Fluid venting in the eastern Aleutian subduction zone. J. Geophys. Res. Solid Earth 103, 2597–2614 (1998).

20. Sasaki, T., Okutani, T. & Fujikura, K. Molluscs from hydrothermal vents and cold seeps in Japan: a review of taxa recorded in twenty recent years (1984–2004). Venus 64, 87–133 (2005).

21. Okutani, T., Fujikura, K., Watanabe, H. & Ohara, Y. Calyptogena (Abyssogena) mariana: discovery of a new vesicomyid clam from the Mariana Trench. Venus 71, 39–47 (2013).

22. Okumura, T. et al. Brucite chimney formation and carbonate alteration at the Shinkai SeepField, a serpentinite-hosted vent system in the southern Marianaforearc. Geochem. Geophys. Geosys. 17, 3775–3796 (2016).

23. Jeffrey, A. W. A., Pflaum, R. C., McDonald, T. J., Brooks, J. M. & Kvenvolden, K. A. in Initial Reports of the Deep Sea Drilling Project Leg Vol. 84 (ed. Orlofsky, S.) 719–726 (US Government Printing Office, 1985).

24. Kvenvolden, K. A. A review of the geochemistry of methane in natural gas hydrate. Org. Geochem. 23, 997–1008 (1995).

25. Schoell, M. Multiple origins of methane in the Earth. Chem. Geol. 71, 1–10 (1988).

26. Mayumi, D. et al. Hydrogenotrophic methanogens overwrite isotope signals of subsurface methane. Science 386, 1372–1376 (2024).

27. Bueno de Mesquita, J., Wu, D. & Tringe, S. G. Methyl-based methanogenesis: an ecological and genomic review. Microbiol. Mol. Biol. Rev. 87, e0002422 (2023).

28. Milkov, A. V. & Etiope, G. Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples. Org. Geochem. 125, 109–120 (2018).

29. Joye, S. B., Bowles, M. W., Samarkin, V. A., Hunter, K. S. & Niemann, H. Biogeochemical signatures and microbial activity of different cold-seep habitats along the Gulf of Mexico deep slope. Deep Sea Res. II 57, 1990–2001 (2010).

30. Liu, W. et al. Pore-water dissolved inorganic carbon sources and cycling in the shallow sediments of the Haima cold seeps, South China Sea. J. Asian Earth Sci. 201, 104495 (2020).

31. Reitz, A. et al. Sources of fluids and gases expelled at cold seeps offshore Georgia, eastern Black Sea. Geochim. Cosmochim. Acta 75, 3250–3268 (2011).

32. Suess, E. et al. Calcium carbonate hexahydrate from organic-rich sediments of the Antarctic Shelf: precursors of glendonites. Science 216, 1128–1131 (1982).

33. Rathburn, A. E. et al. Geological and biological heterogeneity of the Aleutian Margin (1965–4822 m). Prog. Oceanogr. 80, 22–50 (2009).

34. Watson, S. J. et al. Focused fluid seepage related to variations in accretionary wedge structure, Hikurangi Margin, New Zealand. Geology 48, 56–61 (2019).

35. Riedel, M. et al. Distributed natural gas venting offshore along the Cascadia margin. Nat. Commun. 9, 3264 (2018).

36. Floodgate, G. & Judd, A. G. The origins of shallow gas. Cont. Shelf Res. 12, 1145–1156 (1992).

37. Parkes, R. J., Cragg, B. A., Fry, J. C., Herbert, R. A. & Wimpenny, J. T. Bacterial biomass and activity in deep sediment layers from the Peru margin. Proc. R. Soc. Lond. A 391, 139–153 (1990).

38. Danovaro, R., Della Croce, N., Dell’Anno, A. & Pusceddu, A. A depocenter of organic matter at 7800 m depth in the SE Pacific Ocean. Deep Sea Res. I 50, 1411–1420 (2003).

39. Glud, R. N. et al. High rates of microbial carbon turnover in sediments in the deepest oceanic trench on Earth. Nat. Geosci. 6, 284–288 (2013).

40. Glud, R. N. et al. Hadal trenches are dynamic hotspots for early diagenesis in the deep sea. Commun. Earth Environ. 2, 21 (2021).

41. Itou, M. A large flux of particulate matter in the deep Japan Trench observed just after the 1994 Sanriku-Oki earthquake. Deep Sea Res. I 47, 1987–1998 (2000).

42. Hyndman, R. D. & Davis, E. E. A mechanism for the formation of methane hydrate and seafloor bottom-simulating reflectors by vertical fluid expulsion. J. Geophys. Res. 97, 7025–7041 (1992).

43. Stockton, W. L. & DeLaca, T. E. Food falls in the deep sea: occurrence, quality, and significance. Deep Sea Res. A 29, 157–169 (1982).

44. Åström, E. K. L., Bluhm, B. A. & Rasmussen, T. L. Chemosynthetic and photosynthetic trophic support from cold seeps in Arctic benthic communities. Front. Mar. Sci. 9, 910558 (2022).

45. Bradley, J. A. et al. Widespread energy limitation to life in global subseafloor sediments. Sci. Adv. 6, eaba0697 (2020).

46. Parkes, R. J., Cragg, B. A. & Wellsbury, P. Recent studies on bacterial populations and processes in subseafloor sediments: a review. Hydrogeol. J. 8, 11–28 (2000).

47. Harrison, W. E. & Curiale, J. A. in Initial Reports of the Deep Sea Drilling Project Vol. 67 (eds Aubouin, J. et al.) 591–594 (US Government Printing Office, 1982).

48. Kvenvolden, K. A. & Kastner, M. Gas hydrates of the Peruvian outer continental margin. Proc. Ocean Drill. Prog. Sci. Results 112, 517–526 (1990).

49. Kelemen, P. B. & Manning, C. E. Reevaluating carbon fluxes in subduction zones, what goes down, mostly comes up. Proc. Natl Acad. Sci. USA 112, E3997–E4006 (2015).

50. Plank, T. & Manning, C. E. Subducting carbon. Nature 574, 343–352 (2019).

51. Seeberg-Elverfeldt, J., Schluter, M., Feseker, T. & Kolling, M. Rhizon sampling of porewaters near the sediment-water interface of aquatic systems. Limnol. Oceanogr. Methods 3, 361–371 (2005).

52. Holmes, R. M., Aminot, A., Kerouel, R., Hooker, B. A. & Peterson, B. J. A simple and precise method for measuring ammonium in marine and freshwater ecosystems. Can. J. Fish. Aquat. Sci. 56, 1801–1808 (1999).

53. Duan, Z. & Sun, R. A model to predict phase equilibrium of CH_4 and CO_2 clathrate hydrate in aqueous electrolyte solutions. Am. Mineral. 91, 1346–1354 (2006).

54. Sun, R. & Duan, Z. Prediction of CH_4 and CO_2 hydrate phase equilibrium and cage occupancy from ab initio intermolecular potentials. Geochim. Cosmochim. Acta 69, 4411–4424 (2005).

55. Sun, R. & Duan, Z. An accurate model to predict the thermodynamic stability of methane hydrate and methane solubility in marine environments. Chem. Geol. 244, 248–262 (2007).

Acknowledgements

We thank the crews, pilots and scientists aboard RV Tan Suo Yi Hao with full-ocean-depth human-occupied vehicle Fendouzhe. X.P. and M.D. are supported by the National Key R&D Program of China (grant no. 2022YFC2805400), the Program for Fostering International Mega-Science of the Chinese Academy of Sciences (grant no. 183446KYSB20210002), and the Hainan Provincial Outstanding Talent Team Program ‘Research, Operation, and Application Team for Specialized Large-Scale Deep-Sea Submersible Equipment’. V.V.M. is supported by the Ministry of Science and Higher Education of the Russian Federation for NSCMB FEB RAS (project reg. nos. 124021900009-6 and 124021900011-9). A.G. is supported by the Russian Science Foundation (grant no. 24-17-00321). This work was under the scheme of the Global Trench Exploration and Dive Programme (Global TREnD).

Author information

Author notes

1. These authors contributed equally: Xiaotong Peng, Mengran Du

Authors and Affiliations

1. State Key Laboratory of Deep-sea Science and Intelligence Technology, Institute of Deep-sea Science and Engineering, Chinese Academy of Sciences, Sanya, China

Xiaotong Peng, Mengran Du, Shuangquan Liu, Zhaoming Gao, Peng Zhou, Ruoheng Wang, Dominic Papineau, Shun Chen, Jinwei Gao, Helu Liu, Yuan He, Hanyu Zhang, Xuegong Li, Shamik Dasgupta, Shuting Liu, Tongtong Xie, Yuangao Qu, Xikun Song, Haibin Zhang, Hao Liu, Weijia Zhang, Xiaoxia Huang, Hongzhou Xu & Wenjing Xu

2. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia

Andrey Gebruk

3. Department of Biology, Danish Center for Hadal Research, University of Southern Denmark, Odense, Denmark

Ronnie N. Glud

4. National Institute of Water and Atmospheric Research, Wellington, New Zealand

Ashley A. Rowden

5. School of Biological Sciences, Victoria University of Wellington, Wellington, New Zealand

Ashley A. Rowden

6. A.V. Zhirmunsky National Scientific Center of Marine Biology, Russian Academy of Sciences, Vladivostok, Russia

Gennady M. Kamenev, Anastassya S. Maiorova, Inna L. Alalykina, Igor Yu. Dolmatov, Marina V. Malyutina, Anastasiia A. Saulenko, Vladimir A. Shilov, Vladimir V. Mordukhovich & Andrey V. Adrianov

Contributions

X.P., M.D., A.G. and V.V.M. conceived the research. M.D., Shuangquan Liu, Shuting Liu, X.P., P.Z. and T.X. performed the geochemical measurements. A.G., G.M.K., A.S.M., I.L.A., I.Yu.D., M.V.M., A.A.S., V.A.S., A.V.A., Z.G. and V.M. contributed to fauna data analysis. R.W. performed methane phase modelling. X.P., M.D., Shuangquan Liu, R.N.G., D.P., T.X. and Y.Q. contributed to the geochemical data interpretation. Z.G., A.R., A.G., A.V.A., X.P., M.D., X.S. and V.V.M. contributed to the fauna data interpretation. M.D., X.P., Shuangquan Liu, P.Z., A.G., G.M.K., S.C., Hao Liu, J.G., Z.G., Y.H., H.X., Hanyu Zhang, X.L., S.D., A.S.M., M.V.M., A.A.S., V.A.S., Haibin Zhang, W.X., Helu Liu, W.Z., X.H. and V.V.M. conducted the cruise and collected samples. All co-authors participated in the discussion. X.P., M.D. and V.V.M. wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to Mengran Du or Vladimir V. Mordukhovich.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Lisa Levin, April Stabbins and Andreas Teske for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Some samples of Siboglinidae collected during cruise.

a, FDZ 271, short tubeworms cf. Spirobrachia (from the Deepest seep field). b, FDZ 294, mix of ultra slender & long wide tubeworms (from Blue Marsh, Icy River). c, FDZ 295, beard of ultra slender tubeworms (from Blue Marsh, Icy River). Scale bars=20 mm.

Extended Data Fig. 2 Representative fauna at three hadal cold seeps.

a, Dead Valley. b, Clam Valley. c, Turtle Egg. Scale bars=20 mm.

Extended Data Fig. 3 Representative samples of Bivalvia recovered from seeps.

a, FDZ 286, Tartarothyasira cf. hadalis. b, FDZ 296, Isorropodon fossajaponicum. c, FDZ 298, Axinus sp. d, FDZ 297, Abyssogena phaseoliformis. Scale bars=20 mm.

Extended Data Fig. 4 Vertical profiles of porewater geochemistry in two sediment pushcores (FDZ292-S05 and FDZ294-S08).

a, CH_4. b, \({{\rm{SO}}}_{4}^{2-}\). c, H_2S. d, \({{\rm{NH}}}_{4}^{+}\). e, DOC. f, DIC. g, δ^13C-DIC. h, Salinity.

Extended Data Fig. 5 Representative ikaite samples recovered from cold seeps.

a, Ikaite specimens. b, Photomicrograph of ikaite. Scale bar=1 cm in a and 2 mm in b.

Extended Data Fig. 6 A phase diagram illustrating hydrate stability conditions in the sediments of the investigated hadal zone.

The horizontal black dashed line denotes the 9,533-meter water depth, corresponding to 98.0 MPa of hydrostatic pressure (assuming an average water density of 1.045 g/cm³), above which lies the unconsolidated sub-seafloor sediments. The gray circle denotes the seafloor temperature-pressure conditions at 9,533 meters, with a temperature of 2.25 °C and a pressure of 98.0 MPa. The purple and red lines represent the minimum and maximum geothermal gradients (ranging from 25 to 60 °C/km) within the unconsolidated sediments, respectively. The point of intersection between these geothermal gradients and HLV delineates the vertical limits of the hydrate stability zone (HSZ) within the sediment.

Extended Data Fig. 7 A coexistence example of frenulate siboglinids with Elpidia hanseni.

FDZ 271, at 9532 m at The Deepest. Scale bar=3 cm.

Extended Data Table 1 Typical chemosynthetic invertebrates and their close relatives based on coxI gene sequences

Extended Data Table 2 Gas compositions and isotopic compositions of gases from cold seep sediment cores

Extended Data Table 3 Carbon and oxygen isotope of ikaite

Supplementary information

Supplementary Table 1

Location of all dive sites during the expedition and descriptions of seep fields.

Reporting Summary

Supplementary Video 1

Typical cold seep fauna in the Kuril–Kamchatka Trench and the western Aleutian Trench.

Peer Review File

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Peng, X., Du, M., Gebruk, A. et al. Flourishing chemosynthetic life at the greatest depths of hadal trenches. Nature 645, 679–685 (2025). https://doi.org/10.1038/s41586-025-09317-z

- Received: 31 December 2024

- Accepted: 23 June 2025

- Published: 30 July 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09317-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Microbial community structure in hadal sediments: high similarity along trench axes and strong changes along redox gradients

Article Open access 08 June 2021

Microbial ecology of the newly discovered serpentinite-hosted Old City hydrothermal field (southwest Indian ridge)

Article Open access 02 November 2020

Metabolic adaptations underpin high productivity rates in relict subsurface water

Article Open access 05 August 2024

Earth’s deepest ecosystem discovered six miles below the sea

- Benjamin Thompson

- Nick Petrić Howe

Nature Nature Podcast 30 Jul 2025

Chemicals seeping from the sea floor sustain an extreme-depth ecosystem

Nature Research Briefing 30 Jul 2025

The ocean's deepest animal ecosystem

- Shamini Bundell

Nature Nature Video 31 Jul 2025

Article Open access Published: 06 August 2025

Whole-genome sequencing of 490,640 UK Biobank participants

The UK Biobank Whole-Genome Sequencing Consortium

Nature volume 645, pages 692–701 (2025)

Abstract

Whole-genome sequencing provides an unbiased and complete view of the human genome and enables the discovery of genetic variation without the technical limitations of other genotyping technologies. Here we report on whole-genome sequencing of 490,640 UK Biobank participants, building on previous genotyping effort[1]. This advance deepens our understanding of how genetics associates with disease biology and further enhances the value of this open resource for the study of human biology and health. Coupling this dataset with rich phenotypic data, we surveyed within- and cross-ancestry genomic associations and identified novel genetic and clinical insights. Although most associations with disease traits were primarily observed in individuals of European ancestries, strong or novel signals were also identified in individuals of African and Asian ancestries. With the improved ability to accurately genotype structural variants and exonic variation in both coding and UTR sequences, we strengthened and revealed novel insights relative to whole-exome sequencing2,3 analyses. This dataset, representing a large collection of whole-genome sequencing data that is available to the UK Biobank research community, will enable advances of our understanding of the human genome, facilitate the discovery of diagnostics and therapeutics with higher efficacy and improved safety profile, and enable precision medicine strategies with the potential to improve global health.

Similar content being viewed by others

Main

The UK Biobank (UKB) is a population‐based study that collected detailed information from 490,640 UK participants, including biological samples and comprehensive health‐related and demographic measures[1]. Numerous subsequent data collection and generation efforts, including multimodal brain imaging[4], proteomics[5], metabolomics[6] and others, have markedly increased the depth of the dataset. Here we present a step change in the UKB resource, and for the life sciences, with the completion of whole-genome sequencing (WGS) in 490,640 participants. In the original release, all samples were genotyped[1] and imputed to about 96 million single nucleotide polymorphisms (SNPs). SNP genotyping and imputation allow the accurate characterization of relatively common variants, but these technologies are not suitable for rare genetic variation and complex regions of the genome. UKB samples also underwent whole-exome sequencing[7] (WES), which allows for characterization of the 2–3% of the genome that is exonic but omits nearly all non-coding variation and is limited in the detection of structural variants (SVs). Rare non-coding variation is known to contribute to human diseases and other complex traits, although this remains relatively understudied8,9,10. This large-scale, deeply phenotyped WGS dataset brings enormous potential to expand our understanding of the role of rare non-coding variation in health and disease.

We demonstrate the utility of WGS in the identification of about 1.5 billion variants (comprising SNPs, insertion–deletion (indel) variants and SVs) in the UKB participants. We observed an 18.8-fold and greater than 40-fold increase in observed human variation compared to imputed array and WES, respectively. These variants were associated with many disease features and traits, enabling improved characterization of disease mechanisms, such as variants influencing disease risk through non-coding mechanisms. These data can be used to address multiple drug discovery and development questions, including target selection, validation, assessment of safety concerns, identification of patient populations with specific underlying genetic drivers of disease, and repositioning opportunities11,12. A valuable unique benefit is that these data will facilitate an improved understanding of the selective constraints acting on disruption outside the coding genome, which will improve the ability to prioritize rare non-coding variants with a large effect on disease risk[13].

This resource will enable exploration of human genetic variation and its effect on disease pathogenesis. The aims of the current study are twofold: to describe and characterize the UKB 490,640 WGS resource; and to highlight some initial examples of unique insights and future avenues for exploration (summarized in Extended Data Fig. 1).

Data processing

Sequencing

The whole genomes of 490,640 UKB participants were sequenced to an average coverage of 32.5× (with at least 23.5× per individual; Supplementary Fig. 1) using Illumina NovaSeq 6000 sequencing machines; in addition, 1,175 samples were sequenced in duplicate for quality control purposes (Supplementary Methods).

Cohorts

We defined five cohorts with distinct ancestry in the UKB WGS dataset using a classifier trained with data from the Genome Aggregation Database[14] (gnomAD; Supplementary Methods), which identified 9,229 participants being of African ancestry (AFR), 2,869 of Ashkenazi Jewish ancestry (ASJ), 2,245 of East Asian ancestry (EAS), 458,855 of non-Finnish European ancestry (NFE) and 9,674 of South Asian ancestry (SAS), and the remaining 7,768 individuals of other ancestries or non-confidently assigned to one group. Most individuals (93.5%) were of non-Finnish European ancestry, with the remaining 31,785 individuals representing other continental populations. Although this resource is largely European, this effort also marks an extensive WGS effort so far in non-European individuals (Supplementary Fig. 2). The increase is notable in the SAS group, where the UKB WGS SAS cohort is two times larger than any other WGS cohort of this ancestry available in gnomAD v315,16 (2,419 SAS individuals), the 1000 Genomes Project[17] (601), Trans-Omics for Precision Medicine[18] (4,599)[18] or the Human Genome Diversity Project[19] (181).

SNPs and indels

This study reports findings from three different SNP and indel datasets: joint calling across all individuals using GraphTyper; single-sample calling with DRAGEN 3.7.8; and multi-sample aggregated DRAGEN 3.7.8 dataset release 2 (Supplementary Methods). This diversity of approaches reflects developments of these methods throughout the course of this project and gives the opportunity to explore the various workflows used by consortium members and other users of the UKB.

We called 1,037,556,156 SNPs and 101,188,713 indels using GraphTyper (Fig. 1a). Most variants, 1,025,188,151 (98.80%) SNPs and 97,190,353 (96.05%) indels, were reliable (AAscore >0.5 and <5 duplicate inconsistencies; Supplementary Methods). All GraphTyper analyses are restricted to this set unless otherwise noted. The number of variants identified in at least 1 individual using GraphTyper was 42 times larger than the number of variants identified through WES[7] (Table 1 and Supplementary Methods). Notably, in the WES dataset, variants in exons that are transcribed but not translated were missed; 69.2% and 89.9% of the 5′ and 3′ untranslated region (UTR) variants are missing from the WES dataset, respectively. We estimate that, even inside coding exons curated by ENCODE[20] at present, 13.7% of variants are missed in the WES dataset (Table 1 and Supplementary Tables 1 and 2). A subset of the missed variants is explained by the 25,853 fewer samples that are available in the WES dataset release. Manual inspection of a subset of the missing variants in the WES dataset, in which both whole-exome and whole-genome calls were available, suggests that these are absent owing to both missing coverage in some regions and genotyping filters. Almost all variants identified in the WES dataset are found in the WGS dataset (Table 1).

Fig. 1: Variant call sets.

a, The density (counts) of the per-individual number of variants split up by the five populations considered in this study from the GraphTyper call sets. Panels show number of SNPs, indels, singleton SNPs and indels, combined number of SV insertions and duplications and SV deletions. b, The length of SV deletions discovered in this study, split by the frequency of the variant. Data are represented as box plots; the middle line represents the median, the lower and upper part of the red box plot correspond to the first and third quartiles, and the upper whisker extends from the 75th percentile to the 95th percentile. n indicates the number of SV deletions per frequency bin. c, The number of variants discovered split by variant class (duplication, insertion and deletion). d, The size of insertions and deletions discovered shown in range from 50 bp up to 1,000 bp, 10,000 bp and 100,000 bp.

Table 1 Numbers of variants identified in at least one individual stratified by annotation across the GraphTyper dataset, using Ensembl version 101 annotations comparing WES and WGS data releases

We compared the DRAGEN single-sample WGS dataset to the previously published DRAGEN WES dataset[21] to explore the number of variants identified across coding, splice and 5′ and 3′ UTR annotation categories. As previously described[22], a greater number of variants were captured in the WGS data across all annotation categories, with most (98.26%–99.67%) variants identified in the WES dataset being captured in the WGS data (Table 2). WES did not capture many of the UTR variants, particularly 3′ UTR variants, for which only 24.78% of variants present across both datasets were found in the WES data, compared to 99.67% in the WGS data (Table 2). Notably, the pattern of variant numbers was generally similar between GraphTyper and DRAGEN single-sample datasets.

Table 2 Numbers of variants identified in at least one individual stratified by annotation across the DRAGEN single-sample dataset annotated using SnpEff v4.3 against Ensembl Build 38.92

Using the DRAGEN aggregated dataset release 2, we called 1,081,661,407 PASS SNPs and 129,273,976 PASS indels on autosomes, sex chromosomes, mitochondria and alternative contigs of the whole cohort (Supplementary Table 3).

Quality assessment is based on Genome in a Bottle samples extracted from the joint call set after cohort-level filtering (genotype inconsistency among 1,043 trios and between 177 monozygotic twins) and cohort-level genotype missingness. In high-confidence regions, for Genome in a Bottle samples, the sensitivity and precision of PASS SNPs are 98.95% and 99.97%, respectively, and the sensitivity and precision of PASS indels are 97.43% and 99.85%, respectively (Supplementary Table 4). In autosomes, for trios, genotype inconsistency of PASS variants is 0.029% in high-confidence regions, and 0.829% in low-confidence regions. For twins, genotype inconsistency of PASS variants is 0.036% in high-confidence regions, and 1.650% in low-confidence regions (Supplementary Table 5). Across the cohort, genotype missingness of PASS variants is 0.005% in high-confidence regions, and 0.010% in low-confidence regions (Supplementary Table 6).

Using random downsampling of samples, we investigated the gain in number of variants in the UKB DRAGEN aggregated variant dataset as sample size increases from 1,000 to 490,541 (Extended Data Fig. 2). As expected, for common variants (for example, >1% frequency), we do not observe an increase in number of variants with increasing sample size, but for the rarest variants (for example, ≤0.001% frequency), we observe substantial increases in number of variants with sample size, even at the highest sample size, supporting the value of continuing very large-scale sequencing efforts to discover novel and high-impact rare variants (Extended Data Fig. 2).

SVs

We identified SVs in each individual using the DRAGEN SV caller and combined these with variants from a long-read study[23] and the assemblies of seven individuals[24]. The resulting 2,739,152 SVs were genotyped with GraphTyper[24], of which 70.3% (1,926,132; Fig. 1b) were considered reliable (Supplementary Methods); 262,720 duplications, 479,265 insertions and 1,184,147 deletions. SVs were defined as variants being at least 50 base pairs (bp) and the size distribution showed a well-documented skew towards short variants (Fig. 1d).

On average, we identified 13,102 reliably called SVs per individual; 7,340 deletions and 5,762 insertions or duplications (Fig. 1b). These numbers are greater than the 7,439 SVs per individual found by gnomAD-SV[25], another short-read study, but considerably smaller than the 22,636 high-quality SVs found in a long-read sequencing study[23], mostly owing to an under-representation of insertions and SVs in repetitive regions. Despite the number of SVs being much smaller than the number of SNPs and indels, the number of base pairs affected per haploid genome on average (3.6 Mb) is comparable to that of SNPs (2.9 Mb) and indels (1.5 Mb). Most of the SVs are very rare; 1,470,329 (76.3%) are carried by fewer than 10 individuals (<0.001% frequency). We observed that rare variants are generally longer than common variants with a median length of 1,660 bp for deletions carried by fewer than 10 individuals and 169 bp for deletions with frequency above 1% (Fig. 1b).

Variant identification was performed analogously to that for the UKB 150,119 release[22] but replacing Manta[26] with the DRAGEN SV caller, which identifies a greater number of insertions. Owing to the improved discovery step and a modified variant filtering procedure, the number of reliably called SVs is approximately threefold larger in the current set compared to the previous release[22]. Out of the 637,321 SVs reliably called in our previous call set, 590,037 (92.6%) are also reliably called in the current call set. An additional 11,958 (1.8%) were part of the genotyping set but no longer considered reliable when genotyped, and the remaining 35,327 (5.5%) were not part of the current set of variants.

The number of variants called per individual varies by population, with the largest number of variants called in individuals in the AFR cohort, followed by the EAS, SAS, ASJ and finally the NFE cohort, for which individuals had the lowest number of called variants when compared to the current reference genome (Fig. 1a).

Phenotype associations

We integrated deep phenotyping data[27] available for most UKB participants and performed genetic association analysis across selected disease outcomes captured with electronic health records and molecular and physical measurement phenotypes, many of which are well-established disease biomarkers. Association testing was performed for all observed genetic variants and using several genetic models; we included single-variant tests, multi-ancestry meta-analysis, rare-variant collapsing analysis and SV analysis (Supplementary Methods).

Genome-wide association analysis

Genome-wide association analysis for individual SNPs and small indels was performed using the GraphTyper dataset in each ancestry cohort for 764 ICD-10 codes (n cases >200) and 71 selected quantitative phenotypes (n > 1,000; Supplementary Table 7). For the NFE cohort, we estimated the gain in discovery and improvement of fine mapping in association signals observed with the WGS call set versus variants observed in the imputed array genetic dataset[1] using equivalent analysis results with the same cohort and phenotyping strategy. We observed that whereas the increase in discovery was modest for common variant associations (Supplementary Fig. 3), the ability to fine map association signals was improved, and this was not due only to the loss of power in association tests attributable to imputation accuracy in the array dataset. We identified 33,123 associations (P value < 5 × 10−8) across 763 binary and 71 quantitative genome-wide association study (GWAS) datasets (Supplementary Methods). Of these, 3,991 (12.05%) are new to the WGS data when compared to those identified using only array imputed variants. As expected, most associated variants novel to WGS are rare variants, including 86% of associations with minor allele frequency (MAF) <0.0001, whereas only 2% of associations with MAF > 0.1 are novel to WGS (Supplementary Fig. 3). Among the 29,357 associations identified using array imputed variants, 2,984 had a different, more significant, lead variant in the WGS variants, resulting in improved fine mapping of the association signals observed (Supplementary Table 8). For example, a common variant association uncovered by WGS that was previously missed by the imputed array data is near genes MRC1 and TMEM236 in chromosome 10, where we identified an association between rs371858405 (NFE MAF = 0.24) and reduced hypothyroidism risk (odds ratio (OR) = 0.94, P value = 2.6 × 10−11). In the imputed data, the region within the WGS lead variant has sparse SNP coverage when compared to adjacent regions (Supplementary Fig. 4b), probably a result of a patch to the hg19 reference genome (chr10_gl383543_fix) that occurred after the UKB genotyping array was designed. A second example illustrating a new biological findings with rare genetic variation is the observation of a rare frameshift variant (MAF = 5.1 × 10−5) in FOXE3 chr. 1: 47417015:GC:G (rs1176723126) found to be significantly associated with the first occurrence phenotype ‘other cataract’ (ICD-10 code H26; P value = 6.2 × 10−9; Supplementary Fig. 4b). The link between FOXE3 and cataract, and other ocular diseases, was reported in previous familial studies and human and mouse disease models[28], but the association was not observed in the UKB imputed array or meta-analyses that included the UKB imputed array[29].

Multi-ancestry meta-GWAS

To examine multi-ancestry genetics of tested health-related phenotypes, we performed trans-ancestry meta-analysis of the GraphTyper GWAS data across 5 ancestries for 68 quantitative traits with ≥1,000 measurements in at least 2 ancestries and 228 ICD-10 disease outcomes with ≥200 cases in at least 2 ancestries. We identified 28,674 genome-wide significant (GWS; P value < 5.0 × 10−8) associations in the meta-analysis (Supplementary Methods, Supplementary Fig. 5 and Supplementary Table 9); of these, 1,934 associations were observed only in the meta-analysis, 26,478 were also observed in the NFE analysis, 82 were observed only in 1 of the non-NFE cohort analyses, and the remaining 180 associations were observed in more than 1 ancestry cohort (Fig. 2 and Supplementary Table 10). Among the 28,674 identified associations, 4,760 (16.6%) were not previously reported in the GWAS Catalog or OpenTargets[30] (Supplementary Methods, Supplementary Fig. 3b and Supplementary Table 9).

Fig. 2: UpSet plot of GWS associations across ancestries.

Ancestry labels are sorted by number of GWS associations in each set: meta-analysis (Meta), NFE, SAS, AFR, ASJ and EAS.

Of the meta-analysis significant associations, 126 were more significant in non-NFE ancestries (lead variant with the smallest P value) despite the much smaller sample size compared to NFE (Supplementary Fig. 6a): 83 with strongest signals in AFR, 37 in SAS, 5 in EAS and 1 in ASJ. Almost all 126 significant sentinel variants had MAF <0.5% in NFE; the median MAF enrichment compared with NFE is highest in AFR (MAFAFR/MAFNFE) = 828.49, followed by EAS and SAS with a relatively wide range of enrichment (Supplementary Fig. 6b). For example, we observed ancestry-specific associations in the HBB locus (Extended Data Fig. 3). The lead variant, rs334 (chr. 11:5227002:T:A), a missense variant in the HBB gene, is the primary cause of sickle cell disease, resulting in abnormal haemoglobin. Despite causing sickle cell disease, rs334-A is specifically common in AFR, driven by its protective effect against malaria and selective advantage in AFR[31]. One HBB splice site variant rs33915217 (chr. 11:5226925:C:G) is associated with β-thalassaemia and anaemia with elevated frequency specifically in SAS, potentially shaped by genetic drift, founder effect or unknown selective advantage[32]. Another HBB nonsense variant, rs11549407 (chr. 11:5226774:G:A), is associated with thalassaemia and anaemia detectable only in NFE given the large size (P value < 5.6 × 10−62, β = 6.9). rs11549407-A introduces a premature stop codon, leading to an unstable haemoglobin molecule, but it has not been shown to confer protection against malaria or other pathogens. Under the same selection pressure of malaria, a G6PD missense variant rs1050828 (chr. X:154536002:C:T), which causes the G6PD deficiency and haemolytic anaemia but provides protection against severe malaria, reaches high frequency in AFR (14.7%) but remains rare in NFE (0.005%). It is an AFR-specific GWS signal linked to increased reticulocyte and bilirubin levels, indicating compensatory release triggered by haemolysis.

Loss-of-function variants in WGS

Naturally occurring human genetic variation known to result in disruption of protein-coding genes provides an in vivo model of human gene inactivation. Individuals with loss-of-function (LoF) variants, particularly those with homozygous genotypes, can therefore be considered a form of human ‘knockouts’. Studying human knockouts affords an opportunity to predict phenotypic consequences of pharmacological inhibition. Besides putative LoF (pLoF) variants that can be predicted on the basis of variant annotation, ClinVar[23] also reported pathogenic or likely pathogenetic (P or LP, respectively) variants with clinical pathogenicity. Among the 490,000 UKB WGS participants (GraphTyper dataset), we found that there are 10,071 autosomal genes with at least 100 heterozygous carriers and 1,202 autosomal genes with at least 3 homozygous carriers. Among the 81 genes recommended by the American College of Medical Genetics and Genomics (ACMG)[33] for clinical diagnostic reporting, we found 7,313 pLoF, P or LP variants carried by 51,107 individuals. Furthermore, there are 81 homozygous carriers of pLoF, P or LP variants found in 14 ACMG genes, of which 56 participants carry mutations in DNA repair pathway genes such as MUTYH, PMS2 and MSH6 (Supplementary Table 11). Among them, a subset are clinically actionable genotypes with a confirmed functional impact in the corresponding inheritance mode. Further validation, and confirmation with ACMG diagnostic criteria, is needed to determine which variants are clinically actionable.

Comparing the UKB WGS dataset versus the WES dataset, among the same set of 450,000 participants, about 16,000 autosomal genes harbouring pLoF, P or LP variants in ≥1 carriers in both WGS and WES. However, WGS enabled us to find more carriers of high-impact variants (for example, the median difference in the number of carriers is 44 more in the WGS dataset compared to the WES dataset for the gene sets with >100 carriers; Fig. 3). Partially attributable to quality control criteria (Supplementary Methods), this is also expected given the more even and deeper coverage in WGS.

Fig. 3: Observed number of genes in carriers of heterozygous pLoF, P or LP variants in WGS and WES.

The number of autosomal genes (y axis) with at least 1, 25, 50 and 100 heterozygous carriers among the number of individuals (x axis) to the total number of 452,728 participants with both WES and WGS data.

Rare-coding-variant association studies with WES and WGS

Gene-level collapsing analysis, in which aggregation of rare variants is tested for association with disease, has emerged as a powerful method for identifying gene–phenotype associations with high allelic heterogeneity21,34. So far, most collapsing analyses have used WES data[35]. We reasoned that the greater coverage of WGS compared to WES could increase power to detect gene–phenotype associations. We performed two collapsing analysis-based phenome-wide association studies (PheWAS) on an identical sample of 460,552 individuals using both WES- and WGS-based protein-coding regions (Supplementary Methods). All results for rare-variant collapsing analyses use the single-sample DRAGEN variant calls. In total, we tested for the association between 18,930 genes and 751 phenotypes (687 binary ‘first occurrence’ phenotypes and 64 quantitative traits that met our inclusion criteria; Supplementary Methods and Supplementary Table 12) using 10 non-synonymous and 1 synonymous control collapsing analysis models (Supplementary Table 13 and Supplementary Methods). We meta-analysed the separate ancestry strata and set the significance threshold at P value ≤ 1 × 10−8, which was previously empirically validated[21].

In total, we identified 1,359 significant gene–phenotype associations, of which 87.4% (1,188) were significant in both the WES and WGS PheWASs (184 binary and 1,004 quantitative associations), 7.7% (105) were significant only in the WGS PheWAS (23 binary and 82 quantitative associations), and 4.9% (66) were significant only in the WES PheWAS (15 binary and 51 quantitative associations; Supplementary Table 14). There was high correlation between −log_10[P values] derived from WES and WGS (Spearman’s rank correlation coefficient = 0.95, P < 2.2 × 10−16; Supplementary Fig. 7). Across both binary and quantitative traits, there were 29 genes with significant associations unique to WGS and 20 genes with significant associations unique to WES (Supplementary Fig. 8). Three genes uniquely associated with either technology are in the major histocompatibility complex region: VWA7 (WES) and HLA-C and C2 (WGS). Fewer than 3.3% of gene–phenotype pairs had an absolute difference in −10 × log_10[P values] of greater than 5 units and fewer than 0.56% had greater than 10 units (Supplementary Fig. 9). Across all 14,130,325 gene–phenotype associations (significant and non-significant), there were 54,818 with greater than a 10-unit difference that achieved a lower P value in the WGS results, compared to 23,687 that achieved a lower P value in the WES results (Extended Data Fig. 4).

We identified 95 significant gene–phenotype associations with 15 genes recurrently mutated in clonal haematopoiesis and myeloid cancers as described previously[36], which are potentially driven by somatic qualifying variants. Of these, 70 were detected by both technologies, 11 were unique to WGS and 14 were unique to WES. Associations unique to WGS included protein-truncating variants in TET2 and other disorders of white blood cells (WGS P value = 3.62 × 10−13, OR = 8.08, 95% confidence interval (CI) = 5.02–12.40; WES P value = 4.23 × 10−7, OR = 6.18, 95% CI = 3.26–10.70). We also found an association between protein-truncating and predicted damaging missense variants in SRSF2 and reticulocyte percentage (WGS P value = 1.92 × 10−6, β = 0.30, 95% CI = 0.17–0.42; WES P value = 3.7 × 10−18, β = 0.60, 95% CI = 0.47–0.74) significant only in the WES results (Supplementary Table 14).

Overall, although association results between the WES and WGS DRAGEN datasets are highly correlated, there are genes for which coverage is improved in WGS, resulting in modestly improved association statistics. One example is PKHD1, for which associations with three quantitative phenotypes were more significant in WGS than WES: γ-glutamyl transferase (WES P value = 4.63 × 10−18, β = 0.19, 95% CI = 0.15–0.24; WGS P value = 1.24 × 10−19, β = 0.20, 95% CI = 0.16–0.24), creatinine (WES P value = 3.85 × 10−10, β = −0.04, 95% CI = −0.06 to −0.03; WGS P value = 2.14 × 10−12, β = −0.05, 95% CI = −0.06 to −0.03) and cystatin C, which achieves significance only in the WGS data (WES P value = 3.02 × 10−8, β = −0.05, 95% CI = −0.07 to −0.03; WGS P value = 3.04 × 10−9, β = −0.04, 95% CI = −0.06 to −0.03; Supplementary Table 14). The number of samples with ≥10× coverage of PKHD1 is lower in WES than WGS at specific protein-coding sites (Supplementary Fig. 10), demonstrating the value of WGS to ascertain variants and associations in regions not well captured by WES.

We calculated coverage statistics in the WES and WGS datasets for each protein-coding gene (Supplementary Table 15). There are only 638 genes in the WGS for which <95% of the protein-coding sequence had on average at least 10× coverage across the cohort, compared to around twice as many (1,299) in the WES dataset[21]. This improved coverage of some genes in the WGS data compared to WES demonstrates the value of WGS for improved discovery potential in some protein-coding regions.

Rare-variant PheWAS of UTRs

To understand the contributions of rare UTR variants to phenotypes, we used the UKB single-sample DRAGEN WGS data to compile about 13.4 million rare (MAF < 0.1%) variants from both 5′ and 3′ UTRs of protein-coding genes across the 5 defined ancestries. We performed two multi-ancestry collapsing PheWASs: UTR alone and UTR plus protein coding.

We tested the aggregate effect of UTR-alone qualifying variants on binary and quantitative phenotypes for 5′ UTRs alone, 3′ UTRs alone and 5′ and 3′ UTRs combined (Supplementary Table 12). Each was run using six collapsing analysis models to capture a range of MAF and CADD37,38,39 thresholds. Any UTR sites that overlapped a protein-coding site were omitted. Using a previously described n-of-1 permutation approach[21], we confirmed that P value ≤ 1 × 10−8 is an appropriate significance threshold (Supplementary Methods). We observed 63 significant associations (1 binary trait and 62 quantitative traits) comprising 32 unique genes and 37 unique phenotypes (Fig. 4 and Supplementary Table 16). Many of these gene–phenotype associations have previously been identified with rare protein-coding variants or have GWAS support38,39. For example, 32 of 63 (51%) signals were also significant in the WGS protein-coding collapsing PheWAS already described, and 52 of 63 (83%) had a common variant within 500 kilobases (kb) significantly associated with the same phenotype in the UKB WGS Consortium GWAS already described (Supplementary Methods and Supplementary Table 16). The observed associations are likely to include some UTR variants that are causally linked to the phenotype, and some that are in partial linkage disequilibrium with nearby common variant associations.

Fig. 4: UTR-based collapsing analysis.

Miami plot of UTR-based rare-variant PheWAS associations for 687 binary (top) and 64 quantitative (bottom) phenotypes across all 6 collapsing models. Significant 5′, 3′ and 5′ and 3′ combined associations are represented in different colours. The top significant binary associations and the significant quantitative associations with P value < 1 × 10−30 are labelled. P values are unadjusted and are from Fisher’s exact two-sided tests (for binary traits) and linear regression (for quantitative traits).

We next explored the combined effect of rare UTR variants and protein-truncating variants using two different models. We observed 27 and 157 significant associations for binary and quantitative phenotypes, respectively (Supplementary Table 16). Ten associations that achieved significance in this UTR plus protein-coding PheWAS were not significant in the protein-coding-alone collapsing PheWAS, suggesting that those associations were augmented by incorporating UTRs (Supplementary Table 16). Furthermore, 27 suggestive (1 × 10−8 < P < 1 × 10−6) associations in the UTR plus protein-coding PheWASs did not reach this threshold in the protein-coding-alone collapsing PheWAS (Supplementary Table 16). For instance, NWD1 is suggestively associated with kidney calculus (P value = 7.53 × 10−7, OR = 1.63) in the UTR plus protein-coding PheWAS, but not in the protein-coding-alone or the UTR-alone collapsing PheWASs. This is mostly driven by rare 3′ UTR variants (Supplementary Table 17), although the qualifying variants are distributed throughout the gene. No significant common variant associations were observed between NWD1 (±500 kb) and kidney calculus in the UKB WGS Consortium GWAS; however, a common synonymous variant, rs773852, is associated with kidney calculus in a Chinese Han population[40] Our study demonstrates the potential of WGS in identifying non-protein-coding variant to phenotype associations.

Phenotypic effects of SVs

Associations identified in the previous UKB 150,119 release[22] from the WGS consortium were mostly replicated. The new UKB release allows the identification of rarer SVs and assesses their impact on phenotypes. We present exemplary associations, anchoring on genes and variants that have a well-established association with phenotype.

Genes are typically affected by several SVs. Previously[22], we highlighted an association of non-HDL cholesterol with a 14,154-bp deletion overlapping PCSK9, a gene encoding a proprotein convertase involved in the degradation of LDL receptors in the liver. In the current release, 13 SVs overlapping coding exons in PCSK9 are found, carried by 163 individuals, bringing the total number of PCSK9 pLoF carriers to 1,124 The previously reported SV is the most common of the 13 variants, seen in 111 individuals. The carriers had (1.22 s.d.) lower levels of non-HDL cholesterol, with carriers of other PCSK9 deletions collectively averaging 0.51 s.d. lower levels.

A 5,200-bp deletion on chr. 12: 56,451,164–56,456,364, is carried by 15 NFE individuals and it strongly associates with cataracts (OR = 25.3, P value = 6.3 × 10−7, MAF = 0.0015%). It deletes all 4 coding exons of MIP while preserving its 5′ UTR region and not affecting other genes. MIP encodes the major intrinsic protein of the lens fibre and rare deleterious missense, and LoF variants are linked to autosomal dominant cataract41,42.

The ACMG[43] recommends reporting actionable genotypes in genes linked with diseases that are highly penetrant with established interventions. We previously reported[22] that 4.1% of UKB individuals carry an actionable SNP or indel genotype. An additional 0.60% of individuals carry SVs predicted to cause LoF in autosomal dominant LoF, P or LP genes. If confirmed[44], this increases the number of individuals with an actional genotype by 14.8%.

ClinVar[45], a database of clinically significant variants, contains 2,256,088 records at present, but only 4,062 are SVs. Of these, 458 SVs presented here matched 486 (12.0%) in ClinVar. As expected, benign or likely benign variants have a higher frequency than P or LP variants (Supplementary Table 18). The large cohort and rich medical history allows us to assess the likely clinical impact of these variants and potentially refine the ClinVar classification.

Most ClinVar-annotated pathogenic SVs are very rare (MAF < 0.01%; Supplementary Table 18). One example is a 52-bp deletion on chr. 19: 12,943,750–12,943,802 in the first exon of CALR resulting in a stop gain. This recurrent somatic mutation46,47,48 is listed as pathogenic for primary myelofibrosis and thrombocythaemia is carried by 47 NFE individuals and 1 AFR individual. It strongly associates with measures of platelet distribution; most strongly with platelet width, effect 2.02 s.d. (95% CI = 1.72–2.34, P value = 3.1 × 10−38). It is present in the SNP and indel call set, but is not found in the WES data, despite being exonic.

Although most ClinVar variants are very rare in the UKB some have a higher frequency in the sub-cohorts. One example is a 2,502-bp deletion on chr. 2: 151,645,755–151,648,057 deleting exon 55 of NEB, linked with nemaline myopathy and traced to a single founder mutation[49]; it is carried by 33 individuals in the cohort, 17 of whom belong to the ASJ cohort. Another example is a 613-bp deletion on chr. 11 : 5,225,255–5,225,868 removing the first 3 exons of HBB seen in 19 individuals all belonging to the SAS cohort. The deletion has been annotated in ClinVar to be clinically significant for β-thalassaemia, and we find it to be associated with a 1.96 s.d. (95% CI = 1.49–2.43, P value = 5.4 × 10−16) decrease in haemoglobin concentration.

Discussion

The UKB WGS project offers a groundbreaking opportunity to explore human genetic variation and its application to disease research. The vast dataset generated in this study will advance our understanding of human genetics and substantially impact drug discovery and development, disease risk assessment and precision medicine applications on a global scale. Furthermore, this work will provide essential insights into the contribution of rare non-coding variation to human biological variation and will facilitate the translation of human genetics into therapies over the next decade.

UKB WGS identified an 18.8-fold increase in variants compared with the imputed array and a greater than 40-fold increase compared with WES. This is consistent with multiple studies that highlight the power of WGS versus WES for identifying coding variants[5], especially considering the decreased cost of WGS over time[6]. In accordance with previous efforts14,22, this information can also be used to identify regions that have a lower tolerance of variation. WGS allowed us to identify more genes harbouring pLoF, P or LP variants in more carriers, which offers more opportunities for evaluating gene targets in LoF heterozygous carriers or even human knockouts. WGS also allowed us to find many clinically relevant and disease-associated SVs.

Current human genomic reference and biobank data do not fully reflect the diversity of human populations and are still dominated by European ancestries[50], thus limiting the detection of variation specific to non-European regions and leading to a fundamental bias in the understanding of the genetic basis of disease in diverse populations. In this study, we used cross-ancestry meta-analysis to confirm known associations and identify new ones with new indications and/or in non-European ancestries. Even though non-NFE ancestries had smaller sample sizes, 82 meta-GWS associations were found significant only in non-NFE ancestries (Supplementary Table 10), probably driven by selection pressure from regional-specific environment factors. For example, the missense causal variants of HBB and G6PD for sickle cell disease and anaemia, respectively, were >1,500× more common in AFR versus NFE, owing to their protection against severe malaria and the fact that 95% of malaria cases occur in Africa[51]. By contrast, a thalassaemia-causing HBB LoF mutation (rs11549407-A) and splice site variant (rs33915217-G) were most prevalent in NFE and SAS. These variants are rare in AFR and have no reported protective effects against malaria or other infectious diseases endemic to Africa. Whereas an HBB nonsense variant was detected in WES (allele frequency = 0.003%) but more enriched in WGS (allele frequency = 0.005%), the splice site variant was exclusively detected in WGS (not in WES or in imputed array genotypes), again highlighting the unique value of WGS.

To understand the impact of rare variants captured by WGS on human disease, we present a series of examples using collapsing analysis including protein-coding and non-protein-coding variants. Our observation that WGS can boost significance for certain genetic associations compared to WES in a collapsing analysis PheWAS context is consistent with other studies that show better coverage (and therefore better sensitivity to call variants) in WGS compared to WES for particular genes[52]. The benefit of WGS for protein-coding SNVs and indels is modest, which is expected and consistent with previous reports[53]. Defining qualifying variants in non-protein-coding regions remains challenging. In silico predictions of variant functional effect are less accurate in non-protein-coding regions than in protein-coding regions. Additionally, biological effects of variation in non-protein-coding regions are likely to be on average more modest than those in protein-coding regions. Nevertheless, our observation of significant rare-variant associations in UTRs, and a few phenotypes for which adding UTRs augments protein-coding signals, demonstrates the great potential of using this dataset to explore disease-relevant rare-variant associations in neglected non-protein-coding regions. Next steps could include further refining the non-protein-coding qualifying variant definitions with additional filters, conditional analysis to test for independence of non-protein-coding signals, expanding to other phenotypes, and expanding to other classes of non-protein-coding regions. In the UKB, additional data modalities provide a valuable opportunity to discriminate functionally important variants and therefore refine qualifying variant criteria. For example, a recent study using Olink plasma proteomics data in the UKB boosts signals by combining protein quantitative trait loci with protein-truncating variants in collapsing analyses[36].

We have described and characterized this large WGS-based genetic study and provided examples showing that combining WGS data with the rich phenotypic data in the UKB gives new insights into the complex relationship between human variation and sequence variation. This resource not only can facilitate improved imputation performance for rare variants in individuals across five different ancestries22,54, but also will be useful for describing variation in complex regions, such as HLA, KIR and red blood cell antigen systems, and serve as a gold standard for future population-scale studies. We are confident that leveraging the combined expertise of scientists worldwide will lead to new insights that will meaningfully affect our understanding of human disease biology and thereby advance the search for safe and effective medicines.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

WGS data are available via the UKB research analysis platform (https://ukbiobank.dnanexus.com/landing), which is open to researchers from academic, charity, government and commercial organizations with an approved UKB project (https://www.ukbiobank.ac.uk/enable-your-research/apply-for-access). The Allele Frequency Browser is available at https://afb.ukbiobank.ac.uk/. Single-variant analysis results are available through the GWAS Catalog (study accession numbers are available in Supplementary Table 19). Rare-variant collapsing analysis association statistics are available through the AstraZeneca Centre for Genomics Research PheWAS Portal (http://azphewas.com/). SV association data are available at https://www.decode.com/summarydata/. All association summary statistics are made available for general research use and available at the time of access without access request. Human reference genome data GRCh38 are available at http://ftp.1000genomes.ebi.ac.uk/vol1/ftp/technical/reference/GRCh38_reference_genome/. Genome in a Bottle WGS samples are available at https://ftp-trace.ncbi.nlm.nih.gov/ReferenceSamples/giab/data/ and ENSEMBL annotation data at https://m.ensembl.org/info/data/mysql.html, versions 92 and 101.

References

1. Bycroft, C. et al. The UK Biobank resource with deep phenotyping and genomic data. Nature 562, 203–209 (2018).

2. Szustakowski, J. D. et al. Advancing human genetics research and drug discovery through exome sequencing of the UK Biobank. Nat. Genet. 53, 942–948 (2021).

3. Van Hout, C. V. et al. Exome sequencing and characterization of 49,960 individuals in the UK Biobank. Nature 586, 749–756 (2020).

4. Miller, K. L. et al. Multimodal population brain imaging in the UK Biobank prospective epidemiological study. Nat. Neurosci. 19, 1523–1536 (2016).

5. Sun, B. B. et al. Plasma proteomic associations with genetics and health in the UK Biobank. Nature 622, 329–338 (2023).

6. Julkunen, H. et al. Atlas of plasma NMR biomarkers for health and disease in 118,461 individuals from the UK Biobank. Nat. Commun. 14, 604 (2023).

7. Backman, J. D. et al. Exome sequencing and analysis of 454,787 UK Biobank participants. Nature 599, 628–634 (2021).

8. Smedley, D. et al. 100,000 Genomes pilot on rare-disease diagnosis in health care — preliminary report. N. Engl. J. Med. 385, 1868–1880 (2021).

9. Selvaraj, M. S. et al. Whole genome sequence analysis of blood lipid levels in >66,000 individuals. Nat. Commun. 13, 5995 (2022).

10. Hawkes, G. et al. Whole genome association testing in 333,100 individuals across three biobanks identifies rare non-coding single variant and genomic aggregate associations with height. Nat. Commun. 15, 8549 (2024).

11. Carss, K. J. et al. Using human genetics to improve safety assessment of therapeutics. Nat. Rev. Drug Discov. 22, 145–162 (2022).

12. Nelson, M. R. et al. The support of human genetic evidence for approved drug indications. Nat. Genet. 47, 856–860 (2015).

13. Vitsios, D., Dhindsa, R. S., Middleton, L., Gussow, A. B. & Petrovski, S. Prioritizing non-coding regions based on human genomic constraint and sequence context with deep learning. Nat. Commun. 12, 1504 (2021).

14. Chen, S. et al. A genome-wide mutational constraint map quantified from variation in 76,156 human genomes. Nature 625, 92–100 (2024).

15. Chen, S. et al. A genomic mutational constraint map using variation in 76,156 human genomes. Nature 625, 92–100 (2023).

16. Karczewski, K. J. et al. The mutational constraint spectrum quantified from variation in 141,456 humans. Nature 581, 434–443 (2020).

17. Auton, A. et al. A global reference for human genetic variation. Nature 526, 68–74 (2015).

18. Jun, G. et al. Structural variation across 138,134 samples in the TOPMed consortium. Preprint at bioRxiv https://doi.org/10.1101/2023.01.25.525428 (2023).

19. Bergström, A. et al. Insights into human genetic variation and population history from 929 diverse genomes. Science 367, eaay5012 (2020).

20. Moore, J. E. et al. Expanded encyclopaedias of DNA elements in the human and mouse genomes. Nature 583, 699–710 (2020).

21. Wang, Q. et al. Rare variant contribution to human disease in 281,104 UK Biobank exomes. Nature 597, 527–532 (2021).

22. Halldorsson, B. V. et al. The sequences of 150,119 genomes in the UK Biobank. Nature 607, 732–740 (2022).

23. Beyter, D. et al. Long-read sequencing of 3,622 Icelanders provides insight into the role of structural variants in human diseases and other traits. Nat. Genet. 53, 779–786 (2021).

24. Eggertsson, H. P. et al. GraphTyper2 enables population-scale genotyping of structural variation using pangenome graphs. Nat. Commun. 10, 5402 (2019).

25. Collins, R. L. et al. A structural variation reference for medical and population genetics. Nature 581, 444–451 (2020).

26. Chen, X. et al. Manta: rapid detection of structural variants and indels for germline and cancer sequencing applications. Bioinformatics 32, 1220–1222 (2016).

27. Sudlow, C. et al. UK Biobank: an open access resource for identifying the causes of a wide range of complex diseases of middle and old age. PLoS Med. 12, e1001779 (2015).

28. Brémond-Gignac D. et al. Identification of dominant FOXE3 and PAX6 mutations in patients with congenital cataract and aniridia. Mol. Vis. 22, 1705–1711 (2010).

29. Choquet, H. et al. A large multiethnic GWAS meta-analysis of cataract identifies new risk loci and sex-specific effects. Nat. Commun. 12, 3595 (2021).

30. Buniello, A. et al. Open Targets Platform: facilitating therapeutic hypotheses building in drug discovery. Nucleic Acids Res. 53, D1467–D1475 (2025).

31. Band, G. et al. Malaria protection due to sickle haemoglobin depends on parasite genotype. Nature 602, 106–111 (2021).

32. Hu, Y. et al. Whole-genome sequencing association analysis of quantitative red blood cell phenotypes: the NHLBI TOPMed program. Am. J. Hum. Genet. 108, 874–893 (2021).

33. Miller, D. T. et al. ACMG SF v3.2 list for reporting of secondary findings in clinical exome and genome sequencing: a policy statement of the American College of Medical Genetics and Genomics (ACMG). Genet. Med. 25, 100866 (2023).

34. Petrovski, S. et al. An exome sequencing study to assess the role of rare genetic variation in pulmonary fibrosis. Am. J. Respir. Crit. Care Med. 196, 82–93 (2017).

35. Povysil, G. et al. Rare-variant collapsing analyses for complex traits: guidelines and applications. Nat. Rev. Genet. 20, 747–759 (2019).

36. Dhindsa, R. S. et al. Rare variant associations with plasma protein levels in the UK Biobank. Nature 622, 339–347 (2023).

37. Rentzsch, P., Witten, D., Cooper, G. M., Shendure, J. & Kircher, M. CADD: predicting the deleteriousness of variants throughout the human genome. Nucleic Acids Res. 47, D886–D894 (2019).

38. Ochoa, D. et al. The next-generation Open Targets Platform: reimagined, redesigned, rebuilt. Nucleic Acids Res. 51, D1353–D1359 (2023).

39. Sollis, E. et al. The NHGRI-EBI GWAS Catalog: knowledgebase and deposition resource. Nucleic Acids Res. 51, D977–D985 (2023).

40. Li, Y., Lu, X., Yu, Z., Wang, H. & Gao, B. Meta-data analysis of kidney stone disease highlights ATP1A1 involvement in renal crystal formation. Redox Biol. 61, 102648 (2023).

41. Shiels, A. & Bassnett, S. Mutations in the founder of the MIP gene family underlie cataract development in the mouse. Nat. Genet. 12, 212–215 (1996).

42. Gu, F. et al. A novel mutation in major intrinsic protein of the lens gene (MIP) underlies autosomal dominant cataract in a Chinese family. Mol. Vis. 13, 1651–1656 (2007).

43. Miller, D. T. et al. ACMG SF v3.0 list for reporting of secondary findings in clinical exome and genome sequencing: a policy statement of the American College of Medical Genetics and Genomics (ACMG). Genet. Med. 23, 1381–1390 (2021).

44. Jensson, B. O. et al. Actionable genotypes and their association with life span in Iceland. N. Engl. J. Med. 389, 1741–1752 (2023).

45. Landrum, M. J. et al. ClinVar: public archive of interpretations of clinically relevant variants. Nucleic Acids Res. 44, D862–D868 (2016).

46. Klampfl, T. et al. Somatic mutations of calreticulin in myeloproliferative neoplasms. N. Engl. J. Med. 369, 2379–2390 (2013).

47. Maier, C. L. et al. Development and validation of CALR mutation testing for clinical diagnosis. Am. J. Clin. Pathol. 144, 738–745 (2015).

48. Seghatoleslami, M. et al. Coexistence of p190 BCR/ABL transcript and CALR 52-bp deletion in chronic myeloid leukemia blast crisis: a case report. Mediterr. J. Hematol. Infect. Dis. 8, e2016002 (2016).

49. Lehtokari, V. L. et al. The exon 55 deletion in the nebulin gene - one single founder mutation with world-wide occurrence. Neuromuscul. Disord. 19, 179 (2009).

50. Fatumo, S. et al. A roadmap to increase diversity in genomic studies. Nat. Med. 28, 243–250 (2022).

51. Thiam, F. et al. G6PD and HBB polymorphisms in the Senegalese population: prevalence, correlation with clinical malaria. PeerJ 10, e13487 (2022).

52. Lelieveld, S. H., Spielmann, M., Mundlos, S., Veltman, J. A. & Gilissen, C. Comparison of exome and genome sequencing technologies for the complete capture of protein-coding regions. Hum. Mutat. 36, 815–822 (2015).

53. Gaynor, S. M. et al. Yield of genetic association signals from genomes, exomes and imputation in the UK Biobank. Nat. Genet. 56, 2345–2351 (2024).

54. Rubinacci, S., Hofmeister, R. J., Sousa da Mota, B. & Delaneau, O. Imputation of low-coverage sequencing data from 150,119 UK Biobank genomes. Nat. Genet. 55, 1088–1090 (2023).

Acknowledgements

This research has been conducted using the UKB resource (application no. 52293) and with the support of Wellcome (grant numbers 218880/Z/19/Z to Amgen, 218723/Z/19/Z to AstraZeneca, 218789/Z/19/Z to GSK, 219414/Z/19/Z to Janssen and 219603/Z/19/Z to UKB), UK Research and Innovation (Innovate UK grant numbers 105637 to Amgen, 105635 to AstraZeneca, 105634 to GSK and 105636 to Janssen) and a Medical Research Council award for the Vanguard programme (grant number MC_PC_17223). We thank the laboratory and wider support teams at UKB for contributions; all 500,000 UKB participants; S. Mehtalia and the Illumina DRAGEN team for technical support with DRAGEN data processing and aggregate calling; J. Jacob for the design of the DRAGEN data processing pipeline; and F. Middleton, R. Wenier and B. Smalley for technical leadership.

Author information

Authors and Affiliations

1. Centre for Genomics Research, Discovery Sciences, BioPharmaceuticals R&D, AstraZeneca, Cambridge, UK

Keren Carss, Eleanor Wheeler, Kousik Kundu, Slavé Petrovski, Fengyuan Hu, Oliver S. Burren, Sri V. V. Deevi, Carolina Haefliger, Kieren Lythgow, Peter H. Maccallum, Karyn Mégy, Jonathan Mitchell, Sean O’Dell, Amanda O’Neill, Katherine R. Smith, Haeyam Taiy, Sebastian Wasilewski & Agnar Helgason

2. Amgen deCODE genetics, Reykjavik, Iceland

Bjarni V. Halldorsson, Kari Stefansson, Hannes P. Eggertsson, Kristjan H. S. Moore, Hannes Hauswedell, Ogmundur Eiriksson, Aron Skaftason, Nokkvi Gislason, Svanhvit Sigurjonsdottir, Magnus O. Ulfarsson, Gunnar Palsson, Marteinn T. Hardarson, Asmundur Oddsson, Brynjar O. Jensson, Snaedis Kristmundsdottir, Brynja D. Sigurpalsdottir, Olafur A. Stefansson, Doruk Beyter, Guillaume Holley, Vinicius Tragante, Arnaldur Gylfason, Pall I. Olason, Florian Zink, Margret Asgeirsdottir, Sverrir T. Sverrisson, Brynjar Sigurdsson, Sigurjon A. Gudjonsson, Gunnar T. Sigurdsson, Gisli H. Halldorsson, Gardar Sveinbjornsson, Unnur Styrkarsdottir, Droplaug N. Magnusdottir, Steinunn Snorradottir, Kari Kristinsson, Emilia Sobech, Gudmar Thorleifsson, Frosti Jonsson, Pall Melsted, Ingileif Jonsdottir, Thorunn Rafnar, Hilma Holm, Hreinn Stefansson, Jona Saemundsdottir, Daniel F. Gudbjartsson, Olafur T. Magnusson, Gisli Masson, Unnur Thorsteinsdottir, Hakon Jonsson & Patrick Sulem

3. School of Technology, Reykjavik University, Reykjavik, Iceland

Bjarni V. Halldorsson, Marteinn T. Hardarson & Brynja D. Sigurpalsdottir

4. AI/ML, Data Science & Digital Health, Janssen Research & Development, Spring House, PA, USA

Liping Hou, Mary Helen Black, Shuwei Li, Julio Molineros, Yanfei Zhang, Alexander H. Li, Evan H. Baugh, Elisabeth Mlynarski, Abolfazl Doostparast Torshizi, Gamal Abdel-Azim, Brian Mautz, Karen Y. He, Jingyue Xi, Shirley Nieves-Rodriguez, Asif Khan, Songjun Xu, Xingjun Liu, Brice Sarver, Dongnhu Truong, Mohamed-Ramzi Temanni & Tommaso Mansi

5. Human Genetics & Genomics, GSK, Collegeville, PA, USA

Jimmy Liu, Yancy Lo, Chloe Robins, Dongjing Liu, Jonathan Davitte & Erik Ingelsson

6. Population Genetics, Illumina, San Diego, CA, USA

Zhuoyi Huang

7. UK Biobank, Stockport, UK

Ben Lacey, Rory Collins, Mark Effingham, Naomi Allen, Jonathan Sellors, Simon Sheard, Mahesh Pancholi, Caroline Clark, Lucy Burkitt-Gray, Samantha Welsh, Daniel Fry, Rachel Watson, Lauren Carson & Alan Young

8. Centre for Genomics Research, Discovery Sciences, BioPharmaceuticals R&D, AstraZeneca, Waltham, MA, USA

Ryan S. Dhindsa & Quanli Wang

9. Wellcome Sanger Institue, Hinxton, UK

Diana Rajan, Neil Marriott, Carol E. Scott, Ian Johnston, Shaheen Akhtar, Siobhan Austin-Guest, Robert Barber, Daniel Barrett, Tristram Bellerby, Adrian Clarke, Richard Clark, Maria Coppola, Linda Cornwell, Abby Crackett, Joseph Dawson, Callum Day, Alexander Dove, Jillian Durham, Robert Fairweather, Marcella Ferrero, Michael Fenton, Howerd Fordham, Audrey Fraser, Paul Heath, Emily Heron, Gary Hornett, Lena Hughes-Hallett, David K. Jackson, Alexander Jakubowski Smith, Adam Laverack, Katharine Law, Steven R. Leonard, Kevin Lewis, Jennifer Liddle, Alice Lindsell, Sally Linsdell, Jamie Lovell, James Mack, Henry Mallalieu, Irfaan Mamun, Ana Monteiro, Leanne Morrow, Barbora Pardubska, Alexandru Popov, Lisa Sloper, Jan Squares, Ian Still, Oprah Taylor, Sam Taylor, Jaime M. Tovar Corona, Elliott Trigg, Valerie Vancollie, Paul Voak, Danni Weldon, Alan Wells, Eloise Wells, Mia Williams, Sean Wright, Louise Aigrain, Nicholas Redshaw, Michael Quail, Lesley Shirley, Scott Thurston, Peter Ellis, Laura Grout, Natalie Smerdon, Emma Gray, Richard Rance & Cordelia Langford

10. Velsera, Charlestown, MA, USA

Jelena Randjelovic, Ahmet Sinan Yavuz, Nevena Miletic, Lea Lenhardt Ackovic, Marijeta Slavkovic-Ilic & Mladen Lazarevic

11. External Innovation, Data Science & Digital Health, Janssen Research & Development, London, UK

Trevor Howe

12. Faculty of Medicine, School of Health Sciences, University of Iceland, Reykjavik, Iceland

Kari Stefansson, Ingileif Jonsdottir & Unnur Thorsteinsdottir

13. Human Genetics & Genomics, GSK, Stevenage, UK

Robert Scott, Tom G. Richardson, Laurence Howe, Mariana Pereira, Daniel Seaton, Yury Aulchenko, John Whittaker, Manolis Dermitzakis & Toby Johnson

14. Human Genetics & Genomics, GSK, Heidelberg, Germany

Adrian Cortes & Patrick Albers

15. ELIXIR, Hinxton, UK

Peter H. Maccallum

16. BioPharmaceuticals R&D, AstraZeneca, Cambridge, UK

Menelas Pangalos

17. Precision Medicine & Biosamples, Oncology R&D, AstraZeneca, Cambridge, UK

Ruth March

18. School of Engineering and Natural Sciences, University of Iceland, Reykjavik, Iceland

Magnus O. Ulfarsson, Pall Melsted & Daniel F. Gudbjartsson

19. Department of Anthropology, University of Iceland, Reykjavik, Iceland

Agnar Helgason

20. R&D Data Science & Data Engineering, Collegeville, PA, USA

Jatin Sandhuria

21. DS NS, Data Science & Digital Health, Janssen Research & Development, Boston, MA, USA

Christopher D. Whelan

22. External Innovation, Discovery, Product Development & Supply, Janssen Research & Development, Beerse, Belgium

Letizia Goretti

23. Data Science & Digital Health, Janssen Research & Development, Spring House, PA, USA

Najat Khan & Belen Fraile

24. Computational Science, Discovery, Product Development & Supply, Janssen Research & Development, Spring House, PA, USA

Guna Rajagopal

25. Software Informatics, Illumina, San Diego, CA, USA

Rami Mehio

26. Population Genetics, Illumina, Cambridge, UK

Ole Schulz-Trieglaff

Consortia

The UK Biobank Whole-Genome Sequencing Consortium

- Manuscript Writing Group

- Keren Carss

- , Bjarni V. Halldorsson

- , Liping Hou

- , Jimmy Liu

- , Eleanor Wheeler

- , Yancy Lo

- , Kousik Kundu

- , Zhuoyi Huang

- , Ben Lacey

- , Ryan S. Dhindsa

- , Diana Rajan

- , Jelena Randjelovic

- , Neil Marriott

- , Carol E. Scott

- , Ahmet Sinan Yavuz

- , Ian Johnston

- , Trevor Howe

- , Mary Helen Black

- , Kari Stefansson

- , Robert Scott

- , Slavé Petrovski

- , Shuwei Li

- & Adrian Cortes

- AstraZeneca

- Keren Carss

- , Eleanor Wheeler

- , Kousik Kundu

- , Fengyuan Hu

- , Quanli Wang

- , Oliver S. Burren

- , Ryan S. Dhindsa

- , Sri V. V. Deevi

- , Carolina Haefliger

- , Kieren Lythgow

- , Peter H. Maccallum

- , Karyn Mégy

- , Jonathan Mitchell

- , Sean O’Dell

- , Amanda O’Neill

- , Katherine R. Smith

- , Haeyam Taiy

- , Menelas Pangalos

- , Ruth March

- , Sebastian Wasilewski

- & Slavé Petrovski

- Amgen deCode genetics

- Bjarni V. Halldorsson

- , Hannes P. Eggertsson

- , Kristjan H. S. Moore

- , Hannes Hauswedell

- , Ogmundur Eiriksson

- , Aron Skaftason

- , Nokkvi Gislason

- , Svanhvit Sigurjonsdottir

- , Magnus O. Ulfarsson

- , Gunnar Palsson

- , Marteinn T. Hardarson

- , Asmundur Oddsson

- , Brynjar O. Jensson

- , Snaedis Kristmundsdottir

- , Brynja D. Sigurpalsdottir

- , Olafur A. Stefansson

- , Doruk Beyter

- , Guillaume Holley

- , Vinicius Tragante

- , Arnaldur Gylfason

- , Pall I. Olason

- , Florian Zink

- , Margret Asgeirsdottir

- , Sverrir T. Sverrisson

- , Brynjar Sigurdsson

- , Sigurjon A. Gudjonsson

- , Gunnar T. Sigurdsson

- , Gisli H. Halldorsson

- , Gardar Sveinbjornsson

- , Unnur Styrkarsdottir

- , Droplaug N. Magnusdottir

- , Steinunn Snorradottir

- , Kari Kristinsson

- , Emilia Sobech

- , Gudmar Thorleifsson

- , Frosti Jonsson

- , Pall Melsted

- , Ingileif Jonsdottir

- , Thorunn Rafnar

- , Hilma Holm

- , Hreinn Stefansson

- , Jona Saemundsdottir

- , Daniel F. Gudbjartsson

- , Olafur T. Magnusson

- , Gisli Masson

- , Unnur Thorsteinsdottir

- , Agnar Helgason

- , Hakon Jonsson

- , Patrick Sulem

- & Kari Stefansson

- GSK

- Jimmy Liu

- , Yancy Lo

- , Jatin Sandhuria

- , Tom G. Richardson

- , Laurence Howe

- , Chloe Robins

- , Dongjing Liu

- , Patrick Albers

- , Mariana Pereira

- , Daniel Seaton

- , Yury Aulchenko

- , John Whittaker

- , Manolis Dermitzakis

- , Toby Johnson

- , Jonathan Davitte

- , Erik Ingelsson

- , Robert Scott

- & Adrian Cortes

- Johnson & Johnson

- Liping Hou

- , Julio Molineros

- , Yanfei Zhang

- , Alexander H. Li

- , Evan H. Baugh

- , Elisabeth Mlynarski

- , Abolfazl Doostparast Torshizi

- , Gamal Abdel-Azim

- , Brian Mautz

- , Karen Y. He

- , Jingyue Xi

- , Shirley Nieves-Rodriguez

- , Asif Khan

- , Songjun Xu

- , Xingjun Liu

- , Brice Sarver

- , Dongnhu Truong

- , Mohamed-Ramzi Temanni

- , Christopher D. Whelan

- , Letizia Goretti

- , Najat Khan

- , Belen Fraile

- , Tommaso Mansi

- , Guna Rajagopal

- , Mary Helen Black

- , Trevor Howe

- & Shuwei Li

- Sanger (Velsera Seven Bridges)

- Shaheen Akhtar

- , Siobhan Austin-Guest

- , Robert Barber

- , Daniel Barrett

- , Tristram Bellerby

- , Adrian Clarke

- , Richard Clark

- , Maria Coppola

- , Linda Cornwell

- , Abby Crackett

- , Joseph Dawson

- , Callum Day

- , Alexander Dove

- , Jillian Durham

- , Robert Fairweather

- , Marcella Ferrero

- , Michael Fenton

- , Howerd Fordham

- , Audrey Fraser

- , Paul Heath

- , Emily Heron

- , Gary Hornett

- , Lena Hughes-Hallett

- , David K. Jackson

- , Alexander Jakubowski Smith

- , Adam Laverack

- , Katharine Law

- , Steven R. Leonard

- , Kevin Lewis

- , Jennifer Liddle

- , Alice Lindsell

- , Sally Linsdell

- , Jamie Lovell

- , James Mack

- , Henry Mallalieu

- , Irfaan Mamun

- , Neil Marriott

- , Ana Monteiro

- , Leanne Morrow

- , Barbora Pardubska

- , Alexandru Popov

- , Carol E. Scott

- , Lisa Sloper

- , Jan Squares

- , Ian Still

- , Oprah Taylor

- , Sam Taylor

- , Jaime M. Tovar Corona

- , Elliott Trigg

- , Valerie Vancollie

- , Paul Voak

- , Danni Weldon

- , Alan Wells

- , Eloise Wells

- , Mia Williams

- , Sean Wright

- , Ahmet Sinan Yavuz

- , Jelena Randjelovic

- , Nevena Miletic

- , Lea Lenhardt Ackovic

- , Marijeta Slavkovic-Ilic

- , Mladen Lazarevic

- , Diana Rajan

- , Louise Aigrain

- , Nicholas Redshaw

- , Michael Quail

- , Lesley Shirley

- , Scott Thurston

- , Peter Ellis

- , Laura Grout

- , Natalie Smerdon

- , Emma Gray

- , Richard Rance

- , Cordelia Langford

- & Ian Johnston

- UK Biobank

- Rory Collins

- , Mark Effingham

- , Naomi Allen

- , Jonathan Sellors

- , Ben Lacey

- , Simon Sheard

- , Mahesh Pancholi

- , Caroline Clark

- , Lucy Burkitt-Gray

- , Samantha Welsh

- , Daniel Fry

- , Rachel Watson

- , Lauren Carson

- & Alan Young

- Illumina

- Rami Mehio

- , Zhuoyi Huang

- & Ole Schulz-Trieglaff

Contributions

Study conceptualization, project coordination and consortium leadership: A. Cortes, A.H., B.F., B.V.H., C.C., C.D.W., C.H., C.L., D.F., D.F.G., F.J., G.M., G.R., I. Johnston, J. Sellors, J.W., K.S., L.B.-G., L. Carson, L.G., M.E., M.H.B., M.P., N.A., N.K., O.T.M., P.S., R. Collins, R. March, R.S., S. Li, S.P., S. Sheard, S. Wasilewski, T.H., T.M. and U.T. DNA sequencing and sample preparation: A. Clarke, A. Crackett, A.D., A.F., A.J.S., A. Laverack, A. Lindsell, A.M., A.P., A.W., B.P., C.D., C.L., D. Barrett, D.F., D.N.M., D.W., E.G., E.S., E.T., E. Wells, G. Hornett, H.F., H.M., I. Johnston, I.M., I.S., J. Dawson, J. Durham, J. Liddle, J. Mack, J. Saemundsdottir, J. Squares, K. Kristinsson, K. Law, L. Cornwell, L.G., L.H.-H., L.M., L. Shirley, M.C., M. Fenton, M. Ferrero, M.W., N. Marriott, N.S., O.T., O.T.M., P.H., P.V., R. Clark, R.F., R.R., R.W., S.A., S.A.-G., S. Linsdell, S. Snorradottir, S. Taylor, S. Welsh, S. Wright, R.B., T.B. and V.V. Design and implementation of statistical analyses and data interpretation: A. Cortes, A.O., B.D.S., B.O.J., B.V.H., D. Beyter, E. Wheeler, F.H., G. Holley, G.P., G.S., G.T., H. Holm, H.J., H.P.E., H.S., I. Jonsdottir, J. Liu, J. Mitchell, J. Molineros, K.C., K.H.S.M., K. Kundu, K.R.S., L. Hou, M.T.H., O.A.S., O.E., O.S.B., O.S.T., P.M., Q.W., R. Mehio, R.S.D., S.L., S.P., T.R., V.T., Y.L. and Z.H. Data processing: A. Cortes, A.D.T., A.G., A.K., A.H.L., A.O’N., A.S.Y., A.Y., B.M., B. Sarver, B. Sigurdsson, B.V.H., C.C., C.E.S., D.K.J., D.T., E.H.B., E.M., F.H., F.Z., G.A.-A., G.M., G.T.S., H. Hauswedell, H.P.E., H.T., J. Davitte, J. Dawson, J. Liu, J. Lovell, J. Molineros, J.M.T.C., J.R., J. Sandhuria, J.X., K. Lewis, K. Lythgow, K.M., K.Y.H., L.B.-G., L. Hou, L.L.A., M.A., M.L., M.P., M.-R.T., M.S.-I., M.T., N. Miletic, O.S.-T., P.I.O., P.M., Q.W., R. Mehio, S.A.G., S.K., S.N.-R., S.O’D., S.R.L., S.T.S., S.X., S.V.V.D., T.G.R., X.L., Y.L., Y.Z. and Z.H. Figure preparation: A. Cortes, E. Wheeler, J. Liu, J. Molineros, K.H.S.M., K. Kundu, L. Hou, M.T.H., S.L., Y.L., Y.Z. and Z.H. Manuscript writing: A. Cortes, A.S.Y., B.L., B.V.H., C.E.S., D.K.J., D.R., E. Wheeler, I. Johnston, J. Liu, J.R., K.C., K. Kundu, K.S., M.H.B., N. Miletic, R.S., R.S.D., S.L., S.P., T.H., Y.L. and Z.H. All of the authors reviewed the manuscript.

Corresponding authors

Correspondence to Bjarni V. Halldorsson, Slavé Petrovski, Shuwei Li or Adrian Cortes.

Ethics declarations

Competing interests

K.C., E. Wheeler, K. Kundu, F.H., Q.W., O.S.B., R.S.D., S.V.V.D., C.H., K. Lythgow, P.H.M., K.M., J. Mitchell, S.O., A.O’N., K.R.S., H.T., M.P., R.M., S. Wasilewski and S.P. are or have been employees or contractors of AstraZeneca during the time of this research and may own stock or stock options. J. Liu, Y.L., J. Sandhuria, T.G.R., L. Howe, C.R., D.L., P.A., M.P., D.S., Y.A., J.W., M.D., T.J., J. Davitte, E.I., R.S. and A. Cortes are or have been employees of GSK during the time of this research and may own stock or stock options. B.V.H., H.P.E., K.H.S.M., H. Hauswedell, O.E., A.S., N.G., S. Snorradottir, M.O.U., G.P., M.T.H., A.O., B.O.J., S.K., B.D.S., O.A.S., D. Beyter, G. Holley, V.T., A.G., P.I.O., F.Z., M.A., S.T.S., B. Sigurdsson, S.A.G., G.T.S., G.H.H., G.S., U.S., D.N.M., S.S., K. Kristinsson, E.S., G.T., F.J., P.M., I.J., T.R., H. Holm, H.S., J.S., D.F.G., O.T.M., G.M., U.T., A.H., H.J., P.S. and K.S. are or have been employees of Amgen deCODE genetics and may own stock or stock options. L. Hou, J. Molineros, Y.Z., A.H.L., E.H.B., E.M., A.D.T., G.A.-A., B.M., K.Y.H., J.X., S.N., A.K., S.X., B.F., T.M., T.H. and S.L. are employees and/or stockholders of Janssen Research & Development. R.M., Z.H. and O.S.-T. are employees and/or stockholders of Illumina. The other authors declare no competing interests.

Peer review

Peer review information

Nature thanks Yukinori Okada and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Graphical summary: framework followed in this UK Biobank study.

Participant’s sample were collected from UK Biobank and underwent whole genome sequencing as described in the Supplementary Information. Sequencing data was analyzed with two distinct bioinformatic pipelines generating datasets GraphTyper and DRAGEN, both datasets, and the followed by variant calling of SNPs, indels, and structural variants (SV). Participants were identified to one of five ancestry groups for association analysis of genetic variants for a series of disease endpoints and quantitative traits. Cross-ancestry meta-analysis was then performed. The UK Biobank logo is reproduced with permission.

Extended Data Fig. 2 Effect of sample size on variant number.

Number of variants in UK Biobank DRAGEN aggregated variant dataset (release 2 PASS variants) in different allele frequency ranges as the number of samples increase from 1000 to 490,541 (based on random downsampling). Variant alleles are collected from all autosomes, sex chromosomes, mitochondria, and ALT contigs.

Extended Data Fig. 3 Regional plot for HBB-HBE1 locus associated with Hemolytic anemias (ICD10: D55-59) and Thalassaemia (ICD10: D56) in NFE, AFR, SAS populations.

NFE: non-Finnish European; AFR: African; SAS: South Asian; EAS: East Asian. GWAS for D56 was not conducted in the AFR population due to a sample size of fewer than 200 cases; therefore, no locuszoom plot is available for D56 in AFR. rs11549407 (no LD estimation for this rare variant) MAF: 0.005% in NFE, 0 in SAS, 0.003% in AFR; rs33915217 MAF: 0.00008% in NFE, 0.41% in SAS, 0.004% in AFR; rs334: 0.004% in NFE, 0.089% in SAS, 6.26% in AFR. P-values are uncorrected and are from two-sided tests performed with approximate Firth logistic regression.

Extended Data Fig. 4 The change in Phred scores (−10*log10[p-values]) between the WGS and WES analyses for 12,963,003 binary genotype-phenotype associations (filled circle) and 1,167,322 quantitative associations (empty circle) stratified by chapter.

For gene–phenotype associations that appear in multiple collapsing models, we display only those with the lowest P value within each dataset. The green circles indicate associations that were not significant in the WES analysis but were significant in the WGS analysis. The orange dots represent associations that were originally significant in the WES analysis but became not significant in the WGS analysis. The y axis is capped at ΔPhred = 60 (and −60), equivalent to a P value change of 0.000001.

Supplementary information

Supplementary Information

Consortia authorship, Supplementary Methods, Figs. 1–24, Tables 1–6, 8, 13, 17, 18 and 20–24, notes 1–4 and references.

Reporting Summary

Supplementary Table 7

GWAS_phenotypes_metadata.

Supplementary Table 9

Trans-ancestry meta-GWAS results for 68 quantitative traits (a) and 228 ICD-10 disease outcomes (b).

Supplementary Table 10

Associations with sentinel variants found significant only in non-NFE ancestries.

Supplementary Table 11

UKB WGS revealed heterozygous and homozygous carriers of pLoF, P or LP variants in the 81 ACMG genes.

Supplementary Table 12

Phenotypes included in region-based collapsing analysis PheWAS.

Supplementary Table 14

Significant (P ≤ 1 × 10−8) gene–phenotype associations identified in the coding PheWAS collapsing analysis across both WES and WGS datasets.

Supplementary Table 15

Gene informativeness.

Supplementary Table 16

Significant and suggestive gene–phenotype associations identified in the UTR PheWAS collapsing analysis across 5′ UTR, 3′ UTR, 5′ + 3′ UTR and coding sequence + 5′ + 3′ UTR.

Supplementary Table 19

GWAS Catalog GCST list.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

The UK Biobank Whole-Genome Sequencing Consortium. Whole-genome sequencing of 490,640 UK Biobank participants. Nature 645, 692–701 (2025). https://doi.org/10.1038/s41586-025-09272-9

- Received: 06 February 2024

- Accepted: 11 June 2025

- Published: 06 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09272-9

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

The sequences of 150,119 genomes in the UK Biobank

Article Open access 20 July 2022

Rare variant contribution to human disease in 281,104 UK Biobank exomes

Article Open access 10 August 2021

Rare coding variant analysis for human diseases across biobanks and ancestries

Article 29 August 2024

Article Open access Published: 23 July 2025

A generic non-invasive neuromotor interface for human-computer interaction

Patrick Kaifosh,

Thomas R. Reardon &

CTRL-labs at Reality Labs

Nature volume 645, pages 702–711 (2025)

Abstract

Since the advent of computing, humans have sought computer input technologies that are expressive, intuitive and universal. While diverse modalities have been developed, including keyboards, mice and touchscreens, they require interaction with a device that can be limiting, especially in on-the-go scenarios. Gesture-based systems use cameras or inertial sensors to avoid an intermediary device, but tend to perform well only for unobscured movements. By contrast, brain–computer or neuromotor interfaces that directly interface with the body’s electrical signalling have been imagined to solve the interface problem[1], but high-bandwidth communication has been demonstrated only using invasive interfaces with bespoke decoders designed for single individuals2,3,4. Here, we describe the development of a generic non-invasive neuromotor interface that enables computer input decoded from surface electromyography (sEMG). We developed a highly sensitive, easily donned sEMG wristband and a scalable infrastructure for collecting training data from thousands of consenting participants. Together, these data enabled us to develop generic sEMG decoding models that generalize across people. Test users demonstrate a closed-loop median performance of gesture decoding of 0.66 target acquisitions per second in a continuous navigation task, 0.88 gesture detections per second in a discrete-gesture task and handwriting at 20.9 words per minute. We demonstrate that the decoding performance of handwriting models can be further improved by 16% by personalizing sEMG decoding models. To our knowledge, this is the first high-bandwidth neuromotor interface with performant out-of-the-box generalization across people.

Similar content being viewed by others

Main

Interactions with computers are increasingly ubiquitous, but existing input modalities are subject to persistent trade-offs between portability, throughput and accessibility. While keyboard text entry, texting, trackpads and mice are important, our aim is to enable computation in settings in which these conventional methods are not feasible, for example, seamless input to mobile computing with smartphones, smart watches or smart glasses.

A neural interface that can obviate trade-offs and provide seamless interaction between humans and machines has long been sought, but has been slow to emerge. In recent years, intracortical neural interfaces that directly interface with brain tissue have advanced the premise2,5, demonstrating translation of thought into language at bandwidth rates comparable with conventional computer input systems3,4. However, existing high-bandwidth interfaces require invasive neurosurgery, and the models that translate neural signals to digital inputs remain bespoke.

Non-invasive approaches relying on recording of electroencephalogram (EEG)[6] signals at the scalp have offered more generality across people, for example, for gaming[7], but EEG can require lengthy setup, and the low signal-to-noise ratio of these devices has limited their use[8].

Regardless of the modality, issues of signal bandwidth, generalization across populations and the desire to avoid per-person or session-to-session calibration remain key technical hurdles in the field of brain–computer interfaces (BCIs)5,9,10,11,12.

To build an interface that is both performant and accessible, we focused on an alternative class of non-invasive neuromotor interfaces based on reading out the electrical signals from muscles using electromyography (EMG). Myoelectric potentials are produced by the summation of motor unit action potentials (MUAPs) and represent a window into the motor commands issued by the central nervous system. Surface EMG (sEMG) recordings offer a high signal-to-noise ratio by amplifying neural signals in the muscle[13], enabling real-time single-trial gesture decoding. The nature of the sEMG signal lends itself naturally to human–computer interface (HCI) applications because it is not subject to problems that vex computer-vision-based approaches, such as occlusion, insufficient lighting or gestures with minimal movement. Indeed, sEMG has been deployed for diverse applications in clinical settings14,15, for diagnosis and rehabilitation[16], as well as prosthetic control1,17,18.

However, current EMG systems, including those for prosthetic control[17], have many limitations for wide-scale use and deployment. Laboratory systems are generally encumbered with wires to external power sources and amplifiers, and placed over uncomfortable locations such as the target muscle belly. Commercially available EMG-based neuromotor interfaces have been historically challenging to control[19], relating to myriad technical issues such as poor robustness across postures[20], a lack of standardized data[21], electrode displacement[22], and a lack of both cross-session[23] and cross-user generalization[24]. More recently, deep learning techniques have shown some success at addressing these limitations[25], but a general lack of available EMG data and low sample sizes are believed to limit their efficacy[21].

To validate the hypothesis that sEMG can provide an intuitive and seamless computer input that works in practice across a population, we developed and deployed robust, non-invasive hardware for recording sEMG at the wrist. We chose the wrist because humans primarily engage the world with their hands, and the wrist provides broad coverage of sEMG signals of hand, wrist and forearm muscles while affording social acceptability26,27. Our sEMG research device (sEMG-RD) is a dry-electrode, multichannel recording platform with the ability to extract single putative MUAPs. It is comfortable, wireless, accommodates diverse anatomy and environments and can be donned or doffed in a few seconds.

To transform sEMG into commands that drive computer interactions, we architected and deployed neural networks trained on data from thousands of consenting human participants. We also created automated behavioural-prompting and participant-selection systems to scale neuromotor recordings across a large and diverse population. We demonstrated the ability of our sEMG-RD to drive computer interactions such as one-dimensional (1D) continuous navigation (akin to pointing a laser-pointer based on wrist posture), gesture detection (finger pinches and thumb swipes) and handwriting transcription.

The sEMG decoding models performed well across people without person-specific training or calibration. In open-loop (offline) evaluation, our sEMG-RD platform achieved greater than 90% classification accuracy for held-out participants in handwriting and gesture detection, and an error of less than 13° s−1 error on wrist angle velocity decoding. On computer-based tasks that evaluate these interactions in closed-loop (online), we achieved 0.66 target acquisitions per second in wrist-based continuous control, 0.88 acquisitions per second on discrete gestures and 20.9 words per minute (WPM) with handwriting.

To our knowledge, this is the highest level of cross-participant performance achieved by a neuromotor interface. Our approach opens up directions of sEMG-based HCI research and development while solving many of the technical problems fundamental to current and future BCI efforts.

Scalable sEMG recording platform

To build generic sEMG decoding models capable of predicting user intent from neuromuscular signals, we developed a hardware and software platform capable of quickly and robustly coupling the neuromotor interface with computers across a diverse population (Fig. 1a). Consenting participants (Methods) were seated in front of a computer while wearing the sEMG-RD at the wrist; the sEMG-RD is a dry electrode, multichannel recording device with a high sample rate (2 kHz) and low-noise (2.46 μVrms), and is compatible with everyday use26,27 (Fig. 1a and Methods). We fabricated the device in four different sizes to ensure coverage across a range of wrist circumferences. The device streamed wirelessly over secure Bluetooth protocols and provided a battery life of more than 4 h.

Fig. 1: A hardware and software platform for high-throughput recording and real-time decoding of sEMG at the wrist.

a, Overview of sEMG data collection. A participant wears the sEMG wristband, which communicates with a computer through a Bluetooth receiver. The participant is prompted to perform diverse movements of the hand and wrist. A webcam captures their hand and wrist, excluding the face. Between sessions within a single day, the participants remove and slightly reposition the sEMG wristband to enable generalization across different recording positions. b, The sEMG wristband consists of 48 electrode pins configured into 16 bipolar channels with the sensing axis aligned with the proximal–distal axis of the forearm and the remainder serving as shield and ground electrodes (top). A 3D printed housing encloses cabling and analogue amplifiers for each channel. A compute capsule digitizes the signal and streams sEMG data using Bluetooth. Inset: overlay of 62 and 72 individual instances of two putative MUAPs evoked by subtle thumb (blue) and pinky extension (pink) movements, respectively, from a single sEMG channel (Methods). Bottom, a proton-density-weighted axial plane magnetic resonance imaging (MRI) scan of the wrist; relevant bone and muscle landmarks are labelled. The coloured dots indicate the approximate position of electrodes, with an adjustable gap between electrodes placed over an area of low muscle density. c, Schematic of the prompters for the three tasks (Methods and Extended Data Fig. 4). In the wrist task, the participants controlled a cursor using wrist movements tracked in real time with motion capture. In the discrete-gesture task, gesture prompts scrolled from right to left. In the handwriting task, the participants wrote words presented on the screen. d, Representative sEMG signals, high-pass filtered at 20 Hz, recorded during performance of discrete gestures reveal intricate patterns of activity across multiple channels accompanying each gesture, with prompt timings above (for example, ‘middle’ indicates middle pinch, and the green left arrow indicates a leftward thumb swipe). Channel colouring corresponds to electrode locations in b. The black arrows highlight activation of flexors and extensors during an index-to-thumb pinch and release, respectively. e, Representative examples of variability in gestural sEMG activations across gesture instances (thumb taps (top) and downward thumb swipe (bottom)). The grey lines show the instantaneous high-pass-filtered sEMG power, summed across channels, for all instances of a gesture during a single band placement. The bold traces show the average. The mean was subtracted from all traces, and the power was offset by 10−7 V^2 to plot on a logarithmic scale without visually exaggerating the baseline variance.

We optimized the sEMG-RD for recording subtle electrical potentials at the wrist (Extended Data Fig. 1). We manufactured the device in four sizes, with a circumferential interelectrode spacing of 10.6, 12, 13 or 15 mm, approaching the spatial bandwidth of EMG signals at the forearm (~5–10 mm)[28], while minimizing the device’s form factor. We placed the gap in electrodes to allow for tightening adjustments along the ulna bone, where muscles are reduced in density. Together, this enabled the sensing of putative MUAPs across the wrist during low-movement conditions (Fig. 1b and Extended Data Fig. 2).

To collect training data for models, we recruited an anthropometrically and demographically diverse group of participants (162–6,627 participants, depending on the task; Extended Data Fig. 3) to perform three different tasks: wrist control, discrete-gesture detection and handwriting. In all cases, the participants wore sEMG bands on their dominant-side wrist and were prompted to perform actions using custom software run on laptops (Fig. 1c). For wrist control, the participants controlled a cursor, the position of which was determined from wrist angles tracked in real time using motion capture. During the discrete-gesture detection task, a prompter instructed participants to perform nine distinct gestures with a randomized order and intergesture interval. During the handwriting task, the participants were prompted to hold their fingers together (as if holding an imaginary writing implement) and ‘write’ the prompted text. Further training data protocol details are provided in the Methods.

We designed the data-collection system to facilitate supervised training of sEMG decoding models. During data collection, we recorded both sEMG activity and the timestamps of labels on the prompter using a real-time processing engine. We designed the engine to be used during recording and model inference to reduce online–offline shift (Methods). To precisely align prompter labels to actual gesture times, which may vary due to a participant’s reaction time or compliance, we developed a time-alignment algorithm that enabled post hoc inference of gesture event times (Methods).

Examination of raw sEMG traces revealed highly structured patterns of activity (Fig. 1d). Discrete gestures evoked patterned activity across a set of channels that roughly corresponded to the position of flexor and extensor muscles for the corresponding movement (Fig. 1d and Extended Data Fig. 1c). Fine differences in sEMG power across instances of a given gesture performed during a session (Fig. 1e) highlight the power of the platform in acquiring repeated time-aligned examples for supervised learning and some of the challenges facing generalization of EMG decoders.

Single-participant models do not generalize

It is well known across BCI modalities that both across-session and across-user generalization are difficult problems5,11,24,29. We wanted to evaluate the difficulty of these generalizations for sEMG decoders. Inspection of the raw data revealed pronounced variability in the sEMG for the same action across different participants and band donnings (which we refer to as sessions), reflective of variations in sensor placement, anatomy, physiology and behaviour that make generalization challenging (Fig. 2a,b). As an example of this variability, we found that the cosine distances between waveforms of the same gesture across sessions and users heavily overlapped with the distribution of distances between waveforms of different gestures (Extended Data Fig. 5a), and intermingled even in a nonlinear embedding of gesture distances (Fig. 2b), highlighting the challenge of the generalization problem.

Fig. 2: Generalization performance of single-participant and multi-participant models.

a, Cross-participant (columns) and cross-session variability (light lines) in gestural sEMG for four discrete gestures (different rows and colours) across seven participants. Four of the possible nine gestures are shown for clarity. The light lines show the high-pass-filtered sEMG power averaged across all channels and all gesture instances during a single band placement. The bold lines correspond to the average across all band placements. b, t-SNE embedding of sEMG activations (Methods) across participants for the four different gestures in a. Gesture colour map as in a, with shading reflecting different participants (n = 20). Each dot reflects an individual gestural instance. c,d, Single-participant models trained and tested on the same participant (c) or different participants (d). Generalization across sessions improves as more training data are used. Generalization across participants remains poor even when more training data are used. Statistical analysis was performed using two-sided Wilcoxon signed-rank tests; all pairwise comparisons are significant; P < 10−10. n = 100 single-participant models. The boxes show the median (centre line) and lower and upper quartiles (box limits), and the whiskers extend to ±1.5 × interquartile range. e–g, The decoding error of models trained to predict wrist angle velocity (e), classify nine discrete gestures (f) and classify handwritten characters (g) as a function of the training set size. Data are the mean ± s.e.m. decoding error evaluated on a test set of held-out participants (n = 22 for wrist, 100 for discrete gestures and 50 for handwriting) (Methods). The dashed lines and inset equations show fitted scaling curves (N is measured in units of hundreds of participants and D in millions of parameters). For discrete gestures, the open circle represents varying numbers of sessions per participant (Methods).

To evaluate the ability of obtaining performant sEMG decoders across sessions for a given participant, we trained single-participant models for 100 participants who had collected at least five sessions on the discrete-gesture-classification task. For each participant, we held out one session for evaluation and then trained models on two, three or four of the remaining sessions (Methods). As an offline evaluation metric, we used the false-negative rate (FNR), defined as the proportion of prompted gestures for which the correct gesture was not detected by the model.

Single-participant models trained and tested on the same participant achieved offline performance that improved substantially with more training data (Fig. 2c). By contrast, models trained on one participant and then tested on another showed substantially worse performance and benefited only mildly from an increasing amount of training data (Fig. 2d), indicating a greater domain shift across people compared with across sessions. For 98% of participants, the model trained on their own data performed better compared with all other single-participant models (Extended Data Fig. 5b).

We wondered whether cross-participant generalization was difficult because there was structure or clusters across people, or whether every participant required a relatively unique single-participant model. The former could motivate an approach where a set of models trained on a small population (within each cluster) could achieve a high level of population coverage. The absence of overt structure in a t-distributed stochastic neighbour embedding (t-SNE; Extended Data Fig. 5c) of the average model transfer FNR between participant pairs suggests that there are no obvious participant clusters. Moreover, there are no people who exhibit the ability to generate performant models for other people, nor are there any people for whom other people’s models always perform well (Extended Data Fig. 5d).

Offline evaluation of generic models

To avoid the need to train and tune models for each individual, we trained generic models that are able to generalize to entirely held-out participants. To do this, we collected data from hundreds to thousands of data-collection participants for each task. These data were then used to train neural network decoding models. In each case, we used preprocessing techniques and network architectures designed for processing multidimensional time series (Methods and Extended Data Fig. 6): multivariate power frequency (MPF) features and a long short-term memory (LSTM) layer for the wrist task, a 1D convolution layer followed by an LSTM layer for the discrete-gesture task, and MPF features and a conformer[30] for the handwriting task, which we anticipated would require an architecture with richer context information (provided through the attention mechanism).

Previous studies on large language models[31] and vision transformers[32] have shown that performance shows power-law scaling with the amount of training data and the model size. To investigate whether such scaling holds for sEMG decoding, we examined the offline decoding performance of models trained on data from varying numbers of participants (Fig. 2e–g). Across all tasks, we observed reliable performance improvements as a function of the increasing number of participants in the training corpus. Consistent with other domains, empirical performance follows a power law both as a function of parameters and data quantity, with the parameters of the scaling relationship shared across architecture sizes (Methods). The largest models showed promising offline performance.

Online evaluation of generic models

Ultimately, closed-loop performance of our sEMG decoding models is the critical evaluation that confirms their viability as a computer interface. For each task, closed-loop evaluation was performed on naive participants who had not previously had meaningful experience using any sEMG decoder on that task (n = 17 (wrist), n = 24 (discrete gestures) and n = 20 (handwriting)). The core tasks involved using the wrist-angle decoder to continuously control a 1D cursor to acquire targets, the discrete-gesture decoder to navigate and perform actions in a discrete lattice, and the handwriting decoder to write out prompted phrases that were then visualized on the screen (Fig. 3a–c; the evaluation tasks are described in the Methods; see Supplementary Videos 1–3 for representative performance, and Extended Data Fig. 7 for a depiction of the task dynamics). For each task, the participants performed three distinct blocks of trials to allow for characterization of learning (50 trials per block for wrist, 10 trials for discrete gestures and handwriting), with the first block always being a practice block that allowed them to adapt to the controller.

For all of the tasks, we observed learning effects, whereby the participants improved with experience. During the practice block, the supervisor gave verbal coaching—for example, “swipe faster” or “write more continuously”—as needed to improve participant’s performance. The participants were typically able to perform each task on their own after the initial practice block but, for the discrete gestures and handwriting tasks, we found that coaching during the evaluation block was valuable for a subset of participants on trials that they struggled to complete (Methods).

Every participant was able to complete every trial of the three tasks. For wrist control, all of the participants were able to successfully navigate to each target and stay on the target for 500 ms to acquire it. Performance was characterized by time to target acquisition (Fig. 3d) and dial-in time, which measures the time taken to acquire the target after having exited it prematurely (Fig. 3e; definitions are provided in the Methods). We found learning effects in which participants improved in both of these metrics from the practice block to the evaluation blocks, and the majority of them subjectively reported that the cursor moved in the intended direction >80% of the time (Extended Data Fig. 8e).

Fig. 3: Generic sEMG decoding models enable closed-loop control in diverse interactions.

a–c, Schematics of the three closed-loop tasks. a, Horizontal cursor (wrist): the participants control a cursor (red circle) to acquire a target (green rectangle) in a row of possible targets (grey rectangles). b, Discrete grid navigation: the participants use thumb swipe gestures to navigate, and perform activation gestures prompted by coloured shapes. c, Text entry: the participants handwrite prompted text. (Methods, Extended Data Fig. 7 and Supplementary Videos 1–3). d,e, The performance of n = 17 naive test participants using the wrist decoder in the horizontal cursor task. d, The mean target-acquisition time (excluding the 500 ms hold) in each task block. e, The mean dial-in time in trials in which the cursor prematurely exited the target before completing the hold. Inset: the fraction of trials with premature exits. The dashed red and orange lines in panels e and d show the median task performance with the ground truth wrist angles measured by motion capture (n = 162, with no previous task exposure) and with the native MacBook trackpad (n = 17, with previous task exposure), respectively (Methods). f–h, The performance of n = 24 naive test participants using the discrete-gesture decoder in the grid navigation task. f, The fraction of prompted gestures in each block for which the first detected gesture matches the prompt (first-hit probability). g, The mean gesture completion rate in each task block. The dashed red lines in panels f and g show the median task performance of a different set of n = 23 participants using a gaming controller (Methods). h, Confusion rates (normalized to expected gestures) in evaluation blocks, averaged across participants. Early release denotes a hold of less than 500 ms. i,j, The performance of n = 20 naive test participants using the handwriting decoder on the text entry task. i, The online CER in each block. j, The WPM in each block. The dashed red line shows the median WPM of a different set of n = 75 participants handwriting similar phrases in open loop without a pen (Methods). For each participant, the online CER and WPM are calculated as the median over trials in each block. For all panels, statistical analysis was performed using two-tailed paired sample Wilcoxon signed-rank tests; *P < 0.05, **P < 0.005; not significant (NS), P > 0.05. The boxes show the median (centre line) and lower and upper quartiles (box limits), and the whiskers extend to ±1.5 × interquartile range. The printed numbers show the median and outliers are marked with open circles. For each baseline device, the dashed lines show the median over participants and the shading shows the 95% confidence intervals estimated using the reverse percentile bootstrap with 10,000 resamples.

For discrete gestures, all of the participants were able to complete the task by navigating with the swipe gestures and performing the activation gestures (thumb tap, index pinch and hold, middle pinch and hold) when required. Performance on the discrete-gesture task was characterized by a measure of how often the first detected gesture following a prompt matched the prompted gesture (Fig. 3f) as well as how long it took to complete each prompted gesture (Fig. 3g). The confusion matrix across discrete gestures is shown in Fig. 3h. Note that errors on this task (reflected in both confusions and first-hit probabilities) are a combination of model decoding errors as well as behavioural errors, whereby the participant performed the wrong gesture. This is evident in the fact that confusions were also present when performing this task using a gaming controller rather than an sEMG decoder (Extended Data Fig. 8b–d). Index and middle holds were sometimes released too early (that is, the detected release followed the detected press less than 0.5 s later), and this was indicated in the confusion matrix as an ‘early release’.

The performance of the closed-loop handwriting decoder was evaluated by participants entering prompted phrases and was characterized by the online character error rate (CER; Fig. 3i) and speed of text entry (Fig. 3j). Improvements from practice to evaluation blocks indicate that participants were able to use the practice trials to discover handwriting movements that were effective for writing accurately with the decoder.

For each of these interactions, we also provide performance metrics for a baseline interface that does not rely on decoding sEMG (dashed horizontal lines in each panel). For 1D continuous control, we find that a MacBook trackpad and motion capture ground-truth wrist-based control lead to improved median acquisition times of 0.68 s and 0.96 s, respectively, compared with 1.51 s for the sEMG wrist decoder. For discrete grid navigation, using a Nintendo Joy-Con game controller showed a median gesture completion rate of 1.45 completions per second versus 0.88 with the sEMG discrete-gesture decoder. For prompted text entry, the participants performed open-loop handwriting on a surface, without a pen, at 25.1 WPM, higher than the 20.9 WPM achieved with the sEMG handwriting decoder (and below 36 WPM achievable with mobile phone keyboard[33]). While our sEMG decoders therefore have room to improve relative to these baseline devices, they are sufficiently performant to reliably complete each task, while not requiring the use of hand-encumbering devices or external instrumentation.

Representations learned by the discrete-gesture model

To develop an intuition about how the generic sEMG decoders function, we visualized the representations learned by the intermediate layers of the discrete-gestures decoder. The network architecture consisted of a 1D convolutional layer, followed by three recurrent LSTM layers (Fig. 4a) and, finally, a classification layer.

Fig. 4: The discrete-gesture decoder learns representations that are physiologically grounded.

a, Schematic of network architecture. Conv1d denotes a 1D convolutional layer. The final linear readout and intermediate normalization layers are not shown (Methods). b, Representative convolutional filter weights (16 input channels × 21 timesteps) from the first layer of the trained model. c, Example heat maps of the normalized voltage across all 16 channels for putative MUAPs recorded with the sEMG wristband (Methods and Extended Data Fig. 2) after high-pass filtering (Methods). d,e, The frequency response of the channel with maximum power (d) and the root mean square (RMS) power per channel (e), both normalized to their respective peaks, for each example convolutional filter (blue lines) and putative MUAP (orange lines) from b and c, respectively (see also Extended Data Fig. 9). For comparison, the dashed black lines show these curves calculated over an entire recording session, averaged over ten randomly sampled sessions from the model training set. For d, we used the mean temporal frequency response over all 16 sEMG-RD channels. The sharp frequency response cut off at 40 Hz is from high-pass filtering (Methods). f–h, Principal component analysis projection of LSTM representations of 500 ms sEMG snippets aligned with instances of each discrete gesture, from three participants held out from the training set, each with three different band placements. Each row shows the representation of each LSTM layer. Each column shows the same data, coloured by discrete gesture category (f), participant identity and band placement (g) or sEMG RMS power (h) at the time of the gesture. i, The proportion of total variance accounted for by each variable, for each layer (n = 50 test participants; Methods). Statistical analysis was performed using two-tailed paired sample t-tests; ***P < 0.001. The error bars (barely visible) show the 95% Student’s t confidence interval for the mean.

To interpret the convolution layer, we visualized representative spatiotemporal filters (Fig. 4b) alongside putative MUAPs (Fig. 4c) detected using the wristband during low-movement conditions (Extended Data Fig. 2). The filters appear to form a coarse basis set spanning the statistics of MUAPs; specifically, Fig. 4d,e shows the general similarity in temporal frequency content and spatial envelope between the putative MUAPs and emergent convolutional filters (Extended Data Fig. 9).

To examine the intermediate LSTM representations, we visualized the changing representational geometry across layers. We analysed the representations of four properties: gesture category, participant identity, band placement and gesture-evoked sEMG power (a proxy for behavioural variability over executions of the same gesture). Figure 4f–h shows LSTM hidden-unit activity at each layer evoked by snippets of sEMG activity triggered on discrete-gesture events, coloured by one of the four aforementioned properties. By examining the dominant principal components (PCs), we observed a trend of gesture category becoming more separable deeper in the network as the representations of each gesture become more tightly clustered and less or equally sensitive to nuisance variables (participant identity, band placement and power). With increasing depth in the network, gesture category accounted for an increasing proportion of the variance in the representation of each layer (Fig. 4i and Methods). In summary, the network learns to solve this task by progressively shaping its representation of the sEMG to be more and more invariant to nuisance variables.

Personalizing handwriting models improves performance

While generic models allow a neuromotor interface to be used with little to no setup, performance can be improved for a particular individual by personalizing the generic model to data from that participant. Personalization has shown benefits to accuracy for related problems in automatic speech recognition in language models[34] and acoustic models[35] as well as speech enhancement[36]. We explored personalization for the handwriting task through the fine-tuning of all of the generic model’s parameters using additional supervised data from a set of 40 held-out participants not included in the training data of the generic model. For each participant, we held out three sessions of data (Methods) and then trained personalized models for 300 epochs without early stopping on varying amounts of data from their remaining sessions (Fig. 5a).

Fig. 5: Personalization of generic sEMG handwriting models improves performance.

a, Schematic of the supervised handwriting decoder personalization. Predictions before and after personalization are shown above and below example prompts (such as ‘howdy!’) for two participants (left and right). The green and purple font denotes correct and incorrect character predictions, respectively. b, The mean performance (n = 40 test participants) of models pretrained on varying numbers of participants (red line) and fine-tuned on varying amounts of personalization data for each test participant (shades of blue). The dashed lines show power law fits (Methods). c, The relative reduction in offline CER that personalization provides beyond a given generic model, for varying amounts of pretraining participants and personalization data. The dashed lines show the relative improvements calculated from the power law fits in b. d, The relative increase in the number of pretraining participants that matches CER reduction from fine-tuning on varying amounts of personalization data (Methods), for generic models with varying amounts of pretraining participants. A value of 1 indicates doubling the number of pretraining participants. The dashed lines show the relative increases calculated from the power law fits in b. e, The relative reduction in offline CER (beyond the 60.2-million-parameter 6,527-participant pretrained generic model) achieved for each test participant (rows) by personalizing on 20 min of data from every other test participant (columns), sorted by the diagonal values. f, The relative reduction in CER achieved for each test participant (n = 40) by fine-tuning on 20 min of personalization data, as a function of the pretrained generic model CER for that test participant (60.2-million-parameter model), across various numbers of pretraining participants. Improvements from personalization are correlated with the CER of the pretrained generic model. We show the range of Pearson correlation coefficients across numbers of pretraining participants and the median P value (two-sided test); the maximum P value over all fits is 0.0035.

Fine-tuning generic models improved their average offline CER for all amounts of additional data and for all numbers of pretraining participants (Fig. 5b). Even for generic models trained on 6,400 participants, using just 20 min of personalization data resulted in a 16% improvement in the median performance (Fig. 5c). In all cases, more personalization data led to further reductions in the average per-user CER across the personalized participants. However, across all generic models, as the generic model was pretrained with data from more participants, the absolute and relative improvement in CER from personalization decreased (Fig. 5c), indicating that there are diminishing returns to personalizing already performant generic models.

Personalizing models is therefore an alternative to expanding the generic corpus size to decrease a model’s CER on the target participant (Fig. 5d). For example, for the model pretrained on the smallest corpus of 25 participants (or 1,900 min), personalization with 20 min of data from the target participant was equivalent to training a generic model with 14,000 min of additional data from other participants—7× as much data as in the original pretraining corpus. However, as more data from other participants are added, the effective enhancement of the generic training corpus achieved through personalization diminishes. Adding 14,000 min of pretraining data is equivalent to 20 min of personalization data for the 25 participant model and only about 1 min for the 200 participant model.

While personalization improved performance on the target participant, model performance improvements from personalization caused the model to overfit to the target participant and did not transfer across participants. For the most performant generic model trained (6,527 participants, 60.2 million parameters), personalizing on one participant and evaluating on another participant generally had a negative impact on performance when compared to the generic model performance (Fig. 5e). Personalization on the same participant improved the performance in 88% of the participants and led to a relative improvement of 8.35 ± 2.36% (median ± s.e.m. over participants), whereas data from one participant used to personalize another participant improved performance on only 7% of such participant pairs and led to an average relative decrease of 8.86 ± 0.53% (median ± s.e.m., taken across each evaluation participant after averaging across personalized models; Methods).

Personalization disproportionately improved the performance of poorly performing participants across all generic models (Fig. 5f). For example, for generic models pretrained with 6,527 participants, personalization provided larger relative gains for participants with higher generic model CER (Fig. 5f) and more moderate gains or occasional regressions for those with already low CERs. In Extended Data Fig. 10, we show that these regressions can be mitigated with early stopping during fine-tuning, albeit at the cost of increased data required for validation.

Overall, these results highlight clear trends and trade-offs for personalization, facilitating the rational design of data collection. We expect that personalization will provide a practical solution for enhancing the average per-user performance when further scaling generic data collection to achieve a target performance level is prohibitive. Moreover, personalization can effectively address the long tail of users experiencing poor performance with the generic model, as it ensures considerable relative performance improvements for these users.

Discussion

Here, we introduce an easily donned/doffed wrist-based neuromotor interface capable of enabling a diverse range of computer interactions for novel users. We developed a scalable data-collection framework and collected a large training corpora across diverse participants (Fig. 1). We used supervised deep learning to produce generic sEMG models (Fig. 2) that overcome issues that have long stymied generalization in BCIs and sEMG systems. The resulting sEMG decoders enabled continuous control, discrete input and text entry in closed-loop evaluations without the need for session- or participant-specific data or calibration (Fig. 3). A dissection of intermediate representations in the discrete-gesture neural-network decoder highlighted its ability to disentangle nuisance parameters related to band placement and behavioural style (Fig. 4). Finally, we demonstrated improvements to handwriting decoding performance with additional personalization data (Fig. 5). Together, this work defines a framework for building generic interaction models using non-invasive biological signals.

Related work in HCI and BCI

The work presented here sits at the nexus between HCI and BCI. The HCI community has placed significant emphasis on advancing gestural input for various technology applications by deploying machine-learning-backed solutions for differing sensing modalities such as computer vision (for example, Kinect, Meta Quest) inertial measurement units37,38, sEMG24,39,40, bio-acoustic signals[41], electrical impedance tomography[42], electromagnetic signals[43] and ultrasonic beamforming[44]. The most direct antecedent of our work uses the discontinued commercial sEMG Myo armband (worn on the forearm) for gesture detection, and wrist movement[39], in datasets with more than 600 participants45,46. However, to date, sEMG-based approaches have typically been offline or necessitated within-session or participant-specific calibration, limiting their real-world use[47].

Our non-invasive sEMG work has intimate connections to BCI. EEG-based BCI systems (notably, spellers) can achieve impressive bitrates of 100–300 bits per minute[48] (versus 528 bits per minute for our handwriting decoder). However, EEG performance generally lags behind other BCI modalities due to issues with signal quality, interpretation and lack of standardized hardware or software[49]. As a result, efforts have been focused on small models and relatively small datasets (for example, <50 users[50]).

Intracortical BCI offers higher signal-to-noise ratio, but has been limited to single-participant studies due to nonstationarities in recordings and over sessions5,11,12,29. While the field of BCI is transitioning to neural network decoders4,29,51,52, it remains focused on solving these calibration issues, which are largely a function of limited data. Given that sEMG signals derive from the summed activity of motor unit firing, it is possible that sEMG-decoding methods such as those described here can guide methods development for intracortical BCI systems. The large-scale approaches demonstrated here may provide direction to the larger BCI field, such as BrainGate2,4 or Neuralink[53].

Comparison to HCI baselines

To contextualize the absolute performance of our sEMG decoders, we compared their performance to both common input methods and those using similar gestures as our sEMG decoders use: a MacBook trackpad and motion capture ground truth wrist angles for 1D continuous control, a Joy-Con game controller for discrete grid navigation and open-loop prompted handwriting for text entry. In each case, these baseline devices outperform our sEMG decoders.

However, we note that these baseline interfaces cannot fulfil the same role as an always-available sEMG wristband, as they require cumbersome equipment: tracking wrist angles requires multiple calibrated cameras, using a laptop trackpad or a gaming controller encumbers the hand, and handwriting requires a pen, paper and a surface. For tasks in which constant availability is important (such as on-the-go scenarios), the reductions in current decoder performance may therefore be acceptable.

Regardless, we expect further improvements in sEMG decoding through continued development of user familiarity/skill over time, improved models (including through personalization), post-processing and hardware innovations for superior sensing. We also note that the gestures used with our sEMG decoders are novel, and we found that coaching typically improved sEMG decoder performance (Methods). We expect user proficiency to grow with increased familiarity with the sEMG-RD and underlying gestures.

Future directions

Our sEMG decoder enables direct intentional motor signal detection from the muscle, thereby opening directions in novel and accessible computer interactions. For example, such a decoder could be used to directly detect an intended gesture’s force, which is generally unobservable with existing camera or joystick controls. While we demonstrated accurate, fully continuous control over only one degree of freedom, it is also likely that joint control of multiple degrees of freedom is achievable through additional, separate biomimetic mappings such as adding ulnar/radial deviation of the wrist for vertical control. Moreover, the sensitivity of sEMG to detect signals as subtle as putative individual MUAPs (Fig. 1b and Extended Data Fig. 2) enables the creation of extremely low-effort controls—an important innovation with a potential impact for people with a diverse range of motor abilities or ergonomic requirements[54]. Explorations of interactions in neuromotor signal space—as opposed to gesture space—may enable entirely new forms of control, for example, by exploring the limits of novel muscle synergies or interaction schemes that directly depend on individual motor unit recruitment or firing-rate control.

As a research platform, the sEMG-RD and associated software tooling could enable study of the effects of neurofeedback on motor unit activity for novel human–machine interactions55,56, the learning of novel motor skills[57] or the limits and mechanisms of motor unit control[58].

Finally, in the clinic, the ability to design interactions that require only minimal muscular activity, rather than performance of a specific movement, could enable viable interaction schemes for those with reduced mobility, muscle weakness or missing effectors entirely[59], as well as the development of effective closed-loop neurorehabilitation paradigms[60]. It is unclear whether the generalized models developed here and trained on able-bodied participants will be able to generalize to clinical populations, although early work appears promising[54]. Personalization can be applied selectively to users for whom the generic model works insufficiently well due to differences in anatomy, physiology or behaviour. However, all of these new applications will be facilitated by continued improvements in the sensing performance of future sEMG devices, increasingly diverse datasets covering populations with motor disabilities, and potentially combining with other signals recorded at the wrist, such as IMU or biosignals.

Methods

Hardware

sEMG-RD

The sEMG devices consisted of two primary subcomponents: a digital compute capsule and an analogue wristband (Extended Data Fig. 1). The digital compute capsule comprised the battery, antenna for Bluetooth communication and a printed circuit board that contained a microcontroller, an analogue-to-digital converter and an inertial measurement unit. The analogue wristband comprised discrete links that each housed a multilayer rigid printed circuit board that contained the low-noise analogue front-end circuits and gold-plated electrodes. We manufactured the sEMG-RD device in four sizes. The analogue front end applied 20-Hz high-pass and 850-Hz low-pass filters to the data.

These printed circuit boards were inserted into Nylon 12 PA 3D printed housings and then strung together with a multilayer flexible printed circuit board along with a strain-relieving fabric. An elastic nylon cord was routed continuously between the links and was tied together at the wristband gap to form a clasp and tensioning mechanism. Finally, the digital compute capsule was connected to the analogue wristband through a connector on the flexible printed circuit board and fastened together with screws for mechanical stability. The device underwent a biocompatibility testing process to ensure its safety. The band is easily donned at the wrist with the only requirements being that the compute capsule is on the dorsal side and the gap is near the ulna bone.

Data collection

MRI scan

To visualize the position of the sEMG-RD’s electrodes relative to wrist anatomy, we collected a high-resolution anatomical MRI scan (Siemens Magnetom Verio 3T) from a consenting participant’s right forearm. We collected axial scans along the forearm, beginning from just distal to the wrist and ending just distal to the elbow. The scan was collected pursuant to an IRB governed study protocol conducted by Imperial College London.

Participant experience

All data collection was done at either Meta’s internal data-collection facilities or at third-party vendor sites. Study recruitment and participant onboarding was performed according to protocol(s) approved by an external IRB (Advarra). All studies began by providing the participants with information about the study protocol and asking them to review and sign an IRB-reviewed consent form before beginning the study. The participants were provided with the opportunity to ask questions before their participation and were able to discontinue their participation at any time. On-site research administrators monitored participants during the study protocol(s) to ensure participant well-being. The participants were financially compensated for their time participating in the study.

Collection at scale

The participants visited data-collection and laboratory facilities to perform the study protocols. On a given day, there were up to 300 participants who partook in a study. Once a participant was in the facility, measurements of the wrist and hand were taken, including the forearm circumference and wrist circumference. Next, we fitted them with an appropriately sized band to collect sEMG data; small, 130–148 mm; medium, 148–169 mm; large, 169–193 mm; and extra large, 193–220 mm.

All of the participants received general coaching in the form of a study introduction, in-person demonstration of the correct and incorrect movements, and general supervision of participant compliance by research assistants. Study sessions lasted around 2–3 h (including rests and briefing). All responses and information provided during the study were collected and stored using de-identification technique(s) in a secure database.

While all collection occurred in controlled environments, training and testing datasets demonstrated large variance along band placement, sweating, skin condition, demographic diversity, local climate and other axes.

Prompted study design

All of our tasks were framed as supervised machine learning problems. For the handwriting and discrete-gesture recognition tasks, we relied on prompting to obtain approximate ground truth for our data, rather than direct instrumentation using physical sensors. While prompt labels depend on participant compliance, we found that instrumentation imposed constraints on what could be explored, as dedicated sensors need to be built for each individual modelling task. Furthermore, the use of sensors such as gloves or pressure sensitive pads limited the ecological validity of the signal, as physical sensors can restrict the movement range, poses and conditions examined.

For the wrist task, we used motion capture to continuously track the participant’s wrist angle (see below). In this case, we used a mixture of open-loop prompting (as for the discrete-gesture and handwriting tasks) and closed-loop interactions, in which participants performed cursor control tasks in which the cursor’s position was determined from their wrist angles tracked in real time (see below).

Training and evaluation protocols were implemented in a custom, internal software framework that took advantage of the abilities of Lab.js, an established open-source web-based study builder[61]. This framework orchestrated both the presentation of task-specific prompter applications and the recording of annotations from these applications. The framework was developed using TypeScript and the task-specific prompters were built on the React framework.

We created the overview figure of our data-collection approach in Fig. 1a using a photograph taken at our data-collection facility as a reference, which was then traced and edited in Procreate, with additional colour and graphical elements added in Adobe Photoshop.

Real-time data-collection system

Data collection for our studies was performed using an internal framework for real-time data processing that supports data collection, offline model training, and benchmarking and online evaluation. At its core, the framework offers an engine for defining and scheduling a data-processing graph. On the periphery, it provides well-defined APIs for real-time performance monitoring and interaction with consumer applications (for example, prompting software, applications for stream visualization).

For data collection, our internal platform served as the host for recording real-time signals and annotations to a standardized data format (that is, HDF5). For offline model training and benchmarking, our internal platform provides an API for batch processing of data corpora. This helps to generate featurized data from the recorded raw-signals and apply model inference for offline evaluation. To ensure online and offline parity, the internal platform also supports running the same sequence of processing steps on real-time signals for online evaluation.

Offline training data corpora

Wrist corpus

The wrist decoder training corpus included simultaneous recordings of sEMG and ground truth flexion-extension wrist angle (measured with motion capture) from 162 participants, 96 of whom recorded 2 sessions (both sessions from each of these participants were included in the same train or test split to which they were assigned). To track flexion-extension and ulnar-radial deviation wrist angles, we placed two light (16 g) 3D printed rigid bodies on the back of the hand and on the digital compute capsule of the sEMG-RD. Each of these rigid bodies had three retroreflective markers attached, which together defined a 3D plane that was tracked in 3D in real time (60 Hz) with <1 mm resolution using 18–30 PrimeX 13 W cameras (OptiTrack). We used the relative orientation of these two planes to calculate the flexion-extension and ulnar-radial deviation wrist angles. Only the flexion-extension angle was used for training and evaluating wrist decoders.

Each session consisted of an open-loop stage, a calibration stage and a closed-loop stage, in which the participants controlled a cursor that determined its position from these two wrist angles. Throughout all stages, the participants were instructed to keep their hand in a ‘laser pointer’ posture, with a loose fist in front of the body, thumb on top and elbow at approximately 90°.

In the open-loop stage, the participants performed centre-out wrist deflections in eight possible directions (four cardinal directions and four intercardinal directions) following a visual prompt (Extended Data Fig. 4a), for a total of 40 repetitions (5 per direction) in a pseudorandomized order.

In the closed-loop stage, the participants were asked to perform two tasks to the best of their abilities: a cursor-to-target task and a smooth pursuit task. In both tasks, the flexion-extension and radial-ulnar deviation wrist angles were normalized by their range of motion (measured in a calibration stage), centred by the neutral position (measured by prompting the user to hold a neutral wrist angle), and then respectively mapped to the horizontal and vertical position of a cursor on the screen, in real-time (60 Hz). This mapping consisted of simply scaling the (normalized and centred) wrist angles by a constant gain, gx. To encourage both small and large wrist movements, two different gains were used: gx = 2.0 pixels per normalized radian (half of range of motion) and gx = 4.0 pixels per normalized radian (quarter of range of motion). Gains larger than 1.0 were required for every user to be able to reach the corners of the workspace.

In the cursor-to-target task, the participants were prompted to move the cursor to one of the equally sized rectangular targets presented on the screen. During each trial, one of the targets was highlighted, and the participant was instructed to move the cursor towards that target. The target was acquired when the cursor remained within the target for 500 ms. Once a target was acquired, the rectangular target disappeared, and one of the remaining targets was prompted, initiating the next trial, in a random sequence. Once all of the targets were acquired, a new set of targets was presented. Three different target configurations were used: horizontal (10 targets presented side-by-side along the horizontal axis, with the cursor confined to this axis; Extended Data Fig. 7a), vertical (10 targets presented one on top of the other along the vertical axis, with the cursor confined to this axis) and 2D (25 targets presented in a 5 × 5 square grid; Extended Data Fig. 4b). These three configurations were presented in this order in a block structure. In the horizontal target configuration block, the participants had to acquire all 10 horizontal targets, and repeat this 10 times, for a total of 100 trials. The first 5 repetitions (50 trials) were performed with the lower cursor gain and the last 5 repetitions (50 trials) were performed with the higher cursor gain. The vertical target configuration block followed the same structure, and the 2D target configuration block consisted of 4 repetitions (for a total of 100 trials), with the first 2 performed with the lower cursor gain and the last 2 with the higher cursor gain.

Finally, in the smooth pursuit task, the participants were instructed to move the cursor to follow a moving target on the screen as closely as possible (Extended Data Fig. 4c). Each trial consisted of a 1-min random target trajectory, generated by taking a random combination of 0.1 Hz to 0.25 Hz sinusoids (with randomly sampled phases) along the horizontal and vertical axes. The participants performed a total of four trials, the first two of which were performed with the lower cursor gain and the last two with the higher cursor gain.

Only data within these task stages (open-loop, cursor-to-target and smooth pursuit) were used for model training and offline evaluation. All data outside of these stages were excluded from the model training and test sets. We also excluded data from the cursor-to-target task with the vertical target configuration, as the flexion-extension wrist angle was mostly constant during this task.

Discrete-gesture corpus

The discrete-gesture training corpus was composed of data from 4,900 participants. As noted in the main text, there were nine prompted gestures: index and middle finger presses and releases, thumb tap and thumb left/right/up/down swipes. Each session consisted of stages in which combinations of gestures were prompted at specific times (Extended Data Fig. 4d,e). These combinations usually included the full set of trained gestures but, in some stages, were restricted to specific subsets (for example, pinches only, thumb swipes only). During data collection for these stages, the participants were asked to hold their hand and arm in one of a range of postures (hand in front, palm facing in/out/up, hand in lap, arm hanging by side, forearm pronated inwards) or to translate/rotate their arms while completing gestures. In around 10% of stages, instead of prompting specific timing, the participants were asked to complete sequences of 3–5 gestures at their own pace. About one-third of the training corpus was composed of a range of null data in which participants were either asked to generate specifically timed null gestures (such as snaps, flicks) or to engage in more loosely prompted longer-form null behaviours (such as typing on a keyboard). On average, gestures occur in around 6% of samples. The gestures were unevenly distributed, with thumb gestures being more frequent. Given that an event has occurred, individual gesture probabilities range from around 9% to 13%. When considering the entire dataset including null cases, the probability of correctly guessing any specific gesture falls below 1%.

Handwriting corpus

The handwriting recognition corpus comprised sEMG recordings from a total of 6,627 participants. The data were collected in short blocks, during which the participants were prompted to write a series of randomly selected items, including letters, numbers, words, random alphanumeric strings or phrases (Extended Data Fig. 4f,g). The participants were prompted with spaces inserted both implicitly and explicitly between words. In implicit space prompting, the participants advance from one word to the next naturally as with pen and paper writing. In explicit space prompting, prompts with a right dash character would be presented after each word, instructing the participants to perform a right swipe with their index finger that would later be remapped to a space. This can constrain the modelling problem, avoiding the need for the model to infer spaces implicitly by relying on factors such as the linguistic context of the text being written. We sampled phrases from a dump of Simple English Wikipedia in June of 2017, the Google Schema-guided Dialogue Dataset[62] and the Reddit corpus from ConvoKit[63], after filtering to remove offensive words and phrases. Each participant contributed varying amounts of data, but approximately 1 h and 15 min each on average. Each block was performed in one of three randomly chosen postures: seated writing on a surface, seated writing on their leg as the surface or standing writing on their leg. Note that we did not have ground truth information about the fidelity with which participants wrote these prompts but, for a subset of participants, handwriting was performed with a Sensel Morph touch surface device. Visual examinations of a subset of the Sensel recordings suggested that approximately 98% of prompted characters were executed successfully.

sEMG preprocessing

Putative motor unit action potential waveform estimation

Figure 1b shows the spatiotemporal waveforms of MUAPs evoked by subtle contractions of the thumb and pinky extensors in one participant. For each digit, the participant selected the sEMG channel with maximum variance during sustained contractions based on visual inspection of the raw signals. Down-selecting to one channel enabled greater acuity for visual biofeedback during data collection. Subsequently, the participant was prompted to alternate between resting and performing sustained contractions of the chosen digit for three repetitions while receiving visual feedback about the raw sEMG signal on the selected channel. Each rest and movement prompt was 10 s long with 1 s interprompt intervals. The participant used the visual feedback on the selected channel to titrate the amount of generated force to recruit as few motor units as possible with each contraction64,65.

We estimated the MUAP spatiotemporal waveforms W (W ∈ \({\mathbb{R}}\)L×C, where L is the number of samples (40) and C is the number of channels (16)) for each digit using a simple offline spike-detection algorithm. The sEMG traces were first preprocessed by filtering with a second-order Savitzky–Golay differentiator filter with a width of 2.5 ms (5 samples). The filtered sEMG was rectified to improve the alignment of detected MUAPs, averaged over channels, then smoothed with a 2.5 ms Gaussian filter to obtain a 1D sEMG envelope. Spikes were detected by peak finding on the sEMG envelope using scipy.signal.find_peaks with prominence=0.5 (ref. [66]). MUAPs were extracted using a 20-ms-long window across all sEMG channels, centred on each peak. The waveforms shown in Fig. 1b were obtained from the selected channel for thumb extension (12; blue) and pinky extension (14; pink) using all MUAPs detected during the second prompted movement period; no attempt was made to cluster MUAPs into different units. For visualization, the opacity of each trace was scaled as 1/(1 + |ai − median(a)|), where ai is the peak-to-peak amplitude of the ith MUAP and a is the amplitudes of all detected MUAPs for each contraction.

MPF features

The wrist and handwriting generic sEMG decoders used custom features extracted from the raw sEMG; we refer to this feature set as MPF features. To obtain these features, we first rescaled the sEMG by 2.46 × 10−6, to normalize the s.d. of the noise to 1.0 (this value was determined empirically). Motivated by the need to remove motion artifacts[67], we then applied a 40 Hz high-pass filter (fourth-order Butterworth) to the sEMG recordings sampled at 2 kHz. We then extracted the squared magnitude of the cross-spectral density with a rolling window of T sEMG samples and a stride of 40 samples (20 ms). We used T = 200 samples (100 ms) for the wrist decoder and T = 160 samples (80 ms) for the handwriting decoder. The cross-spectral density was chosen to preserve cross-channel relationships in the spectral domain. We estimated the magnitude of cross-spectral density by first taking the outer product (over channels) of the discrete Fourier transform of the signal (64 sample (32 ms), stride of 10) with its complex conjugate. We then binned the result into 6 frequency bins (0–62.5, 62.5–125, 125–250, 250–375, 375–687.5, 687.5–1,000 Hz). We summed this product over each frequency bin, and took the square of the absolute value of the sum over frequencies. This produced a set of 6 symmetric and positive definite 16 × 16 square matrices that update every 40 samples, for an output frequency of 50 Hz. Building on robust results in the EEG space for this class of features, we applied a log-matrix operation on each of these matrices[68]. Finally, the diagonal and the first three off-diagonals (rolled over the matrix edge to account for the band being circular) were preserved and half-vectorized for each matrix, and then concatenated across the 6 frequency bins, producing a single 384 (6 × 4 × 16) dimensional vector for each 80 ms window. An implementation for both the cross spectral density estimation and taking the matrix logarithm can be found in the pyRiemann Python toolbox[69].

Discrete-gesture time alignment

As all discrete-gesture data collection was performed by prompting participants, we had access to only approximate timing of the gesture execution (that is, the time at which the participant was prompted to perform the gesture). However, training sEMG decoding models to infer when the participant performs a gesture required more precise alignment of labels with the signal to be effective. While a task like handwriting used an alignment free loss (that is, connectionist temporal classification, CTC) and would be applicable in this task as well, forced-alignment enabled us to gain much finer control over the latency of the detections produced by our models, which was critical for practical use of discrete gestures as control inputs.

When gestures were well isolated, that is, when the intergesture interval was greater than the uncertainty of the timing, existing solutions from the literature could be readily deployed on sEMG data, leading to robust inference of gesture timing[70]. However, realistic data collection involved rapid sequence of gestures in close succession, which made identification of timing of individual gestures a challenging problem and required a dedicated solution. We therefore developed an approach to infer the precise timing of the gestures.

Our approach was to infer the timing of all gestures in a sequence, defined as a series of consecutive gestures for which uncertainty bounds overlap. We did this by searching for the sequence of gesture timings that best explained the observed data according to a generative model of our MPF features.

First, for the purposes of this timing adjustment stage, we defined the generative model for a set of K gesture instances as the sum of gesture-specific templates centred at corresponding event times, tk, with additive noise:

$$x(t)={\sum }_{k=0}^{K}{\phi }_{k}(t-{t}_{k})+n(t)$$

where x(t) is our features over time, ϕk(t) is a prototypical spatiotemporal waveform for gesture of index k (that is, the gesture template for the class of gesture corresponding to event k) and n(t) is a noise term. We note that this generative model is only valid for ballistic gesture execution and power-based features. We also note that templates are shared across executions of the same gesture type, but specific to each participant and band placement.

We define the generative inference as the joint optimization of gesture templates and times at which each gesture occurred. For each recording, we solved this through an iterative algorithm: we first estimated the templates based on prompted times, then inferred timestamps of the gesture sequence, and repeated with new inferred event times until convergence (that is, when the timestamp updates across iterations of the EM algorithm were smaller than a tolerance value).

Templates were estimated by an EMG analogue of the regression-based estimator of the event-related potential (rERP), to disentangle overlapping contributions of gestures performed in a fast sequence[71]. Timings were obtained by the following optimization problem:

$${\min }_{{t}_{k}={\rm{0..}}.K}{\int }_{t}{(x(t)-{\sum }_{k=0}^{K}{\phi }_{k}(t-{t}_{k}))}^{2}{\rm{d}}t$$

We optimized this numerically through a beam search algorithm, subject to additional ad hoc constraints that bounded how far the adjusted times could deviate from the prompted times based on priors from the data-collection protocol.

Direct application of the above procedure produced timestamps that were referenced to the session template, and there was an indeterminacy as to the timing offset within the gesture, which can vary due to initial conditions. To better standardize alignment of template timing across individuals, we performed a global recentring step at the end of timestamp estimation. Specifically, we found the time of maximal correlation between the session template (that is, for a particular participant) and a global template (grand average of all templates across participants).

Gesture-trigged sEMG activations

To inspect the structure of sEMG activations across gestures and participants (Fig. 2b), we used EMG covariance features. Specifically, we concatenated the 0-, 1- and 2-diagonals of the sEMG covariance matrix over a 300 ms window centred on each gesture, yielding a 48 × 60-dimensional feature space. To produce the embeddings, we ran t-SNE in two dimensions with perplexity 35 on the flattened feature space.

Single-participant discrete-gesture modelling

Training details

To train the single-participant models for the discrete-gesture classification task, we selected 100 participants who had completed at least five sessions of data collection and selected five of those sessions. We then randomly picked four of these sessions for training and the remaining held-out session for testing. From these four sessions we randomly created nested subsets of two, three and all four sessions to train three different models for each participant. Given the limited amount of training data per model, we used the MPF features and a small neural network as described below.

Architecture

The single-participant discrete-gesture model took as input the MPF features. The network architecture consisted of (a) one fully-connected (FC) layer with Leaky ReLU activation function followed by (b) cascaded time-depth separable (TDS) blocks[72] across time scales and (c) three more FC layers to produce a logit value for each of the nine discrete gestures to be predicted. For (b), we used two TDS blocks per time-scale: at each scale s, an AveragePool layer with kernel size 2s was applied to the output of (a) and fed to a TDS block with dilation 2s. The output was then added to the output of scale s − 1 (if it existed) and passed through another TDS block with dilation 2s as the output of scale s to be used by the next scale s + 1 (if it exists) or subsequent layers. We used 6 scales (s = 0, …, 5), and the feature dimension was set to 256 for all TDS blocks and all but the very last FC layer.

Optimization

We used the standard Adam optimizer with the following learning rate schedule: the learning rate increased linearly from 0 to 1 × 10−3 over a five-epoch warm-up phase, then underwent a one-time decay to 5 × 10−4 after epoch 25, and remained constant thereafter. Each model was trained for 300 epochs to avoid under- or over-fitting for single-user models, based on previous empirical observations. A binary cross-entropy loss was used as with the generic model.

Offline evaluation

To evaluate the performance of each model on the given held-out sessions, we followed the same procedure described under the ‘Discrete gestures’ part of the ‘Generic sEMG decoder modelling’ section. In brief, we triggered gesture detections on the corresponding model probability crossing a threshold of 0.35, filtered all detected gestures through debouncing and state machine filtering, and then used the Needleman–Wunsch algorithm to match each ground-truth label with a corresponding model prediction. We then quantified performance using the FNR, defined as the proportion of ground-truth labels for which either the matched model prediction is incorrect or there is no matched model prediction. We calculated the FNR independently for each gesture and then took the average over the nine gestures. We used FNR rather than CLER (the metric used for generic models) owing to the very small number of events detected for some poorly performing models, which lead to a large number of labels without a matched model prediction, which are ignored by the CLER metric.

Generic sEMG decoder modelling

Related deep learning architectures and approaches

The three HCI tasks described here—continuous wrist angle prediction, discrete action recognition and the transcription of handwriting into characters—represent related but distinct time-series modelling and recognition tasks. Machine learning and, specifically, deep learning approaches have become extremely popular solutions to these problems, including convolutional models[73], recurrent neural networks[74] and streaming transformers[30].

As an example of the similarity between our tasks and established machine learning problems, consider the relationship between handwriting recognition from sEMG and automatic speech recognition (ASR) from audio waveforms. Both tasks map continuous waveform signals (with dimensionality equal to the number of microphones or sEMG channels) at a fixed sample rate, to a sequence of tokens (phonemes or words for ASR, characters for our sEMG-RD). Components of our modelling pipeline have analogues in ASR, including feature extraction, data augmentation, model architecture, loss function, decoding and language modelling. As noted below, each of these modelling pipeline components required substantial domain-specific modification for sEMG models.

For feature extraction, ASR typically uses log mel filterbanks; we used our analogous MPF features (see the section ‘MPF features’), as discussed below. For data augmentation, we used the ASR technique of SpecAugment[75], which applies time- and frequency-aligned masks to these spectral features during training. A popular model architecture for ASR is the Conformer[30], which provides the advantages of attention-based processing in a form that is compatible with causal time-series modelling. We found that this method worked well for sEMG-based handwriting recognition as well. A popular loss function for ASR is CTC[76], which allows neural networks to be trained from waveforms and their textual transcriptions, without the need for a precise temporal alignment. As we similarly had pairs of sEMG recordings and transcriptions without precise temporal alignment, we also used CTC to train our models. When decoding models at test time, ASR typically uses a beam search[77] to approximate the full forward-backward algorithm lattice[78] while still incorporating predictions from a language model, biasing decoding towards more likely character and word sequences. Experimentation presented in this work used ‘greedy’ CTC decoding, although beam decoding with language modelling in our decoders would have been possible[79].

In addition to ASR, we drew from an established literature of machine learning approaches for EEG and EMG analysis that explores different signal featurizations and both classical and deep learning architectures. In the case of EMG, more expressive raw sEMG or time-frequency decomposed features (for example, Fourier or Wavelet features) have been shown to achieve stronger performance than coarser temporal statistics like RMS power80,81. In the case of EEG, MPF features[68] have proven to be a simple and robust featurization achieving state of the art, or near state of the art, performance for many tasks[10]. In agreement with the literature, we find that MPF features offer clear advantages on the wrist classification task over RMS power (Extended Data Fig. 6). As MPF features are computed across a sliding window of 100 ms, which is comparable to the temporal extent of our discrete gestures, we chose to instead use raw EMG features for the discrete-gestures task.

Both EMG interfaces and BCIs have been approached with a variety of different learning architectures in the literature, including both classical machine learning approaches (for example, random forest, support vector machine) and deep-learning-based approaches[81]. While the choice of modelling approach is problem dependent, in general, for large datasets, deep learning approaches outperform more classical machine learning techniques[82].

Wrist

To train wrist decoders, we trained a neural network to predict instantaneous flexion-extension wrist angle velocities measured by motion capture (see the ‘Wrist corpus’ section above). We consistently held out a fixed set of 10 participants for validation and 22 participants for testing, and varied the number of training participants from 20 to 130.

Architecture

The wrist decoder network architecture took as input our custom MPF features of the sEMG signal. These features were passed through a rotational-invariance module, which comprised a fully connected layer with 512 hidden units and LeakyReLU activation. This module was applied to sEMG channels that were discretely rotated by +1, 0 and −1 channels, and the resulting outputs were then averaged over the rotation process. This output was then passed through two LSTM layers of 512 hidden units each, a LeakyReLU activation, and a final linear layer producing a 1D output. For the smaller network architecture reported in Fig. 2e, we used only 16 hidden units in the initial MLP and LSTM, and only 1 rather than 2 LSTM layers. A forward pass of the larger architecture required 1.2 million floating point operations (FLOPs) per output sample.

Optimization

We trained each network with the Adam optimizer for a maximum of 300 epochs, with a learning rate of 1 × 10−3. We used an L1 loss function and a batch size of 1,024, with each sample in the batch consisting of 4 (contiguous) seconds of recordings. We evaluated the test performance of the training checkpoint with the lowest L1 loss of the validation data. Training the largest model on the largest training set took 36 s per epoch, for a total of 3 h on a single NVIDIA A10G Tensor Core GPU.

Discrete gestures

To train discrete-gesture models, we segmented training data from participants into groups of 40, 80, 160, 320, 640, 1,280, 2,800 and 4,800 participants. For each group, we tested the generalization performance of models on offline data from the same set of 100 held-out participants. For validation, another set of held-out users was used; we used a random set of 16 users for the training groups of size 40 and 80. For larger groups, 10% of the training users were used for validation. Each dataset used in training, validation and testing contained recordings from only a single session per participant. For the largest model, denoted with a separate marker in Fig. 2f, we used 4,800 training participants and we included multiple sessions of data when available (that is, many participants collected multiple repeats of the open-loop training protocol). This last point was not included in the fitting procedure for the scaling law, but this model was used in the closed-loop evaluations.

Discrete-gesture labels were obtained from the gesture prompts by first aligning them to the EMG using the algorithm described above in the ‘Discrete-gesture time alignment’ section. To facilitate gesture detection, we then shifted these labels forward in time by 100 ms to provide the model with a 100 ms longer context of sEMG signal before making a prediction. These shifted labels were used both in model training and for offline evaluation.

For offline evaluation, we first converted the logits outputted by the model into discrete-gesture predictions. Gesture predictions were triggered whenever the probability for any gesture went above the threshold value, set to 0.35 (based on a hyperparameter search using the validation set). These predictions were then filtered using three steps: debouncing, event matching and state-machine filtering. In debouncing, whenever a gesture was predicted within 50 ms of another gesture, the second gesture was removed. The sole exception was release events, which were not debounced when preceded by a different gesture, to ensure the inclusion of quick index/middle taps (that is, a press immediately followed by a release). In event matching, we matched ground-truth labels to model predictions using the Needleman–Wunsch algorithm for sequence alignment[83]. We included the constraint that ground-truth labels and model predictions can only be matched if their offset falls within a tolerance window of −50 to +250 ms (centred at the aforementioned +100 ms label shift). This provided us with a sequence of ground-truth events and a corresponding sequence of matching predicted events. The predicted events were then further processed with a state-machine filter, in which predicted release gestures were removed if the previous gesture in the ground truth sequence was not the expected press gesture (that is, index press for index release and middle press for middle release). State-machine filtering was done to avoid penalizing the model for mistaken release predictions that would not influence online performance, where releases were only used for index/middle holds, which first had to be triggered by a press (see the ‘Discrete gestures’ part of the ‘Online evaluation’ section below). Following this state-machine filtering step, we performed event matching again to match the ground truth gestures with the state-machine-filtered model predictions.

Given this sequence of ground truth gestures and matching predictions, we evaluated model performance with the classification error rate (CLER), defined as the proportion of ground-truth labels for which the matching prediction is incorrect. In calculating this metric, we ignored any ground-truth labels without a matching model prediction to reduce sensitivity to false negatives that can occur from participant noncompliance and for consistency with online metrics for which no prompt-based ground truth is available. We calculated CLER independently for each gesture and then aggregated these into a single value by taking the average of the nine per-gesture CLERs.

Architecture

The discrete-gesture network architecture took as input rescaled and high-pass filtered sEMG signal. sEMG was rescaled by 2.46 × 10−6, filtered through a 40 Hz high-pass filter (fourth-order Butterworth, as was done for the MPF features used for the other models; see the ‘MPF features’ section) and then passed through a sigmoidal function (\(f(x)=x/(\mu +| x| )\)) to reduce the effect of outliers, with μ = 32 (found to be performant through a hyperparameter sweep). The network architecture consisted of a 1D convolutional layer (with a stride of 10 to downsample the input from 2 kHz to 200 Hz), followed by a dropout layer with dropout probability 0.1, a layer norm layer, three LSTM layers with dropout probability 0.1 in between them, a second layer norm layer and a final linear readout layer with a sigmoid nonlinearity on top to predict the probability of each of the nine gestures (index/middle finger press and release, thumb tap and thumb left/right/up/down swipe). For the smaller model, the dimensions of the convolutional layer and the number of hidden units in the recurrent blocks were set to 128. For the larger model, they were set to 512. A forward pass of the larger architecture required 353,300 FLOPs per output sample.

Optimization

Networks were trained using the Adam optimizer. To mitigate divergence during training, gradient clipping was applied throughout. We additionally used a learning rate scheduler that linearly ramped up the learning rate from 5 × 10−7 to 5 × 10−4 over the first 5 epochs, and then decayed it by a factor of 0.5 every 25 epochs thereafter. For the smaller model, a larger learning rate was used: the maximum learning rate was ramped up from 10−6 to 10−3 and then decayed in the same way. For all models, we used a batch size of 512. Training was done using a multilabel binary cross-entropy loss, whereby each gesture is independently evaluated against its own absence. Each model was trained for a fixed wall clock duration equal to the time it took the largest model to reach convergence. Final checkpoints were selected based on the model that yielded the highest validation score, defined as a proxy of the CLER metric that can be run online. This proxy CLER is obtained by computing the argmax of the model output probabilities and comparing them against a temporal window (50 ms before–150 ms after) around each ground truth event. Training the largest model on the largest training set took 10 min per epoch, for a total of 12 h on an NVIDIA A10G Tensor Core GPU.

Handwriting

To train handwriting models, we used the CTC loss as described previously[76]. Notably, we used characters instead of phonemes for this purpose. The characters predicted included all lower-case letters [a-z], numbers [0-9], punctuation marks [,.?'!], and four gestures for text input control [space,dash,backspace,pinch]. When spaces were explicitly prompted with a right dash during data collection to perform a right index swipe gesture, model targets were both a <dash> and <space>, for example, “hello<dash><space>there”. In prompts where spaces were implicitly prompted, the model target was simply <space>, that is, “hello<space>there”. Moreover, we integrated a greedy implementation of the FastEmit regularization technique[84]. This regularization approach effectively reduced the streaming latency of our models by penalizing sequences of ‘blank’ outputs.

Nine training corpora were generated, each containing a varying number of participants ranging from 25 to 6,527 in a geometric sequence (excluding the last point). Each corpus was a superset of the previous corpus’s participants, ensuring that participants in the 25-participant corpus are also present in the 50-participant and 100-participant corpora, and so on. The participants were uniformly sampled without replacement from the entire corpus, preserving the distribution of data quantity per participant found in the full corpus. We used 100 held-out participants to create our evaluation corpora, which remained constant throughout our investigation. The validation corpus comprised data from 50 participants and was used for hyperparameter selection and early stopping during model training. The test corpus contained data from 50 participants and served for the final evaluation of each handwriting model’s generalization performance. We also used a subset of these 50 test participants for our personalization corpus (see the ‘Personalization experiments’ section).

Two primary data-augmentation strategies were used. The first involved SpecAugment[75], which applies time- and frequency-aligned masks to spectral features during training. The second strategy involved rotational augmentation, randomly rotating all channels by either −1, 0 or +1 position uniformly. This meant that channel signals were shifted one channel to the left, remained unshifted or were all shifted to the right, respectively.

For evaluating the model’s offline performance for each user, we used the WPM and CER aggregated over all prompts collected for that user, for instance:

$${\rm{CER}}=\frac{{\sum }_{i}{\rm{edit}}\_{{\rm{distance}}}_{i}}{{\sum }_{i}{\rm{prompt}}\_{{\rm{length}}}_{i}},$$

where edit_distancei is the Levenshtein distance between the prompt and the model output for prompt i and prompt_lengthi is the length of the prompt.

Architecture

The handwriting network architecture took our custom MPF features of the sEMG signal as input. These features were passed through a rotational-invariance module, exactly as described for the wrist decoder above. The channel rotation in this module was performed in addition to the channel rotation data augmentation described above. The signal was then passed through a conformer[30] architecture consisting of 15 layers. Each layer encompassed 4 attention heads and used a time-convolutional kernel with a size of 8. Throughout the conformer layer convolutional blocks, a stride of 1 was used, except for layers 5 and 10, where the stride was set to 2. To ensure that the model functioned in a streaming manner, a modified conformer architecture was used. This adaptation is similar to the approach outlined previously[85], but with adjustments to ensure causality. Specifically, self-attention is solely applied to a fixed local window situated directly before the current time step. In our networks, the size of this attention window was 16 for the initial 10 conformer layers and then decreased to 8 for the subsequent 5 layers. Finally, the outputs from the conformer blocks were subjected to average pooling across channels. They were then passed through a linear layer, which projected the output to match the size of the character dictionary. A softmax function was applied thereafter. During decoding, the model’s best estimate at each output time step was greedily followed, and repeating characters in the prediction were removed to reduce the output.

In our investigation, we explored various trainable model parameter counts. We manipulated the parameter count of our models by adjusting the feed-forward dimension and input dimension within our conformer architecture. Importantly, we upheld a consistent 1:2 ratio between the input dimension and the feed-forward dimension in the conformer blocks. A forward pass of the larger architecture required 801.7 million FLOPs per output sample.

Optimization

The training of our conformer architecture was executed using AdamW as the optimization algorithm. This process spanned a maximum of 200 epochs and involved a learning rate set at 6 × 10−4 for the 1 million parameter model and 3 × 10−4 for the 60 million parameter model, both with a weight decay of 5 × 10−2. A cosine annealing learning rate schedule was implemented, featuring a warm-up period lasting 1,500 steps and a minimum learning rate of 0. Our chosen batch size was a total of 512 across 32 processes each with a batch size of 16, wherein each sample within the batch represented a prompt that was zero-padded to match the length of the longest prompt within that batch. To prevent gradient explosion, we applied gradient clipping with a norm threshold of 0.1 throughout the training process. The training length was chosen to ensure that models trained would converge at all training corpus scales by visually inspecting past experimentation of similar experiments. Other hyperparameters such as learning rate, weight decay, learning rate schedule and gradient clipping were determined based on previous hyperparameter searches optimizing performance on the 50 participant validation corpus. Lastly, we assessed the test performance of the training checkpoint corresponding to the lowest validation CER. Training the largest model on the largest training set took 33 min per epoch, for a total of 4 days 17 h on 4 NVIDIA A10G Tensor Core GPU running a distributed data parallel pipeline.

Generic decoder scaling laws

Fitted function

In Fig. 2d–f, we show the fits of the generic error scaling with the number of training participants. The fits follow a functional form taken from the large language model literature[31], where the error is a function of both model size (D, in number of parameters) and data quantity (N, in number of participants):

$$Er=e+{A}_{N}/{N}^{{\alpha }_{N}}+{A}_{D}/{D}^{{\alpha }_{D}}$$

where all fitted parameters are positively bounded. It is generally understood that the e term in this equation is the irreducible error of the task and the second and third terms both contribute to the error reduction as N and D are increased, respectively. Note that there exist diminishing return regimes if either N or D are increased individually, as the other term fixes the asymptotic error floor. Also note that the definitions of N and D are swapped relative to ref. [31].

Fitting procedure

A single set of parameters fits all of the observed points in each graph, with the exception of the heterogeneous datapoint in the discrete-gesture experiments that we keep held out because of its training corpus distinction with the rest of the points. The fitted parameters were obtained by minimizing the mean squared logarithmic error (MSLE) using the L-BFGS-B optimization algorithm[86] along with 200 iterations of the basin hopping strategy[87]. The initial guess and the bounds for the fitted parameters are shown in Supplementary Table 1.

Online evaluation

Task participants and structure

For online studies, we recruited participants who had no prior experience with the sEMG task being studied and, in the majority of cases, had no previous experience with sEMG. Demographic information about these participants is provided in Extended Data Fig. 8f–i.

All closed-loop experiments were structured into three blocks: practice block, evaluation block 1 and evaluation block 2. During the practice block, the participants were explicitly instructed to explore performing the required gestures/movements in different ways to understand how to best perform the task. During the evaluation blocks, the participants were instructed to be as fast and accurate as possible.

Coaching

During the practice block of online experiments, we provided explicit verbal and demonstrative coaching to guide the participants towards styles of movement that were known to be well-suited for the given sEMG decoder. For the wrist decoder and discrete-gestures decoder, coaching was provided for about 20–25% of participants, who did not perform the gestures as expected; for example, by pronating their forearm while flexing their wrist, or by performing thumb swipes too slowly. For the handwriting decoder, we found that initial coaching was given to the majority (around 80%) of participants as they tended to write individual characters slowly and deliberately, a style that did not always trigger the sEMG decoder. We explicitly instructed these participants to write faster and more smoothly, as if they were writing with a pen. For some participants, it was also useful to explore a few different postures to facilitate writing in this style despite the lack of a pen and paper. During the evaluation blocks, further coaching was only provided when necessary if the participant was stuck on a given trial, for example, if a participant could not complete a given gesture in the discrete grid navigation task or could not write a given word or character in the handwriting task. We found that this was only necessary for a minority of participants with the discrete gestures and handwriting decoders. For the wrist decoder, we also instructed users to make quick wrist deflections whenever they observed significant drift between the decoder’s predictions and their perceived wrist angle. Such quick deflections tended to fix this drift and allow the participant to proceed at higher performance. Any time spent on this is subsumed in the acquisition time and dial-in time metrics.

Wrist

To evaluate continuous closed-loop control with the wrist decoder, users first completed a calibration procedure (rapid wrist flexions and extensions) to determine their minimum and maximum wrist angle velocities predicted by the decoder, vmin, vmax. Model outputs, vt, were then normalized to these values using a normalization function, ηt, and scaled by a constant velocity gain, gv, and handedness normalization parameter, h. To estimate the cursor position, we integrated the velocity starting from x_0 = 0 at the start of the session to determine the unbounded horizontal cursor position, \({\mathop{x}\limits^{ \sim }}_{t}\), and the cursor position bounded by the edges of the workspace, xt:

$$\begin{array}{c}{\mathop{x}\limits^{ \sim }}_{t}={x}_{t-1}+h\frac{{g}_{{\rm{v}}}}{{\eta }_{t}}{v}_{t}\\ {x}_{t}=\text{min}(\text{max}({\mathop{x}\limits^{ \sim }}_{t},\,-1),\,1)\\ {\eta }_{t}={v}_{\text{max}}\varTheta ({v}_{t})+{v}_{\text{min}}(1-\varTheta ({v}_{t}))\end{array}$$

where Θ(⋅) is the Heaviside function. We used gain gv = 0.75 normalized pixels per radian (determined empirically to work well for comfortable closed-loop control) and set h = 1 if the sEMG wristband is on the right hand (so that wrist flexion/extension maps to left/right, respectively) and −1 if it is on the left hand (so that wrist flexion/extension maps to right/left, respectively). The second equation ensured that the horizontal cursor position, xt, was bounded to the left and right edges of the workspace, −1 and 1.

Before engaging in the online evaluation task, the minimum and maximum wrist angle velocities obtained from the calibration procedure were verified by asking the user to move the cursor in an empty workspace. If they were unable to hit the edges of the workspace, the calibration procedure was repeated to get a better estimate of vmin, vmax. This was necessary for 3 out of 17 participants.

We evaluated cursor-control performance using the same horizontal cursor-to-target task described under the ‘Wrist corpus’ section above. In brief, in each trial, the participant was prompted to move the cursor to 1 out of 10 equally sized rectangular targets presented on a horizontal grid, with the outer edges of the leftmost and rightmost targets touching the left and right edges of the workspace (±1). A target was acquired by hovering over it for 500 ms (Fig. 3a, Extended Data Fig. 7a and Supplementary Video 1). Once all 10 targets were acquired, a new set of 10 targets was presented, and each one was prompted in a random sequence. This was repeated 5 times in each block, for a total of 50 trials per block, where one trial corresponds to one target presentation and acquisition. The cursor position was continually decoded from sEMG throughout the session and never reset between trials or blocks.

We first quantified performance using the acquisition time per trial, which is the time taken to acquire the target, not including the 500 ms hold time. In other words, the acquisition time is the trial duration minus the 500 ms hold time. All trials with acquisition times below 200 ms were discarded (29 out of 2,550 trials, or 1.1%), as this is below typical human reaction times[88]. Such trials sometimes occurred when, by chance, the next prompted target happened to be immediately next to the current cursor position and the cursor happened to be moving in that direction. Figure 3d shows the mean acquisition time over all non-discarded trails in each block, for each participant. Note that this average is over trials with varying starting distances from the target. In Extended Data Fig. 8a, we further examine performance in this task using Fitts’ law throughput[89], which accounts for trial-to-trial differences in reach distances and has been previously used in HCI[90] and BCI settings[5].

An additional measure that we used to quantify performance was the dial-in time (Fig. 3e), which is a measure of precise control around the target, adapted from the BCI literature[91]. Dial-in time was measured as the time from the first target entry to the last target entry, not including the 500 ms target hold time. Figure 3e shows the mean dial-in time over all non-discarded trials in which the cursor prematurely exited the target before completing the 500 ms hold time (that is, trials in which the dial-in time was greater than 0).

Discrete gestures

To evaluate the discrete-gesture decoder, we used a discrete grid navigation task in which each of the thumb swipes (left/right/up/down) was used to move a yellow circular character, named Chomper, along a discrete grid (Fig. 3b, Extended Data Fig. 7b and Supplementary Video 2). Movements were prompted with a series of targets indicating the direction in which Chomper should move and, every few steps, the participant was prompted to perform one of the three ‘activation’ gestures: thumb tap, index hold or middle hold.

A given gesture detection was triggered whenever the model output probability of a given gesture rose above a threshold value of 0.5. As in the offline setting, these gesture detections were filtered by debouncing and state machine filtering. The only differences with the offline setting, were that the state machine (1) removed release gestures preceded by any event other than the corresponding press and (2) synthetically added a corresponding release gesture whenever a press event was followed by any event other than the corresponding release. Index/middle holds were defined as a press followed by a release at least 500 ms later.

We defined a ‘trial’ as a randomly sampled sequence of targets and activation prompts requiring 8 thumb swipes and 5 activations. If the model detected a thumb swipe in the wrong direction, Chomper would move in the detected direction and the participant would therefore be prompted to swipe in the opposite direction to move Chomper back to its previous position. The total number of prompted thumb swipe gestures in each trial could therefore vary depending on how many times the wrong thumb swipe direction was detected. Incorrect activation gesture detections would be indicated to the participant, but would not alter Chomper’s position. If, on an index or middle hold prompt, the release followed the press less than 500 ms later, this was classified as an ‘early release’ error. The participants performed ten trials in each block and were explicitly instructed to favour accuracy over speed when performing the task.

Completion rate (Fig. 3g) was defined as the minimum number of discrete gestures required to complete a trial (8 thumb swipes + 5 activations = 13 gestures) divided by the time required to complete a trial. Mistakenly making additional gestures that were counterproductive to completing the trial added to the time required, but did not increase the number of required gestures. To calculate the confusion matrix for each participant, we counted the number of times that each gesture was detected when a given gesture was expected. To get a proportion, we then divided this by the total number of gestures executed when that given gesture was expected. Figure 3h shows the average confusion matrix across all participants, using the trials in the two evaluation blocks only. The first hit probability (Fig. 3f) was calculated by taking the proportion of prompted gestures in which the first executed gesture was the expected one. For both the first hit probability and the confusion matrix metrics, we included the 13 prompted gestures in each trial as well as any additional prompted thumb swipes resulting from swiping in the wrong direction.

Note that, to complete the discrete-gesture task, the participant was required to perform all gestures correctly. Therefore, before this task began, all of the participants were screened to confirm that each gesture worked for them; however, no participants had prohibitive issues with any gesture.

Handwriting

To evaluate the handwritten character decoder in a closed loop, we used a handwriting task in which, in each trial, the participants were prompted to handwrite a five-word phrase randomly sampled from the Mackenzie corpus[92]. Characters ([a-z], [0-9], [space], [,.?'!_]) and a single gesture ([space]) were decoded online with the decoder and displayed to the participant in real time (Fig. 3c, Extended Data Fig. 7c and Supplementary Video 3). The participants were instructed to ensure that the decoded phrase was understandable before submitting it and moving on to the next trial. If the participant produced any incorrect characters, they could use the backspace key on the keyboard to erase errors and then rewrite them. Trials were completed when the participants made their best attempt to write the prompted phrase and then submitted the written text by pressing a key on the computer keyboard using their non-dominant hand. Each block consisted of ten trials.

In our analysis, we report the median CER and WPM over all trials in each block. For each trial i, we calculate the CER according to a previous study[33]:

$${{\rm{CER}}}_{i}=\frac{{\rm{edit}}\_{{\rm{distance}}}_{i}}{\max \{{{\rm{prompt}}\_{\rm{length}}}_{i},{\rm{output}}\_{{\rm{length}}}_{i}\}},$$

where edit_distancei is the Levenshtein distance between the prompt and the model output submitted by the user in trial i, prompt_lengthi is the length of the prompt and output_lengthi is the length of the model output. The maximum between these two is used in the denominator to ensure that the CERi is between 0 and 1. For WPM, we assume an average of 5 characters per word (including spaces), so we determine the number of words in each prompt by counting the total number of written characters and dividing this by 5. We measured the prompt duration with the time elapsed between the first and last character emission from the model during that trial, to remove any time spent reading the prompt or clicking the submit button to advance onto the next prompt.

For each user and block in Fig. 3i,j, we calculate the CERi and WPM independently for each trial and report the median over trials. Note that this online CER metric is therefore not directly comparable with the offline CER metric reported in Fig. 2g, which was calculated by aggregating errors over all prompts (see the ‘Handwriting’ part of the ‘Generic sEMG decoder modelling’ section). Computing the median over trials was necessary for quantifying online performance due to the presence of outlier trials with poor performance (for example, due to accidentally pressing the submit button before completing the prompt), which had an outsize influence on the aggregate number of errors in each block due to the small sample size of ten trials per block.

Generic sEMG decoder baselines

Wrist

As baseline performance for the sEMG wrist decoder (Fig. 3d,e (dashed red line)), we used horizontal cursor-to-target task performance from the wrist corpus, in which the cursor was controlled by the ground truth wrist angle tracked through motion capture (see the ‘Wrist corpus’ section). This offers a behaviourally controlled comparison for our EMG model because it uses the same instructed wrist movement. The cursor position was determined by scaling the normalized and centred ground truth flexion/extension wrist angle by a constant gain. For our baseline, we use the cursor-to-target task with the horizontal target configuration and a gain of 2.0, as we found performance was slightly higher than with the larger gain of 4.0.

For each metric in Fig. 3d,e, we calculate the mean over all 50 trials for each participant in the wrist corpus (n = 162) and report the median over participants. This pool of participants is non-overlapping with the participants who performed the sEMG wrist decoder online evaluation task. For those participants who recorded multiple datasets, we used only the data from the first session and discarded the second session, to eliminate learning effects from having been previously exposed to the task. Note that performance may therefore be slightly lower than it would be after more extensive practice, as in the case in the online evaluation experiment where participants performed a practice block of 50 trials before performing the evaluation blocks.

To contextualize wrist-based control performance with a more conventional interface, we also measured performance on this task using a MacBook trackpad. In this case, the cursor’s horizontal position was set to that of the native laptop mouse controlled by the trackpad, with default trackpad settings. The vertical position of the cursor was fixed to the height of the targets at all times. The same n = 17 participants who performed the wrist decoder online evaluation study subsequently performed 50 trials of the same cursor-to-target game under trackpad control, and we measured metrics over these 50 trials to obtain the baseline values reported above. Note that participants therefore had 150 trials of experience with this task (while using the sEMG wrist angle decoder) before performing it with the trackpad.

Discrete gestures

As the baseline performance for the discrete-gesture decoder, we used performance on the discrete grid navigation task using a commercially available Nintendo Switch Joy-Con controller. This device enables us to evaluate the baseline performance without an sEMG decoder while still requiring similar one-handed motions to those required by the discrete-gesture decoder. We mapped controller buttons to the discrete gestures used in the task as follows: left/right/up/down thumb swipes were replaced by analogous joystick movements, thumb taps were replaced by pressing the ‘b’ button just above the joystick, and index and middle press and release were replaced by upper and lower bumper press and release, respectively. To avoid simultaneous inputs, no other gestures were decoded after a button press until that button was released. Left/right/up/down joystick movements were detected any time the joystick x or y value exceeded 15% of its maximum value. Once a joystick movement was detected, the total distance travelled along the x and y axes was compared and the direction of the movement was determined from the axis with greater distance travelled. While all interactions were one-handed, the Joy-Con controller was mounted in a commercially available Nintendo Switch Joy-Con grip, to allow participants to hold the controller with two hands if this improved their comfort.

A different set of n = 23 participants performed this task, non-overlapping with the participants who performed the sEMG discrete-gesture decoder online evaluation task. Apart from changes to controller-specific prompts and instructions, the discrete grid navigation task and performance metrics used were otherwise identical to those for the sEMG discrete-gesture decoder. The participants were also screened to confirm that each button worked for them, following exactly the same procedure as for the EMG decoder. As baseline values in Fig. 3f,g, we used median performance in the last evaluation block, which we found to be the block with highest performance (Extended Data Fig. 8b,c).

Handwriting

To generate a baseline of handwriting speed, we calculated how fast people wrote during the ‘phrases’ portion of offline data collection used for training and testing the Handwriting model (see the ‘Handwriting corpus’ section). We used a set of n = 75 participants for this purpose, non-overlapping with the participants who performed the sEMG handwriting decoder online evaluation task. Each of these participants were prompted to handwrite a selection of phrases on top of a Sensel Morph touch surface device, without a pen. This device was used to measure the time taken to write a prompt, by using the time elapsed between the first touch on and last lift off the surface over the duration of the prompt. Using only the prompt start and end times resulted in a lower WPM (21 WPM), reflecting the latency for a participant to initiate writing after a prompt appeared and to advance to the next prompt once complete. For consistency with the WPM metric used to evaluate the sEMG decoder, we counted the number of words in a prompt by counting the total number of characters (including spaces) and dividing by 5.

Discrete-gesture detection model investigation

Network convolutional filter analysis

To examine the initial Conv1d layer of the trained discrete-gesture decoder, we first measured various spatiotemporal properties of each of the Conv1d filter weights. Each filter is a spatiotemporal weight matrix of shape 16 input channels × 21 timesteps. It produces one output feature by convolving each row of the weight matrix with the corresponding sEMG-RD channel and summing the outputs over the rows. Below, we refer to each row as an input channel.

We first measured the RMS power of each input channel and identified the input channel with maximum power. We then measured the temporal frequency response of this max input channel using a discrete Fourier transform and identified the peak frequency with strongest magnitude response. We measured the bandwidth of the temporal frequency response as the range of contiguous frequencies around this peak that had a magnitude response within 50% of the peak. We additionally counted how many input channels had RMS power within 50% of the max channel. The distributions of these metrics across all Conv1d filters are shown in Extended Data Fig. 9.

We next identified the set of Conv1d filters that fell within the interquartile range of these three metrics (peak frequency, bandwidth, number of active channels), and randomly selected six filters with different peak channels. These are the representative examples shown in Fig. 4b,d,e. The six putative MUAPs shown in Fig. 4c were extracted using the procedure described in the section ‘Putative motor unit action potential waveform estimation’ and Extended Data Fig. 2, and then the raw EMG signal in the central 10 ms of each snippet was high-pass filtered with the same preprocessing procedure applied to the discrete-gesture model training data (see the section ‘Architecture’ under ‘Generic sEMG decoder modelling’). This allowed a direct comparison with the 10 ms convolutional filters trained on data preprocessed in this way. The same procedure for measuring RMS power and frequency response was applied to the six putative MUAPs after this preprocessing to obtain the curves shown in Fig. 4d,e.

Discrete-gesture detection network LSTM representation analysis

To examine the LSTM representations of the trained discrete-gesture decoder, we used recordings from 3 different sessions from each of 50 randomly selected users from the test set. From each of these recording sessions, we randomly sampled forty 500 ms sEMG snippets ending at labels for each gesture class (after label timing alignment; see the ‘Discrete-gesture time alignment’ section), for a total of 40 × 9 = 360 sEMG snippets per session. We then passed each of these snippets through the trained discrete-gesture decoder, with the LSTM state initialized to zeros, to obtain vector representations, X ∈ \({\mathbb{R}}\)512, of each snippet. PC projections of the vectors from three randomly selected users are plotted in Fig. 4f–h, in each case coloured by a different property. Gesture-evoked sEMG power was measured as the RMS of the last 100 ms of each sEMG snippet. For each participant and gesture, this was then binned into 20 bins with a matched number of snippets, dividing the sEMG power into the categories plotted in Extended Data Fig. 8l.

To quantify the structure in these representations, we used the proportion of variance in LSTM representations accounted by a given variable, ξ:

$${{\rm{Var}}}_{\xi }[{E}_{X}[X| \xi ]]/{{\rm{Var}}}_{X}[X].$$

The numerator is the variance in the mean representations of each category of ξ, and the denominator is the total variance of the representations. In each case, variance is calculated as the trace of the covariance of the representations. For the discrete-gesture identity and participant-identity analysis, we divided the 50 participants into 10 non-overlapping sets of 5 participants and calculated the proportion of variance separately for each set. The curves in Fig. 4i show the mean and 95% confidence interval over these 10 sets. For the band placement and gesture-evoked sEMG power curves, the proportion was calculated separately for each of the 50 participants, and the mean and 95% confidence interval over participants was shown. For this analysis, the sEMG power was binned as indicated above but into only 3 bins (low/medium/high) rather than 20.

Personalized modelling

We studied the personalization of handwriting models with 40 participants from the test corpus that were held out from the 6,527 participants in the pretraining corpus. For each participant, we further trained, that is, fine-tuned, a chosen generic handwriting model on a fixed budget of data solely taken from that participant’s sessions. The resulting personalized model was then evaluated on held-out data from the same participant on whom it was personalized. We considered personalization data budgets of 1, 2, 5, 10 and 20 min. We repeated this process for each of our 40 participants and reported the population average of the personalized model performance.

Data

We created a training and testing set for each of our 40 personalization participants by holding out three sessions for the test set, with each session containing data collected in one of the three postures (seated writing on a surface, seated writing on their leg and standing writing on their leg). The remaining sessions for that user were included in the training set, subsampled to obtain the desired number of minutes of labelled sEMG recording. The subsampling was done through random uniform sampling of the prompts from all of the sessions in the training set. Each subsample of the full training set was a superset of the preceding data budget size, ensuring that the prompts in the 1 min budget were also present in the 2 min and 5 min budget, and so on.

Optimization

The optimization details closely resemble the procedure followed for generic training (see the ‘Handwriting’ section under ‘Generic sEMG decoder modelling’) with a few differences. We used a cosine annealing learning rate schedule without warmup. We also varied the fine-tuning learning rate as a function of the number of pretraining participants used to pretrain the upstream generic model, such that: LR(N) = 1.24 × 10−5 × N−0.42, with N being the number of pretraining participants. The learning rate relationship with generic pretraining participants was found through grid learning rate sweeps for the models pretrained on 25, 400 and 6,527 participants, then fitting a power law to the population average performance minima found. We did not use weight decay during fine-tuning. We fine-tuned the model for 300 epochs, at a batch size of 256, with no early stopping such that the training is always 300 epochs.

Statistics

In Fig. 5e, we found negative transfer of personalized models across participants. To characterize each participant’s performance on other fine-tuned models, we first computed the mean of each row without the diagonal. We then computed the median of the means along with the s.e.m. This was compared with the median of the diagonal values.

In Extended Data Fig. 10, we added early stopping to the personalization procedure to disambiguate the contribution of increased personalized data budget per user from an increase in the number of fine-tuning iterations. We found very similar results with (Extended Data Fig. 10) and without (Fig. 5) early stopping, except that a few of the best performing users exhibited regressions from personalization without early stopping. This verified that the benefits from including more personalization data were not due to an increase in training iterations. Note that, in practice, early stopping would require additional data from the participant to use for validation. Here we used the test set for early stopping, so the results in Extended Data Fig. 10 should be considered validation numbers.

Personalization scaling laws

Fitted function

In Fig. 5b, we show the fits of the 60.2 million parameter model error rate as a function of the number of pretraining participants for the generic model and for each personalization data budget. We used a simple power law fit with respect to pretraining data quantity (N, number of pretraining participants), such that:

$$Er=e+A/{N}^{\alpha }.$$

We did not include the contribution from model size, as we only fitted observations from a single model size (the error from finite model size was therefore absorbed into e).

Fitting procedure

The fitted parameters for each personalization data budget were obtained by minimizing the MSLE using the L-BFGS-B optimization algorithm[86] along with 200 iterations of the basin hopping strategy[87]. The initial guess and the bounds for the fitted parameters are shown in Supplementary Table 2.

Personalization equivalence calculations

Relative increase calculation

To determine the equivalent pretraining participant budget needed to match a given personalization performance, we needed a continuous estimate of generic model performance as a function of the number of pretraining participants. For this, we used logspace piecewise linear interpolation of the generic performance values, which we denote by fgeneric(N). Given the number of pretraining participants, N, and personalization minutes, m, personalized models have an observed CER given by CER(N,m). To find the equivalent additional pretraining participants ΔN needed to match performance between generic and personalized models we set fgeneric(N + ΔN) = CER(N,m) and solve for ΔN using the Newton conjugate-gradient method. This gives the points in Fig. 5d. Overlaid on the plot as dotted lines, we used the power law fit of the points corresponding to each number of personalization minutes in Fig. 5b to infer continuous curves of equivalent fold-increase in pretraining data required using the approach described above.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

We have publicly released 1,060 sEMG recordings from 300 participants spanning the 3 tasks in the study: 100 participants (74 h) of wrist data, 100 participants (63 h) of discrete gestures data and 100 participants (126 h) of handwriting data. Each participant was randomly selected from the set of training users described in the study. We also provide labels, gesture times and regression targets for these datasets. All data are anonymized and contain no identifying information. The data are hosted online (https://fb-ctrl-oss.s3.amazonaws.com/generic-neuromotor-interface-data).

Code availability

We have also published a GitHub repository (https://github.com/facebookresearch/generic-neuromotor-interface-data) with implementations of the models described in the manuscript for wrist, handwriting and discrete gesture tasks. We also provide a framework for training and evaluating models on the data that we have released. Data and code are available under a Attribution-NonCommercial-ShareAlike 4.0 license. Instructions for downloading the data, training models and evaluating models can be found in the site’s README file.

References

1. Battye, C. K., Nightingale, A. & Whillis, J. The use of myo-electric currents in the operation of prostheses. J. Bone Joint Surg. Br. 37-B, 506–510 (1955).

2. Hochberg, L. R. et al. Reach and grasp by people with tetraplegia using a neurally controlled robotic arm. Nature 485, 372–375 (2012).

3. Collinger, J. L. et al. High-performance neuroprosthetic control by an individual with tetraplegia. Lancet 381, 557–564 (2013).

4. Willett, F. R. et al. A high-performance speech neuroprosthesis. Nature 620, 1031–1036 (2023).

5. Gilja, V. et al. A high-performance neural prosthesis enabled by control algorithm design. Nat. Neurosci. 15, 1752–1757 (2012).

6. Abiri, R., Borhani, S., Sellers, E. W., Jiang, Y. & Zhao, X. A comprehensive review of EEG-based brain-computer interface paradigms. J. Neural Eng. 16, 011001 (2019).

7. Kerous, B., Skola, F. & Liarokapis, F. EEG-based BCI and video games: a progress report. Virtual Real. 22, 119–135 (2018).

8. Défossez, A., Caucheteux, C., Rapin, J., Kabeli, O. & King, J.-R. Decoding speech perception from non-invasive brain recordings. Nat. Mach. Intel. 5, 1097–1107 (2023).

9. Brandman, D. M., Cash, S. S. & Hochberg, L. R. Human intracortical recording and neural decoding for brain-computer interfaces. IEEE Trans. Neural Syst. Rehabil. Eng. 25, 1687–1696 (2017).

10. Lotte, F. et al. A review of classification algorithms for EEG-based brain-computer interfaces: a 10 year update. J. Neural Eng. 15, 031005 (2018).

11. Degenhart, A. D. et al. Stabilization of a brain-computer interface via the alignment of low-dimensional spaces of neural activity. Nat. Biomed. Eng. 4, 672–685 (2020).

12. Brandman, D. M. et al. Rapid calibration of an intracortical brain-computer interface for people with tetraplegia. J. Neural Eng. 15, 026007 (2018).

13. Kandel, E. R., Schwartz, J. H., Jessell, T. M., Siegelbaum, S. A. & Hudspeth, A. J. Principles of Neural Science, Fifth Edition Vol. 4 (McGraw-Hill Medical, 2000).

14. De Luca, C. J. The use of surface electromyography in biomechanics. J. Appl. Biomech. 13, 135–163 (1997).

15. Pullman, S. L., Goodin, D. S., Marquinez, A. I., Tabbal, S. & Rubin, M. Clinical utility of surface EMG: report of the therapeutics and technology assessment subcommittee of the American Academy of Neurology: report of the Therapeutics and Technology Assessment Subcommittee of the American Academy of Neurology. Neurology 55, 171–177 (2000).

16. Campanini, I., Disselhorst-Klug, C., Rymer, W. Z. & Merletti, R. Surface EMG in clinical assessment and neurorehabilitation: barriers limiting its use. Front. Neurol. 11, 934 (2020).

17. Farina, D. et al. The extraction of neural information from the surface EMG for the control of upper-limb prostheses: emerging avenues and challenges. IEEE Trans. Neural Syst. Rehabil. Eng. 22, 797–809 (2014).

18. Scheme, E. & Englehart, K. Electromyogram pattern recognition for control of powered upper-limb prostheses: state of the art and challenges for clinical use. J. Rehabil. Res. Dev. 48, 643–659 (2011).

19. Biddiss, E. A. & Chau, T. T. Upper limb prosthesis use and abandonment: a survey of the last 25 years: a survey of the last 25 years. Prosthet. Orthot. Int. 31, 236–257 (2007).

20. Scheme, E., Fougner, A., Stavdahl, Ø., Chan, A. D. C. & Englehart, K. Examining the adverse effects of limb position on pattern recognition based myoelectric control. In Proc. IEEE Eng. Med. Biol. Soc. 6337–6340 (IEEE, 2010).

21. Phinyomark, A. & Scheme, E. EMG pattern recognition in the era of big data and deep learning. Big Data Cogn. Comput. 2, 21 (2018).

22. Young, A. J., Hargrove, L. J. & Kuiken, T. A. The effects of electrode size and orientation on the sensitivity of myoelectric pattern recognition systems to electrode shift. IEEE Trans. Biomed. Eng. 58, 2537–2544 (2011).

23. Zia Ur Rehman, M. et al. Multiday EMG-based classification of hand motions with deep learning techniques. Sensors 18, 2497 (2018).

24. Saponas, T. S., Tan, D. S., Morris, D. & Balakrishnan, R. Demonstrating the feasibility of using forearm electromyography for muscle-computer interfaces. In Proc. SIGCHI Conference on Human Factors in Computing Systems 515–524 (ACM, 2008).

25. Côté-Allard, U. et al. Deep learning for electromyographic hand gesture signal classification using transfer learning. IEEE Trans. Neural Syst. Rehabil. Eng. 27, 760–771 (2019).

26. Jiang, S. et al. Feasibility of wrist-worn, real-time hand, and surface gesture recognition via sEMG and IMU sensing. IEEE Trans. Industr. Inform. 14, 3376–3385 (2018).

27. Mendez Guerra, I., Barsakcioglu, D. Y., Vujaklija, I., Wetmore, D. Z. & Farina, D. Far-field electric potentials provide access to the output from the spinal cord from wrist-mounted sensors. J. Neural Eng. 19, 026031 (2022).

28. Merletti, R. & Farina, D. Surface Electromyography: Physiology, Engineering, and Applications (John Wiley & Sons, 2016).

29. Sussillo, D., Stavisky, S. D., Kao, J. C., Ryu, S. I. & Shenoy, K. V. Making brain-machine interfaces robust to future neural variability. Nat. Commun. 7, 13749 (2016).

30. Gulati, A. et al. Conformer: convolution-augmented transformer for speech recognition. In Proc. Interspeech 5036–5040 (ISCA, 2020).

31. Hoffmann, J. et al. An empirical analysis of compute-optimal large language model training. In Proc. Advances in Neural Information Processing Systems 30016–30030 (NeurIPS, 2022).

32. Zhai, X., Kolesnikov, A., Houlsby, N. & Beyer, L. Scaling vision transformers. In Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition 12104–12113 (Computer Vision Foundation, 2022).

33. Palin, K., Feit, A. M., Kim, S., Kristensson, P. O. & Oulasvirta, A. How do people type on mobile devices? Observations from a study with 37,000 volunteers. In Proc. 21st International Conference on Human-Computer Interaction with Mobile Devices and Services 1–12 (ACM, 2019).

34. McGraw, I. et al. Personalized speech recognition on mobile devices. In Proc. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 5955–5959 (IEEE, 2016).

35. Mdhaffar, S., Tommasi, M. & Estève, Y. Study on acoustic model personalization in a context of collaborative learning constrained by privacy preservation. Speech Comput. 12997, 426–436 (2021).

36. Eskimez, S. E. et al. Personalized speech enhancement: new models and comprehensive evaluation. In Proc. 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 356–360 (IEEE, 2022).

37. Wen, H., Ramos Rojas, J. & Dey, A. K. Serendipity: finger gesture recognition using an off-the-shelf smartwatch. In Proc. 2016 CHI Conference on Human Factors in Computing Systems 3847–3851 (ACM, 2016).

38. Amma, C., Georgi, M. & Schultz, T. Airwriting: a wearable handwriting recognition system. Pers. Ubiquitous Comput. 18, 191–203 (2014).

39. Mendez, I. et al. Evaluation of the Myo armband for the classification of hand motions. In Proc. 15th IEEE International Conference on Rehabilitation Robotics 1211–1214 (2017).

40. Tripathi, A., Prathosh, A. P., Muthukrishnan, S. P. & Kumar, L. SurfMyoAiR: a surface electromyography-based framework for airwriting recognition. IEEE Trans. Instrum. Meas. 72, 1–12 (2023).

41. Laput, G., Xiao, R. & Harrison, C. ViBand: high-fidelity bio-acoustic sensing using commodity smartwatch accelerometers. In Proc. 29th Annual Symposium on User Interface Software and Technology 321–333 (ACM, 2016).

42. Zhang, Y. & Harrison, C. Tomo: wearable, low-cost electrical impedance tomography for hand gesture recognition. In Proc. 28th Annual ACM Symposium on User Interface Software & Technology 167–173 (ACM, 2015).

43. Laput, G., Yang, C., Xiao, R., Sample, A. & Harrison, C. EM-Sense: touch recognition of uninstrumented, electrical and electromechanical objects. In Proc. 28th Annual ACM Symposium on User Interface Software & Technology 157–166 (ACM, 2015).

44. Iravantchi, Y., Goel, M. & Harrison, C. BeamBand: hand gesture sensing with ultrasonic beamforming. In Proc. 2019 CHI Conference on Human Factors in Computing Systems 1–10 (ACM, 2019).

45. Barona López, L. I., Ferri, F. M., Zea, J., Valdivieso Caraguay, Á. L. & Benalcázar, M. E. CNN-LSTM and post-processing for EMG-based hand gesture recognition. Intel. Syst. Appl. 22, 200352 (2024).

46. Benalcazar, M. E., Barona, L., Valdivieso, L., Aguas, X. & Zea, J. EMG-EPN-612 dataset. Zenodo https://doi.org/10.5281/ZENODO.4023305 (2020).

47. Eddy, E., Campbell, E., Bateman, S. & Scheme, E. Understanding the influence of confounding factors in myoelectric control for discrete gesture recognition. J. Neural Eng. 21, 036015 (2024).

48. Maslova, O. et al. Non-invasive EEG-based BCI spellers from the beginning to today: a mini-review. Front. Hum. Neurosci. 17, 1216648 (2023).

49. Jayaram, V. & Barachant, A. MOABB: trustworthy algorithm benchmarking for BCIs. J. Neural Eng. 15, 066011 (2018).

50. Lawhern, V. J. et al. EEGNet: a compact convolutional neural network for EEG-based brain-computer interfaces. J. Neural Eng. 15, 056013 (2018).

51. Sussillo, D. et al. A recurrent neural network for closed-loop intracortical brain-machine interface decoders. J. Neural Eng. 9, 026027 (2012).

52. Metzger, S. L. et al. A high-performance neuroprosthesis for speech decoding and avatar control. Nature 620, 1037–1046 (2023).

53. Musk, E. & Neuralink, An integrated brain-machine interface platform with thousands of channels. J. Med. Internet Res. 21, e16194 (2019).

54. Despradel Rumaldo, D. et al. Enabling advanced interactions through closed-loop control of motor unit activity after tetraplegia. In Proc. 37th Annual ACM Symposium on User Interface Software and Technology Vol. 19, 1–3 (ACM, 2024).

55. Formento, E., Botros, P. & Carmena, J. M. Skilled independent control of individual motor units via a non-invasive neuromuscular-machine interface. J. Neural Eng. 18, 066019 (2021).

56. Bräcklein, M., Ibáñez, J., Barsakcioglu, D. Y. & Farina, D. Towards human motor augmentation by voluntary decoupling beta activity in the neural drive to muscle and force production. J. Neural Eng. 18, 016001 (2021).

57. Radhakrishnan, S. M., Baker, S. N. & Jackson, A. Learning a novel myoelectric-controlled interface task. J. Neurophysiol. 100, 2397–2408 (2008).

58. Marshall, N. J. et al. Flexible neural control of motor units. Nat. Neurosci. 25, 1492–1504 (2022).

59. Yamagami, M., Portnova-Fahreeva, A. A., Kong, J., Wobbrock, J. O. & Mankoff, J. How do people with limited movement personalize upper-body gestures? Considerations for the design of personalized and accessible gesture interfaces. In Proc. 25th International ACM SIGACCESS Conference on Computers and Accessibility 1–15 (ACM, 2023).

60. Mugler, E. M. et al. Myoelectric computer interface training for reducing co-activation and enhancing arm movement in chronic stroke survivors: a randomized trial. Neurorehabil. Neural Repair 33, 284–295 (2019).

61. Henninger, F., Shevchenko, Y., Mertens, U. K., Kieslich, P. J. & Hilbig, B. E. lab.js: a free, open, online study builder. Behav. Res. Methods 54, 556–573 (2022).

62. Rastogi, A., Zang, X., Sunkara, S., Gupta, R. & Khaitan, P. Towards scalable multi-domain conversational agents: the schema-guided dialogue dataset. In Proc. 34th Conf. AAAI Artif. Intell. 8689–8696 (AAAI, 2020).

63. Chang, J. P. et al. ConvoKit: A toolkit for the analysis of conversations. In Proc. 21th Annual Meeting of the Special Interest Group on Discourse and Dialogue (eds Pietquin, O. et al.) 57–60 (ACM, 2020).

64. Harrison, V. F. & Mortensen, O. A. Identification and voluntary control of single motor unit activity in the tibialis anterior muscle. Anat. Rec. 144, 109–116 (1962).

65. Basmajian, J. Control of individual motor units. Am. J. Phys. Med. 46, 480–486 (1967).

66. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).

67. De Luca, C. J., Donald Gilmore, L., Kuznetsov, M. & Roy, S. H. Filtering the surface EMG signal: movement artifact and baseline noise contamination. J. Biomech. 43, 1573–1579 (2010).

68. Barachant, A., Bonnet, S., Congedo, M. & Jutten, C. Multiclass brain-computer interface classification by Riemannian geometry. IEEE Trans. Biomed. Eng. 59, 920–928 (2012).

69. Barachant, A. et al. pyRiemann/pyRiemann: v0.5. (2023).

70. Williams, A. H. et al. Discovering precise temporal patterns in large-scale neural recordings through robust and interpretable time warping. Neuron 105, 246–259 (2020).

71. Smith, N. J. & Kutas, M. Regression-based estimation of ERP waveforms: II. Nonlinear effects, overlap correction, and practical considerations. Psychophysiology 52, 169–181 (2015).

72. Hannun, A., Lee, A. Xu, Q. & Collobert, R. Sequence-to-sequence speech recognition with time-depth separable convolutions. In Proc. Interspeech 3785–3789 (ISCA, 2019)

73. Karpathy, A. et al. Large-scale video classification with convolutional neural networks. In Proc. 2014 IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2014).

74. Graves, A., Mohamed, A.-R. & Hinton, G. Speech recognition with deep recurrent neural networks. In Proc. 2013 IEEE International Conference on Acoustics, Speech and Signal Processing 6645–6649 (IEEE, 2013).

75. Park, D. S. et al. SpecAugment: a simple data augmentation method for automatic speech recognition. In Proc. Interspeech 2613–2617 (ISCA, 2019).

76. Graves, A., Fernández, S., Gomez, F. & Schmidhuber, J. Connectionist temporal classification: labelling unsegmented sequence data with recurrent neural networks. In Proc. 23rd International Conference on Machine Learning 369–376 (ACM, 2006).

77. Ney, H., Mergel, D., Noll, A. & Paeseler, A. A data-driven organization of the dynamic programming beam search for continuous speech recognition. In Proc. ICASSP ′87: IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005); https://doi.org/10.1109/icassp.1987.1169844.

78. Rabiner, L. R. A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE Inst. Electr. Electron. Eng. 77, 257–286 (1989).

79. Pratap, V. et al. Scaling up online speech recognition using ConvNets. In Proc. Interspeech 2020 (ISCA, 2020); https://doi.org/10.21437/interspeech.2020-2840.

80. Yang, J., Soh, M., Lieu, V., Weber, D. J. & Erickson, Z. EMGBench: benchmarking out-of-distribution generalization and adaptation for electromyography (2024).

81. Sultana, A., Ahmed, F. & Alam, M. S. A systematic review on surface electromyography-based classification system for identifying hand and finger movements. Healthc. Anal. 3, 100126 (2023).

82. Deo, D. R. et al. Brain control of bimanual movement enabled by recurrent neural networks. Sci. Rep. 14, 1598 (2024).

83. Needleman, S. B. & Wunsch, C. D. A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 48, 443–453 (1970).

84. Yu, J. et al. FastEmit: low-latency streaming asr with sequence-level emission regularization. Preprint at arxiv.org/abs/2010.11148 (2020).

85. Beltagy, I., Peters, M. E. & Cohan, A. Longformer: the long-document transformer. Preprint at arxiv.org/abs/2004.05150 (2020).

86. Byrd, R. H., Lu, P., Nocedal, J. & Zhu, C. A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16, 1190–1208 (1995).

87. Olson, B., Hashmi, I., Molloy, K. & Shehu, A. Basin hopping as a general and versatile optimization framework for the characterization of biological macromolecules. Adv. Artif. Intel. 2012, 19 (2012).

88. Gribble, P. L., Everling, S., Ford, K. & Mattar, A. Hand-eye coordination for rapid pointing movements. Arm movement direction and distance are specified prior to saccade onset: arm movement direction and distance are specified prior to saccade onset. Exp. Brain Res. 145, 372–382 (2002).

89. Fitts, P. M. The information capacity of the human motor system in controlling the amplitude of movement. J. Exp. Psychol. 47, 381–391 (1954).

90. MacKenzie, I. S. Fitts’ law as a research and design tool in human-computer interaction. Hum. Comput. Interact. 7, 91–139 (1992).

91. Fan, J. M. et al. Intention estimation in brain-machine interfaces. J. Neural Eng. 11, 016004 (2014).

92. MacKenzie, I. S. & Soukoreff, R. W. Phrase sets for evaluating text entry techniques. In Proc. CHI ‘03 Extended Abstracts on Human Factors in Computing Systems—CHI ‘03 754–755 (ACM, 2003); https://doi.org/10.1145/765891.765971.

93. Gray, H. Anatomy of the Human Body (Lea & Febiger, 1918).

Acknowledgements

We thank S. Druckmann, D. Farina, A. Haith, J. Krakauer, A. Orsborn, C. Pandarinath, L. Paninski, K. Shenoy and D. Wolpert for technical and scientific advice and feedback; and D. Farina, D. Barsakcioglu and P. Rente Vicente for assistance with the wrist MRI scans.

Author information

Author notes

1. These authors contributed equally: Patrick Kaifosh, Thomas R. Reardon

Authors and Affiliations

1. Reality Labs at Meta, New York, NY, USA

Patrick Kaifosh, Thomas R. Reardon, Brian D. Allen, Chris Anderson, Sacha Arnoud, Rahul Arora, Mridu Atray, Lana Awad, Francisco Ayerbe, Christopher Baker, Nicholas Baker, Alexandre Barachant, Philip Bard, Wilman Pimentel Beltran, Adam Berenzweig, Rohin Bhasin, Joe Bienkowski, Sean Bittner, Luke Boegner, Anu Bolarinwa, Don Bosley, Matthew Bracaglia, Mario Bräcklein, Maclyn Brandwein, Joe Bravate, Matt Butler, Adam J. Calhoun, Chia-Jung Chang, Daniel Chenet, Joshua Chester, Rudi Chiarito, Rohan Chitnis, John Choi, Won Chun, Jeremiah Chung, James Connors, Jota Costa, Mark Cramer, Raven Cunningham, William F. Cusack, Nathan Danielson, Thomas J. Davidson, Bruno De Araujo, Bob DiMaiolo, Scott Draves, Alan Du, Zaina Edelson, Phina Enemuo, Mina Fahmi, Nariman Farsad, Ali Farshchian, Randy Feliz, Jake Fine, Emanuele Formento, Dustin Freeman, Jianing Fu, Jean-Christophe Gagnon-Audet, Rupesh Gajurel, Jonathan Gamutan, Sida Gao, Jonateal Garcia, Nathalie Therese Helene Gayraud, Minha Ghani, Sayan Ghosh, Vickram Gidwani, Danny Giebisch, Greg Gimler, Alexandre Gramfort, Lauren Grosberg, Bryn Gunther, Ning Guo, Chetan Gupta, Sinem Guven Kaya, Austin Ha, Katarina Hadjer, Carlos Xavier Hernández, Stav Hertz, Carl Hewitt, Daniel N. Hill, Kirak Hong, Lillian Hong, Helen Hou, Stepan Hruda, Alex Hsieh, Vivian Hsiung, Rongqing Huang, Yue Hui, Hazel Hulet, Shaker Islam, Vinay Jayaram, Connie Jiang, Xiaodong Jiang, Brooke Juarez, James Jaeyoon Jun, Na Young Jun, Nirag Kadakia, Nishant Kakar, Ajay Kamdar, Ta-Chu Kao, Steven Kober, TW Koh, Christina Shabu Koshy, Andrzej Lawn, Claire Lee, Jennifer Lee, JinHyung Lee, Juheui Amy Lee, Tiffanie Li, Jonathan Liao, Yingru Liu, Yuxuan Liu, Saar Lively, Kati London, Roddy Louie, Francisco Luongo, Attila Maczak, Niru Maheswaranathan, Michael Mandel, Jesse Marshall, Najja Marshall, Mirek Martincik, Nicolas Yvan Masse, Stephen McAnearney, Ashley McHugh, Jorge Aurelio Menendez, Josh Merel, David Miller, Ilya Milyavskiy, Ricardo Pio Monti, Sean Moore, Yonathan Morin, Brock Morrell, Dano Morrison, Anthony Moschella, Suman Mulumudi, Conner Muth, Krunal Naik, Norris Nakagaki, Ajay Nathan, Romario Nelson, Jimson Ngeo, Keven Nguyen, Luke O’Connor, Shay Ohayon, Garrick Orchard, Chris Osborn, Timothy M. Otchy, Emmanuella Owolabi, Adam M. Packer, Tejaswy Pailla, Julia Paredes, Sean Parker, Diogo Peixoto, Matias Perez, Zavion Perez, Adrien Piérard, Stephen M. Plaza, Natalie Plotkin, Eftychios Pnevmatikakis, Brandon Pool, Shanil Puri, Sunaina Rajani, Jose Ramirez Fuentes, Julian Ramos Rojas, Tanvi Ranjan, Devin Reardon, Jonathan Reid, Jason Reisman, Lain Warawao Nemo Mora y Rivera, Sebi Rolotti, Andrew Rosenkranz, Ian Roth, Likhon Roy, Ran Rubin, Alexander Rudnicki, Sam Russell, Abby Russo, James Sacra, Amir Sadoughi, Roxanna Salim, Aichatou Savane, Collin Schlager, David Schwab, Jeffrey Seely, Mike Seltzer, Nurettin Dorukhan Sergin, Ami Shah, Anish Shah, Philip Shamash, Vandita Sharma, Stephie Shen, Kevin Shi, Olivia Shiah, Yasmin Siahpoosh, Noor Siddiqi, Jeremy Simpson, Gagandip Singh, Viswanath Sivakumar, Jeff Smith, Seyyid Emre Sofuoglu, Ivy Jiyoung Song, Morgan Springer, Adrian Spurr, Fabio Stefanini, Connor Stout, Emanuel Strauss, Swetha Suresh, Ananya Suri, David Sussillo, Ziyi Tang, Vikram Tank, Jesslyn Tannady, Aliqyan Tapia, Tugce Tasci, Tiberiu Tesileanu, Aman Tiwari, Anoushka Tiwari, Calvin Tong, Blizelle Tormis, Julia Trabulsi, Migmar Tsering, Kyle Urquhart, Peter Walkington, Megan Wang, Renxiong Wang, Zhuo Wang, Christy Warden, Richard Warren, Claire L. Warriner, Ron J. Weiss, Daniel Z. Wetmore, Ezri White, Christopher Wiebe, Steve Williams, Yuguan Xing, Chris Ye, Akshay Yembarwar, Shuibenyang Yuan, Michael Zawadzki, Mingrui Zhang, Jiesi Zhao, Kevin Zheng, Joseph Zhong, Lei Zhou & Danny Zlobinsky

Consortia

CTRL-labs at Reality Labs

- Brian D. Allen

- , Chris Anderson

- , Sacha Arnoud

- , Rahul Arora

- , Mridu Atray

- , Lana Awad

- , Francisco Ayerbe

- , Christopher Baker

- , Nicholas Baker

- , Alexandre Barachant

- , Philip Bard

- , Wilman Pimentel Beltran

- , Adam Berenzweig

- , Rohin Bhasin

- , Joe Bienkowski

- , Sean Bittner

- , Luke Boegner

- , Anu Bolarinwa

- , Don Bosley

- , Matthew Bracaglia

- , Mario Bräcklein

- , Maclyn Brandwein

- , Joe Bravate

- , Matt Butler

- , Adam J. Calhoun

- , Chia-Jung Chang

- , Daniel Chenet

- , Joshua Chester

- , Rudi Chiarito

- , Rohan Chitnis

- , John Choi

- , Won Chun

- , Jeremiah Chung

- , James Connors

- , Jota Costa

- , Mark Cramer

- , Raven Cunningham

- , William F. Cusack

- , Nathan Danielson

- , Thomas J. Davidson

- , Bruno De Araujo

- , Bob DiMaiolo

- , Scott Draves

- , Alan Du

- , Zaina Edelson

- , Phina Enemuo

- , Mina Fahmi

- , Nariman Farsad

- , Ali Farshchian

- , Randy Feliz

- , Jake Fine

- , Emanuele Formento

- , Dustin Freeman

- , Jianing Fu

- , Jean-Christophe Gagnon-Audet

- , Rupesh Gajurel

- , Jonathan Gamutan

- , Sida Gao

- , Jonateal Garcia

- , Nathalie Therese Helene Gayraud

- , Minha Ghani

- , Sayan Ghosh

- , Vickram Gidwani

- , Danny Giebisch

- , Greg Gimler

- , Alexandre Gramfort

- , Lauren Grosberg

- , Bryn Gunther

- , Ning Guo

- , Chetan Gupta

- , Sinem Guven Kaya

- , Austin Ha

- , Katarina Hadjer

- , Carlos Xavier Hernández

- , Stav Hertz

- , Carl Hewitt

- , Daniel N. Hill

- , Kirak Hong

- , Lillian Hong

- , Helen Hou

- , Stepan Hruda

- , Alex Hsieh

- , Vivian Hsiung

- , Rongqing Huang

- , Yue Hui

- , Hazel Hulet

- , Shaker Islam

- , Vinay Jayaram

- , Connie Jiang

- , Xiaodong Jiang

- , Brooke Juarez

- , James Jaeyoon Jun

- , Na Young Jun

- , Nirag Kadakia

- , Patrick Kaifosh

- , Nishant Kakar

- , Ajay Kamdar

- , Ta-Chu Kao

- , Steven Kober

- , TW Koh

- , Christina Shabu Koshy

- , Andrzej Lawn

- , Claire Lee

- , Jennifer Lee

- , JinHyung Lee

- , Juheui Amy Lee

- , Tiffanie Li

- , Jonathan Liao

- , Yingru Liu

- , Yuxuan Liu

- , Saar Lively

- , Kati London

- , Roddy Louie

- , Francisco Luongo

- , Attila Maczak

- , Niru Maheswaranathan

- , Michael Mandel

- , Jesse Marshall

- , Najja Marshall

- , Mirek Martincik

- , Nicolas Yvan Masse

- , Stephen McAnearney

- , Ashley McHugh

- , Jorge Aurelio Menendez

- , Josh Merel

- , David Miller

- , Ilya Milyavskiy

- , Ricardo Pio Monti

- , Sean Moore

- , Yonathan Morin

- , Brock Morrell

- , Dano Morrison

- , Anthony Moschella

- , Suman Mulumudi

- , Conner Muth

- , Krunal Naik

- , Norris Nakagaki

- , Ajay Nathan

- , Romario Nelson

- , Jimson Ngeo

- , Keven Nguyen

- , Luke O’Connor

- , Shay Ohayon

- , Garrick Orchard

- , Chris Osborn

- , Timothy M. Otchy

- , Emmanuella Owolabi

- , Adam M. Packer

- , Tejaswy Pailla

- , Julia Paredes

- , Sean Parker

- , Diogo Peixoto

- , Matias Perez

- , Zavion Perez

- , Adrien Piérard

- , Stephen M. Plaza

- , Natalie Plotkin

- , Eftychios Pnevmatikakis

- , Brandon Pool

- , Shanil Puri

- , Sunaina Rajani

- , Jose Ramirez Fuentes

- , Julian Ramos Rojas

- , Tanvi Ranjan

- , Devin Reardon

- , Thomas R. Reardon

- , Jonathan Reid

- , Jason Reisman

- , Lain Warawao Nemo Mora y Rivera

- , Sebi Rolotti

- , Andrew Rosenkranz

- , Ian Roth

- , Likhon Roy

- , Ran Rubin

- , Alexander Rudnicki

- , Sam Russell

- , Abby Russo

- , James Sacra

- , Amir Sadoughi

- , Roxanna Salim

- , Aichatou Savane

- , Collin Schlager

- , David Schwab

- , Jeffrey Seely

- , Mike Seltzer

- , Nurettin Dorukhan Sergin

- , Ami Shah

- , Anish Shah

- , Philip Shamash

- , Vandita Sharma

- , Stephie Shen

- , Kevin Shi

- , Olivia Shiah

- , Yasmin Siahpoosh

- , Noor Siddiqi

- , Jeremy Simpson

- , Gagandip Singh

- , Viswanath Sivakumar

- , Jeff Smith

- , Seyyid Emre Sofuoglu

- , Ivy Jiyoung Song

- , Morgan Springer

- , Adrian Spurr

- , Fabio Stefanini

- , Connor Stout

- , Emanuel Strauss

- , Swetha Suresh

- , Ananya Suri

- , David Sussillo

- , Ziyi Tang

- , Vikram Tank

- , Jesslyn Tannady

- , Aliqyan Tapia

- , Tugce Tasci

- , Tiberiu Tesileanu

- , Aman Tiwari

- , Anoushka Tiwari

- , Calvin Tong

- , Blizelle Tormis

- , Julia Trabulsi

- , Migmar Tsering

- , Kyle Urquhart

- , Peter Walkington

- , Megan Wang

- , Renxiong Wang

- , Zhuo Wang

- , Christy Warden

- , Richard Warren

- , Claire L. Warriner

- , Ron J. Weiss

- , Daniel Z. Wetmore

- , Ezri White

- , Christopher Wiebe

- , Steve Williams

- , Yuguan Xing

- , Chris Ye

- , Akshay Yembarwar

- , Shuibenyang Yuan

- , Michael Zawadzki

- , Mingrui Zhang

- , Jiesi Zhao

- , Kevin Zheng

- , Joseph Zhong

- , Lei Zhou

- & Danny Zlobinsky

Contributions

B.D.A.: EMG interaction design; software for real-time data collection, prompted EMG studies and model training. C.A.: EMG interaction design; software for real-time data collection, prompted EMG studies and model training. S.A.: software for real-time data collection, prompted EMG studies and model training; data processing, deep learning architectures, model training, data analysis and data interpretation. R.A.: EMG interaction design. M.A.: data processing, deep learning architectures, model training, data analysis and data interpretation. L.A.: software for real-time data collection, prompted EMG studies and model training. F.A.: sEMG-RD design, testing, manufacturing and support. C.B.: sEMG-RD design, testing, manufacturing and support. N.B.: sEMG-RD design, testing, manufacturing and support. A. Barachant: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation. P.B.: EMG data collection. W.P.B.: EMG data collection. A. Berenzweig: data processing, deep learning architectures, model training, data analysis and data interpretation. R.B.: software for real-time data collection, prompted EMG studies and model training. J. Bienkowski: software for real-time data collection, prompted EMG studies and model training. S.B.: data processing, deep learning architectures, model training, data analysis and data interpretation. L.B.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. A. Bolarinwa: EMG data collection. D.B.: sEMG-RD design, testing, manufacturing and support. M. Bracaglia: EMG data collection. M. Bräcklein: manuscript drafting and editing. M. Brandwein: software for real-time data collection, prompted EMG studies and model training. J. Bravate: software for real-time data collection, prompted EMG studies and model training. M. Butler: EMG data collection. A.J.C.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing. C.-J.C.: data processing, deep learning architectures, model training, data analysis and data interpretation. D.C.: data processing, deep learning architectures, model training, data analysis and data interpretation. J. Chester: EMG data collection. R. Chiarito: software for real-time data collection, prompted EMG studies and model training; manuscript drafting and editing. R. Chitnis: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution; developed open source repositories; software for real-time data collection, prompted EMG studies and model training. J. Choi: data processing, deep learning architectures, model training, data analysis and data interpretation. W.C.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. J. Chung: software for real-time data collection, prompted EMG studies and model training. J. Connors: sEMG-RD design, testing, manufacturing and support. J. Costa: EMG interaction design; manuscript drafting and editing; data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. M.C.: data processing, deep learning architectures, model training, data analysis and data interpretation. R. Cunningham: EMG data collection. W.F.C.: data processing, deep learning architectures, model training, data analysis and data interpretation. N.D.: data processing, deep learning architectures, model training, data analysis and data interpretation. T.J.D.: data processing, deep learning architectures, model training, data analysis and data interpretation. B.D.A.: EMG interaction design. B.D.: software for real-time data collection, prompted EMG studies and model training. S.D.: software for real-time data collection, prompted EMG studies and model training. A.D.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training; developed open source repositories. Z.E.: EMG interaction design; software for real-time data collection, prompted EMG studies and model training. P.E.: software for real-time data collection, prompted EMG studies and model training. M.F.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training; EMG interaction design. N.F.: data processing, deep learning architectures, model training, data analysis and data interpretation. A.F.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution; developed open source repositories. R.F.: EMG data collection. J. Fine: sEMG-RD design, testing, manufacturing and support. E.F.: manuscript drafting and editing. D.F.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training; EMG interaction design. J. Fu: data processing, deep learning architectures, model training, data analysis and data interpretation. J.-C.G.-A.: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation; developed open source repositories. R.G.: sEMG-RD design, testing, manufacturing and support. J. Gamutan: EMG data collection. S. Gao: data processing, deep learning architectures, model training, data analysis and data interpretation. J. Garcia: EMG data collection. N.T.H.G.: data processing, deep learning architectures, model training, data analysis and data interpretation. M.G.: EMG data collection. S. Ghosh: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. V.G.: data processing, deep learning architectures, model training, data analysis and data interpretation; sEMG-RD design, testing, manufacturing and support. D.G.: software for real-time data collection, prompted EMG studies and model training. G.G.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. A.G.: manuscript drafting and editing; experimental design and execution; software for real-time data collection, prompted EMG studies and model training. L.G.: data processing, deep learning architectures, model training, data analysis and data interpretation. B.G.: EMG data collection. N.G.: sEMG-RD design, testing, manufacturing and support; manuscript drafting and editing. C.G.: data processing, deep learning architectures, model training, data analysis and data interpretation. S.G.K.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. A. Ha: EMG interaction design. K. Hadjer: EMG data collection. C.X.H.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing. S. Hertz: software for real-time data collection, prompted EMG studies and model training. C.H.: EMG data collection. D.N.H.: data processing, deep learning architectures, model training, data analysis and data interpretation. K. Hong: software for real-time data collection, prompted EMG studies and model training. L.H.: EMG interaction design. H. Hou: data processing, deep learning architectures, model training, data analysis and data interpretation. S. Hruda: software for real-time data collection, prompted EMG studies and model training. A. Hsieh: software for real-time data collection, prompted EMG studies and model training. V.H.: sEMG-RD design, testing, manufacturing and support. R.H.: data processing, deep learning architectures, model training, data analysis and data interpretation. Y.H.: data processing, deep learning architectures, model training, data analysis and data interpretation. H. Hulet: software for real-time data collection, prompted EMG studies and model training. S.I.: software for real-time data collection, prompted EMG studies and model training. V.J.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution; software for real-time data collection, prompted EMG studies and model training. C.J.: EMG data collection. X.J.: software for real-time data collection, prompted EMG studies and model training. B.J.: EMG data collection. J.J.J.: data processing, deep learning architectures, model training, data analysis and data interpretation. N.Y.J.: data processing, deep learning architectures, model training, data analysis and data interpretation; experimental design and execution. N. Kadakia: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing. P.K.: senior leadership; manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation. N. Kakar: software for real-time data collection, prompted EMG studies and model training; manuscript drafting and editing. A.K.: software for real-time data collection, prompted EMG studies and model training. T.-C.K.: software for real-time data collection, prompted EMG studies and model training; manuscript drafting and editing; experimental design and execution. S.K.: sEMG-RD design, testing, manufacturing and support; manuscript drafting and editing. T.K.: data processing, deep learning architectures, model training, data analysis and data interpretation. C.S.K.: EMG data collection. A.L.: software for real-time data collection, prompted EMG studies and model training. C.L.: software for real-time data collection, prompted EMG studies and model training. Jennifer Lee: software for real-time data collection, prompted EMG studies and model training. JinHyung Lee: data processing, deep learning architectures, model training, data analysis and data interpretation. J.A.L.: EMG data collection. T.L.: EMG data collection. J. Liao: EMG data collection. Yingru Liu: data processing, deep learning architectures, model training, data analysis and data interpretation. Yuxuan Liu: software for real-time data collection, prompted EMG studies and model training. S.L.: EMG data collection. K.L.: manuscript guidance for public accessibility and understanding; data processing, deep learning architectures, model training, data analysis and data interpretation. R.L.: sEMG-RD design, testing, manufacturing and support. F.L.: data processing, deep learning architectures, model training, data analysis and data interpretation. A. Maczak: software for real-time data collection, prompted EMG studies and model training. N. Maheswaranathan: experimental design and execution. M. Mandel: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing. J. Marshall: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation; developed open source repositories. N. Marshall: manuscript drafting and editing; experimental design and execution; software for real-time data collection, prompted EMG studies and model training. M. Martincik: sEMG-RD design, testing, manufacturing and support. N.Y.M.: data processing, deep learning architectures, model training, data analysis and data interpretation. S. McAnearney: data processing, deep learning architectures, model training, data analysis and data interpretation. A. McHugh: software for real-time data collection, prompted EMG studies and model training. J.A.M.: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation; developed open source repositories; software for real-time data collection, prompted EMG studies and model training. J. Merel: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation. D. Miller: data processing, deep learning architectures, model training, data analysis and data interpretation. I.M.: EMG data collection. R.P.M.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing. S. Moore: software for real-time data collection, prompted EMG studies and model training. Y.M.: data processing, deep learning architectures, model training, data analysis and data interpretation. B.M.: EMG data collection. D. Morrison: software for real-time data collection, prompted EMG studies and model training; EMG interaction design. A. Moschella: sEMG-RD design, testing, manufacturing and support. S. Mulumudi: data processing, deep learning architectures, model training, data analysis and data interpretation. C.M.: EMG data collection. K. Naik: software for real-time data collection, prompted EMG studies and model training. N.N.: software for real-time data collection, prompted EMG studies and model training. A.N.: software for real-time data collection, prompted EMG studies and model training. R.N.: EMG data collection. J.N.: data processing, deep learning architectures, model training, data analysis and data interpretation. K. Nguyen: EMG data collection. L.O.: EMG interaction design. S.O.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. G.O.: software for real-time data collection, prompted EMG studies and model training. C.O.: software for real-time data collection, prompted EMG studies and model training. T.M.O.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing. E.O.: EMG data collection. A.M.P.: data processing, deep learning architectures, model training, data analysis and data interpretation. T.P.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution. J.P.: EMG data collection. S. Parker: EMG data collection. D.P.: data processing, deep learning architectures, model training, data analysis and data interpretation; experimental design and execution; manuscript drafting and editing. M.P.: data processing, deep learning architectures, model training, data analysis and data interpretation. Z.P.: EMG data collection. A.P.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. S.M.P.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. N.P.: EMG data collection. E.P.: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation. B.P.: sEMG-RD design, testing, manufacturing and support; manuscript drafting and editing. S. Puri: software for real-time data collection, prompted EMG studies and model training; data processing, deep learning architectures, model training, data analysis and data interpretation. S. Rajani: data processing, deep learning architectures, model training, data analysis and data interpretation. J.R.F.: software for real-time data collection, prompted EMG studies and model training. J.R.R.: EMG interaction design; data processing, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. T.R.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution. D.R.: EMG data collection. T.R.R.: senior leadership. J. Reid: sEMG-RD design, testing, manufacturing and support. J. Reisman: EMG interaction design. L.W.N.M.y.R.: EMG data collection. S. Rolotti: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution. A. Rosenkranz: sEMG-RD design, testing, manufacturing and support. I.R.: software for real-time data collection, prompted EMG studies and model training. L.R.: EMG data collection. R.R.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. A. Rudnicki: EMG data collection. S. Russell: software for real-time data collection, prompted EMG studies and model training. A. Russo: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; software for real-time data collection, prompted EMG studies and model training. J. Sacra: software for real-time data collection, prompted EMG studies and model training. A. Sadoughi: software for real-time data collection, prompted EMG studies and model training. R.S.: EMG data collection. A. Savane: EMG data collection. C. Schlager: software for real-time data collection, prompted EMG studies and model training; developed open source repositories. D. Schwab: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution. J. Seely: data processing, deep learning architectures, model training, data analysis and data interpretation. M. Seltzer: data processing, deep learning architectures, model training, data analysis and data interpretation. N.D.S.: software for real-time data collection, prompted EMG studies and model training. Ami Shah: EMG data collection. Anish Shah: software for real-time data collection, prompted EMG studies and model training. P.S.: data processing, deep learning architectures, model training, data analysis and data interpretation; developed open source repositories. V. Sharma: sEMG-RD design, testing, manufacturing and support. S. Shen: EMG data collection. K.S.: software for real-time data collection, prompted EMG studies and model training. O.S.: software for real-time data collection, prompted EMG studies and model training. Y.S.: data processing, deep learning architectures, model training, data analysis and data interpretation. N.S.: EMG data collection. J. Simpson: software for real-time data collection, prompted EMG studies and model training. G.S.: EMG data collection. V. Sivakumar: data processing, deep learning architectures, model training, data analysis and data interpretation; developed open source repositories. J. Smith: software for real-time data collection, prompted EMG studies and model training; data processing, deep learning architectures, model training, data analysis and data interpretation. S.E.S.: data processing, deep learning architectures, model training, data analysis and data interpretation. I.J.S.: EMG data collection. M. Springer: data processing, deep learning architectures, model training, data analysis and data interpretation. A. Spurr: data processing, deep learning architectures, model training, data analysis and data interpretation. F.S.: data processing, deep learning architectures, model training, data analysis and data interpretation. C. Stout: software for real-time data collection, prompted EMG studies and model training. E.S.: software for real-time data collection, prompted EMG studies and model training; data processing, deep learning architectures, model training, data analysis and data interpretation. S. Suresh: EMG data collection. A. Suri: software for real-time data collection, prompted EMG studies and model training. D. Sussillo: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation. Z.T.: data processing, deep learning architectures, model training, data analysis and data interpretation; software for real-time data collection, prompted EMG studies and model training. V.T.: data processing, deep learning architectures, model training, data analysis and data interpretation. J. Tannady: software for real-time data collection, prompted EMG studies and model training. A. Tapia: software for real-time data collection, prompted EMG studies and model training. T. Tasci: data processing, deep learning architectures, model training, data analysis and data interpretation. T. Tesileanu: software for real-time data collection, prompted EMG studies and model training. Aman Tiwari: data processing, deep learning architectures, model training, data analysis and data interpretation. Anoushka Tiwari: software for real-time data collection, prompted EMG studies and model training. C.T.: software for real-time data collection, prompted EMG studies and model training; data processing, deep learning architectures, model training, data analysis and data interpretation. B.T.: EMG data collection. J. Trabulsi: data processing, deep learning architectures, model training, data analysis and data interpretation; sEMG-RD design, testing, manufacturing and support; EMG data collection. M.T.: EMG data collection. K.U.: software for real-time data collection, prompted EMG studies and model training. P.W.: data processing, deep learning architectures, model training, data analysis and data interpretation; sEMG-RD design, testing, manufacturing and support. M.W.: data processing, deep learning architectures, model training, data analysis and data interpretation; manuscript drafting and editing; experimental design and execution; software for real-time data collection, prompted EMG studies and model training. R. Wang: software for real-time data collection, prompted EMG studies and model training; data processing, deep learning architectures, model training, data analysis and data interpretation. Z.W.: manuscript drafting and editing; experimental design and execution; data processing, deep learning architectures, model training, data analysis and data interpretation. C. Warden: software for real-time data collection, prompted EMG studies and model training. R. Warren: developed open source repositories; manuscript drafting and editing. C.L.W.: data processing, deep learning architectures, model training, data analysis and data interpretation. R.J.W.: data processing, deep learning architectures, model training, data analysis and data interpretation. D.Z.W.: manuscript drafting and editing. E.W.: software for real-time data collection, prompted EMG studies and model training. C. Wiebe: data processing, deep learning architectures, model training, data analysis and data interpretation. S.W.: EMG data collection. Y.X.: software for real-time data collection, prompted EMG studies and model training. C.Y.: software for real-time data collection, prompted EMG studies and model training. A.Y.: sEMG-RD design, testing, manufacturing and support. S.Y.: software for real-time data collection, prompted EMG studies and model training. M. Zawadzki: software for real-time data collection, prompted EMG studies and model training. M. Zhang: EMG interaction design. J. Zhao: software for real-time data collection, prompted EMG studies and model training. K.Z.: software for real-time data collection, prompted EMG studies and model training. J. Zhong: software for real-time data collection, prompted EMG studies and model training. L.Z.: software for real-time data collection, prompted EMG studies and model training. D.Z.: software for real-time data collection, prompted EMG studies and model training.

Corresponding authors

Correspondence to Patrick Kaifosh or Thomas R. Reardon.

Ethics declarations

Competing interests

All contributors are current or former employees of Meta Platforms, Inc.

Peer review

Peer review information

Nature thanks Cynthia Chestek, Guoying Gu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Schematic and anatomical interfacing of sEMG Research Device.

a, The sEMG Research Device electrical system architecture. The sEMG-RD uses 48 pogo-pin style round electrodes in order to provide good comfort and contact quality. The 48 channels are configured into 16 bipolar channels arranged proximo-distally, with the remainder electrodes serving as either shield or ground. Each electrode is 6.5 mm in diameter (gold plated brass). For each differential sensing channel (16 in total), centre-to-centre spacing between paired sensing electrodes is 20 mm. The sEMG-RD has low noise analog sensors with input-referred RMS noise of 2.46 μVrms, measured during benchtop testing with differential inputs shorted to their mid-point voltage. With analog sensors’ nominal gain value of 190 and Analog to Digital Converter’s (ADC) full-scale range of 2.5 V, the sEMG-RD offers a dynamic range of approximately 65.5 dB. Each channel is sampled at 2000 Hz. The Inertial Measurement Unit (IMU) functional block includes sensors of 3-axis accelerometer, 3-axis gyroscope, and 3-axis magnetometer sampled at 100 Hz. We note that the IMU was not utilized for any online or offline experiments described in this manuscript. The microcontroller facilitates the transfer of unprocessed data from all ADCs and IMU directly to the bluetooth radio. No skin preparation or gels are needed for using the sEMG-RD, because its analog sensors have very high input-impedance — approximately 10 pF capacitance in parallel with 10 TOhm resistance — providing excellent signal robustness against large variations of electrode-skin impedance among the population. b, Computer-aided design rendering of the sEMG-RD. The mechanical architecture consists of a kinematic chain with flexible joints connecting 16 pods that house the pogo-pin style electrodes that comprise the sEMG channels. This enables broad population coverage in maintaining consistent quality contact between the dry electrode and skin. Since each differential sensing channel is placed along the proximal-distal direction, the device is able to maintain symmetry with respect to wrist anatomy and provide generalizability across right and left hands, as long as the wearer keeps the gap location on the ulna side. c, Anatomical depiction of electrode locations relative to relevant muscle and skeletal landmarks, adapted from a public domain image[93]. Pink overlays cover muscles that predominantly control the wrist, blue overlays cover muscles less involved in wrist control, red overlays cover blood vessels and yellow overlays cover nerves. The green diamond indicates the position of the electrode gap. Note the gap that arises between channels 0 and 15, due to variation in wrist circumference and elasticity between compartments, is aligned with the region of the wrist where the ulna is located.

Extended Data Fig. 2 Extraction and validation of putative MUAPs.

a-b, To evoke putative MUAPs, one participant followed a series of prompts instructing the execution of various low-force muscle contractions interspersed with periods of rest. To facilitate generating sparse and spatially focal EMG signals, the participant was provided visual feedback about the raw EMG on a manually selected channel during prompted rest (a) and movement (b) epochs. Each epoch lasted 10 s and was repeated three times. High-pass EMG on all channels (top) and on the manually selected channel (12) for visual feedback (middle) during a prompted rest epoch during data collection for putative thumb extension MUAPs. Grey vertical scale bars indicate 20 μV. MUAPs on any channel were detected using peak finding on the channel-averaged rectified and smoothed EMG (see Methods). The timings of detected MUAPs were used to construct a spike train capturing the activity of this multi-unit activity, whose instantaneous firing rate was computed by taking the inverse of each event’s interspike interval (ISI) in seconds (bottom). c, Mean instantaneous firing rates (computed as the total number of detected MUAPs over the epoch duration) during rest and movement epochs for each tested movement (IF: index flexion; MF: middle flexion; PE: pinky extension; TAb: thumb abduction; TE: thumb extension; WP: wrist pronation). Each sample corresponds to one prompt (rest or move) epoch. d, Coefficient of variation (CoV) during the prompted movement periods. CoV was computed as the standard deviation of interspike intervals (b; bottom) normalized by their mean. e, Multi-channel waveforms for putative MUAPs extracted during the prompted movement epochs for each action. For visualization, MUAPs for each movement were normalized by the 99.95th percentile of the absolute maximum (over samples and channels) of each MUAP. Thin lines correspond to individual MUAPs (total number detected indicated as n) and thick lines correspond to the median waveform over MUAPs for each movement. Each waveform is 20 ms long. Vertical scale bars indicate 20 uV. f, MUAP spatial profiles. The spatial profile for each MUAP was constructed using the peak-to-peak value of the waveform on each channel. The mean (solid line) and standard error (shading; nearly within solid lines) of the spatial profiles are shown for each movement. Angular locations represent approximate channel locations around the wrist (indicators) and the radii represent the peak-to-peak value.

Extended Data Fig. 3 Anthropometric and demographic features of sEMG datasets.

a, The number of participants in each corpus. b-e, Histograms of anthropometric characteristics of all participants (n = 11,236): (b) wrist circumference, (c) self-reported age, (d) BMI calculated from self-reported height and weight, and (e) self-reported height. The irregularity in the histogram of self-reported age is likely due to participants rounding their age to nearby values. We measured wrist circumferences with a standard measuring tape at the wrist just below the ulnar styloid process where the participants are expected to don the band. Values outside of the range of 10–30 cm were truncated. We calculated BMI as the weight (in kilograms) divided by height (in metres) squared. f-i, Distributions of the demographic characteristics across all participants (n = 11,236): (f) dominant handedness, (g) self-reported proficiency at typing on a computer keyboard, (h) self-reported gender, and (i) arm exercise frequency, chosen from one of the following options: Never (never), Less than once per week (rarely), 1-2 times per week (occasionally), more than twice per week (often).

Extended Data Fig. 4 Examples of prompting used to collect training data for the three tasks.

a, Time series of example prompter frames from the open-loop task used to collect training data for the wrist decoder. The participant was instructed to make wrist movements following a cursor (pink circle) making centre-out movements. For the user to be able to preempt the direction of the cursor movement, a line emanated out from the cursor to indicate the direction it was going to move to before subsequently moving. b, Time series of example prompter frames from the cursor-to-target closed-loop control task used to collect training data for the wrist decoder, with the 2D target configuration. In this task the participant was prompted to move the cursor to a highlighted target (light blue rectangle in panel labelled t_0). When the cursor (red) landed on the target, a short timer began, marked by the black fill of the cursor and black border of the target region (panel t_3). In this trial, the cursor was held on the target for 500 ms to complete the timer, so the target was acquired and therefore disappeared as the next target was prompted (light blue rectangle in panel t_4). c, Example prompter from the smooth pursuit closed-loop control task used to collect training data for the wrist decoder. In this task the participant was instructed to move the cursor (red) to follow a target (black) moving in a randomly sampled smooth trajectory. d, Example of prompting for open-loop task used to collect training data for the discrete gesture recognizer. A series of gestures to be performed are depicted, with colours and labels corresponding to the gesture type. Gestures were separated by blank intervals in which no gesture was to be performed. Prompts scroll from the right of the screen to the left. Participants were instructed to perform each gesture when the corresponding prompt reached the indicator line (highlighted with an arrow) – either instantaneous gestures such as finger pinches or thumb swipes that are depicted as single lines, or held gestures such as index and middle holds that are depicted as solid bars. Participants were instructed to release held gestures when the indicator line reached the end of the rectangle. Gestures that have already been prompted are shown in grey. e, Detailed example of prompting during holds. At t_0 an index hold gesture prompt appeared on the right side of the screen, with the time indicator line in white. At t_1 the gesture prompt reached the time indicator, and the hold prompt changed colour to indicate the hold should be performed by the participant. At t_2 the hold was no longer selected by the indicator bar and turned grey, indicating that the participant should release the hold. f, Example prompter shown during the handwriting task. The screen instructed the participant to write “how was your day” with their hand on the surface of the table, while seated. g, During the experimental session, different prompts, including numbers and punctuation, were shown, ranging from single characters to full sentences. Besides writing on a desk surface, the participant was also asked to perform handwriting on their leg while standing and on their leg while seated.

Extended Data Fig. 5 sEMG event similarities and single-participant sEMG decoder generalization performance.

a, Purple: cosine similarity between individual sEMG activations of a given gesture and the sEMG template (event-triggered average) for that gesture. From left to right: cosine similarities are plotted for all events within a single session (single band placement), across all sessions of a single participant, or across all sessions from all participants from Fig. 2a (100 sessions, 5 from each of 20 users). While similarity was relatively high within a single band placement, sEMG activations became progressively more distinct across different band placements and individuals. Orange: same, except for the cosine similarity of one gesture compared to the template for a distinct gesture. These were lower than similarity within the same gesture, irrespective of whether the grouping was done over a single band placement or across the population. Differences shown across sessions, participants and gestures are representative for all gestures and pairs of gestures. Boxes show median, lower quartile, and upper quartile, with whiskers extending to ±1.5×IQR. b, For each held-out individual, the fraction of other single-participant models in the discrete gesture detection task (Fig. 2c,d) that outperform that individual’s own model (i.e. had lower FNR). For all except two participants, none of the other single-participant models outperformed their own model. All the results in panels b-d are based on n = 100 single-participant models, each trained on 4 sessions from that participant. c, For each pair of participants, we computed the FNR of each participant’s model on data from every other participant. We embedded the resulting distance matrix in 2D using t-SNE. Qualitative inspection of t-SNE embeddings reveal no prominent similarity structure. d, Scatter plot comparing each person’s model’s average offline performance on every other participant’s data (donor FNR, x-axis) against the average performance of other participant’s models on that person’s held-out session (receiver FNR, y-axis). The dashed line shows x = y. There is not a significant Pearson correlation between the donor and receiver score (r = 0.11, p = 0.26, two-sided test, n = 100 participants). All models show high FNR, and the lack of correlation indicates that the generalizability of a given participant’s model to other individuals is not predictive of the other individual’s model’s generalizability to that participant.

Extended Data Fig. 6 Multivariate power frequency features improve wrist decoder performance over root mean square power features.

Decoding error of 4.4 M parameter wrist decoders trained to predict wrist angle velocity from MPF EMG features (black) or root mean square power EMG features (gold). Each dot shows mean +/- SEM decoding error evaluated on a fixed test set of held-out participants (n = 22), following the same conventions as in Fig. 2e. Asterisks below each pair of points indicate p < 10−4, two-tailed paired sample Wilcoxon signed-rank test. Root mean square power EMG features were calculated by first rescaling and high-pass filtering the EMG signal as in the MPF features (see Methods) and then taking the root mean square of each channel in a rolling window of length 200 samples (100 ms) strided by 40 samples (20 ms). The reduced dimensionality of these features (16 dimensions, as opposed to 384) implied a smaller number of input dimensions to the fully connected layer in the rotational-invariance module, which we compensated for by increasing the number of hidden dimensions from 512 to 600 to keep the total parameter count at 4.4 M.

Extended Data Fig. 7 Example screenshots of closed-loop evaluation tasks.

a, Screenshots from an example trial of 1D horizontal cursor control task, in which the participant was prompted to reach to the rightmost target (in panel labelled t_0, light blue rectangle). When the cursor (red) landed on the target, the target was marked with a black border and a short timer began, marked by the black fill of the cursor (middle panel, t_1). In this trial, the cursor was held on the target for 500 ms to complete the timer, so the target was acquired and therefore disappeared as the next target was prompted (right panel, t_2). b, Screenshots from an example sequence in the discrete grid navigation task, in which the participant was prompted to perform (from left to right, marked as t_0-t_4): thumb swipe up, index hold, thumb swipe right, thumb swipe right, middle hold. c, Screenshots from an example trial in the handwriting task, in which the participant is prompted to write the phrase “example flashing red light means” (top) and the handwriting decoding model output in response to the participant’s behavior in the handwriting task (below).

Extended Data Fig. 8 Additional online evaluation metrics.

a, Mean Fitts’ law throughput on the 1D horizontal cursor control task. Throughput is defined as the index of difficulty divided by acquisition time, with the index of difficulty defined as in[5]: \({\log }_{2}(1+{d}_{i}/w)\), where \({d}_{i}\) is the distance to the target at the start of trial i and w is the target width. Each box shows the distribution of trial-averaged throughput over participants (n = 17), following the same conventions as Fig. 3d,e. Throughput significantly improved from the practice block to the evaluation blocks (p < 0.005, two-tailed Wilcoxon signed-rank test), indicating learning effects consistent with the improvements in acquisition time and dial-in time shown in the main text. Dashed red line and shading shows median and 95% confidence interval of the performance of a different set of n = 162 participants controlling the cursor with ground truth wrist angles measured via motion capture (see Methods). Dashed orange line and shading shows median and 95% confidence interval of the performance of the same n = 17 participants controlling the cursor with MacBook trackpad (see Methods). For each baseline, confidence intervals for medians were calculated using the reverse percentile bootstrap. b-d, Performance on the discrete grid navigation task with Nintendo Switch Joy-Con controller (n = 23 participants). (b) Fraction of prompted gestures in each block in which the first gesture detected by the model was the correct one (out of 130 total prompted gestures in each block), as in Fig. 3f. This value was used as the baseline in Fig. 3f. (c) Mean gesture completion rate in each task block, as in Fig. 3g. This value was used as the baseline in Fig. 3g. (d) Discrete gesture confusion rates in evaluation blocks, averaged across participants, as in Fig. 3h. Confusion rates are expressed as a percent of instances in which the corresponding gesture was expected (across rows). Note that, despite using a commercially available and widely used controller, confusion rates remain non-zero, reflecting behavioural errors. e, Distribution of subjective impressions about the reliability of each EMG decoding model. At the end of each online evaluation task, participants were asked to respond to a multiple choice question about how reliably their intended action was detected. For the discrete gestures task, they were asked to answer this question separately for each of the thumb swipe directions and “activation” gestures. f-i, Demographics of participants that performed the online evaluation tasks for the wrist decoder (n = 17), discrete gestures decoder (n = 24), and handwriting decoder (n = 20): (f) self-declared gender, (g) self-declared dominant hand, (h) self-declared age, (i) measured wrist circumference. For all boxplots, boxes show median, lower quartile, and upper quartile, with whiskers extending to ±1.5×IQR. Any values beyond these are marked with open circles. One and two asterisks respectively indicate p < 0.05 and p < 0.005, and “ns” indicates “not significant” (p > 0.05); two-tailed paired sample Wilcoxon signed-rank test.

Extended Data Fig. 9 Spatiotemporal properties of all discrete gesture decoder convolutional filters.

a, Index of channel with max root mean square (RMS) power (n = 512 convolutional filters). Here and in all other panels in this figure, the triangles at the top mark the values of the 6 example convolutional filters from Fig. 4b (blue triangles) and the 6 example putative MUAPs from Fig. 4c (orange triangles). b, Number of channels with RMS power within 50% of the peak channel. c, Peak frequency response of the channel with max RMS power. d, Bandwidth of the channel with max RMS power (see Methods).

Extended Data Fig. 10 Influence of early stopping during personalization.

In this figure, we employ early stopping during personalization to disambiguate the role of more personalization data from increased fine-tuning iterations as well as to mitigate regressions among the best-performing users. Specifically, we used mean CER on held out test data as a selection criteria for epoch-wise early stopping. Aside from early stopping, the setup here is identical to that in Fig. 5b,e,f) of the main text. Overall, results are very similar to Fig. 5 of the main text, indicating that the increase in personalization data is the primary driver of improved performance. Regressions among the best-performing users are now absent. Note also that we do not have separate validation and test sets, so these results should be understood as validation performance. a, Same as Fig. 5b of the main text, except with the inclusion of early stopping during fine-tuning. b, Same as Fig. 5e of the main text, except with the inclusion of early stopping during fine-tuning. Compared with Fig. 5e, transfer of personalized models to other participants yields overall smaller regressions likely because early-stopped models remain closer to the pre-trained model. c, Same as Fig. 5f of the main text, except with the inclusion of early stopping during fine-tuning. Regressions exhibited by a few of the best performing users in Fig. 5f are now absent due to early stopping. We show the range of Pearson correlation coefficients for each fit and the median p-value (two-sided test); maximum p-value over all fits is 0.020.

Supplementary information

Supplementary Tables

Supplementary Tables 1 and 2.

Reporting Summary

Supplementary Video 1 Example session of the 1D horizontal cursor control task with generic wrist decoding model.

Example user performing the 1D horizontal cursor control task with the generic wrist decoding model evaluated in Fig. 3d,e. This participant has previous experience with sEMG decoders on this task, but is not in the training or test corpus. In each trial, the participant was prompted to move the cursor to a target and acquire it by holding the cursor within the target region for 500 ms. Once that target is acquired, the target disappears and another is prompted. Once all 10 targets are acquired, another 10 identical targets are presented and prompted in random order. The video shows all 50 trials in one task block, where a trial is defined as a single target acquisition. The video at the bottom right shows the user’s hand during the task. In this block, this user achieved a mean acquisition time of 1.23 s, a mean throughput of 2.26 bits per s, prematurely exited the target on 44% of trials and had a mean dial-in time of 1.07 s on those trials with premature exits.

Supplementary Video 2 Example session of the discrete grid navigation task with a generic discrete-gesture decoding model.

Example user performing the discrete grid navigation task with the generic discrete-gesture decoding model evaluated in Fig. 3f–h. This user has previous experience with sEMG decoders on this task, but is not in the training or test corpus. In each trial, the participant is instructed to move a character along a sequence of points on a grid by using the four navigation gestures (thumb swipe left/right/up/down). Every few steps, a coloured point with text prompts the participant to perform an activation gesture (thumb tap, index hold, middle hold). The video shows all 10 trials in one task block. The video at the bottom right shows the user’s hand during the task. In this block, this user achieved a first hit probability of 0.99, a mean gesture completion rate of 1.31 gestures per s and a mean accuracy (mean of diagonal of the confusion matrix) of 99.2%.

Supplementary Video 3 Example session of the handwriting task with handwriting decoding model.

Example user performing the handwriting task with the generic handwriting decoding model evaluated in Fig. 3i,j. This user has previous experience with sEMG decoders on this task, but is not in the training corpus. In each trial, the participant is prompted to write a phrase. The video shows all 10 trials in one task block. The video at the bottom right shows the user’s hand during the task. In this block, this user achieved a CER of 0.057 and a WPM of 28.4. While we instructed users to make corrections to decoded text that was not understandable, in this particular session, the user did not have to make any such corrections.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Kaifosh, P., Reardon, T.R. & CTRL-labs at Reality Labs. A generic non-invasive neuromotor interface for human-computer interaction. Nature 645, 702–711 (2025). https://doi.org/10.1038/s41586-025-09255-w

- Received: 23 February 2024

- Accepted: 06 June 2025

- Published: 23 July 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09255-w

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

- Brain–computer interface control with artificial intelligence copilots

- Johannes Y. Lee

- Sangjoon Lee

- Jonathan C. Kao

Nature Machine Intelligence (2025)

Finger Movement Recognition via High-Density Electromyography of Intrinsic and Extrinsic Hand Muscles

Article Open access 29 June 2022

Hand gesture recognition using sEMG signals with a multi-stream time-varying feature enhancement approach

Article Open access 27 September 2024

Electromyographic typing gesture classification dataset for neurotechnological human-machine interfaces

Article Open access 15 March 2025

Interacting with computers through a wristband

- Yan Huang

Nature Electronics Research Highlight 19 Aug 2025

A very handy neural interface

- William P. Olson

Nature Neuroscience Research Highlight 05 Sept 2025

Article Open access Published: 06 August 2025

Lithium deficiency and the onset of Alzheimer’s disease

Liviu Aron,

Zhen Kai Ngian,

Chenxi Qiu,

Jaejoon Choi,

Marianna Liang,

Derek M. Drake,

Sara E. Hamplova,

Ella K. Lacey,

Perle Roche,

Monlan Yuan,

Saba S. Hazaveh,

Eunjung A. Lee,

David A. Bennett &

…

Bruce A. Yankner

Nature volume 645, pages 712–721 (2025)

Abstract

The earliest molecular changes in Alzheimer’s disease (AD) are poorly understood1,2,3,4,5. Here we show that endogenous lithium (Li) is dynamically regulated in the brain and contributes to cognitive preservation during ageing. Of the metals we analysed, Li was the only one that was significantly reduced in the brain in individuals with mild cognitive impairment (MCI), a precursor to AD. Li bioavailability was further reduced in AD by amyloid sequestration. We explored the role of endogenous Li in the brain by depleting it from the diet of wild-type and AD mouse models. Reducing endogenous cortical Li by approximately 50% markedly increased the deposition of amyloid-β and the accumulation of phospho-tau, and led to pro-inflammatory microglial activation, the loss of synapses, axons and myelin, and accelerated cognitive decline. These effects were mediated, at least in part, through activation of the kinase GSK3β. Single-nucleus RNA-seq showed that Li deficiency gives rise to transcriptome changes in multiple brain cell types that overlap with transcriptome changes in AD. Replacement therapy with lithium orotate, which is a Li salt with reduced amyloid binding, prevents pathological changes and memory loss in AD mouse models and ageing wild-type mice. These findings reveal physiological effects of endogenous Li in the brain and indicate that disruption of Li homeostasis may be an early event in the pathogenesis of AD. Li replacement with amyloid-evading salts is a potential approach to the prevention and treatment of AD.

Similar content being viewed by others

Main

The identification of treatable causes of AD requires a fundamental understanding of the pathogenic processes leading to memory loss. Although substantial progress has been made in defining gene variants that confer risk for AD, the environmental factors that affect the timing of disease onset are not as well understood1,6. Several factors relating to diet, lifestyle and the environment have been identified, but their contributions to AD pathogenesis are unclear1,6,7. Altered homeostasis of metals is one such factor7,8,9,10,11,12. These studies have focused primarily on the toxic effects of metals such as iron, copper and zinc, which can promote amyloid-β (Aβ) aggregation, tau phosphorylation or oxidative stress in model systems6,7,8,9,10,11,12. However, metals also have essential roles in brain function, and disruption of this normal physiology in AD is relatively unexplored.

Lithium deficiency in MCI and AD

To explore the role of metal-ion homeostasis in AD, we used inductively coupled plasma mass spectrometry (ICP–MS) to assess 27 abundant and trace metals in the brain and blood of aged individuals with no cognitive impairment (NCI) and individuals with amnestic MCI or AD. Metal levels were determined in the prefrontal cortex (PFC), which is a prominently affected region in AD, and the cerebellum, which is relatively unaffected. Of all the metals surveyed, only one, Li, showed significantly reduced levels in the PFC of individuals with both MCI and AD (Fig. 1a,b and Supplementary Table 1). The mean and median Li cortex-to-serum ratio and total cortical Li were significantly reduced in the PFC of people with MCI and AD (Fig. 1c,d), but not in the cerebellum (Extended Data Fig. 1a,b). In a second independent cohort, Li levels were also significantly reduced in the PFC of people with AD (Fig. 1e). By contrast, the mean serum Li levels in MCI and AD were not significantly different from controls (Extended Data Fig. 1c). Li levels were not significantly affected by sex or the range of postmortem intervals in this study (see Methods). The cortex-to-serum ratios of several other metals also changed in AD, but not in MCI (Fig. 1a,b and Supplementary Table 1). However, the change in Li showed the lowest adjusted P value of all the metals analysed (Fig. 1b). Together, these results indicate that endogenous Li homeostasis is perturbed in the brain in MCI and AD.

Fig. 1: Lithium deficiency and the onset of AD.

a,b, Volcano plots showing changes in metal cortex-to-serum ratios in the PFC of MCI versus NCI (a) and AD versus NCI (b) cases, along with their statistical significance, determined by one-way analysis of variance (ANOVA) with Tukey’s post-hoc test, followed by the Benjamini–Hochberg correction for the number of metals assessed. c,d, Li cortex-to-serum ratios (c) and total cortical Li levels (d) in cases from ROSMAP. Each point represents an individual case. e, Total cortical Li in cases from a replication cohort. f, Li is concentrated in Aβ plaques in MCI and AD. Aβ immunolabelling in the PFC of an AD case (left). LA-ICP–MS was done on an adjacent unfixed section to quantify Li in Aβ plaques (white circles) and neighbouring non-plaque regions (yellow circles). Scale bar, 50 μm. The ratios of Li level in plaque (P) to non-plaque (NP) regions are shown (right) in MCI and AD cases. g, Cortical brain samples were subfractionated into plaque-enriched and non-plaque fractions. Li levels in non-plaque fractions were measured by ICP–MS and normalized to the mean of NCI. P values were calculated by one-way (a–d) or two-way (f) ANOVA with Tukey’s post-hoc and Benjamini–Hochberg corrections (a–c) or Tukey’s post-hoc corrections (d,f), or by two-tailed unpaired t-test (e,g). c–g, Box plots show individual values, median (line), box limits (25th and 75th percentiles) and whiskers (minimum and maximum). a–c, NCI n = 133, MCI n = 58, AD n = 94. d, NCI n = 177, MCI n = 66, AD n = 105. e, NCI n = 22, AD n = 21. f, MCI n = 7, AD n = 5. g, NCI n = 74, AD n = 42.

Source Data

We next investigated whether endogenous Li homeostasis in the brain might be perturbed by AD pathology. Previous studies have implicated the interaction of several metals with Aβ8,9. To determine whether amyloid deposition affects the distribution of Li, we performed laser absorption (LA)-ICP–MS and quantified Li in amyloid plaques compared with plaque-free regions in the frontal cortex. A highly significant concentration of Li in Aβ plaques was detected in every case of MCI and AD, which increased from MCI to AD (Fig. 1f). To complement this in situ analysis, PFC samples were subfractionated into a plaque-enriched insoluble fraction and a soluble fraction devoid of amyloid plaques (Supplementary Fig. 1). The mean and median Li levels in the PFC non-plaque fraction were significantly reduced in AD relative to control NCI cases (Fig. 1g). Furthermore, lower Li levels in the non-plaque cortical fraction correlated with reduced cognitive test scores for episodic and semantic memory, and for a global index of cognitive function, across the entire ageing population (Supplementary Table 2). In patients with AD, lower Li levels in the non-plaque cortical fraction correlated with reduced scores for episodic memory and the index of global cognitive function (Supplementary Table 2).

To further explore the relationship of Li to Aβ, we examined the cortical distribution of endogenous Li in J20 Aβ precursor protein (App)-transgenic mice[13] that exhibit widespread Aβ deposition. LA-ICP–MS showed an approximately 3–4-fold concentration of Li in cortical Aβ deposits in 12-month-old J20 mice relative to adjacent plaque-free cortical regions (Extended Data Fig. 1d). Furthermore, subfractionation of the cortex showed that Li in the non-plaque cortical fraction was significantly reduced in J20 relative to wild-type mice, consistent with Li sequestration by amyloid deposits (Extended Data Fig. 1e). By contrast, 3-month-old J20 mice before the onset of amyloid deposition did not exhibit reduced Li in the soluble cortical fraction relative to age-matched wild-type mice (Extended Data Fig. 1e). Together, these results indicate that Li is sequestered by Aβ deposits, reducing its bioavailability.

Lithium deficiency in mouse models

To explore the biology of endogenous Li, mice were maintained on a chemically defined diet that is calorically and nutritionally equivalent to the typical grain-based mouse diet, including the same Li concentration. Serum and cortical Li levels in mice on this diet were in a similar range to those in the ageing human population, and the mean values were not significantly different (see Methods section on Mouse diet). Selective removal of Li from the mouse diet (a 92% reduction) led to an 89% reduction in mean serum Li and a 47–52% reduction in mean cortical Li in the non-plaque fraction (Extended Data Fig. 2a–c and Supplementary Fig. 2).

The pathological effects of reducing endogenous Li were determined in the 3xTg AD mouse model[14], which accumulates Aβ deposits and phospho-tau, the J20 AD mouse model[13], which accumulates abundant Aβ deposits, and ageing wild-type mice without AD-type pathology. The 3xTg and J20 mice maintained on the Li-deficient diet showed a significant elevation in Aβ deposition in the hippocampus (Fig. 2a,b). An increased amyloid plaque burden was observed as early as five weeks on the Li-deficient diet and continued to increase with longer-term treatment (Fig. 2a,b and Extended Data Fig. 2d). In ageing wild-type mice, the Li-deficient diet reduced cortical Li by approximately 50% (Extended Data Fig. 2c). This resulted in a significant elevation of cortical and hippocampal Aβ42, the major pathogenic Aβ species in AD, and a trend towards an increase in Aβ40 (Fig. 2c and Extended Data Fig. 2e). Thus, Li deficiency accelerates Aβ deposition in AD mouse models and increases Aβ42 levels in ageing wild-type mice.

Fig. 2: Lithium deficiency accelerates AD pathology and cognitive decline.

a,b, Aβ immunolabelling and plaque quantification (right) in the hippocampus of 3xTg (a) and J20 (b) mice on Li-deficient (DEF) or control (CTRL) diets. c, Aβ42 and Aβ40 levels in the frontal cortex of wild-type (WT) mice on DEF or CTRL diets, normalized to total protein (n = 5 per group). d–f, Immunolabelling of pSer202-tau (CP13; d) or pSer396/Ser404-tau (PHF1, e) and thioflavin S labelling (f) in the hippocampal CA1 region of 3xTg mice on DEF or CTRL diets, and quantification of phospho-tau-positive cell density (d,e, right). In f, arrows indicate neurofibrillary tangle-like structures. g–k, Behavioural assessment of 3xTg mice on DEF or CTRL diets: Morris water-maze learning (g) and memory (h,i), Y-maze (j) and novel-object recognition (k). l–o, Behavioural assessment of ageing WT mice on DEF or CTRL diets: Morris water-maze learning (l) and memory (m,n), and novel-object recognition (o). Diets were administered to 3xTg mice from 6 months to 15 months of age (a,d–f) or 6 months to 13.5 months of age (g–k); to J20 mice from 3 months to 6 months of age (b); and to WT mice from 12 months to 20 months of age (c,l–o). In a–e, data were normalized to CTRL. In a–e, h–k and m–o, box plots show individual values, median (line), box limits (25th and 75th percentiles) and whiskers (minimum to maximum). In g and l, data are mean ± s.e.m. P values were calculated by two-tailed unpaired t-test (a–e, h–k, m–o) or mixed-effects models with Šídák’s post-hoc test (g,l); selected P values shown. No significant differences were detected in l. Scale bars, all 25 μm. a, CTRL n = 17, DEF n = 10; b, CTRL n = 7, DEF n = 6; d, CTRL n = 10, DEF n = 9; e, n = 10 per group; g–i, CTRL n = 16, DEF n = 22; j, CTRL n = 27, DEF n = 17; k, CTRL n = 13 (left), n = 14 (right); DEF n = 11; l–m, CTRL n = 25, DEF n = 34; n, CTRL n = 25, DEF n = 33; o, CTRL n = 39, DEF n = 28.

Source Data

The role of Li homeostasis in tau pathology was explored in 3xTg mice by assessing the phospho-tau isoforms associated with early (pSer202-tau) and advanced (pSer396/Ser404-tau) stages of neurofibrillary tangle (NFT) formation in AD. Both pSer202-tau and pSer396/Ser404-tau were increased 3–4-fold in hippocampal neurons of Li-deficient 3xTg mice (Fig. 2d,e and Extended Data Fig. 2f,g). A subset of the affected neurons showed elevated phospho-tau in thioflavin S-positive structures that resemble NFTs (Fig. 2f). As observed for Aβ, elevated phospho-tau was evident as early as five weeks into the Li-deficient diet and continued to increase with longer-term treatment (Fig. 2d,e and Extended Data Fig. 2f). These results indicate that Li deficiency promotes neuronal phospho-tau accumulation.

We next assessed whether endogenous Li affects cognitive function in the setting of AD-type pathology and during normal ageing. Administration of the Li-deficient diet to 3xTg mice significantly impaired learning (Fig. 2g) and long-term memory (Fig. 2h,i), as determined in the Morris water-maze paradigm. There were no significant changes in swimming speed, visible platform recognition or performance in the open-field test, consistent with intact visual perception, locomotor activity and exploratory behaviour (Extended Data Fig. 2h–l). Li deficiency in 3xTg mice also gave rise to significant deficits in the Y-maze and novel-object recognition tests of memory (Fig. 2j,k). Furthermore, ageing Li-deficient wild-type mice also showed significant memory loss in the Morris water maze (Fig. 2m,n) and the novel-object recognition test (Fig. 2o). These cognitive deficits in ageing wild-type mice appeared in the absence of significant changes in spatial learning (Fig. 2l), swimming speed, visible platform recognition or performance in the open-field test (Extended Data Fig. 2m–q). Thus, endogenous Li protects against memory loss in the presence of AD-type pathology, as well as during normal ageing in mice.

The transcriptome of lithium deficiency

We next characterized the effects of Li deficiency on the transcriptome of cell populations in the hippocampus, an early site of disease progression in MCI and AD. Single-nucleus RNA-seq (snRNA-seq) analysis of the hippocampus was done in 3xTg mice after administering the Li-deficient diet for 5 weeks. We analysed 64,772 and 54,374 high-quality nuclei from Li-deficient and control mice, respectively (Supplementary Fig. 3). Based on the expression of previously validated cell-type-specific markers (Supplementary Fig. 4), the relative abundance of the resolved cell types was unchanged after 5 weeks of Li deficiency (Fig. 3a).

Fig. 3: Cell-type-specific regulation of gene expression by endogenous lithium.

a, Uniform manifold approximation and projection (UMAP) plots of nuclei from snRNA-seq of hippocampi from 12-month-old 3xTg mice fed Li-deficient (DEF, n = 5) or control (CTRL, n = 4) diets for 5 weeks, coloured by cell type. b, Number of DEGs per cell type, stratified by directionality. c, GO analysis of DEGs showing enriched downregulated (blue) and upregulated (red) pathways. d, Heatmap showing the expression changes (log_2FC) for selected DEGs across cell types. FC, fold change. e, Overlap of DEGs associated with Li deficiency and human AD pathology. DEGs from snRNA-seq of 3xTg mice on a DEF diet were overlapped with DEGs from snRNA-seq of human biopsy samples with Aβ or Aβ/tau pathology[15]. Shown is the significance level (−log_10Padj) for the overlap of upregulated and downregulated DEGs in each cell type, calculated using Fisher’s exact test and corrected for multiple comparisons across cell types and gene directions using the Benjamini–Hochberg method. f–j, Synaptic and structural alterations in 3xTg mice fed CTRL or DEF diets from 6–12 (f) or 6–15 (g–j) months of age. Golgi labelling and spine density quantification in cortex and hippocampal CA1 (f). Immunolabelling and quantification of synaptophysin (SYP; g) and PSD-95 (h) in the hippocampal CA1 region; IF, immunofluorescence. Immunolabelling and quantification of myelin (fluoromyelin; i), oligodendrocyte (Asp-acylase, aspartoacylase; j) and axon (SMI-312; j) densities in the corpus callosum. In f–j, box plots show individual values, median (line), box limits (25th and 75th percentiles) and whiskers (minimum and maximum). In g–j, data are normalized to the CTRL group means. In f–j, P values were calculated by two-tailed unpaired t-tests. Scale bars: 5 μm (f) and 25 μm (g–j). f,h, n = 8 per group; g, CTRL n = 8, DEF n = 9; i, n = 7 per group; j, CTRL n = 8, DEF n = 6. Ast, astrocytes; End, endothelial cells; Exc, excitatory neurons; GC, granule cells; Inh, inhibitory neurons; Mic, microglia; Olig, oligodendrocytes.

Source Data

Analysis of differentially expressed genes (DEGs) showed significant transcriptome changes in excitatory, granule cell and inhibitory neurons, as well as oligodendrocytes, astrocytes, microglia and oligodendrocyte progenitor cells (OPCs) (Fig. 3b and Supplementary Tables 3 and 4). In excitatory neurons, Gene Ontology (GO) terms for synaptic signalling, organization and transmission were downregulated, whereas electron transport and pathways of neurodegeneration and AD were upregulated (Fig. 3c and Supplementary Tables 5 and 6). Downregulated synaptic genes included Homer1, Grm3, Mef2c, Lrrk2, Grik1, Grik3, Btbd9, Dlgap3 and Dlgap4 (Fig. 3d). In oligodendrocytes, GO terms for axon ensheathment and myelination, as well as neuron projection development, were strongly downregulated (Fig. 3c and Supplementary Tables 5 and 6). Downregulated myelin-related genes included Mbp, Mog, Mag, Plp1 and Opalin (Fig. 3d). In astrocytes, pathways of neurodegeneration, electron transport chain and monovalent cation transport were upregulated (Supplementary Fig. 5 and Supplementary Tables 5 and 6). Proteomic analysis of the hippocampus in Li-deficient 3xTg mice showed significantly reduced abundance of synaptic and myelin protein components and increased abundance of proteins involved in neuroinflammation, lipid metabolism and mitochondrial membrane organization (Supplementary Fig. 6 and Supplementary Table 7). These results indicate that endogenous Li broadly affects the composition of the brain transcriptome and proteome.

We next investigated whether the transcriptome of Li deficiency overlapped with that of AD by comparing our findings with a recent snRNA-seq study of cortical biopsy samples from living individuals with a range of AD pathology[15]. Samples from the human biopsy study that exhibited early stage Aβ deposition showed cell-type-specific overlap of DEGs with 3xTg mice on a Li-deficient diet (Fig. 3e). Concordant DEGs included both upregulated and downregulated genes in excitatory and inhibitory neurons, upregulated genes in microglia and OPCs, and downregulated genes in oligodendrocytes (Fig. 3e and Supplementary Table 8). Overlap with Li-deficient DEGs was more extensive in human cortical samples with both Aβ and phospho-tau pathology that were diagnosed with AD before or within one year of biopsy[15] (Fig. 3e). Concordant DEGs included both upregulated and downregulated genes in excitatory and inhibitory neurons, microglia and oligodendrocytes, and upregulated genes in astrocytes, endothelial cells and OPCs (Fig. 3e and Supplementary Table 8). Thus, the transcriptome of Li deficiency broadly overlaps with the transcriptome of AD pathology in humans.

Maintenance of synapses and myelin

Genes involved in synaptic signalling and structure were broadly downregulated by Li deficiency (Fig. 3c). Dendritic spine loss was detected by Golgi staining in Li-deficient 3xTg and wild-type mice (Fig. 3f and Extended Data Fig. 3a,b), together with reduced immunolabelling of the presynaptic and postsynaptic proteins synaptophysin and PSD-95, respectively (Fig. 3g,h). Reduced abundance of synaptic proteins was confirmed by proteomic analysis of the Li-deficient 3xTg hippocampus (Supplementary Fig. 6a,b and Supplementary Table 7). Thus, endogenous Li contributes to synapse maintenance in the ageing mouse brain.

Li deficiency downregulated the expression of myelin-related genes in oligodendrocytes and reduced the abundance of myelin-associated proteins (Fig. 3c,d and Supplementary Fig. 6b). Fluoromyelin labelling indicated a significant loss of myelin in 3xTg mice after long-term Li deficiency (Fig. 3i). This was associated with reduced numbers of oligodendrocytes, OPCs and axons in Li-deficient 3xTg and wild-type mice (Fig. 3j and Extended Data Fig. 3c,d). To assess myelin ultrastructure, transmission electron microscopy was performed on the corpus callosum in Li-deficient and control 3xTg mice (Extended Data Fig. 3e). Li-deficient mice had thinner electron-dense myelin sheaths surrounding neuronal axons and a significantly elevated g-ratio (the ratio of the inner axonal diameter to the total axon plus myelin fibre diameter), consistent with reduced axonal myelin. These results indicate that endogenous lithium contributes to the maintenance of myelin integrity.

Lithium and microglial function

The snRNA-seq analysis of Li deficiency showed a reduction in the number of microglia expressing the gene Cx3cr1, which encodes a homeostatic marker, and an increase in microglia expressing Apoe (Supplementary Fig. 7a), similar to the reactive microglial state observed in AD[15]. To obtain greater insight into the regulation of microglia by Li, viable microglia were isolated from the brain and analysed by deep RNA sequencing. Isolated microglia showed a high degree of purity and did not exhibit stress-related markers[16] (Supplementary Fig. 7b,c). RNA sequencing showed major transcriptome changes in microglia associated with Li deficiency in both 3xTg and wild-type mice with highly significant overlap (Supplementary Tables 9–12). Genes upregulated by Li deficiency in 3xTg and wild-type microglia were enriched in GO terms corresponding to AD and pathways of neurodegeneration, electron transport chain and respiration, regulation of amyloid fibril formation, translation and oxidative stress. Genes downregulated by Li deficiency were enriched in the GO terms DNA damage response, cellular response to stress, import into cell and protein catabolic process (Fig. 4a,b and Supplementary Table 12).

Fig. 4: Lithium deficiency activates microglia and impairs Aβ clearance.

a, GO analysis of DEGs shared between Li-deficient (DEF) 3xTg (treatment from 5 to 9 months of age; n = 4 mice per group) and wild-type (WT; treatment from 12 to 20 months of age; n = 4 per group) microglia. b,c, 3xTg mice were fed a DEF or CTRL diet for either 5 weeks (starting at 10.8 months of age; n = 8 per group) or 9 months (starting at 6 months of age; n = 7 per group). Immunolabelling (b, left) of total (Iba1) and activated (CD68) microglia in the hippocampus (9-month treatment). Quantification of CD68+ cell density (b, right) and GPNMB and LPL microglial expression (c) in the hippocampus. d, Cytokine levels in culture medium of primary cortical microglia isolated from WT mice on CTRL or DEF diets from 12 to 18 months of age (n = 3 per group), after stimulation with 50 ng ml−1 LPS. Signals were normalized to internal controls from the cytokine array. Data are mean ± s.d. a.u., arbitrary units. e, Aβ42 uptake (left) and degradation (right) by primary cortical microglia isolated from 18-month-old WT mice after 6 months on CTRL or DEF diets (n = 3 per group). f, Immunolabelling (left) and quantification (right) of GSK3β in Iba1+ microglia in the hippocampus of 3xTg mice after 9 months on CTRL or DEF diets (n = 7 per group). g, Aβ42 uptake (left) and degradation (right) by primary microglia isolated from WT mice fed CTRL or DEF diets from 12 to 16 months of age, and then incubated in culture with the GSK3β inhibitors CHIR99021 (CH) or PF-04802367 (PF) (n = 6 biological replicates per group). In b–g, data were normalized to the mean of CTRL groups. In b,c,e–g, box plots show individual values, median (line), box limits (25th and 75th percentiles) and whiskers (minimum and maximum). P values calculated by unpaired two-tailed t-tests (a–f) or two-way ANOVA with Tukey’s post-hoc test (g). Scale bars, 20 μm.

Source Data

Transcriptome changes in Li-deficient wild-type microglia were enriched for many risk genes for AD identified in genome-wide association studies (GWAS)[17], including Apoe, Trem2, Bin1, Clu, Picalm, Cd33, H2-Eb1 (HLA-DRB1 orthologue), Inpp5d, Abca1, Abca7 and Adam10 (Multi-marker Analysis of GenoMic Annotation (MAGMA), false discovery rate (FDR) < 0.05). We also observed significant overlap of the transcriptome signature of Li-deficient microglia with that of microglia in AD, particularly for microglia that express glycoprotein NMB (GPNMB) (P < 10−21 for 3xTg and P < 10−14 for wild type), which expand with the progression of AD[15]. Furthermore, GPNMB expression was significantly upregulated in Li-deficient microglia (Supplementary Table 11). Thus, Li deficiency alters the microglial transcriptome in a manner that overlaps with AD.

We next examined reactive changes in microglia following Li deficiency. Immunolabelling showed that Li deficiency increased CD68-immunoreactive microglia in 3xTg mice (Fig. 4b) and elevated microglial protein expression of GPNMB and lipoprotein lipase (LPL), which are markers of microglial reactivity in AD[15] (Fig. 4c). Li deficiency also increased the density of CD68+ reactive microglia in a second transgenic AD mouse model, J20 (Supplementary Fig. 7d). To explore functional changes, isolated microglia were stimulated in culture with lipopolysaccharide (LPS). Microglia from Li-deficient wild-type mice showed elevated release of the pro-inflammatory cytokines IL-6, TNF and G-CSF, as well as the immune activating chemokines CCL3, CCL4, CCL5 and CXCL2 (Fig. 4d). Finally, microglia isolated from Li-deficient wild-type mice showed significantly reduced Aβ42 uptake and subsequent degradation of Aβ42 relative to microglia from control mice (Fig. 4e). Thus, Li deficiency leads to a reactive pro-inflammatory state and impaired Aβ clearance.

GSK3β regulation by endogenous lithium

We next identified signalling pathways that are altered by Li deficiency using Ingenuity/IPA network analysis of DEGs. Wnt–β-catenin signalling was significantly affected and was predicted to be repressed in microglia, excitatory neurons and oligodendrocytes (Extended Data Fig. 4a–c). Immunolabelling showed significantly reduced nuclear β-catenin levels in Li-deficient hippocampal CA1 neurons in 3xTg and wild-type mice (Extended Data Fig. 5a,b). Nuclear β-catenin levels were also reduced in Li-deficient oligodendrocytes and microglia (Extended Data Fig. 5c,d).

A central regulator of β-catenin signalling is the serine-threonine kinase GSK3β, which phosphorylates β-catenin, targeting it for proteasomal degradation. Another GSK3β substrate is tau, which is phosphorylated by GSK3β in AD18,19,20,21 and showed 3–4-fold elevated phosphorylation in Li-deficient 3xTg mice (Fig. 2d,e). Li deficiency elevated total GSK3β levels in hippocampal CA1 neurons, oligodendrocytes and microglia in 3xTg mice (Fig. 4f and Extended Data Fig. 5e,f). Elevated total GSK3β protein was confirmed by proteomic analysis of the hippocampus in Li-deficient mice (Supplementary Table 7). GSK3β mRNA was also elevated by Li deficiency (Extended Data Fig. 5g), consistent with increased GSK3β expression.

GSK3β is activated by autophosphorylation of tyrosine 216, which is increased in AD18,21. The levels of pTyr216-GSK3β were significantly elevated by Li deficiency in hippocampal CA1 neurons and oligodendrocytes in 3xTg and wild-type mice (Extended Data Fig. 5h,i). Phosphorylation of GSK3β at Ser9, which inhibits GSK3β activity, did not change in absolute level, but the ratio of pSer9:total GSK3β was reduced, consistent with elevated GSK3β activity (Extended Data Fig. 5j,k). By contrast, the level of inositol, which is modulated by Li at pharmacological concentrations through inositol monophosphatase[22], was not altered by endogenous Li deficiency (Extended Data Fig. 5l).

To assess the role of GSK3β in the pathogenic effects of Li deficiency, the GSK3β inhibitor CHIR99021 was administered to Li-deficient 3xTg mice. Treatment with CHIR99021 reversed the Li deficiency-associated activation of microglia (Extended Data Fig. 6a) and normalized the levels of multiple pro-inflammatory cytokines and chemokines (Extended Data Fig. 6b). Furthermore, incubation of primary microglia from Li-deficient wild-type mice with CHIR99021 resulted in the restoration of Aβ42 uptake and degradation (Fig. 4g). A similar outcome was achieved using a second GSK3β inhibitor, PF-04802367 (Fig. 4g). Moreover, treatment of Li-deficient 3xTg mice with CHIR99021 reversed the elevated Aβ deposition and tau phosphorylation and restored oligodendrocyte cell number and expression of myelin basic protein (MBP) (Extended Data Fig. 6c–e). Thus, GSK3β activation contributes to a broad range of pathology associated with Li deficiency.

Lithium replacement therapy

The observation that Li is sequestered by amyloid deposits in MCI and AD prompted a search for therapeutic Li salts with reduced amyloid binding. We reasoned that the electrostatic interaction of the Li ion with Aβ deposits would be a function of the ionization capacity of the salt, and that Li salts with reduced ionization might show reduced amyloid sequestration. To assess ionization directly, we measured the conductivity of 16 lithium salts. Inorganic Li salts, including the clinical standard lithium carbonate (Li_2CO_3, hereafter LiC), showed significantly elevated conductivity, indicative of increased ionization, relative to organic Li salts (P = 8 × 10−4; Fig. 5a and Extended Data Fig. 7a). Of the organic Li salts, lithium orotate (C_5H_3LiN_2O_4, hereafter LiO) showed the lowest conductance across a broad Li concentration range (Fig. 5a and Extended Data Fig. 7a) and was therefore selected for further comparison with the clinical standard LiC.

Fig. 5: Therapeutic efficacy of a plaque-evading lithium salt.

a, Organic Li salt solutions exhibit lower conductivity than inorganic Li salts. All solutions contained 430 µEq l−1 Li. b,c, Li binds to human Aβ1–42 fibrils (b) and oligomers (c). Binding curves are shown for all tested concentrations (b, left) and the 0–30 µEq l−1 range (b, right). LiC shows higher affinity than LiO (EC_50 values and 95% confidence intervals are in Supplementary Table 13). d, Immunolabelling of Aβ and pSer202-tau in the hippocampus (left) and quantification of plaque burden (middle) and pSer202-tau+ cell density (right) in 3xTg mice treated with LiO or LiC (4.3 µEq l−1) from 9 to 18 months of age (vehicle n = 3, LiC n = 11, LiO n = 13). e, Aβ immunolabelling (left) and quantification (right) in J20 mice treated with LiO (4.3 µEq l−1) from 17 to 22 months of age (water n = 9, LiO n = 11). f, GO analysis of DEGs from RNA-seq analysis of the hippocampus of 3xTg mice treated with LiO (4.3 µEq l−1) or vehicle from 6 to 12 months of age (n = 9 per group). g, Memory retrieval in the Morris water maze for 3xTg mice treated from 5 to 12 months of age; WT mice (12 months) served as controls. WT n = 16, 3xTg n = 25, LiO 4.3 n = 17, LiO 430 n = 16 (left), n = 15 (right), LiC n = 10, NaO n = 9. In d,e, data were normalized to the mean for the water vehicle. In a–c, mean ± s.d. values are shown from n = 3 independent solution replicates (a) or n = 3 biological replicates (b,c). In d,e,g, box plots show individual values, median (line), box limits (25th and 75th percentiles) and whiskers (minimum and maximum). In d,e, P values were calculated by one-way ANOVA with Tukey’s post-hoc test. In g, WT and 3xTg (water) groups were compared using a preplanned unpaired two-tailed t-test; all other P values were derived from one-way ANOVA with Dunnett’s post-hoc comparisons to the 3xTg (water) control. Scale bars, 50 μm.

Source Data

We next investigated whether conductivity predicts Li binding to the aggregated forms of Aβ that accumulate in AD. Equilibrium dialysis binding assays demonstrated that Li binds to both fibrils and oligomers formed from synthetic human Aβ1–42 in vitro (Fig. 5b,c and Extended Data Fig. 7b). Li binding was saturable and occurred in a high-affinity range that included the physiological concentration range of Li in brain and serum (0–2 µEq l−1), as well as a lower-affinity range corresponding to clinical pharmacological doses. Notably, LiC exhibited higher binding affinity than LiO for both Aβ42 fibrils and oligomers across a broad Li concentration range (Fig. 5b,c and Supplementary Table 13).

To further explore the Li–Aβ interaction in vivo, LiO and LiC were administered to J20 and 3xTg mice at a low dose in the drinking water (4.3 μEq l−1 Li), resulting in a serum Li level in the physiological concentration range observed in ageing humans and mice (Supplementary Fig. 8a,c,d, Extended Data Fig. 1c and Methods). Serum and hippocampal Li levels were not significantly different after administration of low-dose LiO or LiC (Supplementary Fig. 8a,b). However, Li was highly concentrated in Aβ plaques after the administration of LiC, but to a much smaller extent after administration of LiO in both 3xTg and J20 mice (Extended Data Fig. 7c,d). Moreover, LiO, but not LiC, significantly elevated parenchymal Li in the non-plaque fraction in 3xTg and J20 mice (Extended Data Fig. 7e,f). Thus, LiO shows reduced amyloid sequestration relative to LiC and more effectively elevates non-plaque Li in the brain.

When LiO was administered to adult 3xTg mice, the physiological dose almost completely prevented Aβ plaque deposition and phospho-tau accumulation; by contrast, administration of LiC or the sodium orotate control had no significant effect (Extended Data Fig. 8a,b). We next investigated whether LiO could reverse more-advanced pathology in ageing mice. Administration of LiO to 3xTg mice from 9 to 18 months of age significantly reduced the Aβ plaque burden and the density of phospho-tau-positive NFT-like structures in the hippocampus, whereas LiC had no significant effect at the same dose (Fig. 5d). LiO also reduced the Aβ plaque burden by about 70% in older J20 mice with abundant and widespread Aβ deposition (Fig. 5e). Thus, LiO is highly effective at reducing Aβ deposition and phospho-tau accumulation.

LiO, but not LiC, increased the expression of the synaptic marker PSD-95 (Extended Data Fig. 8c), increased myelin-associated MBP immunoreactivity and elevated oligodendrocyte cell number (Extended Data Fig. 8d,e). LiO was also more effective than LiC in suppressing microgliosis and astrogliosis in aged 3xTg mice (Extended Data Fig. 8f,g). Administration of low-dose LiO, but not LiC, also reduced total GSK3β levels in hippocampal CA1 neurons and white matter (Extended Data Fig. 9a,b), reduced the level of activated pTyr216-GSK3β (Extended Data Fig. 9c) and elevated nuclear β-catenin (Extended Data Fig. 9d).

RNA-seq analysis of the hippocampus of LiO-treated 3xTg mice showed downregulation of genes corresponding to the GO terms translation, electron transport chain, pathways of neurodegeneration, Alzheimer’s disease, β-catenin degradation and interleukin-1 signalling, and upregulation of genes corresponding to the GO terms synapse organization and signalling, neuron projection morphogenesis and learning or memory (Fig. 5f and Supplementary Tables 14 and 15). These GO terms are similar to those associated with Li deficiency but with opposite directionality of change (Figs. 3c and 4a).

The effects of LiO on genes involved in learning and memory prompted us to explore cognitive function in 3xTg mice, which show memory loss relative to wild-type mice (Fig. 5g). LiO at the lowest dose (4.3 μEq l−1) almost completely reversed the memory loss, whereas LiC and the sodium orotate control did not show significant effects (Fig. 5g). Furthermore, LiO improved learning and spatial memory in ageing J20 mice with advanced amyloid pathology (Extended Data Fig. 10a–c). LiO did not significantly affect swimming speed, visual platform localization or locomotor performance in the open-field test (Extended Data Fig. 10d–h and Supplementary Fig. 9a–f). Thus, LiO suppresses AD-type pathology, neuroinflammation and synapse loss, and restores memory.

Lithium and brain ageing

To explore the effects of Li on normal brain ageing, low-dose LiO (4.3 μEq l−1 Li) was administered to wild-type mice from 12 to 24 months of age. This resulted in a modest elevation of mean serum and cortical Li levels that overlap with the range of endogenous Li in untreated mice (Supplementary Fig. 10a). LiO almost completely prevented age-related microgliosis and astrogliosis in the hippocampus, cortex and corpus callosum (Extended Data Fig. 11a,b). Moreover, LiO reduced the age-related production of the pro-inflammatory cytokines IL-6 and IL-1β (Extended Data Fig. 12a).

Microglia isolated from aged mice showed a marked reduction in the ability to degrade Aβ42 relative to microglia from young adult mice. Treatment with LiO in vivo reversed this age-related loss of Aβ degradative capacity (Extended Data Fig. 12b). Similar results were obtained by incubating microglial BV2 cells with LiO in culture. LiO significantly elevated Aβ42 uptake and degradation in BV2 cells, whereas the control sodium orotate had no significant effect (Extended Data Fig. 12c–e). Thus, LiO reduces age-related neuroinflammatory changes and restores the ability of microglia to clear Aβ.

Synapse loss and cognitive decline are characteristic features of brain ageing in mice. Administration of LiO to wild-type mice prevented age-related loss of dendritic spines in CA1 and CA3 hippocampal neurons, whereas the control salt NaO had no significant effect (Supplementary Fig. 10b). Importantly, the decline in learning and memory associated with ageing was largely reversed by LiO, as determined by tests in the Morris water maze (Extended Data Fig. 13a,b). LiO did not affect swimming speed or localization of a visible platform (Extended Data Fig. 13c,d). LiO also prevented age-related decline in novel-object recognition memory (Extended Data Fig. 13e). Notably, long-term administration of LiO to ageing wild-type, 3xTg or J20 mice did not alter serum levels of blood urea nitrogen, creatinine or thyroid-stimulating hormone (TSH) (Supplementary Fig. 11). Thus, low dose LiO prevents age-related pro-inflammatory changes, synapse loss and cognitive decline in mice without evidence of toxicity.

These observations prompted an examination of endogenous brain Li and cognitive resilience in normal ageing humans. Expression levels of the presynaptic proteins complexin 1 and 2, which regulate synaptic vesicle exocytosis, predict resistance to AD23,24. Complexin 1 and 2 expression showed a highly significant positive correlation with Li cortex-to-serum ratio in aged individuals without MCI or AD (Extended Data Fig. 13f). Furthermore, cortical Li was positively correlated with cognitive test scores for working memory (P = 0.04) and performance on the Mini Mental State Examination (MMSE; P = 0.02). Together, these results in normal ageing mice and humans indicate that Li homeostasis may contribute to cognitive resilience.

Discussion

These observations indicate a physiological role for endogenous Li that affects brain ageing and vulnerability to AD. In humans, Li is used in psychiatry for the treatment of bipolar disorder at a dose range that raises levels in serum to approximately 1,000 times the endogenous level. We found that in normal ageing mice, low micromolar levels of endogenous Li preserve cognitive function, reduce inflammation and suppress Aβ generation. In AD mouse models, endogenous Li protects against amyloid deposition, tau hyperphosphorylation, neuroinflammation and loss of synapses, axons and myelin. These effects are mediated, at least in part, through repression of the kinase GSK3β in multiple cell types in the brain.

Metallomic profiling of the brain also uncovered alterations in other metals that have been previously observed in AD, such as increased sodium[25] and zinc[26] and reduced copper[12]. However, decreased cortical Li was the only statistically significant metal alteration observed in both MCI and AD in our dataset. This observation is consistent with a population study in Denmark that found a significant inverse correlation between Li levels in local drinking water and the incidence of dementia[27]. We were able to recapitulate the reduced Li levels observed in humans with AD in mouse models with a Li-deficient diet. snRNA-seq showed that reduced cortical Li significantly alters the transcriptome of the major brain cell types. Furthermore, DEGs associated with Li deficiency in the mouse models overlapped with DEGs previously identified in snRNA-seq of human brain biopsy samples with AD pathology[15]. Overlapping DEGs were enriched in microglia, excitatory and inhibitory neurons, OPCs, oligodendrocytes, endothelial cells and astrocytes. Consistent with these transcriptome alterations, Li deficiency resulted in deleterious effects on neurons, microglia and oligodendrocytes with loss of synapses and axons, impaired Aβ clearance and reduced myelination.

Li deficiency altered microglial expression of some of the most penetrant risk-factor genes identified in GWAS studies of AD, including Apoe, Trem2, Bin1, Picalm, Clu, Cd33 and the mouse orthologues of human MS4A6A[17]. These expression changes were associated with elevated markers of microglial activation such as CD68, as well as increased production of multiple pro-inflammatory cytokines and chemokines that are also elevated in AD[28]. Furthermore, Li deficiency impaired the ability of microglia to phagocytose and degrade Aβ, a phenotype that has been linked to Aβ deposition in AD[29]. These findings indicate that endogenous Li maintains microglial homeostatic function and prevents pro-inflammatory changes associated with AD.

One of the first molecular targets of Li to be characterized at pharmacological doses was the kinase GSK3β[30]. GSK3β activity is increased in AD and has been implicated in Aβ and tau pathology18,20,21,31. Moreover, the GSK3β substrate β-catenin is reduced in AD18,32,33. The reported IC_50 of the Li-GSK3β interaction in vitro is in the millimolar range[30], making this a seemingly unlikely interaction at the low micromolar concentration range of endogenous Li in the brain. However, our findings indicate that GSK3β activation and expression are elevated by endogenous Li deficiency. Moreover, GSK3β inhibitors can reverse many of the pathological consequences of Li deficiency, including Aβ deposition, phospho-tau accumulation, myelination and microglial pro-inflammatory activation, as well as restoring the ability of microglia to clear Aβ. Previous reports have shown that GSK3β activation can promote cytokine production in monocytic and microglial cells[34] and impair oligodendrocyte differentiation and myelination by inhibiting β-catenin signalling[35]. Together, our findings implicate increased GSK3β activity in the multisystem effects of Li deficiency in the brain.

Treatment with Li at pharmacologic doses has been shown to reduce Aβ33,36,37,38,39,40,41,42,43,44,45 and tau37,38,43,46,47,48,49 pathology in various neurodegenerative disease models. Similarly, Li prevented or reversed cognitive decline in several studies36,37,38,39,43,44, but not in one short-term study[47]. More direct evidence for a therapeutic role of Li in AD emerged from several small clinical trials. In two initial trials50,51, Li treatment did not improve cognitive function, but in three subsequent trials, Li at lower concentrations (0.25–0.5 mEq l−1 in serum) reduced cognitive decline52,53,54,55. A limitation of these clinical trials might have been the use of Li salts with high levels of amyloid binding. We have characterized a Li salt, lithium orotate, with reduced binding that can bypass amyloid sequestration in AD mouse models. Treatment with LiO at a dose that maintains serum and cortical Li levels in the endogenous range prevents and reverses AD pathology, neuroinflammatory changes and memory loss in AD mouse models and ageing wild-type mice. An important limitation in the treatment of aged individuals with pharmacological doses of lithium is kidney and thyroid toxicity[56]. It is encouraging that toxicity could not be detected following long-term treatment of ageing mice with a low dose of LiO.

Disruption of Li homeostasis may contribute to the long prodromal period of neuropathological changes that occur prior to the onset of clinical AD. Our findings indicate that sequestration of Li by amyloid depletes Li in affected brain regions. Li depletion can, in turn, impair microglial clearance of Aβ, which would accelerate amyloid pathology in a positive feedback loop. In parallel, Li deficiency may promote phospho-tau accumulation, inflammation and the loss of synapses, axons and myelin. The progression of this neurodegenerative process may be modulated by genetic risk variants17,57, as well as environmental factors and dietary Li intake. Li deficiency is therefore a potential common mechanism for the multisystem degeneration of the brain that leads to the onset of AD.

Methods

Human brain samples

Post-mortem human brain and serum samples were obtained in accordance with institutional guidelines and with approval from the Harvard Medical School Institutional Review Board. All procedures complied with relevant ethical regulations. All post-mortem human brain and serum samples were fully deidentified before receipt, and no identifiable private donor information was accessible to the researchers. As such, informed consent was not applicable. Frozen post-mortem samples from the prefrontal cortex (BA9/10/47) were available for all cases included in the analysis. Cerebellar tissue and the most recently collected pre-mortem serum samples were available for a subset of individuals. The primary analysis was performed on tissue samples procured from the Rush Alzheimer’s Disease Center, derived from participants in the Religious Orders Study (ROS) or Rush Memory and Aging Project (MAP) (referred to as ROSMAP). The ROSMAP is a longitudinal, clinical–pathological study of ageing, cognitive decline and AD[58]. Study participants agreed to comprehensive annual clinical and neuropsychological evaluation and brain donation at death. To assess cognitive function, 21 cognitive-function tests were used, 19 were in common and 11 were used to inform on clinical diagnoses, as previously described59,60. The follow-up rate exceeded 95% and the autopsy rate exceeded 90%. All individuals who underwent autopsy were subject to a uniform structured neuropathological evaluation of AD. Informed consent, an Anatomic Gift Act and a repository consent were obtained and the studies were approved by an Institutional Review Board of Rush University Medical Center. A second set of frozen frontal cortical brain samples was obtained from brain banks at the Massachusetts General Hospital, Duke University and Washington University, and is referred to as “a second independent cohort”. Brain tissue obtained from these sources had a confirmed pathological diagnosis of AD or NCI. Samples were randomly selected by the source institutions based on tissue availability and alignment with the requested diagnostic categories (NCI, MCI and AD). Within each diagnostic group, samples were matched for age and sex to ensure group comparability.

Absolute and relative metal levels were measured by ICP–MS, with relative levels calculated as the ratio of cortical or cerebellar to serum concentrations from the same individual. Post-mortem interval had no significant effect on total or relative Li levels in this cohort. The study population comprised 40.2% male individuals and 59.8% female individuals. Within diagnostic subgroups, NCI cases comprised 40.8% male individuals and 59.2% female individuals; MCI cases, 42% male individuals and 58% female individuals; and AD cases, 36.4% male individuals and 63.6% female individuals. Individuals of both sexes were analysed, and those with MCI and AD, regardless of sex, exhibited significantly reduced cortical-to-serum Li ratios and lower total cortical Li levels. Donor sex was self-reported and provided by Rush Medical Center (ROSMAP study) and by further tissue sources, including Massachusetts General Hospital, Duke University and Washington University.

Isolation of plaque-enriched and non-plaque fractions

To fractionate brain parenchymal homogenates into amyloid plaque-enriched and non-plaque fractions, we modified a previously described protocol61,62. Frozen brain samples were weighed and then Dounce-homogenized (40 strokes per sample) in 5 volumes (v/w) of ultrapure buffer containing 2% SDS (stock of ultrapure SDS 10%, ThermoFisher Scientific, 24730020) and 0.1 M β-mercaptoethanol (VWR, 97064-878) in 50 mM Tris HCl, pH 7.6 (ultrapure Tris-HCl, pH 7.5, Invitrogen, 15567-027) and water (Aristar Ultra, VWR 87003-236). The Li concentration of the complete buffer was below the detection threshold (<0.02 µg l−1). The homogenates were heated at 100 °C for 10 min and then transferred to a 15-ml Falcon tube fitted with a sieve consisting of woven mesh (polyethylene terephthalate) with a pore size of 100 µm (pluriSelect, SKU 43-10100-60). The samples were passed through the sieve by gravity and the filtrate was then centrifuged (300g for 30 min). The supernatant (soluble non-plaque fraction) was removed and stored at −80 °C. The pellet was resuspended in water at a ratio of 5 ml per gram of pellet mass and stored at –80 °C (plaque-enriched fraction). To image subfractionated Aβ and phospho-tau (Supplementary Fig. 1), 10 μl of the freshly collected plaque-enriched and non-plaque fractions was layered onto albumin-coated glass slides and allowed to dry overnight. They were then washed with ultrapure PBS (which we determined contained less than 25 parts per trillion (ppt) Li) and incubated with a rabbit monoclonal anti-Aβ antibody (Cell Signaling, 8243) and a mouse monoclonal antibody to pSer202-tau (clone CP13) overnight in 2% BSA, 0.1% Triton X-100 in PBS, followed by labelling with secondary anti-rabbit IgG coupled to Alexa Fluor 594, or anti-mouse IgG coupled to Alexa Fluor 488 (1:300 in blocking buffer). The slides were then washed three times in ultrapure PBS and mounted.

ICP–MS

For the analysis of metals in human and mouse biological samples, we modified previous protocols to optimize the detection of ultra-trace elements. We tested several protocols and found that the use of precleaned polyvinylidene difluoride (PVDF) vials fitted with perfluoroalkoxy alkane (PFA) caps, the use of ultra-trace grade reagents (nitric acid, hydrogen peroxide and water), combined with an extended sample digestion and homogenization, and a highly sensitive ICP–MS instrument (PerkinElmer NexION 2000C), allowed the robust detection of ultra-trace metals in human and mouse samples. The commercial precleaned PVDF vials (Elemental Scientific, V-14-0712-C) and PFA caps (Elemental Scientific, V-14-0309-C) were further processed by fully immersing them in 10% trace-grade nitric acid (Fisher Chemical, A509-P212) for at least 48 h, followed by abundant rinsing with double-distilled and deionized water and drying in a chemical hood for 48 h. The chemical hood was thoroughly cleaned before the experiment and was used exclusively for ICP–MS for the entire duration of the experiment to prevent contamination. We also used a protocol allowing for the simultaneous analysis of a large number of human brain samples (approximately 80–120 mg frozen brain material per region per case). First, we determined that the dry-to-wet ratio was unchanged in AD versus NCI. This was established in n = 45 NCI and n = 45 AD frozen cortical samples (100–200 mg per sample) that were weighed and then dried to a constant weight (48 h in a dry oven at 60 °C). The dry-to-wet ratios were 0.127 ± 0.048 for NCI and 0.123 ± 0.034 for AD and were not statistically different (P = 0.67), in agreement with previous work[63].

The frozen cortical and cerebellum samples were first allowed to thaw, and were then weighed and digested in 5 volumes of nitric acid 67% (w/m, relative to wet mass; BDH Aristar Ultra, VWR, 87003-226) for 72 h with regular vortexing (20 s per vial every 12 h). The samples were fully digested after about 36 h. The serum, the brain non-plaque fractions and the aqueous solutions were digested in an equal volume of nitric acid (67%) for 48 h with regular vortexing (20 s per vial every 12 h). After digestion with nitric acid, hydrogen peroxide (30%; BDH Aristar Ultra, VWR, 87003-224) was added for 24 h with regular vortexing (20 s per vial every 12 h). We added one volume of hydrogen peroxide (w/m, relative to starting wet mass) to digested brain tissues and 0.75 volumes (relative to starting sample volume) to digested serum, non-plaque fractions and aqueous solutions. The samples were then diluted using a 2% nitric solution in ultrapure water (BDH Aristar, VWR, 87003-236). Indium was added to each solution as an internal standard (50 parts per billion; ppb). For all ICP–MS runs, we also measured freshly made solutions of element standards (0, 10 ppt, 50 ppt, 100 ppt, 1 ppb, 10 ppb and 50 ppb) using a 30-element ICP standard (Aristar, VWR, 89800-580). Each run included n = 10 digestion blanks as well as n = 20–30 blank measurements to calculate the detection limits. The samples were injected into a PerkinElmer NexION 2000C ICP–MS instrument fitted with a cross-flow nebulizer and peristaltic pump for sample introduction. The sample delay time was 30 s with a pump speed of 24 rpm. A wash solution of 2% nitric was used between analyses of samples. The human cortex, cerebellum and serum samples were each measured twice on two consecutive days (two technical replicates per sample) and the average value was obtained for each sample. The correlation coefficients between the lithium concentrations measured on day 1 and day 2 were r > 0.99 for frontal cortex, cerebellum and serum, showing that the ICP–MS measurement was highly reproducible. After each run, ICP–MS signal processing was done using GeoPro 2010 Software (Cetac Technologies). We derived the standard curves for each element, calculated the concentration of each element in the diluted solution, and used the dilution factors to derive elemental abundance in the original samples. Li levels in the cortex and cerebellum are reported per unit of wet weight (Fig. 1d,e, Extended Data Fig. 1b and Supplementary Table 1). Limits of detection (LODs) and limits of quantification (LOQs) were calculated as follows: LOD = YB + 2tSB and LOQ = YB + 10SB, where YB is the average blank signal, t is the critical value of the one-tailed t-test (one-tailed, 95% confidence interval; for example, for 27 blank samples, df = 26 and t = 1.706) and SB is the standard deviation of a blank signal. LOD and LOQ values for all metals can be found in Supplementary Table 1. All individual Li measurements in human samples (prefrontal cortex, cerebellum and serum) were above the LOQ. In recovery experiments, wet brain samples or fluids were spiked with lithium standard added at three levels (n = 7 replicates per spiking level). The recovery of Li from spiked samples ranged from 91% to 105%. All human sample measurements were double-blinded: one lab member not involved in the study relabelled the samples and kept a file with the old and new codes. After the ICP–MS measurements, the samples were unblinded in the presence of the researchers involved in the study, as well as the lab member who was not involved in the study.

The ICP–MS findings from post-mortem human samples were replicated as follows. First, reduced Li content in the cortex of patients with AD was observed using two independent methods, after measurement of total Li levels in frozen cortical material of cases from both ROSMAP (Fig. 1d) and other sources (Fig. 1e), as well as after fractionation and removal of amyloid plaques (Fig. 1g). Second, decreased Li levels in the AD versus NCI prefrontal cortex (P = 2 × 10−3) were also independently confirmed when n = 60 NCI and AD cases were processed and analysed by ICP–MS in a different laboratory (the Spectroscopy Core Facility at the University of Nebraska, Lincoln). Third, decreased Li levels in the AD versus NCI prefrontal cortex (P = 3 × 10−3) were also confirmed when n = 48 NCI and AD cases were processed using an alternative protocol. Frozen samples were thawed and dried to a constant weight by incubating in a dry oven at 60 °C for 48 h. The dried tissue was then digested in 1 ml of 67% nitric acid using a heating block at 95 °C for 3 h. After digestion, 0.3 ml of 30% hydrogen peroxide was added and the mixture was heated for a further 3 h. Finally, the samples were diluted and analysed using ICP–MS.

Li levels measured in the PFC of ageing NCI cases (ROSMAP cases: mean 2.36 ± 1.23 ng per g, range 0.52–6.0 ng per g; non-ROSMAP cases: mean 3.50 ± 2.27 ng per g, range 0.89–9.94 ng per g; Fig. 1d,e) were similar to those measured in a previous study[64] (4.1 ± 1.7 ng per g in the prefrontal cortex of aged non-diseased cases; age, 71 ± 12 years). Similarly, Li levels measured in the cerebellum (ROSMAP cases: mean 2.90 ± 1.69 ng per g, range 0.58–8.40 ng per g; Extended Data Fig. 1b) were similar to those measured in the previous study[64] (2.9 ± 1.3 ng per g). Finally, consistent with previous studies, we observed significantly elevated levels of sodium[25] and zinc[26], along with reduced copper12,65 levels, in the AD cortex (Fig. 1a,b and Supplementary Table 1).

LA-ICP–MS

The Li composition in the human and mouse brains in situ was analysed using LA-ICP–MS. Frozen human and mouse brains were first embedded in OCT medium and then sectioned using a cryostat, and the resulting sections (80 μm thick) were mounted onto glass slides. Before data acquisition, the samples were placed vertically in a rack and air-dried for 1 h. The LA-ICP–MS spectrometer consisted of a laser ablation system (213 nm Nd:YAG, Cetac Technologies) connected to a Perkin Elmer NexION 2000C ICP–MS (Perkin Elmer). Using the line tool, we manually selected the area to be ablated. For human samples, we ablated a region of the prefrontal cortex. For mouse samples, we processed coronal sections where the cortex and hippocampus were readily identifiable. The analyte signal was collected using multiple parallel line scans along the entire selected area, progressing in the direction of ablation cell gas flow, using a spot size of 200 µm at 75 µm s−1. The laser operated at an energy level of 70% and a pulse repetition rate of 20 Hz. The typical run time for one sample was about 4–5 h. We also ablated parts of each section that did include brain tissue but contained embedding medium (OCT) and subtracted this background signal from the total signal. Levels of 7Li were normalized to carbon (12C) to correct for any variations in the amount of tissue ablated. Similar conclusions were reached when the analysis did not include normalization to 12C. Matrix-matched standards were obtained by spiking homogenized samples of human or mouse tissue with three different concentrations of metal standard solution containing the analytes of interest. After homogenization, the mixtures were frozen and 80-μm sections were cut using the cryostat. The final concentrations of these standards were validated by ICP–MS. After LA-ICP–MS data acquisition, signal processing was done using Iolite Software 2018 (Iolite). A Li distribution matrix was generated computationally, using the multiple parallel line rasters. To identify the regions occupied by amyloid plaques, the section immediately adjacent to the section analysed by LA-ICP–MS was processed for Aβ immunofluorescence. In brief, the adjacent section was first fixed with 4% PFA for 2 h then washed three times with PBS. The section was then blocked for 1 h with 2% BSA, 2% fetal bovine serum, 0.1% Triton X-100 in PBS. The anti-Aβ primary antibody (Cell Signaling, 8243), diluted 1:250 in blocking buffer, was then added and the section was incubated overnight at 4 °C. The next day, the section was washed three times with PBS (in total, 30 min), and a secondary anti-rabbit Alexa 594 antibody (diluted 1:300 in blocking buffer) was added for 3 h. The section was finally washed three times with PBS (for 30 min) and mounted. We acquired multiple pictures of Aβ immunofluorescence spanning the entire section using an Olympus FV3000 confocal microscope. The images were then stitched together and imported into Iolite, where the distribution of Aβ immunofluorescence was computationally superimposed on the LA-ICP–MS Li distribution matrix. For each human or mouse sample, we manually selected multiple regions containing Aβ plaques (plaque or ‘P regions’) as well as neighbouring regions devoid of plaques (non-plaque or ‘NP regions’).

The mean Li levels in P and NP regions were determined, and after correcting for background and normalizing to 12C, the P:NP ratios were calculated. Three other isotopes were also assessed: 57Fe, 63Cu and 66Zn. All measurements in P and NP regions exceeded the LOQ, which was 0.82 ng per g for 7Li, 0.23 µg per g for 57Fe, 0.44 µg per g for 63Cu and 55.1 ng per g for 66Zn). As positive controls, 57Fe, 63Cu and 66Zn were all enriched in plaques relative to non-plaque regions in the AD brain, consistent with previous observations[66].

Lithium salts

LiO was obtained from Innophos Nutrition and LiC was from Rockwood Lithium. The purity and Li content were verified by mass spectrometry and ICP–MS, respectively. Sources for other Li salts used in conductivity assays are provided in Supplementary Table 16.

Li salts were dissolved in distilled, deionized drinking water and administered ad libitum to mice. The low Li dose corresponded to 4.3 μEq l−1 (equivalent to 0.03 mg (30  µg) of elemental Li per litre). The background Li concentration in the water was minimal (0.109 µg l−1). Solutions of 4.3 µM LiO and 2.15 µM LiC were prepared to deliver equivalent amounts of elemental Li, accounting for the two Li atoms per molecule of LiC (Li_2CO_3). A 4.3 µM sodium orotate (NaO) solution was also prepared to assess the effects of the orotate anion in the absence of Li. Two more Li doses were also tested: 43 µEq l−1 (delivered as 43 µM LiO) and 430 µEq l−1 (delivered as 430 µM LiO or 215 µM Li_2CO_3). To control for the orotate anion at the high dose, a 430 µM NaO solution was also tested. Average daily water consumption was comparable across all treatment groups and the vehicle (water-only) group. To evaluate Li uptake and its biological effects in the brain, mice received the Li-containing water for defined periods. Animals were randomly assigned to treatment and control groups, with control mice receiving plain drinking water.

Conductivity measurements

To measure the conductivity of Li salts, the salts were dissolved in water to achieve Li concentrations of 4.3 mEq l−1, 430 μEq l−1, 43 μEq l−1 or 21.5 μEq l−1 in each case. Conductivity was measured using an ST300C conductivity meter (OHAUS, 83033964) equipped with a STCON7 electrode (OHAUS, 30080693) calibrated with potassium chloride conductivity standards. For each lithium salt, three independent solution replicates (n = 3) were prepared. Conductivity values are reported in μS per cm at 25 °C.

In vitro binding of lithium to Aβ

To assess the in vitro binding of Li to Aβ, both oligomeric and fibrillar forms of Aβ42 were prepared. Human Aβ1–42 peptide (1 mg) was initially dissolved in 80 μl of 1% NH_4OH then diluted with PBS to a final concentration of 1 mg ml−1 (stock solution) and stored at −80 °C. Oligomeric Aβ42 was generated by resuspending the stock solution in PBS followed by overnight incubation at 4 °C. Fibrillar Aβ42 was obtained by incubating the same stock at 37 °C for 72 h. For Li binding assays, 10 µg of either oligomeric or fibrillar Aβ42 (10 µl of the 1 mg ml−1 stock) was added to 90 µl of Li-containing solutions. These solutions included varying concentrations of either LiO or LiC, matched for Li content and dissolved in ultrapure water (BDH Aristar, VWR, 87003-236). Ultrapure water alone served as the negative control. Samples were incubated at 37 °C for 16 h. After incubation, the mixtures were transferred to dialysis membranes for 24 h to remove unbound Li (Pur-A-Lyzer mini dialysis kits were used: 6–8 kDa cut-off for oligomers and 25 kDa for fibrils). After dialysis, the samples were transferred into precleaned PVDF vials and digested by adding an equal volume of 67% nitric acid (final volume, 200 µl), followed by a 24-h digestion period. The digested samples were then diluted to 800 µl with 2% nitric acid prepared in ultrapure water. Li content was quantified using a PerkinElmer NexION 2000C ICP–MS instrument. Elemental Li standards were prepared and standard curves showed excellent linearity (r > 0.99). The bound 7Li levels were calculated across a range of Li salt concentrations, and binding curves were plotted using GraphPad Prism (v.9.4.1). Binding affinities (EC_50) and 95% confidence intervals for LiO and LiC were determined using nonlinear regression analysis ([agonist] versus response–variable slope, four-parameter model; Supplementary Table 13). Binding to Aβ42 oligomers and fibrils was modelled across the full concentration range (0–500 μEq l−1) as well as within the higher-affinity subranges (0–50 μEq l−1 for oligomers and 0–30 μEq l−1 for fibrils; Supplementary Table 13).

Mice

Animal housing and experimental procedures were approved by the Institutional Animal Care and Use Committee of Harvard Medical School. All mice were housed socially (2–4 animals per cage) in a room with a 12 h:12 h  light:dark cycle (lights on at 06:00), controlled for temperature (18–22 °C) and humidity (40–60%). Sentinel mice housed in each rack were tested quarterly and confirmed to be free of pathogens. All cages were individually ventilated. The standard diet 5053, as well as the chemically defined control and Li-deficient diets, were irradiated. Reverse osmosis deionized water and deionized water containing LiO, LiC or NaO was provided ad libitum in bottles that were changed at least weekly.

Wild-type mice were on a C57BL/6J background. We analysed both adult (3–6 months old) and aged (up to 26 months old) wild-type mice, treated for varying durations. The 3xTg mice[14] carried APPSwe and tauP301L mutant transgenes, as well as a PS1 knock-in mutation, and were in a hybrid C57BL/6J and 129Sv/Ev background. The J20 mice[13] transgenic mice expressed a mutant form of the human amyloid protein precursor bearing both the Swedish (K670N/M671L) and the Indiana (V717F) mutations (APPSwInd) in a C57BL/6J background. For breeding, 10–20 females (all litter-mates derived from the same cross) were typically mated with 8–12 males (all litter-mates derived from the same cross). Mice were identified by numbered ear tags and were randomly selected for behavioural and histological analyses.

To assess treatment effects on disease onset and progression, animals were treated either before pathology emerged (5–6 months old for 3xTg; 3 months old for J20) or after pathology was established (starting at 9 months old for 3xTg and 17 months old for J20). To investigate age-related effects in wild-type mice, chronic treatments were initiated in adulthood (10–12 months old) and continued for 10–14 months during ageing. Experiments included both sexes, and results were consistent between males and females. The number and sex of animals used in each experimental group can be found in the Source Data file. Investigators remained blinded to genotypes and treatment conditions throughout data collection and analysis. No prior sample-size calculations were done, but the number of animals used was consistent with similar studies in the field.

Mouse diet

Li levels in the cortex were comparable between human NCI cases (RUSH cohort: range 0.52–6.0 ng per g; non-RUSH cohort: range 0.89–9.94 ng per g) and mice (wild type and J20: range 1.61–4.59 ng per g). Similarly, serum Li levels in human NCI cases (range 1.53–10.41 ng ml−1) overlapped with those in mice (wild type, J20, 3xTg: range 0.75–4.50 ng ml−1), supporting the relevance of mouse models for studying the biological effects of lithium.

The regular mouse 5053 is a grain-based diet that does not allow Li levels to be manipulated experimentally. To obtain a Li-deficient diet, we used a standard, chemically defined mouse AIN-93M diet that is calorically and nutritionally equivalent to the 5053 diet and was formulated as a standard diet for laboratory rodents by the American Institute of Nutrition in 1993. We tested 5 samples of the regular mouse 5053 diet and 5 samples of the AIN-93M diet and found that the average Li content was 104.8 ng per g in the 5053 diet and 103 ng per g in the AIN-93M diet. The AIN-93M chemically defined diet was modified to exclude Li. The Li-deficient and control AIN-93M diets were formulated by Dyets. We measured Li levels in the Li-deficient diet and confirmed that Li was depleted by 92.0% relative to the chemically defined control diet. The abundances of the other 26 metals that we measured by ICP–MS were identical (data not shown). The solid diets were irradiated before administration to animals. The diets were stored in closed plastic bags that were placed inside cardboard boxes (devoid of light) at −20 °C for up to 4 months before administration to animals.

DNA extraction and genotyping by PCR

We collected about 0.5–1.0 cm of mouse tails in clean Eppendorf tubes; 500 μl of tail lysis buffer (10 mM Tris pH 8, 100 mM NaCl, 10 mM EDTA, 0.5% SDS) containing 0.4 mg ml−1 Proteinase K was added to each tube, and the tubes were incubated overnight in a 56 °C water bath. The next day, 500 μl of isopropanol was added to precipitate the DNA, and the tubes were shaken vigorously for 20 s. Tubes were centrifuged for 10 min at 18,000g and the isopropanol was carefully removed, avoiding the DNA pellet. We then added 70% ethanol and shook the tubes to wash the DNA pellet. We next centrifuged the tubes for 10 min at 18,000g. We removed the ethanol and air-dried the DNA pellet for 2–16 h. The DNA was resuspended in 100 μl acetate-EDTA buffer and placed in a 56 °C water bath overnight. To amplify DNA regions by PCR, we mixed 3 μl of DNA sample with corresponding amounts of forward and reverse PCR primers, PCR master mix and nuclease-free water, and ran the reactions in a thermocycler. Sample loading dye was added to the PCR products and the samples were run on 1–3% agarose gels (prepared by dissolving agarose in TAE buffer, to which Gel Red was added to allow DNA visualization). We also loaded a 100-bp DNA ladder. Gels were visualized using a UV transilluminator.

Quantitative RT–PCR

Total RNA was extracted from cells and tissues using TRIzol reagent (Invitrogen) followed by DNase treatment to remove genomic DNA contamination. Primers were obtained from Harvard’s PrimerBank: for mouse Gsk3b, forward 5′-TGGCAGCAAGGTAACCACAG-3′ and reverse 5′-CGGTTCTTAAATCGCTTGTCCTG-3′; for mouse Gapdh, forward 5′-CTTTGTCAAGCTCATTTCCTGG-3′ and reverse 5′-TCTTGCTCAGTGTCCTTGC-3′. Real-time PCR was performed for 40 cycles. The specificity and purity of PCR and RT–PCR products were confirmed by the presence of single-peak melting curves.

GSK3β inhibitor treatment

Li-deficient and control 3xTg mice 12 months old, maintained on their respective diets for three months, were treated with the GSK3β inhibitor CHIR-99021 or a vehicle control. A stock solution of CHIR-99021 was prepared in DMSO and diluted in 0.9% saline to a final concentration of 10 mg ml−1, containing 2% DMSO. The solution was warmed to 70 °C to ensure dissolution of the compound. Mice received intraperitoneal injections of CHIR99021 at a dose of 50 mg per kg body weight, once daily for 14 consecutive days. Control animals received equivalent volumes of vehicle (2% DMSO in saline). All animals tolerated the treatment without visible abnormalities and were included in the analysis.

Blood chemistry

BUN and creatinine measurements were done by IDEXX Laboratories, using mouse serum samples. TSH levels in the mouse serum were assessed by ELISA (Elabscience, E-EL-M1153).

Behavioural testing

Open field

Mice were placed in an open field box (75 cm × 75 cm) and movements were tracked in real-time using TopScan Lite software (CleverSys) coupled to a camera. Each mouse was recorded for 10 min, and the average speed and distance travelled were automatically recorded. Mice had no prior exposure to the open-field arena (spontaneous test). All behavioural experiments were performed by researchers who were blinded to the experimental conditions.

Morris water maze

To assess spatial learning and memory, we trained and tested mice in a large circular pool (1.1 m in diameter) filled with 21 °C water, which was rendered opaque by the addition of non-toxic white paint. We placed four distinct visual cues (representing different geometric shapes, patterns and colours) on each wall, to facilitate spatial orientation and the acquisition of spatial memory. Mice were given four training trials a day for 5–7 consecutive days. Each training trial lasted for 1 min. Mice were trained to remember the location of a hidden platform that was submerged 2.5 cm below the water surface. The location of the hidden platform (south-east) remained the same during the 5–7-day training period. If, after a 60-second trial, the animal failed to locate the platform, it was placed on the platform and allowed to remain on the platform for 15 s. Mice were trained four times a day and entered the pool in a randomized order of rotating entrance points (compass directions N, S, E, W, NE and SW). During each training trial, the latency to find the hidden platform was recorded. Then, 24 h after the last training trial, a probe trial was conducted. The platform was removed and mice entered the arena from the NW location (opposite from the platform). The number of entries in the target area (representing the area where the platform had been located during the training trials), the total time spent in the target area, as well as the time spent in all quadrants, and the swimming speed were recorded during the 60-s probe trial. We also conducted separate trials in which a visible platform (platform elevated above the water level, on which a small red flag had been placed) was presented. Mice were given several training sessions and the time (latency) to reach the visible platform was recorded. Mouse movements, as well as average speed, distance travelled, latency to reach a quadrant or target area and number of entries in the target area, were tracked in real time using TopScan Lite software (Clever Sys) and the different measures were automatically recorded. For measurements of learning (latency to reach the platform during the training trials), mice underwent repeated measurements (four measurements a day for 6–7 consecutive days).

Novel-object recognition

Mice were placed in the same open-field box with two novel identical objects for 10 min and allowed to freely explore the identical objects. The next day, mice were reintroduced in the open-field box and presented with a novel object, as well as one of the two objects they explored the previous day. The mice were allowed to explore the objects for 10 min and their movements were tracked in real time using TopScan Lite software (Clever Sys) coupled to a camera. The box and items were cleaned with 70% ethanol between mice. We automatically recorded the time each mouse spent exploring each object, on both day 1 (two identical objects) or day 2 (one novel object and one familiar object), and derived a novelty (discrimination) index, defined as the ratio of time spent exploring the novel object relative to the familiar one.

Y maze

Spontaneous alternation, which is a measure of spatial working memory, was assessed by allowing the mice to freely explore a Y-shaped maze for 8 min. The Y maze consisted of 3 arms (each 40 cm × 8 cm x 15 cm) at an angle of 120° from each other. Mice typically preferred to investigate a new arm of the maze, rather than returning to one that was previously visited. Using TopScanLite software, we recorded each entry in one of the three arms (A, B and C) and then derived the percentage of total correct alternations over the 8-min duration of the trial. A correct alternation (triad) is a succession of entries into three different arms (A–B–C, A–C–B, B–A–C, B–C–A, C–A–B or C–B–A).

Mouse neuropathology

Mice were anaesthetized with isoflurane and carbon dioxide and then perfused with PBS at 4 °C for 20 min. Brains were rapidly removed and the two hemispheres were separated. One hemisphere was dissected into subregions (frontal cortex, temporal cortex, occipital cortex, hippocampus and cerebellum). Each subregion was placed in a separate Eppendorf tube, snap-frozen in liquid nitrogen and then stored in a freezer at −80 °C. The second hemisphere was placed in 4% paraformaldehyde for 48 h. The fixed brain was then processed for paraffin embedding, using standard procedures. Paraffin-embedded blocks were sectioned and 6-μm sections were mounted on glass slides and used for histological analyses.

Paraffin-embedded mouse brain blocks were sectioned and the sections were mounted on glass slides. We deparaffinized the sections by immersion in two xylene baths for a total of 10 min, followed by a 5-min immersion in a 50% xylene:50% ethanol solution. The sections were then rehydrated by immersion in solutions of decreasing concentrations of ethanol (95%, 90%, 70% and 50%) and then placed in water. Sections then underwent antigen retrieval using the Diva decloaker (BioCare). Sections were blocked with 3% BSA, 3% fetal bovine serum (FBS) and 0.1% Triton X-100 in PBS for 45 min at room temperature. Primary antibodies (Supplementary Table 16 has a list of antibodies used for immunolabelling) were diluted in 3% BSA, 3% FBS and 0.1% Triton X-100 in PBS. After overnight incubation at 4 °C, sections were washed three times with PBS. Secondary antibodies, diluted in 3% BSA, 3% FBS and 0.1% Triton X-100 in PBS were either biotin-coupled (1:200; Vector Labs) or coupled to Alexa fluorophores (1:300, Invitrogen). After three 10-min washes with PBS, sections were mounted with Pro-Long anti-fade mounting medium with DAPI (Invitrogen) and then imaged using confocal microscopy. For the Aβ labelling shown in Extended Data Fig. 1e, we incubated sections with an anti-rabbit biotinylated IgG secondary antibody (VectorLabs) for 1 h, followed by three washes in PBS (1 min each) and the addition of avidin-streptavidin-HRP-coupled complex (1:200 in 2% BSA and 0.1% Triton X-100 in PBS; VectorLabs). After three washes with PBS, we added diaminobenzidine (DAB) substrate (prepared by dissolving DAB and peroxide tablets in PBS; Sigma-Aldrich) and incubated for several minutes, until a brown precipitate formed. Sections were then washed with PBS, dehydrated with increasing ethanol concentrations (50%, 70%, 90%, 95% and 100%), followed by incubation with a 50% ethanol:50% xylene solution and two immersions in 100% xylene (5 min each). Sections were mounted with a hydrophobic mounting medium (Permount). For Thioflavin S staining, after deparaffinization the brains were incubated with filtered 1% aqueous Thioflavin-S for 8 min at room temperature, then washed twice (3 min each) in 80% ethanol, once in 95% ethanol (3 min), three times in distilled water and finally mounted. For sections labelled by immunofluorescence, multiple confocal images were acquired using an Olympus Fluoview Confocal Microscope FV3000. For DAB-stained sections, we acquired pictures using a bright-field microscope coupled with a camera.

For analysis of the Aβ plaque burden, pictures of Aβ immunoreactivity (using the rabbit anti-Aβ monoclonal antibody, clone D54D2, Cell Signaling, 8243, dilution 1:250) in the hippocampus were processed using a macro developed for use with Fiji/ImageJ 2.9.0. In brief, confocal pictures were all saved in the same folder and were all automatically opened in Fiji and processed serially. For each picture, the background was subtracted (rolling ball radius was set for 25). Pictures then underwent de-noising, using a Gaussian blur filter (radius of one pixel). The images were then thresholded using the Default Fiji threshold set at 120. Particles with a minimal size of 5 μm^2 were retained and their number, average size and mean fluorescence intensity were automatically recorded for each picture in an Excel file. To calculate the Aβ plaque burden, the total area occupied by Aβ plaques was divided by the area of the selection. Three coronal sections (6 μm thick) were sampled for each animal, in the rostral, intermediate and ventral hippocampus. Two 20× images were acquired per section, using an Olympus FluoView LV1000 confocal microscope. The average Aβ burden was obtained by averaging the Aβ plaque density (area occupied by Aβ plaques divided by the total area analysed) in all pictures acquired for each animal.

For analysis of tau pathology, pictures of p-Ser202 tau (CP13, dilution 1:150) or p-Ser396/Ser404 tau (PHF1, dilution 1:200) immunoreactivity in the hippocampus CA1 were processed using a macro developed for use with Fiji/ImageJ 2.9.0. In brief, confocal pictures were all saved in the same folder and were all automatically opened in Fiji and processed serially. Pictures underwent de-noising, using a Gaussian blur filter (radius of one pixel). The images were then thresholded using the Default Fiji threshold set at 150. The number of tau-positive neurons in the selected CA1 area was then manually counted for each thresholded picture and the area was measured. For each picture, we calculated the average density of tau-positive neurons (the total number of tau-positive neurons divided by the area of the region). The average tau-positive neuron densities were calculated for each animal by averaging all the pictures acquired.

Fluorescent image analysis was also performed using MetaMorph NX 2.5 (Meta Series, Molecular Devices). Mean fluorescence intensity for specific markers was quantified in each animal either in the nucleus (β-catenin) or across the entire cell body (for example, GSK3β, pSer9-GSK3β, pTyr216-GSK3β, GPNMB and LPL), based on co-labelling with cell-type-specific markers (such as MAP2, aspartoacylase and Iba1). Between 50 and 300 cells per mouse were analysed, and background signal was subtracted. Synaptophysin and PSD-95 fluorescence intensities were quantified in the CA1 region of the hippocampus, and FluoroMyelin, MBP and SMI-312 intensities were measured in the corpus callosum, with background subtraction applied in all cases. Cell densities of Iba1+, CD68+, aspartoacylase+, PDGFRα+ and GFAP+ populations were also determined in relevant brain regions by quantifying 50–500 cells per mouse. For each measurement, multiple images were acquired at 4×, 10×, 20× or 40× magnification per animal, spanning the region of interest. Values were averaged for each animal before statistical analysis. The following primary antibodies were also used: anti-aspartoacylase [N1C3-2] (GeneTex, GTX113389; rabbit polyclonal, dilution 1:200), anti-aspartoacylase (clone D-11; Santa Cruz Biotechnology, sc-377308, mouse monoclonal, dilution 1:50), anti-β-catenin (clone E247; Abcam, ab32572; rabbit recombinant monoclonal, dilution 1:250), anti-β-catenin (clone 1B8A1; PTGlab, 66379-1-Ig, mouse monoclonal, dilution 1:200), anti-CD68 (clone KP1; Abcam, ab955; mouse monoclonal, dilution 1:200), anti-GFAP (Sigma-Aldrich, G9269; rabbit polyclonal, dilution 1:200), anti-GSK3β (clone 3D10; Novus Bio, NBP1-47470SS; mouse monoclonal, dilution 1:200), anti-pTyr216-GSK3β (Millipore Sigma, SAB4300237; rabbit polyclonal, dilution 1:100), anti-pSer9-GSK3β (Abcam, ab131097; rabbit polyclonal, dilution 1:100), anti-Iba1 (clone EPR16588; Abcam ab178846; rabbit recombinant monoclonal, dilution 1:2,000), anti-PSD-95 (clone K28/43; Biolegend, 810401; mouse monoclonal, dilution 1:250), anti-synaptophysin (clone SY38; Millipore Sigma, mouse monoclonal, MAB5258-I; dilution 1:200), anti-neurofilament marker (pan axonal marker; clone SMI-312; Biolegend, 837904; mouse monoclonal, dilution 1:200), anti-GPNMB (clone 2B10B8; PTGlab, 66926-1-Ig; mouse monoclonal, dilution 1:200), anti-LPL (Novus Bio, AF7197-SP; goat polyclonal, dilution 1:200), anti-MAP2 (Phosphosolutions, 1099-MAP2; goat polyclonal, dilution 1:500), anti-MBP (clone D8X4Q; Cell Signaling, 78896; rabbit monoclonal, dilution 1:200) and anti-PDGFRα (R&D Systems, AF1062; goat polyclonal, dilution 1:200). Secondary antibodies were used at a 1:300 dilution: donkey anti-goat Alexa 594 (Invitrogen, A-11058), donkey anti-rabbit IgG (H+L) Highly Cross-Adsorbed antibody, Alexa 488 (ThermoFisher Scientific, A21206), donkey anti-mouse IgG (H+L) Highly Cross-Adsorbed antibody, Alexa 594 (ThermoFisher Scientific, A21203), donkey anti-mouse Alexa 647 (Invitrogen, A-31571), donkey anti-rabbit Alexa 647 (Invitrogen, A-31573) and donkey anti-goat Alexa 488 (Invitrogen, A-11055).

Golgi labelling

The brains were processed and stained using the FD Rapid Golgistain Kit (FD Neurotechnologies, PK401) following the manufacturer’s protocol with minor modifications. Immediately after dissection, the brains were fixed overnight in 4% PFA. After cryosectioning, free-floating sections of 100 μm were shortly (10 min) fixed in 4% PFA, then stained using the kit’s reagents and mounted using a glycerin-containing medium. Then 12 dendrites per mouse were imaged in the hippocampus or the cortex using a confocal microscope. Dendritic spine density was quantified using Fiji software v.2.9.0.

Transmission electron microscopy

The 3xTg mice were fed either a Li-deficient diet (n = 8) or a control diet (n = 8) from 6 to 12 months of age. At the end point, mice were perfused with a fixative containing 2.5% glutaraldehyde and 2.5% paraformaldehyde in 0.1 M sodium cacodylate buffer, pH 7.4 (Electron Microscopy Sciences, 15949). After perfusion, 1–2-mm^3 brain sections were generated and post-fixed overnight at 4 °C in fresh fixative. The corpus callosum was subsequently dissected and processed for embedding in TAAB Epon resin at the Harvard Electron Microscopy Core Facility. In brief, tissue was washed in 0.1 M cacodylate buffer, post-fixed in 1% osmium tetroxide and 1.5% potassium ferrocyanide for 1 h, rinsed in distilled water and incubated in 1% aqueous uranyl acetate for 1 h. After two further water rinses, samples were dehydrated through graded ethanol (50%, 70%, 90% and twice in 100%, for 10 min each) followed by 1 h in propylene oxide. Samples were then infiltrated overnight in a 1:1 mixture of propylene oxide and TAAB Epon (Marivac), embedded in pure TAAB Epon the next day and polymerized at 60 °C for 48 h. Ultrathin sections (approximately 80 nm thick) were cut on a Reichert Ultracut-S microtome, mounted on copper grids, stained with lead citrate and imaged using either a JEOL 1200EX or a Tecnai G^2 Spirit BioTWIN transmission electron microscope. Images were captured using an AMT 2k CCD camera and saved in TIFF format. Quantification of myelin sheath thickness, axon diameter and g-ratio was performed using MetaMorph NX 2.5 software (Meta Series, Molecular Devices). A total of 1,376 axons (control group) and 1,396 axons (Li-deficient group) were analysed from eight randomly selected fields per animal (×4,800 magnification) spanning the corpus callosum.

Aβ detection by ELISA

Mouse endogenous Aβx–40 and Aβx–42 levels were measured using a previously established protocol[67]. In brief, hippocampi or cortices were homogenized in 20 volumes (v/w) of tissue lysis buffer consisting of 20 mM Tris-HCl (pH 7.4), 1 mM EDTA, 1 mM EGTA and 250 mM sucrose, supplemented with protease inhibitors (Roche) and 100 μM AEBSF. Soluble Aβ species were extracted from tissue homogenates by diethanolamine treatment. Mouse Aβ(x–40) and Aβx–42 were quantified using Wako ELISA kits (292-64501 and 294-62501, respectively). The LOQs were 7.44 pmol l−1 for Aβ(x–40) and 4.75 pmol l−1 for Aβx–42. Sample concentrations ranged from 26.21 to 52.98 pmol l−1 for Aβ(x–40) and from 11.72 to 22.40 pmol l−1 for Aβx–42, all above the respective LOQs.

Assessment of microglial function in vitro

Microglial purification for cell-culture assays

Wild-type Li-deficient and control mice were transcardially perfused with 1× cold PBS. The cortex and hippocampus were dissected and minced using a scalpel before transferring them to 5 ml digestion buffer (2 U ml−1 of Dispase II, 20 U ml−1 DNase I, 10 μM HEPES in HBSS without calcium or magnesium). Samples were incubated for 30 min at 37 °C on an orbital shaker. The tissue was then homogenized by successive trituration with a Pasteur pipette followed by a 1 ml pipette. An equal volume of 1× HBSS was added to the homogenate and the resulting mix was passed through a 70-µm cell strainer, then centrifuged at 300g for 10 min at 4 °C. Samples were resuspended with 40% Percoll (GE Healthcare, 17-0891-02) to remove myelin, and microglia were enriched using CD11b beads, as described above. Microglia were resuspended in pre-warmed media (DMEM/F12 with 2% FBS, 100 ng ml−1 IL-34, 50 ng ml−1 TGFβ1, 25 ng ml−1 M-CSF) and counted using a haemocytometer. Microglia were seeded into 96-well glass-bottom plates precoated with poly-l-ornithine (Sigma, P4957) at 5,000 cells per well using 100 μl of medium. A half-medium change was performed on day 2 and the downstream assay was done on day 3.

Primary microglia were also purified using an alternative protocol. After perfusion, the cortex and hippocampus were dissected, placed in 3 ml buffer (0.9% Hepes, 50 mM NaCl, pH 7.4) and minced with small scissors for 4 min. Then, 7 ml Dispase buffer (2 U ml−1 Dispase II in 0.9% Hepes, 50 mM NaCl, pH 7.4) was added and the tissue was incubated for 1 h at 37 °C on an orbital shaker. The tissue was then homogenized by gently triturating with a 10 ml pipette with a wide bore, to prevent cell shearing. The enzyme activity was halted by the 1:1 addition of 10% fetal bovine serum in PBS (10 ml) at 4 °C. The homogenate was passed through a 70-µm cell strainer to remove meninges and clumped cells. The homogenate was then spun for 10 min at 1,000g and 4 °C, and the supernatant was discarded. The pellet was resuspended in 6 ml of 75% isotonic percoll in PBS (high percoll; GE Healthcare, 17-0891-02). Then 5 ml of 35% isotonic percoll in PBS (low percoll) was added, followed by 4 ml of PBS. The resulting discontinuous gradient was allowed to settle for 15 min at 4 °C. We then centrifuged the tubes at 800g for 45 min at 4 °C. We then aspirated the top (PBS-containing) layer and part of the upper percoll layer. The band containing microglia (approximately 1.5 ml), situated at the interface between the 35% percoll and 75% percoll layers, was gently collected. Then 50 ml of PBS was gently added and the tube was inverted 20 times. The microglia were then centrifuged at 1,000g for 10 min. The supernatant was discarded and the pellet was resuspended in a pre-warmed (at 37 °C) buffer containing 2% fetal bovine serum, 50 U ml−1 penicillin and 50 µg ml−1 streptomycin in RPMI medium.

The BV2 microglial cell line has been maintained in the Yankner laboratory for more than 20 years and stored long-term in liquid nitrogen at –180 °C. After revival, the BV2 cells were authenticated based on their characteristic microglial morphology (small, round to slightly elongated shape, clear cytoplasm and occasional short processes) as well as positive immunolabelling for the microglial markers CD11b and Iba1. Mycoplasma contamination testing was not done.

Microglial Aβ uptake and degradation assays

Microglial Aβ uptake and degradation assays were done as previously described[68]. Human amyloid Aβ1–42 was purchased from Anaspec (AS-20276). Next, 1 mg of Aβ1–42 peptide was dissolved in 80 μl 1% NH_4OH, followed by dilution with PBS to 1 mg ml−1 (stock) and storage at −80 °C. Oligomeric Aβ1–42 was prepared by resuspending the stock solution in DMEM/F12 to 500 μg ml−1 (100 μM) and overnight incubation at 4 °C. On day 3, the medium was replaced with DMEM/F12 containing 2% FBS and Aβ42 oligomers diluted to a final concentration of 2 μg ml−1 (0.4 µM). To assess Aβ42 uptake, cells were incubated for 3 h at 37 °C, followed by three washes with 1× PBS and fixation with 4% PFA for 15 min. To assess microglial Aβ42 degradation, cells incubated with Aβ42 oligomers for 3 h were first washed three times with warm medium. The cells were then incubated with warm medium devoid of Aβ42 for an extra 3 h. They were then washed with 1× PBS and fixed with 4% PFA for 15 min. The fixed cells were washed twice with PBS and blocked with 2% BSA, 2% FBS, 0.1% Triton X-100 in PBS for 1 h. Anti-Iba1 and anti-Aβ (6E10) antibodies, diluted 1:500 in the blocking buffer, were then added and incubated overnight at 4 °C. The next day, the cells were washed three times with PBS 1× and incubated with secondary antibodies (1:300 in blocking buffer) at room temperature for 2 h. Cells were washed three times with 1× PBS, then mounted and analysed by confocal microscopy. We also assessed Aβ42 uptake and clearance by microglia using fluorescently labelled (HiLyte Fluor 555) human Aβ1–42 (AnaSpec, AS-60480). The fluorescently labelled Aβ42 was directly added to the medium containing 2% FBS to reach a concentration of 2 ng µl−1, and the uptake and degradation assays were conducted as detailed above.

Microglial stimulation and treatment with GSK3β inhibitors

To assess cytokine release, primary microglia isolated from control and Li-deficient mice were treated with 50 ng ml−1 LPS on day 2 for 16 h followed by supernatant collection. Inflammatory cytokines were detected and measured using a mouse cytokine array kit (R&D Systems, ARY006). To assess the effects of GSK3β inhibitors on microglial function, microglia were pretreated with 3 μM CHIR99021 or 1 μM of PF-04802367 on day 2 for 24 h before Aβ42 uptake and clearance or cytokine-detection assays.

snRNA-seq

Sample preparation

We performed snRNA-seq on the hippocampus of 12-month-old 3xTg mice that were fed a Li-deficient (n = 5 mice) or chemically defined control (n = 4 mice) diet for five weeks. Mice were transcardially perfused with ice-cold PBS at a speed of 6 ml min−1 for 8 min to repress the transcriptional response during the brain dissection and sample preparation69,70. Hippocampal tissue was dissected on ice and flash frozen in liquid nitrogen. Both frozen hippocampal tissues were subsequently thawed together in 500 µl HB buffer (0.25 M sucrose, 25 mM KCl, 5 mM MgCl2, 20 mM Tricine-KOH, pH 7.8, 1 mM DTT, 0.15 mM spermine and 0.5 mM spermidine) and homogenized with the tight pestle of a dounce homogenizer in the same HB buffer with the addition of 0.32% of IGEPAL (Sigma) (average of 25–30 times per sample) on ice. Subsequently, single nuclei were diluted to 9 ml in HB buffer, passed through a 40-μm filter and separated from debris and multinuclei by iodixanol gradient centrifugation. Specifically, we prepared a 50% iodixanol solution by diluting 60% iodixanol (Optiprep density gradient medium, Sigma D1556) with diluent (150 mM KCl, 30 mM MgCl_2, 120 mM Tricine-KOH, pH7.8), and subsequently diluted them with HB buffer and supplemented with 0.04% BSA and 64 U ml−1 RNasin Plus ribonuclease inhibitor (Promega, N2611) to prepare 40% iodixanol and 30% iodixanol. We layered 1 ml of 40% iodixanol in the bottom, 1 ml of 30% iodixanol in the middle and gently layered 9 ml of the diluted nuclei suspension on top of the 30% iodixanol layer. The three layers were visually confirmed to be distinct and were subjected to 18 min of 10,000g centrifugation. Single nuclei were carefully recovered from the 30% iodixanol layer in between the 30% and 40% interface. An aliquot was taken for trypan blue staining and visual inspection of nucleic morphology under a microscope, which showed a homogeneous size distribution and absence of major debris or doublets. The numbers of nuclei were determined initially by haemocytometer and subsequently confirmed with an automated counter. The remainder of the nucleic suspension was diluted for nuclei encapsulation and sequencing library preparation at the Harvard Single Cell Core, according to the 10X Genomics manual. The size and quality of the prepared libraries were confirmed on Agilent high-sensitivity TapeStation and the library was independently quantified by qPCR. The prepared libraries were sequenced by Nova-Seq S4 at the Harvard Biopolymers Facility, at an average coverage of 32,897 reads per nucleus (Supplementary Table 3). Sequencing data and individual animal metadata have been deposited at the NCBI Gene Expression Omnibus GSE272344 and linked to BioProject PRJNA1136488.

Single-nucleus RNA-seq quality control

We aligned the demultiplexed raw sequencing reads to the mouse genome (mm10 from 10X Genomics) using Cell Ranger (v.6.1.2)[71], with the –include-introns option, to account for nuclear pre-mRNAs. The generated counts table was loaded to Seurat (v.4)[72] to generate Seurat objects. Cells with more than 10% of reads being attributed to mitochondrial transcripts were filtered out. Cells that expressed fewer than 200 features (low-quality cells) or more than 8,000 features (apparent doublets) were also filtered out. These thresholds were determined by visual inspection of the distribution of features among cells (Seurat, VlnPlot) and are generally consistent with previous reports57,73. The cells that passed quality controls were log-normalized using the NormalizeData function from Seurat with a scale factor of 10,000. Variable features were identified using the FindVariableFeatures function from Seurat with the vst selection method and 2,000 features. Data were scaled using ScaleData and principal component analysis (PCA) was performed using RunPCA with the identified variable features using Seurat. Nearest neighbours were found using FindNeighbors with dimension 1:30, which was determined by ElbowPlot following the Seurat manual. The number of clusters was determined by the FindClusters function using Seurat v.4. UMAP and TSNE were performed using RunUMAP and RunTSNE using Seurat with dimensions 1:30 and do.fast=TRUE parameter. Potential doublets were removed using DoubletFinder (v.3)[74] following the default parameters. After filtration, cluster-specific markers were determined using the FindAllMarkers function (Seurat v.4), with parameters only.pos = F, min.pct = 0.25 and max.cell.per.ident = 500.

Cell-type-specific annotation and differential gene expression analyses

Cell types were identified by cross-referencing the transcriptome of each individual cell to the Mouse Cell Atlas[75] and independently validated by confirming the expression of established cell-type-specific markers on a cluster-to-cluster basis. Violin and heat scatter plots to demonstrate the expression distribution of selected established markers were plotted using the VlnPlot and FeaturePlot functions of Seurat. Examples of cell-type markers include Slc17a7 (excitatory neurons), Prox1 (granule cells), Gad1 and Gad2 (inhibitory neurons), Mbp (oligodendrocytes), Aldoc, Aqp4 (astrocytes), Pdgfra (OPCs), Vtn (pericytes), Cx3cr1 and Tgfbr1 (microglia), Cldn5 and Flt1 (endothelial cells), Prlr and Folr1 (choroid plexus cells; Supplementary Fig. 4). Cell type-specific abundance and differential gene expression analyses were performed on the main cell types (excitatory neurons, inhibitory neurons, granule cells, microglia, astrocytes, oligodendrocytes, OPCs and endothelial cells). Clusters of the same cell types were combined to increase the statistical power, as described previously69,70,76, and clusters with mixed cell types (less than 80% homogenous) were removed for cell-type-specific analyses. The relative abundance of each cell type was computed by dividing the number of cells of the particular cell type by the total number of cells. Two-tailed unpaired Student’s t-tests were done to determine whether there were significant differences in the relative abundance of each cell type between the control and Li-deficient conditions. DEGs were computed by the MAST[77] test in Seurat. Genes expressed in fewer than 1% of the cells in each cell type were filtered out. All the DEGs (FDR < 0.05) are reported in Supplementary Table 4. DEGs with FDR < 0.05 and |log_2fold change| > 0.1 were used for Gene Ontology enrichment analyses using Metascape[78] v.3.5.20240101. The heat scatter plot for DEGs (Fig. 3d) was generated using the FeaturePlot function of Seurat.

Purified microglia RNA-seq

Purification of microglia

Li-deficient or control wild-type and 3xTg mice were perfused transcardially using PBS at 4 °C. The cortex and hippocampus were quickly dissected and pooled, then minced using a scalpel, before transferring to 5 ml dissection buffer (HBSS without calcium and magnesium) and Protector RNase inhibitor (Sigma) at 4 °C in a dounce homogenizer. Brain samples were dounced 20 times with a loose pestle and 10 times with a tight pestle. The cell suspension was passed through a pre-wetted 70-μm cell strainer into a pre-chilled 15 ml tube. Cells were then spun down at 300g for 10 min at 4 °C. Cell pellets were resuspended in 10 ml ice-cold 40% Percoll and centrifuged at 800g for 20 min at 4 °C. Myelin debris was removed by vacuum suction and the cell pellet was washed with 5 ml ice-cold HBSS and spun again for 5 min at 300g at 4 °C. The pellets were resuspended in 180 μl ice-cold MACs buffer (0.5% BSA, 2 mM EDTA, Protector RNase inhibitor in PBS) with 20 μl of CD11b microbeads (Miltenyi Biotec, 130-049-601) and incubated on ice for 15 min. After incubation, 1 ml of MACs buffer was added to samples and cells were centrifuged for 5 min at 300g and 4 °C. Microglia were then isolated using LS columns with QuadroMACS Separator following the manufacturer’s instructions. In brief, LS columns were pre-washed three times with 3 ml MACs buffer. Samples were resuspended in 500 µl MACs buffer and transferred to LS columns, followed by three more washes with 3 ml MACs buffer. Finally, microglia were released with 5 ml MACs buffer (without EDTA), then used for RNA extraction.

Microglial RNA sequencing quality control and analysis

Total microglial RNA was extracted from MACs-purified microglia using RNAzol RT (Sigma, R4533). RNA extracted from each microglial preparation was quantified using an Agilent Tapestation 4200 instrument, with a corresponding Agilent Tapestation High Sensitivity RNA assay (5067-5579). The samples were normalized to 4 ng of input in 9.5 μl, and the polyadenylated mRNA was selected for using 3′ SMART-Seq CDS Primer II A as part of the Takara SMART-Seq v.4 Ultra Low Input RNA (634894) workflow, which generated cDNA. From there, an Agilent Bioanalyzer High Sensitivity DNA assay (5067-4626) was used to quantify the cDNA concentration. Libraries were obtained using the Illumina NexteraXT kit (FC-131-1096). Adapter ligation, indexing and amplification were done subsequently as part of the same workflow. After amplification, residual primers were eluted away using KAPA Pure Beads (07983298001) in a 0.6× SPRI-based clean-up. The resulting purified libraries were run on an Agilent 4200 Tapestation instrument, with a corresponding Agilent D5000 ScreenTape assay (5067-5588 and 5067-5589) to visualize the libraries and check the size and concentration of each library. Molarity values obtained from this assay were used to normalize all samples in equimolar ratio for one final pool. The pooled library was denatured and loaded onto a single lane of an Illumina NovaSeq 6000 S4 flow cell to generate 100-bp paired-end reads. The pool was loaded at 200 pM (normalized to 1 nM pre-denaturation), with 1% PhiX spiked in as a sequencing control. The base-call files were demultiplexed through the Harvard BPF Genomics Core pipeline and the resulting fastq files were used in subsequent analysis. Raw RNA-sequencing data in FASTQ format were subjected to quality assessment using FastQC (v.0.11.9) and sequencing reads were aligned to mouse genome (mm10) using a STAR aligner[79] with the following options: --outFilterMismatchNmax 999 --outFilterMismatchNoverLmax 0.04 --alignSJDBoverhangMin 1 --alignSJoverhangMin 8 --outFilterMultimapNmax 20 --outFilterType BySJout --alignIntronMin 20 --alignIntronMax 1000000 --alignMatesGapMax 1000000. Microglia RNA-seq yielded an average of 100 million uniquely mapped reads for each sample, and gene expression levels were quantified using htseq-count[80]. To reduce the computational burden and focus on biologically relevant genes, we initially prefiltered the count data. Genes were retained if they had at least five counts in at least three samples. To validate the purity of the isolated microglia, we determined that microglial markers (Csf1r, P2ry12 and Tmem119) were strongly enriched, whereas neuronal (Map2 and Nsg2), astrocytic (Gfap and Aldh1l1) and oligodendrocyte (Olig2 and Mog) marker genes were negligibly expressed (Supplementary Fig. 7b,c). We also verified that markers of ex vivo microglia activation[81] (Fos, Jun, Hspa1a and Zfp36) were minimally expressed in our samples (Supplementary Fig. 7b,c). Differential gene expression analysis was done using DESeq2 (ref. [82]) to identify DEGs between Li-deficient and control microglia, with an adjusted P value cut-off of 0.05 (Supplementary Tables 10 and 11). Upregulated and downregulated DEGs from Li-deficient wild-type and 3xTg microglia were further analysed for overlapping DEGs, and the overlapping DEGs were subjected to Gene Ontology enrichment analysis using Metascape[78] v.3.5.20240101. Results are summarized in Fig. 4a and provided in Supplementary Table 12.

Ingenuity Pathway Analysis

Signalling pathway and molecular network analyses were done on DEGs identified from the snRNA-seq and microglia RNA-seq datasets (FDR < 0.05) using Ingenuity Pathway Analysis (IPA)[83]. Significantly enriched pathways and disease or function annotations were identified and ranked based on the FDR, calculated using a one-sided Fisher’s exact test followed by a Benjamini–Hochberg correction for multiple comparisons. To visualize the results, the top pathway-enriched DEGs were integrated into a signalling network using IPA’s build and overlay function (Extended Data Fig. 4b,c).

RNA-seq of hippocampus from 3xTg mice treated with LiO

RNA extraction

Twelve-month-old 3xTg mice that were treated with 4.3 µM LiO (n = 9 females) or vehicle (water; n = 9 females) from 6 to 12 months of age were transcardially perfused with cold PBS 1× and the hippocampi were rapidly dissected and snap frozen. The total hippocampal RNA was extracted using Trizol reagent (Ambion, 15596018) and purified using a Direct-zol RNA Mini Prep kit (Zymo Research, R2050) according to the manufacturer’s instructions. RNA integrity and concentration were assayed using an Agilent 2100 Bioanalyzer instrument. All RNA samples had an RNA integrity number of more than 8.2.

RNA library preparation and sequencing

Libraries were prepared using Illumina TruSeq Stranded mRNA sample-preparation kits from 500 ng of purified total RNA according to the manufacturer’s protocol. The finished dsDNA libraries were quantified using a Qubit fluorometer, Agilent TapeStation 2200, and RT–qPCR using a Kapa Biosystems library quantification kit according to the manufacturer’s protocols. Uniquely indexed libraries were pooled and sequenced on an Illumina NextSeq 500 instrument with paired-end 75-bp reads by the Dana-Farber Cancer Institute Molecular Biology Core Facilities. Samples were pooled with multiple samples per lane and sequenced. There were two sequencing batches (batch 1, n = 5 mice per group; batch 2, n = 4 mice per group).

RNA sequencing quality control and quantification of gene expression

Quality control of sequencing reads (Supplementary Table 14) was done using FastQC v.0.11.5 (https://www.bioinformatics.babraham.ac.uk/projects/fastqc/). Reads were aligned to the Mouse GRCm38 genome with GENCODE M21 gene models using STAR[79] v.2.7.0f with options --outSAMunmapped Within --alignSJDBoverhangMin 1 --alignSJoverhangMin 8 --outFilterMultimapNmax 20 --outFilterType BySJout --alignIntronMin 20 --alignIntronMax 5000000 --alignMatesGapMax 5000000 --twopassMode Basic. The expression of genes was quantified as gene counts using STAR at the same time as alignment with option --quantMode GeneCounts.

Gene-expression normalization and covariate adjustment

Gene counts were input to edgeR. Genes were deemed expressed if at least n = 9 samples (where n is the group size) had more than one count per million (CPM). Genes not satisfying these criteria were removed, keeping the original library sizes. This filtering retained n = 14,862 expressed genes out of 55,536 annotated genes for subsequent analyses. Counts were then normalized using the TMM method in edgeR. Finally, log(CPM) values were calculated for analyses other than differential expression.

To adjust gene expression for covariates, we fit the linear regression model for each gene and cohort separately using lm() in R: gene expression ~ group + covariates, where gene expression is log(CPM), and using the group and covariates: factor, two levels: LiO and water (reference level), covariates (sequencing batch (factor, two levels)) and one RUV with residuals (RUVr) covariate (continuous). The final normalized and adjusted gene-expression values were derived from adding the regression residuals to the estimated effect of the group level to preserve the effect of the group on expression. These normalized and adjusted gene-expression values were used to perform gene–gene regression analysis and gene–gene group regression analysis, and to visualize gene expression.

To adjust for technical variation, we used the RUVr method[84] implemented in the RUVSeq v.1.18.0 Bioconductor package. We performed a first pass edgeR analysis, up to and including the glmFit() step with the covariates listed above, excluding the RUVr covariates. Then we used residuals() with argument type = ‘deviance’ to obtain a matrix of deviance residuals. The specified number of unwanted factors (RUVr covariates) used in final analyses were then estimated by the RUVr function using log(CPM) expression values and the residuals. The number of unwanted factors was selected based on separation of groups in PC plots using normalized and adjusted gene-expression values and checking that histograms of differential expression P values showed a uniform or anti-conservative pattern.

Differential expression and gene set enrichment analysis

Differential expression analysis between groups with covariate adjustment using the covariates listed above was performed for expressed genes using edgeR (estimateDisp, glmFit and glmLRT with default arguments) in R. Genes were considered differentially expressed if FDR < 0.05. Gene Ontology enrichment analysis was done separately for upregulated genes and downregulated genes using Metascape v.3.5.20240101 and is summarized in Supplementary Table 15 and Fig. 5f.

GWAS-DEG enrichment analysis

Before doing the GWAS-DEG enrichment analysis, we converted the mouse gene symbols to their human orthologues, using a two-step process. First, we used the alias2SymbolTable function in the Limma R package[85] v.3.58.1 to map any gene aliases to their corresponding main symbols. Subsequently, the resulting gene symbols were converted to human orthologues using the MGI orthologue table[86]. If there were multiple mapping candidates, all possible conversions were applied. For example, if a mouse gene had multiple human orthologues, records with all the relevant human gene symbols were generated. This standardized gene nomenclature enabled cross-species comparisons in subsequent analyses.

To do the GWAS-DEG enrichment analysis for microglia isolated from Li-deficient mice, we used MAGMA[87] v.1.10. The gene set of DEGs identified by microglia bulk RNA-seq analysis was used and the summary statistics from the GWAS catalogue AD (accession ID: MONDO_0004975)[88] were obtained and formatted for MAGMA input. The GWAS catalogue AD contains GWAS records from multiple studies. If multiple records were found for the same variant, we retained the entry with the lowest P value. Gene-set analysis was conducted using the default MAGMA settings, with multiple testing correction applied to account for the number of gene sets tested. Enrichment results were considered significant at a false discovery rate (FDR) of 0.05.

Overlap of mouse and human DEGs

To assess the overlap between DEGs derived from our transcriptomic analyses and DEGs derived from the analysis of human brain samples with varying degrees of AD pathology[15] (Fig. 3d), we first converted mouse gene symbols to their human orthologues, as described above. We matched the cell types analysed in our mouse studies with those analysed in humans[15]. To assess the statistical significance of the overlap between the two DEG sets, we did a Fisher’s exact test. To control for multiple comparisons arising from the analysis of different cell types and DEG directions (upregulated and downregulated), we adjusted the P values using the Benjamini–Hochberg procedure. Two sets of adjusted P values were calculated (Fig. 3d and Supplementary Table 8): one set for the overlap of genes upregulated in both datasets (indicated in red), and another for the overlap of genes downregulated in both datasets (indicated in blue).

Proteome analysis by mass spectrometry

The proteomic analysis was done at the Harvard Center for Mass Spectrometry. Hippocampal homogenates from Li-deficient and control 3xTg mice containing an equal amount (100 µg) of protein were reduced with 200 mM tris[2-carboxyethyl] phosphine (TCEP) at 55 °C for 1 h, then alkylated with 375 mM iodoacetamide at room temperature for 30 min in the dark. Proteins were precipitated using the methanol/chloroform/water precipitation method and then digested with trypsin overnight at 37 °C. TMT labelling of digested samples was done according to the manufacturer’s instructions (ThermoFisher). In brief, TMT labelling reagents were dissolved with 41 µl anhydrous acetonitrile, and an equal volume of TMT reagent mix was added to each sample. After incubation for 1 h at room temperature, the reaction was quenched with 8 µl of 5% hydroxylamine. Equal amounts of peptides from each sample were combined and dried in a SpeedVac. The peptides were then separated using an Agilent 1200 HPLC system with a PolyWAX LP column (PolyLC), 200 × 2.1 mm, 5 μm and 300 A running under electrostatic repulsion–hydrophilic interaction chromatography (ERLIC) mode conditions. Peptides were separated across a 90-minute gradient from 0% buffer A (90% acetonitrile, 0.1% acetic acid) to 75% buffer B (30% acetonitrile, 0.1% formic acid) with 20 fractions collected by time. Each fraction was dried in a SpeedVac and resuspended in 0.1% formic acid solution before analysis by mass spectrometry. Each ERLIC fraction was submitted for a single liquid chromatography–tandem mass spectrometry (LC-MS/MS) experiment that was done on a Q Exactive HF-X High Resolution Orbitrap (Thermo Fisher) coupled with an Ultimate 3000 nanoLC (Thermo Fisher) at the Harvard Center for Mass Spectrometry. Peptides were first isolated on a trapping cartridge (300 µm × 5 mm PepMap Neo C18 trap cartridge, Thermo Scientific) before separation on an analytical column (µPAC, C18 pillar surface, 50-cm bed, Thermo Scientific). The LC gradient was as follows: 2–27% in mobile phase B (0.1% formic acid in acetonitrile) for 70 min and increased to 98% mobile phase B for 15 min at a flow rate of 300 nl min−1. The mass spectrometer operated in data-dependent mode for all analyses. Electrospray-positive ionization was enabled with a voltage of 2.1 kV. A full scan ranging from 400 to 1,600 m/z was done with a mass resolution of 12 × 10^4 and an automated gain control (AGC) target set to 1 × 10^6.

Proteomics quality control

The top three most intensive precursor ions from each scan were used for MS2 fragmentation (normalized collision energy of 32) at a mass resolution of 3.0 × 10^4 and an AGC of 1 × 10^5. The dynamic exclusion was set at 50 s with a precursor isolation window of 1.2 m/z. Raw data were submitted for analysis in Proteome Discoverer 3.0 software (Thermo Scientific). The MS/MS data were searched against the UniProt reviewed Mus musculus (mouse) database along with known contaminants, such as human keratins and common lab contaminants. Sequest HT searches were performed using the following guidelines: a 10-ppm MS tolerance and 0.02-Da MS/MS tolerance; trypsin digestion with up to two missed cleavages; carbamidomethylation (+57.021 Da) on cysteine, TMT 6-plex tags on peptide amino termini and lysine residue (+229.163 Da) were set as static modification; oxidation (+15.995 Da) of methionine was set as variable modification; minimum required peptide length was set to ≥6 amino acids. At least one unique peptide per protein group was required to identify proteins. Of 13,404 proteins identified, only n = 3,392 proteins were identified with high confidence (MS2 spectra assignment, FDR < 0.01 on both protein and peptide level by applying the target-decoy database search by Percolator) and were included in the statistical analysis, as per the standard procedures of the Harvard Center for Mass Spectrometry89,90,91. The sample labels were control (samples 1, 3, 5 and 7) and Li-deficient (samples 2, 4, 6 and 8) and were all 3xTg homozygous females, aged 15 months (treatment from 6 to 15 months of age). An ANOVA followed by Tukey’s post-hoc test was used to assess differences in protein abundance between Li-deficient and control samples. P values were adjusted for multiple comparisons using the Benjamini–Hochberg method to control the FDR. Proteins with an adjusted P < 0.05 were considered differentially abundant (Supplementary Table 7). The proteins identified with high confidence and included in the statistical analysis are listed in Supplementary Table 7. All other proteins, identified with lower confidence, can be accessed from the files deposited at the ProteomeXchange Consortium through the PRIDE partner repository with the dataset identifier PXD063039. This represents 21 files, including one .msf file (containing all search results: peptide-spectrum matches, peptide groups, protein groups, modifications, scores, FDR and metadata) and 20 .raw files (containing MS1/2 spectra and metadata), one for each of the 20 fractions analysed by mass spectrometry.

Statistics and reproducibility

Statistical analysis was done using GraphPad software v.10.3.0 (507). The statistical tests used are noted in the figure legends. Throughout the paper, all tests are two sided and unpaired unless stated otherwise. A significance level of 0.05 was used to reject the null hypothesis. The sample size, age and sex of experimental animals, as well as the summary of each statistical test (including degrees of freedom, confidence intervals and P values) can be found in the Source Data file. All animal experiments were done once per condition using biologically independent samples (individual animals), with group sizes indicated in the corresponding figure legends. Representative immunolabelling images shown in the figures are from one animal per group, selected from multiple animals that consistently showed similar results.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

The snRNA-seq, microglia RNA-seq and LiO RNA-seq data have been deposited in the Gene Expression Omnibus repository (GSE272344, GSE275326 and GSE295788). The mass-spectrometry proteomics data have been deposited in the ProteomeXchange Consortium through the PRIDE[92] partner repository with the dataset identifier PXD063039. The MS/MS proteomic data were searched against the UniProt Mus musculus protein database (FASTA format, including isoforms) and were downloaded on 17 July 2022. For the GWAS DEG enrichment analysis using MAGMA, summary statistics for Alzheimer’s disease (accession ID: MONDO_0004975) were obtained from the GWAS Catalog (https://www.ebi.ac.uk/gwas/efotraits/MONDO_0004975). Clinico-pathological data on post-mortem human samples from ROSMPAP can be requested at https://www.radc.rush.edu. Source data are provided with this paper.

Code availability

The code used in this study is available from the corresponding author upon reasonable request.

References

1. James, B. D. & Bennett, D. A. Causes and patterns of dementia: an update in the era of redefining Alzheimer’s disease. Annu. Rev. Public Health 40, 65–84 (2019).

2. Sperling, R., Mormino, E. & Johnson, K. The evolution of preclinical Alzheimer’s disease: implications for prevention trials. Neuron 84, 608–622 (2014).

3. De Strooper, B. & Karran, E. The cellular phase of Alzheimer’s disease. Cell 164, 603–615 (2016).

4. Murdock, M. H. & Tsai, L.-H. Insights into Alzheimer’s disease from single-cell genomic approaches. Nat. Neurosci. 26, 181–195 (2023).

5. Mathys, H. et al. Single-cell multiregion dissection of Alzheimer’s disease. Nature https://doi.org/10.1038/s41586-024-07606-7 (2024).

6. Migliore, L. & Coppedè, F. Gene–environment interactions in Alzheimer disease: the emerging role of epigenetics. Nat. Rev. Neurol. 18, 643–660 (2022).

7. Killin, L. O. J., Starr, J. M., Shiue, I. J. & Russ, T. C. Environmental risk factors for dementia: a systematic review. BMC Geriatr. 16, 175 (2016).

8. Kawahara, M., Kato-Negishi, M. & Tanaka, K. Cross talk between neurometals and amyloidogenic proteins at the synapse and the pathogenesis of neurodegenerative diseases. Metallomics 9, 619–633 (2017).

9. Huat, T. J. et al. Metal toxicity links to Alzheimer’s disease and neuroinflammation. J. Mol. Biol. 431, 1843–1868 (2019).

10. Bakulski, K. M. et al. Heavy metals exposure and Alzheimer’s disease and related dementias. J. Alzheimers Dis. 76, 1215–1242 (2020).

11. Bush, A. I. et al. Rapid induction of Alzheimer Aβ amyloid formation by zinc. Science 265, 1464–1467 (1994).

12. James, S. A. et al. Elevated labile Cu is associated with oxidative pathology in Alzheimer disease. Free Radic. Biol. Med. 52, 298–302 (2012).

13. Mucke, L. et al. High-level neuronal expression of Aβ1-42 in wild-type human amyloid protein precursor transgenic mice: synaptotoxicity without plaque formation. J. Neurosci. 20, 4050–4058 (2000).

14. Oddo, S. et al. Triple-transgenic model of Alzheimer’s disease with plaques and tangles: intracellular Aβ and synaptic dysfunction. Neuron 39, 409–421 (2003).

15. Gazestani, V. et al. Early Alzheimer’s disease pathology in human cortex involves transient cell states. Cell 186, 4438–4453 (2023).

16. Herron, S., Delpech, J.-C., Madore, C. & Ikezu, T. Using mechanical homogenization to isolate microglia from mouse brain tissue to preserve transcriptomic integrity. STAR Protoc. 3, 101670 (2022).

17. Kunkle, B. W. et al. Genetic meta-analysis of diagnosed Alzheimer’s disease identifies new risk loci and implicates Aβ, tau, immunity and lipid processing. Nat. Genet. 51, 414–430 (2019).

18. Folke, J., Pakkenberg, B. & Brudek, T. Impaired Wnt signaling in the prefrontal cortex of Alzheimer’s disease. Mol. Neurobiol. 56, 873–891 (2019).

19. Lauretti, E., Dincer, O. & Praticò, D. Glycogen synthase kinase-3 signaling in Alzheimer’s disease. Biochim. Biophys. Acta Mol. Cell. Res. 1867, 118664 (2020).

20. Leroy, K. et al. The active form of glycogen synthase kinase-3β is associated with granulovacuolar degeneration in neurons in Alzheimer’s disease. Acta Neuropathol. 103, 91–99 (2002).

21. Leroy, K., Yilmaz, Z. & Brion, J.-P. Increased level of active GSK-3β in Alzheimer’s disease and accumulation in argyrophilic grains and in neurones at different stages of neurofibrillary degeneration. Neuropathol. Appl. Neurobiol. 33, 43–55 (2007).

22. Guilliot, S., Gauthier, S., Touchon, J. & Soto, M. E. Lithium, a treatment option for Alzheimer’s disease? A review of existing evidence and discussion on future perspectives. J. Alzheimers Dis. 96, 473–482 (2023).

23. Yu, L. et al. Cortical proteins associated with cognitive resilience in community-dwelling older persons. JAMA Psychiatry 77, 1172–1180 (2020).

24. Ramos-Miguel, A. et al. Presynaptic proteins complexin-I and complexin-II differentially influence cognitive function in early and late stages of Alzheimer’s disease. Acta Neuropathol. 133, 395–407 (2017).

25. Graham, S. F. et al. Quantitative measurement of [Na+] and [K+] in postmortem human brain tissue indicates disturbances in subjects with Alzheimer’s disease and dementia with Lewy bodies. J. Alzheimers Dis. 44, 851–857 (2015).

26. Religa, D. et al. Elevated cortical zinc in Alzheimer disease. Neurology 67, 69–75 (2006).

27. Kessing, L. V. et al. Association of lithium in drinking water with the incidence of dementia. JAMA Psychiatry 74, 1005–1010 (2017).

28. Heneka, M. T. et al. Neuroinflammation in Alzheimer’s disease. Lancet Neurol. 14, 388–405 (2015).

29. Romero-Molina, C., Garretti, F., Andrews, S. J., Marcora, E. & Goate, A. M. Microglial efferocytosis: diving into the Alzheimer’s disease gene pool. Neuron 110, 3513–3533 (2022).

30. Klein, P. S. & Melton, D. A. A molecular mechanism for the effect of lithium on development. Proc. Natl Acad. Sci. USA 93, 8455–8459 (1996).

31. Sofola, O. et al. Inhibition of GSK-3 ameliorates Aβ pathology in an adult-onset Drosophila model of Alzheimer’s disease. PLoS Genet. 6, e1001087 (2010).

32. Aghaizu, N. D., Jin, H. & Whiting, P. J. Dysregulated Wnt signalling in the Alzheimer’s brain. Brain Sci. 10, 902 (2020).

33. Liu, C.-C. et al. Deficiency in LRP6-mediated Wnt signaling contributes to synaptic abnormalities and amyloid pathology in Alzheimer’s disease. Neuron 84, 63–77 (2014).

34. Martin, M., Rehani, K., Jope, R. S. & Michalek, S. M. Toll-like receptor-mediated cytokine production is differentially regulated by glycogen synthase kinase 3. Nat. Immunol. 6, 777–784 (2005).

35. Azim, K. & Butt, A. M. GSK3β negatively regulates oligodendrocyte differentiation and myelination in vivo. Glia 59, 540–553 (2011).

36. Nunes, M. A. et al. Chronic microdose lithium treatment prevented memory loss and neurohistopathological changes in a transgenic mouse model of Alzheimer’s disease. PLoS ONE 10, e0142267 (2015).

37. Zhao, L. et al. Beneficial synergistic effects of microdose lithium with pyrroloquinoline quinone in an Alzheimer’s disease mouse model. Neurobiol Aging 35, 2736–2745 (2014).

38. Trujillo-Estrada, L. et al. In vivo modification of Abeta plaque toxicity as a novel neuroprotective lithium-mediated therapy for Alzheimer’s disease pathology. Acta Neuropathol. Commun. 1, 73 (2013).

39. Zhang, X. et al. Long-term treatment with lithium alleviates memory deficits and reduces amyloid-β production in an aged Alzheimer’s disease transgenic mouse model. J. Alzheimers Dis. 24, 739–749 (2011).

40. Fiorentini, A., Rosi, M. C., Grossi, C., Luccarini, I. & Casamenti, F. Lithium improves hippocampal neurogenesis, neuropathology and cognitive functions in APP mutant mice. PLoS ONE 5, e14382 (2010).

41. Phiel, C. J., Wilson, C. A., Lee, V. M.-Y. & Klein, P. S. GSK-3α regulates production of Alzheimer’s disease amyloid-β peptides. Nature 423, 435–439 (2003).

42. Su, Y. et al. Lithium, a common drug for bipolar disorder treatment, regulates amyloid-β precursor protein processing. Biochemistry 43, 6899–6908 (2004).

43. Rockenstein, E. et al. Neuroprotective effects of regulators of the glycogen synthase kinase-3β signaling pathway in a transgenic model of Alzheimer’s disease are associated with reduced amyloid precursor protein phosphorylation. J. Neurosci. 27, 1981–1991 (2007).

44. Wilson, E. N. et al. NP03, a microdose lithium formulation, blunts early amyloid post-plaque neuropathology in McGill-R-Thy1-APP Alzheimer-like transgenic rats. J. Alzheimers Dis. 73, 723–739 (2020).

45. Sofola-Adesakin, O. et al. Lithium suppresses Aβ pathology by inhibiting translation in an adult Drosophila model of Alzheimer’s disease. Front. Aging Neurosci. 6, 190 (2014).

46. Leroy, K. et al. Lithium treatment arrests the development of neurofibrillary tangles in mutant tau transgenic mice with advanced neurofibrillary pathology. J. Alzheimers Dis. 19, 705–719 (2010).

47. Caccamo, A., Oddo, S., Tran, L. X. & LaFerla, F. M. Lithium reduces tau phosphorylation but not Aβ or working memory deficits in a transgenic model with both plaques and tangles. Am. J. Pathol. 170, 1669–1675 (2007).

48. Nakashima, H. et al. Chronic lithium treatment decreases tau lesions by promoting ubiquitination in a mouse model of tauopathies. Acta Neuropathol. 110, 547–556 (2005).

49. Noble, W. et al. Inhibition of glycogen synthase kinase-3 by lithium correlates with reduced tauopathy and degeneration in vivo. Proc. Natl Acad. Sci. USA 102, 6990–6995 (2005).

50. Hampel, H. et al. Lithium trial in Alzheimer’s disease: a randomized, single-blind, placebo-controlled, multicenter 10-week study. J. Clin. Psychiatry 70, 922–931 (2009).

51. Macdonald, A. et al. A feasibility and tolerability study of lithium in Alzheimer’s disease. Int. J. Geriatr. Psychiatry 23, 704–711 (2008).

52. Forlenza, O. V. et al. Disease-modifying properties of long-term lithium treatment for amnestic mild cognitive impairment: randomised controlled trial. Br. J. Psychiatry 198, 351–356 (2011).

53. Nunes, M. A., Viel, T. A. & Buck, H. S. Microdose lithium treatment stabilized cognitive impairment in patients with Alzheimer’s disease. Curr. Alzheimer Res. 10, 104–107 (2013).

54. Forlenza, O. V., Radanovic, M., Talib, L. L. & Gattaz, W. F. Clinical and biological effects of long-term lithium treatment in older adults with amnestic mild cognitive impairment: randomised clinical trial. Br. J. Psychiatry 215, 668–674 (2019).

55. Damiano, R. F. et al. Revisiting global cognitive and functional state 13 years after a clinical trial of lithium for mild cognitive impairment. Braz. J .Psychiatry 45, 46–49 (2023).

56. Kakhki, S. & Ahmadi-Soleimani, S. M. Experimental data on lithium salts: From neuroprotection to multi-organ complications. Life Sci. 306, 120811 (2022).

57. Haney, M. S. et al. APOE4/4 is linked to damaging lipid droplets in Alzheimer’s disease microglia. Nature 628, 154–161 (2024).

58. Bennett, D. A. et al. Religious Orders Study and Rush Memory and Aging Project. J. Alzheimers Dis. 64, S161–S189 (2018).

59. Bennett, D. A. et al. Decision rules guiding the clinical diagnosis of Alzheimer’s disease in two community-based cohort studies compared to standard practice in a clinic-based cohort study. Neuroepidemiology 27, 169–176 (2006).

60. Bennett, D. A. et al. Natural history of mild cognitive impairment in older persons. Neurology 59, 198–205 (2002).

61. Ihara, Y., Abraham, C. & Selkoe, D. J. Antibodies to paired helical filaments in Alzheimer’s disease do not recognize normal brain proteins. Nature 304, 727–730 (1983).

62. Selkoe, D. J., Abraham, C. R., Podlisny, M. B. & Duffy, L. K. Isolation of low-molecular-weight proteins from amyloid plaque fibers in Alzheimer’s disease. J. Neurochem. 46, 1820–1834 (1986).

63. Xu, J. et al. Evidence for widespread, severe brain copper deficiency in Alzheimer’s dementia. Metallomics 9, 1106–1119 (2017).

64. Ramos, P. et al. Alkali metals levels in the human brain tissue: anatomical region differences and age-related changes. J. Trace Elem. Med. Biol. 38, 174–182 (2016).

65. Squitti, R. et al. Copper imbalance in Alzheimer’s disease: meta-analysis of serum, plasma, and brain specimens, and replication study evaluating ATP7B gene variants. Biomolecules 11, 960 (2021).

66. Hutchinson, R. W. et al. Imaging and spatial distribution of β-amyloid peptide and metal ions in Alzheimer’s plaques by laser ablation-inductively coupled plasma-mass spectrometry. Anal. Biochem. 346, 225–233 (2005).

67. Teich, A. F., Patel, M. & Arancio, O. A reliable way to detect endogenous murine β-amyloid. PLoS ONE 8, e55647 (2013).

68. Griciuc, A. et al. Alzheimer’s disease risk gene CD33 inhibits microglial uptake of amyloid beta. Neuron 78, 631–643 (2013).

69. Kalish, B. T. et al. Single-cell transcriptomics of the developing lateral geniculate nucleus reveals insights into circuit assembly and refinement. Proc. Natl Acad. Sci. USA 115, E1051–E1060 (2018).

70. Qiu, C. et al. Cis P-tau underlies vascular contribution to cognitive impairment and dementia and can be effectively targeted by immunotherapy in mice. Sci. Transl. Med. 13, eaaz7615 (2021).

71. Zheng, G. X. Y. et al. Massively parallel digital transcriptional profiling of single cells. Nat. Commun. 8, 14049 (2017).

72. Hao, Y. et al. Integrated analysis of multimodal single-cell data. Cell 184, 3573–3587 (2021).

73. Yang, A. C. et al. A human brain vascular atlas reveals diverse mediators of Alzheimer’s risk. Nature 603, 885–892 (2022).

74. McGinnis, C. S., Murrow, L. M. & Gartner, Z. J. DoubletFinder: doublet detection in single-cell RNA sequencing data using artificial nearest neighbors. Cell Syst. 8, 329–337 (2019).

75. Sun, H., Zhou, Y., Fei, L., Chen, H. & Guo, G. scMCA: a tool to define mouse cell types based on single-cell digital expression. Methods Mol. Biol. 1935, 91–96 (2019).

76. Pálovics, R. et al. Molecular hallmarks of heterochronic parabiosis at single-cell resolution. Nature 603, 309–314 (2022).

77. Finak, G. et al. MAST: a flexible statistical framework for assessing transcriptional changes and characterizing heterogeneity in single-cell RNA sequencing data. Genome Biol. 16, 278 (2015).

78. Zhou, Y. et al. Metascape provides a biologist-oriented resource for the analysis of systems-level datasets. Nat. Commun. 10, 1523 (2019).

79. Dobin, A. et al. STAR: ultrafast universal RNA-seq aligner. Bioinformatics 29, 15–21 (2013).

80. Anders, S., Pyl, P. T. & Huber, W. HTSeq—a Python framework to work with high-throughput sequencing data. Bioinformatics 31, 166–169 (2015).

81. Marsh, S. E. et al. Dissection of artifactual and confounding glial signatures by single-cell sequencing of mouse and human brain. Nat. Neurosci. 25, 306–316 (2022).

82. Love, M. I., Huber, W. & Anders, S. Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biol. 15, 550 (2014).

83. Krämer, A., Green, J., Pollard, J. Jr & Tugendreich, S. Causal analysis approaches in Ingenuity Pathway Analysis. Bioinformatics 30, 523–530 (2014).

84. Risso, D., Ngai, J., Speed, T. P. & Dudoit, S. Normalization of RNA-seq data using factor analysis of control genes or samples. Nat. Biotechnol. 32, 896–902 (2014).

85. Ritchie, M. E. et al. limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Res. 43, e47 (2015).

86. Baldarelli, R. M. et al. Mouse Genome Informatics: an integrated knowledgebase system for the laboratory mouse. Genetics 227, iyae031 (2024).

87. de Leeuw, C. A., Neale, B. M., Heskes, T. & Posthuma, D. The statistical properties of gene-set analysis. Nat. Rev. Genet. 17, 353–364 (2016).

88. Sollis, E. et al. The NHGRI-EBI GWAS Catalog: knowledgebase and deposition resource. Nucleic Acids Res. 51, D977–D985 (2023).

89. Elias, J. E. & Gygi, S. P. Target-decoy search strategy for increased confidence in large-scale protein identifications by mass spectrometry. Nat. Methods 4, 207–214 (2007).

90. Chen, M. et al. Common proteomic profiles of induced pluripotent stem cell-derived three-dimensional neurons and brain tissue from Alzheimer patients. J. Proteomics 182, 21–33 (2018).

91. Lee, H.-K. et al. Three dimensional human neuro-spheroid model of Alzheimer’s disease based on differentiated induced pluripotent stem cells. PLoS ONE 11, e0163072 (2016).

92. Perez-Riverol, Y. et al. The PRIDE database at 20 years: 2025 update. Nucleic Acids Res. 53, D543–D553 (2025).

Acknowledgements

We thank A. Johnston, A. Stebbins and J. Seravalli for assistance with ICP–MS; M. Chen for assistance with mass spectrometry; S. Valentin and A. Thompson for assistance with tissue processing; G. Klein for assistance with sample selection; and S. Nadarajan for technical assistance. This work was supported by NIH grants RO1AG046174 and RO1AG069042 to B.A.Y.; K01AG051791 and DP2AG072437 to E.A.L.; P30AG10161, P30AG72975, R01AG15819, R01AG17917, U01AG46152 and U01AG61356 to D.A.B.; and grants from the Ludwig Family Foundation, the Glenn Foundation for Medical Research and the Aging Mind Foundation to B.A.Y.

Author information

Authors and Affiliations

1. Department of Genetics, Harvard Medical School, Boston, MA, USA

Liviu Aron, Zhen Kai Ngian, Chenxi Qiu, Jaejoon Choi, Marianna Liang, Derek M. Drake, Sara E. Hamplova, Ella K. Lacey, Perle Roche, Monlan Yuan, Saba S. Hazaveh & Bruce A. Yankner

2. Division of Genetics and Genomics, Boston Children’s Hospital, Boston, MA, USA

Eunjung A. Lee

3. Rush Alzheimer’s Disease Center, Rush University Medical Center, Chicago, IL, USA

David A. Bennett

Contributions

L.A. performed metallomic analysis of human and mouse brain by ICP–MS, with assistance from M.L., analysed human and mouse brain by quantitative immunohistochemistry, did cell-culture studies with BV2 cells and carried out mouse behavioural studies with assistance from M.L., S.E.H., E.K.L., P.R., M.Y. and S.S.H. Z.K.N. isolated and characterized primary microglia, did RNA sequencing and analysis of cytokine production and Aβ clearance, and did Li-Aβ equilibrium binding assays. C.Q. prepared single-nucleus libraries and did RNA sequencing. J.C., Z.K.N., C.Q., D.M.D., L.A. and B.A.Y. did computational and statistical analyses, with input from E.A.L. D.A.B. provided human brain samples and phenotypic data from the ROSMAP study. L.A. and B.A.Y. wrote the manuscript with input from all authors. B.A.Y. supervised all aspects of the work.

Corresponding author

Correspondence to Bruce A. Yankner.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Ashley Bush, Junmin Peng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Analysis of brain and serum lithium levels.

a-c Li cortex-to-serum ratio in the cerebellum (a), total Li levels in the cerebellum (b), and serum Li levels (c) are not significantly different in NCI, MCI, and AD. a, n = 125 NCI, n = 55 MCI and n = 101 AD cases. b, n = 129 NCI, n = 58 MCI and n = 102 AD cases. c, n = 141 NCI, n = 62 MCI and n = 101 AD cases. d, Lithium is concentrated in Aβ plaques in AD mice. Aβ immunolabeling in the cortex of 12-month-old J20 mice. Laser ablation ICP-MS was performed on an adjacent unfixed section to quantify Li in Aβ plaques (P; white circles) and in neighboring non-plaque regions (NP; yellow circles). The ratios of Li levels in P to NP regions are shown (right) for n = 4 mice. e, Aβ immunolabeling of the cortex in J20 mice at 3 months of age, prior to onset of Aβ deposition, and 12 months of age, following widespread Aβ deposition. Cortical samples were subfractionated from 3-month-old (WT n = 6; J20 n = 7) and 12-month-old (WT n = 9, J20 n = 7) mice and Li in non-plaque fractions was measured by ICP-MS (middle and right panels). The data was normalized to the mean of WT. Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). P-values by one-way ANOVA with Tukey’s post-hoc test (a-c) or two-tailed unpaired t-tests (d,e). Scale bars, 50 μm.

Source Data

Extended Data Fig. 2 Lithium deficiency does not impair exploratory behavior or motor function in mice.

a–c, Li levels measured by ICP-MS in serum (a) and cortex (b) of 15-month-old 3xTg mice, and in cortex of 20-month-old WT mice (c) fed CTRL or DEF diets (n = 5 per group). d, Amyloid plaque burden in the hippocampus of 12-month-old 3xTg mice after 5 weeks of CTRL or DEF diet (n = 7 per group). e, Aβx-40 and Aβx-42 levels in the hippocampus of 26-month-old WT mice (treated from 12–26 months of age; CTRL n = 7; DEF n = 6), normalized to total protein. f, Immunofluorescence for pSer202-tau (CP13) in CA1 of 12-month-old 3xTg mice after 5 weeks of CTRL or DEF diet (n = 7 per group). g, pSer202-tau pathology in 15-month-old 3xTg mice fed either standard PicoLab® Rodent Diet 20 (CTRL 5053, n = 7) or a chemically-defined control diet (CTRL AIN-93M, n = 10), compared to those on Li-deficient chemically-defined AIN-93M diet (n = 9) for 9 months. h–l, Behavioral testing of 3xTg mice fed CTRL or DEF diets from 6–13.5 months of age: Open field activity (h–j), Morris water maze swim speed (k), and latency to reach a visible platform elevated above water level (l). m–q, Behavioral testing of 20-month-old WT mice fed CTRL or DEF diets from 12–20 months of age: Open field activity (m–o), swim speed (p), and latency to reach a visible platform (q). a–g, Data normalized to CTRL group means. l,q, Data are the mean ± s.e.m. a-k,m-p, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). P-values by unpaired two-tailed t-test, except g (one-way ANOVA with Tukey’s post-hoc test). h-l, n = 16 CTRL. h, j-l, n = 21 DEF. i, n = 20 DEF. m-o, n = 33 CTRL, n = 43 DEF. p,q, n = 25 CTRL, n = 34 DEF.

Source Data

Extended Data Fig. 3 Li deficiency results in loss of dendritic spines, axons and oligodendrocytes.

a, Golgi staining and quantification (right) of dendritic spine density in hippocampus CA1 (middle) and CA3 (right) subdomains of WT mice fed Li-deficient (DEF) or CTRL diets from 12–24 months of age (n = 8 mice per group). b, Golgi staining and quantification of spine density (right) in the hippocampus CA1 of 12-month-old 3xTg mice after 5 weeks of CTRL or DEF diet (n = 8 mice/group) for 5 weeks. c, Immunolabeling and quantification (right) of mature oligodendrocytes (marker Aspartoacylase) and axons (marker SMI-312) in the corpus callosum of WT mice treated from 12–24 months of age (CTRL n = 8; DEF n = 6). d, Immunolabeling of OPCs (marker PDGFRα) in the hippocampus of 3xTg mice treated with CTRL and DEF diets from 6–15 months of age and quantification of OPC density (n = 7 per group). e, Lithium deficiency impairs myelin integrity. Transmission electron microscopy (left panel) showing structural abnormalities in the myelin of the corpus callosum of Li-deficient 3xTg mice (treatment from 6–12 months). Violin plots show g-ratios (middle) and myelin sheath thickness (right) for individual axons (CTRL n = 1,376; DEF n = 1,396; pooled from n = 8 mice per group). a-d, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). c,d, The data was normalized to the mean of CTRL groups. a-e, P-values by unpaired two-tailed t-tests. Scale bars, 5 μm (a,b) or 25 μm (c, d).

Source Data

Extended Data Fig. 4 Lithium deficiency and Wnt/β-catenin signaling.

a, Pathways associated with Li deficiency in WT microglia. Wnt/β-catenin/TCF signaling is among the most significantly enriched signaling pathways and is predicted to be inhibited (predicted activation and inhibition are depicted as orange and blue, respectively). b,c, Functional network diagrams of Wnt/β-catenin/TCF signaling in Li-deficient WT and 3xTg microglia (b), and in excitatory neurons (c, left panel) and oligodendrocytes (c, right panel) from Li-deficient 3xTg mice. In each network, associated DEGs (FDR < 0.05) are highlighted in red (upregulated) or green (downregulated). In a, color intensity reflects z-score strength. Analysis was performed using the Ingenuity Pathway Analysis (IPA) platform. False discovery rate (FDR) was determined using a one-sided Fisher’s exact test followed by Benjamini-Hochberg correction for multiple comparisons.

Source Data

Extended Data Fig. 5 Regulation of GSK3β and β-catenin by endogenous lithium.

a-d, Immunolabeling and quantification of nuclear β-catenin in hippocampal CA1 neurons (a, b), corpus callosum oligodendrocytes (c), and microglia (d), co-labeled for MAP2, aspartoacylase (Asp-Acl), and Iba1, respectively. Additional β-catenin quantification shown for CA1 neurons after 5 weeks of DEF diet (a, middle). WT mice fed CTRL or DEF diets from 12–24 months of age shown in b. e,f, Immunolabeling (e, CA1 neurons) and quantification (e, right panel; f) of total GSK3β levels in CA1 neurons (e, MAP2 co-labeling) and oligodendrocytes (f, Aspartoacylase co-labeling) in 15-month-old 3xTg mice. g, Gsk3b mRNA in hippocampus of 12-month-old 3xTg mice was measured by qRT-PCR and normalized to Gapdh. h,i, pTyr216-GSK3β immunolabeling (h, 3xTg CA1 neurons) and quantification (h, middle and right panels; i) in CA1 neurons (h, MAP2 co-labeling) and oligodendrocytes (i, Aspartoacylase co-labeling) of 15-month-old 3xTg (h, middle; i, left) and 24-month-old WT (h, right; i, right) mice on CTRL or DEF diets. j,k, Immunolabeling of pSer9-GSK3β (j, left) and quantification of absolute (j, right) and relative (k) levels of inhibitory pSer9-GSK3β in the hippocampal CA1 region of 15-month-old 3xTg mice. l, Inositol levels measured by mass spectrometry in the hippocampus of 15-month-old 3xTg mice. 3xTg mice were fed CTRL or DEF diets for 9 months (from 6–15 months of age: a, left and right; c, d-f, h-l) or 5 weeks (from 10.85–12 months of age: a, middle; g). WT mice were treated from 12–24 months of age (b; h, right; i, right). Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). Data was normalized to CTRL group means. P-values by unpaired two-tailed t-test. WT CTRL n = 8, DEF n = 6. 3xTg CTRL (n = 6 in l, n = 7 in a, middle, d-f,j,k; n = 8 in a, right and c,g-i), 3xTg DEF (n = 6 in l, n = 7 in a, middle and d-f,j,k; n = 8 in g; n = 9 in a, right, and c,h,i). Scale bars, 25 μm.

Source Data

Extended Data Fig. 6 Inhibition of GSK3β rescues Li deficiency.

12-month-old 3xTg mice, maintained on Li-deficient (DEF) or CTRL diets for 3 months, received CHIR99021 (CHIR; 50 mg/kg body weight, intraperitoneally) or vehicle, once daily for 14 days. a, Immunolabeling and quantification (right) of CD68+/Iba1+ microglia density in the hippocampus. b, Cytokine and chemokine levels in the hippocampus (n = 3 mice per group), normalized to the mean of CTRL/Vehicle group. Means ± s.d. shown. c, Aβ immunolabeling and quantification (right) of plaque burden in the hippocampus. d, Phospho-Ser202-tau (CP13 antibody) labeling and quantification (right) of CP13+ cell density in the hippocampus CA1 region. e, Immunolabeling of oligodendrocytes (Aspartoacylase+) and myelin basic protein (MBP) labeling of myelin in the corpus callosum with quantification (middle and right) of oligodendrocyte density and MBP immunofluorescence (IF) intensity. a,c-e, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). Data was normalized to CTRL/Vehicle and analyzed by two-way ANOVA with Tukey’s post hoc (a,c-e) or two-tailed unpaired t-test (b); p-values indicated. Sample sizes: CTRL/Vehicle n = 6 (a,c,d), n = 7 (e); CTRL/CHIR99021, DEF/Vehicle n = 7 (a,c–e); DEF/CHIR99021 n = 6 (a,c–e). Scale bars, 25 μm.

Source Data

Extended Data Fig. 7 Lithium orotate exhibits reduced conductivity and Aβ binding compared to lithium carbonate.

a, Organic Li salts show reduced conductivity relative to inorganic Li salts. Solution conductivities are shown for Li concentrations of 4.3 mEq/L (left panel), 43 µEq/L (middle panel), and 21.5 µEq/L (right panel). P-values by unpaired two-tailed t-tests comparing organic versus inorganic salts. b, Binding of LiO and LiC to Aβ42 oligomers across a concentration range of 0–500 µEq/L Li. c,d, LiO exhibits less sequestration in Aβ plaques than LiC. The plaque to non-plaque (P/NP) Li ratios were quantified by laser ablation ICP-MS in 18-month-old 3xTg (c) and J20 (d) mice treated with LiO or LiC (4.3 µEq Li/L) for 7 days. 3xTg/LiC n = 7, 3xTg/LiO n = 8; J20/LiC n = 4 J20/LiO n = 4. e,f, Treatment with LiO achieves higher Li levels in non-plaque fractions relative to tratment with LiC. Subfractionation of the hippocampus was performed in 18-month-old J20 (e) and 3xTg (f) mice that were administered LiO or LiC (4.3 µEq Li/L) for 7 days. Age-matched WT mice without Aβ deposition served as controls. e, WT n = 8, J20 n = 8, J20/LiC n = 6, J20/LiO n = 7. f, WT n = 12, 3xTg n = 9, 3xTg/LiC n = 7, 3xTg/LiO n = 8. a,b, Shown are means ± s.d. for n = 3 independent solution replicates (a) or n = 3 biological replicates (b). c-f, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). Data was normalized to the mean of NP (c,d) or WT (e,f). P-values by unpaired two-tailed t-tests (a,c,d; pre-planned comparisons: WT vs. J20 in e; and WT vs 3xTg in f) or one-way ANOVA with Tukey’s post-hoc test (e,f).

Source Data

Extended Data Fig. 8 Suppression of AD patholog by lithium orotate.

a,b, Immunolabeling of Aβ (a) and pSer202-tau (p-tau/CP13, b) and quantification of Aβ plaque burden (a, right) and CP13+ cell density (b, right) in the hippocampus of 3xTg mice treated with the indicated concentrations of LiO, LiC, NaO or vehicle (water) from 5–12 months of age. c, Immunolabeling and quantification (right) of postsynaptic PSD-95 in hippocampus CA1 of 3xTg mice administered LiO or LiC (4.3 µEq/L), or vehicle from 9–18 months of age. d,e, Immunolabeling of myelin basic protein (MBP) (d) and oligodendrocytes (Aspartoacylase labeling) and quantifications of MBP expression (d, right) and oligodendrocyte density (e, right) in the corpus callosum of 3xTg mice. f,g, Quantification of Iba1+ microglia (f) and GFAP+ astrocyte (g) densities in the hippocampus of 18-month-old 3xTg mice treated with LiO or LiC (4.3 µEq/L) or vehicle from 9–18 months of age. Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). a-g, Data was normalized to the vehicle group means and analyzed by one-way ANOVA with Tukey’s post-hoc test. Scale bars, 25 μm. a,b, vehicle n = 17, LiO 4.3 n = 17, LiO 43 n = 8, LiO 430 n = 15, LiC 430 n = 10, NaO 4.3 n = 8, NaO 430 n = 6. c-g, water n = 4 (c), n = 6 (d-f), n = 7 (g); LiC n = 8, LiO n = 8.

Source Data

Extended Data Fig. 9 Lithium orotate suppresses GSK3β activity.

a-d, Treatment with LiO broadly reduces both total and activated GSK3β. 3xTg mice were treated from 9–18 months of age with LiO, LiC (4.3 µEq/L), or vehicle (water). a,c,d, Left panels show representative immunolabeling of total GSK3β (a), pTyr216-GSK3β (c), and nuclear β-catenin (d) in hippocampal CA1 neurons double-labeled for MAP2. Nuclei were labeled with DAPI (d). a,c,d, Right panels show quantification of total GSK3β, pTyr216-GSK3β and nuclear β-catenin in hippocampal CA1 neurons. b, Quantification of total GSK3β in corpus callosum oligodendrocytes (double-labeled for GSK3β and Aspartoacylase). a-d, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). Data was analyzed by one-way ANOVA with Tukey’s post-hoc test; P-values are shown. water n = 6, LiO n = 8, LiC n = 8. Scale bars, 50 µm.

Source Data

Extended Data Fig. 10 Lithium orotate restores spatial memory in J20 mice with advanced amyloid pathology.

a, Time course of spatial learning in the Morris water maze for J20 mice administered LiO (4.3 µEq/L) or vehicle (water) from 17–22 months of age. Shown are means ± S.E.M. b,c, Memory retrieval in the probe trial of the Morris water maze. Shown is the number of entries and time spent in the target area (b), and the latency to reach the target area (c). d,e, Swim speed and the latency to find a visible platform. f-h, LiO does not affect exploratory behavior in the open field test. Shown is distance travelled, distance traveled in the center of the arena, and the speed in the open field. b-h, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). a, Learning data were analyzed using mixed-effects models with repeated measures, followed by Šídák’s post-hoc test. b-h, P-values by two-tailed unpaired Mann Whitney U test (b) or two-tailed unpaired t-tests (c-h). e, no significant differences were found. Vehicle n = 8 (b, left; c), n = 9 (a, b right, d-h); LiO n = 10 (a-e,g), n = 11 (f,h).

Source Data

Extended Data Fig. 11 Lithium orotate prevents age-related neuroinflammation.

a,b, LiO prevents age-related neuroinflammatory changes in the hippocampal CA1 and CA3 regions, cortex, and corpus callosum of WT mice. Top panels: Microglia (a, Iba1 labeling) and astrocytes (b, GFAP labeling) were immunolabeled in 6-month-old WT mice (adult), 24-month-old WT mice (aged), and 24-month-old WT mice administered LiO (4.3 µEq/L) from 12–24 months of age (Aged/LiO). Bottom panels: Quantification of Iba1- (a) and GFAP-positive (b) cell densities. DAPI labeled cell nuclei. Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). The data was analyzed by two-way ANOVA with Tukey’s post-hoc test and the P-values for comparisons are indicated. n = 7 mice/group, except in panel b (cortex: adult n = 5). Scale bars, 25 µm.

Source Data

Extended Data Fig. 12 Lithium orotate promotes microglial clearance of Aβ.

a, LiO reverses age-related elevation of the proinflammatory cytokines IL-6 and IL-1β. Adult n = 4, Aged n = 6, Aged/LiO n = 6. b, LiO rescues the ability of aged microglia to clear Aβ. Left panel: Uptake of fluorophore-labeled human Aβ42 (red) by Iba1+ microglia (green). Right: Quantification of uptake and clearance. Microglia from 6-month-old WT controls (adult) were also analyzed. To assess Aβ42 uptake, microglia were incubated for 3 hr with Aβ42-containing medium. After the 3 hr preincubation, the medium was replaced with Aβ42-free medium and cells were incubated for an additional 3 hr to assess Aβ_42 clearance. Microglia were purified from n = 6 mice per group. c-e LiO promotes microglial uptake and degradation of Aβ42. BV2 cells were pre-treated with 20-500 µM LiO or NaO for 6 hr, then incubated for 3 hr with fluorophore-labeled human Aβ42 in the continued presence of the respective compound. c, Shown is Aβ_42 (red) and phalloidin (green) labeling. d,e Quantification of Aβ42 uptake (d) and clearance (e). Water n = 4, LiO n = 4, NaO n = 3 biological replicates. The LiO and NaO concentrations (20–500) were in µM. The data was normalized to the mean of adult controls (b, left) or water vehicle (d). a,b, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). d,e, Shown are individual values, as well as means ± S.E.M. Data was analyzed by one-way (d,e) or two-way (a,b) ANOVA with Tukey’s (a), Šídák’s (b) or Dunnett’s (d,e) post-hoc tests and P-values are indicated. d,e, P-values are for comparisons to the water control. Scale bars, 15 μm.

Source Data

Extended Data Fig. 13 Lithium and cognitive resilience during aging.

a-e LiO prevents age-related cognitive decline in WT mice. WT mice were treated with LiO (4.3 µEq/L) or vehicle from 12–24 months of age and then assessed behaviorally, together with 6-month-old WT mice (adult). a, Time course of spatial learning in the Morris water maze. b, Spatial memory was assessed in the probe trial of the Morris water maze. Shown are entries and time spent in the target area. c-d, Administration of LiO does not affect the latency to find a visible platform (c) or swim speed (d) in the Morris water maze. e, LiO restores the ability of aged WT mice to recognize a novel object. Shown is the discrimination index for identical objects (left) and for a novel object (right). a,c, Shown are means ± S.E.M. b,d,e, Box plots show individual values, median (line), box limits (25th-75th percentiles), and whiskers (min-max). a-e, Adult n = 18; Aged n = 14 (d,e) n = 15 (a-c); Aged/LiO n = 15 (d,e), n = 16 (a-c). a,c, Data was analyzed using mixed-effects models with repeated measures, followed by Tukey’s post-hoc test. b,d,e, Data was analyzed by two-way ANOVA with Tukey’s post-hoc test. a, shown are adjusted P-values for comparisons between Aged/LiO vs. Aged. c, No significant differences were seen between the 3 groups. f, Linear regression curves between cortical Li cortex-to-serum ratios and expression of cortical Complexin 1 (ROSMAP variable: synap_3cort_complex1), Complexin 2 (ROSMAP variable: synap_3cort_complex2), as well as a measure of mean Complexin1/2 expression in 3 brain regions (mid-cortex, inferior temporal cortex, and hippocampus; (ROSMAP variable: zcomplexin_3cort) for n = 47 aged cases with no cognitive impairment (NCI). Pearson correlation coefficients (r) and P-values are indicated.

Source Data

Supplementary information

Supplementary Figures

This file contains Supplementary Figs. 1–11.

Reporting Summary

Supplementary Table 1

Metallomic analysis of NCI, MCI and AD.

Supplementary Table 2

Correlations between cortical Li in the non-plaque fraction and cognitive and pathological indices in the ageing population.

Supplementary Table 3

snRNA-seq analysis of the hippocampus in 3xTg mice: summary of quality control and DEGs.

Supplementary Table 4

DEGs in cell populations of Li-deficient 3xTg hippocampus analysed by snRNA-seq.

Supplementary Table 5

GO analysis of downregulated pathways identified by snRNA-seq analysis of the Li-deficient 3xTg hippocampus.

Supplementary Table 6

GO analysis of upregulated pathways identified by snRNA-seq analysis of the Li-deficient 3xTg hippocampus.

Supplementary Table 7

Proteomic analysis of the Li-deficient 3xTg hippocampus.

Supplementary Table 8

Overlap between snRNA-seq DEGs and AD DEGs.

Supplementary Table 9

Purified microglia RNA-seq: alignment and mapping statistics.

Supplementary Table 10

DEG list and GO analysis of Li-deficient 3xTg microglia.

Supplementary Table 11

DEG list and GO analysis of Li-deficient wild-type microglia.

Supplementary Table 12

DEGs shared by Li-deficient 3xTg and wild-type microglia and GO analysis.

Supplementary Table 13

Binding characteristics of LiO and LiC to Aβ42 oligomers and fibrils.

Supplementary Table 14

RNA-seq of LiO-treated 3xTg hippocampus: alignment and mapping statistics.

Supplementary Table 15

RNA-seq of LiO-treated 3xTg hippocampus: DEGs and GO analysis.

Supplementary Table 16

Antibodies and reagents.

Supplementary Data

Source Data file for Supplementary Figs. 2 and 5–11.

Peer Review File

Source data

Source Data Figs. 1–5 and Source Data Extended Data Figs. 1–13

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Aron, L., Ngian, Z.K., Qiu, C. et al. Lithium deficiency and the onset of Alzheimer’s disease. Nature 645, 712–721 (2025). https://doi.org/10.1038/s41586-025-09335-x

- Received: 04 September 2024

- Accepted: 30 June 2025

- Published: 06 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09335-x

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

- A role for lithium in Alzheimer disease

- Ian Fyfe

Nature Reviews Neurology (2025)

- Does lithium deficiency contribute to Alzheimer’s disease?

- Ashley I. Bush

Nature (2025)

- New hope for Alzheimer’s: lithium supplement reverses memory loss in mice

- Lynne Peeples

Nature (2025)

- Lithiumbehandlung und Senkung des Suizidrisikos: Evidenz und klinische Bedeutung

- Michael Bauer

Der Nervenarzt (2025)

Myelin dysfunction drives amyloid-β deposition in models of Alzheimer’s disease

Article Open access 31 May 2023

Supervised latent factor modeling isolates cell-type-specific transcriptomic modules that underlie Alzheimer’s disease progression

Article Open access 17 May 2024

Independent replication of advanced brain age in mild cognitive impairment and dementia: detection of future cognitive dysfunction

Article Open access 16 August 2022

New hope for Alzheimer’s: lithium supplement reverses memory loss in mice

- Lynne Peeples

Nature News 06 Aug 2025

Does lithium deficiency contribute to Alzheimer’s disease?

- Ashley I. Bush

Nature News & Views 06 Aug 2025

Lithium limiting AD pathology

- Laura Zelenka

Nature Neuroscience Research Highlight 05 Sept 2025

Article Open access Published: 16 July 2025

Mitochondrial origins of the pressure to sleep

Raffaele Sarnataro,

Cecilia D. Velasco,

Nicholas Monaco,

Anissa Kempf &

…

Gero Miesenböck

Nature volume 645, pages 722–728 (2025)

Abstract

To gain a comprehensive, unbiased perspective on molecular changes in the brain that may underlie the need for sleep, we have characterized the transcriptomes of single cells isolated from rested and sleep-deprived flies. Here we report that transcripts upregulated after sleep deprivation, in sleep-control neurons projecting to the dorsal fan-shaped body1,2 (dFBNs) but not ubiquitously in the brain, encode almost exclusively proteins with roles in mitochondrial respiration and ATP synthesis. These gene expression changes are accompanied by mitochondrial fragmentation, enhanced mitophagy and an increase in the number of contacts between mitochondria and the endoplasmic reticulum, creating conduits3,4 for the replenishment of peroxidized lipids[5]. The morphological changes are reversible after recovery sleep and blunted by the installation of an electron overflow6,7 in the respiratory chain. Inducing or preventing mitochondrial fission or fusion8,9,10,11,12,13 in dFBNs alters sleep and the electrical properties of sleep-control cells in opposite directions: hyperfused mitochondria increase, whereas fragmented mitochondria decrease, neuronal excitability and sleep. ATP concentrations in dFBNs rise after enforced waking because of diminished ATP consumption during the arousal-mediated inhibition of these neurons[14], which augments their mitochondrial electron leak[7]. Consistent with this view, uncoupling electron flux from ATP synthesis[15] relieves the pressure to sleep, while exacerbating mismatches between electron supply and ATP demand (by powering ATP synthesis with a light-driven proton pump[16]) precipitates sleep. Sleep, like ageing17,18, may be an inescapable consequence of aerobic metabolism.

Similar content being viewed by others

Main

Sleep pressure, the process variable in sleep homeostasis, has lacked a physical interpretation. Although prolonged waking is associated with numerous changes in the brain—of neuronal firing patterns19,20, the strengths of synaptic connections[21], the organization of subcellular compartments22,23,24, metabolite concentrations25,26 and metabolic and gene expression programs23,27,28—it remains generally indeterminable whether these changes are causes or consequences of a growing need for sleep. Perhaps the only opportunity for separating causation from correlation exists in specialist neurons with active roles in the induction and maintenance of sleep[29]; in these cells, sleep’s proximate (and maybe also its ultimate) causes must interlock directly with the processes that regulate spiking. To delineate the molecular determinants of these processes in as complete and unbiased a manner as possible, we collected single-cell transcriptomes[30] of the brains of rested and sleep-deprived flies (Extended Data Fig. 1a). An encodable fluorescent marker allowed us to identify and enrich for two dozen sleep-inducing neurons with projections to the dorsal fan-shaped body of the central complex1,2 (dFBNs) and compare their transcriptomic response to sleep loss with that of other identifiable cell types.

Traces of sleep loss in mitochondria and synapses

Drosophila brains were dissociated into single-cell suspensions, and neurons expressing GFP under the control of R23E10-GAL4 (ref. [31]) were isolated by flow cytometry (Extended Data Fig. 1b). We performed single-cell RNA sequencing (scRNA-seq; 10X Chromium) on cells contained in the GFP-positive and GFP-negative fractions; among the 13,173 high-quality cells retrieved (Extended Data Fig. 1c,d), neurons nominated by R23E10-GAL4 were identified by the expression of GFP, the neuronal markers embryonic lethal abnormal vision (elav) and neuronal synaptobrevin (nSyb), and Allatostatin A (AstA) receptor 1 (AstA-R1), whose transcriptional enhancer provides the genomic fragment driving expression in the R23E10-GAL4 line. Most neurons in the R23E10-GAL4 domain contained machinery for the synthesis and release of either glutamate or GABA (γ-aminobutyric acid) (Extended Data Fig. 1e); some also transcribed the gene encoding the vesicular acetylcholine transporter (VAChT) (Extended Data Fig. 1e)—a common occurrence in non-cholinergic neurons, which rely on a microRNA to suppress its translation[32]. Indeed, fluorescent sensors detect the release of glutamate, but not of acetylcholine, from dFBNs[2].

In the Drosophila CNS, glutamate and GABA both act on ligand-gated chloride channels, consistent with the known inhibitory effect of dFBNs on their postsynaptic partners2,33. Members of the R23E10-GAL4 pattern that signal via one or the other of these inhibitory transmitters are anatomically segregated[2]: a pair of GABAergic cells target the suboesophageal ganglion, while a larger glutamatergic population innervates the dorsal fan-shaped body. This latter group of bona fide dFBNs formed a distinct gene expression cluster of 323 cells among all glutamatergic neurons in the brain (Fig. 1a and Extended Data Fig. 1f,g). The cluster was defined by genes controlled by known dFBN enhancers (Extended Data Fig. 1h) and encoding known dFBN markers, such as the Rho GTPase-activating protein[31] crossveinless-c, the dopamine receptor[14] Dop1R2, the serotonin receptor[34] 5-HT2B and the neuropeptide[33] AstA (Fig. 1b), but the distributions of some markers suggested further subdivisions. For example, AstA was confined to a subset of dFBNs (Fig. 1b), consistent with the comparatively mild sleep phenotype following RNA-mediated interference (RNAi) with its expression in the entire dFBN population[33].

Fig. 1: The transcriptional response of dFBNs to sleep deprivation.

a, Uniform manifold approximation and projection (UMAP) representation of glutamatergic neurons (grey) according to their gene expression profiles. dFBNs (purple) form a distinct cluster containing cells from rested (blue, n = 237 cells) and sleep-deprived brains (red, n = 86 cells). b, log-normalized expression levels of dFBN markers. c, Volcano plot of sleep history-dependent gene expression changes in dFBNs. Signals with Bonferroni-corrected P < 0.05 (two-sided Wilcoxon rank-sum test) are indicated in black; labels identify protein products localized to synapses or mitochondria; colours denote subunits of mitochondrial respiratory complexes. The P value of unc-13 exceeds the y-axis limit and is plotted at the top of the graph. d, Enrichment of the top ten downregulated (left) and upregulated (right) ‘biological process’ gene ontology terms in the set of differentially expressed dFBN genes.

Source data

Gene ontology analyses of the 122 transcripts whose levels in dFBNs changed after 12 h of overnight sleep deprivation pointed to only two sleep need-dependent processes: mitochondrial energy metabolism and synaptic transmission (Fig. 1c,d and Extended Data Fig. 2a–e). Sleep loss led to the selective upregulation of transcripts encoding components of electron transport complexes I–IV, ATP synthase (complex V), the ATP–ADP carrier sesB and enzymes of the tricarboxylic acid cycle (the citrate synthase kdn, the B subunit of succinate dehydrogenase and the malate dehydrogenase Men-b), whereas gene products involved in synapse assembly, synaptic vesicle release and presynaptic homeostatic plasticity[35] were selectively downregulated (Fig. 1c). Within the practical limits of our analysis, which cannot extend to every conceivable neuron type, this transcriptomic signature of sleep loss appeared unique to dFBNs: it was absent from two cell populations with comparable numerical representation in our data, namely projection neurons of the antennal lobe (317 cells) (Extended Data Fig. 3a–d) and Kenyon cells of the mushroom body (603 cells) (Extended Data Fig. 3e–h), and it was also undetectable in a combined analysis of all 12,850 non-dFBN cells (Extended Data Fig. 3i,j). There are, however, subtle hints from an independent transcriptomic study that sleep history may alter the levels of mitochondrial components not only in dFBNs but also in R5 neurons of the ellipsoid body, another element of the sleep homeostat[28].

The remainder of this Article examines the causes and consequences of the differential expression of genes encoding mitochondrial proteins in dFBNs; a parallel study[2] investigates the role of presynaptic plasticity in the wider context of sleep need-dependent dFBN dynamics.

A mitochondrial electron surplus induces sleep

The prominence of mitochondrial components in the transcriptional response of dFBNs to sleep deprivation (Fig. 1c,d and Extended Data Fig. 2) offers unbiased support for the hypothesis that sleep and aerobic metabolism are fundamentally connected. This hypothesis gained a firm mechanistic footing with the discovery that dFBNs regulate sleep through machinery that gears their sleep-inducing spike discharge to mitochondrial respiration[7]. The centrepiece of this mechanism is Hyperkinetic, the β-subunit of the voltage-gated potassium channel Shaker, which regulates the electrical activity of dFBNs7,14. Hyperkinetic is an unusual aldo-keto reductase with a stably bound nicotinamide adenine dinucleotide phosphate cofactor whose oxidation state (NADPH or NADP+) reflects the fate of electrons entering the respiratory chain5,7. When the demands of ATP synthesis are high, the vast majority of electrons reach O_2 in an enzymatic reaction catalysed by cytochrome c oxidase (complex IV); only a small minority leak prematurely from the upstream mobile carrier coenzyme Q (CoQ), producing superoxide and other reactive oxygen species17,36 (ROS) (Fig. 2a). The probability of these non-enzymatic single-electron reductions of O_2 increases sharply under conditions that overfill the CoQ pool as a consequence of increased supply (high NADH to NAD+ ratio) or reduced demand (large protonmotive force (∆p) and high ATP to ADP ratio)17,18,36 (Fig. 2a). The mitochondria of dFBNs are prone to this mode of operation during waking[7], when caloric intake is high but the neurons’ electrical activity is reduced, leaving their ATP reserves full. Indeed, measurements with the genetically encoded ATP sensors iATPSnFR and ATeam showed approximately 1.2-fold higher ATP concentrations in dFBNs, but not projection neurons, after a night of sleep deprivation than at rest (Fig. 2b,c and Extended Data Fig. 4a,b). ATP concentrations rose acutely when dFBNs were inhibited by an arousing heat stimulus, which releases dopamine onto their dendrites2,14 (Fig. 2a,d), and fell below baseline when dFBNs themselves were stimulated, mimicking sleep[2] (Fig. 2a,e).

Fig. 2: A mitochondrial electron surplus induces sleep.

a, Proton-pumping complexes I, III and IV convert the energy of electron transfers from NADH to O_2—through intermediates CoQ and cytochrome c (cyt c)—into a proton electrochemical gradient, ∆p, across the IMM. Ucp4 discharges, whereas illumination (hν) of mito-dR charges, the IMM. The return of extruded protons to the matrix spins the blades of the ATP synthase and produces ATP, which leaves the matrix via sesB in exchange for cytoplasmic ADP. Neuronal ATP consumption is activity-dependent, in part because the plasma membrane Na+–K+ ATPase must restore ion gradients dissipated by action and excitatory synaptic currents. An oversupply (relative to ATP demand) of electrons to CoQ increases the risk of single-electron reductions of O_2 to O_2− at complexes I and III. AOX mitigates this risk. b,c, Summed-intensity projections of dFBN dendrites expressing iATPSnFR plus RFP (b) or ATeam (c), in rested and sleep-deprived (SD) flies. Emission ratios are intensity-coded according to the keys below and increase after sleep deprivation (P < 0.0001 (b) and P = 0.0003 (c); two-sided Mann–Whitney test). d, Arousing heat elevates ATP in dFBNs expressing iATPSnFR plus tdTomato. Mean fluorescence was quantified in 20-s windows immediately before and after stimulation (P = 0.0152, two-sided paired t-test) and is plotted as a change in fluorescence intensity ratio (∆R/R) with co-expressed tdTomato relative to pre-stimulation baseline. e, Optogenetic stimulation dissipates ATP in dFBNs expressing iATPSnFR and CsChrimson, but not in dFBNs lacking CsChrimson (P = 0.0076, two-sided t-test). ∆F/F is the change in fluorescence intensity relative to pre-stimulation baseline. f, Sleep in flies expressing R23E10 ∩ VGlut-GAL4-driven Ucp4A or Ucp4C and parental controls (P ≤ 0.0381, Holm–Šídák test after analysis of variance (ANOVA)). g,h, Sleep during the first 60 min after illumination (g; P ≤ 0.0432, Dunn’s test after Kruskal–Wallis ANOVA) and cumulative sleep percentages in flies expressing R23E10 ∩ VGlut-GAL4-driven mito-dR, with or without retinal, and parental controls (h; ∆p photogeneration effect: P < 0.0001, time × ∆p photogeneration interaction: P < 0.0001, mixed-effects model). Asterisks indicate significant differences (P < 0.05) from both parental controls or in planned pairwise comparisons. Data are means ± s.e.m.; n, number of dendritic regions (b,c) or flies (d–h). Scale bars, 5 μm (b,c). For statistical details see Supplementary Table 1.

Source data

Even if the chance of an individual electron spilling from the CoQ pool is low, however, metabolically highly active cells, such as neurons, will by the sheer number of electrons passing through their respiratory chains generate significant amounts of ROS17,18,36,37. Their anti-cyclical relationship between energy availability (which peaks during waking) and energy consumption (which in a sleep-active neuron peaks during sleep) may thus predispose dFBNs to an exaggerated form of the electron leak experienced by many neurons in the awake state, making them an effective early warning system against widespread damage. Because polyunsaturated membrane lipids are especially at risk[5], dFBNs estimate the size of the mitochondrial electron leak indirectly, by counting reductions of lipid peroxidation-derived carbonyls at Hyperkinetic’s active site[5].

Several lines of evidence point to a mismatch between the number of electrons entering the mitochondrial transport chain and the number needed to fuel ATP production as a root cause of sleep. First, opening an exit route for surplus electrons from the CoQ pool (by equipping the mitochondria of dFBNs with the alternative oxidase[6] (AOX) of Ciona intestinalis, which produces water in a controlled four-electron reduction of O_2) not only relieved the basal pressure to sleep[7] but also remedied the excessive sleep need of flies whose ability to remove breakdown products of peroxidized lipids was impaired[5]. Second, increasing the demand of dFBNs for electrons (by overexpressing the uncoupling proteins Ucp4A or Ucp4C, which short-circuit the proton electrochemical gradient across the inner mitochondrial membrane (IMM)[15]) (Fig. 2a) decreased sleep (Fig. 2f and Extended Data Fig. 4c). And third, powering ATP synthesis with photons rather than electrons (by illuminating a mitochondrially targeted version of the light-driven archaeal proton pump delta-rhodopsin[16]) (Fig. 2a and Extended Data Fig. 4d) made NADH-derived electrons in dFBNs redundant and precipitated sleep (Fig. 2g,h and Extended Data Fig. 4e,f).

Sleep alters mitochondrial dynamics

Given this wealth of evidence, it is not surprising that mitochondria would emerge as one of two pivots in the reorganization of dFBN gene expression after sleep deprivation (Fig. 1c,d and Extended Data Fig. 2). However, it remains ambiguous whether the upregulation of transcripts encoding mitochondrial proteins signals a net increase in mitochondrial mass or a compensatory response to organelle damage. To disambiguate these scenarios, we labelled the mitochondria of dFBNs with matrix-localized GFP (mito-GFP) and, in independent series of experiments, imaged the neurons’ dendritic fields by confocal laser-scanning microscopy (CLSM) or optical photon reassignment microscopy[38] (OPRM). Both forms of light microscopy were validated against ultrastructure: automated morphometry of deconvolved image stacks established that, although both optical methods overestimated the true organelle size to some extent, the size ratios of mitochondria in dFBNs and uniglomerular olfactory projection neurons of the antennal lobes matched that determined by volume electron microscopy[39] (Extended Data Fig. 5a,b). Although diffraction undoubtedly inflated the absolute dimensions of mitochondria, especially in CLSM images, valid inferences about relative morphological differences could therefore still be drawn.

A night of sleep loss, regardless of whether caused by mechanical agitation or an artificial elevation of arousing dopamine[14], reduced the size, elongation and branching of dFBN mitochondria (Fig. 3a,b and Extended Data Fig. 5c–f) and led to the relocation of dynamin-related protein 1 (Drp1), the key fission dynamin of the outer membrane8,9,10, from the cytosol to the mitochondrial surface (Fig. 3c). OPRM, which achieves lateral super-resolution approximately twofold above the diffraction limit[38], detected a concomitant increase in mitochondrial number (Fig. 3b), indicative of organelle division, which eluded CLSM (Extended Data Fig. 5f, but see Methods for a cautionary remark about the interpretation of absolute mitochondrial counts). This seemingly incomplete tally of daughter mitochondria notwithstanding, the two methods painted congruous pictures of mitochondrial fission after sleep loss (Fig. 3a,b and Extended Data Fig. 5c–f). The mitochondria of antennal lobe projection neurons, by contrast, bore no vestiges of sleep history (Extended Data Fig. 6).

Fig. 3: Sleep history alters mitochondrial dynamics.

a,b, Volumetric renderings (a) and morphometric parameters (b) of automatically detected mitochondria in OPRM image stacks of dFBN dendrites in rested flies, sleep-deprived flies and flies allowed to recover for 24 h after sleep deprivation. Sleep history-dependent changes in mitochondrial number (P < 0.0001, Holm–Šídák test after ANOVA), volume (P = 0.0470, Dunn’s test after Kruskal–Wallis ANOVA), sphericity (P = 0.0124, Dunn’s test after Kruskal–Wallis ANOVA) and branch length (P = 0.0033, Dunn’s test after Kruskal–Wallis ANOVA) are occluded by the co-expression of AOX (P ≥ 0.2257, two-sided t-test or Mann–Whitney test) or the simultaneous activation of TrpA1 (P ≥ 0.0625, two-sided t-test or Mann–Whitney test) and (over)corrected after recovery sleep (number of mitochondria: P = 0.1551, all other parameters: P ≤ 0.0302, Dunn’s test after Kruskal–Wallis ANOVA). Two data points exceeding the y-axis limits are plotted as triangles at the top of the graphs; mean and s.e.m. are based on the actual values. c, Drp1 recruitment. Single confocal image planes through dFBN somata of flies expressing R23E10-GAL4-driven mito-GFP (top) and Drp1Flag from the endogenous locus (bottom). Sleep deprivation increases the percentage of cellular anti-Flag fluorescence (intensity-coded according to the key below) within automatically detected mitochondrial contours (P < 0.0001, two-sided Mann–Whitney test). d, Mitochondria–endoplasmic reticulum contacts. Isosurface renderings (voxel value 128) of SPLICS puncta in distal dFBN dendritic branches (dashed outlines), obtained by trilinear interpolation of thresholded and despeckled confocal image stacks. Sleep deprivation increases the number of SPLICS puncta per dendritic field (P < 0.0001, two-sided Mann–Whitney test). e, Mitophagy. Summed-intensity projections of dFBN dendrites expressing mito-QC. Emission ratios are intensity-coded according to the key below and increase after sleep deprivation (P = 0.0101, two-sided t-test). Data are means ± s.e.m.; n, number of dendritic regions (b,d,e) or somata (c); asterisks, significant differences (P < 0.05) in planned pairwise comparisons. Scale bars, 10 μm (a), 2 μm (c), 10 μm (d), 5 μm (e). For statistical details see Supplementary Table 1.

Source data

AOX protected dFBN mitochondria against sleep loss-induced fragmentation (Fig. 3b and Extended Data Fig. 5e–g), underlining that ROS generation during waking[7] is the initial spark that triggers fission36,40. In the same vein, depolarization of dFBNs during mechanical sleep deprivation, which increases ATP consumption by the Na+–K+ pump and thereby reduces the diversion of electrons into ROS (Fig. 2a), preserved the morphology of their mitochondria (Fig. 3b and Extended Data Fig. 5e–g).

Mitochondrial fission is a prelude to the proliferation of mitochondria at contact sites with the endoplasmic reticulum[41] and/or the shedding and clearance of dysfunctional organelle fragments by mitophagy[42] (Fig. 3c). Sleep deprivation stimulated both processes: the reconstitution of fluorescence from GFP fragments anchored in the outer mitochondrial and endoplasmic reticulum membranes (SPLICSshort, whose mere presence had no effect on sleep (Extended Data Fig. 5h)) showed a higher contact site count in dFBNs of sleep-deprived flies (Fig. 3d), whereas mito-QC, a ratiometric sensor detecting the entry of mitochondria into acidic autophagolysosomes, reported enhanced mitophagy (Fig. 3e). Mitochondria–endoplasmic reticulum contacts concentrate the fission and fusion machineries41,43 whose dynamic equilibrium determines the steady-state morphology of the mitochondrial network and support mitochondrial biogenesis by allowing the passage of phospholipids from the endoplasmic reticulum3,4. The abundance of mitochondria–endoplasmic reticulum contacts in sleep-deprived dFBNs (Fig. 3d) may thus not only echo a recent wave of mitochondrial fission (Fig. 3a,b and Extended Data Fig. 5c–f), but also prefigure, as we suspect the abundance of transcripts for mitochondrial proteins does (Fig. 1c), the proliferation and fusion of mitochondria during subsequent recovery sleep, which caused their volume, shape and branch length to rebound above baseline values (Fig. 3a,b and Extended Data Fig. 5e, f).

Mitochondrial dynamics alter sleep

If shifts in the balance between mitochondrial fission and fusion are part of a feedback mechanism that corrects mismatches between NADH supply and ATP demand36,44,45 that cause sleep pressure to rise or fall, then the experimental induction of these homeostatic responses in dFBNs should move the set points for sleep: mitochondrial fragmentation is predicted to decrease, and mitochondrial fusion is predicted to increase, sleep duration and depth. To test these predictions, we took experimental control of the three GTPases with central regulatory roles in mitochondrial dynamics (Fig. 4a and Extended Data Fig. 7a–c): the fission dynamin Drp1 (refs. 8,9,10), and integral proteins of the inner and outer mitochondrial membranes, termed optic atrophy 1 (Opa1) and mitofusin or mitochondrial assembly regulatory factor (Marf), respectively, whose oligomerization in cis and trans fuses the corresponding membranes9,11,12,13. As in our manipulations of mitochondrial protonmotive force (Fig. 2f–h and Extended Data Fig. 4c–f), R23E10-GAL4 and the intersectional driver R23E10 ∩ VGlut-GAL4, which targets bona fide glutamatergic dFBNs of the central brain[2] (Fig. 1a), were used interchangeably in these experiments (Fig. 4 and Extended Data Fig. 8).

Fig. 4: Mitochondrial dynamics alter sleep.

a, The mitochondrial fission (green) and fusion machineries (blue) comprise Drp1, the outer and inner membrane proteins Marf and Opa1, and the mitoPLD zuc, which releases phosphatidic acid (PA) from cardiolipin (CL). Miga stimulates zuc activity and/or supplies phosphatidic acid from other membranes. b,c, Sleep profiles (b, genotype effect: P < 0.0001, time × genotype interaction: P < 0.0001, two-way repeated-measures ANOVA) and daily sleep (c) in flies expressing R23E10 ∩ VGlut-GAL4-driven fission or fusion proteins, or RNAi transgenes targeting transcripts encoding these proteins (left) or those regulating phosphatidic acid levels (right), and their parental controls. Manipulations that increase fission (green) or fusion (blue) alter sleep in opposite directions (GTPases: P ≤ 0.0332, Holm–Šídák test after ANOVA; phosphatidic acid regulators: P ≤ 0.0198 for all planned pairwise comparisons after Kruskal–Wallis ANOVA). d, Manipulations that increase fission (R23E10 ∩ VGlut-GAL4 > Opa1RNAi, green) or fusion (R23E10 ∩ VGlut-GAL4 > Marf,Opa1, blue) alter the time courses (left-hand panels, genotype effects: P ≤ 0.0003, time × genotype interactions: P < 0.0001, two-way repeated-measures ANOVA) and percentages of sleep rebound after deprivation in opposite directions (right-hand panel, genotype effect: P ≤ 0.0450 for all planned pairwise comparisons after Kruskal–Wallis ANOVA). Four data points exceeding the y-axis limits are plotted as triangles at the top of the right-hand graph; mean and s.e.m. are based on the actual values. e, Example voltage responses to current steps of dFBNs expressing mCD8::GFP (grey) and Drp1 (green) or Marf plus Opa1 (blue). f, Manipulations that increase fission (green) or fusion (blue) alter the membrane resistance (Rm)-normalized spike frequency in opposite directions (genotype effect: P < 0.0001, time × genotype interaction: P < 0.0001, mixed-effects model, sample sizes in g). g, Membrane resistances (genotype effect: P = 0.4806, Kruskal–Wallis ANOVA). h, The overexpression of Marf plus Opa1 increases the percentage of dFBNs generating bursts of action potentials (P = 0.0241, χ^2-test; standardized residuals +2.01). Data are means ± s.e.m.; n, number of flies (b–d) or cells (f,g). Asterisks, significant differences (P < 0.05) in planned pairwise comparisons. For statistical details see Supplementary Table 1.

Source data

Fragmenting dFBN mitochondria through the overexpression of Drp1 or the RNAi-mediated depletion of Opa1—and, to a lesser extent, of Marf—decreased sleep (Fig. 4b,c and Extended Data Fig. 8a–e), abolished the homeostatic response to sleep deprivation (Fig. 4d and Extended Data Fig. 8f) and reduced ATP concentrations in dFBNs regardless of sleep history (Extended Data Fig. 7d). Tipping the equilibrium towards mitochondrial fusion had the opposite effect: dFBN-restricted knockdown of Drp1 or the overexpression of Opa1 plus Marf—or of Opa1 alone, but not of Marf alone—increased baseline as well as rebound sleep (Fig. 4b–d and Extended Data Fig. 8a,f,g) and elevated the arousal threshold (Extended Data Fig. 9a,b) without causing overexpression artefacts or overt developmental defects (Extended Data Fig. 9c,d). None of these interventions altered sleep when targeted to projection neurons or Kenyon cells (Extended Data Fig. 10). The indiscriminate sleep losses reported[24] after pan-neuronal or glial RNAi knockdowns of either Drp1 or Marf—which in dFBNs alter sleep bidirectionally (Fig. 4b–d and Extended Data Fig. 8a,f), reflecting their antagonistic mitochondria-shaping roles—are difficult to interpret without parallel measurements of mitochondrial (and possibly peroxisomal) form and function. Taken at face value, they could hint that the fusion–fission cycles of many non-dFBN cells are not tied to the sleep–wake cycle but operate continuously to mix and re-compartmentalize mitochondrial content for maintenance or metabolic control44,45.

In dFBNs, the large and opposite behavioural consequences of promoting mitochondrial fission or fusion (Fig. 4b–d) went hand-in-hand with established biophysical signatures of low or high sleep pressure5,31. dFBNs in short sleepers overexpressing Drp1 had shallower current–spike frequency functions than neurons in control animals, whereas the converse was true in somnolent overexpressers of Opa1 and Marf (Fig. 4e–g), whose dFBNs generated an elevated number of somnogenic bursts[2] as part of their enhanced responses (Fig. 4e,h).

A striking feature of sleep-deprived brains is the depletion of phosphatidic acid[5], a fusogenic[46] glycerophospholipid. Mitochondrial phosphatidic acid is a cleavage product of cardiolipin, generated by a local phospholipase D (mitoPLD)[46] (Fig. 4a). Underlining the importance of phosphatidic acid for the fusion reaction, and of mitochondrial fusion for the regulation of sleep, R23E10 ∩ VGlut- or R23E10-GAL4-restricted interference with the expression of the mitoPLD zucchini or the outer membrane protein Mitoguardin (Miga), which stabilizes catalytically active mitoPLD[47] and/or transfers phospholipids (including phosphatidic acid) from other cellular membranes to mitochondria48,49, recapitulated the sleep losses seen when the protein-based fusion machinery of these neurons was targeted by RNAi or antagonized by the overexpression of Drp1 (Fig. 4c and Extended Data Fig. 8b).

Discussion

Aerobic metabolism was the innovation that, following the first of two large increases in atmospheric O_2 levels 2.4 billion and 750–570 million years ago, allowed eukaryotes to maximize the free energy yield of electron transfers, setting the stage for the Cambrian explosion of multicellular life in the wake of the second O_2 revolution[50]. Power-hungry nervous systems appeared[51]—and with them, apparently, the need for sleep[52]. Although sleep is likely to have since acquired additional functions, such as synaptic homeostasis or memory consolidation[21], an empirical power law[53] that relates daily sleep amount to mass-specific O_2 consumption[54] suggests that sleep serves an ancient metabolic purpose also in mammals. The allometric exponent in this power law is a multiple of \(\frac{1}{4}\) rather than the \(\frac{1}{3}\) expected from Euclidean geometric scaling—a sign that the distribution of resources by centralized networks, such as the vascular and respiratory systems, is responsible53,55. Thanks to higher terminal branch densities, these networks allocate more O_2 to each cell in small animals, allowing their metabolism to run ‘hotter’ than that of large mammals, whose cells are supply-limited[55]. The price to pay is a shorter life, a greater fraction of which is spent asleep. Even within species, variations in the sleep requirements of individuals (including those with identical nuclear genomes, such as our isogenic flies) could arise, in part, from differences in the resistance to electron flow[18] of respiratory complexes containing subunits encoded by mitochondrial DNA. An overwhelming sense of tiredness (which is unrelated to muscle fatigue) is in fact a common symptom of human mitochondrial disease[56].

If sleep indeed evolved to fulfil a metabolic need, it is not surprising that neurons controlling sleep and energy balance would be regulated by similar mechanisms. In the mammalian hypothalamus, the mitochondria of orexigenic neurons expressing agouti-related protein (AgRP) and of anorexigenic neurons expressing pro-opiomelanocortin undergo antiphasic cycles of fission and fusion[57]. These cycles are coupled to changes in the energy balance of mice[57], just as cycles of mitochondrial fission and fusion in dFBNs are coupled to changes in the sleep balance of flies. The electrical output of AgRP neurons increases after mitochondrial fusion to promote weight gain and fat deposition[57], just as the electrical output of dFBNs increases after mitochondrial fusion to promote sleep. Deletions of mitofusins from AgRP neurons impair the consumption of food[57], just as interference with mitochondrial fusion in dFBNs impairs the induction of sleep. These parallels suggest that sleep pressure and hunger both have mitochondrial origins, and that electrons flow through the respiratory chains of the respective feedback controllers like sand in the hourglass that determines when balance must be restored.

Methods

Drosophila strains and culture

Flies were grown on media of cornmeal (62.5 g l−1), inactive yeast powder (25 g l−1), agar (6.75 g l−1), molasses (37.5 ml l−1), propionic acid (4.2 ml l−1), tegosept (1.4 g l−1) and ethanol (7 ml l−1) under a 12 h light–12 h dark cycle at 25 °C in approximately 60% relative humidity, unless stated otherwise. To prevent the undesired activation of optogenetic actuators or the photoconversion of all-trans retinal by ambient light, flies expressing CsChrimson or mito-dR and their controls were reared and housed in constant darkness and transferred to food supplemented with 2 mM all-trans retinal (Molekula) in dimethylsulfoxide (DMSO), or to DMSO vehicle only, 2 days before the optical stimulation experiments, at an age of 1–2 days post eclosion. Flies expressing TrpA1 and their controls were cultured and maintained at 21 °C and shifted to 29 °C for 12 h.

Transgene expression was directed to dFBNs by driver lines R23E10-GAL4 (ref. [58]) or R23E10 ∩ VGlut-GAL4 (ref. [2]) (created by reconstituting GAL4 from hemidrivers[59] R23E10-DBD[60] and VGlut-p65AD[61]); projection neurons, Kenyon cells and dopaminergic neurons were targeted by GH146-GAL4 (ref. [62]), OK107-GAL4 (ref. [63]) and TH-LexA[64], respectively. Effector transgenes encoded fluorescent markers for flow cytometry (UAS-6xEGFP[65]), visually guided patch-clamp recordings (UAS-mCD8::GFP[66]), mitochondrial morphometry (UAS-mito-GFP67,68) or ratiometric imaging (UAS-RFP or UAS-tdTomato); integral proteins of the outer mitochondrial membrane[69] (UAS-OMM-mCherry), endoplasmic reticulum[70] (UAS-tdTomato-Sec61β) or plasma membrane[71] (UAS-CD4-tdTomato); the ATP sensors iATPSnFR1.0 (refs. 72,73) or ATeam1.03NL74,75; the mitochondrial alternative oxidase AOX of Ciona intestinalis[76]; delta-rhodopsin of Haloterrigena turkmenica with an IMM-targeting sequence16,77 (mito-dR); the opto- or thermogenetic actuators[78] CsChrimson[79] or TrpA1 (the latter in UAS- and lexAop-driven versions80,81); the mitochondria–endoplasmic reticulum contact site82,83 or mitophagy84,85 reporters SPLICSshort or mito-QC; overexpression constructs encoding Ucp4A or Ucp4C86,87, Drp1 (3 independent transgenes88,89,90), Opa1 (ref. [89]) or Marf (2 independent transgenes89,91); or RNAi transgenes for interference with the expression of Drp1 (ref. [91]), Opa1 (7 independent transgenes88,92,93), Marf (5 independent transgenes88,92,93), zucchini[93] or Mitoguardin (2 independent transgenes[92]). Recombinant strains carrying the UAS-Marf and R23E10-GAL4 or R23E10-DBD transgenes on the third chromosome were generated to enable the co-expression of Opa1 and Marf. Endogenous Drp1 was colocalized with mitochondria in Drp1::FLAG-FlAsH-HA flies[94]. Supplementary Table 3 lists all fly strains and their sources.

Sleep measurements and sleep deprivation

In standard sleep assays, females aged 2–4 days were individually inserted into 65-mm glass tubes containing food reservoirs, loaded into the Trikinetics Drosophila Activity Monitor system and housed under 12 h light–12 h dark conditions at 25 °C in 60% relative humidity. Flies were allowed to habituate for 1 day before sleep—classified as periods of inactivity lasting more than 5 min95,96 (Sleep and Circadian Analysis MATLAB Program[97])—was averaged over two consecutive recording days. Immobile flies (fewer than two beam breaks per 24 h) were manually excluded.

Our standard method of sleep deprivation used the sleep-nullifying apparatus[98]: a spring-loaded platform stacked with Trikinetics monitors was slowly tilted by an electric motor, released and allowed to snap back to its original position. The mechanical cycles lasted 10 s and were repeated continuously for 12 h, beginning at zeitgeber time 12. Flies expressing TrpA1 in dFBNs (and relevant controls) were mechanically sleep-deprived at 29 °C.

To guard against potential side effects of regular mechanical agitation, we explored two alternative methods of sleep deprivation, with comparable results. In some behavioural experiments (Extended Data Fig. 8f), an Ohaus Vortex Mixer stacked with Trikinetics monitors produced horizontal circular motion stimuli with a radius of about 1 cm at 25 Hz for 2 s; in contrast to the rhythmic displacement of flies in the sleep-nullifying apparatus[98], stimulation periods were randomly normally distributed in 20-s bins, hindering adaptation. In some morphometric experiments, flies expressed TrpA1 in arousing dopaminergic neurons[14], whose activation at 29 °C produced sleep deprivation without sensory stimulation (Extended Data Fig. 5c,d).

Rebound sleep was measured in the 24-h window after deprivation. Cumulative sleep loss was calculated for each individual by comparing the percentage of sleep lost during overnight sleep deprivation with the immediately preceding unperturbed night. Individual sleep regained was quantified by normalizing the difference in sleep amount between the rebound and baseline days to baseline sleep. Only flies losing more than 95% of baseline sleep were included in the analysis.

Arousal thresholds were determined by applying horizontal circular motion stimuli with a radius of ~1 cm at 8 Hz, generated by a Talboys Multi-Tube Vortexer. Stimuli lasting 0.5–20 s were delivered once every hour between zeitgeber times 0 and 24, and the percentages of sleeping flies (if any) awakened within 1 min of each stimulation episode were quantified.

Sleep induction by photo-energized mitochondria

For experiments with photo-energized mitochondria16,77, 3–5-day-old females expressing R23E10 ∩ VGlut-GAL4- or R23E10-GAL4-driven mito-dR and their parental controls were reared for 2 days on standard food supplemented with all-trans retinal (or DMSO vehicle only, as indicated) and individually transferred to the wells of a flat-bottom 96-well plate. Each well contained 150 µl of sucrose food (5% sucrose, 1% agar) with or without 2 mM all-trans retinal. The plate was sealed with a perforated transparent lid, inserted into a Zantiks MWP Z2S unit operated at 25 °C and illuminated from below by infrared LEDs while a camera captured 31.25 frames per s from above. Zantiks software extracted time series of individual movements, which were converted to sleep measurements with the help of a custom MATLAB script detecting continuous stretches of zero-speed bins lasting more than 5 min. After flies had been allowed to habituate for at least one day in the absence of stimulation light, high-power LEDs running on an 80% duty cycle at 2 Hz (PWM ZK-PP2K) delivered about 7 mW cm−2 of 530-nm light for 1 h. Movement was monitored for 24 h, including the initial hour of optogenetic stimulation. If flies were found dead at the end of the experiment, data from the 1-h time bin preceding the onset of continuous immobility (>98% zero-speed bins during two or more consecutive hours until the end of the recording) onward were excluded. The >98% threshold was applied to avoid scoring rare instances of video tracker noise as movement.

Brain dissociation and cell collection for scRNA-seq

On each experimental day, averages of 186 rested and 144 sleep-deprived female flies were retrieved alive from Trikinetics monitors (Extended Data Fig. 1a) and dissected in parallel in ice-cold Ca2+- and Mg2+-free Dulbecco’s PBS (Thermo Fisher) supplemented with 50 µM d(-)−2-amino-5-phosphonovaleric acid, 20 µM 6,7-dinitroquinoxaline-2-3-dione and 100 nM tetrodotoxin (tDPBS) to block excitatory glutamate receptors and voltage-gated sodium channels. The lower number of sleep-deprived flies recovered reflects accidental mortality associated with the operation of the sleep-nullifying apparatus. Brains were transferred to Protein LoBind microcentrifuge tubes containing ice-cold Schneider’s medium supplemented with the same toxins (tSM), washed once with 1 ml of tSM, incubated in tSM containing 1.11 mg ml−1 papain and 1.11 mg ml−1 collagenase I for 30 min at room temperature, washed again with tSM and subsequently triturated with flame-rounded 200-μl pipette tips. Dissociated brain cells were collected by low-speed centrifugation (2,000 rpm, 3 min), resuspended in 1 ml tDPBS, and filtered through a 20-μm CellTrics strainer. For the isolation of cells by flow cytometry, dead cells were excluded with the help of a DAPI viability dye (1 μg ml−1; BD Pharmingen). Single cells were gated for on the basis of forward and side scatter parameters, followed by subsequent gating for EGFP-positive and EGFP-negative cells, using the integrated fluorescence excited at 488 nm and collected in the 500–526-nm band (Becton Dickinson FACSDiva software). Both the EGFP-positive fraction and the EGFP-negative flow-through were collected for sequencing. Samples were partitioned into single cells and barcoded using droplet microfluidics[30] (10X Chromium v.3 and v.3.1) and multiplexed during Illumina NovaSeq6000 sequencing. Brains and dissociated cells were kept on ice or at ice-cold temperatures from dissection to sample submission, including during flow cytometry, but not during the enzymatic and mechanical dissociation steps, which took place at room temperature.

scRNA-seq data processing and alignment

Raw transcriptomic data were pre-processed with a custom command line script30,99,100, which extracted cell barcodes and aligned associated reads to a combination of the Drosophila melanogaster genome release BDGP6.22 and the reference sequences of the GAL4 and EGFP-p103’UTR transgenes, using STAR 2.6.1b with default settings[101]. Flybase version FB2018_03 gene names were used for annotation. The cumulative fraction of reads as a function of cell barcodes, arranged in descending order of the number of reads, was inspected, and only cells with a high number of reads, up to a clearly visible shoulder, were retained[30]; beads with few reads, potentially ambient RNA, were discarded. All subsequent analyses were performed in R, using the Seurat v.4.1 package[102].

Three biological replicates, collected on different days from independent genetic crosses, were merged, variation driven by individual batches was regressed out, and the data were normalized by dividing by the number of unique molecular identifiers per cell and multiplying by 10,000. Applying standard criteria for fly neurons28,100,103,104, we rejected genes detected in fewer than three cells and retained only cells associated with 800–10,000 unique molecular identifiers and 200–5,000 transcripts.

Principal component analysis was used to compress the expression data from an initial dimensionality of 10,000 (the number of variable features) to 50 (the number of principal components we chose to consider); the scores along these 50 dimensions were then visualized in a two-dimensional uniform manifold approximation and projection embedding. Clusters were identified by constructing a shared nearest neighbour graph and applying the Louvain algorithm with resolution 0.2. Clusters were annotated manually according to the presence of established markers100,103: cholinergic, glutamatergic and GABAergic neurons expressed elav and nSyb and, respectively, genes encoding VAChT or the glutamate transporter (VGlut) or glutamic acid decarboxylase 1 (Gad1) at levels >2; Kenyon cells were identified by the expression of eyeless and Dop1R2 and partitioned into αβ, α′β′ and γ divisions according to the distributions of sNPF, fasciclin 2 and trio; monoaminergic neurons were identified by the presence of the vesicular monoamine transporter Vmat and divided into dopaminergic, serotonergic and octopaminergic–tyraminergic neurons by the co-expression of genes encoding biosynthetic enzymes (dopa decarboxylase, tyrosine hydroxylase, tyrosine decarboxylase 2, tryptophan hydroxylase and tyramine β-hydroxylase) and vesicular transporters for dopamine or serotonin (DAT and SerT); projection neurons were defined and classified by the expression of the transcription factors cut and abnormal chemosensory jump 6 (acj6), with or without Lim1; glia lacked elav and nSyb but expressed the Na+–K+ ATPase encoded by the nervana 2 gene, whereas astrocytes also contained the astrocytic leucine-rich repeat molecule (alrm); cells of the fat body were recognized by the expression of Secreted protein, acidic, cysteine-rich (SPARC), Metallothionein A (MtnA), I’m not dead yet (Indy) and pudgy; R23E10 neurons expressed elav and nSyb plus AstAR-1 and EGFP at a level >2. Expression level cutoffs for VAChT, VGlut, Gad1 and EGFP were chosen to bisect bimodal distributions (Extended Data Fig. 1e). For reclustering neurons expressing specific fast-acting neurotransmitters, dFBNs, Kenyon cells or projection neurons, 150 genes were used as variable features.

Differential gene expression and gene ontology analyses

Differentially expressed genes were identified in Seurat by means of the ‘FindMarkers’ function, using the ‘RNA assay’ counts of the two comparison groups, and restricted to genes detected in ≥1% of cells in either of the two groups with, on average, a ≥0.01-fold (log scale) expression level difference between the rested and sleep-deprived states. Expression levels were compared by Bonferroni-corrected Wilcoxon rank-sum test.

Gene ontology terms enriched in the set of differentially expressed nuclear genes were identified using PANTHER v.17 or the ViSEAGO v.1.4.0 and topGO v.2.42.0 packages. PANTHER compared the list of differentially expressed genes with the Drosophila melanogaster reference list and the gene ontology annotation database (https://doi.org/10.5281/zenodo.7942786, version 2023-05-10). In ViSEAGO and topGO, differentially expressed genes were compared to a reference set of all variable genes used in Seurat and annotated in Ensembl; only gene ontology terms with more than 40 attached genes were considered, and enriched terms with unadjusted P < 0.001 were clustered hierarchically according to Wang’s distance[105].

Two-photon imaging

Females aged 3–4 days were head-fixed to a custom mount with eicosane (Sigma) and imaged on Movable Objective Microscopes with galvanometric or resonant scanners (Sutter Instruments) controlled through ScanImage v.5.4.0 software (Vidrio Technologies). Cuticle, adipose tissue and trachea were removed to create an optical window, and the brain was superfused with carbogenated extracellular solution (95% O_2–5% CO2, pH 7.3, 275 mOsm) containing 103 mM NaCl, 3 mM KCl, 5 mM TES, 8 mM trehalose, 10 mM glucose, 7 mM sucrose, 26 mM NaHCO_3, 1 mM NaH_2PO_4, 1.5 mM CaCl_2 and 4 mM MgCl_2. To excite iATPSnFR and co-expressed tdTomato, Mai Tai DeepSee (Spectra Physics model eHP DS) or Coherent Chameleon Ultra II Ti:sapphire lasers produced 930-nm excitation light pulses whose power was modulated by Pockels cells (302RM, Conoptics). Emitted photons were collected by ×20 (1.0 numerical aperture (NA)) water immersion objectives (W-Plan-Apochromat, Zeiss), split into green and red channels by dichromatic mirrors (Chroma 565dcxr or Semrock BrightLine 565 nm) and detected by GaAsP photomultiplier tubes (H10770PA-40 SEL, Hamamatsu Photonics). The emission paths contained bandpass filters for iATPSnFR (Semrock BrightLine FF01-520/60) and tdTomato (Chroma ET605/70 m), respectively. Photocurrents were passed through high-speed amplifiers (HCA-4M-500K-C, Laser Components) and integrators (BLP-21.4+, Mini-Circuits, or EF506, Thorlabs) to maximize the signal-to-noise ratio.

To gate open the conductance of CsChrimson, a 625-nm LED (M625L3, ThorLabs) controlled by a dimmable LED driver (ThorLabs) delivered 0.5–25 mW cm−2 of optical power through a bandpass filter (Semrock BrightLine FF01-647/57-25) to the head of the fly. Stimulus trains lasted for 2 min and consisted of ten 25-ms light pulses in 500-ms bursts recurring once per s. To apply arousing heat, an 808-nm laser diode (Thorlabs L808P500MM) was mounted on a temperature-controlled heat sink (ThorLabs TCDLM9 with ThorLabs TED200C controller) and aimed at the abdomen of the fly. The diode was restricted to a maximal output of 50 mW by a ThorLabs LDC210C laser diode controller, and 2-s pulses were delivered every 30 s for 2 min. Images of 256 × 256 pixels were acquired at a rate of 29.13 Hz. The voltage steps controlling the LED or laser diode were recorded in a separate imaging channel for post-hoc alignment.

To drive proton pumping by mito-dR, a 530-nm LED (M530L3, ThorLabs) controlled by a dimmable LED driver (ThorLabs) delivered about 25 mW cm−2 of optical power through an ACP2520-A collimating lens (ThorLabs) to the head of the fly. Stimuli lasted for 400 ms and were repeated every 10 s. Two shutters, one in the combined fluorescence emission path (∅1/2″ stainless steel diaphragm optical beam shutter with controller, Thorlabs) and one on the LED (Vincent/UniBlitz VS35S2ZM1R1-21 Uni-Stable Shutter with UniBlitz VMM-T1 Shutter Driver/Timer controller), opened alternately during imaging and green light stimulation. Images of 128 × 50 pixels were acquired at a rate of 41.59 Hz. The voltage steps controlling the LED were recorded in a separate imaging channel for post-hoc alignment.

Time series of average fluorescence in manually selected dendritic regions of interest were analysed in MATLAB, following the subtraction of a time-varying background. ΔF/F curves were calculated separately for each trial as \(\frac{\Delta {F}_{t}}{{F}_{0}}=\frac{({F}_{t}-{F}_{0})}{{F}_{0}}\), where F_0 is the mean fluorescence intensity before stimulation onset (170 s for heat and CsChrimson, 4 s for mito-dR) and Ft is the fluorescence intensity in frame t; \(\frac{\Delta {R}_{t}}{{R}_{0}}\) represents the iATPSnFR–tdTomato (green–red) intensity ratio. The stimulus-aligned \(\frac{\Delta {R}_{t}}{{R}_{0}}\) signals were averaged across two trials in the case of CsChrimson and 30 trials in the case of mito-dR and then across flies; the statistical units are flies. For display purposes, traces were smoothed with moving-average filters (15-s windows for heat and CsChrimson, followed by downsampling by a factor of 100; 1-s window for mito-dR).

Super-resolution and confocal imaging

Single-housed females aged 6 days post eclosion were dissected at zeitgeber time 0, following ad libitum sleep or 12 h of sleep deprivation. Experimental and control samples were processed in parallel. Brains were fixed for 20 min in 0.3% (v/v) Triton X-100 in PBS (PBST) with 4% (w/v) paraformaldehyde, washed five times with PBST, incubated with primary antibodies and secondary detection reagents where indicated, mounted in Vectashield and imaged. Only anatomically intact specimens from live flies (at the point of dissection) were analysed, blind to sleep history, using existing, adapted or newly developed (semi-)automated routines in Fiji 2.14.0/1.54f. The specific acquisition and analysis parameters for different experiments are as follows and further detailed in Supplementary Table 4.

For mitochondrial morphometry[106], z-stacks of the dendritic fields of mito-GFP-expressing dFBNs (or the glomerular arborizations of projection neurons) were collected at the Nyquist limit, with identical image acquisition settings across all conditions. Dendrites were chosen as an optically favourable compartment for analysis because their branches (and the mitochondria within them) were well separated along all axes.

OPRM super-resolution images were collected on an Olympus IX83 P2ZF microscope (Olympus cellSense Dimension 4.3.1) equipped with a UplanSApo ×60 (1.30 NA) silicon oil objective and a Yokogawa CSU-W1 super-resolution by optical pixel reassignment spinning-disc module[38]. Image stacks were passed through a ‘low’ Olympus Super Resolution spatial frequency filter and deconvolved in five iterations of a constrained maximum likelihood algorithm (Olympus cellSense Dimension 4.3.1).

CLSM images were acquired on a Leica TCS SP5 confocal microscope (Leica LAS AF 2.7.3.9723) with an HCX IRAPO L ×25 (0.95 NA) water immersion objective. Point-spread functions were created with the PSF Generator plugin[107] in Fiji and used to deconvolve the images with DeconvolutionLab2 2.1.2 software108,109 using the Richardson–Lucy algorithm with total variation regularization (set to 0.0001) and a maximum of two iterations[106].

Functions of the Mitochondria Analyzer 2.3.1 plugin in Fiji were applied in an automated fashion to the deconvolved OPRM and CLSM images to remove background noise (‘subtract background’ with a radius of 1.25 μm), reduce noise and smooth objects while preserving edges (‘sigma filter plus’), enhance dim areas while minimizing noise amplification (‘enhance local contrast’ with slope 1.4) and optimize the use of image bits (‘gamma correction’ with a value of 0.90) before thresholding (‘weighted mean’ with block size 1.25 μm and a ‘C value’ of 5 for dFBNs and 12 for projection neurons, determined empirically to minimize background noise[106]). The resulting binary images were examined by means of Batch 3D analysis on a ‘per-cell’ basis to extract morphological metrics; OPRM image stacks were rendered in three dimensions with the Volume Viewer 2.02 plugin in Fiji, using trilinear interpolation in volume mode with default settings and a greyscale transfer function. The full dendritic fields of dFBNs were analysed, but the high packing density of projection neuron dendrites in the glomeruli of the antennal lobe forced us to select 20 substacks per glomerulus, each with an axial depth of 6 µm (for OPRM) or 5.8 µm (for CLSM), using a Fiji random number generator function, to make computations practical. Morphometric parameters were then averaged across all substacks per glomerulus.

When other UAS-driven transgenes were present in addition to UAS-mito-GFP, the dilution of a limiting amount of GAL4 among several promoters led to a noticeable dimming of mitochondrial fluorescence, especially in OPRM images. We therefore sought to compare mitochondrial morphologies within (Fig. 3a,b and Extended Data Figs. 5g and 6a,b) or among (Extended Data Figs. 5c,d and 7a,b) genotypes carrying the same number of UAS-driven transgenes. Although shape metrics, such as the mean volume, sphericity and branch length of mitochondria, seemed robust under variations in brightness, the number of fluorescent objects crossing the detection threshold was not. Because the absolute number of mitochondria in an image stack also depends on the volume fraction occupied by dFBN dendrites, these limitations should be borne in mind when interpreting mitochondrial counts.

For ratiometric snapshot imaging of the ATP sensors iATPSnFR (normalized to co-expressed RFP) and ATeam and the mitophagy sensor mito-QC, fluorescence was quantified on summed z-stacks of the relevant channels, following the subtraction of average background in manually defined areas close to the structures of interest. Brains expressing ATeam were imaged on a Zeiss LSM980 with Airyscan2 microscope (ZEN blue 3.3) with a Plan-Apochromat ×40 (1.30 NA) oil immersion objective, an excitation wavelength of 445 nm for the FRET donor mCFP, and emission bands of 454–507 nm for CFP and 516–693 nm for the YFP variant mVenus[75]. In ATP calibration experiments (see below), the biocytin-filled dFBN soma was identified after staining with Alexa Fluor 633 streptavidin (ThermoFisher, 1:600 in 0.3% PBST at 4 °C overnight) at excitation and emission wavelengths of 639 nm and 649–693 nm, respectively. Images of iATPSnFR plus RFP and mito-QC were acquired on a Leica TCS SP5 confocal microscope with HCX IRAPO L ×25 (0.95 NA) water and HCX PL APO ×40 (1.30 NA) oil immersion objectives, respectively. The excitation and emission wavelengths were 488 nm and 498–544 nm for iATPSnFR, 555 nm and 565–663 nm for RFP, and 488 nm and 503–538 nm, and 587 nm and 605–650 nm, for the GFP and mCherry moieties of mito-QC, respectively.

To convert the emission ratios of ATeam1.03NL into approximate ATP concentrations, we constructed a calibration curve in vivo by including 0.15, 1.5 or 4 mM MgATP, along with 10 mM biocytin, in the intracellular solution during whole-cell patch-clamp recordings. After dialysing the recorded dFBN for 30 min, the patch electrode was withdrawn, and the brain was recovered, fixed and processed for detection and ratiometric imaging of the biocytin-labelled soma. A standard curve was obtained by fitting the Hill equation, with a dissociation constant[75] of 1.75 mM and a Hill coefficient[74] of 2.1, to the YFP–CFP fluorescence ratios of dFBN somata containing known ATP concentrations.

SPLICS puncta82,110 were imaged on a Leica TCS SP5 confocal microscope with an HCX PL APO ×40 (1.30 NA) oil immersion objective, excitation and emission wavelengths of 488 and 500–540 nm, respectively, and analysed in Fiji with a custom macro based on the Quantification 1 and 2 plugins[110]. Only puncta exceeding 10 voxels were counted.

For localizing Drp1, we labelled the mitochondria of dFBNs with mito-GFP in Drp1::FLAG-FlAsH-HA flies[94], whose genomic Drp1 coding sequence is fused in frame with a Flag-FlAsH-HA tag. Fixed brains were incubated sequentially at 4 °C in blocking solution (10% goat serum in 0.3% PBST) overnight, with mouse monoclonal anti-Flag antibody (anti-DDK; 1:1,000, OriGene) in blocking solution for 2–3 days, and with goat anti-Mouse Alexa Fluor 633 (1:500, ThermoFisher) in blocking solution for two days. The samples were washed five times with PBST before and after the addition of secondary antibodies, mounted and imaged on a Leica TCS SP5 confocal microscope with an HCX PL APO ×40 (1.30 NA) oil immersion objective. The excitation and emission wavelengths were 488 and 500–540 nm for mito-GFP and 631 and 642–690 nm for Alexa Fluor 633, respectively. dFBN somata were identified manually in the green channel, which was then thresholded, despeckled and binarized by an automated custom macro in Fiji. The mitochondria-associated fraction of endogenous Flag-tagged Drp1 in dFBNs was quantified in summed z-stacks as the proportion of red-fluorescent pixels in the somatic volume that colocalized with mitochondrial objects.

Electrophysiology

For whole-cell patch-clamp recordings in vivo, female flies aged 2–4 days post eclosion were prepared as for functional imaging, but the perineural sheath was also removed for electrode access. The GFP-labelled somata of dFBNs were visually targeted with borosilicate glass electrodes (8–10 MΩ) filled with internal solution (pH 7.3, 265 mOsm) containing: 10 mM HEPES, 140 mM potassium aspartate, 1 mM KCl, 4 mM MgATP, 0.5 mM Na_3GTP, 1 mM EGTA and 10 mM biocytin. Signals were acquired at room temperature (23 °C) in current-clamp mode with a MultiClamp 700B amplifier (Molecular Devices), lowpass-filtered at 5 kHz, and sampled at 10 kHz using an Axon Digidata 1550B digitizer controlled through pCLAMP 11.2 (Molecular Devices). Series resistances were monitored but not compensated. Data were analysed using v.3.0c of the NeuroMatic package[111] (http://neuromatic.thinkrandom.com) in Igor Pro 8.04 (WaveMetrics). Current–spike frequency functions were determined from voltage responses to a series of current steps (5-pA increments from −20 to 105 pA, 1 s duration) from a pre-pulse potential of −60 ± 5 mV. Spikes were detected by finding minima in the second derivative of the membrane potential trace. Spike frequencies were normalized to membrane resistances, which were calculated from linear fits of the steady-state voltage changes elicited by hyperpolarizing current steps. Only dFBNs firing more than one action potential in response to depolarizing current injections, with resting potentials below −30 mV and series resistances remaining below 50 MΩ throughout the recording, were characterized further. Spike bursts were defined as sets of spikes with an average intra-burst inter-spike interval (ISI) less than 50 ms and an inter-burst ISI more than 100 ms. These ISI thresholds were set after visual inspection of the voltage traces of all recorded neurons. Cells were scored as bursting if they generated at least one action potential burst during the series of depolarizing current steps.

Analysis of mitochondria in volume electron micrographs

The hemibrain v.1.2.1 connectome[39] was accessed in neuPrint+ (ref. [112]). The volumes of mitochondria in all R23E10-GAL4-labelled dFBNs[113] and uniglomerular olfactory projection neurons[39] in the left hemisphere (which contains mostly the dendritic compartments of projection neurons) were retrieved through Neo4j Cypher and neuPrint-python queries and analysed with custom MATLAB scripts. Supplementary Table 5 lists the identification numbers (Body_IDs) of all analysed cells.

Quantification and statistical analysis

With the exception of sleep measurements, no statistical methods were used to predetermine sample sizes. Flies of the indicated genotype, sex and age were selected randomly for analysis and assigned randomly to treatment groups if treatments were applied (for example, sleep deprivation). The investigators were blind to sleep history and/or genotype in imaging experiments but not otherwise. All behavioural experiments were run at least three times, on different days and with different batches of flies. The figures show pooled data from all replicates.

Gene expression levels were compared by Bonferroni-corrected two-sided Wilcoxon rank-sum test. Gene ontology enrichment was quantified using Fisher’s exact test in PANTHER (with a false discovery rate-adjusted significance level of P < 0.05) or ViSEAGO (with an unadjusted significance level of P < 0.001).

Behavioural, imaging and electrophysiological data were analysed in Prism v.10 (GraphPad) and SPSS Statistics 29 (IBM). All null hypothesis tests were two-sided. To control type I errors, P values were adjusted to achieve a joint α of 0.05 at each level in a hypothesis hierarchy; multiplicity-adjusted P values are reported in cases of several comparisons at one level. Group means were compared by t-test, one-way ANOVA, two-way repeated-measures ANOVA or mixed-effects models, as stated, followed by planned pairwise analyses with Holm–Šídák’s multiple comparisons test where indicated. Repeated-measures ANOVA and mixed-effect models used the Geisser–Greenhouse correction. Where the assumption of normality was violated (as indicated by D’Agostino–Pearson test), group means were compared by Mann–Whitney test or Kruskal–Wallis ANOVA, followed by planned pairwise analyses using Dunn’s multiple comparisons test, as indicated. Frequency distributions were analysed by χ²-test, and categories responsible for pairwise differences[114] were detected by locating cells with standardized residuals ≥2.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

Single-cell transcriptomic data can be found in NCBI’s Gene Expression Omnibus repository under accession number GSE256379. Source data are provided with this paper.

Code availability

The code used to analyse transcriptome data is available in the Drop-seq Alignment Cookbook via GitHub at https://github.com/broadinstitute/Drop-seq and at https://satijalab.org/seurat/.

References

1. Donlea, J. M., Thimgan, M. S., Suzuki, Y., Gottschalk, L. & Shaw, P. J. Inducing sleep by remote control facilitates memory consolidation in Drosophila. Science 332, 1571–1576 (2011).

2. Hasenhuetl, P. S. et al. A half-centre oscillator encodes sleep pressure. Preprint at BioRxiv https://doi.org/10.1101/2024.02.23.581780 (2024).

3. Vance, J. E. Phospholipid synthesis in a membrane fraction associated with mitochondria. J. Biol. Chem. 265, 7248–7256 (1990).

4. Kornmann, B. et al. An ER–mitochondria tethering complex revealed by a synthetic biology screen. Science 325, 477–481 (2009).

5. Rorsman, H. O. et al. Sleep pressure accumulates in a voltage-gated lipid peroxidation memory. Nature 641, 232–239 (2025).

6. Maxwell, D. P., Wang, Y. & McIntosh, L. The alternative oxidase lowers mitochondrial reactive oxygen production in plant cells. Proc. Natl Acad. Sci. USA 96, 8271–8276 (1999).

7. Kempf, A., Song, S. M., Talbot, C. B. & Miesenböck, G. A potassium channel β-subunit couples mitochondrial electron transport to sleep. Nature 568, 230–234 (2019).

8. Bleazard, W. et al. The dynamin-related GTPase Dnm1 regulates mitochondrial fission in yeast. Nat. Cell Biol. 1, 298–304 (1999).

9. Sesaki, H. & Jensen, R. E. Division versus fusion: Dnm1p and Fzo1p antagonistically regulate mitochondrial shape. J. Cell Biol. 147, 699–706 (1999).

10. Smirnova, E., Griparic, L., Shurland, D. L. & van der Bliek, A. M. Dynamin-related protein Drp1 is required for mitochondrial division in mammalian cells. Mol. Biol. Cell 12, 2245–2256 (2001).

11. Hales, K. G. & Fuller, M. T. Developmentally regulated mitochondrial fusion mediated by a conserved, novel, predicted GTPase. Cell 90, 121–129 (1997).

12. Hwa, J. J., Hiller, M. A., Fuller, M. T. & Santel, A. Differential expression of the Drosophila mitofusin genes fuzzy onions (fzo) and dmfn. Mech. Dev. 116, 213–216 (2002).

13. Cipolat, S., Martins de Brito, O., Dal Zilio, B. & Scorrano, L. OPA1 requires mitofusin 1 to promote mitochondrial fusion. Proc. Natl Acad. Sci. USA 101, 15927–15932 (2004).

14. Pimentel, D. et al. Operation of a homeostatic sleep switch. Nature 536, 333–337 (2016).

15. Heaton, G. M., Wagenvoord, R. J., Kemp, A. & Nicholls, D. G. Brown-adipose-tissue mitochondria: photoaffinity labelling of the regulatory site of energy dissipation. Eur. J. Biochem. 82, 515–521 (1978).

16. Hara, K. Y., Wada, T., Kino, K., Asahi, T. & Sawamura, N. Construction of photoenergetic mitochondria in cultured mammalian cells. Sci. Rep. 3, 1635 (2013).

17. Balaban, R. S., Nemoto, S. & Finkel, T. Mitochondria, oxidants, and aging. Cell 120, 483–495 (2005).

18. Lane, N. The costs of breathing. Science 334, 184–185 (2011).

19. Steriade, M., Timofeev, I. & Grenier, F. Natural waking and sleep states: a view from inside neocortical neurons. J. Neurophysiol. 85, 1969–1985 (2001).

20. Vyazovskiy, V. V. et al. Cortical firing and sleep homeostasis. Neuron 63, 865–878 (2009).

21. Tononi, G. & Cirelli, C. Sleep and the price of plasticity: from synaptic and cellular homeostasis to memory consolidation and integration. Neuron 81, 12–34 (2014).

22. de Vivo, L. et al. Loss of sleep affects the ultrastructure of pyramidal neurons in the adolescent mouse frontal cortex. Sleep 39, 861–874 (2016).

23. Aboufares El Alaoui, A. et al. Increased interaction between endoplasmic reticulum and mitochondria following sleep deprivation. BMC Biol. 21, 1 (2023).

24. Haynes, P. R. et al. A neuron–glia lipid metabolic cycle couples daily sleep to mitochondrial homeostasis. Nat. Neurosci. 27, 666–678 (2024).

25. Reich, P., Geyer, S. J. & Karnovsky, M. L. Metabolism of brain during sleep and wakefulness. J. Neurochem. 19, 487–497 (1972).

26. Porkka-Heiskanen, T. et al. Adenosine: a mediator of the sleep-inducing effects of prolonged wakefulness. Science 276, 1265–1268 (1997).

27. Cirelli, C., Gutierrez, C. M. & Tononi, G. Extensive and divergent effects of sleep and wakefulness on brain gene expression. Neuron 41, 35–43 (2004).

28. Dopp, J. et al. Single-cell transcriptomics reveals that glial cells integrate homeostatic and circadian processes to drive sleep–wake cycles. Nat. Neurosci. 27, 359–372 (2024).

29. von Economo, C. in Handbuch der normalen und pathologischen Physiologie Vol. 17 (eds Adler, L. et al.) 591–610 (Springer, 1926).

30. Macosko, E. Z. et al. Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets. Cell 161, 1202–1214 (2015).

31. Donlea, J. M., Pimentel, D. & Miesenböck, G. Neuronal machinery of sleep homeostasis in Drosophila. Neuron 81, 860–872 (2014).

32. Chen, N. et al. Widespread posttranscriptional regulation of cotransmission. Sci. Adv. 9, eadg9836 (2023).

33. Donlea, J. M. et al. Recurrent circuitry for balancing sleep need and sleep. Neuron 97, 378–389.e4 (2018).

34. Qian, Y. et al. Sleep homeostasis regulated by 5HT2b receptor in a small subset of neurons in the dorsal fan-shaped body of drosophila. eLife 6, e26519 (2017).

35. Harrell, E. R., Pimentel, D. & Miesenböck, G. Changes in presynaptic gene expression during homeostatic compensation at a central synapse. J. Neurosci. 41, 3054–3067 (2021).

36. Willems, P. H., Rossignol, R., Dieteren, C. E., Murphy, M. P. & Koopman, W. J. Redox homeostasis and mitochondrial dynamics. Cell Metab. 22, 207–218 (2015).

37. Chance, B., Sies, H. & Boveris, A. Hydroperoxide metabolism in mammalian organs. Physiol. Rev. 59, 527–605 (1979).

38. Azuma, T. & Kei, T. Super-resolution spinning-disk confocal microscopy using optical photon reassignment. Opt. Express 23, 15003–15011 (2015).

39. Scheffer, L. K. et al. A connectome and analysis of the adult Drosophila central brain. eLife 9, e57443 (2020).

40. Jendrach, M., Mai, S., Pohl, S., Vöth, M. & Bereiter-Hahn, J. Short- and long-term alterations of mitochondrial morphology, dynamics and mtDNA after transient oxidative stress. Mitochondrion 8, 293–304 (2008).

41. Abrisch, R. G., Gumbin, S. C., Wisniewski, B. T., Lackner, L. L. & Voeltz, G. K. Fission and fusion machineries converge at ER contact sites to regulate mitochondrial morphology. J. Cell Biol. 219, e201911122 (2020).

42. Twig, G. et al. Fission and selective fusion govern mitochondrial segregation and elimination by autophagy. EMBO J. 27, 433–446 (2008).

43. Friedman, J. R. et al. ER tubules mark sites of mitochondrial division. Science 334, 358–362 (2011).

44. Chen, H., Chomyn, A. & Chan, D. C. Disruption of fusion results in mitochondrial heterogeneity and dysfunction. J. Biol. Chem. 280, 26185–26192 (2005).

45. Ryu, K. W. et al. Cellular ATP demand creates metabolically distinct subpopulations of mitochondria. Nature 635, 746–754 (2024).

46. Choi, S. Y. et al. A common lipid links Mfn-mediated mitochondrial fusion and SNARE-regulated exocytosis. Nat. Cell Biol. 8, 1255–1262 (2006).

47. Zhang, Y. et al. Mitoguardin regulates mitochondrial fusion through MitoPLD and is required for neuronal homeostasis. Mol. Cell 61, 111–124 (2016).

48. Kim, H., Lee, S., Jun, Y. & Lee, C. Structural basis for mitoguardin-2 mediated lipid transport at ER-mitochondrial membrane contact sites. Nat. Commun. 13, 3702 (2022).

49. Hong, Z. et al. Mitoguardin-2-mediated lipid transfer preserves mitochondrial morphology and lipid droplet formation. J. Cell Biol. 221, e202207022 (2022).

50. Sperling, E. A., Knoll, A. H. & Girguis, P. R. The ecological physiology of Earth’s second oxygen revolution. Annu. Rev. Ecol. Evol. Syst. 46, 215–235 (2015).

51. Galliot, B. & Quiquand, M. A two-step process in the emergence of neurogenesis. Eur. J. Neurosci. 34, 847–862 (2011).

52. Nath, R. D. et al. The jellyfish Cassiopea exhibits a sleep-like state. Curr. Biol. 27, 2984–2990.e3 (2017).

53. Savage, V. M. & West, G. B. A quantitative, theoretical framework for understanding mammalian sleep. Proc. Natl Acad. Sci. USA 104, 1051–1056 (2007).

54. Zepelin, H. & Rechtschaffen, A. Mammalian sleep, longevity, and energy metabolism. Brain Behav. Evol. 10, 425–470 (1974).

55. West, G. B., Woodruff, W. H. & Brown, J. H. Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. Proc. Natl Acad. Sci. USA 99 (Suppl. 1), 2473–2478 (2002).

56. Gorman, G. S. et al. Perceived fatigue is highly prevalent and debilitating in patients with mitochondrial disease. Neuromuscul. Disord. 25, 563–566 (2015).

57. Dietrich, M. O., Liu, Z. W. & Horvath, T. L. Mitochondrial dynamics controlled by mitofusins regulate Agrp neuronal activity and diet-induced obesity. Cell 155, 188–199 (2013).

58. Jenett, A. et al. A GAL4-driver line resource for Drosophila neurobiology. Cell Rep. 2, 991–1001 (2012).

59. Luan, H., Peabody, N. C., Vinson, C. R. & White, B. H. Refined spatial manipulation of neuronal function by combinatorial restriction of transgene expression. Neuron 52, 425–436 (2006).

60. Dionne, H., Hibbard, K. L., Cavallaro, A., Kao, J. C. & Rubin, G. M. Genetic reagents for making split-GAL4 lines in Drosophila. Genetics 209, 31–35 (2018).

61. Lacin, H. et al. Neurotransmitter identity is acquired in a lineage-restricted manner in the Drosophila CNS. eLife 8, e43701 (2019).

62. Stocker, R. F., Heimbeck, G., Gendre, N. & de Belle, J. S. Neuroblast ablation in Drosophila P[GAL4] lines reveals origins of olfactory interneurons. J. Neurobiol. 32, 443–456 (1997).

63. Tanaka, N. K., Tanimoto, H. & Ito, K. Neuronal assemblies of the Drosophila mushroom body. J. Comp. Neurol. 508, 711–755 (2008).

64. Berry, J. A., Cervantes-Sandoval, I., Chakraborty, M. & Davis, R. L. Sleep facilitates memory by blocking dopamine neuron-mediated forgetting. Cell 161, 1656–1667 (2015).

65. Shearin, H. K., Macdonald, I. S., Spector, L. P. & Stowers, R. S. Hexameric GFP and mCherry reporters for the Drosophila GAL4, Q, and LexA transcription systems. Genetics 196, 951–960 (2014).

66. Lee, T. & Luo, L. Mosaic analysis with a repressible cell marker for studies of gene function in neuronal morphogenesis. Neuron 22, 451–461 (1999).

67. Rizzuto, R., Brini, M., Pizzo, P., Murgia, M. & Pozzan, T. Chimeric green fluorescent protein as a tool for visualizing subcellular organelles in living cells. Curr. Biol. 5, 635–642 (1995).

68. Pilling, A. D., Horiuchi, D., Lively, C. M. & Saxton, W. M. Kinesin-1 and dynein are the primary motors for fast transport of mitochondria in Drosophila motor axons. Mol. Biol. Cell 17, 2057–2068 (2006).

69. Vagnoni, A. & Bullock, S. L. A simple method for imaging axonal transport in aging neurons using the adult Drosophila wing. Nat. Protoc. 11, 1711–1723 (2016).

70. Summerville, J. B. et al. The effects of ER morphology on synaptic structure and function in Drosophila melanogaster. J. Cell Sci. 129, 1635–1648 (2016).

71. Han, C., Jan, L. Y. & Jan, Y. N. Enhancer-driven membrane markers for analysis of nonautonomous mechanisms reveal neuron–glia interactions in Drosophila. Proc. Natl Acad. Sci. USA 108, 9673–9678 (2011).

72. Lobas, M. A. et al. A genetically encoded single-wavelength sensor for imaging cytosolic and cell surface ATP. Nat. Commun. 10, 711 (2019).

73. Mann, K., Deny, S., Ganguli, S. & Clandinin, T. R. Coupling of activity, metabolism and behaviour across the Drosophila brain. Nature 593, 244–248 (2021).

74. Imamura, H. et al. Visualization of ATP levels inside single living cells with fluorescence resonance energy transfer-based genetically encoded indicators. Proc. Natl Acad. Sci. USA 106, 15651–15656 (2009).

75. Tsuyama, T. et al. In vivo fluorescent adenosine 5′-triphosphate (ATP) imaging of Drosophila melanogaster and Caenorhabditis elegans by using a genetically encoded fluorescent ATP biosensor optimized for low temperatures. Anal. Chem. 85, 7889–7896 (2013).

76. Fernandez-Ayala, D. J. M. et al. Expression of the Ciona intestinalis alternative oxidase (AOX) in Drosophila complements defects in mitochondrial oxidative phosphorylation. Cell Metab. 9, 449–460 (2009).

77. Imai, Y. et al. Light-driven activation of mitochondrial proton-motive force improves motor behaviors in a Drosophila model of Parkinson’s disease. Commun. Biol. 2, 424 (2019).

78. Zemelman, B. V., Lee, G. A., Ng, M. & Miesenböck, G. Selective photostimulation of genetically chARGed neurons. Neuron 33, 15–22 (2002).

79. Klapoetke, N. C. et al. Independent optical excitation of distinct neural populations. Nat. Methods 11, 338–346 (2014).

80. Hamada, F. N. et al. An internal thermal sensor controlling temperature preference in Drosophila. Nature 454, 217–220 (2008).

81. Burke, C. J. et al. Layered reward signalling through octopamine and dopamine in Drosophila. Nature 492, 433–437 (2012).

82. Cieri, D. et al. SPLICS: a split green fluorescent protein-based contact site sensor for narrow and wide heterotypic organelle juxtaposition. Cell Death Differ. 25, 1131–1145 (2018).

83. Hewitt, V. L. et al. Decreasing pdzd8-mediated mito-ER contacts improves organismal fitness and mitigates Aβ_42 toxicity. Life Sci. Alliance 5, e202201531 (2022).

84. Allen, G. F., Toth, R., James, J. & Ganley, I. G. Loss of iron triggers PINK1/Parkin-independent mitophagy. EMBO Rep. 14, 1127–1135 (2013).

85. Lee, J. J. et al. Basal mitophagy is widespread in Drosophila but minimally affected by loss of Pink1 or parkin. J. Cell Biol. 217, 1613–1622 (2018).

86. Mao, W. et al. UCP4, a novel brain-specific mitochondrial protein that reduces membrane potential in mammalian cells. FEBS Lett. 443, 326–330 (1999).

87. Bischof, J. et al. A versatile platform for creating a comprehensive UAS-ORFeome library in Drosophila. Development 140, 2434–2442 (2013).

88. Deng, H., Dodson, M. W., Huang, H. & Guo, M. The Parkinson’s disease genes pink1 and parkin promote mitochondrial fission and/or inhibit fusion in Drosophila. Proc. Natl Acad. Sci. USA 105, 14503–14508 (2008).

89. Park, J., Lee, G. & Chung, J. The PINK1–Parkin pathway is involved in the regulation of mitochondrial remodeling process. Biochem. Biophys. Res. Commun. 378, 518–523 (2009).

90. DuBoff, B., Götz, J. & Feany, M. B. Tau promotes neurodegeneration via DRP1 mislocalization in vivo. Neuron 75, 618–632 (2012).

91. Sandoval, H. et al. Mitochondrial fusion but not fission regulates larval growth and synaptic development through steroid hormone production. eLife 3, e03558 (2014).

92. Dietzl, G. et al. A genome-wide transgenic RNAi library for conditional gene inactivation in Drosophila. Nature 448, 151–156 (2007).

93. Perkins, L. A. et al. The Transgenic RNAi Project at Harvard Medical School: resources and validation. Genetics 201, 843–852 (2015).

94. Verstreken, P. et al. Synaptic mitochondria are critical for mobilization of reserve pool vesicles at Drosophila neuromuscular junctions. Neuron 47, 365–378 (2005).

95. Hendricks, J. C. et al. Rest in Drosophila is a sleep-like state. Neuron 25, 129–138 (2000).

96. Shaw, P. J., Cirelli, C., Greenspan, R. J. & Tononi, G. Correlates of sleep and waking in Drosophila melanogaster. Science 287, 1834–1837 (2000).

97. Vecsey, C. G., Koochagian, C., Porter, M. T., Roman, G. & Sitaraman, D. Analysis of sleep and circadian rhythms from Drosophila activity-monitoring data using SCAMP. Cold Spring Harb. Protoc. 2024, pdb.prot108182 (2024).

98. Shaw, P. J., Tononi, G., Greenspan, R. J. & Robinson, D. F. Stress response genes protect against lethal effects of sleep deprivation in Drosophila. Nature 417, 287–291 (2002).

99. Satija, R., Farrell, J. A., Gennert, D., Schier, A. F. & Regev, A. Spatial reconstruction of single-cell gene expression data. Nat. Biotechnol. 33, 495–502 (2015).

100. Croset, V., Treiber, C. D. & Waddell, S. Cellular diversity in the Drosophila midbrain revealed by single-cell transcriptomics. eLife 7, e34550 (2018).

101. Dobin, A. et al. STAR: ultrafast universal RNA-seq aligner. Bioinformatics 29, 15–21 (2013).

102. Hao, Y. et al. Integrated analysis of multimodal single-cell data. Cell 184, 3573–3587.e29 (2021).

103. Davie, K. et al. A single-cell transcriptome atlas of the aging Drosophila brain. Cell 174, 982–998.e20 (2018).

104. Konstantinides, N. et al. Phenotypic convergence: distinct transcription factors regulate common terminal features. Cell 174, 622–635.e13 (2018).

105. Wang, J. Z., Du, Z., Payattakool, R., Yu, P. S. & Chen, C. F. A new method to measure the semantic similarity of GO terms. Bioinformatics 23, 1274–1281 (2007).

106. Chaudhry, A., Shi, R. & Luciani, D. S. A pipeline for multidimensional confocal analysis of mitochondrial morphology, function, and dynamics in pancreatic β-cells. Am. J. Physiol. Endocrinol. Metab. 318, E87–E101 (2020).

107. Kirshner, H., Aguet, F., Sage, D. & Unser, M. 3-D PSF fitting for fluorescence microscopy: Implementation and localization application. J. Microsc. 249, 13–25 (2013).

108. Dey, N. et al. Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution. Microsc. Res. Tech. 69, 260–266 (2006).

109. Sage, D. et al. DeconvolutionLab2: an open-source software for deconvolution microscopy. Methods 115, 28–41 (2017).

110. Calì, T. & Brini, M. Quantification of organelle contact sites by split-GFP-based contact site sensors (SPLICS) in living cells. Nat. Protoc. 16, 5287–5308 (2021).

111. Rothman, J. S. & Silver, R. A. NeuroMatic: an integrated open-source software toolkit for acquisition, analysis and simulation of electrophysiological data. Front. Neuroinform. 12, 14 (2018).

112. Plaza, S. M. et al. NeuPrint: an open access tool for EM connectomics. Front. Neuroinform. 16, 896292 (2022).

113. Hulse, B. K. et al. A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection. eLife 10, e66039 (2021).

114. Agresti, A. Categorical Data Analysis (Wiley, 2013).

Acknowledgements

We thank C. Talbot for instrumentation; L. Ballenberger, K. Christodoulou, C. Hartmann, A. Krebbers, Y. Siu and T. Wong for help with genetics and dissections; W. Budenberg for support in customizing the Zantiks MWP unit; the Don Mason Facility of Flow Cytometry and the Light Microscopy Facility, Sir William Dunn School of Pathology, University of Oxford, for cell sorting and access to the Olympus SoRa microscope, respectively; the Oxford Genomics Centre at the Wellcome Centre for Human Genetics (funded by Wellcome grant 203141/A/16/Z) for RNA sequencing; the Oxford Micron Bioimaging Facility (funded by Wellcome grants 091911/B/10/Z and 107457/Z/15/Z) for access to the Zeiss LSM980 microscope; H. Bellen, S. Bullock, J. Chung, T. Clandinin, R. Davis, M. Feany, M. Guo, Y. Imai, H. Jacobs, Y. Jan, V. Jayaraman, L. Luo, J. McNew, G. Rubin, W. Saxton, R. Stowers, S. Waddell, A. Whitworth, the Bloomington Stock Center, the Vienna Drosophila Resource Center, the Transgenic RNAi Project (TRiP) and the FlyORF Zurich ORFeome Project for flies; V. Croset, C. Treiber and S. Waddell for advice on single-cell RNA sequencing; the FlyLight Project Team at Janelia Research Campus for anatomical images reproduced in Extended Data Fig. 1h; and T. Calì, P. Hasenhuetl, R. Klemm, V. Savage and E. Vrontou for discussions. This work was supported by grants from the European Research Council (832467) and Wellcome (209235/Z/17/Z and 106988/Z/15/Z) to G.M.; R.S. held a Wellcome Four-Year PhD Studentship in Basic Science (215200/Z/19/Z); AK. received postdoctoral fellowships from the Swiss National Science Foundation and EMBO.

Author information

Author notes

1. Anissa Kempf

Present address: Biozentrum, Universität Basel, Basel, Switzerland

Authors and Affiliations

1. Centre for Neural Circuits and Behaviour, University of Oxford, Oxford, UK

Raffaele Sarnataro, Cecilia D. Velasco, Nicholas Monaco, Anissa Kempf & Gero Miesenböck

Contributions

R.S. performed and analysed all transcriptomic, imaging and behavioural experiments. C.D.V. performed and analysed all electrophysiological recordings. R.S. analysed volume electron microscopy data. N.M. assisted with imaging, genetics and behaviour. A.K. conducted initial studies with Ucp4. R.S. and G.M. designed the study, interpreted the results and prepared the manuscript. G.M. devised and directed the research and wrote the paper.

Corresponding author

Correspondence to Gero Miesenböck.

Ethics declarations

Competing interests

The other authors declare no competing interests.

Peer review

Peer review information

Nature thanks Martin Picard and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Identification of dFBNs and their transcriptomic response to sleep deprivation by single-cell RNA-sequencing.

a, Sleep profiles of flies expressing R23E10-GAL4-driven 6xEGFP under control (blue, n = 558) and sleep deprivation (SD) conditions (red, n = 432) before single-cell RNA sequencing. b, Pseudocolour plot of the gating strategy used to isolate EGFP-positive (0.03% of total) and EGFP-negative cells (14.64% of total) by flow cytometry. c, Uniform manifold approximation and projection (UMAP) representation of cells in the fly brain. Highlighted cell types, including neurons nominated by R23E10-GAL4 (yellow), were identified as detailed in Methods. d, Distribution of the number of unique molecular identifiers (UMIs) and genes per cell for each annotated cell type. e, log-normalized distribution of the expression levels of markers for the fast-acting neurotransmitters glutamate, acetylcholine, and GABA in R23E10-GAL4 neurons. f, R23E10-GAL4 neurons (black) mapped onto re-clustered representations of cells expressing glutamatergic, cholinergic, and GABAergic markers. Bona fide dFBNs form a distinct glutamatergic cluster (dashed outline). g, h, Compared to the rest of the glutamatergic brain, dFBNs are enriched in EGFP (g) and transcripts of genes whose enhancer fragments label dFBNs in GAL4 lines generated and imaged by the FlyLight project[58] (h). log-normalized expression levels are colour-coded according to the keys below each panel. Scale bars in h, 100 µm. Anatomical images in panel h reproduced from ref. [58], Cell Press, under a Creative Commons licence CC BY 4.0.

Extended Data Fig. 2 Gene ontology analysis of sleep history-dependent gene expression in dFBNs.

a–d, Enrichment of gene ontology (GO) ‘biological process’ (a, c) and ‘cellular component’ (b, d) terms in the set of genes whose expression in dFBNs varies with sleep history. Panels a and b plot the top ten enriched terms by PANTHER Overrepresentation Test (fold enrichments >100 are truncated). Panels c and d show heatmaps (computed with ViSEAGO and topGO) of GO terms attached to downregulated (left) and upregulated (right) differentially expressed genes. Dendrograms represent semantic groupings among GO terms. P-values are colour-coded according to the keys on the right. e, Enrichment (top) and uncorrected P-values (bottom, dotted lines at P = 0.05) of the ‘cellular component’ GO terms ‘mitochondrion’ and ‘synapse’ in the sets of up- and downregulated genes by PANTHER Overrepresentation Test, in the full data set (dark grey) and after randomly downsampling (light grey) the number of rested dFBN transcriptomes to the number of sleep-deprived dFBN transcriptomes (n = 86 cells in either condition). The downsampling process was repeated ten times using the ‘max.cells.per.ident’ argument of the ‘FindMarkers’ function in Seurat, with reproducible seedings from 1 to 10.

Extended Data Fig. 3 Sleep history-dependent gene expression in Kenyon cells, projection neurons and non-dFBN cells.

a, UMAP representation of projection neurons (PNs, n = 317) from rested (blue) and sleep-deprived brains (red) according to their gene expression profiles. b, Volcano plot of sleep history-dependent gene expression changes in PNs. A single signal with Bonferroni-corrected P < 0.05 (two-sided Wilcoxon rank-sum test) is indicated in black. c, d, PANTHER Overrepresentation Test fails to detect enriched ‘biological process’ (g) and ‘cellular component’ (h) gene ontology (GO) terms in the set of differentially expressed PN genes. e, UMAP representation of Kenyon cells (KCs, n = 603) from rested (blue) and sleep-deprived brains (red) according to their gene expression profiles. f, Volcano plot of sleep history-dependent gene expression changes in PNs. Signals with Bonferroni-corrected P < 0.05 (two-sided Wilcoxon rank-sum test) are indicated in black. g, h, Enrichment of the top ten downregulated and upregulated ‘biological process’ (g) and ‘cellular component’ (h) GO terms in the set of differentially expressed KC genes by PANTHER Overrepresentation Test (fold enrichments >100 are truncated). i, j, Enrichment of the top ten downregulated and upregulated ‘biological process’ (i) and ‘cellular component’ (j) GO terms in the set of genes with differential expression in all non-dFBN cells by PANTHER Overrepresentation Test.

Source data

Extended Data Fig. 4 Relationships between ATP levels, mitochondrial protonmotive force, and sleep in PNs and dFBNs.

a, Maximum-intensity projection of dFBNs expressing R23E10-GAL4-driven ATeam (top left, CFP channel). One dFBN has been filled with biocytin and a defined ATP concentration through a whole-cell electrode (bottom left). The right panel shows the least-squares fit of a Hill equation (dissociation constant 1.75 mM ATP, Hill coefficient 2.1) to the mean yellow-to-cyan emission ratio of biocytin-labelled dFBNs containing 0.15, 1.5, and 4 mM ATP (n = 3 cells each). b, Summed-intensity projections of PN dendrites expressing iATPSnFR plus RFP, in rested and sleep-deprived (SD) flies. Emission ratios are intensity-coded according to the key below and unaltered by sleep deprivation (P = 0.6616, two-sided t-test). c, Sleep in flies expressing R23E10-GAL4-driven Ucp4A or Ucp4C and parental controls (P ≤ 0.0139, Dunn’s test after Kruskal-Wallis ANOVA). d, A 400-ms pulse of green light elevates ATP in dFBNs expressing iATPSnFR plus tdTomato and mito-dR but not in dFBNs lacking mito-dR (n = 5 flies of either genotype, ∆p photogeneration effect: P < 0.0001, time × ∆p photogeneration interaction: P < 0.0001, two-way ANOVA). e, f, Sleep during the first 60 min after illumination (e, P ≤ 0.0279, Dunn’s test after Kruskal-Wallis ANOVA) and cumulative sleep percentages in flies expressing R23E10-GAL4-driven mito-dR, with or without retinal, and parental controls (f, ∆p photogeneration effect: P < 0.0001, time × ∆p photogeneration interaction: P < 0.0001, mixed-effects model). Asterisks, significant differences (P < 0.05) from both parental controls or in planned pairwise comparisons. Data are means ± s.e.m.; n, number of cells (a), antennal lobe glomeruli (b), or flies (c–f). Scale bars, 20 µm (a,b). For statistical details see Supplementary Table 2.

Source data

Extended Data Fig. 5 Sleep history alters the morphology of dFBN mitochondria.

a, Mean volumes (left y-axes) and volume ratios (right y-axis) of dFBN and PN mitochondria determined by volume electron microscopy (EM), optical photon reassignment microscopy (OPRM), and confocal laser-scanning microscopy (CLSM). b, Correlation between dFBN and PN mitochondrial volume estimates obtained by EM, OPRM, and CLSM (residual s.d. = 0.0041). EM data are from the hemibrain connectome[39]; OPRM and CLSM measurements of mitochondrial volumes in flies expressing mito-GFP are re-plotted from Fig. 3b and Extended Data Fig. 6b, and from f and Extended Data Fig. 6d, respectively. c, d, Sleep deprivation via thermogenetic activation of arousing dopaminergic neurons (c) causes mitochondrial fragmentation detected by OPRM (d, number of mitochondria: P = 0.1812, volume: P = 0.0010, sphericity: P = 0.0192, branch length: P = 0.2013, two-sided t-test). Experimental and control flies (n = 30 and 33, respectively) were reared and maintained at 21 °C and shifted to 29 ˚C between zeitgeber times 12 and 24 on day 2. The arrowhead marks the time point when 11 experimental and 13 control flies were removed and dissected for mitochondrial morphometry. e, f, Maximum intensity projections (e) and morphometric parameters (f) of automatically detected mitochondria in CLSM image stacks of dFBN dendrites in rested flies, sleep-deprived flies, flies allowed to recover for 24 h after sleep deprivation, and rested and sleep-deprived flies co-expressing R23E10-GAL4-driven AOX or TrpA1, which was activated at 29 °C. Sleep history-dependent changes in mitochondrial volume (P = 0.0025, Holm-Šídák test after ANOVA), sphericity (P = 0.0001, Holm-Šídák test after ANOVA), and branch length (P = 0.0414, Holm-Šídák test after ANOVA) are occluded by the co-expression of AOX (P ≥ 0.1515, two-sided t- or Mann-Whitney test) or the simultaneous activation of TrpA1 (P ≥ 0.2002, two-sided t- or Mann-Whitney test) and overcorrected after recovery sleep (all parameters: P < 0.0001, Holm-Šídák test after ANOVA). The number of mitochondria is unchanged by sleep deprivation (P > 0.9999) but elevated after recovery sleep (P < 0.0001, Dunn’s test after Kruskal-Wallis ANOVA). Two data points exceeding the y-axis limits are plotted as triangles at the top of the graphs; mean and s.e.m. are based on the actual values. g, Volumetric renderings of automatically detected mitochondria in OPRM image stacks of dFBN dendrites in rested and sleep-deprived flies co-expressing R23E10-GAL4-driven AOX or TrpA1, which was activated at 29 °C. h, Sleep in flies expressing R23E10-GAL4-driven split-GFP-based contact site sensors (SPLICS) or fluorescent fusion proteins located in the outer mitochondrial (OMM), endoplasmic reticulum (Sec61β), or plasma membrane (CD4) (P = 0.0648, ANOVA). Data are means ± s.e.m. or ratios of means ± error-propagated s.e.m. (a, light gray); n, number of cells (a, b, EM), dendritic fields (a, b, OPRM and CLSM, d, f), or flies (c, h); asterisks, significant differences (P < 0.05) in planned pairwise comparisons. Scale bars, 10 µm (e,g). For statistical details see Supplementary Table 2.

Source data

Extended Data Fig. 6 Sleep history does not alter the morphology of PN mitochondria.

a, b, Volumetric renderings (a) and morphometric parameters (b) of automatically detected mitochondria in OPRM image stacks of PN dendrites in rested and sleep-deprived flies. Mitochondrial number (P = 0.7077, two-sided t-test), volume (P = 0.8074, two-sided t-test), sphericity (P = 0.6500, two-sided t-test), and branch length (P = 0.5326, two-sided t-test) are unaffected by sleep deprivation. c, d, Maximum intensity projections (c) and morphometric parameters (d) of automatically detected mitochondria in CLSM image stacks of PN dendrites in rested and sleep-deprived flies. Mitochondrial number (P = 0.2534, two-sided Mann-Whitney test), volume (P = 0.7637, two-sided Mann-Whitney test), sphericity (P = 0.1953, two-sided Mann-Whitney test), and branch length (P = 0.6972, two-sided t-test) are unaffected by sleep deprivation. One data point exceeding the y-axis limits is plotted as a triangle at the top of the right-hand graph; mean and s.e.m. are based on the actual values. Scale bars, 10 µm (a), 20 µm (c). For statistical details see Supplementary Table 2.

Source data

Extended Data Fig. 7 Morphological and metabolic consequences of inducing mitochondrial fission or fusion in dFBNs.

a, b, Volumetric renderings (a) and morphometric parameters (b) of automatically detected mitochondria in OPRM image stacks of dFBN dendrites. Flies carried R23E10-GAL4-driven overexpression constructs or RNAi transgenes targeting mitochondrial fission or fusion machinery. Manipulations that increase fission (green) or fusion (blue) have opposite effects on mitochondrial volume (P ≤ 0.0480, Holm-Šídák test after ANOVA), sphericity (P ≤ 0.0344, Holm-Šídák test after ANOVA), and branch length (P ≤ 0.0326, Holm-Šídák test after ANOVA). c, Morphometric parameters of automatically detected mitochondria in CLSM image stacks of dFBN dendrites. Flies carried R23E10-GAL4-driven overexpression constructs or RNAi transgenes targeting mitochondrial fission or fusion machinery. Manipulations that increase fission (green) or fusion (blue) have opposite effects on mitochondrial volume (P ≤ 0.0062, Dunn’s test after Kruskal-Wallis ANOVA), sphericity (P ≤ 0.0170, Holm-Šídák test after ANOVA), and branch length (P ≤ 0.0427, Dunn’s test after Kruskal-Wallis ANOVA). Five data points exceeding the y-axis limits are plotted as triangles at the top of the graphs; mean and s.e.m. are based on the actual values. d, Summed-intensity projections of dFBN dendrites expressing Drp1 and iATPSnFR plus RFP, in rested and sleep-deprived (SD) flies. Emission ratios are intensity-coded according to the key below and reduced in dFBNs expressing Drp1, irrespective of sleep history (Drp1 effect: P < 0.0001, sleep history effect: P < 0.0001, Drp1 × sleep history interaction: P = 0.1112; two-way ANOVA). Data are means ± s.e.m.; n, number of dendritic fields; asterisks, significant differences (P < 0.05) from both manipulations increasing fission. Scale bars, 10 µm (a), 5 µm (d). For statistical details see Supplementary Table 2.

Source data

Extended Data Fig. 8 Inducing mitochondrial fission or fusion in dFBNs alters sleep.

a, b, Sleep in flies expressing R23E10-GAL4-driven fission or fusion proteins, or RNAi transgenes targeting transcripts encoding these proteins (a) or proteins regulating phosphatidic acid levels (b), and their parental controls. With the exception of the overexpression of Marf alone (P ≥ 0.1622, Holm-Šídák test after ANOVA), manipulations that increase fission (green) or fusion (blue) alter sleep in opposite directions (GTPases: P ≤ 0.0115, phosphatidic acid regulators: P ≤ 0.0381; Holm-Šídák test after ANOVA). c–e, Sleep in flies carrying R23E10-GAL4-driven Drp1 overexpression constructs or RNAi transgenes targeting mitochondrial fusion proteins not included in a, b and Fig. 4c: two independent constructs for Drp1 overexpression (c, P ≤ 0.0209, Dunn’s test after ANOVA); six independent RNAi transgenes directed against Opa1 (d, P ≤ 0.0199, Holm-Šídák test after ANOVA); and five independent RNAi transgenes directed against Marf (e, P ≥ 0.1017 relative to ≥1 parental control with the exception of R23E10 > Marf sm(II), Holm-Šídák test after ANOVA). f, Manipulations that increase fission (R23E10-GAL4 > Opa1RNAi, green) or fusion (R23E10 > Marf,Opa1, blue) alter the time courses (left panels, genotype effects: P ≤ 0.0213, time × genotype interactions: P < 0.0001, two-way repeated-measures ANOVA) and percentages of sleep rebound after deprivation (SD) in opposite directions (right panel, genotype effect: P ≤ 0.0186, Dunn’s test after ANOVA). One data point exceeding the y-axis limits is plotted as a triangle at the bottom of the right-hand graph; mean and s.e.m. are based on the actual values. g, Sleep in flies carrying an R23E10-GAL4-driven Marf overexpression construct not included in a and Fig. 4c (P ≥ 0.1252, Dunn’s test after Kruskal-Wallis ANOVA). Data are means ± s.e.m.; n, number of flies; asterisks, significant differences (P < 0.05) from both parental controls. For statistical details see Supplementary Table 2.

Source data

Extended Data Fig. 9 Inducing mitochondrial fission or fusion in dFBNs alters arousal thresholds without causing overexpression artefacts or anatomical defects.

a, b, Percentages of flies awakened by mechanical stimuli lasting 0.5 s (left panels), 2 s, or 20 s (right panels). The average percentages awakened by 0.5-s stimuli in the left panels are reproduced on the right. Manipulations that increase fission fail to lower the arousal threshold, possibly because of a floor effect linked to the R23E10-GAL4 strain (a, P ≥ 0.3354 relative to ≥1 parental control, Dunn’s test after Kruskal-Wallis ANOVA). With the exception of the overexpression of Marf alone (P > 0.9999), manipulations that increase fusion raise the arousal threshold (b, P ≤ 0.0371, Dunn’s test after Kruskal-Wallis ANOVA). c, Sleep in flies expressing R23E10-GAL4-driven Marf is insensitive to the co-expression of fluorescent proteins in the cytoplasm (tdTomato) or the outer mitochondrial membrane (OMM-mCherry) (P ≥ 0.1106, Dunn’s test after Kruskal-Wallis ANOVA), in contrast to the synergistic effect of overexpressing Opa1 (Fig. 4c, Extended Data Fig. 8a). d, Maximum-intensity projections of dFBNs in flies carrying R23E10-GAL4-driven overexpression constructs or RNAi transgenes targeting the mitochondrial fission or fusion machinery. Five brains per genotype were imaged; representative examples are shown. Data are means ± s.e.m.; n, number of flies; asterisks, significant differences (P < 0.05) from both parental controls. Scale bar, 100 µm (d). For statistical details see Supplementary Table 2.

Source data

Extended Data Fig. 10 Inducing mitochondrial fission or fusion in PNs or KCs has no effect on sleep.

a, Sleep in flies carrying GH146-GAL4-driven overexpression constructs or RNAi transgenes targeting the mitochondrial fission or fusion machinery in PNs (P ≥ 0.0842 relative to ≥1 parental control, Holm-Šídák test after ANOVA). b, Sleep in flies carrying OK107-GAL4-driven overexpression constructs or RNAi transgenes targeting the mitochondrial fission or fusion machinery in KCs (P ≥ 0.0660 relative to ≥1 parental control, Holm-Šídák test after ANOVA). Data are means ± s.e.m.; n, number of flies. For statistical details see Supplementary Table 2.

Source data

Supplementary information

Supplementary Tables

Supplementary Tables 1–5.

Reporting Summary

Peer Review File

Source data

Source Data Figs. 1–4 and Extended Data Figs. 3–10.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Sarnataro, R., Velasco, C.D., Monaco, N. et al. Mitochondrial origins of the pressure to sleep. Nature 645, 722–728 (2025). https://doi.org/10.1038/s41586-025-09261-y

- Received: 22 February 2024

- Accepted: 09 June 2025

- Published: 16 July 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09261-y

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Variation in mitochondrial DNA affects locomotor activity and sleep in Drosophila melanogaster

Article Open access 28 June 2022

Single-cell transcriptomics and cell-specific proteomics reveals molecular signatures of sleep

Article Open access 19 August 2022

Singular and short-term anesthesia exposure in the developing brain induces persistent neuronal changes consistent with chronic neurodegenerative disease

Article Open access 11 March 2021

Article Open access Published: 23 July 2025

A gut sense for a microbial pattern regulates feeding

Winston W. Liu,

Naama Reicher,

Emily Alway,

Laura E. Rupprecht,

Peter Weng,

Chloe Schaefgen,

Marguerita E. Klein,

Jorge A. Villalobos,

Carlos Puerto-Hernandez,

Yolanda Graciela Kiesling Altún,

Amanda Carbajal,

José Alfredo Aguayo-Guerrero,

Alam Coss,

Atharva Sahasrabudhe,

Polina Anikeeva,

Alan de Araujo,

Avnika Bali,

Guillaume de Lartigue,

Elvi Gil-Lievana,

Ranier Gutierrez,

Edward A. Miao,

John F. Rawls,

M. Maya Kaelberer &

…

Diego V. Bohórquez

Nature volume 645, pages 729–736 (2025)

Abstract

To coexist with its resident microorganisms, the host must have a sense to adjust its behaviour in response to them. In the intestine, a sense for nutrients transduced to the brain through neuroepithelial circuits guides appetitive choices1,2,3,4,5. However, a sense that allows the host to respond in real time to stimuli arising from resident gut microorganisms remains to be uncovered. Here we show that in the mouse colon, the ubiquitous microbial pattern flagellin—a unifying feature across phyla[6]—stimulates Toll-like receptor 5 (TLR5) in peptide YY (PYY)-labelled colonic neuropod cells. This stimulation leads to PYY release onto NPY2R vagal nodose neurons to regulate feeding. Mice lacking TLR5 in these cells eat more and gain more weight than controls. We found that flagellin does not act on the nerve directly. Instead, flagellin stimulates neuropod cells from the colonic lumen to reduce feeding through a gut–brain sensory neural circuit. Moreover, flagellin reduces feeding independent of immune responses, metabolic changes or the presence of gut microbiota. This sense enables the host to adjust its behaviour in response to a molecular pattern from its resident microorganisms. We call this sense at the interface of the biota and the brain the neurobiotic sense[7].

Similar content being viewed by others

Main

Every organism interprets the world through its senses—its Umwelt8,9. Although five canonical senses have been extensively studied, emerging evidence has established the neural basis of a gut sense, a sense that constantly assesses stimuli arising from the gut lumen1,2,3,4,5,10,11,12. Nutrients, stretch, and microorganisms are among the most salient stimuli that the gut encounters. In the small intestine, epithelial neuropod cells1,13,14,15 rapidly detect nutrients and relay the sensory information, through the vagus nerve, to influence an animal’s appetitive choices in real time4,16,17,18,19. Growing evidence suggests that gut microorganisms, which are most abundant in the colon[20], substantially modulate feeding behaviour21,22,23,24, potentially through neuromodulators25,26,27, immune signals[28] and vagal pathways23,24,29,30,31,32,33,34. However, a direct neural circuit through which the host interprets microbial sensory information to adjust its feeding remains unknown.

In the colon, vagal neurons form neuroepithelial circuits with neuropod cells, labelled by the neuromodulator PYY1,3. These, and other colonic epithelial cells, are constantly exposed to microorganisms, which can be recognized by molecular patterns such as flagellin, collectively known as microbe-associated molecular patterns. Flagellin is a structural component of one of the three most ancient organelles, flagella[35], and a protein conserved across bacterial phyla[6] that activates the pattern recognition receptor TLR5 (refs. 36,37). Deleting Tlr5 in all intestinal epithelial cells of mice leads to obesity, metabolic inflammation, and spontaneous colitis[28]. Furthermore, evidence from immortalized gut cell lines suggests that Toll-like receptors may be expressed by specialized sensory epithelial cells, including those that secrete the satiety-inducing protein PYY[38]. Here we determined that feeding behaviour is regulated by a previously unrecognized gut–brain sensory modality for microbial patterns. We call this sense, at the interface of the biota and the brain, the neurobiotic sense.

PYY cells express Tlr5

In the gut, sensory epithelial cells are dispersed among other epithelial cells at a ratio of less than 1 in 1,000 (ref. [39]). They encompass two main lineages: those that express serotonin and substance P, and those that express several neuromodulators including cholecystokinin (CCK), glucagon-like peptide 1 (GLP-1) and PYY40,41. The expression of these neuropeptides is preceded by that of the transcription factor Neurod1 (ref. [42]). In different regions of the intestine, Neurod1-labelled cells favour the expression of specific neuromodulators. For example, CCK prevails in the proximal small intestine, whereas PYY is enriched in the distal ileum and colon13,39 (Fig. 1a). The colon is a habitat rich in microorganisms[20]. Using reporter mice expressing green fluorescent protein (GFP) driven by the CCK and PYY promoters, we sequenced the transcriptome of epithelial cells from the small intestine and colon (Extended Data Fig. 1). In each segment, we compared the transcriptome of sensory epithelial cells to that of their neighbouring epithelial cells to identify enriched receptors that detect microbial signals, including byproducts of dietary fermentation, metabolites, and patterns23,27,28.

Fig. 1: The absence of microbial pattern recognition receptor TLR5 in colonic PYY-labelled cells increases food intake.

a, Mouse colon with GFP-labelled PYY-labelled cells was rolled longitudinally (proximal colon in the centre); representative of n = 3 mice. Inset: magnified view of the outlined area showing a single PYY–GFP cell with apical process reaching into the lumen and neuropod reaching towards the base of the crypt. DAPI, 4′,6-diamidino-2-phenylindole. Scale bars, 10 μm. b, Volcano plot of microbial pattern recognition receptor gene expression in epithelial PYY–GFP and non-GFP cells by RNA sequencing. Compared to non-GFP cells, PYY–GFP cells are enriched for the pattern recognition receptor gene Tlr5 (n = 6 mice; adjusted P < 0.01 by DESeq2 with two-tailed t-test). c, Fluorescence in situ hybridization of Tlr5 in PYY–GFP cells. Error bars represent s.e.m. Left: regional expression of Tlr5 in PYY–GFP cells (n = 3 mice, each dot represents 50 cells). n.d., not detected (no cells expressing Tlr5). Dist. distal; Duo., duodenum; Jej., jejunum; Ile., ileum; Prox., proximal. Right, PYY-labelled cell (green) expressing Tlr5 (red) in the distal colon; representative of n = 3 mice. Scale bar, 10 μm. White dashed line represents PYY-labelled cell outline. d, Left, genetic deletion of Tlr5 exclusively in PYY-labelled cells causes increased weight gain in male and female mice (males (M) Pyycre;Tlr5fl/fl: n = 7 mice, starting weight = 5.78 g ± 0.61; Tlr5fl/fl littermate controls: n = 15 mice, starting weight = 14.28 g ± 0.71; females (F) Pyycre;Tlr5fl/fl: n = 6 mice, starting weight = 15.04 g ± 0.53; Tlr5fl/fl littermate controls: n = 11 mice, starting weight = 14.16 g ± 0.39; *P < 0.05 genotype–time interaction by repeated-measures analysis of variance (ANOVA) with post hoc Tukey honestly significant difference (HSD). Error bars represent s.e.m. Right, meal duration in females and meal size in males and females significantly increased in Pyycre;Tlr5fl/fl mice (Tlr5fl/fl males: n = 413 meals, n = 6 mice; 5Pyycre;Tlr5fl/fl males: n = 612 meals, n = 9 mice; Tlr5fl/fl females: n = 399 meals, n = 8 mice; Pyycre;Tlr5fl/fl females: n = 468 meals, n = 9 mice; n = 2 independent experiments; *P < 0.05 by two-way ANOVA with post hoc Tukey HSD; P < 0.05 main effect of genotype and sex for meal size and duration with P > 0.05 genotype–sex interaction). No changes observed in meal frequency (see Extended Data Fig. 5 for further analyses). Box plots represent interquartile range; white lines indicate median; whiskers extend to the furthest point above the third quartile or below the first quartile within 1.5× the interquartile range.

Both CCK–GFP cells in the proximal small intestine and PYY–GFP cells in the ileum and colon were significantly enriched in genes encoding receptors of microbial byproducts, such as Ffar1, Ffar2, Gpbar1 and Gpr119 (n ≥ 5 mice, P < 0.001; Extended Data Fig. 1). However, only PYY–GFP cells were significantly enriched in genes for pattern recognition receptors, the most prominent being Tlr5 (n = 6 mice, P < 0.01; Fig. 1b). TLR5 detects flagellin36,37, a ubiquitous microbial pattern, classically associated with host immune defence and commensal tolerance43,44,45.

The robust expression of Tlr5 in PYY-labelled cells was corroborated using in situ hybridization. Overall, co-localization significantly increased from 24.1 ± 2.9% in the ileum to 57.5 ± 5.3% in the distal colon (n = 3 mice, 50 cells per segment; P < 0.005, Fig. 1c), where PYY-labelled cell density is highest (n = 3; Extended Data Fig. 2a). Tlr5 was not expressed in PYY-labelled cells of the brain[46] or serotonin-labelled cells of the colon; in fact, Tlr5 was predominantly expressed in PYY-labelled cells of the ileum and colon (n = 3 mice; Extended Data Fig. 2b–h).

TLR5 in PYY cells regulates feeding

To determine the role of TLR5 in PYY-labelled cells, we bred Pyycre;Tlr5fl/fl mice. In these mice, Tlr5 is knocked out of all PYY-labelled cells (n = 3 mice; Extended Data Fig. 3a). Studies have shown that a global knockout of Tlr5 in mice causes metabolic dysfunction, inflammation, and obesity[21]. Furthermore, when TLR5 is ablated in all gut epithelial cells, both the metabolic dysfunction and inflammation persist[28]. However, we found that when TLR5 is ablated specifically in PYY-labelled cells, mice show no evidence of metabolic dysfunction or inflammation (Extended Data Fig. 3).

Compared to littermate controls, Pyycre;Tlr5fl/fl mice had normal oral glucose tolerance, fasting blood glucose (n ≥ 4 mice, P > 0.1; Extended Data Fig. 3b,c), and fat pad weight (n ≥ 5 mice, P > 0.1, Extended Data Fig. 3d). Pyycre;Tlr5fl/fl mice also showed no change in the serum levels of the metabolic neuromodulators GLP-1 and PYY following 1 h of food consumption, suggesting that the circulating levels of gut hormones were no different from those of littermate controls (n ≥ 5 mice, P > 0.1; Extended Data Fig. 3e). Moreover, these mice showed no signs of spontaneous colitis and exhibited normal colon length, weight and spleen size (n ≥ 3 mice, P > 0.1; Extended Data Fig. 3f–h). Levels of the inflammatory markers colonic myeloperoxidase and fecal lipocalin-2 were unchanged between Pyycre;Tlr5fl/fl mice and controls (n ≥ 5 mice, P > 0.1; Extended Data Fig. 3i). Furthermore, there were no histological differences in the colon, including crypt depth and sensory cell density (n = 3 mice, P > 0.05; Extended Data Fig. 3j–l), TLR gene expression in epithelial cells remained unaltered (n = 6 mice, P > 0.05; Extended Data Fig. 3m), and no changes in tight junctions were observed (n = 6 mice, P > 0.05; Extended Data Fig. 3n) in Pyycre;Tlr5fl/fl mice compared to littermate controls.

Notably, when TLR5 is ablated specifically in PYY-labelled cells, mice eat more and gain more weight (n ≥ 4 mice, P < 0.05; Fig. 1d, Extended Data Fig. 3o–p and Supplementary Table 1). As TLR5 is known to canonically trigger immune responses through intracellular activation of myeloid differentiation factor 88 (MyD88)[47], we bred Pyycre;Myd88fl/fl mice to determine the effect of MyD88 ablation in PYY-labelled cells. We found that, compared to littermates, Pyycre;Myd88fl/fl mice did not show increased body weight gain or food intake (n ≥ 3 mice, P > 0.1; Extended Data Fig. 4). Therefore, independent of canonical immune signalling, metabolic dysfunction, or inflammation, TLR5 in PYY-labelled cells regulates body weight gain.

Furthermore, we performed meal pattern analysis to determine the quantity, frequency, and timing of food ingestion. We optimized an automated home-cage behavioural system that records food intake to the nearest 0.01 g with temporal resolution of 1 s (Extended Data Fig. 5a). Both male and female Pyycre;Tlr5fl/fl mice ate significantly larger meals compared to littermate controls (males: n = 6–9 mice; females: n = 8–9 mice; P < 0.05; Fig. 1d and Extended Data Fig. 5b,c). Moreover, female Pyycre;Tlr5fl/fl mice also ate longer meals than littermate controls (n = 8–9, P < 0.05; Fig. 1d and Extended Data Fig. 5d–g), revealing that the length and size of meals are modulated by TLR5 in PYY-labelled cells.

PYY cells use TLR5 to sense flagellin

The established ligand for TLR5 is flagellin. Although transcriptional models suggest that diet influences microbial signals[48], it is unclear whether the amount of colonic flagellin changes with feeding. Using a cell-based assay, we found that relative flagellin levels in the stool are significantly higher in fed compared to fasted mice (n = 5, mice P < 0.05; Fig. 2a). This response is unaltered in Pyycre;Tlr5fl/fl mice (n = 5 mice, P > 0.1; Fig. 2a), indicating that flagellin levels in the colon are independent of Tlr5 expression in PYY-labelled cells. Thus, feeding correlates with increased flagellin in the colon.

Fig. 2: PYY-labelled cells sense microbial flagellin through TLR5.

a, Relative stool flagellin concentration from Pyycre;Tlr5fl/fl mice and Tlr5fl/fl littermate controls following 16-h fast or ad libitum feeding. No differences across genotype. Feeding increased stool flagellin (n = 5 mice; *P < 0.05 by repeated-measures ANOVA with post hoc two-tailed Tukey HSD). b, Heat map (n = 6 mice; adjusted *P < 0.01 by DESeq2 with two-tailed t-tests; P values in Extended Data Fig. 1; left) and qRT–PCR (non-PYY+, n = 5 mice; PYY+, n = 6 mice; *P < 0.05 by repeated-measures ANOVA with post hoc Tukey HSD; right) of TLR gene expression in non-GFP and PYY–GFP colonic epithelial cells. c, Selected calcium responses of Pyycre;Salsa6f colonic cells to poly(I:C) (19%, n = 63 cells, n = 4 mice), lipopolysaccharide (LPS; 0%, n = 80 cells, n = 3 mice) and flagellin (26%, n = 121 cells, n = 5). Grey bar indicates 30-s infusion. d, Calcium responses to poly(I:C) and flagellin before (solid) and after (dashed) TLR5 inhibitor TH1020 (1 μM). e, Calcium response quantification. Only flagellin, not poly(I:C), responses were reduced (poly(I:C): n = 12 cells; flagellin: n = 9 cells; *P < 0.05 by paired, two-tailed t-test). NS, not significant. f, Colonic epithelial monolayer cultures from Pyycre;Tlr5fl/fl mice and Tlr5fl/fl littermate controls stimulated with buffer, 100 ng ml−1 flagellin and 1 μM forskolin (F) + 10 μM IBMX (I; positive control (ctrl)). PYY concentration in cell lysates and supernatants measured using enzyme-linked immunosorbent assay. Flagellin stimulated PYY release in Tlr5fl/fl but not Pyycre;Tlr5fl/fl cultures (n = 4 mice; *P < 0.05 by repeated-measures ANOVA with post hoc two-tailed Tukey HSD). g, Heat map of synaptic gene expression in non-GFP and PYY–GFP colonic cells (n = 6 mice; adjusted P < 0.01 by DESeq2 with two-tailed t-tests, P values in Extended Data Fig. 1). h, Colonic PYY–GFP tissue immunostained for PGP9.5 (red). Representative of n = 3 mice; regions quantified in Extended Data Fig. 7. Scale bars, 10 μm. i, Left: vagal responses to intracolonic PBS and stimulation by a 473-nm and 532-nm light-emitting diode (LED) in Pyycre;ChR2 mice (n = 3 mice). Right: quantification of peak vagal responses (n = 3 mice; *P < 0.05 by two-tailed Wilcoxon signed ranked test with non-parametric comparisons). Error bars and shading represent s.e.m.

Analysis by quantitative reverse transcription PCR (qRT–PCR) confirmed expression of Tlr1–Tlr5 in colonic PYY–GFP cells; however, compared to the expression levels in neighbouring epithelial cells, only Tlr5 expression showed significant enrichment in PYY-labelled cells (n ≥ 5 mice, P < 0.05; Fig. 2b). To determine whether these cells respond to ligands for Toll-like receptors, we recorded intracellular calcium activity from colonic PYY-labelled cells. We bred a Pyycre;Salsa6f mouse in which PYY-labelled cells express the SALSA6F protein. This fusion protein, linking tdTomato and GCaMP6f, allows for sorting primary cells on the basis of their red fluorescence, and recording their intracellular calcium activity while avoiding the toxicity of calcium indicator dyes[49].

Of all Pyycre;Salsa6f cells imaged, none responded to the TLR4 ligand lipopolysaccharide (1 mg ml−1, n = 80 cells from 3 mice; Fig. 2c), 19% responded to the TLR3 ligand poly(I:C) (1 μg ml−1, n = 63 cells from 4 mice; Fig. 2c) and 26% responded to the TLR5 ligand flagellin (100 ng ml−1, n = 121 cells from 5 mice; Fig. 2c). The calcium responses to poly(I:C) were unaltered in the presence of the TLR5 inhibitor TH1020 (n = 12 cells from 3 mice, P > 0.5; Fig. 2d,e), but the responses to flagellin were significantly attenuated (n = 9 cells from 3 mice, P < 0.05; Fig. 2d,e), demonstrating that flagellin activation of PYY-labelled cells requires TLR5. Similar results were confirmed using NeuroD1-Cre;Salsa6f mice (Extended Data Fig. 6a,b).

We then determined whether the activation of PYY-labelled cells by TLR ligands leads to the release of PYY. Although poly(I:C) (1 μg ml−1) did not stimulate PYY release from dissociated colonic crypts compared to buffer (n ≥ 5 mice, P < 0.01; Extended Data Fig. 6c), flagellin (100 ng ml−1) stimulated significant release of PYY (n = 5 mice, P < 0.05; Extended Data Fig. 6c). This release was significantly suppressed in colonic crypts from mice lacking TLR5 in PYY-labelled cells (n = 4 mice, P < 0.05; Fig. 2f). Therefore, PYY-labelled cells sense flagellin using TLR5 and transduce it by releasing PYY—a known inducer of satiety[50].

PYY cells connect with vagal neurons

Besides the circulatory functions of intestinal PYY50,51, recent work shows local paracrine and synaptic signalling onto the vagus nerve52,53. Previously, monosynaptic rabies tracing has shown that PYY-labelled cells in the colon form synaptic connections with vagal neurons. These cells, known as neuropod cells, rapidly and directly transduce sensory cues to the nervous system3,54.

Compared to neighbouring epithelial cells, PYY-labelled cells are significantly enriched in genes encoding proteins involved in synaptic signalling, synaptic formation and neurotransmission (n = 6 mice, P < 0.01; Fig. 2g and Extended Data Fig. 7a,b). In addition, approximately one in five PYY-labelled cells contact peripheral neurons labelled by PGP9.5 in the ileum and colon (21.7 ± 0.6%, n = 50 cells per segment; Fig. 2h and Extended Data Fig. 7c). To confirm that PYY-labelled cells are functionally connected with the vagus nerve, we paired luminal optogenetics with in vivo whole-nerve electrophysiology of the cervical vagus nerve. We bred a Pyycre;ChR2 mouse in which PYY-labelled cells express channelrhodopsin-2 (ChR2), which is an opsin activated by 473-nm light (Extended Data Fig. 7d,e). In Pyycre;ChR2 mice, a control 532-nm-light stimulus applied to the lumen of the colon did not activate the cervical vagus, but a 473-nm-light luminal stimulus led to a rapid and significant increase in the vagal firing rate (n = 3 mice, P < 0.05; Fig. 2i). Vagal firing peaked within seconds of 473-nm-light stimulus, demonstrating that PYY-labelled cells directly activate the vagus nerve. These results establish a direct PYY-labelled cell–vagal circuit for rapid signalling between the colon and the hindbrain, where the afferent vagus nerve terminates[55].

Flagellin is transduced to vagal neurons

We then recorded cervical vagal activity in response to colonic perfusion of flagellin. Intralipid served as a positive control (n = 4 mice, P < 0.05; Extended Data Fig. 7f,g). Perfusing flagellin (2 μg ml−1) through the colon resulted in a significant increase in vagal firing rate within seconds (n = 7 mice, P < 0.05; Fig. 3a). To determine whether the PYY-labelled cell is necessary to transduce luminal flagellin onto the vagus, we bred a Pyycre;Halo mouse. In these mice, PYY-labelled cells express the optogenetic silencing protein halorhodopsin (Extended Data Fig. 7h), an anion channel that hyperpolarizes cells in response to 532-nm light. A control 473-nm-light stimulus applied to the lumen of the colon did not alter vagal activity in response to flagellin (2 μg ml−1), but a silencing 532-nm-light luminal stimulus ablated vagal firing in response to flagellin (n = 4 mice, P < 0.05; Fig. 3b). Moreover, in Pyycre;Tlr5fl/fl mice, luminal flagellin produced no rapid vagal response compared to the case in littermate controls (n ≥ 3 mice, P < 0.05; Fig. 3c and Extended Data Fig. 8a). Therefore, PYY-labelled neuropod cells use TLR5 to sense luminal flagellin and rapidly transduce this microbial stimulus to the vagus nerve.

Fig. 3: PYY–vagal circuits transduce colonic flagellin.

a, Left, vagal responses to intracolonic perfusion of PBS or 2 μg ml−1 flagellin in wild-type mice (n = 7 mice). Right, quantification of peak response to flagellin (n = 7 mice; *P < 0.05 by two-tailed paired t-test). b, Left, vagal responses to intracolonic perfusion of PBS and 2 μg ml−1 flagellin with simultaneous 473-nm-LED or 532-nm-LED stimulation in Pyycre;Halo mice (n = 4 mice). Right, quantification of the peak vagal response to flagellin (n = 4 mice; *P < 0.05 by two-tailed Wilcoxon signed ranked test with non-parametric comparisons using the Wilcoxon method). c, Vagal responses to intracolonic perfusion of flagellin in Pyycre;Tlr5fl/fl mice (n = 5 mice) and Tlr5fl/fl littermate controls (n = 3 mice; for quantification, see Extended Data Fig. 8). d, Fluorescence in situ hybridization of PYY receptor Y2R (encoded by Npy2r) in a subpopulation of neurons in the vagal nodose ganglion. Representative of n = 4 ganglia. Scale bars, 10 μm. e, Left, vagal responses to intracolonic perfusion of PBS or 2 μg ml−1 flagellin before and after intraperitoneal delivery of the Y2R inhibitor (Y2Ri) BIIE-0246 (1 μM; n = 4 mice). Right, quantification of the peak vagal response to flagellin with and without the addition of Y2R inhibitor 1 μM BIIE-0246 (n = 4 mice; *P < 0.05 by Kruskal–Wallis test with non-parametric comparisons using the Wilcoxon method). f, In vivo calcium imaging of vagal nodose neurons positive for Npy2r in response to colonic perfusion of flagellin (2 µg ml−1; n = 4 mice, n = 144 neurons). A total of 43.37% of NPY2R+ cells respond to 2 µg ml−1 flagellin. g, Left, in vivo calcium imaging of vagal nodose neurons in response to colonic perfusion of either intralipid (7%) or flagellin (2 µg ml−1). n = 520 neurons, n = 4 mice. Right, number of responding neurons to each stimulus (n = 4 mice, n = 520 neurons). Grey dashed lines in the heat maps represent start and end of perfusion. Error bars and shading represent s.e.m. Graphics in f adapted with permission from ref. [3], AAAS.

Notably, molecular analyses using RNA sequencing, qRT–PCR and in situ hybridization show that vagal neurons do not express Tlr5 (n ≥ 3 mice; Extended Data Fig. 8b–d). Moreover, calcium imaging of acutely dissociated vagal nodose neurons revealed that whereas capsaicin (the control stimulus) elicits calcium transients, flagellin does not, indicating that vagal nodose neurons themselves do not sense flagellin (n = 227 neurons from 4 mice; Extended Data Fig. 8e), further establishing PYY-labelled neuropod cells as flagellin transducers.

Vagal NPY2 receptor is required

We then sought to determine whether vagal activity in response to flagellin requires PYY release from neuropod cells. Published RNA-sequencing data show that vagal neurons innervating the colon express the PYY receptor Y2R[56] (n = 44 cells; Extended Data Fig. 8f). In the gut, this receptor is thought to mediate local PYY signalling[51]. Using in situ hybridization, we confirmed the expression of Y2R in vagal nodose neurons (n = 4 mice; Fig. 3d). Then, we found that blocking Y2R using BIIE-0246 (10 μM) ablates cervical vagal activity in response to flagellin perfused through the lumen of the colon (n = 4 mice, P < 0.05; Fig. 3e).

To better understand how individual vagal neurons respond to flagellin in the gut, we used intravital calcium imaging to observe the activity of these neurons in response to stimuli perfused through the colon. We used a triple-transgenic mouse model, Snap25-FosTRAP-tdTomato57,58, that enables real-time tracking of calcium changes in individual vagal neurons and subsequent labelling of these responsive neurons for further analysis. After imaging, we extracted the nodose ganglia and using compartment analysis of temporal activity by fluorescence in situ hybridization[59], we confirmed that 43.37% of 332 NPY2R-labelled neurons reacted to flagellin in the colon (Fig. 3f and Extended Data Fig. 8g–i).

Moreover, calcium imaging of vagal nodose neurons revealed distinct response patterns: 11.7% of neurons responded only to intralipid (a positive control), 27.7% responded to both intralipid and flagellin, and 60.6% responded exclusively to flagellin (n = 520 neurons; n = 4 mice; Fig. 3g and Extended Data Fig. 8j). This observation—that almost two thirds of the neurons activated by colonic infusions specifically responded to flagellin—suggests the existence of a unique neuroepithelial circuit for sensing flagellin, separate from the pathways involved in nutrient detection. Although future studies should investigate the neurons responding to both intralipid and flagellin, these results highlight a distinct pathway for gut–brain signalling in response to the microbial pattern flagellin.

Flagellin regulates feeding through PYY cells

Our discovery of a neuroepithelial circuit for rapid sensing of a microbial pattern in the colon led us to investigate how flagellin influences behaviour in real time. We reasoned that the presence of flagellin in the colon would lead to a rapid decrease in food intake. To test this, we fasted mice overnight to induce hunger and then administered either flagellin (1 μg ml−1, 0.1 ml) or a PBS control by means of enema. We found that a flagellin enema significantly reduced food intake within 20 min in littermate control mice but had no effect on mice lacking TLR5 in PYY-labelled cells (Pyycre;Tlr5fl/fl; n = 5 mice, P < 0.05; Fig. 4a,b and Extended Data Fig. 9a). This response to flagellin was consistent across juvenile (5-week-old) and adult (10-week-old) mice, suggesting that this sensory pathway is conserved throughout development (n = 5 mice, P < 0.05; Extended Data Fig. 9b).

Fig. 4: PYY–vagal circuits use TLR5 and Y2R to drive changes in food intake.

Mice were fasted overnight and given an enema of either 1 μg ml−1 flagellin or PBS before receiving access to standard chow ad libitum. a,b, Tlr5fl/fl littermate control mice ate significantly less food post-flagellin enema at 20, 40 and 60 min (a), whereas Pyycre;Tlr5fl/fl mice did not (b; n = 5 mice per genotype; *P < 0.05 genotype–enema–time interaction by repeated-measures ANOVA with post hoc two-tailed Tukey HSD). c,d, In wild-type mice, PBS and flagellin enemas were performed with the addition of either 10 μM TH1020 in the enema solution (n = 8 mice; c); or intraperitoneal injection of 1 μM BIIE-0246 before enema (n = 10 mice; d). TLR5 and Y2R inhibition attenuated the reduction of food intake post-flagellin enema (P < 0.05 drug–enema–time interaction by repeated-measures ANOVA with post hoc Tukey HSD; see Extended Data Fig. 9c,d for vehicle controls). i.p., intraperitoneal. e, Crunch Master (top schematic) tracks feeding microstructure by means of audio and video recording. Black ticks (bottom) indicate biting patterns of n = 7 mice post-PBS or flagellin enema. f, Left, flagellin enema significantly delayed onset of the first three bites (black: bite 1; blue: bite 2; green: bite 3; *P < 0.0001 main effect of treatment by repeated-measures ANOVA). Right, intake (spillage-corrected) was significantly decreased over 1-h test session after flagellin enema (two-tailed unpaired t-test, *P < 0.01). Violin plots show median indicated by thick line and mean indicated by thin line. g, In wild-type germ-free mice, flagellin enema decreased food intake compared to PBS enema (n = 12 mice; *P < 0.05, enema–time interaction by repeated-measures ANOVA with post hoc two-tailed Tukey HSD). Error bars represent s.e.m. h, Model for microbial pattern sensing by neuroepithelial circuits to drive behavioural change. Bacterial flagellin is detected by TLR5 in colonic PYY-labelled cells, which in turn release PYY to activate vagal neurons through Y2R. Activation of this circuit contributes to overall food intake. Graphics in h adapted with permission from ref. [3], AAAS.

To examine the specificity of the flagellin effect, we conducted an enema containing poly(I:C), a TLR3 ligand, and found that this stimulus did not affect food intake (n ≥ 5 mice, P < 0.05; Extended Data Fig. 9c). Furthermore, flagellin caused a temporary decrease in food intake, which dissipated after 3 h (n = 5 mice, P < 0.05; Extended Data Fig. 9c). Finally, pharmacologically inhibiting either TLR5 or the Y2 receptor prevented the flagellin-induced reduction in food intake (n ≥ 8 mice, P < 0.05; Fig. 4c,d and Extended Data Fig. 9d,e). These data strongly suggest that luminal flagellin rapidly and reversibly suppresses food intake by acting on TLR5 and triggering the release of PYY within this neuroepithelial circuit.

To analyse feeding behaviour with greater precision, we developed a behavioural system using video and audio recordings. The system, referred to as Crunch Master, serves to automatically quantify individual bite bouts in real time (Fig. 4e and Supplementary Videos 1 and 2). This analysis revealed that a flagellin enema delayed the onset of feeding and reduced overall food consumption without affecting bite frequency or eating duration within a 1-h period (n = 7 mice per group, P < 0.0001; Fig. 4f and Extended Data Fig. 9e). This further demonstrates that colonic flagellin stimulation modulates feeding behaviour in real time.

Notably, levels of flagellin delivered by means of enema were within the range of physiological concentrations found in fed versus fasted mice (n ≥ 5 mice, P < 0.05; Extended Data Fig. 9f). In addition, mice showed no signs of malaise, diarrhoea, pain, or physical limitations, and there was no significant increase in cytokine expression in the colon or spleen within 1 h post-enema (n ≥ 5 mice, P < 0.05; Extended Data Fig. 10a,b). Thus, neuroepithelial sensing of flagellin reduces food intake in the absence of an immune response.

Finally, to confirm that the effects of flagellin on food intake were due to direct activation of epithelial cells, and not interactions with gut microorganisms, we administered a flagellin enema to germ-free mice. Although germ-free mice can exhibit behavioural variations compared to conventionally raised animals[60], they are a useful model for studying this gut–brain neural circuit without a microbiome. Our results show that a flagellin enema significantly reduced food intake in these germ-free mice within 1 h (n = 12 mice, P < 0.05; Fig. 4g). This demonstrates that direct sensing of flagellin by colonic epithelial cells is sufficient to suppress food intake, irrespective of other microbial signals. Collectively, these findings demonstrate that a gut sense for the microbial pattern flagellin regulates feeding (Fig. 4h).

Conclusion

This gut–brain neural circuit forms the foundation of a ‘neurobiotic sense’—a sense by which the host adjusts its behaviour by monitoring a gut microbial pattern. While previous research has focused on nutrient sensory transduction in the small intestine4,16,17,19, we discovered that the specialized colonic cells, PYY-labelled neuropod cells, utilize the pattern recognition receptor TLR5 to detect bacterial flagellin. These cells then rapidly signal to the brain, through the vagus nerve, to regulate feeding behaviour.

It is important to acknowledge that, in this study, one type of flagellin from Salmonella typhimurium, a stereotypical pathogen, was used. However, bacteria can be pathogenic or commensal depending on the specific flagellin variant expressed[45]. Therefore, the effects of other molecular variants of flagellin warrant investigation. Future research should leverage developing technologies for real-time modulation of microbial populations to investigate the effects of flagellin fluctuations independently of exogenous induction.

Just as organisms rely on sight, sound, scent, taste and touch to navigate the world, they also adjust their behaviour in response to stimuli shaping their gut Umwelt[7].

Methods

Mouse strains

All experiments on mice were performed following approval by the Institutional Animal Care and Use Committee at Duke University Medical Center under the protocol A212-21-10. Mice were group-housed in Duke University’s Division of Laboratory Animal Resources, where they were kept on a 12-h light–dark cycle (0700–1900) with access to water and standard mouse chow (Purina 5001) ad libitum, unless otherwise indicated. The facility maintained an ambient temperature of 18–23 °C and humidity of 40–60%. Male and female adult mice aged 6–20 weeks were used in all experiments. The following experimental mouse strains were purchased, received or bred in-house and used directly: C57BL6/J (JAX 000664), PYY–GFP[13], CCK–GFP[61], Pyycre[62], NeuroD1-Cre (JAX 028364), loxP-STOP-loxP cassette (LSL)_tdTomato (JAX 007914), LSL_Halo-YFP (JAX 014539), LSL_ChR2-tdTomato (JAX 012567), LSL_Salsa6f (JAX 031968), Tlr5fl (JAX 028599), Myd88fl (JAX 008888), B6.Cg-Snap25tm3.1Hze/J (JAX 025111) and Fostm2.1(icre/ERT2)Luo/J (JAX 030323). The following double-transgenic mouse strains were bred in-house: Pyycre;Salsa6f, NeuroD1-Cre_Salsa6f, Pyycre;Halo-YFP and Pyycre;ChR2-tdTomato. Pyycre mice were also bred to floxed Tlr5fl/fl (floxed exon 4) and Myd88fl/fl (floxed exon 3) mice to generate the following conditional knockout mice: Pyycre;Tlr5fl/fl and Pyycre;Myd88fl/fl.

Dissociation and isolation of single intestinal epithelial cells

Colons and small intestines of mice were dissociated for qPCR (PYY–GFP), calcium imaging (Pyycre;Salsa6f) or sequencing (CCK–GFP and PYY–GFP) as previously described[1]. In brief, the entire colon or proximal one-third of the small intestine was removed, flushed with cold PBS and cut into 2–3-mm sections. Tissue was rinsed with cold PBS and then shaken in 1.5 mM EDTA in PBS for 30 min before a 15-min incubation at 37 °C. The epithelial layer was then mechanically detached from the muscle layer by shaking in cold PBS. Following centrifugation at 800 r.p.m. (Eppendorf 5702 RH; rotor A-4-38), the pellet was resuspended and incubated in HBSS (Gibco) with dispase and collagenase for 10 min at 37 °C. Samples were then centrifuged (800 r.p.m.), filtered twice through a 70-μm and 40-μm filter, and resuspended in L15 medium (5% FBS, 10 μl ml−1 10 mM HEPES, 2,000 U ml−1 penicillin–streptomycin and 100 μl of 1,700 U ml−1 DNAse) to produce a single-cell suspension for further analysis. For whole-epithelial-layer analyses, first the pellet was resuspended in lysis buffer and further processed for RNA extraction.

Dissociation and isolation of single nodose neurons

Nodose neurons of mice were dissociated for qPCR (C57BL/6J), calcium imaging (NeuroD1-Cre;Salsa6f) or sequencing (C57BL/6J) as previously described[1]. In brief, nodose ganglia were dissected and immediately placed into 500 μl of ganglia dissociation solution containing 10 mM HEPES, 1× glutamine, 1× N2 supplement, 1× B27 supplement, 0.5 μg ml−1 nerve growth factor and 55 μg ml−1 liberase (Roche, 5401054001) in Advanced DMEM/F-12. Following digestion, ganglia were rinsed twice with PBS, mechanically dissociated in dissociation solution, and filtered through a 70-μm cell strainer. The dissociated solution was then carefully laid on a density gradient of 500 μl 12% and 500 μl 28% Percoll (Sigma) and centrifuged for 10 min at 2,900g at room temperature. Once centrifugation was complete, the top 700 μl was removed, and 700 μl of fresh dissociation solution was added. Cells were then centrifuged for 15 min at 2,900g, and the final pellet was resuspended in 500 μl PBS plus 0.04% BSA.

RNA sequencing

RNA was extracted from single-cell suspensions using the Single Cell RNA Purification Kit (Norgen). All samples were assessed with a Bioanalyzer (Agilent), and only samples with RNA integrity number scores >8.0 were used for downstream analysis. Given the rarity of the cells, Single-cell RNA barcoding sequencing was used to generate libraries. Libraries were sequenced on an Illumina NextSeq 500. STAR was used with the mm10 mouse reference genome to align reads, and count tables were generated using featureCounts. Pairwise comparisons between genes from the PYY–GFP+ and PYY–GFP− groups were made using DESeq2. Gene ontology analyses were conducted using topGO.

qPCR

The colonic epithelium of PYY–GFP mice was dissociated, and cells were sorted as described above. An equal number of GFP+ and GFP− cells were collected directly into lysis buffer. Whole epithelium was dissociated from Pyycre;Tlr5fl/fl and Tlr5fl/fl control littermates and collected into lysis buffer as described above. Nodose was dissected and flash-frozen in liquid nitrogen. RNA was extracted on the basis of the manufacturer’s protocol using the RNeasy Micro Plus Kit (Qiagen no. 74034). Spleen and whole-colon tissues were collected and homogenized in TRIzol reagent (Thermo Fisher,15596026), and RNA was extracted per the manufacturer’s protocol. cDNA was produced per the manufacturer’s protocol using the High-Capacity cDNA Reverse Transcription Kit (Applied Biosystems, 4368814). The following TaqMan probes were used for transcript identification: Pyy (Mm00520716_g1), 18s (Mm03928990_g1), Tlr1 (Mm00446095_m1, Mm01208874_m1), Tlr2 (Mm00442346_m1, Mm01213946_g1), Tlr3 (Mm01207404_m1), Tlr4 (Mm00445273_m1), Tlr5 (Mm00546288_s1), Actb (Mm02619580_g1), Tnf (Mm00443258_m1), Il1b (Mm00434228_m1), Il6 (Mm00446190_m1), Tjp1 (Mm01320638), Tjp2 (Mm00495620_m1), Ocln (Mm00500910_m1) and Cldn (Mm01342184). qPCR was run on a StepOnePlus System (Thermo Fischer), using TaqMan Fast Universal PCR Master Mix (Applied Biosystems no. 4352042) according to the manufacturer’s protocol. Transcription rate was determined as 2−ΔCt or compared as fold change using 2−ΔΔCt. All values are reported as mean ± s.e.m.

In situ hybridization with immunofluorescence

NeuroD1_tdTomato and PYY–GFP mice were transcardially perfused with PBS for 3 min followed by 4% PFA for 3 min at a rate of 600 µl min−1. The entire intestine was collected, opened lengthwise and divided into different sections: proximal, middle and distal third of the small intestine; and proximal and distal halves of the large intestine. Intestinal tissue was then rolled with the proximal end in the centre, and post-fixed in 4% PFA for 24 h. Nodose ganglia and dorsal root ganglia at the levels of L5, L6 and S1 were also dissected bilaterally. Neuronal ganglia were rinsed in PBS and post-fixed in 4% PFA for 24 h. Tissue was then dehydrated in 10% sucrose for 1 h and 30% sucrose for at least 12 h. Samples were embedded in OCT (VWR) and stored at −80 °C. Tissue was sectioned onto slides at 16 μm using a cryostat. RNA detection was performed using the RNAscope Multiplex Fluorescent Reagent Kit v2 Assay (ACD). In brief, tissue slides were baked for 30 min at 60 °C, and post-fixed in 10% neutral buffered formalin (VWR) for 60 min before being washed in PBS twice (Sigma). Slides were then dehydrated using successive alcohol washes of 50%, 70% and 100%, and a second 100% of ethanol for 5 min each. Slides were then incubated with hydrogen peroxide for 10 min before undergoing target retrieval using RNAscope reagents in a steamer. Slides were submerged into the RNAscope target retrieval solution at >99 °C for 5 min. Slides were then treated with protease III for 30 min at 40 °C before subsequent hybridization and amplification steps per the manufacturer’s instructions. The probes used were all purchased from ACD: Mm-Tlr5 (catalogue no. 468888), Mm-Pyy-C3 (catalogue no. 420681) and Mm-Npy2r (catalogue no. 515431). Hybridization signal was detected using Opal dyes (Akoya Biosciences) at a dilution of 1:1,500. Tissue was then blocked in 10% donkey serum (Jackson ImmunoResearch) for 1 h. Tissue was then incubated with primary antibody dissolved in antibody dilution solution (PBS with 1% BSA and 0.0025% Triton X-100) for 24 h at 4 °C, followed by 1 h at room temperature. Primary antibodies and dilutions were as follows: Rb-anti-PYY (1:250; gift from the Liddle laboratory), Rb-anti-PGP9.5 (1:500; Abcam: ab27053), Gt-anti-serotonin (1:500; Abcam, ab66047) and CHK-anti-GFP (1:500; Abcam: ab13970). Following primary antibody incubation, tissue was washed in 0.05% Tween-20 in TBS buffer (TBST) and then incubated with secondary antibody in antibody dilution solution for 1 h at room temperature: Dk-anti-Rb-488 (1:250, catalogue no. 711-546-152), Dk-anti-Rb-Cy3 (1:250, catalogue no. 11-166-152), Dk-anti-Ck-488 (1:250, catalogue no. 703-546-155), Dk-anti-Gt-647 (1:500, catalogue no. 705-606-147), all from Jackson ImmunoResearch. Tissue was then washed with TBST, stained with DAPI (1:4,000) for 10 min, washed in TBST, and mounted using Fluoro-Gel with Tris buffer (Electron Microscopy Sciences). Imaging was carried out on a Zeiss 880 Airyscan inverted confocal microscope. Images were adjusted for brightness and contrast using ImageJ (Fiji V.2.9.0). In each region of the intestine, the 50 most proximal cells were analysed from a total of n = 3 mice. Cells with >2 puncta within the cell body were considered positive for the gene. Control slides using the negative control probes (ACD) were used to ensure that background staining was <3 puncta per cell. Counts are presented as the mean percentage of co-localization ± s.e.m.

Assessment of basal phenotypes

Pyycre;Tlr5fl/fl, Pyycre;Myd88fl/fl and their Cre-negative littermates were weighed following weaning, and every week thereafter until 3 months of age. Mice were then euthanized, and colon length, colon weight and spleen weight were measured. Colonic tissues were flushed with cold PBS, incubated in 10% neutral buffered formalin (VWR) for ≥24 h at 4 °C, dehydrated in a graded series of ethanol and embedded in paraffin. Tissues were sectioned and stained with haematoxylin and eosin (Abcam, ab245880) per the manufacturer’s protocol and imaged for assessment of developmental and immune phenotypes.

Measurement of food intake

Age-matched Pyycre;Tlr5fl/fl and littermates were placed into clean cages with food hoppers. The hoppers are designed to minimize the ability of mice to remove entire pellets. The weight of the food in the hopper was recorded at both the start and end of a 24-h period. Mice were then returned to their home cage for at least 2 days before repeating the test twice more. The mean of three separate testing days for each individual mouse is reported.

Detailed feeding, activity and meal pattern analysis

Age- and sex-matched Pyycre;Tlr5fl/fl, Pyycre;Myd88fl/fl and their Cre-negative littermates were placed in a custom-built PhenoMaster behavioural phenotyping system for 10 days (TSE Systems). The first week was considered an acclimation period, and all meal pattern analyses were performed on the last 3 days within the system. The PhenoMaster was programmed (software version 6.6.9) to automatically maintain a light cycle (07:00 lights on; 19:00 lights off), temperature control (22 °C) and humidity control (40%). The PhenoMaster holds 12 clear cages, in which animals were singly housed. Cages were industrially washed, and bedding (ALPHA-dri) was replaced weekly. Animals were provided with standard mouse chow (Purina 5001) and reverse-osmosis water ad libitum. All cages also housed an enrichment device, which also served to weigh the animals. Food hopper, water bottle and weigh container were attached to weight sensors (TSE). Food intake, water intake and weight were automatically measured every 5 s to the nearest 0.01 g. For drinking measurements, a 10-s smoothing interval with a maximum raw analog-to-digital conversion count difference of 40,000 was permitted. For weight measurements, a 15-s smoothing interval with a 15-g threshold and a maximum raw analog-to-digital conversion count difference of 1,000,000 was permitted. Intake was measured every 5 s and binned every minute for analyses unless otherwise indicated. Animal activity was determined by beams crossed in the x and y planes and was collected with a 100-Hz scan rate. Unless otherwise indicated, all activity, food intake and water intake measurements were binned in 1-min intervals for analysis. Data were corrected for minor fluctuations by only permitting a monotonically increasing function for both food and water intake: values that represented negative food intake were replaced by the most recent value. Meal size, frequency and timing were defined on the basis of parameters within the PhenoMaster system. Inter-meal intervals were required to be >10 min. Only meals of size 0.1–1 g and rate <0.25 g min−1 were included in the meal pattern analysis.

Fasting blood glucose and oral glucose tolerance test

Blood glucose was measured in age-matched Pyycre;Tlr5fl/fl and Tlr5fl/fl mice following an overnight fast of 18 h. For oral glucose tolerance test, a separate cohort of mice were food- and water-deprived for 5 h. Then, mice were gavaged with sucrose (2 g kg−1 body weight in sterile PBS). Blood glucose was measured (True Metrix 60 Blood Glucose Meter) after the deprivation, and 15, 30, 60, 90 and 120 min following gavage.

Fecal lipocalin-2 measurements

Colonic inflammation was assessed by assaying for fecal lipocalin-2 using an ELISA (Ray Biotech). Stool samples were collected from age-matched Pyycre;Tlr5fl/fl and Cre-negative controls during the beginning of the light cycle. Fecal samples were reconstituted in PBS to a final concentration of 100 mg ml−1 and vortexed for 5 min to obtain a homogeneous mixture. Fecal matter was then centrifuged for 10 min at 14,000g. Supernatants were collected and stored at −80 °C. Lipocalin-2 levels were assessed following the manufacturer’s instructions, and optical density was measured at 450 nm (Tecan Infinite 200 Pro).

Colonic myeloperoxidase assay

Neutrophil activity in tissue was assessed by testing for the enzymatic activity of myeloperoxidase using a colorimetric kit (Abcam). A 2–3-mm segment of the distal colon from age- and sex-matched Pyycre;Tlr5fl/fl and littermates was dissected and weighed. Tissue was then washed in PBS, and mechanically homogenized in the lysis buffer provided in the kit. Tissue was then freeze–thawed twice and sonicated. Myeloperoxidase activity was assessed following the manufacturer’s protocol and normalized to the tissue mass, and optical density was measured at 450 nm (Tecan Infinite 200 Pro).

Serum hormone measurement

Age-matched Pyycre;Tlr5fl/fl and Cre-negative controls were fasted for 15 h and then fed ad libitum for 2 h. Following the re-feeding period, mice were euthanized, and serum was collected. DPP-4 inhibitor and aprotinin were added to serum samples to prevent peptide degradation. Total PYY3-36 (RayBiotech) and total GLP-1 (Alpco) levels were assessed using an ELISA per the manufacturer’s protocols.

Stool flagellin assay

Flagellin levels were assessed using HEK-Blue-mTLR5 cells (Invivogen). Stool was collected from age-matched wild-type, Pyycre;Tlr5fl/fl and Cre-negative controls during the start of the light cycle, following ad libitum feeding, an 18-h overnight fast or an 18-h overnight fast followed by a flagellin enema (1 μg ml−1 in 100 μl). Fecal material was resuspended in PBS to a final concentration of 100 mg ml−1. Solutions were mechanically homogenized and vortexed for 5 min to form a suspension. Samples were then centrifuged at 8,000g for 2 min, and serum was collected and either immediately assessed or stored at −20 °C for later testing. Serial dilutions of the solution were placed onto the HEK-TLR5 cells, and purified S. typhimurium flagellin (Invivogen) was used to generate a standard curve. After 18 h of stimulation, cell culture supernatant was applied to QUANTI-Blue medium and incubated for 30 min at 37 °C. QUANTI-Blue alkaline phosphatase activity was then read at 620 nm (Tecan Infinite 200 Pro).

Calcium imaging of dissociated cells

For neurons, NeuroD1-Cre_Salsa6f nodose neurons were dissociated as described above. Neurons were plated on 12-mm coverslips and placed in a 37 °C incubator overnight. Neuronal medium included: 1× GlutaMAX, 10 mM HEPES, 200 U ml−1 penicillin–streptomycin, 1× N2 supplement, 1× B27 supplement and 10 ng ml−1 nerve growth factor in Advanced DMEM/F-12. Cells were imaged 2–3 days after plating. For enteroendocrine cells, Neurod1Cre_Salsa6f cells were dissociated as described above and fluorescence-sorted (BD FACSAria), selecting for tdTomato+ fluorescent cells. Cells were then plated on coverslips coated with 2.5% Matrigel (Corning no. 356231). Enteroendocrine cells were imaged 2–6 h after plating. Cells were washed twice in imaging buffer (120 mM NaCl, 3 mM KCl, 2 mM CaCl_2, 2 mM MgCl_2, 10 mM HEPES, 10 mM glucose; 305 mOsm ± 3 mOsm) and placed in the dark for 5 min until they reached room temperature. Coverslips were then placed in the recording chamber of a Zeiss Examiner Z1 and imaged with a Hamamatsu camera (Orca-flash4.0; C11440) using the Zeiss ZEN Blue software package. GCaMP6f emission images were obtained using 570-nm excitation. Images were collected at 1.5-s intervals with a 100-ms exposure time. Each recording was 180 s long, with a stimulus perfused between 30 and 60 s. Imaging buffer was continuously perfused (about 2 ml min−1) over the coverslips throughout the imaging session. Each coverslip underwent four recordings: buffer, test stimulus, repeat of the test stimulus, and KCl. Each recording session concluded with 50 mM KCl as an activity control (KCl concentration was achieved by substituting for NaCl, and not an addition of more KCl). A response to KCl was defined as a ratio >10% increase above baseline. Cells that did not reach this KCl threshold were not included in analyses. A 5-min wash-out period with continuous perfusion of imaging buffer was carried out between the two test stimuli. For experiments involving the TLR5 inhibitor, TH1020 was added to the well to reach a final concentration of 1 μM following the wash-out period. Buffer flow was stopped, and cells were incubated with the inhibitor for 10 min before restarting flow and retesting with the stimulus.

Analysis

Fluorescence values for each individual cell were calculated as the mean fluorescence intensity in a user-defined region of interest on Fiji software. Intracellular calcium changes were then calculated as ∆F/F = (F – Fo)/Fo, in which Fo is the average intensity of the cell within the first 15 s. Ratiometric values were then normalized to the peak KCl response. A positive response was defined as an increase in ratio >10% above baseline.

PYY release assay

Colons from wild-type and knockout mice were dissected, flushed with cold PBS, opened lengthwise and cut into pieces of about 1 cm. Tissue pieces were incubated on ice in PBS for 2 h before incubation with 1.5 mM EDTA on ice for 30 min, and then 37 °C for 15 min. Crypts were detached by shaking in cold PBS, pelleted at 100g and plated on 12-mm coverslips coated with 2.5% Matrigel (Corning no. 356231). Crypts were then incubated in 50% L-WRN Buffer (ATCC) with 10 μM Y-27632 (Enzo) for 16 h before stimulation. Crypts were then stimulated with buffer (120 mM NaCl, 3 mM KCl, 2 mM CaCl_2, 2 mM MgCl_2, 10 mM HEPES, 10 mM glucose), 100 ng ml−1 flagellin in buffer, or a mixture of 1 μM IBMX (Sigma) and 1 nM forskolin (Sigma) in buffer for 30 min at 37 °C. Supernatant was collected, and the crypts were then incubated in lysis buffer for 30 min at 4 °C. Lysate was collected, and both lysate and supernatant were centrifuged for 10 min at 13,000g to remove insoluble material, and stored at −20 °C for up to 2 weeks. PYY concentration in samples was assessed using the PYY ELISA Kit (Ray BioTech) following the manufacturer’s protocol. Each experimental condition was run in duplicate on every plate. A PYY standard was run for every plate. Absorbance at 450 nm was measured on a plate reader (Tecan Infinite 200 Pro). PYY amount and concentration was calculated using the standard curve. PYY release was calculated as supernatant/(supernatant + lysate).

Vagus nerve recordings

Whole-nerve recordings were performed in wild-type mice, Pyycre;Halo-YFP mice, Pyycre;ChR2 mice, Pyycre;Tlr5fl/fl mice, Pyycre;Myd88fl/fl mice and negative genetic controls. Whole-nerve electrophysiology recordings of the cervical vagus nerve were performed as previously reported[4]. A 20-gauge gavage needle with two connected tubes for PBS perfusion and stimulant delivery was surgically inserted through the caecum wall into the proximal colon. A perfusion exit incision was made just proximal to the rectum for colon. Fecal pellets were gently expressed from the colon using cotton applicators. PBS was constantly perfused through the isolated intestinal region at about 400 μl min−1 as a baseline and volume pressure control. Stimulation conditions were applied after recording 2 min of baseline activity. During stimulation conditions, PBS perfusion was continuous, and 200 μl of 2 µg ml−1 flagellin was perfused over 1 min using a syringe pump (Fusion 200, Chemyx). As a positive control to activate the vagus nerve from the colon lumen, intralipid (7%, Sigma) was infused.

Data acquisition

Extracellular voltage was recorded as previously described[4]. The raw data were analysed using Spike Tailor, a custom MATLAB software (Mathworks) script[4]. Spikes were detected using a threshold detected on the basis of root-mean-square noise. The firing rate was calculated using a Gaussian kernel smoothing algorithm in 200-ms bins.

Optogenetic inhibition and stimulation

The optoelectronic colon fibre was threaded along the gavage needle into the colonic lumen. MicroLED stimulation was applied simultaneously with nutrient infusion. The microLED was pulsed for 1 min at 40 Hz, 5 V peak and 20% duty cycle (473 nm, 532 nm).

Pharmacologic inhibition

Following recording of a pre-inhibitor response, the inhibitor was delivered over 1 min (10 μl g−1 BIIE-0246) and allowed to incubate for 10 min before re-infusion of flagellin.

Data analysis

Stimulation response was quantified as the maximum firing rate after stimulation (stimulant conditions) or during recording (baseline). Each trial served as its own control by normalizing the firing rate to the pre-stimulus baseline firing rate (first 2 min of recording). Throughout experiments, intralipid response was used as a positive control. For all nutrient and laser stimulation conditions, data were excluded if an intralipid response was not seen throughout the recording session. Maximum firing rate and area under the curve were analysed across stimulation condition.

Optoelectronic colon fibre fabrication

The preform assembly for optoelectronic graded-index fibres began with moulding polystyrene-block-poly(ethene-co-butadiene)-block-polystyrene (SEBS) pellets (Kraton G1657M) into desired geometrical patterns in a CNC machined inverse aluminium mould at 200 °C for 8 h under vacuum. The top layer defined the hollow square channels (3.6 mm × 3.6 mm × 30 cm) with a pitch size of 4 mm for hosting the interconnect microwires. The SEBS convergence channels were subsequently lined with a U-shaped PC layer that had a wall thickness of 1 mm and channel size of 1.6 mm × 1.6 mm produced by standard CNC machining process. This preform was consolidated in an oven (130 °C, 45 min) and subsequently drawn into metres-long microscale fibres at a size reduction ratio of 40–45, while simultaneously feeding three spools of 40-μm Ag–Cu microwires.

Fibre device fabrication

Fabrication of graded-index fibre device began with dissolving away the SEBS layer in the distal 1 cm of fibre (8.5 cm total length) in dichloromethane for 10 min, which exposed the interconnect microwires. The interconnects were subsequently soldered onto male header pins that were assembled inside a custom 3D-printed box (5 mm × 7 mm × 0.5 mm) and secured using UV curable epoxy. About 0.5 cm of the interconnect microwires was exposed by low-end machining with a razor blade at the distal end of the fibre under an optical microscope, followed by mounting of blue (473-nm emission maxima) and green (532-nm emission maxima) InxGa1−xN microLED chips (CREE TR2227 and SR2130) using two-part silver epoxy (Epo-tek). Subsequently, a 10-μm layer of vapour-deposited parylene-C defined the bio-fluid barrier layer. Finally, the device was encapsulated in an approximately 50–100-μm layer of medical-grade silicone by inserting the fibre device in a PTFE tubing with an inner diameter of 0.8 mm, which acted as a sacrificial mould. The silicone mixture was filled and cured in the tubing, and subsequently the tubing was cut open to yield a silicone-coated soft device. The final fibre had an overall length of 8.5 cm with three green and blue microLEDs hosted on the distal 2 cm of the fibre at a separation of 1 cm.

In vivo two-photon calcium imaging and compartment analysis of temporal activity by fluorescence in situ hybridization

Snap25-FosTRAP-tdTomato triple-transgenic mice were used to generate landmark tdTomato+ vagal nodose neurons for compartment analysis of temporal activity by fluorescence in situ hybridization (catFISH) analysis through targeted recombination in active populations (TRAP) at least 10 days before calcium imaging as previously described[57]. In brief, 6-h-fasted mice were given intragastric infusions of nutrients (500 μl; 100 μl min−1) 30 min before dark cycle onset. At 3 h after stimulus delivery, mice were injected with 4-hydroxytamoxifen (30 mg kg−1, intraperitoneal; Sigma) to induce tdTomato expression in a subpopulation of nutrient-responsive vagal sensory neurons, allowing for post hoc landmarking and alignment. Chow was returned 3 h after 4-hydroxytamoxifen injection. For calcium imaging, mice were fasted overnight (18 h) and maintained under continuous anaesthesia (isoflurane–oxygen) on a heating pad to sustain body temperature throughout the procedure. An abdominal incision was first made in the anaesthetized mice to expose the caecum and colon. A 20-gauge gavage needle with dual tubing for PBS perfusion and stimulant delivery was surgically inserted through the caecal wall into the proximal colon and secured with a suture. The rectum was severed to create an exit for fluid drainage. Fecal pellets were gently expelled from the colon using cotton applicators. Next, an incision (about 2 cm) was made above the sternum and below the jaw. The carotid artery and vagus nerve were exposed by separating the salivary glands. Retractors were used to pull the sternomastoid, omohyoid and posterior belly of the digastric muscle aside to visualize the nodose ganglion. The vagus nerve was transected just above the nodose ganglion, which was carefully separated from the hypoglossal nerve and small adjacent branches. The vagus nerve was then dissected away from the carotid artery and surrounding tissues. The right nodose ganglion was gently positioned on a stable imaging platform consisting of a 5-mm-diameter coverslip attached to a metal arm fixed to a magnetic base. Surgical silicone adhesive (Kwik-Sil, WPI) was applied to immobilize the vagus nerve on the coverslip, and the nodose ganglion, immersed in Dulbecco’s modified Eagle medium (Corning), was covered with a second coverslip before imaging.

Stimulus perfusion

Perfusions were performed using a precision pump connected to silicone tubing filled with PBS, flagellin (2 µg ml−1) or 7% intralipid. PBS (1,000 µl min−1) was continuously perfused throughout the recording. Baseline neuronal activity was recorded for 30 s, followed by a 2-min flagellin infusion (333 µl min−1) and an additional 2 min of recording post-infusion.

In mice in which responses to both flagellin and intralipid were tested, the colon was flushed with 10 ml of PBS after flagellin perfusion to remove residual flagellin through the exit port. A second baseline activity recording was then taken, followed by a 2-min intralipid perfusion (333 µl min−1) and another 2-min post-perfusion recording.

Imaging

In vivo imaging was performed using a two-photon microscope (Bruker) equipped with a galvanometer for image acquisition and a piezo objective combined with a galvo/resonant scanner, enabling image capture at 29 frames per second (Prairie View v.5.7). The microscope was set up for in vivo conditions with a Somnosuite (isoflurane) anaesthesia device coupled to a homeothermic control warming pad (Kent Scientific) and a programmable syringe pump (Harvard Apparatus PHD 2000) for nutrient perfusion into the gut. Imaging was conducted using a 16× water-immersion upright objective.

RNAscope and alignment

For nodose catFISH analysis, we adapted a previously reported protocol for registration of vagal neurons between in vivo calcium imaging and RNAscope fluorescent in situ hybridization images[59]. After in vivo imaging, immobilized nodose ganglia were immediately fixed in 4% PFA for 2 h and then placed in 30% sucrose for 1 h before being embedded in OCT and frozen at −20 °C. Nodose ganglia were then sliced into 10-µm sections, and an RNAscope assay was performed to probe for Npy2r mRNA expression as described above, without slide baking, post-fixation and target retrieval. To align RNAscope sections to in vivo imaging z-stacks, ‘guidepost’ neurons were used as positional landmarks for mapping between in vivo and sectioned images. In brief, tdTomato+ neurons visible in both RNAscope sections and in vivo planes were identified as landmark reference points and were manually paired using the BigWarp tool within the Fiji BigDataViewer plugin. Using this tool, RNAscope sections were transformed and aligned to corresponding planes within the in vivo imaging z-stack, allowing visualization of NPY2R+ neurons overlaid on GCaMP6s-fluorescent neurons. Cells with ambiguous or unsuccessful alignment were not used for further analysis.

Quantification of neural activity

GCaMP6s fluorescence changes were quantified by outlining regions of interest (ROIs), each corresponding to a single cell throughout the imaging session. For nodose images processed using catFISH alignment, ROIs were selectively generated around NPY2R+ cells. Pixel intensities in ROIs (average across pixels) were calculated frame by frame using ImageJ and exported to Excel for analysis. The z-score for each neuron was calculated by subtracting the mean baseline fluorescence (over a 30-s period) from the fluorescence intensity at each time point and dividing by the standard deviation of the baseline fluorescence. This normalized value represents the number of standard deviations from the baseline fluorescence. A neuron was considered responsive if: the peak GCaMP6s fluorescence reached a z-score of ≥2.5, and the mean GCaMP6s fluorescence was ≥2.5 above the baseline mean for at least 5 s during or after infusion. Neurons without baseline activity were excluded from the analysis.

Food intake behavioural system

Mice were acclimated to enema two times before the start of the test. Tests were started 3 h into the start of the light cycle. Mice were fasted overnight for 18 h. At the start of the test, mice received a 100-µl enema of 1 µg ml−1 flagellin or PBS and were then placed into a clean cage. A pre-weighed pellet of standard rodent chow (5001 Purina) was then introduced to the cage, and then weighed at 20, 40, 60 and 180 min following the enema. At the end of the test, mice were returned to their home cages. The start of all test sessions was separated by at least 48 h. For pharmacological inhibition of TLR5, C57BL/6J wild-type mice were acclimated to enema, a baseline response to flagellin was established, and then mice received enemas of 1 μg ml−1 flagellin or PBS combined with 10 μM TH1020 (Sigma). Food intake was then measured as described above.

For pharmacologic inhibition of Y2 receptors with intraperitoneal injections, C57BL/6J wild-type mice were acclimated to enema and intraperitoneal injections two times before the start of the test. At the start of the test, mice received an intraperitoneal injection with 2 ng kg−1 BIIE-0246 or vehicle and were then placed into a clean cage. After 10 min, mice received a 100-μl enema of 1 μg ml−1 flagellin or PBS. Food intake was then measured as described above.

Germ-free mice

Age- and sex-matched germ-free C57BL/6J wild-type mice were transferred from the Duke Gnotobiotic core in sterile, individual cages. Tests were started 3 h into the start of the light cycle. Mice were fasted overnight for 18 h. At the start of the test, mice received a 100-μl enema of PBS, followed by an enema 1 μg ml−1 flagellin 7 days later. Food intake was measured as described above.

Crunch Master behavioural system

Female and male, 8-week-old, wild-type C57BL/6J mice were habituated for 1 h a day for 2 days in the behavioural device before the test session. Mice were food-deprived 18 h before the test session, which was performed during the light phase of the mice. Preceding the test session, mice were weighed and subsequently administered a 100-μl enema of either 1 μg ml−1 flagellin or PBS. Immediately following the enema administration, the mice were placed into the acrylic box and allowed to feed ad libitum for 1 h. After the test session, the mice were returned to their home cages.

Behavioural device

An acrylic box (37 cm × 27 cm) was equipped with a microphone (FIFINE T-669) attached to one wall. To enhance sound recording, 12 small drill holes (0.5 cm diameter) were incorporated into the wall near the microphone. A video camera (Kayeton Technology, model KYT-U400-MCS2812R01) was positioned 57 cm beneath the acrylic box to capture a bottom-up view of the mouse’s feeding behaviour. On the same wall as the microphone, a single standard chow food pellet was glued to a plastic lid that was then affixed to the wall. The weight of the food pellet was measured both before and after the test session to calculate food intake, with adjustments made for any food spillage. The audio and video data were recorded using the OBS 29.1.3 software.

Audio processing

Audio recordings were converted into .ogg format. Initial recordings were captured at a sampling frequency of 44.1 kHz, and then subsampled to 2,205 Hz for power spectrogram computation. The biting frequency was determined to lie between 400 and 1,000 Hz, the absolute power spectrum was averaged, and a band-pass filter between 400 and 1,000 Hz was applied to accurately identify biting frames. From the filtered signal, a threshold of 0.5 standard deviations above the mean was calculated. Each audio frame exceeding this threshold was binarized to 1 (indicating a potential bite), whereas those below were set to 0 (non-bite). This procedure further helped to eliminate false bite events. The binarized signal was then used to compute the bite start and end. A bite was defined as a sequence of binarized audio frames (with values of 1) separated by pauses in feeding (values of 0) longer than 10 s. These pauses were referred to as inter-bite intervals. A minimum of three consecutive audio frames with a value of 1 was required to be considered a bite.

Video processing

To ensure accurate bite identification, video snippets were automatically generated for each potential bite event. These snippets were then reviewed and validated by a human observer. Only the video snippets depicting correctly identified bites were included in the subsequent analysis. All video snippets utilized in this study are available in the Supplementary Information. The original video footage was recorded in .mkv format at a frame rate of 30 frames per second.

Statistics and reproducibility

We performed statistical analyses using R (3.1) and JMP Pro (SAS, version 16), unless otherwise indicated. Data were evaluated for normality using a Q–Q plot. For normally distributed data, ANOVA was used and Tukey HSD post hoc testing was performed when applicable. For behaviour studies, we used a repeated-measures ANOVA to account for each individual, followed by post hoc paired Student’s t-tests. For data not normally distributed, means were evaluated by Kruskal–Wallis test with non-parametric comparisons using the Wilcoxon method. For other studies, comments on statistical tests performed are included throughout the Methods and in the figure legends. All error bars and shaded regions represent s.e.m. unless otherwise indicated. Sample size was not predetermined using power analyses. Standardized randomization was not performed for in vitro or in vivo experiments. All behavioural studies were counterbalanced across age and sex to control for variables including position in cage and order effect. Experimenters were not blinded to treatment condition, genotype or outcome.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

All data supporting the findings of this study are available within the paper and its Supplementary Information. The mm10 mouse reference genome is available from GENCODE vM23/Ensembl 98. RNA-sequencing datasets are available on the NIH Gene Expression Omnibus (GEO database under accession GSE288590. Data from single-cell RNA-sequencing analysis of whole mouse brain are available at ref. [46] or via the Allen Institute Brain Atlas at https://portal.brain-map.org/atlases-and-data/bkp/abc-atlas.

Code availability

The analysis code used for Crunch Master feeding behaviour analysis is available via the OSF at https://doi.org/10.17605/OSF.IO/7XGFD.

References

1. Bohórquez, D. V. et al. Neuroepithelial circuit formed by innervation of sensory enteroendocrine cells. J. Clin. Invest. 125, 782–786 (2015).

2. Bellono, N. W. et al. Enterochromaffin cells are gut chemosensors that couple to sensory neural pathways. Cell 170, 185–198 (2017).

3. Kaelberer, M. M. et al. A gut-brain neural circuit for nutrient sensory transduction. Science 361, eaat5236 (2018).

4. Buchanan, K. L. et al. The preference for sugar over sweetener depends on a gut sensor cell. Nat. Neurosci. 25, 191–200 (2022).

5. Furness, J. B., Rivera, L. R., Cho, H. J., Bravo, D. M. & Callaghan, B. The gut as a sensory organ. Nat. Rev. Gastroenterol. Hepatol. 10, 729–740 (2013).

6. Hu, D. & Reeves, P. R. The remarkable dual-level diversity of prokaryotic flagellins. mSystems 5, e00705–e00719 (2020).

7. The Bohorquez Lab at Duke University. A gut sense for a microbial pattern regulates feeding. YouTube https://www.youtube.com/watch?v=3vXD_SXKT5U (2025).

8. von Uexküll, J. Umwelt und Innenwelt der Tiere (Springer, 1909).

9. Yong, E. An Immense World: How Animal Senses Reveal the Hidden Realms around Us (Random House, 2022).

10. de Hoyos-Vega, J. M. et al. Modeling gut neuro-epithelial connections in a novel microfluidic device. Microsyst. Nanoeng. 9, 144 (2023).

11. Servin-Vences, M. R. et al. PIEZO2 in somatosensory neurons controls gastrointestinal transit. Cell 186, 3386–3399 (2023).

12. Bayrer, J. R. et al. Gut enterochromaffin cells drive visceral pain and anxiety. Nature 616, 137–142 (2023).

13. Bohórquez, D. V., Chandra, R., Samsa, L. A., Vigna, S. R. & Liddle, R. A. Characterization of basal pseudopod-like processes in ileal and colonic PYY cells. J. Mol. Histol. 42, 3–13 (2011).

14. Bohórquez, D. V. et al. An enteroendocrine cell - enteric glia connection revealed by 3D electron microscopy. PLoS ONE 9, e89881 (2014).

15. Lu, V. B. et al. Adenosine triphosphate is co-secreted with glucagon-like peptide-1 to modulate intestinal enterocytes and afferent neurons. Nat. Commun. 10, 1029 (2019).

16. Hayashi, M. et al. Enteroendocrine cell lineages that differentially control feeding and gut motility. Elife 12, e78512 (2023).

17. Bai, L. et al. Enteroendocrine cell types that drive food reward and aversion. Elife 11, e74964 (2022).

18. Liu, W. W. & Bohórquez, V. D. The neural basis of sugar preference. Nat. Rev. Neurosci. 23, 584–595 (2022).

19. Gribble, F. M. & Reimann, F. Enteroendocrine cells: chemosensors in the intestinal epithelium. Annu. Rev. Physiol. 78, 277–299 (2016).

20. Martinez-Guryn, K., Leone, V. & Chang, E. B. Regional diversity of the gastrointestinal microbiome. Cell Host Microbe 26, 314–324 (2019).

21. Vijay-kumar, M. et al. Metabolic syndrome and altered gut microbiota in mice lacking Toll-like receptor 5. Science 344, 228–232 (2010).

22. O’Donnell, M. P., Fox, B. W., Chao, P. H., Schroeder, F. C. & Sengupta, P. A neurotransmitter produced by gut bacteria modulates host sensory behaviour. Nature 583, 415–420 (2020).

23. Ye, L. et al. Enteroendocrine cells sense bacterial tryptophan catabolites to activate enteric and vagal neuronal pathways. Cell Host Microbe 29, 179–196 (2021).

24. Gabanyi, I. et al. Bacterial sensing via neuronal Nod2 regulates appetite and body temperature. Science 376, eabj3986 (2022).

25. Tolhurst, G. et al. Short-chain fatty acids stimulate glucagon-like peptide-1 secretion via the G-protein-coupled receptor FFAR2. Diabetes 61, 364–371 (2012).

26. Lin, V. H. et al. Butyrate and propionate protect against diet-induced obesity and regulate gut hormones via free fatty acid receptor 3-independent mechanisms. PLoS ONE 7, e35240 (2012).

27. Chimerel, C. et al. Bacterial metabolite indole modulates incretin secretion from intestinal enteroendocrine L cells. Cell Rep. 9, 1202–1208 (2014).

28. Chassaing, B., Ley, R. E. & Gewirtz, A. T. Intestinal epithelial cell toll-like receptor 5 regulates the intestinal microbiota to prevent low-grade inflammation and metabolic syndrome in mice. Gastroenterology 147, 1363–1377 (2014).

29. Chiu, I. M. et al. Bacteria activate sensory neurons that modulate pain and inflammation. Nature 501, 52–57 (2013).

30. Sgritta, M. et al. Mechanisms underlying microbial-mediated changes in social behavior in mouse models of autism spectrum disorder. Neuron 101, 246–259 (2018).

31. Muller, P. A. et al. Microbiota modulate sympathetic neurons via a gut–brain circuit. Nature 583, 441–446 (2020).

32. Fülling, C., Dinan, T. G. & Cryan, J. F. Gut microbe to brain signaling: what happens in vagus…. Neuron 101, 998–1002 (2019).

33. Margolis, K. G., Cryan, J. F. & Mayer, E. A. The microbiota-gut-brain axis: from motility to mood. Gastroenterology 160, 1486–1501 (2021).

34. Bravo, J. A. et al. Ingestion of Lactobacillus strain regulates emotional behavior and central GABA receptor expression in a mouse via the vagus nerve. Proc. Natl Acad. Sci. USA 108, 16050–16055 (2011).

35. Sagan, L. On the origin of mitosing cells. J. Theoret. Biol. 14, 225–274 (1967).

36. Gewirtz, A. T., Navas, T. A., Lyons, S., Godowski, P. J. & Madara, J. L. Cutting edge: bacterial flagellin activates basolaterally expressed TLR5 to induce epithelial proinflammatory gene expression. J. Immunol. 167, 1882–1885 (2001).

37. Hayashi, F. et al. The innate immune response to bacterial flagellin is mediated by Toll-like receptor 5. Nature 410, 1099–1103 (2001).

38. Bogunovic, M. et al. Enteroendocrine cells express functional Toll-like receptors. Am. J. Physiol. Gastrointest. Liver Physiol. 7032, 1770–1783 (2007).

39. Lundberg, J. M. et al. Localization of peptide YY (PYY) in gastrointestinal endocrine cells and effects on intestinal blood flow and motility. Proc. Natl Acad. Sci. USA 79, 4471–4475 (1982).

40. Gehart, H. et al. Identification of enteroendocrine regulators by real-time single-cell differentiation mapping. Cell 176, 1158–1173 (2019).

41. Billing, L. J. et al. Single cell transcriptomic profiling of large intestinal enteroendocrine cells in mice–identification of selective stimuli for insulin-like peptide-5 and glucagon-like peptide-1 co-expressing cells. Mol. Metab. 29, 158–169 (2019).

42. Li, H. J. et al. Intestinal Neurod1 expression impairs paneth cell differentiation and promotes enteroendocrine lineage specification. Sci. Rep. 9, 19489 (2019).

43. Rhee, S. H. et al. Pathophysiological role of Toll-like receptor 5 engagement by bacterial flagellin in colonic inflammation. Proc. Natl Acad. Sci. USA 102, 13610–13615 (2005).

44. Sun, J., Fegan, P. E., Desai, A. S., Madara, J. L. & Hobert, M. E. Flagellin-induced tolerance of the Toll-like receptor 5 signaling pathway in polarized intestinal epithelial cells. Am. J. Physiol. Gastrointest. Liver Physiol. 292, G767–G778 (2007).

45. Clasen, S. J. et al. Silent recognition of flagellins from human gut commensal bacteria by Toll-like receptor 5. Sci. Immunol. 8, eabq7001 (2023).

46. Yao, Z. et al. A high-resolution transcriptomic and spatial atlas of cell types in the whole mouse brain. Nature 624, 317–332 (2023).

47. Rakoff-Nahoum, S., Paglino, J., Eslami-Varzaneh, F., Edberg, S. & Medzhitov, R. Recognition of commensal microflora by toll-like receptors is required for intestinal homeostasis. Cell 118, 229–241 (2004).

48. Thaiss, C. A. et al. Microbiota diurnal rhythmicity programs host transcriptome oscillations. Cell 167, 1495–1510 (2016).

49. Dong, T. X. et al. T-cell calcium dynamics visualized in a ratiometric tdTomato-GCaMP6f transgenic reporter mouse. Elife 6, e32417 (2017).

50. Batterham, R. L. et al. Gut hormone PYY3-36 physiologically inhibits food intake. Nature 418, 650–654 (2002).

51. Abbott, C. R. et al. Blockade of the neuropeptide Y Y2 receptor with the specific antagonist BIIE0246 attenuates the effect of endogenous and exogenous peptide YY (3–36) on food intake. Brain Res. 1043, 139–144 (2005).

52. Koda, S. et al. The role of the vagal nerve in peripheral PYY3–36-induced feeding reduction in rats. Endocrinology 146, 2369–2375 (2005).

53. Alonso, A. M. et al. The vagus nerve mediates the physiological but not pharmacological effects of PYY3-36 on food intake. Mol. Metab. 81, 101895 (2024).

54. Kaelberer, M. M., Rupprecht, L. E., Liu, W. W., Weng, P. & Bohórquez, V. D. Neuropod cells: emerging biology of the gut-brain sensory transduction. Annu. Rev. Neurosci. 43, 337–353 (2020).

55. Han, W. et al. A neural circuit for gut-induced reward. Cell 175, 665–678 (2018).

56. Bai, L. et al. Genetic identification of vagal sensory neurons that control feeding. Cell 179, 1129–1143 (2019).

57. McDougle, M. et al. Separate gut-brain circuits for fat and sugar reinforcement combine to promote overeating. Cell Metab. 36, 393–407 (2024).

58. Williams, E. K. K. et al. Sensory neurons that detect stretch and nutrients in the digestive system. Cell 166, 209–221 (2016).

59. Zhao, Q. et al. A multidimensional coding architecture of the vagal interoceptive system. Nature 603, 878–884 (2022).

60. Luczynski, P. et al. Growing up in a bubble: using germ-free animals to assess the influence of the gut microbiota on brain and behavior. Int. J. Neuropsychopharmacolog. 19, pyw020 (2016).

61. Wang, Y. et al. Amino acids stimulate cholecystokinin release through the Ca2+-sensing receptor. Am. J. Physiol. Gastrointest. Liver Physiol. 300, G528–G537 (2011).

62. Schonhoff, S. et al. Energy homeostasis and gastrointestinal endocrine differentiation do not require the anorectic hormone peptide YY. Mol. Cell. Biol. 25, 4189–4199 (2005).

Acknowledgements

We thank J. Kotula and M. Toh for assistance with sequencing; R. A. Liddle, S. G. Lisberger, M. D. Gunn, J. A. Alspaugh, N. K. Surana, G. J. Schwartz, Z. Lorsch, M. Toc Sagra and E. B. Bohórquez for editorial input. We acknowledge the following funding sources: National Institutes of Health (NIH) F30 DK122712 (W.W.L.); NIH F32 DK139628 (N.R.); NIH F30 DK136229 (E.A.); NIH F32 DK127757 and NIH K01 DK138286 (L.E.R.); NIH F30DK127650 (P.W.); J.A.A.G. is a doctoral student from the Programa de Doctorado en Ciencias Biomédicas of the Universidad Nacional Autónoma de México and has received CONAHCyT fellowship no. CVU959984; CONAHCyT CF-2023-G-518 (R.G.); NIH K01 DK131403 (M.M.K.); and NIH DP2 MH122402, NIH R21 AT010818, NIH R03 DK114500, NIH R01 DK131112 and NIH R01 DK132070 (D.V.B.).

Author information

Author notes

1. Winston W. Liu

Present address: Department of Dermatology, Stanford University School of Medicine, Redwood City, CA, USA

2. These authors contributed equally: Winston W. Liu, Naama Reicher, Emily Alway

3. These authors jointly supervised this work: M. Maya Kaelberer, Diego V. Bohórquez

Authors and Affiliations

1. Laboratory of Gut Brain Neurobiology, Duke University, Durham, NC, USA

Winston W. Liu, Naama Reicher, Emily Alway, Laura E. Rupprecht, Peter Weng, Chloe Schaefgen, Marguerita E. Klein, Jorge A. Villalobos, Carlos Puerto-Hernandez, Yolanda Graciela Kiesling Altún, Amanda Carbajal, José Alfredo Aguayo-Guerrero, Alam Coss, M. Maya Kaelberer & Diego V. Bohórquez

2. Department of Neurobiology, Duke University, Durham, NC, USA

Winston W. Liu, Emily Alway, Peter Weng, Marguerita E. Klein, M. Maya Kaelberer & Diego V. Bohórquez

3. Department of Medicine, Duke University, Durham, NC, USA

Winston W. Liu, Naama Reicher, Emily Alway, Laura E. Rupprecht, Peter Weng, Marguerita E. Klein, Jorge A. Villalobos, Carlos Puerto-Hernandez, Yolanda Graciela Kiesling Altún, Amanda Carbajal, José Alfredo Aguayo-Guerrero, Alam Coss, John F. Rawls, M. Maya Kaelberer & Diego V. Bohórquez

4. Trinity College of Arts & Sciences, Duke University, Durham, NC, USA

Chloe Schaefgen

5. Laboratory of Immunometabolism, Research Division, General Hospital of Mexico Dr. Eduardo Liceaga, Mexico City, Mexico

José Alfredo Aguayo-Guerrero

6. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

Atharva Sahasrabudhe & Polina Anikeeva

7. McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, USA

Atharva Sahasrabudhe & Polina Anikeeva

8. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

Polina Anikeeva

9. Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

Polina Anikeeva

10. Monell Chemical Senses Center, Philadelphia, PA, USA

Alan de Araujo, Avnika Bali & Guillaume de Lartigue

11. Department of Neuroscience, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA

Alan de Araujo, Avnika Bali & Guillaume de Lartigue

12. Laboratory Neurobiology of Appetite, Department of Pharmacology, CINVESTAV, Mexico City, Mexico

Elvi Gil-Lievana & Ranier Gutierrez

13. Center for Research on Aging (CIE), CINVESTAV Sede Sur, Mexico City, Mexico

Elvi Gil-Lievana & Ranier Gutierrez

14. Department of Integrative Immunobiology, Duke University, Durham, NC, USA

Edward A. Miao

15. Department of Molecular Genetics and Microbiology, Duke University, Durham, NC, USA

Edward A. Miao & John F. Rawls

16. Department of Pathology, Duke University, Durham, NC, USA

Edward A. Miao & Diego V. Bohórquez

17. Department of Cell Biology, Duke University, Durham, NC, USA

Edward A. Miao, John F. Rawls & Diego V. Bohórquez

18. Department of Physiology, University of Arizona, Tucson, AZ, USA

M. Maya Kaelberer

19. Duke Institute for Brain Sciences, Duke University, Durham, NC, USA

Diego V. Bohórquez

Contributions

W.W.L., N.R., E.A., L.E.R., P.W., C.S., M.E.K., J.A.V., C.P.-H., Y.G.K.A., A. Carbajal, J.A.A.G. and A. Coss conducted experiments and acquired data; A.S. and P.A. generated luminal optogenetic resources and optoelectronic microLED; E.G.-L. and R.G. developed the Crunch Master assay, conducted experiments, and acquired and analysed data; A.d.A, A.B. and G.d.L. conducted in vivo calcium imaging and catFISH, acquired and analysed data; W.W.L., N.R., E.A., L.E.R., P.W., J.F.R., E.A.M., M.M.K. and D.V.B. analysed and interpreted data. W.W.L., N.R., E.A., M.M.K. and D.V.B. conceptualized and wrote the manuscript with input from all authors. M.M.K. and D.V.B. developed the idea and supervised the project. D.V.B. acquired funding for the project.

Corresponding authors

Correspondence to M. Maya Kaelberer or Diego V. Bohórquez.

Ethics declarations

Competing interests

D.V.B. and M.M.K. are founders and board directors of the Gastronauts Foundation, Inc, a 501(c)3 non-profit company. Some of the findings have been filed by D.V.B. as a provisional patent application. All other authors declare no competing interests.

Peer review

Peer review information

Nature thanks John Lukens and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 RNASeq of Cck- and Pyy-labeled cells.

Heatmap showing expression of (a,e) neuropeptide, (b,f) nutrient sensor, and (c,g) metabolite receptor genes in non-GFP and CckGFP epithelial cells from the proximal half of the (a-d) small intestine or non-GFP and PyyGFP epithelial cells from the (e-h) ileum and colon (n ≥ 5 mice; adjusted P values by DESeq2 with two-tailed t-tests). (d,h) Table of base mean expression, fold change, and adjusted P value of Toll-like receptors between (d) CckGFP cells and non GFP cells and (h) PyyGFP cells and non-GFP cells.

Extended Data Fig. 2 Tlr5 transcripts in neuropod cells.

(a) (Left) Pyy-labeled neuropod cells per crypt: This panel shows the number of Pyy-positive cells per crypt in female and male mice. Each dot represents the average of 50 crypts analyzed. P > 0.05 by two-tailed t-test. (Right) Ileal and colonic tissues from PyyGFP mice (n = 3 mice) were evaluated for Pyy cell quantities per segment. (b) (Left) Neurod1Cre_tdTomato (red) cell with ISH labeling of Pyy, representative of n = 3 mice. (Right) Quantification of overlap between Neurod1Cre_tdTomato cells with 5HT and Pyy in the colon (n = 3 mice, each dot represents n = 50 cells). (c) (Left) Neurod1Cre_tdTomato (green) cell with ISH labeling of Tlr5 (red), representative of n = 3 mice. (Right) Regional expression of Tlr5 in Neurod1-labeled neuropod cells (n = 3 mice, each dot represents n= 50 cells). (d) (Left) Antibody-labeled serotonin (green) cell with ISH labeling of Tlr5 (red), representative of n = 3 mice. (Right) Regional expression of Tlr5 in 5HT cells (n = 3 mice, each dot represents n = 50 cells). Scale bars=10μm. Error bars represent S.E.M. e-h: Single-cell RNA sequencing (scRNAseq) analysis of whole mouse brain[46] (Allen Institute Brain Atlas). (f,g) Cluster of Pyy-labeled cells in the medulla. (g,h) These Pyy-labeled cells do not express Tlr5. e–h, adapted from ref. [46], Springer Nature Limited, under a Creative Commons licence CC BY 4.0.

Extended Data Fig. 3 Metabolic and immune phenotype of PyyCre_Tlr5fl/fl mice.

(a) In-situ hybridization of Tlr5 transcripts in colonic Pyy-labeled cells in PyyCre_Tlr5fl/fl mice and _Tlr5fl/fl littermates (n = 3 mice per genotype; two-tailed unpaired t-test *P < 0.05). Scale bar=10μm. Genetic deletion of Tlr5 in Pyy-labeled cells did not affect (b) oral glucose tolerance, (c) fasting blood glucose, (d) fat pad weights, (e) serum PYY or GLP-1 levels (fasted overnight, one-hour refed), (f) colon length, and (g) weight, or (h) spleen weight (P > 0.05 by ANOVA, for sample sizes see Supplementary Table 2). (i) Colonic myeloperoxidase levels (n = 6 mice per genotype) and fecal lipocalin-2 levels (n = 5 mice per genotype) across genotypes (P > 0.05 by two-tailed unpaired t-test). (j) Morpho-pathological analysis of Hematoxylin & Eosin-stained colon sections from PyyCre_Tlr5fl/fl mice and _Tlr5fl/fl control littermates. Proinflammatory lamina propria cells in both groups were within normal limits, representative of n = 3 mice. Scale bar=100μm. Comparison of colons from PyyCre_Tlr5fl/fl mice and _Tlr5fl/fl control littermates showed no change in (k) crypt depth (n = 3 mice), (l) PYY and 5-HT cell density (n = 3 mice), (m) epithelial Tlr expression (n = 6 mice), or (n) tight junction expression (n = 6 mice) (P > 0.05 by two-tailed unpaired t-test). (o) Genetic deletion of Tlr5 in Pyy-labeled cells significantly increased weight gain in males and females (males: n = 7 mice for PyyCre_Tlr5fl/fl, n = 15 mice for _Tlr5fl/fl littermate controls; females: n = 6 mice for PyyCre_Tlr5fl/fl, n = 11 mice for _Tlr5fl/fl littermate controls; *P < 0.05 genotype*time interaction per sex by rmANOVA with post-hoc two-tailed Tukey HSD). (p) 24 h food consumption was significantly higher in PyyCre_Tlr5fl/fl mice compared to _Tlr5fl/fl littermate controls (males: n = 4 mice for PyyCre_Tlr5fl/fl, n = 7 mice for _Tlr5fl/fl littermate controls; females: n = 4 mice for PyyCre_Tlr5fl/fl, n = 4 mice for _Tlr5fl/fl littermate controls; *P < 0.05, genotype main effect by ANOVA with post-hoc two-tailed Tukey HSD, no significant differences between days, intake averaged across 3 consecutive days at 21 weeks of age). Error bars represent S.E.M.

Extended Data Fig. 4 Phenotype of PyyCre_Myd88fl/fl mice.

(a) In situ hybridization validating the lack of Myd88 transcripts in colonic Pyy-labeled cells in PyyCre_Myd88fl/fl mice (n = 3, 4 mice; *P < 0.05 by two-tailed unpaired t-test). (b) Genetic deletion of Myd88 exclusively in Pyy-labeled cells caused no significant change in the relative concentration of flagellin in the stool (n = 4 mice, P > 0.05 by two-tailed unpaired t-test). PyyCre_Myd88fl/fl mice had no changes in weight gain compared to their littermate controls in both (c) females (PyyCre_Myd88fl/fl: n = 3 mice, _Myd88fl/fl: n = 4 mice; P > 0.05 by rmANOVA) and (d) males (PyyCre_Myd88fl/fl: n = 4 mice, _Myd88fl/fl: n = 7 mice; P > 0.05 by rmANOVA). (e) PyyCre_Myd88fl/fl had no changes in 24-hour food consumption averaged across 3 consecutive days (n = 4 mice; P > 0.05 by ANOVA). Error bars represent S.E.M.

Extended Data Fig. 5 Meal pattern analysis in PyyCre_Tlr5fl/fl mice.

(a) Schematic of meal pattern analysis showing that meals are defined as consumption >0.1 g with at least 10 min in between bouts. Cumulative food consumption was assessed for PyyCre_Tlr5fl/fl and _Tlr5fl/fl littermate control mice across 3 days in the TSE Phenomaster for (b) male and (c) female mice. Quantification of meals across 72 h in the dark and light cycles in males and females of (d) meal duration, (e) meal size, and (f) inter-meal interval. Box plots represent interquartile range, white lines indicate median. and (g) meal count (PyyCre_Tlr5fl/fl: n = 9 male mice and n = 9 female mice; _Tlr5fl/fl: n = 6 male mice and n = 8 female mice; *P < 0.05 genotype main effect by ANOVA with post-hoc two-tailed Tukey HSD).

Extended Data Fig. 6 Enteroendocrine cells are activated by flagellin.

(a) (Left) Selected Calcium trace from acutely dissociated Neurod1Cre_Salsa6f colonic cells demonstrating experimental paradigm, representative of n = 18 cells. Each cell was exposed to each stimulus twice, and a responder was defined as a cell that responded twice. (Right) Quantification of calcium response magnitude of flagellin responders (*P < 0.05 by rmANOVA with post-hoc two-tailed Tukey HSD). (b) Calcium traces from acutely dissociated Neurod1Cre_Salsa6f colonic cells. 9% of cells responded to 1 μg/mL PolyI:C (n = 63 cells, n = 4 mice), 3% of cells responded to 1 mg/mL lipopolysaccharide (LPS) (n = 80 cells, n = 4 mice), and 13% of cells responded to 100 ng/mL flagellin (n = 121 cells, n = 6 mice). Gray indicates 30 s infusion. (c) (Left) Immunofluorescence image showing plated colonic crypts with individual Pyy-labeled cells (green) in PyyGFP mice. Scale bar=10μm. (Middle) Stimulation of colonic crypts with cAMP activators 1 μM forskolin and 10 μM IBMX, but not 1 μg/mL PolyI:C induce PYY release (n = 6 mice). (Right) Stimulation of colonic crypts with cAMP activators 1 μM forskolin and 10 μM IBMX, and 100 ng/mL flagellin induce PYY release (n = 5 mice; *P < 0.05 by one way ANOVA with post-hoc Tukey HSD). Error bars indicate S.E.M.

Extended Data Fig. 7 Vagal neurons are contacted by Pyy-labeled cells and are activated by intracolonic stimuli.

(a) List of significantly enriched gene ontology terms related to neuronal connection in Pyy-labeled cells (n = 6 mice; adjusted *P < 0.05 by topGO analysis). (b) Table of base mean, fold change, and adjusted P value for pre-synaptic genes between PyyGFP cells and non-GFP cells (DESeq2 with two-tailed t-tests). (c) Quantification of contacts between Pyy-labeled cells and Pgp9.5 neuronal fibers in different regions of the intestine (n = 3 mice). (d) Schematic of the vagal recording technique. The cervical vagus was recorded while the entire colon was simultaneously perfused with stimulus. (e) (Left) Schematic demonstrating 473 nm light via an intracolonic light emitting diode (LED) activating the cation channel Channelrhodopsin (ChR2) and depolarizing a Pyy-labeled cell. (Right) Representative image showing expression of ChR2-tdTomato (red) in a colonic Pyy-labeled cell (green). (f) Spike raster from vagal recordings in which PBS, 2 μg/mL flagellin, or 7% intralipid was perfused into the colon, representative of n = 4 mice. Gray bar represents the perfusion interval. (g) (Left) Vagal responses to intracolonic perfusion of PBS or 7% intralipid in wild-type mice (n = 4 mice). Error bars indicate S.E.M. (Right) Quantification of peak response to intralipid (*P < 0.05 by two-tailed paired t-test). (h) (Left) Schematic demonstrating 532 nm light activating the anion channel Halorhodopsin (Halo) and hyperpolarizing a Pyy-labeled cell. (Right) Representative image showing expression of Halorhodopsin-YFP (Green) in a colonic Pyy-labeled cell (red). Scale bars=10μm. Graphics in d,e,h adapted from ref. [3], AAAS.

Extended Data Fig. 8 Vagal neurons neither express Tlr5 nor respond directly to flagellin.

(a) Quantification of the peak vagal response to flagellin in PyyCre_Tlr5fl/fl and _Tlr5fl/fl littermate controls (PyyCre_Tlr5fl/fl: n = 5 mice; _Tlr5fl/fl: n = 3 mice; *P < 0.05 by Kruskal Wallis test with non-parametric comparisons using the Wilcoxon method). (b) RNAseq of vagal nodose neurons showed no expression of Tlr5 (PyyGFP+ cells: n = 5 mice, PyyGFP- cells: n = 8 mice, nodose neurons: n = 8 mice; DESeq2 normalization). (c) qPCR of synaptic markers and Toll-like receptors in vagal nodose neurons (n = 3 mice). (d) In situ hybridization of Nissl (green) stained neurons of the nodose ganglion showed no expression of Tlr5 (red), representative of n = 3 mice. Scale bars=100μm. (e) Representative trace of calcium transient in acutely dissociated Neurod1Cre_Salsa6f nodose neurons showed responses in 57% of neurons to capsaicin, but not to flagellin (n = 227 neurons, n = 4 mice). (f) Secondary analysis of data from Bai et al., 2018 of the colon-projecting vagal neurons showed expression of the PYY receptor Npy2r (n = 44 cells). (g) Spatial overlay of vagal nodose neurons using tdTomato and GCaMP6s fluorescence. (h) Spatial overlay of vagal nodose neurons using compartment analysis of temporal activity by fluorescence in situ hybridization (CatFISH). (i) Representative image of CaTFISH mapping of in vivo calcium transients onto Npy2r positive neurons. Scale bars=10μm. (j) Calcium traces from vagal nodose neurons responsive to either only flagellin (2 µg/mL) (top), intralipid (7%) and flagellin (2 µg/mL) infused separately (middle), or only intralipid (7%) (bottom), representative of n = 520 neurons. Error bars and shades indicate S.E.M. f, adapted from ref. [56], Cell Press.

Extended Data Fig. 9 Intracolonic flagellin modulates food intake.

Mice were fasted overnight and received flagellin (1 μg/mL) or PBS enemas prior to gaining ad libitum access to standard chow for 60 min. Flagellin reduced food intake compared to PBS in (a) PyyCre mice (n = 6 mice); (b) 5-week-old mice (n = 5 mice); and 10-week-old mice (n = 5 mice; *P < 0.05, enema*time interaction by rmANOVA with post-hoc two-tailed Tukey HSD). (c) (Left) PolyI:C (1 μg/mL) enema was not sufficient to alter food intake compared to PBS enema (n = 5 mice; P < 0.05, enema*time interaction by rmANOVA with post-hoc two-tailed Tukey HSD). (Right) Effects of flagellin dissipated after 180-minutes post-enema (n = 9 mice; P > 0.05 at 180 min by post-hoc Tukey HSD). (d) Neither vehicle enema (dimethyl sulfoxide, DMSO; n = 8 mice) nor vehicle intraperitoneal injection (saline; n = 10 mice) altered feeding response to flagellin enema (P < 0.05 by two-tailed t-test. (e) Crunch Master analysis of bites for number of bites, bite time, which is the average time of a single feeding bout, and feeding time which is the number of minutes that mice engaged in feeding, did not change during the 1-hour recording session (n = 7 mice per treatment group; P > 0.05 by two-tailed unpaired t-test). Violin plots show median indicated by thick line and mean indicated by thin line. (f) Relative flagellin concentration was measured in stool collected from wildtype mice following an 18-hour fast (n = 5 mice), ad libitum feeding (n = 5 mice), or an 18-hour fast plus enema of PBS (n = 6 mice) or flagellin [1 μg/mL] (n = 6 mice). Feeding significantly increased stool flagellin, however, flagellin enema was not sufficient to rescue flagellin levels to the fed state (*P < 0.05 by rmANOVA with post-hoc two-tailed Tukey HSD). Error bars indicate S.E.M.

Extended Data Fig. 10 Flagellin enema is not sufficient to induce an immune response.

(a) Cytokine expression in the colon 1 h after enema of PBS (n = 5 mice), flagellin [1 µg/mL] (n = 6 mice), flagellin [3 µg/mL] (n = 6 mice), PolyI:C [1 µg/mL] (n = 6 mice), or intraperitoneal (i.p.) injection of PBS (n = 6 mice), flagellin [20 µg/mL] (n = 6 mice), PolyI:C [4 mg/mL] (n = 5 mice), LPS [500 µg/mL] (n = 6 mice) (*P < 0.05 significance from PBS enema group by non-parametric two-tailed Wilcoxon each pair test). (b) Cytokine expression in the spleen 1 h after enema of PBS (n = 6 mice), flagellin [1 µg/mL] (n = 6 mice), flagellin [3 µg/mL] (n = 6 mice), PolyI:C [1 µg/mL] (n = 6 mice), or intraperitoneal (i.p.) injection of PBS (n = 6 mice), flagellin [20 µg/mL] (n = 6 mice), PolyI:C [4 mg/mL] (n = 5 mice), LPS [500 µg/mL] (n = 6 mice) (*P < 0.05 significance from PBS enema group by non-parametric two-tailed Wilcoxon each pair test). Error bars indicate S.E.M.

Supplementary information

Supplementary Tables 1 and 2

Supplementary Table 1. Body weights of knockout mice and littermate controls. Absolute body weights of _Tlr5fl/fl and PyyCre_Tlr5fl/fl mice (males: n = 7 mice for PyyCre_Tlr5fl/fl, n = 15 mice for _Tlr5fl/fl littermate controls; females: n = 6 mice for PyyCre_Tlr5fl/fl, n = 11 mice for _Tlr5fl/fl littermate controls). P values correspond to comparisons between genotype calculated as genotype–time interaction by repeated-measures ANOVA with post hoc Tukey HSD. Supplementary Table 2. Sample sizes analysed in Extended Data Fig. 3 by sex and genotype.

Reporting Summary

Supplementary Video 1

Crunch Master audio and video recording reveals that PBS enema results in high bite frequency and size. Representative audio and video recording of a mouse consuming a chow pellet in the Crunch Master assay within 1 h following PBS enema.

Supplementary Video 2

Crunch Master audio and video recording reveals that flagellin enema results in low bite frequency and size. Representative audio and video recording of a mouse consuming a chow pellet in the Crunch Master assay within 1 h following flagellin (1 μg ml−1) enema.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Liu, W.W., Reicher, N., Alway, E. et al. A gut sense for a microbial pattern regulates feeding. Nature 645, 729–736 (2025). https://doi.org/10.1038/s41586-025-09301-7

- Received: 08 March 2023

- Accepted: 16 June 2025

- Published: 23 July 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09301-7

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

- A gut instinct for microbial patterns

- Sian Lewis

Nature Reviews Neuroscience (2025)

Microbiota–neuroepithelial signalling across the gut–brain axis

Article 02 January 2025

Rapid modulation of gut microbiota composition by hypothalamic circuits in mice

Article Open access 22 April 2025

Gut inflammation promotes microbiota-specific CD4 T cell-mediated neuroinflammation

Article 18 June 2025

Article Open access Published: 23 July 2025

Driving a protective allele of the mosquito FREP1 gene to combat malaria

Zhiqian Li,

Yuemei Dong,

Lang You,

Rodrigo M. Corder,

Jemariz Arzobal,

Audrey Yeun,

Lei Yang,

John M. Marshall,

George Dimopoulos &

…

Ethan Bier

Nature volume 645, pages 746–754 (2025)

Abstract

Malaria remains a substantial global health challenge, causing approximately half a million deaths each year[1]. The mosquito fibrinogen-related protein 1 (FREP1) is required for malaria parasites to infect the midgut epithelium[2]. The naturally occurring FREP1Q allele has been reported to prevent parasite infection, while supporting essential physiological functions in the mosquito[3]. Here we generate congenic strains of Anopheles stephensi, edited to carry either the parasite-susceptible FREP1L224 or the putative-refractory FREP1Q224 alleles. The FREP1Q224 allele confers robust resistance to infection by both human and rodent malaria parasites, with negligible fitness costs. The protective FREP1Q224 allele can be efficiently driven into FREP1L224 mosquito populations using a novel linked allelic-drive system that selectively replaces the L224 codon with the parasite-refractory Q224 allele, thereby rendering populations refractory to parasite infection. This antimalaria drive system provides a novel genetic approach to aid in malaria elimination efforts.

Similar content being viewed by others

Main

Malaria remains one of the world’s most devastating diseases, claiming about 600,000 lives worldwide in 2023[1]. A decline in malaria deaths by approximately 50% during the past decade has been achieved primarily by the widespread use of insecticide-treated bed nets, indoor residual spraying of insecticides and antimalaria drugs[4]. However, these gains have been steadily eroding owing to the increasing prevalence of insecticide resistance in malaria mosquito vectors and the emergence of drug-resistant parasites1,5. An alternative and complementary approach is to develop genetically engineered mosquitoes that either suppress mosquito populations or modify them so that they can no longer sustain parasite transmission5,6,7,8,9,10,11. With regard to modification strategies, various exogenous and mosquito-encoded endogenous anti-Plasmodium effectors have been tested in mosquitoes. In addition, measures to disrupt the function of mosquito-expressed pathogen host factors have been shown to reduce parasite infection12,13. However, many challenges remain to be addressed with these approaches5,6,8,14,15,16,17,18,19,20. Concerns include: limited functionality of effectors due to imperfect synchronization between blood meal-inducible expression and parasite infection kinetics8,21,22; imposition of fitness costs (for example, modulating or disrupting expression of the endogenous target gene by genomic insertion of the transgenes)23,24,25; toxicity associated with high levels of effector expression; requirements for highly tissue-specific regulatory elements; and the potential for evolving mutations to impair effector functionality6,23,26. Furthermore, constitutive genetic inactivation of host factors often negatively affects mosquitoes by reducing viability and/or fertility, owing to a loss of biological functions beyond their roles in parasite infection6,26.

With the above considerations in mind, we envisioned an alternative streamlined strategy in which a genetic system preferentially biases the inheritance of a naturally occurring parasite-refractory allele of the host factor FREP1 that retains its essential physiological functions for the mosquito. FREP1 is a peritrophic matrix-associated factor that has been described as a promising host target for suppressing parasite infection owing to its important role in facilitating the traversal of malaria parasites across the midgut epithelium. This step has been described as a key bottleneck of the infection cycle of Plasmodium during the invertebrate stage, as only a few of the several thousands of ingested parasites successfully develop into oocysts between the midgut epithelium and its basal lamina5,27,28. A genome-wide association study identified a naturally occurring FREP1 allelic variant in which L (leucine) is replaced by Q (glutamine) as a candidate polymorphism that confers resistance to Plasmodium falciparum transmission in Anopheles gambiae mosquitoes[3]. Subsequent antibody blocking and genetic studies have confirmed the essential role of FREP1 in parasite infection; however, the predicted protective role of the FREP1Q allele has not yet been tested in a stable mosquito colony with a defined genotype, and correlative genetic evidence is currently absent for FREP1 orthologues in other anopheline species2,3,13,29,30.

Here we generated congenic strains of A. stephensi differing only in a single amino acid residue that either carries the wild-type (WT) parasite-susceptible FREP1L224 allele or the putative parasite-refractory FREP1Q224 variant. We found that the FREP1Q224 allele retains essential functions for the mosquito but greatly reduces infection by both P. falciparum and Plasmodium berghei parasites at the pre-oocyst stage. We used a linked allelic-drive strategy to achieve efficient super-Mendelian transmission of this protective anti-Plasmodium allele, which should be readily transferable to other genetic loci and diverse Anopheles mosquito species, expanding the genetic toolbox for combating malaria.

Generation of the FREP1 Q allelic variant

We set out to rigorously test the parasite susceptibility of FREP1 allelic variants in A. stephensi, the major Asian malaria mosquito vector by generating congenic strains that carry either the hypothesized parasite-refractory Q224 variant or the susceptible WT L224 allele (Extended Data Fig. 1). We recoded the L224 residue to Q224 (CTA to CAA) in the right homology arm flanking a selectable fluorescence marker cassette targeted for genomic insertion within the second intron of the FREP1 gene using gRNAIntron (cuts at 126 bp upstream of the T > A edit)[3] (Fig. 1a). This design has several notable advantages in that it: (1) enables fluorescence marker-based screening of successful genomic integration events; (2) facilitates tracking of the allelic edit, which is tightly linked to a fluorescence marker; (3) provides congenic strains differing in only a single amino acid (L224 or Q224); and (4) causes minimal effects on endogenous FREP1 gene activity (evidence presented below). We randomly selected and sequenced 20 F_1 transgenic mosquitoes and found that co-integration of the Q224 edit with the fluorescence marker had occurred in half of the primary transformants (Fig. 1b). These results suggest that about 50% of the double-strand breaks (DSBs) generated by gRNAIntron were resolved by homology-directed repair accompanied by a gene conversion tract comprising at least 126 bp, consistent with estimates of DSB resection lengths measured in mammalian cells, fruit flies and other species31,32,33,34,35 (Fig. 1b,c and Extended Data Fig. 2). We established three homozygous transgenic strains, two of which carried the Q224 allele but with differing fluorescence markers (FREP1GFP-Q and FREP1RFP-Q), whereas the third strain carried the L224 allele with a GFP marker (FREP1GFP-L; Fig. 1c–e), which served as a WT control for subsequent experiments in this study.

Fig. 1: Generation of the FREP1 allelic variants.

a, Design of the donor plasmid. The bold grey line denotes genomic DNA at the FREP1 locus; the grey boxes indicate homology arms; the circled light grey lines denote the plasmid backbone; the purple boxes indicate exons; and the green triangles indicate the gRNA cleavage site for gene cassette insertion. CR, cut resistant. b, Two possible editing outcomes: fluorescence marker insertion without (left) or with (right) the Q224 edit through homology-directed repair (HDR). The pink lines denote the RFP fluorescence marker. c, Established FREP1 transgenic lines: FREP1GFP-L, FREP1GFP-Q and FREP1RFP-Q. IR, infection resistant; IS, infection susceptible. d, Nucleotide and amino acid sequences of FREP1 alleles carrying the L224 (top) or Q224 codon (bottom). The shaded boxes indicate altered nucleotides that either alter the codon for the same amino acid residue (the grey box denotes recoded cut susceptible (CS) > CR; C > t, H) or change an amino acid codon (the turquoise box denotes parasite IS > IR; T > a; L > Q). e, Fluorescent images of female transformants. Adult mosquitoes were imaged with a Zeiss Stemi 2000 fluorescence microscope, and images were processed with Fiji (OS version) and Photoshop (Photoshop CC v20.0.7). Scale bars, 0.5 mm. At least three individual mosquitoes for each line were used for imaging.

The FREP1 Q allele is fitness neutral

We assessed possible fitness costs associated with the FREP1Q allele by quantifying the body size, fecundity and longevity of FREP1Q versus FREP1L mosquito strains (Fig. 2). We used wing length as a proxy for body size and vasa-Cas9 as an additional control, as the FREP1-transgenic lines were generated from the vasa-Cas9 strain. Thus, all three strains shared the same genetic background. We found that body size was comparable between the controls and the two FREP1Q strains, except for a slight, but statistically significant, increase in FREP1RFP-Q males. This difference may be attributed to stochastic sampling of a limited sample size and/or minor genetic variations (Fig. 2a). In terms of fecundity, all FREP1 transgenic females displayed similar levels of fecundity to vasa-Cas9 females when crossed with WT males (Fig. 2b), whereas a modest increase in male contribution to reproductive success was observed for FREP1GFP-Q males when crossed with WT females (Fig. 2b). Egg hatching rates were assessed 4 days after egg laying and, once again, no significant difference was noted among the compared strains except for a minor decrease when FREP1RFP-Q males were crossed to WT females (Fig. 2c).

Fig. 2: Characterization of the fitness of FREP1 allelic variants.

a, Length of wings. Cas9, vasa-Cas9; GFP-L, FREP1GFP-L; GFP-Q, FREP1GFP-Q; RFP-Q, FREP1RFP-Q. b, Number of eggs. Each dot indicates egg numbers from a single female mosquito. c, Hatching rate of eggs counted from panel b. The columns with circles indicate females, and the triangles denote males; the blue bars indicate median value; n = 30 individual mosquitoes (a–c). Statistical significance was calculated with a one-way analysis of variance (ANOVA) multiple comparisons test, and adjusted P values are shown in Source Data. d–f, Lifespan of virgin females (d) and males maintained with a 10% sucrose diet (e), and of females maintained with a 10% sucrose diet after mating and blood feeding (f). The red arrow indicates blood meal applied (f). n = 3 biologically independent replicates were used for the lifespan test; statistical significance was calculated by Kaplan–Meier survivability analysis with pooled data from three biological replicates (d–f). Data are mean ± s.d. g,h, The number ratio of RFP:GFP-marked transgenic mosquitoes observed when crossing FREPRFP-Q mosquitoes with FREPGFP-L (g) or with FREPGFP-Q (h). i, Ratio of allele frequencies between FREP1GFP-L and FREP1GFP-Q transgenic mosquitoes. n = 3 biological independent experiments shown by each line (g–i). Not significant (NS) P > 0.05, *0.01 < P < 0.05, ***0.0001 < P < 0.001 and ****P < 0.0001 (a–f).

Source data

We also examined the potential fitness costs of FREP1-transgenic mosquitoes with respect to lifespan using the FREP1GFP-L congenic line as the control to evaluate whether altering the L224 codon (FREP1GFP-L versus FREP1GFP-Q) imposed any fitness cost. In addition, we tested whether any fitness differences resulted from the insertion of alternative fluorescence markers at the same intronic site (FREP1RFP-Q versus FREP1GFP-Q). This analysis revealed that the virgin females of both Q224 alleles exhibited similar lifespans compared with the FREP1GFP-L control (Fig. 2d and Extended Data Fig. 3a). In the case of males, the FREP1GFP-L strain had a more gradual mortality trajectory than the two FREP1Q allelic variants, with the curve levelling off during later timepoints (Fig. 2e and Extended Data Fig. 3b). These modest differences in mortality may have arisen from yet uncharacterized biological functions of FREP1 involved in male developmental processes or from unknown variations in experimental factors affecting the assay (Fig. 2e and Extended Data Fig. 3b). We also noted a minor, but statistically significant, difference in mortality between the two differentially marked Q224 transgenic lines, potentially due to distinct characteristics of the fluorescence markers (Fig. 2e). However, as described in more detail below, these two alleles maintained approximately constant frequencies when competing against each other in multi-generational cage experiments (Fig. 2h), suggesting the overall impact of such differences is most likely quite small. Also, FREP1GFP-Q and FREP1GFP-L females that were blood fed after mating displayed a slightly reduced longevity (compared with virgin females; Fig. 2d,f and Extended Data Fig. 3c). This effect was less pronounced in FREP1RFP-Q mosquitoes, whereas the FREP1GFP-Q and FREP1GFP-L allelic variants exhibited comparable lifespan profiles (Fig. 2f and Extended Data Fig. 3). These parallel comparisons revealed only a significant reduction in male lifespan of the FREP1GFP-Q allele compared with the FREP1RFP-Q and FREP1GFP-L alleles (Fig. 2d–f). In addition, all three transgenic strains exhibited a similar significant longevity decrease relative to WT and vasa-Cas9 controls (Extended Data Fig. 3a–c). This modest difference may reflect a fitness cost associated with the FREP1 transgenic insertion; however, such effects do not appear to impact the multi-generational experiments, in which the transgenic Q224-linked cassette competes effectively with a WT L224 allele (Extended Data Fig. 9, see below).

In addition, we examined pupation and adult emergence rates, again with only minor variations associated in FREP1 transgenic mosquitoes (Extended Data Fig. 3d–f). Overall, we did not note any consistent significant fitness costs across all parameters, suggesting that the observed sporadic fitness costs may arise from stochastic sampling of limited populations. We conclude that changing the codon for a single amino acid (CTA to CAA) results in only modest fitness differences between the FREP1L and FREP1Q congenic allelic variants, which may reflect small differences between the transgene insertions and/or stochastic variations between experiments.

We further assessed the relative fitness of the three FREP1 strains by conducting stringent multi-generational competition experiments between FREP1 alleles in freely mating populations. Cages were initially seeded with transheterozygotes, resulting in a 50% initial frequency for each allele (Fig. 2g–i). Allele frequencies were then scored over 10 consecutive generations (for example, FREP1RFP-Q versus FREP1GFP-L or FREP1RFP-Q versus FREP1GFP-Q) by tallying the ratio of the mosquitoes carrying the distinguishing fluorescence markers at each generation (Fig. 2g,h). We observed an initial pattern of seemingly random fluctuations in allelic ratios during the first few generations, followed by a stable trajectory that gradually approached unity (Fig. 2g,h), indicating that the competing lines had comparable fitness. In addition, we evaluated competition between the FREP1GFP-L and FREP1GFP-Q strains, which carry the same fluorescent marker, using targeted deep sequencing to determine the relative frequency of each allele in each generation (Fig. 2i). Aside from occasional late outlier fluctuations for the paired GFP lines (Fig. 2i), we observed no significant difference in relative competitiveness between these two FREP1 alleles, confirming the findings described above that there are modest, if any, consequential differences between the various tested transgenic strains.

FREP1 Q224 mosquitoes are parasite resistant

Next, we assessed whether the FREP1Q allele reduced infection of A. stephensi by the major human malaria parasite P. falciparum through membrane feeding on parasite gametocytes mixed with human red blood cells and serum6,13 (Fig. 3a). We then measured both oocyst infection prevalence (percentage of mosquito midguts with developed parasite oocysts) and intensity (the number of oocysts per midgut) 8 days after feeding on both low and high gametocytaemia blood[6]. At low gametocyte concentration (0.08% gametocytaemia), infection intensities typical for mosquitoes in the field, we observed a significant reduction in infection prevalence in the FREP1GFP-Q strain, decreasing from around 80% in control (vasa-Cas9 and FREP1GFP-L) mosquitoes to approximately 30% (Table 1, Fig. 3b, Extended Data Fig. 4a–d and Supplementary Table 1). Infection intensity, measured as the median number of oocysts per midgut, was also strikingly decreased from 3 to 0 in the control and the FREP1GFP-Q strains, respectively (Table 1, Fig. 3c and Extended Data Fig. 4b). Similarly, at a high gametocyte concentration (0.15% gametocytaemia), we observed significant decreases in infection prevalence (dropping from 98% in FREP1GFP-L control to 86% in the FREP1GFP-Q line) and intensity (decreasing from a median of about 32 oocysts per midgut in FREP1GFP-L control to less than 10 oocysts per midgut for the FREP1GFP-Q line; Extended Data Fig. 4e,f and Supplementary Tables 1 and 3). By contrast, oocyst infection intensities and prevalence were comparable between FREP1GFP-L and vasa-Cas9 controls, indicating that only mosquitoes carrying the FREP1Q allele were robustly resistant to P. falciparum infection (Table 1 and Fig. 3b,c).

Fig. 3: FREP1Q mosquitoes are resistant to both P. falciparum and P. berghei infection.

a, A standard feeding membrane assay for P. falciparum infection in the mosquito population including females and males with gametocyte (NF54)-infected human blood. b,c, Infection prevalence (b) and infection intensities (c) of P. falciparum (NF54) oocyst loads in the midguts of vasa-Cas9 control and two FREP1 transgenic mosquitoes (FREP1GFP-L and FREP1GFP-Q) at low gametocytaemia (0.08%) at 8 days post-infection (dpi). d,e, Infection prevalence (d) and infection intensities (e) of P. falciparum (NF54) sporozoites in salivary glands (SGs) at 15 dpi. f, Mosquito population with females and males was infected with P. berghei through mouse (no bias on gender) feeding. The schematics in panels a,f were created using BioRender (https://biorender.com). g–j, Prevalence and infection intensities tabulated for P. berghei oocysts at 12 dpi (g and h) and sporozoites at 21 dpi (i and j) at high infection level. Each single dot represents the number of parasites in an individual dissected midgut or one pair of salivary glands. The horizontal lines denote median values (c,e,h,j). n = 3 biological replicates, and the final pooled numbers are indicated in Tables 1 and 2. n denotes the number of tested individual mosquitoes. A two-tailed Mann–Whitney U-test was used to determine statistical significance for infection intensities, and a Fisher’s exact test was used for infection prevalence. NS P > 0.05, ***0.0001 < P < 0.001 and ****P < 0.0001.

Source data

Table 1 P. falciparum infection at a low gametocytaemia level (0.08%)

We also quantified the number of sporozoites present in the salivary glands to assess the efficacy of malaria transmission blocking, as the sporozoite load in salivary glands is directly linked to the ability of a mosquito to transmit malaria parasites36,37. We observed an approximately fivefold reduction in the median number of salivary gland sporozoites from more than 4,650 sporozoites per salivary gland pair for vasa-Cas9 and 4,050 sporozoites for FREP1GFP-L controls compared with a median of zero sporozoites in FREP1GFP-Q salivary glands (Fig. 3d,e and Extended Data Fig. 4d). Similarly, at high infection intensities, large reductions in sporozoite burdens were observed in FREP1Q versus FREP1L strains (Extended Data Fig. 4g,h and Supplementary Table 2). Together, these findings support the hypothesis that mosquitoes carrying the FREP1Q allele are highly refractory to infection by P. falciparum parasites, as indicated by measures of parasite prevalence, median number of oocysts and total sporozoite loads. The parallel observation of the degree of reduction in oocyst numbers and depletion of later-stage sporozoites in FREP1Q224 mosquitoes compared with the congenic FREP1L224 strain suggests that the protective FREP1Q224 allele inhibits parasite development at early pre-oocyst stages.

The FREP1 protein has been identified as a broad-spectrum target for transmission-blocking vaccines that target malaria parasites in the mosquito vector2,38. However, the transmission target epitopes in these diverse studies remain uncharacterized. Thus, we fed FREP1GFP-Q and control lines (vasa-Cas9 and FREP1GFP-L) on mice infected with the divergent rodent parasite P. berghei (WT, ANKA 2.34; Fig. 3f). We found again that only the FREP1GFP-Q transgenic mosquitoes showed a significant reduction in high-intensity P. berghei infection at both the oocyst and the sporozoite stages (for example, the median infection intensity dropped from 43 to 25 oocysts per midgut, respectively, in the FREP1GFP-L versus FREP1GFP-Q strains; Table 2 and Fig. 3g–j). In these experiments, we did not observe a significant reduction in oocyst prevalence in infected FREP1GFP-Q mosquitoes, but this was presumably due to P. berghei not being a natural parasite of A. stephensi and the typically high infection intensities that P. berghei achieves in this unnatural vector.

Table 2 P. berghei infection at a high gametocytaemia level (0.15%)

We also performed parasite challenge assays with FREP1L224/FREP1Q224 transheterozygotes to evaluate whether the FREP1Q224 allele in a heterozygous condition could also confer resistance to the parasite infection. In this case, we did not detect any significant resistance to either P. falciparum or P. berghei infection, consistent with the results reported previously in A. gambiae[3]. We conclude that the FREP1Q allele in A. stephensi confers a broad-spectrum parasite-refractory phenotype when homozygous.

A linked FREP1 Q allelic-drive cassette

We wondered whether it might be possible to use a gene-drive system to promote super-Mendelian transmission of the parasite-resistant FREP1Q224 allele relative to the infection-susceptible FREP1L224 allele. We therefore designed a linked allelic-drive cassette (FREP1RFP-gRNA-Q; Fig. 4a) carrying the RFP fluorescent marker, the Q224 edit and gRNAL224, the last selectively targeting the parasite-permissive FREP1L allele. This gRNAL224-bearing gene-editing cassette was inserted at the same genomic site in the second intron as the RFP-marked and GFP-marked transgenic elements described above (Figs. 1a and 4a). We hypothesized that when combined with Cas9, gRNAL224 would convert the L224 residue on the homologous chromosome to the Q224 residue via homology-directed repair in developing germ cells (Fig. 4a).

Fig. 4: Disseminating the FREP1Q224-refractory allele by the linked allelic-drive system.

a, Linked allelic-drive scheme (top). The grey lines denote genomic DNA; the purple boxes indicate exons; the narrow cyan rectangle denotes the Q224 residue; the narrow grey rectangle indicates the WT L224 residue; the narrow black rectangle denotes the non-synonymous cleavage-resistant residue; and the light pink boxes indicate chromosomal homology between donor and receiver chromosomes. Allelic replacement of the L224 codon on the receiver chromosome with the Q224 edit is also shown (bottom). SeqF and SeqR refer to primers for receiver chromosome-specific amplification. b, Cross schemes and genotyping primer set for controlled three-generation pair-mating crosses. Chr. chromosome. c, Genotyping of the F_2 progeny using fluorescence markers. n = 3 biologically independent crosses. Data indicate mean ± s.d. n Denotes the number of total F_2 progeny counted. d, L224 to Q224 conversion rate quantified by Sanger sequencing. n Denotes the number of F_2 progeny tested. e, Cross scheme for generating transheterozygous used for cage trial seeding. f, Inferred allelic frequencies across 10 generations. Q224 is in cyan, L224 in grey and NHEJ in orange. Three cages were run as biological replicates. Data indicate mean ± s.d. The black line shows the profile of mean Q224 allele frequencies. g, Frequency of individuals carrying each fluorescent marker. h, Allelic frequency in the cage population. The light coloured lines show the experimental data, and the faint lines are 100 stochastic model simulations (g,h). The dashed grey lines denote deterministic model simulations. i, P. falciparum (NF54) oocyst loads in the midguts of controls (WT, vasa-Cas9 and FREP1GFP-L) and generation of 11 cage trial mosquito populations (three cages tested separately and mixed) fed on low gametocytaemic (0.08%) blood. The horizontal lines denote median values (i). A two-tailed Mann–Whitney U-test was used to determine statistical significance for infection intensities, and a Fisher’s exact test for infection prevalence. NS P > 0.05, **0.001 < P < 0.01 and ****P < 0.0001.

Source data

We first tested the above hypothesis in a three-generation controlled pair-mating scheme (Fig. 4b) using an unlinked source of vasa-Cas9 (Extended Data Figs. 6 and 7). In these experiments, we used the above constructed FREP1GFP-L chromosome as the target allele, using distinguishable fluorescence markers (IE1-RFP: FREP1RFP-gRNA-Q and IE1-GFP: FREP1GFP-L) to track the chromosomes (Fig. 4a). Transheterozygous FREP1RFP-gRNA-Q/FREP1GFP-L F_1 mosquitoes (either males or females) were crossed to a WT A. stephensi strain, and the phenotypes and genotypes of the resulting F_2 progeny were tabulated (Fig. 4b). We scored the fraction of the two distinguishing fluorescence markers in F_2 progeny and observed approximately equal inheritance of donor versus target chromosomes, confirming standard Mendelian inheritance of the FREP1RFP-gRNA-Q gene cassette (gRNAIntron used for insertion of the cassettes was not included in this cassette; Fig. 4c). We also assessed the frequency of allelic conversion (L224 > Q224) on the differentially marked FREP1GFP-L target chromosome (that is, GFP+RFP– F_2 progeny) by performing allele-specific amplification (PCR) using a 5′ primer (SeqF) complementary to the GFP, followed by Sanger sequencing of target chromosome-derived amplicons (Fig. 4b,d). This analysis revealed robust gene conversion frequencies of the target chromosome inherited both paternally (72% conversion, or 86% overall Q224 allele frequency) and maternally (86% conversion, 93% overall Q224 allele frequency) when Cas9 was provided from F_0 grandmothers (Fig. 4d). Somewhat lower conversion frequencies (69% paternal and 50% maternal, or 84.5% and 75% of total alleles, respectively) were observed when Cas9 was inherited from grandfathers (Fig. 4d). In addition, a modest frequency of non-homologous end-joining (NHEJ) alleles was observed (ranging from 0% to 11.8% of receiver alleles depending on the crossing scheme). Half of such NHEJ mutations derived from the grandfather crosses were out-of-frame as assessed by DNA Sanger sequencing (Extended Data Fig. 8), whereas mutant alleles arising from grandmother crosses all had large, presumably non-functional insertions. The remaining predominant class of target alleles was WT (L224; Fig. 4d), which we inferred were either precisely repaired or uncut. Thus, under these conditions, we observed a high frequency of target conversion from the FREP1L to the FREP1Q allele (approximately 70% on average, ranging from 50% up to 86%) with only a modest fraction of target site mutations being generated, the latter consisting predominantly of loss-of-function FREP1 alleles that presumably would incur substantial fitness costs.

The FREP1 Q224 allele drives in populations

We further assessed the linked allelic-drive element by testing whether it could sustain efficient drive of the FREP1Q224 allele in multi-generational cages of freely mating mosquitoes. We conducted triplicate non-overlapping small laboratory population cage experiments initiated by seeding transheterozygous mosquitoes carrying the vasa-Cas9; FREP1RFP-gRNA-Q224 gene cassette and the FREP1GFP-L target allele into homozygous FREP1GFP-L populations at a 1:3 allelic ratio (Fig. 4e–h). The fraction of mosquitoes carrying the linked allelic-drive (pink lines) rose from 50% in the first generation to approximately 64% and remained constant through the 10th generation (Fig. 4g; see modelling section below). Reciprocally, mosquitoes carrying the receiver FREP1GFP-L allele (green lines) dropped to a steady-state level of approximately 83% (Fig. 4g). These results are consistent with the data presented in Fig. 2g–i, where competing congenic FREP1RFP-Q and FREP1GFP-L alleles in multi-generational cages displayed approximately equal fitness. In addition, the observation that the FREP1RFP-gRNA-Q and FREP1GFP-L alleles co-existed over several generations (see below) further supports our hypothesis that FREP1Q224 and FREP1L224 alleles have similar fitness.

In each generation, we also genotyped 50 randomly selected mosquitoes by next-generation sequencing (NGS) for their FREP1L224/Q224 genotypes. We selectively amplified the gRNA target site from the FREP1GFP-L receiver chromosome using GFP-specific primers and performed NGS sequencing. We inferred the allelic frequency in the total population on the basis of the observed conversion rates weighted by the fraction of marked donor versus receiver chromosomes scored by their fluorescence phenotype (Fig. 4f,h). The frequency of the FREP1Q224 allele increased rapidly from its initial 25% seeding percentage to more than 90% introduction over the course of 10 generations (Fig. 4f,h).

In all cages, only a modest fraction of NHEJ alleles were generated, which dropped from an initial average of 5.4% at generation 1 to less than 0.5% by generation 10, showing a trend of gradual elimination (Fig. 4f,h). This progressive loss of NHEJ alleles is consistent with potential fitness costs being associated with loss-of-function FREP1 mutations. These results support the hypothesis that the linked allelic-drive system as configured sustains efficient allelic drive of the protective FREP1Q224 allele without producing a significant fraction of interfering alternative NHEJ alleles.

We also tested the performance of the linked FREP1RFP-gRNA-Q drive in the context of the WT FREP1L224 allele, for which there was only limited homology on the intronic side of the gRNA cut side (126 bp between the donor and target chromosomes, compared with more than 1.2 kb of homology in the congenic configuration shown in Fig. 4e–h; Extended Data Fig. 9a,b). In this case of one-sided homology mismatch, a significant fraction of cleavage events resulted in damage to the target chromosome in both germline and somatic cells, leading to the lethality of a substantial significant fraction of individuals carrying both the gRNAL224 and the Cas9 transgenes, a phenomenon that has been well-documented in previous studies[39]. Such a drive configuration could, in principle, be used for localized allelic-drive applications (see Discussion). This experimental configuration also revealed that following an initial abrupt reduction in the frequency of the drive allele (as a consequence of the lethality mentioned above), the gRNA-bearing element remained at an approximately constant frequency for over 10 generations. Thus, the transgenic insertion element can compete effectively with respect to both WT and potentially generated functional NHEJ alleles, despite the observation in Extended Data Fig. 3c that post-blood-fed females exhibited a modest reduction in survival compared with WT.

Given the high level of final introduction of the FREP1Q allele in all cages, we next tested whether these populations could suppress parasite infection. We conducted parasite challenge assays by feeding mosquitoes collected from cages at generation 11 on a P. falciparum gametocyte concentration that would produce a low infection intensity (Fig. 4i). Mosquitoes collected separately from all three population cages, or mixed together, demonstrated robust parasite suppression (the median infection intensity dropped from 9 to 0, 5.5 and 0 oocysts per midgut in cages 1, 2 and 3, respectively; Table 3 and Fig. 4i). These data strongly support the hypothesis that the FREP1Q allelic variant can spread sufficiently to suppress parasite infection in final target mosquito populations.

Table 3 P. falciparum infection at a low gametocytaemia level (0.08%) with cage trial populations

Mathematical modelling of drive dynamics

As a complement to the experiments described above, we also conducted Bayesian mathematical modelling to infer potentially hidden parameters that were not readily extracted from pair-mating or multi-generational experiments, such as subtle potential fitness costs or selective advantages of particular genotypes (Fig. 4g,h and Supplementary Tables 6–11).

A key inference from the model fitting was that the observed proportions of homozygous GFP mosquitoes (Source Data) in the first generation (F_1) were consistently lower than expected (approximately 0.56 according to the model) assuming simple random assortment and an average rate of gene conversion of approximately 0.7 (Fig. 4d and Source Data). We hypothesized that the rapid rise of the linked allelic-drive might result from lethal sterile mosaicism, a process that we have previously described8,10. This process eliminates progeny homozygous for the FREP1GFP-L allele that also inherit Cas9–gRNA complexes (transmitted maternally), and thus lack the repair template (FREP1RFP-gRNA-Q allele). In these individuals, Cas9–gRNAL224 cleavage of both FREP1GFP-L alleles could lead to the generation of homozygous loss-of-function alleles in many somatic cells phenocopying homozygous null FREP1 mutants, which have severely reduced viability and fertility. As discussed further below, the overall drive kinetics can largely be accounted for by a combination of several factors including: (1) substantial allelic conversion (average of approximately 60%); (2) severe fitness costs levied on FREP1L224 homozygotes in the presence of Cas9–gRNAL224 complexes; (3) generation of only a modest number of NHEJ alleles (particularly of functional cleavage-resistant alleles); and (4) comparable fitness of the FREP1RFP-gRNA-Q and FREP1GFP-L alleles.

Discussion

FREP1 Q suppresses parasite infection

Parasite challenge assays conducted in this study using congenic A. stephensi strains carrying either the FREP1Q224 or FREP1L224 allele demonstrated that the FREP1Q224 allele selectively confers potent resistance to infection by two highly divergent malaria parasite species (P. falciparum and P. berghei), highlighting the broad protective effect of the FREP1Q224 allele. How the FREP1 protein facilitates the traversal of malaria parasites across the gut epithelium remains unknown; however, one hypothesis is that the L224 residue mediates a crucial interaction between FREP1 and yet-to-be-identified parasite surface factors15,40. This possibility, or alternatives involving differential FREP1 activities, merit examination in future studies.

Overall, our comparative studies demonstrated that: (1) the insertion of a selectable marker into the FREP1 intron had minimal if any effect on the efficiency of parasite infection (that is, we observed similar intensities of parasite infection in the FREP1GFP-L mosquitoes compared with the vasa-Cas9 L224 control strain); (2) all three FREP1-transgenic lines displayed only modest, if any, overall fitness differences based on parameters including body size, fecundity, longevity and success in undergoing metamorphosis and direct competition between congenic FREP1 strains in multi-generational cages; and (3) the Q224 variant alone is sufficient in A. stephensi to confer resistance to infection by malaria parasites. To our knowledge, this is the first study in which genetic manipulation of a single amino acid of a mosquito factor has achieved robust inhibition of malaria parasite infection using gametocyte challenge levels equal to or greater than those that typically occur in the field.

FREP1 has been investigated previously for its role in malaria parasite infection by using either RNAi-based silencing[2] or CRISPR–Cas9-generated null mutants[13]. However, both of these systems have their limitations. The RNAi studies achieved partial and incomplete protein depletion, whereas null mutants, which displayed comparable parasite-refractory phenotypes to the single allelic replacements reported here, imposed high fitness costs[13]. Furthermore, the high degree of resistance to parasite infection conferred by the FREP1Q224 allele described in this study is comparable with that previously reported for a FREP1-null allele in A. gambiae[13], indicating that this single amino acid change effectively eliminates FREP1 activity for parasite infection while leaving essential physiological functions of this protein in the mosquito intact. These findings in both A. stephensi and A. gambiae also point to FREP1 being a key protein required for parasite infection in two important Anopheles malaria vector species.

These high levels of parasite resistance conferred by the FREP1Q and null alleles are akin to those provided by other infection blocking systems, such as gut-specific over-expression of the endogenous mosquito immune protective genes Rel2 and Akt17,41 and parasite-blocking single-chain antibodies6,21. An important element of our current studies is the near fitness neutrality of the FREP1Q allele in our extensive comparative tests of the congenic FREP1Q224 versus FREP1L224 strains. This fully functional phenotype of the FREP1Q224 allele contrasts with the severe reductions in fecundity and longevity previously reported for A. gambiae FREP1-null mutants[13]. In summary, our detailed results provide rigorous evidence supporting the hypothesis that the FREP1Q224 variant alone is sufficient to potently suppress parasite infection in A. stephensi and does so without appreciable cost to the host mosquito.

Super-Mendelian propagation of FREP1 Q

CRISPR-based gene-drive systems offer the potential for rapid and super-Mendelian dissemination of beneficial alleles through wild populations42,43,44. Efficient gene-drive systems have been developed in diverse organisms, including Drosophila melanogaster45,46,47,48, Saccharomyces cerevisiae[49], Anopheles mosquitoes8,10,50,51, herpesviruses[52] and Escherichia coli[53]. In addition, it is possible to combine canonical gene-drive elements with a second gRNA that selectively targets a non-preferred allele42,43. The linked allelic-drive cassette reported in this study represents an advance over previous allelic-drive systems42,43,54 by utilizing only a single gRNA that is closely linked to its cleavage site. This conjoined design avoids the free recombination between gene-drive cassette and functional drive-resistant insertions and deletions, which could otherwise be driven as ‘runaway’ alleles that potentially compete with the preferred allele for being driven into the population.

Mathematical modelling of the experimental data offered several insights into the factors that contribute to the overall efficiency of the drive process. In several aspects, this analysis parallels that of a conditionally self-eliminating drive system recently analysed in Drosophila[54], in which a passively inherited drive cassette was inserted into the voltage-gated sodium ion channel (vgsc) locus. Extensive modelling, both accompanying the vgsc study and here for the FREP1Q224 drive, has revealed several synergistic factors leading to drive success: (1) substantial level of allelic-drive; (2) relatively low rates of NHEJ generation, and particularly of functional NHEJ alleles; (3) low fitness costs associated with the preferred driven allele; and (4) high fitness costs imposed on individuals inheriting only target alleles (for example, FREP1GFP-L homozygotes in the current case) in combination with Cas9–gRNA (whether inherited genetically or transmitted maternally). The rationale behind the latter condition is that, in the presence of Cas9–gRNA complexes, individuals homozygous for FREP1L224 allele experience pervasive somatic mutagenesis of both copies of the L224 allele, leading to somatic mosaics in which many cells are homozygous for loss-of-function alleles of the FREP1 gene. As there are very severe fitness costs (reduced viability and fertility) associated with FREP1-null alleles[13], such lethal and/or sterile mosaic individuals are most likely to fail to survive or reproduce. On the basis of both the experimental data and in-depth supporting modelling, we conclude that the linked allelic-drive strategy described in this study can efficiently drive the preferred parasite refractory variant of the FREP1 locus into a freely mating population of mosquitoes and render them robustly refractory to parasite infection, providing a promising foundation for future application in vector control.

Looking forwards

In the current study, the linked allelic drive was inserted very near to the edited target site (126 bp) on the basis of practical considerations (that is, for creating equivalent donor and receiver congenic lines for optimal strain comparison). In general, however, the drive cassette could be deployed from various nearby locations relative to its targeted allelic cleavage site. For example, if the goal is to ensure the persistence of the allelic-drive system within a population, the gRNA-bearing cassette could be inserted (with or without a Cas9 transgene) within an exon of the target locus some distance away from the gRNA cut site along with function-restoring recoded sequences, into a neighbouring non-essential gene, or placed in closely linked intergenic regions. In addition, the allele-driving gRNA could be incorporated into gene cassettes designed for more localized effects. For example, although the linked drive tested here efficiently drove the Q224 edit to replace the chromosomally aligned FREP1GFP-L allele (these two alleles share more than 1.2 kb of cassette homology on the intron side of the gRNA cut site), it was less efficient when combined with a WT allele that shares only 126 bp of intronic homology (as such a configuration eliminates a significant fraction of target alleles). Thus, when deployed in the latter configuration, the linked drive could act more locally to achieve a desired frequency of FREP1Q224 allele in a given population. Similarly, self-eliminating allelic-drive systems designed to impose even greater fitness costs could be used in cases when the goal is to completely eliminate the gene cassette from the population[54]. Thus, the driving gRNA could be readily incorporated into various drive architectures including full or split gene drives[47], self-eliminating systems[54], transcomplementing drives[55] or integral drive56,57 configurations depending on specific objectives such as the size of the target population and how long one wished the drive to remain in the population.

In summary, we have shown that a single-nucleotide change in the FREP1 gene is sufficient to confer a strong parasite-refractory phenotype and that inheritance of the protective FREP1Q224 allele can be efficiently biased using a linked allelic-drive system. A similar strategy could also be applied to primary African malaria vectors such as A. gambiae or could be used to convert insecticide-resistant alleles such as knock-down-resistance (kdr) mutation into the WT insecticide-sensitive allele43,54. In the future, such allelic drives might also be engineered to be self-eliminating by designing them to incur a fitness cost such that they act only transiently before disappearing from the population[54], permitting localized allelic replacements with zero transgene end points.

Methods

Mosquito rearing and maintenance

The A. stephensi WT (UCISS2018) and transgenic vasa-Cas9 lines used in this study were shared by A. A. James’s laboratory (University of California Irvine)[58]. These two lines have been bred and stably maintained in the laboratory for over 30 generations. Mosquitoes were grown at 27 °C under standard conditions with 77% humidity and a 12-h day–night lighting cycle. Mosquito larvae were fed with a mixture of powdered fish food (TetraMin) and yeast (2:1; Red Star), and adults were supplied with 10% (wt/vol) sucrose. Five days after mating, females were fed with cold calf blood (Colorado Serum Company) using Hemotek blood-feeding facilities. Mosquitoes used for P. falciparum and P. berghei infections were reared in the Johns Hopkins Insectary Core facility from eggs to adults. Similar rearing conditions were used with additional cat food pellets being added to the regular larvae food mixture.

Ethics statement

This study was carried out in strict accordance with the recommendations in the Guide to the Care and Use of Laboratory Animals of the US National Institutes of Health. The parasite challenge assay protocol was approved by the Animal Care and Use Committee of Johns Hopkins University (permit number #MO21H10). Commercial anonymous human blood from Interstate Blood Bank was used for parasite cultures and mosquito feeding, and informed consent was therefore not applicable. This protocol has been approved by the Johns Hopkins School of Public Health Ethics Committee. For mosquito rearing and blooding feeding, we followed procedures and protocols approved by the Institutional Biosafety Committee from the University of California San Diego, complying with all relevant ethical regulations for animal testing and research (protocol #S18147).

Mosquito transgenesis

Microinjections were performed as previously described by injecting a mixture of donor plasmids into the pre-blastoderm vasa-Cas9 embryos[14]. Donor plasmids were injected at 250 ng μl−1 in the injection buffer (5 mM KCl and 0.1 mM sodium phosphate, pH 6.8) filtered by 0.22-μm filter. F_0 females and males were separated into two cohorts when they pupated and outcrossed to WT UCISS2018 mosquitoes in pools. All F_1 progeny were screened for whole-body RFP (FREP1RFP-Q and FREP1RFP-gRNA-Q) or eGFP (FREP1GFP-L or FREP1GFP-Q) under UV-fluorescence microscopy at late larval stages. Positive F_1 transgenic mosquitoes were used for isolating single colonies by mating with WT counterparts. After egg laying, the transgenic founders were crushed with single-fly preparation buffer (49 μl lysis buffer + 1 μl proteinase K to a final concentration of 0.3 mg ml−1. The lysis buffer included 1 mM EDTA, 10 mM Tris, pH 8.2, and 25 mM NaCl) for genotyping.

The orthologous amino acid (L224) in the A. stephensi FREP1 (ASTEI02574) protein was identified by protein sequence alignment with its A. gambiae FREP1 (AGAP007031) orthologue, which corresponds to the L442 residue in the A. gambiae FREP1 protein[3]. To create a clean FREP1Q224 edit in A. stephensi and avoid mutagenesis caused by NHEJ repair, we inserted a gene cassette carrying a fluorescent marker (either IE1-RFP-SV40 or IE1-eGFP-SV40) into the second intron of the FREP1 locus with a separate plasmid expressing gRNAIntron (5′-GCGACGACGATTGTAGACGCTGG-3′) targeting a site 126 bp upstream from the residue L224. The codon change from CTA (L224) to CAA (Q224) was included in the right homologous arm of the donor plasmid, downstream of the selection marker. With this arrangement, the FREP1Q224 edit only results from co-integration of the desired edit with the gene cassette when DSB end resection proceeds beyond this site (that is, further than 126 bp in the 3′ direction).

The linked allelic-drive cassette, FREP1RFP-gRNA-Q, has the same structure and integration site as the FREP1RFP-Q cassette, but also includes a transgene encoding the allelic gRNAL224 (5′-GCTCCAGCTCGGTTAGCGTT-3′). This donor plasmid was injected into A. stephensi vasa-Cas9 pre-blastoderm embryos together with gRNAIntron expressed from a separate plasmid, resulting in the FREP1RFP-gRNA-Q gene cassette being inserted into the identical site in the FREP1 second intron. F_1 fluorescent-positive progeny were crossed with WT mosquitoes and collected for genotyping after egg laying using primers FREP1F333 and FREP1R334.

Characterizing fitness costs

Fifty randomly selected adult mosquitoes were anaesthetized on ice to measure wing length, which was used as a surrogate examination for mosquito body size[13]. Mosquito fertility was calculated by crossing either transgenic females to the WT males to assess the female reproductivity, or crossing transgenic males to the WT females to examine the male contribution by single mating in plastic vials. At least 30 crosses were performed and the number of eggs produced from the single vial were counted and used for plotting. Three biological replicates were performed. Egg hatching rate was assessed by counting the number of young larvae from single mating at 6 days after egg laying. Significant differences were calculated by unpaired Student’s t-test. The lifespans of the transgenic mosquitoes were measured by collecting pupae, separating them into female and male cohorts, and setting up three cages for each cohort with 30 mosquito adults. Mosquitoes were supplied with a 10% sucrose solution. Dead mosquitoes were recorded and removed from the cages daily to calculate the survival rate until all mosquitoes had died. For cages measuring lifespans with mating and single-blood feeding, 30 randomly selected transgenic females were mated with 90 WT males for 5 days after emergence, then blood-fed with Hemotek, and dead females were continuously counted. Data were collected with Microsoft Excel 2019 (v16.30) and displayed by GraphPad Prism 8 (v8.2.1) with the ratio of survivability on each day. Statistical significance was calculated by Kaplan–Meier survivability analysis with pooled data from three biological replicates, with not significant (NS) P > 0.05, *0.01 < P < 0.05, **0.001 < P < 0.01, ***0.0001 < P < 0.001 and ****P < 0.0001. For assaying pupation time, approximately 100 randomly selected transgenic larvae were maintained in each tray and the number of pupae were recorded daily in three replicates. Adult emergence rates were also tabulated by enumerating female and male adults that emerged from the same tray.

Parasite challenge assays

We determined the competency of A. stephensi FREP1 congenic or control mosquitoes to serve as vectors for P. falciparum using artificial membrane feeding assays performed according to previously established methodology[13]. Transgenic or WT female mosquitoes were randomly selected and fed on NF54W P. falciparum gametocyte cultures at 37 °C by mixing with the fresh blood (red blood cells plus human serum; Interstate Blood Bank) to obtain a final gametocytaemia of 0.08% (low infection levels) or 0.15% (high infection levels). Seven-day-old adult mosquitoes were used for P. falciparum infections using a pumped water bath and glass membrane feeder with stretched parafilm for 1 h until mosquitoes were fully engorged. The adult mosquitoes used for parasite feeding were starved from a sugar source for 3–5 h in advance and any unfed or partially fed mosquitoes were removed immediately after blood feeding. At least three biological replicates were performed as independent replications, and each group contained at least 90 female mosquitoes, according to our established methodology[13]. Eight days after feeding with P. falciparum at 27 °C, the midguts were dissected in phosphate-buffered saline and stained with 0.2% mercurochrome to examine the number of oocysts developed in the midguts[13]. Fourteen days after P. falciparum blood feeding, pairs of salivary glands from individual females were dissected and put into the PCR tubes with 30 µl of phosphate-buffered saline followed by sporozoite counts according to a previously published protocol[13]. At least 60 successfully infected female mosquitoes were randomly selected, dissected and counted for oocysts in the midgut or sporozoites in the salivary glands. Two-tailed Mann–Whitney U-test was used to calculate P values for infection intensities, and Fisher’s exact test for infection prevalence. All parasite challenge assays were conducted with at least three independent biological replicates and the pooled numbers of individual replicates are presented, with the median number of oocysts and sporozoites shown in Figs. 3 and 4i, as the median provides the most definitive measure for distinguishing statistical differences in the distributions of parasite loads. GraphPad Prism 10.0 was used to present both infection intensities and prevalences.

All three FREP1 transgenic mosquito lines and the controls were also fed on P. berghei (WT, ANKA clone 2.34)-infected 8-week old Swiss Webster mice at 19 °C to examine its infection potency to the rodent malaria parasite[13]. Female mosquitoes at 12–13 days after infection were collected to investigate oocyst loads in the midguts, and salivary glands were collected at 19–21 days post-infection to determine sporozoite loads.

Assessment of drive efficiency

Allelic conversion rates were assessed separately through female and male lineages. To track the target chromosome, we combined the vasa-Cas9 with the FREP1GFP-L allelic variant. The vasa-Cas9; FREP1GFP-L mosquitoes were then outcrossed with FREP1RFP-gRNA-Q transgenic mosquitoes to examine the germline allelic conversion rate. F_0 crosses were set up with 25 females and 25 males (all randomly selected) in three replicates. F_1 larvae were first screened for the presence of all fluorescence (IE1-RFP-marked FREP1RFP-gRNA-Q, IE1-GFP-marked FREP1GFP-L and 3xP3-CFP-marked vasa-Cas9) and then used for F_1 crosses with WT A. stephensi in female and male cohorts with the crossing schema displayed in Extended Data Fig. 7. All F_2 progeny were scored for the presence of each fluorescence. Progeny carrying only the IE-GFP receiver chromosome was subjected to genotyping by allele-specific PCR amplification (primers SeqF and SeqR) and Sanger sequencing, and SnapGene (v5.0.7) was used for Sanger sequencing analysis. Allele conversion efficiency was quantified with the percentage of GFP+RFP− individuals carrying Q224 edit.

Allelic competition cage experiments

An allele competition cage trial was conducted to test fitness cost among three FREP1 allelic variants, including FREP1RFP-Q, FREP1GFP-Q and FREP1GFP-L. Intercrosses were performed between pairs of these three transgenic lines to generate transheterozygous mosquitoes for seeding (1:1 allele frequency). Triplicate cages were seeded with 30 randomly selected mosquito couples consisting of age-matched (5 days) F_1 transheterozygous adults, resulting in 50% frequency for each allele. Cages were blood fed 3 days after seeding to stimulate oviposition. Allele frequencies were calculated by counting the fluorescence marker or targeted NGS analysis at 10 consecutive generations. Half of the progeny were passed to the next generation for each generation, and the other half were used for allele frequency quantification.

Multi-generational cage experiments

We set up non-overlapping cage trials to test the performance of the linked allelic-drive in combination with the congenic IE1-GFP intronic insertion allele using the cross scheme as illustrated in Fig. 4e to generate the F_1 transheterozygous carrying vasa-Cas9, FREP1RFP-gRNA-Q and FREP1GFP-L, with the latter being used as the receiver chromosome. Note that the donor and receiver chromosomes share over 1.2 kb of homology on the intronic side of the gRNA cut site, as well as continuous homology on the other side following the 224 codon. These transheterozygous were then seeded with homozygous FREP1GFP-L at 1:1 ratio (randomly selected 25 transheterozygous females, 25 transheterozygous males, 25 FREP1GFP-L females and 25 FREP1GFP-L males), resulting in a 1:3 (FREP1RFP-gRNA-Q:FREP1GFP-L) allelic seeding ratio. To avoid mating bias, all adults were aged for 5 days before seeding and blood meals were offered 3 days after seeding. In each generation, 300 L_1–L_2 larvae (L_1 denotes the first instar larvae) were randomly selected and reared to adults for establishing the next generation, another 300 L_1–L_2 larvae were selected for rearing to adulthood and next-generation deep sequencing analysis of the receiver allele (using a PCR amplification with the SeqF GFP-specific primer as indicated in Fig. 4a). Approximately 1,000 L_4 larvae were also randomly selected for phenotyping by scoring the fluorescence marker (except for generation 1, some of the cages produced less than 1,000 eggs), and the rest of the larvae were counted for population size at L_4. Total allelic frequencies as indicated in Fig. 4e,h were calculated by weighting the frequencies of receiver-specific allelic frequencies determined by NGS based on the proportions of individuals displaying donor (RFP+) versus receiver (GFP+) chromosome phenotypes.

As presented in Extended Data Fig. 9, multi-generational cage experiments were also performed using a WT receiver chromosome (Extended Data Fig. 9a), in which homozygous mosquitoes for the FREP1RFP-gRNA-Q intronic cassette were crossed to a vasa-Cas9 strain carrying the WT L224 allele. Transheterozygous vasa-Cas9/+; FREP1RFP-gRNA-Q/WT-L224 mosquitoes were then used for seeding cages at the same allele frequency as that used in the congenic experiments shown in Fig. 4. Note that in this case, there was only 126 bp of homology between the donor and receiver chromosomes in contrast to the extended homology present for the congenic experiment shown in Fig. 4 (pink boxes in Extended Data Fig. 9b).

Targeted NSG

Genomic DNA was extracted from 20 randomly selected mosquitoes with DNeasy Blood & Tissue Kits according to the manufacturer (Qiagen), followed by column purification and ready for PCR amplification. About 300 ng genomic DNA was used for PCR amplification with gene-specific primers, each containing deep sequencing adaptors at the 5′-terminal (Supplementary Table 5). The NGS DNA libraries were prepared with two rounds of PCR, and then subjected to 100-bp paired-end high-throughput sequencing with IGM (Institute of Genomic Medicine, University of California, San Diego) as we have previously published[59]. Raw reads were demultiplexed using the Barcode Splitter Script by IGM, then analysed with DSB classifiers that we have previously published using RStudio (v4.1.0)[59].

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

All plasmid sequences have been uploaded to the NCBI and are available online with the accession numbers: PP813873, PP813874, PP813875 and PP828956. NGS data have been deposited in the GenBank Sequence Read Archive database with the accession number PRJNA1112832. Source data have been provided for all raw data and model-fitting data generated in this study. NGS data were analysed by our previously published R program[59]. Source data are provided with this paper.

Code availability

The code for mathematical modelling is available from the public data repository in GitHub (https://github.com/lambsUSP/FREP1).

References

1. World Malaria Report 2024: Addressing Inequity in the Global Malaria Response (World Health Organization, 2024).

2. Zhang, G. et al. Anopheles midgut FREP1 mediates Plasmodium invasion. J. Biol. Chem. 290, 16490–16501 (2015).

3. Li, J. et al. Genome-block expression-assisted association studies discover malaria resistance genes in Anopheles gambiae. Proc. Natl Acad. Sci. USA 110, 20675–20680 (2013).

4. Unwin, H. J. T., Sherrard-Smith, E., Churcher, T. S. & Ghani, A. C. Quantifying the direct and indirect protection provided by insecticide treated bed nets against malaria. Nat. Commun. 14, 676 (2023).

5. Wang, S. & Jacobs-Lorena, M. Genetic approaches to interfere with malaria transmission by vector mosquitoes. Trends Biotechnol. 31, 185–193 (2013).

6. Dong, Y., Simões, M. L. & Dimopoulos, G. Versatile transgenic multistage effector-gene combinations for Plasmodium falciparum suppression in Anopheles. Sci. Adv. 6, eaay5898 (2020).

7. Hoermann, A. et al. Gene drive mosquitoes can aid malaria elimination by retarding Plasmodium sporogonic development. Sci. Adv. 8, eabo1733 (2022).

8. Gantz, V. M. et al. Highly efficient Cas9-mediated gene drive for population modification of the malaria vector mosquito Anopheles stephensi. Proc. Natl Acad. Sci. USA 112, E6736–E6743 (2015).

9. James, A. A. Gene drive systems in mosquitoes: rules of the road. Trends Parasitol. 21, 64–67 (2005).

10. Adolfi, A. et al. Efficient population modification gene-drive rescue system in the malaria mosquito Anopheles stephensi. Nat. Commun. 11, 5553 (2020).

11. Collins, F. H. et al. Genetic selection of a Plasmodium-refractory strain of the malaria vector Anopheles gambiae. Science 234, 607–610 (1986).

12. Simões, M. L., Dong, Y., Mlambo, G. & Dimopoulos, G. C-type lectin 4 regulates broad-spectrum melanization-based refractoriness to malaria parasites. PLoS Biol. 20, e3001515 (2022).

13. Dong, Y., Simões, M. L., Marois, E. & Dimopoulos, G. CRISPR/Cas9-mediated gene knockout of Anopheles gambiae FREP1 suppresses malaria parasite infection. PLoS Pathog. 14, e1006898 (2018).

14. Isaacs, A. T. et al. Engineered resistance to Plasmodium falciparum development in transgenic Anopheles stephensi. PLoS Pathog. 7, e1002017 (2011).

15. Niu, G. et al. Targeting mosquito FREP1 with a fungal metabolite blocks malaria transmission. Sci. Rep. 5, 14694 (2015).

16. Moreira, L. A. et al. Bee venom phospholipase inhibits malaria parasite development in transgenic mosquitoes. J. Biol. Chem. 277, 40839–40843 (2002).

17. Dong, Y. et al. Engineered anopheles immunity to Plasmodium infection. PLoS Pathog. 7, e1002458 (2011).

18. Kang, S., Shields, A. R., Jupatanakul, N. & Dimopoulos, G. Suppressing dengue-2 infection by chemical inhibition of Aedes aegypti host factors. PLoS Negl. Trop. Dis. 8, e3084 (2014).

19. Gantz, V. M. & Akbari, O. S. Gene editing technologies and applications for insects. Curr. Opin. Insect Sci. 28, 66–72 (2018).

20. Osta, M. A., Christophides, G. K. & Kafatos, F. C. Effects of mosquito genes on Plasmodium development. Science 303, 2030–2032 (2004).

21. Isaacs, A. T. et al. Transgenic Anopheles stephensi coexpressing single-chain antibodies resist Plasmodium falciparum development. Proc. Natl Acad. Sci. USA 109, E1922–E1930 (2012).

22. Carballar-Lejarazú, R. et al. Dual effector population modification gene-drive strains of the African malaria mosquitoes, Anopheles gambiae and Anopheles coluzzii. Proc. Natl Acad. Sci. USA 120, e2221118120 (2023).

23. Dilani, P. V. D., Dassanayake, R. S., Tyagi, B. K. & Gunawardene, Y. I. N. S. The impact of transgenesis on mosquito fitness: a review. Front. Insect Sci. 2, 957570 (2022).

24. Marrelli, M. T., Moreira, C. K., Kelly, D., Alphey, L. & Jacobs-Lorena, M. Mosquito transgenesis: what is the fitness cost? Trends Parasitol. 22, 197–202 (2006).

25. Abraham, E. G. et al. Driving midgut-specific expression and secretion of a foreign protein in transgenic mosquitoes with AgAper1 regulatory elements. Insect Mol. Biol. 14, 271–279 (2005).

26. Carballar-Lejarazú, R. et al. Next-generation gene drive for population modification of the malaria vector mosquito, Anopheles gambiae. Proc. Natl Acad. Sci. USA 117, 22805–22814 (2020).

27. Bennink, S., Kiesow, M. J. & Pradel, G. The development of malaria parasites in the mosquito midgut. Cell. Microbiol. 18, 905–918 (2016).

28. Dong, S., Dong, Y., Simões, M. L. & Dimopoulos, G. Mosquito transgenesis for malaria control. Trends Parasitol. 38, 54–66 (2022).

29. Dong, Y. et al. Anopheles gambiae immune responses to human and rodent Plasmodium parasite species. PLoS Pathog. 2, e52 (2006).

30. Dong, Y. & Dimopoulos, G. Anopheles fibrinogen-related proteins provide expanded pattern recognition capacity against bacteria and malaria parasites. J. Biol. Chem. 284, 9835–9844 (2009).

31. Symington, L. S. & Gautier, J. Double-strand break end resection and repair pathway choice. Annu. Rev. Genet. 45, 247–271 (2011).

32. Sfeir, A. & Symington, L. S. Microhomology-mediated end joining: a back-up survival mechanism or dedicated pathway? Trends Biochem. Sci. 40, 701–714 (2015).

33. Bazzano, D., Lomonaco, S. & Wilson, T. E. Mapping yeast mitotic 5′ resection at base resolution reveals the sequence and positional dependence of nucleases in vivo. Nucleic Acids Res. 49, 12607–12621 (2021).

34. Cejka, P. & Symington, L. S. DNA end resection: mechanism and control. Annu. Rev. Genet. 55, 285–307 (2021).

35. Yannuzzi, I., Butler, M. A., Fernandez, J. & Larocque, J. R. The role of Drosophila CtIP in homology-directed repair of DNA double-strand breaks. Genes 12, 1430 (2021).

36. Xi, Z., Das, S., Garver, L. & Dimopoulos, G. Protocol for Plasmodium falciparum infections in mosquitoes and infection phenotype determination. J. Vis. Exp. 5, 222 (2007).

37. Kanatani, S., Stiffler, D., Bousema, T., Yenokyan, G. & Sinnis, P. Revisiting the Plasmodium sporozoite inoculum and elucidating the efficiency with which malaria parasites progress through the mosquito. Nat. Commun. 15, 748 (2024).

38. Niu, G. et al. The fibrinogen-like domain of FREP1 protein is a broad-spectrum malaria transmission-blocking vaccine antigen. J. Biol. Chem. 292, 11960–11969 (2017).

39. Xu, X. et al. Active-genetic neutralizing elements for halting or deleting gene-drives. Mol. Cell 80, 246–262 (2020).

40. Zhang, G., Niu, G., Perez, L., Wang, X. & Li, J. Malaria transmission assisted by interaction between Plasmodium α-tubulin-1 and Anopheles FREP1 protein. Preprint at bioRxiv https://doi.org/10.1101/2019.12.16.878082.

41. Corby-Harris, V. et al. Activation of Akt signaling reduces the prevalence and intensity of malaria parasite infection and lifespan in Anopheles stephensi mosquitoes. PLoS Pathog. 6, e1001003 (2010).

42. Guichard, A. et al. Efficient allelic-drive in Drosophila. Nat. Commun. 10, 1640 (2019).

43. Kaduskar, B. et al. Reversing insecticide resistance with allelic-drive in Drosophila melanogaster. Nat. Commun. 13, 291 (2022).

44. Bier, E. Gene drives gaining speed. Nat. Rev. Genet. 23, 5–22 (2022).

45. Gantz, V. M. & Bier, E. The mutagenic chain reaction: a method for converting heterozygous to homozygous mutations. Science 348, 442–444 (2015).

46. Li, Z. et al. CopyCatchers are versatile active genetic elements that detect and quantify inter-homolog somatic gene conversion. Nat. Commun. 12, 2625 (2021).

47. Terradas, G. et al. Inherently confinable split-drive systems in Drosophila. Nat. Commun. 12, 1480 (2021).

48. Terradas, G., Bennett, J. B., Li, Z., Marshall, J. M. & Bier, E. Genetic conversion of a split-drive into a full-drive element. Nat. Commun. 14, 191 (2023).

49. DiCarlo, J. E., Chavez, A., Dietz, S. L., Esvelt, K. M. & Church, G. M. Safeguarding CRISPR–Cas9 gene drives in yeast. Nat. Biotechnol. 33, 1250–1255 (2015).

50. Hammond, A. et al. A CRISPR–Cas9 gene drive system targeting female reproduction in the malaria mosquito vector Anopheles gambiae. Nat. Biotechnol. 34, 78–83 (2016).

51. Kyrou, K. et al. A CRISPR–Cas9 gene drive targeting doublesex causes complete population suppression in caged Anopheles gambiae mosquitoes. Nat. Biotechnol. 36, 1062–1066 (2018).

52. Walter, M. & Verdin, E. Viral gene drive in herpesviruses. Nat. Commun. 11, 4884 (2020).

53. Valderrama, J. A., Kulkarni, S. S., Nizet, V. & Bier, E. A bacterial gene-drive system efficiently edits and inactivates a high copy number antibiotic resistance locus. Nat. Commun. 10, 5276 (2019).

54. Auradkar, A., Corder, M. R., Marshall, M. J. & Bier, E. A self-eliminating allelic-drive reverses insecticide resistance in Drosophila leaving no transgene in the population. Nat. Commun. 15, 9961 (2024).

55. López Del Amo, V. et al. A transcomplementing gene drive provides a flexible platform for laboratory investigation and potential field deployment. Nat. Commun. 11, 352 (2020).

56. Nash, A. et al. Integral gene drives for population replacement. Biol. Open 8, bio037762 (2018).

57. Nash, A., Capriotti, P., Hoermann, A., Papathanos, P. A. & Windbichler, N. Intronic gRNAs for the construction of minimal gene drive systems. Front. Bioeng. Biotechnol. 10, 857460 (2022).

58. Chakraborty, M. et al. Hidden features of the malaria vector mosquito, Anopheles stephensi, revealed by a high-quality reference genome. BMC Biol. 19, 28 (2021).

59. Li, Z. et al. Developmental progression of DNA double-strand break repair deciphered by a single-allele resolution mutation classifier. Nat. Commun. 15, 2629 (2024).

Acknowledgements

We are grateful to A. A. James for sharing the vasa-Cas9 transgenic line and WT A. stephensi line; all members of the E. Bier laboratory for discussions and constructive suggestions on the manuscript; and the Johns Hopkins Malaria Research Institute Parasite and Insectary core facilities for P. falciparum gametocyte cultures and mosquito-rearing equipment. All the NGS was conducted at the IGM Genomics Center, University of California, San Diego. This publication includes data generated at the UC San Diego IGM Genomics Center utilizing an Illumina NovaSeq 6000 that was purchased with funding from a National Institutes of Health SIG grant (#S10 OD026929). Funding was provided by the Bill and Melinda Gates Foundation INV-036579 (to E.B.), INV-043645 (to G.D.), INV-017683 and INV-078535 (to J.M.M.); National Institutes of Health grants R01GM117321, R01GM144608, R01AI162911 (to E.B.), R01AI170692 and R01AI158615 (to G.D.) and R01AI143698 (to J.M.M.); Howard Hughes Medical Institutes grant 90101319 (to G.D.); Bloomberg Philanthropies (to G.D.); and E.B. was supported in part by grant number GV673605686 from Open Philanthropy.

Author information

Author notes

1. These authors contributed equally: Zhiqian Li, Yuemei Dong

Authors and Affiliations

1. Department of Cell and Developmental Biology, University of California, San Diego, La Jolla, CA, USA

Zhiqian Li, Lang You, Jemariz Arzobal, Audrey Yeun, Lei Yang & Ethan Bier

2. Tata Institute for Genetics and Society, University of California, San Diego, La Jolla, CA, USA

Zhiqian Li, Lang You, Lei Yang & Ethan Bier

3. Department of Molecular Microbiology and Immunology, Johns Hopkins Malaria Research Institute, Johns Hopkins University, Bloomberg School of Public Health, Baltimore, MD, USA

Yuemei Dong & George Dimopoulos

4. Department of Parasitology, Institute of Biomedical Sciences, University of São Paulo, São Paulo, Brazil

Rodrigo M. Corder

5. Divisions of Biostatistics and Epidemiology, School of Public Health, University of California, Berkeley, CA, USA

John M. Marshall

6. Innovative Genomics Institute, Berkeley, CA, USA

John M. Marshall

Contributions

Z.L., E.B. and G.D. conceptualized the study. Z.L. and Y.D. provided the methodology. J.M.M. and R.M.C. performed the modelling. Z.L., Y.D., L. You, J.A., A.Y., L. Yang and R.M.C. undertook the investigation. Z.L. and Y.D. performed the vizualization. E.B. and G.D. acquired funding. Z.L., E.B. and G.D. wrote the original draft of the manuscript. Z.L., Y.D., L. You, L. Yang, J.A., G.D., J.M.M. and R.M.C. reviewed and edited the manuscript.

Corresponding authors

Correspondence to George Dimopoulos or Ethan Bier.

Ethics declarations

Competing interests

E.B. has an equity interest in Synbal and Agragene, companies that may potentially benefit from the research results; and serves on the Board of Directors and Scientific Advisory Board for the companies. The terms of this arrangement have been reviewed and approved by the University of California, San Diego in accordance with its conflict of interest policies. The other authors declare no competing interests.

Peer review

Peer review information

Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Multiple protein sequences alignment by CLUSTALW.

a, Protein sequences alignment of FREP1 orthologs from An. stephensi and An. gambiae. b, Protein sequences alignment of two distantly related FREP1 paralogs from An. stephensi. Consensus amino acids are colored purple. The black rectangle in panel a indicates the conserved fibrinogen-like domain and the red rectangle denotes the Leucine residue for editing. Gene accession numbers are labeled on the left and the numbers on the right indicate the number of amino acid residues.

Extended Data Fig. 2 Genotyping of F[1] transformants.

F_1 transformants were collected for genotyping after egg laying using primer sets amplifying sequences outside the two homology arms. The alignment displays partial FREP1 locus sequences focused on the L224 amino acid. Amino acids are labeled with different colors and the T->A single nucleotide edit that recodes the L224 to Q224 is indicated in red. The reference WT sequence is shown on the top. Both female and male F_1 transformants were used for genotyping.

Extended Data Fig. 3 Life spans of three FREP1 allelic variants compared to WT An. stephensi and vasa-Cas9 strains.

a, Life span of females that were maintained with a 10% sucrose solution. b, Life span of males maintained on a 10% sucrose solution. c, Life span of females after mating and blood feeding. Red arrow indicates blood meal applied. The mean values calculated from three replicated cages are shown. In a-c, n = 3 biologically independent replicates, statistical significance was calculated by Kaplan-Meier survivability analysis with pooled data from three biological replicates. Error bars are mean ± S.D. The X-axis represents days after adult emergence, and the Y-axis indicates the percentage of surviving adults. d, Pupation time of FREP1 transgenic lines. e, Pupation rate. f, Adults emergence rate of female and male pupae. For d-f, statistical significance was calculated with an Ordinary One-way ANOVA multiple comparison tests and adjusted p-values shown in the Source Data. n = 3 biologically independent replicates for the experiments, and error bars indicate mean ± S.D., with ns: no significance, P > 0.05, *: 0.01 < P < 0.05, **: 0.001 < P < 0.01. Cas9: vasa-Cas9, GFP-L: FREP1GFP-L; GFP-Q: FREP1GFP-Q; RFP-Q: FREP1RFP-Q.

Source data

Extended Data Fig. 4 FREP1[Q] mosquitoes are resistant to P. falciparum at both low and high parasite infection levels.

a, Prevalence of P. falciparum (NF54) oocysts in response to infections at low infection level (0.08% gametocytemia). b, Infection intensities of P. falciparum (NF54) oocysts in WT, vasa-Cas9, and three FREP1 transgenic mosquitoes at a low infection intensity. c, d, Prevalence (c) and infection intensities (d) of P. falciparum (NF54) sporozoites at a low infection intensity. e-h, Prevalence and infection intensities with P. falciparum (NF54) oocysts (e and f) and sporozoites (g and h) at a high infection intensity (0.15% gametocytemia). At least 40 successfully infected female mosquitoes were randomly selected and dissected for counting oocysts in the midgut or sporozoites in the salivary glands. All mosquitoes counted from the same line were pooled for display, with each single dot representing the parasite load from the individual dissected midgut or a pair of salivary glands. The horizontal lines in panels b, d, f, and h denote median values. Two-tailed Mann-Whitney U test was used to calculate P values. n indicated the total pooled number of individual mosquito midguts or salivary glands measured. All parasite challenge assays were conducted with at least three independent biological replicates. Cas9: vasa-Cas9, GFP-L: FREP1GFP-L; GFP-Q: FREP1GFP-Q; RFP-Q: FREP1RFP-Q. The statistical details were included in Supplementary Tables 1–4.

Source data

Extended Data Fig. 5 Screening for efficient allelic gRNAs.

a, Editing efficiency of three potential candidate allelic gRNAs targeting the FREP1 L224 site. Mosquito embryos were collected for microinjection with Cas9 protein and in vitro synthesized gRNA for microinjection. Two days old larvae hatched after microinjection were collected and pooled together for NGS to test gRNA cutting efficiencies. The graph shows the percentage of mutant indels enumerated below each bar. Gray bars represent WT alleles, and purple bars represent indels. b, Top mutant alleles generated with the gRNAL224. The plot shows a 38 bp reference sequence window centered by the expected gRNA cleavage site. The gray rectangle on the top row marks the protospacer, and PAM is marked with a red rectangle. The vertical gray line shows the expected DSB cutting site. Gray rectangles below the reference sequence are targeted genomic DNA loci, and blue rectangles show editing windows. Insertion alleles are marked with red diamonds. The left side displays the allelic read ratio (%), and the right shows the number of nucleotides that were deleted by color-coded allelic categories (see key below).

Source data

Extended Data Fig. 6 Phenotype of F[2] progeny generated from crosses between FREP1RFP-Q and vasa-Cas9 strains.

a, b, F_2 progeny phenotyping results display the fraction of total F_2 progeny carrying RFP or CFP fluorescence: a, crosses using F_1 trans-heterozygous males. b, Crosses using F_1 trans-heterozygous females. Data display the results from two reciprocal F_0 crosses: F_0 vasa-Cas9 males are crossed with FREP1RFP-Q females or reciprocally, F_0 vasa-Cas9 females are crossed with FREP1RFP-Q males. Fractions of each phenotype (%) are indicated beneath each bar. Pink bars = RFP fluorescence and cyan bars = CFP. Three replicates were conducted for each cross. c, d, The ratio of population size between RFP and CFP phenotypes from F_2 progeny. e, f, Fractions of indicated phenotypes in F_2 progeny. Phenotyping was conducted by counting the presence of fluorescence markers either with whole-body RFP (marks FREP1RFP-gRNA-Q chromosome with IE1-RFP) or eye-specific CFP (marks vasa-Cas9 with 3xP3-CFP). The total number of counted F_2 progeny and the detailed cross information are listed at the bottom table.

Source data

Extended Data Fig. 7 Cross scheme.

vC9 stands for vasa-Cas9, NHEJ: Non-homologous end joining.

Extended Data Fig. 8 DNA sequencing traces illustrating germline repair events that occurred on the target chromosome in the germline.

Traces display DNA sequences flanking the gRNAL224 cleavage point. Single F_2 progeny carrying only vasa-Cas9 (3xP3-CFP) were used for targeted amplification and Sanger sequencing. Three categories of DSB repair events are displayed: WT, HDR, and NHEJ (11nt, 6nt, and 10nt deletions, respectively). The top line shows the gRNAL224 target marked with red arrowheads, followed by translated amino acids. DNA sequences flanking the gRNAL224 target show the repair template or sequences from the donor chromosome at FREP1 loci. The T->A and C->T edits were shown with red letters.

Extended Data Fig. 9 Non-overlapping multi-generational cage trial with a WT population.

a, Genetic crossing scheme used to generate F_1 trans-heterozygous for seeding the cage experiments. b, Comparison of homology pairing between donor and receiver chromosomes in different linked allelic-drive configurations. The donor driving cassette is placed either in trans to the WT L224 allele (top panel) or to the FREP1GFP-L allele as shown in Fig. 4e–h (bottom panel). Pink boxes depict regions of the homology pairing on the intronic side of the gRNA cut site that are shared between the donor and receiver chromosomes. On the intronic side of the WT L224 allele, there is only a shortened homology of 126 bp (indicated by the narrow red bar) shared with the drive cassette resulting in frequent error-prone DSB repair and generation of damaged target alleles. In contrast, the congenic experiments presented in Fig. 4 involve a much longer (>1.2 kb, indicated by wide red bar) span of homology between the two parental chromosomes. Gray lines: genomic DNA at FREP1 locus, purple boxes: exons, cyan narrow rectangle: Q224 residue, gray narrow rectangle: WT L224 residue, black narrow rectangle: non-synonymous cleavage-resistant residue. c, The frequency of individuals carrying each fluorescence marker phenotype (RFP for the gRNA cassette and GFP for the Cas9 cassette) is plotted over 10 generations. The frequency of both the FREP1RFP-gRNA-Q (pink lines) and vasa-Cas9 (cyan lines) alleles drops rapidly in the first generation due to a high rate of target chromosome damage and consequent lethality of a significant fraction of such progeny (see above), but then stabilizes as the frequency of progeny carrying both the gRNA and Cas9 encoding cassette drops to a low level (1–2%, see Source Data). Three replicate cages (R1-R3) were run at the same time under the identical conditions.

Source data

Supplementary information

Supplementary Information

Supplementary Method, Supplementary Results, Supplementary Discussion, Supplementary Tables 1–11

Reporting Summary

Source data

Source Data Fig. 2, 3, 4 and Source Data Extended Data Fig. 3, 4, 5, 6, 9

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Li, Z., Dong, Y., You, L. et al. Driving a protective allele of the mosquito FREP1 gene to combat malaria. Nature 645, 746–754 (2025). https://doi.org/10.1038/s41586-025-09283-6

- Received: 20 June 2024

- Accepted: 12 June 2025

- Published: 23 July 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09283-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Reagent-free detection of Plasmodium falciparum malaria infections in field-collected mosquitoes using mid-infrared spectroscopy and machine learning

Article Open access 27 May 2024

Efficient population modification gene-drive rescue system in the malaria mosquito Anopheles stephensi

Article Open access 03 November 2020

A single-cell atlas of Plasmodium falciparum transmission through the mosquito

Article Open access 27 May 2021

Article Open access Published: 10 September 2025

Fluctuating DNA methylation tracks cancer evolution at clinical scale

Calum Gabbutt,

Martí Duran-Ferrer,

Heather E. Grant,

Diego Mallo,

Ferran Nadeu,

Jacob Househam,

Neus Villamor,

Madlen Müller,

Simon Heath,

Emanuele Raineri,

Olga Krali,

Jessica Nordlund,

Thorsten Zenz,

Ivo G. Gut,

Elias Campo,

Armando Lopez-Guillermo,

Jude Fitzgibbon,

Chris P. Barnes,

Darryl Shibata,

José I. Martin-Subero &

…

Trevor A. Graham

Nature volume 645, pages 764–773 (2025)

Abstract

Cancer development and response to treatment are evolutionary processes1,2, but characterizing evolutionary dynamics at a clinically meaningful scale has remained challenging[3]. Here we develop a new methodology called EVOFLUx, based on natural DNA methylation barcodes fluctuating over time[4], that quantitatively infers evolutionary dynamics using only a bulk tumour methylation profile as input. We apply EVOFLUx to 1,976 well-characterized lymphoid cancer samples spanning a broad spectrum of diseases and show that initial tumour growth rate, malignancy age and epimutation rates vary by orders of magnitude across disease types. We measure that subclonal selection occurs only infrequently within bulk samples and detect occasional examples of multiple independent primary tumours. Clinically, we observe faster initial tumour growth in more aggressive disease subtypes, and that evolutionary histories are strong independent prognostic factors in two series of chronic lymphocytic leukaemia. Using EVOFLUx for phylogenetic analyses of aggressive Richter-transformed chronic lymphocytic leukaemia samples detected that the seed of the transformed clone existed decades before presentation. Orthogonal verification of EVOFLUx inferences is provided using additional genetic data, including long-read nanopore sequencing, and clinical variables. Collectively, we show how widely available, low-cost bulk DNA methylation data precisely measure cancer evolutionary dynamics, and provides new insights into cancer biology and clinical behaviour.

Similar content being viewed by others

Main

Cancer development is an evolutionary process1,2; consequently, the evolutionary history of a cancer may set its future trajectory and allow inference of the clinical path of a patient[5]. However, testing this hypothesis directly is challenging because longitudinal patient samples are required to document evolutionary history. Consequently, evolutionary histories are typically inferred from single timepoint data; for example, somatic (epi)mutations are patterned in distinctive ways by differing evolutionary dynamics[3]. In the haematological system, genome sequencing of single cells or single-cell colonies have been used to infer the phylogenetic relationships among cells6,7,8. The expense of this approach has restricted analyses to small numbers of cases, limiting suitability for clinical translation.

DNA methylation can serve as a lineage marker, recording the clonal architecture of cell populations9,10,11,12,13 or the proliferative history14,15. We have recently identified DNA methylation at some CpG sites, which stochastically fluctuates over time at a timescale measured in years[4]. These fluctuating CpGs (fCpGs) function as a ‘methylation barcode’, providing a low-cost strategy to provide high temporal resolution lineage tracing in patient samples[4]. In this study, we constructed a quantitative modelling framework called evolutionary inference using fluctuating methylation (EVOFLUx). This framework enables precise quantitative inference of the evolutionary history of cancer cells from input fCpG data derived from clinical specimens, at scale (Fig. 1a).

Fig. 1: Selection and characterization of fCpG loci.

a, Schematic representing the study design. Bulk cancer tissue samples were collected, DNA extracted and methylation arrays were performed. Evolutionary dynamics were inferred and these were correlated with clinical variables and outcomes. The illustrations of the body, tumour, eppendorf tube and machine were reproduced courtesy of NIAID. The illustration of the physician was adapted from Science Figures, under an Open Design Licence 1.0. The illustration of the screen was created by Simon Dürr under a CC0 1.0 licence. b, fCpG methylation patterns reflect population evolutionary dynamics. Three scenarios are depicted: in a polyclonal population with a distant MRCA, diverse fCpG methylation (unmethylated in white, heterozygous in grey and methylated in black) results in a unimodal distribution of average methylation near the steady state (top). Following a recent clonal expansion (cell number 3 of the top panel), identical fCpG methylation across cells yields a characteristic ‘W-shape’ in the bulk methylation distribution (middle). Post-bottleneck, ongoing fluctuations generate diverse fCpG methylation patterns, changing the distribution of bulk methylation values (bottom). c, A hierarchically clustered heatmap of the 978 fCpGs identified in lymphoid cells (n = 2,204 samples). Magnified regions represent the homogeneous intermediate methylation pattern in normal lymphoid cells and the speckled pattern in cancer samples. PBMC, peripheral blood mononuclear cell; MGUS, monoclonal gammopathy of undetermined significance; MM, multiple myeloma; NOS, not otherwise specified; RT, Richter transformation. d, Example histograms of fCpG methylation distributions from healthy and neoplastic lymphoid cells (CLLs). e,f, Heatmaps showing the log_2 fold change (FC) in genomic locations (e) and chromatin status (f) of fCpGs compared with non-fCpGs. g, Comparison between fCpG-associated and non-fCpG-associated genes in a single CLL sample (left; P = 5.14 × 10−12, Wilcoxon test, sample SCLL-328), and expression of fCpG-associated genes separated by discretized allele methylation status (right; P values were determined by two-sided Wilcoxon test, no multiple correction; n = 505 for fCpG genes and n = 15,736 for non-fCpG genes). The boxplot centre shows the median, the box shows the quartiles and whiskers represent ±1.5× interquartile range (IQR). TPM, transcripts per million.

Source data

EVOFLUx works by considering the heterogeneity of fCpG methylation values within a sample. At a diploid locus, each fCpG can take one of three states: neither allele methylated, one allele methylated or both alleles methylated (0%, 50% or 100% methylated, respectively), so n fCpG sites can take 3n possible methylation patterns. fCpGs fluctuate methylation status independently, meaning that they function as an ‘evolving barcode’ to track clonal evolution: two somatic cells with close ancestry will share a near-identical pattern of fCpG methylation, whereas distantly related cells will have divergent fCpG methylation patterns (Fig. 1b). In bulk populations of clonal somatic cells, the dominant fCpG pattern represents the fCpG state of the founder cell of the population. Therefore, the precise distribution of fCpG methylation is determined by the evolutionary history of the population, meaning that mathematical modelling can be used to recover the evolutionary history of a sample from input fCpG data.

Here we focused on lymphoid neoplasms, which cover a broad spectrum of diseases and subtypes with highly variable clinicobiological features, from highly proliferative acute disease to indolent chronic leukaemia, arising in infants to older adults, with tumour samples across disease stages16,17. These tumours have been extensively profiled by DNA methylation arrays, which have provided insights into their cellular origin, pathogenesis and clinical behaviour[18]. Although their temporal clonal dynamics has been partially analysed in few patients19,20, their precise evolutionary histories remain poorly characterized. Applying EVOFLUx to 1,976 well-characterized lymphoid malignancies, we precisely measured individual tumour evolutionary history and show that these histories are associated with disease outcome.

Characterization of fCpGs in lymphoid cancers

We assembled bulk Illumina methylation array data of normal and neoplastic lymphoid cells from 2,430 samples14,21,22,23,24,25,26,27,28,29,30 (Methods; Supplementary Tables 1–3). Following quality control, we retained 2,204 samples from 2,054 patients and 389,180 CpGs. As fCpG loci are tissue specific[4], we constructed a pipeline to identify lymphoid-specific fCpGs (Methods; Extended Data Fig. 1a) using 1,471 samples from multiple lymphoid tumour entities (Supplementary Tables 1 and 2). We identified 978 pan-lymphoid cancer fCpGs (Supplementary Table 4). Methylation at fCpGs shows a characteristic ‘speckled’ pattern across cancers (Fig. 1c) because (de)methylation occurs independently in each tumour, in stark contrast to the orderly patterns observed for traditional methylation clocks or a random subset of CpGs (Extended Data Fig. 1b–d). fCpGs did not cluster the samples by disease (Fig. 1c), and there was also no clustering based on disease subtype or array platform (Extended Data Fig. 1e–i), except for some B and T cell acute lymphoblastic leukaemias (B/T-ALLs) and multiple myeloma cases that exhibited global hypermethylation or hypomethylation, respectively, as previously reported[14]. This is consistent with fCpGs behaving as a stochastic ‘barcode’ encoding lineage information. By comparison, methylation at CpGs excluded by our selection filters either did cluster by disease, had very low heterogeneity across samples or had unequal methylation and demethylation rates (Supplementary Figs. 1 and 2).

We then examined the methylation value distribution of these 978 fCpG in individual samples (Supplementary Table 5). In each cancer sample, the fCpGs followed a characteristic ‘W-shaped’ distribution that depicts the fCpG methylation pattern of the founder cell of the cancer sample (Fig. 1d). By contrast, the healthy B cell subpopulations, which were not included in the discovery set, had unimodal distributions with intermediate methylation levels consistent with these being polyclonal populations (that is, average of the three methylation states; Fig. 1d).

Methylation values across fCpGs were uncorrelated, except for a small number of fCpGs located within 1 kb of another fCpG (74 of 978; Extended Data Fig. 2a). In whole-genome bisulfite sequencing (WGBS) data of sorted bulk B and T cell populations[31], methylation at fCpG loci in these polyclonal normal samples was largely intermediate. Over a small window of 100 bp, as the distance from the fCpGs increased, an increasing fraction of the neighbouring CpGs were either hypermethylated or hypomethylated (Extended Data Fig. 2b). Together, these analyses suggest that the local 3D genome structure influences (de)methylation processes.

We sought to verify fCpGs as ‘evolving barcodes’. Analysis of fCpG methylation fluctuation over time confirmed that inter-patient fCpG heterogeneity was not caused by common single-nucleotide polymorphisms (SNPs; Methods; Extended Data Fig. 2c and Supplementary Fig. 3). We generated long-read nanopore sequencing[32] on normal B cells (n = 6) and matched chronic lymphocytic leukaemia (CLL)-Richter transformation samples (n = 2 pairs) to simultaneously detect genetic mutations and DNA methylation, and confirmed that fCpG methylation variation is not a consequence of underlying somatic mutation (Extended Data Fig. 2d and Supplementary Fig. 4). In matched data, fCpG methylation levels measured by bead array or long-read sequencing were highly concordant (Extended Data Fig. 2e), and similar excellent concordance was observed in additional WGBS data (Extended Data Fig. 2f). We constructed fCpG methylation haplotypes using long-read sequencing (Extended Data Fig. 2g) and additional single-cell reduced representation bisulfite sequencing[6], and detected lower intra-haplotype heterogeneity within CLL samples than normal B cell samples (Extended Data Fig. 2h and Supplementary Fig. 5), consistent with the leukaemia being a clonal expansion, whereas normal B cells are polyclonal.

We utilized somatic copy number alterations in 492 CLL and 85 mantle cell lymphoma (MCL) samples26,33 (Supplementary Tables 6 and 7) to distinguish between alleles and show the (de)methylation at fCpGs occurred independently on each allele (Extended Data Fig. 3a), despite copy number alterations being rare in our cohorts (Supplementary Fig. 6). Thus, fCpGs show independent ongoing allele-specific changes to methylation, uniquely labelling cell lineages.

As the DNA methylome is influenced by age[34], we tested whether fCpGs showed evidence of age-dependent epigenetic modulation. In normal blood samples, mean fCpG methylation was not correlated with age, suggesting that fluctuations continue throughout life, whereas fCpG methylation variance increased with age (Extended Data Fig. 3b and Supplementary Fig. 7). Variance is higher in samples where there has been a recent clonal expansion (that is, homozygous methylated or unmethylated alleles become more prominent; Extended Data Fig. 3c), suggesting that fCpGs were detecting age-related clonal expansions of cells of the haematopoietic system4,35,36.

We analysed the genomic features of fCpG sites. fCpGs were enriched on the shores of CpG islands (Fig. 1e), underrepresented in gene-associated regions (Extended Data Fig. 3d) and, notably, were distinct from CpGs used in other epigenetic clocks (Extended Data Fig. 3e and Supplementary Tables 8 and 9). At the chromatin level, fCpGs were enriched in normal and neoplastic B cell weak promoters and enhancers as well as H3K27me3-marked regions, and significantly underrepresented in active promoters and H3K36me3-marked regions (Fig. 1f). RNA-sequencing analysis of CLL samples demonstrated that genes associated with fCpGs have significantly lower expression levels (Fig. 1g and Extended Data Fig. 3f), with no association between fCpG methylation status and associated gene expression in matched cases (Fig. 1g). No correlation was observed between fCpG methylation and the expression of key DNA methylation modifier genes (Extended Data Fig. 3g). Pathway enrichment analysis revealed that fCpG-associated genes were underrepresented in pathways ubiquitously expressed across multiple tissue types but enriched in developmental pathways (Supplementary Tables 10 and 11). Although these results do not provide a detailed molecular understanding of the mechanisms underpinning fCpG fluctuation; together, they indicate that fCpGs tend to be located in silent regions of the genome and do not regulate transcription, so are likely to be neutral lineage markers.

EVOFLUx measures clonal evolution

We developed EVOFLUx, a stochastic mathematical modelling and Bayesian inference framework, to simulate how clonal evolution quantitatively determines fCpG methylation values and enable inference of evolutionary history of individual tumour samples (Fig. 2a).

Fig. 2: The EVOFLUx model accurately captures fCpG data patterns.

a, Schematic of the EVOFLUx method that simulates the evolutionary dynamics of a growing cancer. EVOFLUx relies on a mathematical model describing how the fCpG distributions vary with the evolutionary parameters of a cancer. The model is split into two phases: before the MRCA (τ) in which methylation changes occur in the single-cell lineage that is subsequently transformed, and following the MRCA in which the population grows exponentially (θ). At each time step, epigenetic switching is allowed to occur between the three possible states (rates μ, ν, γ and ζ). b,c, Simulated fCpG methylation distributions for cancer with a distant versus recent MRCA (b), and rapid versus slow growth (c). d, Fisher plot showing the change in the subclonal composition within a simulated set of longitudinal samples (top). Scatter plots showing the marginal fCpG methylation distribution between simulated pairwise longitudinal samples with the subclonal proportions depicted in each corresponding sample timepoint (n = 1,000 simulated fCpGs; bottom). Points in the scatter plot are coloured according to the difference in methylation between the first and the subsequent timepoints. e, Histogram overlaying the fCpG methylation distributions of data simulated at T1 (neutral) and T3 (subclonal; left), and comparison of the fraction of fCpGs at intermediate values between T1 and T3 (right; the P value was determined by chi-squared test).

Source data

EVOFLUx simulates the ongoing gain and loss of methylation at fCpGs within a lineage from the birth of a patient until the beginning of a cancer-associated clonal expansion at some specified time, and then continues to simulate methylation fluctuations within the growing population of cancer cells until the cancer sample was collected at time T (Methods; Fig. 2a and Supplementary Information). The key parameters in the model are:

- Cancer growth rate per year (θ), assuming an exponentially growing population.

- Cancer age, measured in terms of the age of the patient in years at the time the cancer started growing (τ).

- fCpG switching rates per allele per year. Four parameters corresponding to the four possible transitions between homozygous unmethylated, heterozygous methylated and homozygous methylated (μ, ν, γ and ζ).

By combining the cancer growth rate and age, the cancer effective population size (Ne) — the number of long-lived lineages in the cancer — is calculated as Ne = eθ(T −τ).

Computational simulations of the model recapitulated the observed W-shaped fCpG methylation distribution. Altering model parameters caused notable shifts in the distribution: increasing cancer age caused the flanking peaks of the W-shaped distribution to move towards the central peak, whereas slower growth broadened peak width (Fig. 2b,c). Hence, the distribution of fCpGs encoded the evolutionary history of a tumour.

We added simulations of a single advantageous subclone within the cancer (Methods). Sampling longitudinally from model simulations and comparing fCpG methylation between timepoints showed that subclone outgrowth was marked by the small number of fCpGs with distinct methylation status in the subclone, becoming detectable only when the subclone was sufficiently large (Fig. 2d,e).

EVOFLUx contained an extensive Bayesian inference method to learn model parameters from input fCpG methylation distribution data, accounting for tumour purity and the technical noise introduced by the methylation array (Methods; Fig. 3a). We generated simulated fCpG distributions with prespecified (that is, known) model parameters and validated the ability of EVOFLUx to accurately recover the ‘ground truth’ in these simulated data (Extended Data Fig. 4a,b and Supplementary Information), even when the assumptions underlying the method were weakened (Extended Data Fig. 4c–h and Supplementary Information).

Fig. 3: EVOFLUx reveals the evolutionary dynamics of lymphoid cancers.

a, Schematic showing the EVOFLUx Bayesian inference pipeline used to infer patient-specific tumour evolutionary history from input bulk methylation data, patient age and tumour purity. The illustration of human ageing was adapted from Pixabay under a CC0 1.0 licence. The illustration of the tumour was adapted courtesy of NIAID. b, Scatter plot of the inferred growth rate (θ) versus effective population size (Ne = eθ(T − τ)) per sample from patients with cancer, using the posterior median as a descriptive summary statistic of the probability distribution inferred for each evolutionary variable (n = 1,885 samples; coloured according to cancer type). c, Scatter plot of the inferred time since the MRCA (τ) versus the mean epigenetic switching rate (averaged across different rate parameters) per sample (n = 1,885 samples). d–f, Inferred growth rate (top) and effective population size (Ne; bottom) of individual cancer samples separated by molecular subtype in B-ALL (d; two-sided MWU test, n = 767 samples), MCL (e; two-sided MWU test, n = 126 samples) and CLL (f; two-sided MWU test, n = 702 samples). Differences between subtypes were tested using MWU tests, with Holm–Bonferroni corrections applied. In panel d, B-ALL cases with MLL rearranged had significantly higher growth rate than each of the other B-ALL subtypes (all P < 0.005); however, for ease of presentation, only the comparison with t(1;19) is shown here. cMCL, conventional MCL; nnMCL, non-nodal MCL. g, Inferred growth rate (top) and effective population size (bottom) for CLL cases with a TP53 driver mutation in each IGHV CLL subtype (two-sided MWU, n = 646 samples, multiple corrected using false discovery rate together with analysis of other driver mutations; Extended Data Fig. 7). WT, wild type. The boxplot centre shows the median, the box denotes the quartiles and whiskers represent ±1.5× IQR.

Source data

Evolution of lymphoid malignancies

We applied EVOFLUx to 1,976 samples of lymphoid cancers (including T-ALL, B-ALL, CLL, MCL, diffuse large B cell lymphoma (DLBCL) and multiple myeloma) and premalignant conditions (that is, monoclonal B cell lymphocytosis (MBL) and monoclonal gammopathy of undetermined significance) for which we had age and tumour cell purity information, to infer the individual growth rate of each cancer, time since the most recent common ancestor (MRCA) and epigenetic switching rates (Supplementary Table 12). Posterior distributions were well formed (Extended Data Fig. 5a) and posterior predictive distributions recapitulated the input data well (Extended Data Fig. 5b), emphasizing the excellent fit of the model to data. Inferred parameters were not significantly affected by tumour cell content of samples (Supplementary Fig. 8) or exclusion of copy number alteration-altered regions (Extended Data Fig. 5c–e and Supplementary Fig. 9). Most parameters were also insensitive to the number of fCpGs excluded (Extended Data Fig. 5f,g), except the effective population size (Extended Data Fig. 5h).

Paediatric ALL and adult lymphoid neoplasms exhibited markedly different evolutionary histories (Fig. 3b). ALLs demonstrated much higher growth rates (θ; Extended Data Fig. 6a; P = 9.3 × 10−306, Mann–Whitney U (MWU) test, Holm–Sidak correction), smaller effective population sizes (Ne; Extended Data Fig. 6b; P = 8.1 × 10−25) and shorter times since the MRCA (Extended Data Fig. 6c; P = 6.0 × 10−306) than other lymphoid malignancies. T-ALL grew faster than B-ALL (P = 0.0017, Holm–Sidak correction) and showed more homogenous growth rates (P = 0.00044, Levene test). In adult cancers, MBL (a precursor to CLL) displayed lower growth rates and longer time since the MRCA than CLL (Extended Data Fig. 6a,c; P = 9.7 × 10−10 and P = 9.9 × 10−13, respectively). DLBCL notably had the largest Ne despite comparable growth rates.

fCpG switching rates varied significantly across diseases, with paediatric ALLs showing much faster switching than adult malignancies (Fig. 3c and Extended Data Fig. 6d). Paediatric ALLs also demonstrated a strong positive correlation between fCpG switching rate and growth rate (Extended Data Fig. 6e; P = 2.4 × 10−98 and R^2 = 0.44 in B-ALL and P = 5.9 × 10−6 and R^2 = 0.22 in T-ALL) and a strong negative correlation with patient age (Extended Data Fig. 6f–k; P = 3.3 × 10−137 and R^2 = 0.56 in B-ALL and P = 3.6 × 10−18 and R^2 = 0.6 in T-ALL). These findings suggest that fCpG (de)methylation rates are decreased in adult lymphoid cancers.

In CLL, we estimated the ‘contemporary’ growth rate derived from multiple longitudinal clinical measurements of the lymphocyte count preceding treatment. The EVOFLUx inferred growth rate, which represents the rate of the initial clonal expansion of the disease, was moderately correlated with the contemporary growth rate (P = 2 × 10−5, R = 0.27; Extended Data Fig. 6l and Supplementary Fig. 10).

Evolution varies by cancer subtype

We examined how cancer evolutionary history related to molecular subtypes. In B-ALL, MLL-rearranged cases had a significantly higher growth rate (Fig. 3d; P = 1.3 × 10−13, MWU, 44.3 ± 6.1 versus 11.7 ± 0.2 per year (mean ± standard error)), but lower effective population size Ne (P = 3.7 × 10−7, 1.8 × 10^5 ± 0.2 × 10^5 versus 3.0 × 10^5 ± 0.06 × 10^5 cells) than the other subtypes, consistent with their distinct clinical behaviour[37]. In MCL, the generally more indolent leukaemic non-nodal MCL[26] had a lower growth rate (Fig. 3e; P = 1.1 × 10−3, 1.7 ± 0.1 versus 2.1 ± 0.1 per year) and Ne (P = 7.4 × 10−5, 4.7 × 10^5 ± 1.4 × 10^5 versus 1.5 × 10^6 ± 0.2 × 10^6 cells) than the more aggressive conventional MCL. In DLBCL transcriptomic subtypes[38], there was no significant differences, probably due to the smaller number of cases and the lower sample purity (Supplementary Fig. 11).

In CLL, two major molecular subtypes are defined based on the extent of somatic hypermutation in the heavy-chain variable region of the IG gene (IGHV): unmutated CLL (U-CLL) and mutated CLL (M-CLL). The more aggressive U-CLL subtype39,40 showed significantly higher growth rates (Fig. 3e; P = 1.3 × 10−32, 2.3 ± 0.04 versus 1.8 ± 0.02 per year) and larger Ne (P = 2.1 × 10−22, 7.2 × 10^5 ± 0.3 × 10^5 versus 4.1 × 10^5 ± 0.3 × 10^5 cells) than M-CLL, independent of tumour purity (Supplementary Fig. 12). Similar results were obtained when analysing its precursor condition MBL (Supplementary Fig. 12).

Patients with mutations in specific driver genes, such as TP53, are well known to have a worse prognosis[41]. We compared the inferred growth rates and effective population sizes accounting for IGHV status for the most prevalent driver genetic alterations in CLL: TP53, SF3B1, NOTCH1, ATM, POT1 and IGLV3-21R110, del(11)(q22.3), del(13)(q14.3), del(17)(p13.1) and trisomy 12 (Fig. 3g and Extended Data Fig. 7). Patients with M-CLL with TP53 mutations had a higher growth rate and effective population size (P = 0.030 and P = 0.036, respectively, MWU test, false discovery rate corrected; Fig. 3g). Trisomy 12 was associated with increased effective population size in both U-CLL and M-CLL (P = 0.036 and P = 0.036, respectively), but no difference in growth rate.

Most lymphoid cancers grow effectively-neutrally

As new advantageous subclones can arise during cancer evolution, we also examined subclonal architecture in our cohort. In CLL, a small fraction of cases presents two or more clones with independent origins[42]. In genetic data, subclonal, independent and monoclonal (Extended Data Fig. 8a) architectures are distinguishable by characteristic patterning of mutation allele frequencies43,44. Similarly, in fCpG data, clonal architectures are depicted by additional intermediate peaks in the methylation distribution (Fig. 2d,e). Simulations showed that subclone inference by EVOFLUx was limited to detect only strongly selected subclones arising at an intermediate timepoint in the history of the tumour (Supplementary Fig. 13 and Supplementary Information), for reasons analogous to limitations of subclone detection in genetic sequencing data[45]. We describe the evolution in tumours without detectable subclones as effectively-neutral.

Applying EVOLFUx in our cohort revealed that most cancers (1,610 of 1,976) showed no evidence of either subclonal or independent clones (Extended Data Fig. 8b and Supplementary Table 12). The frequency of subclone detection varied considerably between cancer types, ranging from over 30% in CLL (232 of 718) to less than 5% in DLBCL (1 of 57).

We verified EVOFLUx inferences with matched whole-exome sequencing (WES) data from 425 CLL cases (Supplementary Table 13). Using the MOBSTER subclonal deconvolution tool[43], subclones were detected in 78 of 425 cancers (Supplementary Table 14), and these cancers had significantly higher EVOLUFx subclonality weights (P = 2.0 × 10−4, MWU test; Extended Data Fig. 8c). MOBSTER was more likely to detect subclones in cancers with more mutations (Extended Data Fig. 8d), suggesting limited power to detect subclones in WES. We therefore obtained matched whole-genome sequencing (WGS) data for 127 CLL samples (Supplementary Table 15) and observed better agreement between EVOFLUx and MOBSTER subclone calls (P = 3.9 × 10−4; Extended Data Fig. 8e and Supplementary Table 16), in which MOBSTER subclone calls were then independent of single-nucleotide variant count (P > 0.05). A classifier to predict WGS subclone architecture using EVOFLUx outperformed a WES-based classifier (area under the curve (AUC) = 0.73 versus AUC = 0.62) and performed equivalently to a classifier using both EVOFLUx and WES (AUC = 0.74; Extended Data Fig. 8f). Hence, EVOFLUx was more effective at detecting ongoing subclonal selection than MOBSTER applied to WES data.

CLLs with two independent clonal origins were detected in 22 of 718 cases. Validation through comparing IG gene rearrangements from WES or WGS and RNA sequencing[46] (Supplementary Table 17) showed that patients with multiple IG gene rearrangements had elevated independent origin model weightings (Extended Data Fig. 8g; P = 0.028).

fCpGs record clonal dynamics over time

Some patients with CLL undergo Richter transformation, the emergence of an aggressive phenotype with dismal prognosis. We assembled longitudinal matched WGS and methylation data[27] for two patients with CLL developing Richter transformation followed for 19.5 and 14.5 years, respectively. WGS data provided ground-truth measurement of clonal evolution during the decades of longitudinal follow-up, which we contrasted with clonal inference from methylation data (Fig. 4a,b and Supplementary Table 18).

Fig. 4: fCpGs allow for phylogenetic reconstruction of longitudinal lymphoid cancer samples.

a,b, Timelines and Fisher plots derived from WGS of two patients with CLL with longitudinal samples, annotated with treatment received (top). The Richter-transformed clone is shown in puce. Scatter plots showing the marginal fCpG methylation distribution between pairwise samples from above (middle). The points are coloured according to the difference in methylation between the first and the subsequent timepoints. Reconstructed phylogenies of the relationship between samples, annotated with the sample timepoints (bottom). The black triangles represent the time that occurred since the MRCA (T − τ), taken as the posterior median from the single-sample EVOFLUx inferences. The methylation fraction of the 978 fCpG loci are presented as heatmaps (0% blue and 100% red). Benda.-Obi, bendamustine, obinutuzumab; CLB, chlorambucil; CLB-R, chlorambucil and rituximab; CP, cyclophosphamide and prednisone; R-CVP, rituximab, cyclophosphamide, vincristine and prednisone; RFCM, rituximab, fludarabine, cyclophosphamide and mitoxantrone. c, An example of longitudinal samples (SW-BCP-ALL-375) showing the development of the fCpG distribution from diagnostic B-ALL, through remission and relapse. d, Scatter plot showing the marginal fCpG methylation distribution between diagnosis and relapse from panel c.

Source data

In CLL case 12, between T1 and T2 (13.1 years), WGS data showed that a subclonal expansion occurred, and this was mirrored in fCpGs (Fig. 4a). In the short (1 month) period between T2 and T3, the patient received ibrutinib treatment, but there was no clonal expansion detected in WGS nor methylation data. The patient then received rituximab, cyclophosphamide, vincristine and prednisone (R-CVP) combination treatment, but by T4 (5.6 months after T3) presented a clinical manifestation of Richter transformation, and WGS showed that the Richter transformation clone had expanded to form 77% of the tumour. This very large clonal expansion was clearly evident in fCpG methylation data.

In CLL case 19, the initial samples at T1–T4 spanned a period of 7.1 years. WGS showed gradual expansion of a subclone that was mirrored in fCpG methylation data (Fig. 4b). At T5 (5.5 years later), there had been a large nested subclonal expansion detected by WGS that was also evident in fCpG data. At T6 (2.8 years later), the patient was diagnosed with Richter transformation. WGS showed near-fixation of the Richter transformation clone and there was a correspondingly stark signal in fCpG data.

We used EVOFLUX on these longitudinal fCpG methylation data to construct phylogenetic relationships between samples (Methods). In both cases, the phylogenies (Fig. 4a,b) showed that the Richter transformation clone diverged exceptionally early, roughly a decade before the MRCA of the samples containing non-transformed CLL cells (9 and 12 years for cases 12 and 19, respectively). This was consistent with our previous analysis of single-cell RNA sequencing and DNA sequencing that detected Richter transformation cells at low frequencies within the diagnostic CLL sample[27], but suggests, remarkably, that the initial Richter transformation divergence occurred well before diagnosis, over 30 years before the clinical presentation of Richter transformation.

We validated the fCpG phylogenetic inferences by comparing them with phylogenetic trees from matched WGS data[27] and comparing it with methylation data (Methods; Extended Data Fig. 9a,b). fCpGs exactly recapitulated the WGS tree topology and had highly similar branch lengths unlike other CpG sets (Supplementary Figs. 14–16). Hence, fCpGs are a high-resolution phylogenetic character.

We also performed phylogenetic analysis on B-ALL cases from diagnosis to relapse (Extended Data Fig. 9c–e). All relapse samples formed a separate clade from the initial diagnostic sample, suggesting a major treatment-induced evolutionary bottleneck. In patients with B-ALL with matched cancer–remission samples, we consistently observed that the W-shape (indicating a clonal expansion) was replaced by a unimodal distribution (indicating no clonal expansion) following successful treatment, with similar variance as normal blood (Extended Data Fig. 9f,g). In two patients with matched diagnosis, remission and relapse samples, we found that the unimodal fCpG distribution during remission was replaced with a W-shaped distribution at relapse similar in shape to the diagnostic sample, due to the clonal expansion driving recurrence (Fig. 4c and Extended Data Fig. 9h). Comparing the fCpG distributions between diagnostic versus relapse samples revealed subclonal evolution through treatment (Fig. 4d and Extended Data Fig. 9i).

Evolutionary history and clinical outcome

To investigate the relationship between the evolutionary history and future clinical trajectory of a cancer, we leveraged a series of 478 CLL cases with well-annotated follow-up data. Using univariate Cox models, we tested the effect of evolutionary parameters on time to first treatment (TTFT), which reflects the natural cancer biology, and then on overall survival, which is a more complex end point as it convolves disease biology with treatment responses.

In univariate analysis, faster growing CLLs had markedly shorter TTFT (Fig. 5a; P = 1.4 × 10−30, hazard ratio (HR) = 3.95) and worse overall survival (P = 0.0053, HR = 1.51). The Ne of a cancer did not have a strong effect on TTFT (P = 0.058, HR = 1.17), but was associated with shorter overall survival (P = 1.3 × 10−4, HR = 1.41). The patient age at the time of the MRCA of the CLL population was highly correlated with the age of the patient (Supplementary Fig. 17), so unsurprisingly, older patients had worse overall survival (P = 2.3 × 10−11, HR = 1.79). The decrease in risk of progression with cancer age (P = 3.8 × 10−17, HR = 0.65), measured by the time since the MRCA, was probably due to confounding with the growth rate, as these parameters were negatively correlated (Supplementary Fig. 17). The epigenetic switching rate parameters were largely uninformative of prognosis.

Fig. 5: The evolutionary history of a tumour is prognostic of clinical outcome.

a, Univariate survival analysis of the TTFT (blue) and overall survival (OS; red) in the discovery CLL cohort for evolutionary variables inferred via EVOFLUx. b, Kaplan–Meier curves comparing the TTFT between patients with high versus low inferred cancer growth rates, separated by IGHV mutational status. c, Multivariate Cox regression model of the TTFT shows that the cancer growth rate is significant when controlling for IGHV status, TP53 alterations and age at sampling. The error bars represent 95% confidence intervals. A log-rank test was used in the Kaplan–Meier curves and Wald tests for Cox models. A Schoenfeld residuals test was used to test proportional hazard assumptions. No multiple comparison adjustments were done.

Source data

As the growth rate was different between U-CLL and M-CLL (Fig. 5b), we analysed its prognostic impact within each group separately. Higher growth rates consistently correlated with shorter TTFT in both subtypes (Fig. 5b; P = 1.4 × 10−5 for M-CLL, P = 1.56 × 10−7 for U-CLL and overall P = 2.1 × 10−53). In a multivariate Cox regression model, growth rate maintained a strong independent prognostic impact as quantitative variable (P = 2.2 × 10−10, HR = 2.28) even when controlling for the IGHV mutational status and TP53 aberrations, as well as age (Fig. 5c). Of note, the effect of TP53 mutations on TTFT appeared mediated by increased growth rate. The cancer Ne was more significantly correlated with overall survival than the growth rate, and this effect was preserved in the U-CLL subtype (Extended Data Fig. 10a; P = 0.55 for M-CLL, P = 9.90 × 10−7 for U-CLL and overall P = 4.72 × 10−9) and in the multivariate setting with IGHV status, TP53 aberrations and age at sampling (Extended Data Fig. 10b; P = 0.025, HR = 1.33).

Although the inference of the evolutionary parameters on our initial cohort was wholly blinded to the clinical outcomes, we also validated our findings using a second independent cohort of 209 patients with CLL (135 untreated at sampling)28,29 (Supplementary Table 2). These results verified tumour initial growth rate as a predictor of TTFT (Extended Data Fig. 10c–e). Furthermore, the EVOFLUx-derived growth rate was prognostic even when controlling for the contemporary rate of change of lymphocyte counts (P = 0.018; Extended Data Fig. 10f).

These results demonstrate that the evolutionary parameters inferred from a cost-effective methylation array could have a direct clinical application by contributing to predict the clinical behaviour of patients with CLL independently from well-established prognostic variables.

Discussion

Our study establishes a computational framework called EVOFLUx, which enables quantitative measurement of the evolutionary history of human malignancies at massive scale using only widely available and low-cost bulk methylation data as input. Evolutionary histories are fundamentally distinct from characterizations of the contemporary phenotype of cancer cells, such as the fraction of proliferating cells. EVOFLUx methodology should also work identically for sequencing-based methods to measure methylation such as bifulfite-based47,48 and bisulfite-free approaches32,49 (for example, long-read nanopore), which show an excellent correlation with our array data. In theory, these methods allow for assessment of many more fCpGs, increasing inference accuracy. EVOFLUx should also be applicable to tumour-derived cell-free DNA extracted from blood.

Evolutionary histories are strongly associated with disease phenotype and clinical outcomes across lymphoid disease types. We consider this strong evidence that clonal evolution, the fundamental cellular process of disease development, underlies the clinical course of the disease. Consequently, we expect these results to generalize across all cancer types. We note that genome-wide DNA methylation analyses also measure other important biological features of a cancer (for example, molecular subtype[14]) that could be combined with EVOFLUx-based inference of evolutionary history to further improve the prognostic value of DNA methylation data.

In summary, we present a cost-effective high-throughput platform for measuring cancer evolutionary dynamics at the population scale in patient samples. These fundamental measurements of the disease biology hold substantial prognostic value and represent an innovative asset in the field of precision oncology.

Methods

Assembly and quality control of DNA methylation data

We assembled and processed with a harmonized pipeline[14] (v4.1; see Code availability section) 2,430 bulk sample Illumina methylation array data of normal and neoplastic lymphoid cells from previous publications14,21,22,23,24,25,26,27,28,29,30. As healthy control samples, this dataset contained sorted CD19+ B cells (n = 40), CD3+ T cells (n = 35), peripheral blood mononuclear cells (n = 6) and whole-blood samples (n = 6). As tumour samples, we included precursor 797 B-ALLs and 90 T-ALLs at diagnosis, 28 B-ALLs and 2 T-ALLs at relapse, as well as 74 B-ALLs and 12 T-ALLs at complete remission (that is, normal blood); 149 MCLs; 722 CLLs, 55 of its precursor condition MBL and 6 samples from patients with CLL undergoing a DLBCL transformation called Richter transformation; 62 primary DLBCL, not otherwise specified; and 104 multiple myeloma and 16 of its precursor condition monoclonal gammopathy of undetermined significance. In brief, raw idat files were loaded and processed with R (v4.3.1) using the minfi package50,51 (v1.46.0) in batches as specified in the column ‘SSNOB_NORMALIZATION_BATCH’ of Supplementary Table 2. In brief, the data were processed for each batch as follows. First, idats files were loaded into a RGChannelSet object, and minfi quality metrics using the qcReport function were performed, removing samples with unexpected distributions of methylation values (that is, distributions markedly distinct from a bimodal centred around 0 and 1 β-values and/or from the remaining samples) and low signal intensities of internal control probes for each sample, including bisulfite conversions I and II, extension hybridization, hybridization, non-polymorphic, specificities I and II, and target removal probes.

Next, further quality metrics were derived using the function minfiQC on the unnormalized RGChannelSet obejct. Those samples with median signal intensities of unmethylated and methylated channels of at least 10.5 in log_2 scale were considered as having good signal intensities. Subsequently, detection P values were calculated across all CpGs and samples using the detectionP function for the unnormalized RGChannelSet object. Samples were considered as good if having a mean detection P value across all CpGs of P ≤ 0.01. On a CpG level, we retained CpGs with a detection P ≤ 1 × 10−16 in 90% or more of the samples, which has been shown to improve the quality of downstream analyses52,53. The RGChannelSet object was normalized with the single-sample batch-independent preprocessNoob function with dye bias correction. We next retained only CpGs (excluding CH probes) that did not contain any SNP neither in the interrogated CpGs nor in the probe extension using the dropMethylationLoci and dropLociWithSnps functions with default options (minor allele frequency (MAF) = 0). Further analyses using long-read nanopore data, Illumina array control probes, annotation packages and a data-driven approach were used to ensure the lack of any genetic confounding in the methylation values of the resulting fCpGs (see the next sections).

Furthermore, CpGs with any previous evidence of potential cross-hybridization were excluded[54] and only CpGs mapping to autosomal chromosomes were subsequently retained for downstream analyses. Finally, to further confirm the accuracy of the filtering criteria, we checked the distribution of normalized methylation values and performed principal component analyses separately for samples passing all quality checks as well as those considered as bad samples. The final DNA methylation matrix contained 2,204 samples and 389,180 CpGs passing all the aforementioned quality controls, and included 2,054 patients (22 technical replicates, 3 synchronic and 125 longitudinal samples from the same patients)[55] (Supplementary Table 2).

To determine the purity of samples, we used our previously deconvolution strategy to infer tumour cell content by DNA methylation[14], which was used as a consensus purity in all the tumour samples except for DLBCL and multiple myeloma. In these two tumour entities, we have previously identified a DNA methylation signature loss causing inaccurate tumour purity predictions using DNA methylation data, and therefore we used available genetic or flow cytometry data for DLBCL and multiple myeloma, respectively.

Pipeline to select fluctuating CpGs

We constructed a pipeline to identify fCpGs in lymphoid tumours, based on the following criteria:

1. (1)
Heterogeneous across different participants with the same disease (by accepting CpG loci with the top 5% of standard deviation of methylation value within a cancer type).

2. (2)
Equally likely to be methylated or unmethylated (by selecting CpGs with average methylation of approximately 0.5 within a cancer type).

3. (3)
Unlikely to be associated with specific cell or cancer types. We used an unsupervised Laplacian score feature selection metric[56] to rank CpG loci by their tendency to preserve the nearest-neighbour graph, and accepted the 5% least-informative CpGs.

Exclusion of genetic confounding on fCpGs

We performed a series of analyses to exclude the potential genetic confounding (germline SNPs and somatic SNVs) on our fCpGs. We first excluded the possibility that common germline SNPs caused methylation heterogeneity at fCpG sites between individuals. We observed very distinct methylation dynamics of array control probes containing SNPs (which had been removed during the initial array processing) versus fCpGs. SNP probes showed the same distribution in all samples (Extended Data Fig. 2c), including longitudinally followed cases (Supplementary Fig. 3), whereas fCpGs only showed a W distribution in cancer samples with ongoing fluctuations over time. Thus, although SNPs reflect the stable genetic identity of the individual, fCpGs reflect the identity of a single cell and its evolving lineage. In addition, we used the packages SNPlocs.Hsapiens.dbSNP155.GRCh38 (v0.99.24) and MafH5.gnomAD.v4.0.GRCh38 (v3.19) to check for any known significant germline or somatic genetic confounding on the resulting 978 fCpGs. We found approximately 60% of fCpGs reported in the gnomAD v4 database (with the array background having approximately 65%), but with a very low MAF (median of 1 × 10−5 and mean of 1 × 10−3). To exclude the possibility of unknown or very rare genetic confounding, we used the data-driven gaphunting algorithm[57] available in the minfi R package, which further discarded a possible cancer-specific single-nucleotide variation (SNV) that could confound the methylation values at the 978 identified fCpGs. Finally, Oxford Nanopore long read of a subset of normal and neoplastic samples further validated that fCpGs represent de/methylated cytosines (Extended Data Fig. 2d,e; see next section).

Generation and analyses of long-read nanopore data

For long-read methylation sequencing in CLL and Richter transformation samples, concentration was assessed using the Qubit assay and DNA integrity was analysed either with the Femto Pulse System (Agilent) or the Fragment Analyzer (Agilent). When more than 6 µg of material with good integrity was available, DNA was additionally treated with the Short Fragment Eliminator Kit XS (PacBio) and eluted in EB buffer. Approximately 4 µg of DNA was used for library preparation according to the standard LSK114 kit and protocol from Oxford Nanopore. The time for DNA repair and end-prep was increased up to 30 min at 20 °C and 30 min at 65 °C. Adapter ligation was performed for 1 h at room temperature. All elutions were performed at 37 °C for 1.5 h, and 550–600 ng of DNA was loaded onto a FLO-PRO114M (CLL cells) flow cells. Flow cells were washed (EXP-WSH004) after 1–2 days, if pore count decreased to less than 30%. A total of 1–4 washes were performed for each flow cell. Flow cells were run for 100 (CLL cells) hours in total with the Fast model (MinKNOW 23.11.7, Dorado 7.2.13). The raw data were rebasecalled using dorado duplex (v0.5.3) and applying the SUP and modified call to detect 5mC and 5hmC, (model dna_r10.4.1_e8.2_400bps_sup@v4.3.0_5mCG_5hmCG@v1).

In normal B cell samples, 1–3 µg of DNA was used for WGS. Libraries were prepared with the DNA ligation kit LSK110 with no modifications. Libraries were loaded onto a flow cell version FLO-PRO002 (R9.4) and were run for 90–110 h. The basecalling was performed on live mode with the Guppy basecaller (v6.2.7), included in the MinKNOW (v22.08.6), using the SUP model for base modification detection of 5mC and 5hmC (dna_r9.4.1_450bps_modbases_5hmc_5mc_cg_sup.cfg).

In all samples, the generated unmapped BAM files after the basecalling were converted to FASTQ files using the SAMtools fastq -T Mm, Ml command. The FASTQ files were then mapped to BAM files using the command minimap2 -ax map-ont -y../GCA_000001405.15_GRCh38_no_alt_analysis_set.fna.mmi. The methylation values were extracted from the BAMs into bedMethyl files using the in-house tool bam2bedmethyl (v0.3.2) and compressed/indexed using bgzip/tabix. Reads from each strand were combined to generate DNA matrices for each CpG and were used for obtaining the methylation values of all fCpGs.

In addition, mini BAM files containing all reads from the 976 fCpGs were generated (in hg38 genome assembly). The reads showed excellent mappability, with a mean of perfect nucleotide matches (NM tag; Levenshtein distance) for all fCpGs across samples of 96.41% (range of 73.31–97.90), and mean mapping quality (MAPQ) of all the reads covering all fCpGs across samples of 59.510 (range of 2–60). Subsequently, long reads were phased using variants called using Clair 3 (v1.0.9, model r941_prom_hac_g360 + g422)[58] with the Longphase package (v1.7)[59]. The methylation status of each CpG was called using the modcall function within the Longphase package. At fCpGs, only 2.7% of the reads were non-canonical bases (Extended Data Fig. 2d). The variant allele frequency (VAF) of these mutations tended to be low and was negatively correlated with the coverage at that site (Supplementary Fig. 4a). Hence, the majority of these non-canonical base pairs are probably due to errors in nucleotide assignment. There is also no association between the methylation status of different reads and the variants present within a 50-bp window of each fCpG locus (Supplementary Fig. 4b). Hence, assessment of fCpG methylation via bead array was not majorly confounded by miscalled variants. The fCpG methylation patterns seen in the bead array data were replicated in the long-read data (Extended Data Fig. 2e) and the correlation between the fraction methylated measured via bead array and long-read sequencing at fCpGs was excellent (Extended Data Fig. 2e). The same correspondence was observed in WGBS data (Extended Data Fig. 2f).

To assess the intra-sample long-read diversity for each sample, the pairwise Hamming distances were calculated between every read on both haplotypes. The two lists of Hamming distances were concatenated, and the mean calculated as a summary statistic of the read diversity for each sample. One normal B cell sample contained only two reads from one haplotype, and zero from the other, and so was excluded from further analysis.

Analysis of scRRBS data

Previously published single-cell reduced representation bisulfite sequencing (scRRBS) data were obtained[6] and the fCpG methylation values extracted methylation values for normal B cells from 6 donors and CLL cells from 12 patients. There was a high dropout rate, so to extract meaningful patterns we plotted a subset of 40 cells and 20 fCpGs with a high density and overlap of fCpGs across single cells as examples (Supplementary Fig. 5a,b).

To compare the full set of data accounting for the high degree of missing data, we used a metric of heterogeneity at a given fCpG that weights by the number of non-missing fCpGs according to:

$${d}_{i}=\sqrt{\frac{{n}_{i}({n}_{i}-1)}{2}}\sigma ({\beta }_{i})$$

Where ni is the number of non-NaN values for the ith fCpG, \(\frac{n(n-1)}{2}\) is the total possible pairwise comparisons between a set of n objects and σ(βi) is the standard deviation across the methylation values of the ith fCpG (Supplementary Fig. 5c).

Characterization and annotation of fCpGs

To characterize the genomic and regulatory context of fCpGs, we used a series of statistical analyses and database annotations. We annotated fCpGs using Illumina manifest and other genomic annotation packages available at Bioconductor including IlluminaHumanMethylation450kanno.ilmn12.hg19 (v0.6.1) and IlluminaHumanMethylationEPICanno.ilm10b2.hg19 (v0.6.0). We additionally used the packages SNPlocs.Hsapiens.dbSNP155.GRCh38 (v0.99.24) and MafH5.gnomAD.v4.0.GRCh38 (v3.19) to check any possible germline or somatic genetic confounding on the resulting 978 fCpGs. We found approximately 60% of fCpGs reported in the gnomAD v4 database (with the array background having approximately 65%), but with a very low MAF (median of 1 × 10−5 and mean of 1 × 10−3). In addition, we used the Illumina 450k and EPIC array internal SNP probes and showed a dramatically distinct methylation dynamics compared with fCpGs in single-timepoint (Extended Data Fig. 2c) and longitudinal (Supplementary Fig. 3) samples. Finally, the data-driven gaphunting algorithm available in the minfi R package was applied with all the previously published thresholds and cut-offs[57], which further discarded possible cancer-specific SNV that could confound the methylation values at the 978 identified fCpGs.

We used Chi-squared tests to assess the enrichment of fCpGs in distinct genomic regions or elements. We performed gene-set enrichment analysis on the fCpG-associated genes using gProfiler[60], specifically focusing on the Gene Ontology biological processes[61] and the Human Protein Atlas[62]. The statistical domain space was limited to genes targeted by at least one CpG in the 389,180 candidate CpG set and significance was determined using the g:SCS algorithm[63]. Previous chromatin segmentation of normal and neoplastic B cells was used to assess the chromatin-state enrichment of fCpG14,64.

fCpGs were checked for their overlap with previous ‘epigenetic clocks’, including mitotic14,65,66,67,68, chronological age69,70,71,72,73,74,75,76,77,78, gestational age79,80,81,82,83, biological age and mortality84,85,86 and trait predictors87,88. The package methylCIPHER (https://github.com/MorganLevineLab/methylCIPHER) was used to obtain the CpGs for most of the epigenetic clocks. The package methylclock (v1.10.0) was used to calculate all epigenetic clocks but epiCMIT, which was derived as previously described[14].

CLL RNA sequencing data

Previously available RNA sequencing data for 294 patients with CLL were obtained[33] and processed as previously described[26]. Matched RNA sequencing data and DNA methylation data for the same patients at the same timepoint were available for 224 patients with CLL. Transcript per million counts were used to represent differential gene expression values across genes and samples. We used the gene annotation provided in the R Bioconductor package IlluminaHumanMethylationEPICanno.ilm10b2.hg19 to classify genes associated with fCpGs. Genes targeted by any fCpG were considered as ‘fCpG genes’.

In each methylation sample, the 978 fCpGs were discretized as homozygous demethylated, heterozygous methylated or homozygous methylated (coded as [0,1,2], respectively). This was done by separately fitting a β-mixture model with three components to each sample using Stan[89] and extracting the component mixture probability. The gene expression value for genes classified as having and fCpG with 0, 1 or 2 alleles methylated were plotted as previously described.

DNA methylation data from normal blood samples

External DNA methylation data were download from the Gene Expression Omnibus database using the GEOquery R package (v2.72.0). For sorted immune cells, these include GSE137594 and GSE184269. For whole-blood samples, these include GSE72773, GSE55763, GSE40279 and GSE36054. Data were analysed with the normalization procedure used in each study together with the metadata provided. Mean and standard deviation for fCpGs were calculated with fCpGs present in the provided normalized matrices.

A stochastic model of fCpGs in a growing population

We built a generative computational model of how the patterns of fCpGs vary over time (t) according to the evolutionary history of a cancer. Initially, our model focused on neutral evolution, before expanding to non-neutral modes of tumour evolution below. For the full explanation of the model, see the Supplementary Information.

Our model was parameterized in terms of the age of the patient at which the MRCA emerged (τ), the exponential growth rate of the cancer (θ) and the epigenetic switching rates of the fCpGs (μ, ν, γ and ζ). The model was partitioned into two phases: before and after the emergence of the MRCA. At time t = 0, the fCpGs were assumed to be equally likely to be homozygously methylated or demethylated. The fCpG status of the MRCA at time t = τ was calculated by applying matrix exponentiation.

The second phase of the model consisted of a discrete time Markov process. The effective population size of the growing cancer was modelled as growing according to a deterministic exponential growth equation, Ne = eθ(T − τ). Each fCpG was considered independently; at each time step, t → t + δt, the number of homozygous-methylated (m), heterozygous-methylated (k) and homozygous-demethylated cells (w) at a specific fCpG was updated according to the epigenetic switching rates.

At the time of sample, T, the fraction methylation of each simulated fCpG was calculated by summing the number of methylated alleles and normalizing by the total number of alleles in the population:

$${\beta }_{c}=\frac{k+2m}{2{N}_{e}}$$

We further accounted for contaminating normal cells and the technical noise introduced by the methylation bead array. The methylation of the contaminated samples was assumed to be an average of the cancer methylation, βc(t), weighted by the tumour purity ρ, and the average of the normal population, βn, weighted by 1 − ρ. Following our previous work, the bead array was assumed to saturate at extreme methylation values, shifting the minimum and maximum methylation by δ and ε, respectively[4]. The noise of the bead array was assumed to be β-distributed, with precision parameter κ.

Non-neutral models of tumour evolution

Alongside our model of neutral exponentially growing cancer populations, we devised two alternative models of cancer growth:

1. (1)
A subclonal selection model in which a single cell within the cancer develops a selective advantage and begins to grow at an increased growth rate.

2. (2)
An independent clonal origins model, in which a patient has developed two distinct cancers concurrently.

For the subclonal selection model, we replaced the growth rate (θ) and the time of the MRCA (τ) with the growth rates and time of the MRCA of the initial, slower-growing population (θ_1 and τ_1, respectively), and that of the more recently emerging, faster-growing population (θ_2 and τ_2), constraining τ_1 < τ_2 and θ_1 < θ_2 (Extended Data Fig. 8a). We assumed that the initial cancer population began exponentially growing at τ_1 as above, but at time t = τ_2, we selected a single cell with a set of fCpG states drawn according to the cancer population and allowed this second population to grow concurrently with a growth rate θ_2.

The independent-cancer model followed the same scheme as the nested subclonal selection model, except the methylation status of the emerging cancer was that of an independent cell that experienced random fluctuations between t = 0 and t = τ_2.

If we let the number of cells in the less fit subclone in each methylation state be {m_1, k_1, w_1} and in the fitter subclone be {m_2, k_2, w_2}, following the convention above, then in both cases the measured methylation patterns at the time of sample are:

$${\beta }_{c}(T)=\frac{{k}_{1}(T)+2{m}_{1}(T)+{k}_{2}(T)+2{m}_{2}(T)}{2{N}_{e}(T)}$$

Where \({N}_{e}(T)={e}^{{\theta }_{1}(T-{\tau }_{1})}+{e}^{{\theta }_{2}(T-{\tau }_{2})}\).

Adaption of simulations to a longitudinal setting

We modified the simulations of how the fCpG methylation distribution changes over time to allow for multiple sequential sample collections. These simulations allow for neutral, independent clones, a single subclonal expansion or two subclonal expansions, which can either be nested or emerge from the clonal trunk in parallel. This required pre-specification of sampling times, along with the emergence times of any subclones or independent clones, which we collected to form a set of ‘landmark times’. The discrete time steps of the simulation were split into phases between the landmark times, which evolved according to the discrete time Markov process outlined above. At each sampling time, the fCpG methylation fraction was calculated as above and stored as a column in the output matrix.

Prior functions

For each methylation array blood sample, we had matched age (T) and purity (ρ) information. Hence, the parameters to be inferred are the growth rate (θ), the age of the patient when the MRCA emerged (τ), the epigenetic switching rates (μ, ν, γ, ζ), the average fraction methylated of contaminating normal cells (βn), the β-offsets from 0 and 1 due to the background noise on the methylation array (δ and ε, respectively) and the precision of the β-distributed noise (κ).

These parameters are constrained either to be positive (θ, μ, ν, γ, ζ, κ > 0) or to lie within a specified range (0 < τ/T, δ, ε < 1), which we achieved using appropriate prior distributions. To better allow for priors to be set on a biologically meaningful scale, the priors for the log-normal distribution were set in terms of the real scale mean and standard deviation, rather than the standard log-scale. To reduce correlations in the posterior and make sampling more efficient, the variables ν and ζ were normalized by μ and γ, respectively.

The priors are as follows:

$$\theta \sim {\rm{lognormal}}(\mathrm{3,2})$$

$$\frac{\tau }{T} \sim {\rm{beta}}(2,2)$$

$$\mu \sim {\rm{halfnormal}}(0,0.05)$$

$$\gamma \sim {\rm{halfnormal}}(0,0.05)$$

$$\frac{\upsilon }{\mu } \sim {\rm{lognormal}}(1,0.7)$$

$$\frac{\zeta }{\gamma } \sim {\rm{lognormal}}(1,0.7)$$

$${\beta }_{n} \sim {\rm{beta}}(2,2)$$

$$\delta \sim {\rm{beta}}(5,95)$$

$${\epsilon } \sim {\rm{beta}}(95,5)$$

$$\kappa \sim {\rm{halfnormal}}(100,30)$$

When fitting non-neutral models of tumour growth, the inference was parameterized in terms of the relative growth of the fitter subclone, \({\tilde{\theta }}_{2}=\frac{{\theta }_{2}}{{\theta }_{1}}\), and the fraction of the population consisting of the fitter subclone, \(f=\frac{{e}^{{\theta }_{2}(t-{\tau }_{2})}}{{e}^{{\theta }_{1}(t-{\tau }_{1})}+{e}^{{\theta }_{2}(t-{\tau }_{2})}}\). The age at which the second clone emerges is then:

$${\tau }_{2}=T-\frac{(T-{\tau }_{1}){\theta }_{1}}{{\theta }_{2}}-\frac{{\rm{logit}}(f)}{{\theta }_{2}}$$

This parameterization induces less correlation in the resulting posterior, which greatly improves the sampling efficiency. The priors on these additional parameters are:

$$\frac{{\tau }_{1}}{T} \sim {\rm{beta}}(2,2)$$

$${\widetilde{\theta }}_{2} \sim {\rm{lognormal}}(1,0.7)$$

$$f \sim {\rm{beta}}(2,2)$$

All the other priors were the same as in the neutral case.

Bayesian inference

We developed a stochastic estimator of the log-likelihood function at a given set of parameters by simulating the fCpG methylation distribution a large number of times, correcting for the bias inherent with using a finite number of simulations and penalizing the log-likelihood for extreme values of the Ne (see Supplementary Information for details).

The standard Bayesian algorithms developed to infer the posterior for a given set of data (for example, Markov chain Monte Carlo (MCMC), nested sampling) are typically used when the log-likelihood is analytically tractable and can be calculated exactly. It has been shown that, as long as the stochastic approximation of the log-likelihood is unbiased, MCMC methods can obtain an exact Bayesian inference of the true posterior, as in pseudo-marginal Metropolis–Hastings[90].

Here we used a nested sampling approach using the dynesty package91,92,93. Unlike pseudo-marginal Metropolis–Hastings, nested sampling is able to efficiently explore multimodal posterior landscapes (which can occur under the subclonal and independent cancer models).

Model selection for the mode of tumour evolution

We used an expected log pointwise predictive density[94] approach to compare our competing models of evolution for each sample using the arviz Python package[95], which uses PSIS-LOO-CV to compare the out-of-sample prediction accuracy between models while naturally penalizing more complex models. This required the log-likelihood per data point and the posterior predictive for every point in the posterior. The weights of the respective models were calculated using pseudo-Bayesian model averaging using Akaike-type weighting, stabilized using the Bayesian bootstrap[96].

CLL and Richter transformation genomic analyses

Previous mutated annotation files from WES[46] and WGS[27] data were used to further validate our distinct EVOFLUx evolutionary modes (that is, neutral, subclonal and independent) and Richter transformation phylogenies.

Subclonal deconvolution of WES and WGS data

To detect subclones in bulk WES and WGS data, we used MOBSTER[43], which fits the VAF spectrum with a mixture model containing a Pareto distribution to account for the neutral tail[97] and a variable number of β-distributions to account for the clonal and subclonal peaks.

We ran MOBSTER using the default parameters, except using a minimum 5% VAF threshold and lowering the minimum number of mutations to compose a cluster to five in WES samples due to the low number of mutations. We then manually quality controlled all 377 WES samples and 10 WGS, tuning the fitting parameters to better represent the data (for instance, when the clonal peak had been called at a low frequency despite the median tumour purity being 95%).

Phylogenetic inference of longitudinal methylation data

A novel Bayesian phylogenetic method was used to reconstruct the evolutionary relationships and the time to MRCA of longitudinal samples from the same patients. This was carried out in the BEAST (v1.8.4) framework98,99 using custom models implemented in PISCA[100] (v1.1; available from https://github.com/adamallo/PISCA).

EVOFLUx provided an estimate of the age of the patient when the MRCA of each bulk sample emerged. To estimate the methylation status of each fCpG at the MRCA of the sample in each of our longitudinal samples, we discretized the fCpGs as described above (see the section ‘CLL RNA sequencing data’).

We implemented a four-parameter biallelic binary substitution model analogous to the pre-growth EVOFLUx model in PISCA. This plugin contains all the required statistical machinery to use this model for somatic phylogenetic estimation. The biallelic binary substitution model has three relative rate parameters: (1) heterozygous methylation \(\tilde{\upsilon }\), (2) homozygous demethylation \(\tilde{\gamma }\), and (3) heterozygous demethylation \(\tilde{\zeta }\), where homozygous methylation \(\tilde{\mu }\) was normalized to 1. For all relative transition rate parameters, a log-normal prior with mean of 1 and standard deviation of 0.6 was used, with a half-normal prior with mean of 0 and standard deviation of 0.13 for the molecular clock rate, using a strict clock model for the rate of evolution across the tree. Two demographic tree models, constant population size[101] and exponential growth[102], were compared by marginal likelihood estimation using path-sampling[103] and a constant population model was deemed more appropriate.

MCMC chains were run for 100 million generations sampled every 100,000 generations and convergence was assessed using Tracer (v.1.7)[104], ensuring effective sample sizes (ESS) greater than 500 for all parameters. Maximum clade credibility trees were then made using 10% burn-in and medium node heights. The resulting trees were plotted using ggtree[105].

Phylogenetic inference of SNVs from WGS data

Each bulk sample is represented by a set of clonal mutations found during the deconvolution of WGS data (see above). Where a mutation was deemed absent in the clonal peak, the reference nucleotide was used. Mutational signature assignment[106] was used to select mutations in the clock-like SBS1 channel[107]. BEAST (v1.10)[108] was then used with the simple binary substitution model (as SBS1 effectively represents just C-to-T substitutions), a strict clock model, a constant population size prior[101] and a flat prior on the age of MRCA (from zero to earliest patient sample), with ancestral state estimation at the root. Chains were run and ESS values assessed as described above. The distances between the ancestral state of the root at each MCMC state and the clock rate were used to calculate the expected evolution distance between the root and the known germline. This was used to inform the length of the branch between germline (at birth) and the MRCA of the samples.

Survival analysis

Clinical analyses were performed in CLL for TTFT and overall survival from the time of sampling. Tumour growth rate (θ), effective population size (Ne) and epigenetic switching rates were analysed as continuous variables in univariate Cox regression models for both TTFT and overall survival. The effect size of HRs for each evolutionary variable were analysed considering different scaling factors. In particular, the growth rate was analysed assuming exponential growth (that is, for θ = 1, the population is e = 2.71 times bigger per year), the Ne was considered per million cells, and the cancer age or time from the MRCA was analysed for each 10 years. Individual switching rate parameters (μ, ν, γ and ζ) were largely uninformative of prognosis and were summarized into a mean epigenetic switching rate, which was scaled by a factor of 100. In addition, growth rate and effective population were analysed as continuous variables in multivariate Cox regression models together with TP53 aberrations (considering mutations and deletions together), IGHV gene mutational status and the age of patients at sampling. Kaplan–Meier curves were generated for low and high growth rates and effective population size within IGHV subtypes using maximally selected log-rank statistic using the maxstats package (v0.7-25). P values from Kaplan–Meier curves were derived using the log-rank statistic. Survival (v3.5-7), survminer (v0.4.9) and ggsurvfit (v0.3.1) packages were used under R (v4.3.1). Plots were generated using ggplot2 (v3.5.2).

Estimating the rate of change in lymphocyte counts

Historical records of the absolute number of lymphocytes in blood obtained via haemocytometer were collected for patients with CLL over the whole disease course (that is, an approximate of the number of malignant CLL cells in blood). In 231 patients with CLL, we could obtain at least 10 sample timepoints (that is, at least 10 medical appointments, median n = 27 and mean n = 34) before the first treatment, allowing us to track the natural history of the disease before treatment intervention for the tumour (Supplementary Fig. 10). We fitted a linear model to all 231 cases and obtained the slope of the observed log number of lymphocytes (that is, the coefficient of the univariate linear model) and compared it with growth rate estimates derived from EVOFLUx.

Statistical analysis

Statistical tests performed throughout the study were performed as two-sided. Appropriate multiple test correction, such as the Holm–Sidak correction, is noted when applied.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

No new methylation bead array data were generated in the course of this study. The harmonized and filtered methylation matrix has been deposited to Zenodo[55] (https://doi.org/10.5281/zenodo.15479736). Previously published DNA methylation data reanalysed in this study can be found under the accession codes: EGAS00001001196 for B cells; GSE56602, GSE49032, GSE76585 and GSE69229 for ALL; EGAS00001001637 and EGAS00001004165 for MCL; EGAD00010000871, EGAD00010000948 and EGAD00010001975 for CLL; EGAS00001000841 for multiple myeloma; and EGAD00010001974 for DLBCL. External DNA methylation data for sorted immune cells can be found under the accession codes GSE137594 and GSE184269. For whole-blood samples, the accession codes are GSE72773, GSE55763, GSE40279 and GSE36054. CLL gene expression data are available under the accession codes EGAS00001000374 and EGAS00001001306. Chromatin immunoprecipitation followed by sequencing datasets are available from Blueprint (https://www.blueprint-epigenome.eu/) under the accession code EGAS00001000326. Matched WES and WGS data are available under the accession codes EGAS00000000092 and EGAD00001008954, respectively, under controlled access. Pathway analysis was run using the Gene Ontology: Biological Processes release 2023-03-06 and the Human Protein Atlas (v10.0) databases. Matched Oxford Nanopore long-read data were generated for six normal B cells and samples and two CLL-Richter transformation sample pairs. Long-read data are available at the European Genome-Phenome Archive repository under the accession code EGAS50000001192. Source data are provided with this paper.

Code availability

The codes for EVOFLUx used to infer the evolutionary history of cancer samples from methylation array data (https://github.com/CalumGabbutt/evoflux), to curate DNA methylation data and to perform clinical and additional bioinformatic analyses (https://github.com/Duran-FerrerM/evoflux) and for the phylogenetic method (https://github.com/adamallo/PISCA), are available on GitHub.

References

1. Nowell, P. C. The clonal evolution of tumor cell populations. Science 194, 23–28 (1976).

2. Merlo, L. M. F., Pepper, J. W., Reid, B. J. & Maley, C. C. Cancer as an evolutionary and ecological process. Nat. Rev. Cancer 6, 924–935 (2006).

3. Turajlic, S., Sottoriva, A., Graham, T. & Swanton, C. Resolving genetic heterogeneity in cancer. Nat. Rev. Genet. 20, 404–416 (2019).

4. Gabbutt, C. et al. Fluctuating methylation clocks for cell lineage tracing at high temporal resolution in human tissues. Nat. Biotechnol. 40, 720–730 (2022).

5. Greaves, M. & Maley, C. C. Clonal evolution in cancer. Nature 481, 306–313 (2012).

6. Gaiti, F. et al. Epigenetic evolution and lineage histories of chronic lymphocytic leukaemia. Nature 569, 576–580 (2019).

7. Lee-Six, H. et al. Population dynamics of normal human blood inferred from somatic mutations. Nature 561, 473–478 (2018).

8. Williams, N. et al. Life histories of myeloproliferative neoplasms inferred from phylogenies. Nature 602, 162–168 (2022).

9. Yatabe, Y., Tavaré, S. & Shibata, D. Investigating stem cells in human colon by using methylation patterns. Proc. Natl Acad. Sci. USA 98, 10839–10844 (2001).

10. Hong, Y. J., Marjoram, P., Shibata, D. & Siegmund, K. D. Using DNA methylation patterns to infer tumor ancestry. PLoS ONE 5, e12002 (2010).

11. Brocks, D. et al. Intratumor DNA methylation heterogeneity reflects clonal evolution in aggressive prostate cancer. Cell Rep. 8, 798–806 (2014).

12. Hao, J. J. et al. Spatial intratumoral heterogeneity and temporal clonal evolution in esophageal squamous cell carcinoma. Nat. Genet. 48, 1500–1507 (2016).

13. Siegmund, K. D., Marjoram, P., Woo, Y. J., Tavaré, S. & Shibata, D. Inferring clonal expansion and cancer stem cell dynamics from DNA methylation patterns in colorectal cancers. Proc. Natl Acad. Sci. USA 106, 4828–4833 (2009).

14. Duran-Ferrer, M. et al. The proliferative history shapes the DNA methylome of B-cell tumors and predicts clinical outcome. Nat. Cancer 1, 1066–1081 (2020).

15. Endicott, J. L., Nolte, P. A., Shen, H. & Laird, P. W. Cell division drives DNA methylation loss in late-replicating domains in primary human cells. Nat. Commun. 13, 6659 (2022).

16. de Leval, L. et al. Genomic profiling for clinical decision making in lymphoid neoplasms. Blood 140, 2193–2227 (2022).

17. Arber, D. A. et al. International consensus classification of myeloid neoplasms and acute leukemias: integrating morphologic, clinical, and genomic data. Blood 140, 1200–1228 (2022).

18. Duran-Ferrer, M. & Martín-Subero, J. I. Epigenomic characterization of lymphoid neoplasms. Annu. Rev. Pathol. 19, 371–396 (2024).

19. Gruber, M. et al. Growth dynamics in naturally progressing chronic lymphocytic leukaemia. Nature 570, 474–479 (2019).

20. Gutierrez, C. et al. Multifunctional barcoding with ClonMapper enables high-resolution study of clonal dynamics during tumor evolution and treatment. Nat. Cancer 2, 758–772 (2021).

21. Kulis, M. et al. Whole-genome fingerprint of the DNA methylome during human B cell differentiation. Nat. Genet. 47, 746–756 (2015).

22. Nordlund, J. et al. Genome-wide signatures of differential DNA methylation in pediatric acute lymphoblastic leukemia. Genome Biol. 14, r105 (2013).

23. Reinius, L. E. et al. Differential DNA methylation in purified human blood cells: implications for cell lineage and studies on disease susceptibility. PLoS ONE 7, e41361 (2012).

24. Lee, S. T. et al. Epigenetic remodeling in B-cell acute lymphoblastic leukemia occurs in two tracks and employs embryonic stem cell-like signatures. Nucleic Acids Res. 43, 2590–2602 (2015).

25. Queirós, A. C. et al. Decoding the DNA methylome of mantle cell lymphoma in the light of the entire B cell lineage. Cancer Cell 30, 806–821 (2016).

26. Nadeu, F. et al. Genomic and epigenomic insights into the origin, pathogenesis, and clinical behavior of mantle cell lymphoma subtypes. Blood 136, 1419–1432 (2020).

27. Nadeu, F. et al. Detection of early seeding of Richter transformation in chronic lymphocytic leukemia. Nat. Med. 28, 1662–1671 (2022).

28. Oakes, C. C. et al. DNA methylation dynamics during B cell maturation underlie a continuum of disease phenotypes in chronic lymphocytic leukemia. Nat. Genet. 48, 253–264 (2016).

29. Dietrich, S. et al. Drug-perturbation-based stratification of blood cancer. J. Clin. Invest. 128, 427–445 (2018).

30. Agirre, X. et al. Whole-epigenome analysis in multiple myeloma reveals DNA hypermethylation of B cell-specific enhancers. Genome Res. 25, 478–487 (2015).

31. Loyfer, N. et al. A DNA methylation atlas of normal human cell types. Nature 613, 355–364 (2023).

32. Clarke, J. et al. Continuous base identification for single-molecule nanopore DNA sequencing. Nat. Nanotechnol. 4, 265–270 (2009).

33. Puente, X. S. et al. Non-coding recurrent mutations in chronic lymphocytic leukaemia. Nature 526, 519–524 (2015).

34. Seale, K., Horvath, S., Teschendorff, A., Eynon, N. & Voisin, S. Making sense of the ageing methylome. Nat. Rev. Genet. 23, 585–605 (2022).

35. Boddicker, N. J. et al. Relationship among three common hematological premalignant conditions. Leukemia 37, 1719–1722 (2023).

36. Jaiswal, S. & Ebert, B. L. Clonal hematopoiesis in human aging and disease. Science 366, eaan4673 (2019).

37. Rice, S. & Roy, A. MLL-rearranged infant leukaemia: a ‘thorn in the side’ of a remarkable success story. Biochim. Biophys. Acta Gene Regul. Mech. 1863, 194564 (2020).

38. Alizadeh, A. A. et al. Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature 403, 503–511 (2000).

39. Hamblin, T. J., Davis, Z., Gardiner, A., Oscier, D. G. & Stevenson, F. K. Unmutated Ig VH genes are associated with a more aggressive form of chronic lymphocytic leukemia. Blood 94, 1848–1854 (1999).

40. Damle, R. N. et al. Ig V gene mutation status and CD38 expression as novel prognostic indicators in chronic lymphocytic leukemia. Blood 94, 1840–1847 (1999).

41. Zenz, T. et al. TP53 mutation and survival in chronic lymphocytic leukemia. J. Clin. Oncol. 28, 4473–4479 (2010).

42. Plevova, K. et al. Multiple productive immunoglobulin heavy chain gene rearrangements in chronic lymphocytic leukemia are mostly derived from independent clones. Haematologica 99, 329–338 (2014).

43. Caravagna, G. et al. Subclonal reconstruction of tumors by using machine learning and population genetics. Nat. Genet. 52, 898–907 (2020).

44. Williams, M. J. et al. Quantification of subclonal selection in cancer from bulk sequencing data. Nat. Genet. 50, 895–903 (2018).

45. Heide, T. et al. Reply to ‘Neutral tumor evolution?’. Nat. Genet. 50, 1633–1637 (2018).

46. Knisbacher, B. A. et al. Molecular map of chronic lymphocytic leukemia and its impact on outcome. Nat. Genet. 54, 1664–1674 (2022).

47. Leitão, E. et al. Locus-specific DNA methylation analysis by targeted deep bisulfite sequencing. Methods Mol. Biol. 1767, 351–366 (2018).

48. Meissner, A. et al. Reduced representation bisulfite sequencing for comparative high-resolution DNA methylation analysis. Nucleic Acids Res. 33, 5868–5877 (2005).

49. Füllgrabe, J. et al. Simultaneous sequencing of genetic and epigenetic bases in DNA. Nat. Biotechnol. 41, 1457–1464 (2023).

50. Aryee, M. J. et al. Minfi: a flexible and comprehensive Bioconductor package for the analysis of Infinium DNA methylation microarrays. Bioinformatics 30, 1363–1369 (2014).

51. Fortin, J.-P., Triche, T. J. Jr & Hansen, K. D. Preprocessing, normalization and integration of the Illumina HumanMethylationEPIC array with minfi. Bioinformatics 33, 558–560 (2017).

52. Lehne, B. et al. A coherent approach for analysis of the Illumina HumanMethylation450 BeadChip improves data quality and performance in epigenome-wide association studies. Genome Biol. 16, 37 (2015).

53. Zhou, W., Triche, T. J., Laird, P. W. & Shen, H. SeSAMe: reducing artifactual detection of DNA methylation by Infinium BeadChips in genomic deletions. Nucleic Acids Res. 46, e123 (2018).

54. Chen, Y. A. et al. Discovery of cross-reactive probes and polymorphic CpGs in the Illumina Infinium HumanMethylation450 microarray. Epigenetics 8, 203–209 (2013).

55. Duran-Ferrer, M., Gabbutt, C., Martin-Subero, J. I. & Graham, T. Harmonised methylation array matrix related to the article Fluctuating DNA methylation tracks cancer evolution at clinical scale. Zenodo https://doi.org/10.5281/ZENODO.15479737 (2025).

56. He, X., Cai, D. & Niyogi, P. Laplacian score for feature selection. In Advances in Neural Information Processing Systems 18 (eds. Weiss, Y., Schölkopf, B. & Platt, J.) (MIT Press, 2005).

57. Andrews, S. V., Ladd-Acosta, C., Feinberg, A. P., Hansen, K. D. & Fallin, M. D. “Gap hunting” to characterize clustered probe signals in Illumina methylation array data. Epigenetics Chromatin 9, 56 (2016).

58. Zheng, Z. et al. Symphonizing pileup and full-alignment for deep learning-based long-read variant calling. Nat. Comput. Sci. 2, 797–803 (2022).

59. Lin, J. H., Chen, L. C., Yu, S. C. & Huang, Y. T. LongPhase: an ultra-fast chromosome-scale phasing algorithm for small and large variants. Bioinformatics 38, 1816–1822 (2022).

60. Raudvere, U. et al. g:Profiler: a web server for functional enrichment analysis and conversions of gene lists (2019 update). Nucleic Acids Res. 47, W191–W198 (2019).

61. Ashburner, M. et al. Gene Ontology: tool for the unification of biology. Nat. Genet. 25, 25–29 (2000).

62. Uhlén, M. et al. Tissue-based map of the human proteome. Science 347, 1260419 (2015).

63. Reimand, J., Kull, M., Peterson, H., Hansen, J. & Vilo, J. g:Profiler — a web-based toolset for functional profiling of gene lists from large-scale experiments. Nucleic Acids Res. 35, W193–W200 (2007).

64. Beekman, R. et al. The reference epigenome and regulatory chromatin landscape of chronic lymphocytic leukemia. Nat. Med. 24, 868–880 (2018).

65. Yang, Z. et al. Correlation of an epigenetic mitotic clock with cancer risk. Genome Biol. 17, 205 (2016).

66. Teschendorff, A. E. A comparison of epigenetic mitotic-like clocks for cancer risk prediction. Genome Med. 12, 56 (2020).

67. Youn, A. & Wang, S. The MiAge Calculator: a DNA methylation-based mitotic age calculator of human tissue types. Epigenetics 13, 192–206 (2018).

68. Zhou, W. et al. DNA methylation loss in late-replicating domains is linked to mitotic cell division. Nat. Genet. 50, 591–602 (2018).

69. Bocklandt, S. et al. Epigenetic predictor of age. PLoS ONE 6, e14821 (2011).

70. Garagnani, P. et al. Methylation of ELOVL2 gene as a new epigenetic marker of age. Aging Cell 11, 1132–1134 (2012).

71. Hannum, G. et al. Genome-wide methylation profiles reveal quantitative views of human aging rates. Mol. Cell 49, 359–367 (2013).

72. Horvath, S. DNA methylation age of human tissues and cell types. Genome Biol. 14, R115 (2013).

73. Lin, Q. et al. DNA methylation levels at individual age-associated CpG sites can be indicative for life expectancy. Aging 8, 394–401 (2016).

74. Vidal-Bralo, L., Lopez-Golan, Y. & Gonzalez, A. Simplified assay for epigenetic age estimation in whole blood of adults. Front. Genet. 7, 209192 (2016).

75. Weidner, C. I. et al. Aging of blood can be tracked by DNA methylation changes at just three CpG sites. Genome Biol. 15, R24 (2014).

76. Zhang, Q. et al. Improved precision of epigenetic clock estimates across tissues and its implication for biological ageing. Genome Med. 11, 54 (2019).

77. Horvath, S. et al. Epigenetic clock for skin and blood cells applied to Hutchinson Gilford progeria syndrome and ex vivo studies. Aging 10, 1758–1775 (2018).

78. Shireby, G. L. et al. Recalibrating the epigenetic clock: implications for assessing biological age in the human cortex. Brain 143, 3763–3775 (2020).

79. Bohlin, J. et al. Prediction of gestational age based on genome-wide differentially methylated regions. Genome Biol. 17, 207 (2016).

80. Knight, A. K. et al. An epigenetic clock for gestational age at birth based on blood methylation data. Genome Biol. 17, 206 (2016).

81. Lee, Y. et al. Placental epigenetic clocks: estimating gestational age using placental DNA methylation levels. Aging 11, 4238–4253 (2019).

82. Mayne, B. T. et al. Accelerated placental aging in early onset preeclampsia pregnancies identified by DNA methylation. Epigenomics 9, 279–289 (2017).

83. McEwen, L. M. et al. The PedBE clock accurately estimates DNA methylation age in pediatric buccal cells. Proc. Natl Acad. Sci. USA 117, 23329–23335 (2020).

84. Belsky, D. W. et al. DunedinPACE, a DNA methylation biomarker of the pace of aging. eLife 11, e73420 (2022).

85. Levine, M. E. et al. An epigenetic biomarker of aging for lifespan and healthspan. Aging 10, 573–591 (2018).

86. Lu, A. T. et al. DNA methylation GrimAge strongly predicts lifespan and healthspan. Aging 11, 303–327 (2019).

87. McCartney, D. L. et al. Epigenetic prediction of complex traits and death. Genome Biol. 19, 136 (2018).

88. Liang, X. et al. DNA methylation signature on phosphatidylethanol, not on self-reported alcohol consumption, predicts hazardous alcohol consumption in two distinct populations. Mol. Psychiatry 26, 2238–2253 (2020).

89. Carpenter, B. et al. Stan: a probabilistic programming language. J. Stat. Softw. 76, 1 (2017).

90. Andrieu, C. & Roberts, G. O. The pseudo-marginal approach for efficient Monte Carlo computations. Ann. Statist. https://doi.org/10.1214/07-AOS574 (2009).

91. Skilling, J. Nested sampling. In AIP Conference Proceedings 735 (eds Fischer, R. et al.) 395–405 (AIP Publishing, 2004).

92. Skilling, J. Nested sampling for general Bayesian computation. Bayesian Anal. 1, 833–860 (2006).

93. Speagle, J. S. dynesty: A dynamic nested sampling package for estimating Bayesian posteriors and evidences. Mon. Not. R. Astron. Soc. 493, 3132–3158 (2019).

94. Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat. Comput. 27, 1413–1432 (2015).

95. Kumar, R., Carroll, C., Hartikainen, A. & Martin, O. ArviZ a unified library for exploratory analysis of Bayesian models in Python. J. Open Source Softw. 4, 1143 (2019).

96. Yao, Y., Vehtari, A., Simpson, D. & Gelman, A. Using stacking to average Bayesian predictive distributions. Bayesian Anal. 13, 917–1007 (2017).

97. Williams, M. J., Werner, B., Barnes, C. P., Graham, T. A. & Sottoriva, A. Identification of neutral tumor evolution across cancer types. Nat. Genet. 48, 238–244 (2016).

98. Drummond, A. J. & Rambaut, A. BEAST: Bayesian evolutionary analysis by sampling trees. BMC Evol. Biol. 7, 214 (2007).

99. Drummond, A. J., Suchard, M. A., Xie, D. & Rambaut, A. Bayesian phylogenetics with BEAUti and the BEAST 1.7. Mol. Biol. Evol. 29, 1969–1973 (2012).

100. Martinez, P. et al. Evolution of Barrett’s esophagus through space and time at single-crypt and whole-biopsy levels. Nat. Commun. 9, 794 (2018).

101. Kingman, J. F. C. The coalescent. Stoch. Process Appl. 13, 235–248 (1982).

102. Griffiths, R. C. & Tavaré, S. Sampling theory for neutral alleles in a varying environment. Phil. Trans. R. Soc. Lond. B 344, 403–410 (1994).

103. Baele, G. et al. Improving the accuracy of demographic and molecular clock model comparison while accommodating phylogenetic uncertainty. Mol. Biol. Evol. 29, 2157–2167 (2012).

104. Rambaut, A., Drummond, A. J., Xie, D., Baele, G. & Suchard, M. A. Posterior summarization in Bayesian phylogenetics using Tracer 1.7. Syst. Biol. 67, 901–904 (2018).

105. Yu, G., Smith, D. K., Zhu, H., Guan, Y. & Lam, T. T. Y. ggtree: An r package for visualization and annotation of phylogenetic trees with their covariates and other associated data. Methods Ecol. Evol. 8, 28–36 (2017).

106. Díaz-Gay, M. et al. Assigning mutational signatures to individual samples and individual somatic mutations with SigProfilerAssignment. Bioinformatics 39, 12 (2023).

107. Tate, J. G. et al. COSMIC: the catalogue of somatic mutations in cancer. Nucleic Acids Res. 47, D941–D947 (2019).

108. Suchard, M. A. et al. Bayesian phylogenetic and phylodynamic data integration using BEAST 1.10. Virus Evol. 4, vey016 (2018).

Acknowledgements

This research was primarily funded by an Accelerator award Cancer Research UK/AIRC/AECC joint funder-partnership (to J.F., J.I.M.-S. and T.A.G.) and the US National Institutes of Health National Cancer Institute (U54 CA217376 to D.S. and T.A.G., R01 CA140657 to D.M.). Additional funding was provided by Cancer Research UK via direct grants (A19771 and DRCNPG-May21_100001 to T.A.G.), through the CRUK Convergence Science Centre (CTRQQR-2021\100009 to T.A.G.) and via an early detection primer award (EDDPMA-May23/100059 to T.A.G. and C.G.). Further funding was provided by the European Research Council under the European Union’s Horizon 2020 Research and Innovation Program (810287, BCLLatlas, to I.G.G., E.C. and J.I.M.-S.), La Caixa Foundation (CLLEvolution LCF/PR/HR17/52150017 (HR17- 00221LCF) and CLLSYSTEMS LCF/PR/HR22/52420015 (HR22-00172) Health Research 2017 and 2022 Programs to E.C.), Generalitat de Catalunya Suport Grups de Recerca AGAUR (2021-SGR-01343 to J.I.M.-S. and 2021-SGR-01172 to E.C.). C.G. was further supported by the BBSRC London Interdisciplinary Doctoral Programme (1902605), Thorton Foundation funding to the Institute of Cancer Research and the Eric and Wendy Schmidt Foundation. M.D.-F. was supported by a postdoctoral fellowship of the AECC Scientific Foundation. J.N. and O.K. were supported by the Swedish Research Council (2019-01976), the Swedish Childhood Cancer Fund (PR2019-0046/PR2022-0082) and the Swedish Cancer Society (CAN2022-2395). This research utilized the Cancer Research UK City of London High Performance Computing facility, and was partially developed at the Centro Esther Koplowitz. We acknowledge the SciLifeLab National Genomics Infrastructure, SNP&SEQ Technology Platform, funded by the Swedish Research Council and the Knut and Alice Wallenberg Foundation, for assistance with DNA methylation analyses. We thank D. Landau and F. Gaiti for supplying the single-cell reduced representation bisulfite sequencing data for analysis.

Author information

Author notes

1. These authors contributed equally: Calum Gabbutt, Martí Duran-Ferrer

2. These authors jointly supervised this work: José I. Martin-Subero, Trevor A. Graham

Authors and Affiliations

1. Centre for Evolution and Cancer, Institute of Cancer Research, London, UK

Calum Gabbutt, Heather E. Grant, Jacob Househam & Trevor A. Graham

2. I-X Centre for AI in Science, Imperial College London, London, UK

Calum Gabbutt

3. Centre for Genomics and Computational Biology, Barts Cancer Institute, Queen Mary University of London, London, UK

Calum Gabbutt, Jacob Househam, Jude Fitzgibbon & Trevor A. Graham

4. Fundació de Recerca Clínic Barcelona-Institut d’Investigacions Biomèdiques August Pi i Sunyer (FRCB-IDIBAPS), Barcelona, Spain

Martí Duran-Ferrer, Ferran Nadeu, Neus Villamor, Elias Campo, Armando Lopez-Guillermo & José I. Martin-Subero

5. Centro de Investigación Biomédica en Red de Cáncer (CIBERONC), Madrid, Spain

Martí Duran-Ferrer, Ferran Nadeu, Neus Villamor, Elias Campo, Armando Lopez-Guillermo & José I. Martin-Subero

6. Arizona Cancer Evolution Center, Biodesign Institute and School of Life Sciences, Arizona State University, Tempe, AZ, USA

Diego Mallo

7. Hospital Clínic de Barcelona, Barcelona, Spain

Neus Villamor, Elias Campo & Armando Lopez-Guillermo

8. Centro Nacional de Analisis Genomico (CNAG), Barcelona, Spain

Madlen Müller, Simon Heath, Emanuele Raineri & Ivo G. Gut

9. Department of Medical Sciences, Molecular Precision Medicine and Science for Life Laboratory, Uppsala University, Uppsala, Sweden

Olga Krali & Jessica Nordlund

10. Department of Medical Oncology and Hematology, University Hospital and University of Zürich, Zurich, Switzerland

Thorsten Zenz

11. The LOOP Zurich, Medical Research Center, Zurich, Switzerland

Thorsten Zenz

12. Universitat de Barcelona, Barcelona, Spain

Ivo G. Gut, Elias Campo & José I. Martin-Subero

13. Department of Cell and Developmental Biology, University College London, London, UK

Chris P. Barnes

14. Department of Pathology, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA

Darryl Shibata

15. Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain

José I. Martin-Subero

Contributions

T.A.G. and J.I.M.-S. conceived, funded and supervised the study. C.G. and T.A.G. conceived and designed the modelling scheme and the Bayesian inference framework, with support from C.P.B.; C.G. implemented and ran this. M.D.-F. processed and curated DNA methylation and patient metadata, and performed the survival analysis. M.D.-F. and C.G. conceived the phylogenetic analysis; C.G., H.E.G. and D.M. designed and ran them. C.G., M.D.-F., H.E.G., J.H. and F.N. performed the bioinformatic analysis. M.M., S.H., E.R. and I.G.G. performed the experiments and primary analyses of the long-read nanopore sequencing data. M.D.-F., F.N., N.V., O.K., J.N., T.Z., E.C. and A.L.-G. provided data and contributed to sample biological and/or clinical annotation. M.D.-F., N.V., E.C., A.L.-G., J.F., D.S. and J.I.M.-S. provided clinical insight. This study builds on the earlier conception of the fluctuating methylation phenomenon by D.S. C.G., M.D.-F., J.I.M.-S. and T.A.G. wrote the manuscript. All authors approved the final version of the manuscript.

Corresponding authors

Correspondence to Calum Gabbutt, José I. Martin-Subero or Trevor A. Graham.

Ethics declarations

Competing interests

T.A.G., J.I.M.-S., M.D.-F. and C.G., the Institute of Cancer Research, Fundació de Recerca Clínic Barcelona-Institut d’Investigacions August Pi i Sunyer and Institució Catalana de Recerca i Estudis Avançats have filed for a patent on a method to measure the evolutionary dynamics in cancers using DNA methylation (GB2317139.0). T.A.G is named as a co-inventor on adjacent patent applications that describe a method for TCR sequencing (GB2305655.9), and a method to infer drug resistance mechanisms from barcoding data (GB2501439.0). T.A.G has received an honoraria from Genentech and consultancy fees from DAiNA therapeutics. F.N. received honoraria from AbbVie, AstraZeneca, Janssen and SOPHiA GENETICS for speaking at educational activities, research funding from Gilead, and licensed the use of the protected IgCaller algorithm for SOPHiA GENETICS and Diagnóstica Longwood. All other authors declare no competing interests.

Peer review

Peer review information

Nature thanks Pavlo Lutsik, George Vassiliou and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Comparison of the methylation patterns of fCpGs vs epigenetic clocks.

a: fCpGs were selected by combining three filters: (1) CpGs with low intra-disease heterogeneity were removed as sites that were likely not fluctuating, (2) CpGs with a mean methylation far from 0.5 were removed as likely belonging to CpG sites with skewed methylation/demethylation rates, and (3i) CpGs which preserved the nearest-neighbour graph (quantified using the Laplacian Score) were removed as sites that were likely under selection/strict regulation. b-d: Heatmaps of b: Horvath’s CpGs[72], c: epiCMIT CpGs[14], and d: random subset of 1,000 CpGs from the candidate CpGs on the bead array. e-i: Heatmaps of our set of 978 pan-lymphoid fCpGs with disease-specific subtypes annotated in: e chronic lymphocytic leukaemia (CLL), f B-cell acute lymphoblastic leukaemia (B-ALL), g mantle cell lymphoma (MCL), h diffuse large B-cell lymphoma - not otherwise specified (DLBCL-NOS), and i multiple myeloma (MM). Hierarchical clustering with average linkage and a Euclidean metric was used in heatmaps.

Extended Data Fig. 2 Validation of fCpGs as an evolving barcode.

a: Scatterplot showing the pairwise correlation coefficient in the fCpG methylation values of lymphoid cancer samples with other fCpG methylation values on the same chromosome, and the genomic distance between them. b: The average absolute difference from 0.5 methylation value of fCpGs with their local neighbourhood in whole genome bisulphite sequencing (WGBS) data in different B- and T- cell populations[31]. The fraction of hypo- and hyper- methylated CpG loci increases as a function of distance from the reference fCpG locus. c: (left) Heatmap of control single nucleotide polymorphism (SNP) probes from Illumina arrays, showing distinct methylation dynamics compared to fCpGs, with normal and remission samples intermingled with tumours. (middle) A distinct methylation distribution of control SNP probes and the same number of random fCpGs is shown for one healthy naïve B cell sample. (right) The percentage of CpGs in intermediate peaks (i.e., ≥0.2 and ≤0.4 and ≥0.6 and ≤0.8) is notably higher in fCpGs compared to control SNP probes. d: A bar plot showing the fraction of fCpGs that were called as unmodified cytosine (C), 5-Methylcytosine (5mC), 5-hydroxymethylcytosine (5hmC) or a non-canonical base (A, G or T). e-f: Heatmap, histograms and scatterplots showing that the methylation status of fCpGs is validated in Oxford nanopore long-read (e) and WGBS data (f). g: fCpG methylation of phased Oxford nanopore long-reads of 2 CLL and 2 matched RT samples, 3 sorted memory and 3 naïve B cells samples. Long reads which cover the 4 fCpGs within the region chr7:25,854,120-25,856,220 are shown. h: (left) A box plot comparing the mean intra-haplotype Hamming distance of phased reads from cancer and normal samples (p = 0.016, MW-U test). One normal B-cell sample contained only 2 reads and was therefore removed. (right) Paired comparison of the mean intra- and inter-haplotype Hamming distances in 1 CLL and 2 RT samples (p = 0.030, paired T-test). One of the CLL samples only had reads from one haplotype, and thus was not informative for this plot.

Extended Data Fig. 3 fCpGs change methylation in an allele specific and are selectively neutral manner.

a: (top) Illustration of the possible combinations of fCpG states in monosomic and trisomic regions, along with the corresponding fraction methylation value. (bottom) Example histograms showing the fCpG methylation distribution of fCpGs located on just monosomic) or trisomic regions within 2 patient samples. b: Mean and standard deviation of fCpGs as a function of age in 2 independent cohorts of normal lymphoid cells, showing consistent methylation fluctuations but increased variance during aging. c: Boxplots of standard deviation of fCpG methylation values of whole-blood samples divided by age groups together with lymphoid tumour samples. P-values were derived using two-tailed t tests. Boxplots whiskers represent ±1.5 IQR. d: fCpG loci are significantly less likely to be associated with a gene (annotations provided by UCSC, p = 1.6e−15, chi-sq test). e: A comparison of the mutual overlap between different epigenetic clocks: mitotic14,65,66,67,68, chronological age69,70,71,72,73,74,75,76,77,78, gestational age79,80,81,82,83, biological age and mortality84,85,86, and trait predictors87,88 and fCpGs. f: P-P plot demonstrating fCpG associated genes have a lower expression (in transcripts per million) than non-fCpG associated genes. g: Linear regressions of the RNA expression of key methylation maintenance genes (DNMT1, DMT3a, DNMT3B and TET2) vs and the mean (left) and standard deviation (right) of the fCpG distribution.

Extended Data Fig. 4 Synthetic data analysis shows EVOFLUx is robust to varying modelling assumptions.

a: Posterior distributions after fitting the simulated data in Fig. 2b with the Bayesian inference method. The posterior (orange) displays tightening around the ground truth parameter values (red) compared to the prior (grey). b: Histogram of the simulated fCpG methylation distribution (blue) with the posterior predictive of the model fit overlaid (orange). c: Histograms showing the methylation distributions of 10,000 synthetic fCpGs simulated under the logistic growth model with varying carrying capacity (Supplementary Information). d-e: EVOFLUx posterior median and 95% credible interval were run on a subset of 2,000 of the simulated fCpGs in c as a function of the carrying capacity for the growth rate (d) and most recent common ancestor age (e). The dashed red line represents the ground truth parameter value. f: Histograms showing the fCpG methylation distributions of 10,000 synthetic fCpGs simulated under the heterogenous epigenetic switching model with varying switching rate standard deviation (Supplementary Information). g-h: EVOFLUx posterior median and 95% credible interval when run on a subset of 2,000 of the simulated fCpGs in f as a function of the switching rate standard deviation for the growth rate (g) and most recent common ancestor age (h).

Extended Data Fig. 5 EVOFLUx inference is robust to missing data.

a: Example posterior resulting from running EVOFLUx on a CLL sample – a pairs plot showing the marginal (diagonal) and pairwise (off-diagonal) inferred posterior (orange) distributions, with the prior distributions overlaid (gray). Posteriors show marked tightening compared to the priors, demonstrating the parameters were well informed by the data. b: A histogram of the fCpG methylation distribution (blue) with the posterior predictive of the model fit overlaid (orange). c-e: Regression plots between the parameters inferred by running EVOFLUx on all 978 fCpGs (x-axis) vs just those fCpGs present on diploid regions (y-axis) in the CLL cohorts for the growth rate (c), the most recent common ancestor age (d) and the effective population size (e). f: Example histograms showing the distribution of all 978 fCpGs (blue) in a CLL sample (SCLL-001), with a randomly downsampled subset of 20%, 40%, 60% and 80%. g-i: Plots showing the effect of the number of downsampled fCpGs included in the inference process against the inferred growth rate (g), time since the most recent common ancestor (h), and the effective population size (i). For each set of 10% increment, 10 replicate fCpG subsets were generated (grey dots) and the EVOFLUx inference repeated. Mean and standard error of the replicates represented with a blue dot and error bars respectively.

Extended Data Fig. 6 EVOFLUx captures lymphoid cancers’ evolutionary histories and methylation epimutation dynamics.

a-d: Boxplots (whiskers extending to ±1.5×IQR) showing the distribution of inferred growth rate (a), effective population size (b), time since the most recent common ancestor (c), and mean epigenetic switching rate (i.e. mean of μ, ν, γ, ζ; d) by disease. For interpretability, only a subset of the pairwise p values are annotated (Mann-Whitney U tests, hs correction). e: Linear regression between the growth rate and mean epigenetic switching rates separated by cancer types. There is a positive association in B-ALL (P = 2.4e-98, R^2 = 0.44) and T-ALL (P = 5.9e-06, R^2 = 0.22), a weak negative association in MM (P = 1.6e-05, R^2 = 0.18) and no association in CLL (P = 0.060, R^2 = 0.005) or the other entities. f-k: Linear regressions between the patient age at sampling and the mean inferred epigenetic switching rate in B cell acute lymphoblastic leukaemia (B-ALL, f), T cell acute lymphoblastic leukaemia (T-ALL, g), chronic lymphocytic leukaemia (CLL, h), mantle cell lymphoma (MCL, i) multiple myeloma (MM, j) and diffuse large B cell lymphoma (DLBCL, k). l: Linear regression between the EVOFLUx inferred initial evolutionary growth rate and the estimate of a linear model of the number of historical lymphocyte counts with the sampling dates of patients with at least 10 sample timepoints before treatment (P = 2e-5, Supplementary Fig. 10).

Extended Data Fig. 7 Genotype-phenotype driver mutation map.

Inferred growth rate (a) and effective population size (b) of individual CLL samples separated by driver mutational status for common driver alterations (mutations in TP53, SF3B1, NOTCH1, ATM, POT1 and IGLV3-21R110, and copy number alterations (CNAs) in del(11q22.3), del(13q14.3), del(17p13.1) and trisomy12). Differences between genotypes were tested using Mann-Whitney U tests and Benjamini-Hochberg FDR corrected. Tests were performed on U-CLL and M-CLL patients separately to remove differences solely due to with IGHV status.

Extended Data Fig. 8 Inference and validation of subclonal selection using fCpG loci.

a: Illustrations of three alternative evolutionary models: neutral evolution, in which the cancer population with a MRCA emerging at time τ grows exponentially at rate θ; subclonal selection, in which an initial population emerging at time τ_1 growing at rate θ_1 is outcompeted by a fitter subclonal emerging at time τ_2 with growth rate θ_2; and independent clonal origins, in which the fitter clone emerging at time τ_2 with growth rate θ_2 bears no clonal relationship to the initial clone. b: Bar chart comparing the fraction of cancer samples identified as subclonal by EVOFLUx across disease (pairwise chi-sq tests, holm-sidak (hs) correction). c: Boxplots comparing the distribution of subclonal weightings inferred by EVOFLUx in samples called as neutral vs under subclonal selection via whole exome sequencing (WES) data. d: Logistic regression between the probability of a cancer being identified as subclonal via running MOBSTER[43] on WES data and the number of mutations detected in the sample. Regression were run separately for samples also identified as subclonal/neutral via EVOFLUx (subclonal weighting > 95%). e: Boxplots comparing the distribution of subclonal weightings inferred by EVOFLUx in samples called as neutral vs under subclonal selection within whole genome sequencing (WGS) data. f: Receiver operating characteristic (ROC) curves showing the accuracy at predicting the subclonality of WGS data of competing logistic classifiers trained on just the EVOFLUx subclonality weighting, just the WES subclonality call and a model trained on both sources of data. g: Boxplots comparing the distribution of independent model weightings inferred by EVOFLUx in samples containing multiple IGHV rearrangements (independent cancers) vs those with only a single IGHV rearrangement detected via WGS, WES and/or RNA-seq[46] (likely a single clonal origin).

Extended Data Fig. 9 Matched whole genome sequencing data validates fCpGs as a phylogenetic character.

a-b: Corresponding phylogenies reconstructed on matched WGS SNVs for CLL case 12 and 19 to Fig. 4a,b, respectively. c-e: The reconstructed phylogenies of the relationship between samples collected longitudinally in 3 individual ALL patients, annotated with the clinical classification of each sample. The black triangles represent the time that occurred since the most recent common ancestor, taken as the posterior median of T - τ from the single-sample EVOFLUx inferences. f: Paired boxplot showing the standard deviation of the fCpG methylation distributions of B-ALL samples is greater than their matched remission sample (p = 9.6e-39, paired t-test). g: Comparison of the standard deviation of the fCpG methylation distributions of B-ALL patients in remission (i.e. no cancer cells present in blood) vs normal whole blood (p = 0.067, MW-U test). h: Example longitudinal samples from one patient showing the development of the fCpG distribution from diagnostic B-ALL, through remission and relapse. i: Scatterplots showing the marginal fCpG methylation distribution between diagnosis and relapse for the ALL case in h.

Extended Data Fig. 10 Additional survival analyses.

a: Kaplan-Meier curves comparing the OS between patients with high vs low (cut-off values identified using maxstat statistics) inferred effective population sizes (Ne) in the discovery cohort[33], separated by IGHV mutational status. b Multivariate Cox regression of the OS shows the Ne is significant when controlling for IGHV status, TP53 alterations and age at sampling in the discovery cohort. c: Univariate survival analysis of the time to first treatment (TTFT, blue) and overall survival (OS, red) in the validation CLL cohort28,29 for evolutionary variables inferred via EVOFLUx. Note this cohort contains a mixture of treated and untreated samples, of which only the untreated samples were included in the TTFT analysis. d: Kaplan-Meier curves comparing the TTFT between patients with high vs low (cut-off values identified using maxstat statistics) inferred cancer growth rates in the validation cohort, separated by IGHV mutational status. e: Multivariate Cox regression of the effect of the cancer growth rate on the TTFT in the validation cohort, controlling for IGHV status, TP53 alteration and age at sampling. f: Multivariate Cox proportional hazard regression on the TTFT for 229 CLL patients where longitudinal measurements of the lymphocyte numbers were available and therefore the contemporary growth rate could be estimated. The contemporary lymphocyte counts refer to the estimate of a linear model of the number of historical lymphocyte counts with the sampling dates of patients with at least 10 sample timepoints before treatment.

Supplementary information

Supplementary Information

Supplementary Figs. 1–20 and Supplementary Methods.

Reporting Summary

Supplementary Tables

Supplementary Tables 1–18.

Peer Review File

Source data

Source Data Fig. 1

Source Data Fig. 2

Source Data Fig. 3

Source Data Fig. 4

Source Data Fig. 5

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Gabbutt, C., Duran-Ferrer, M., Grant, H.E. et al. Fluctuating DNA methylation tracks cancer evolution at clinical scale. Nature 645, 764–773 (2025). https://doi.org/10.1038/s41586-025-09374-4

- Received: 17 October 2023

- Accepted: 09 July 2025

- Published: 10 September 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09374-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Whole-genome methylation profiling of extracellular vesicle DNA in gastric cancer identifies intercellular communication features

Article Open access 29 August 2025

Integration of genome-level data to allow identification of subtype-specific vulnerability genes as novel therapeutic targets

Article Open access 06 July 2021

Multimodal analysis of cell-free DNA whole-genome sequencing for pediatric cancers with low mutational burden

Article Open access 28 May 2021

Epigenetic clues from cancer’s past foretell its future

- Pavlo Lutsik

- Veselin Manojlovic

- George S. Vassiliou

Nature News & Views Forum 10 Sept 2025

Article Open access Published: 06 August 2025

Excised DNA circles from V(D)J recombination promote relapsed leukaemia

Zeqian Gao,

James N. F. Scott,

Matthew P. Edwards,

Dylan Casey,

Xiaoling Wang,

Andrew D. Gillen,

Sarra Ryan,

Lisa J. Russell,

Anthony V. Moorman,

Ruth de Tute,

Catherine Cargo,

Anthony M. Ford,

David R. Westhead &

…

Joan Boyes

Nature volume 645, pages 774–783 (2025)

Abstract

Extrachromosomal DNA amplification is associated with poor cancer prognoses[1]. Large numbers of excised signal circles (ESCs) are produced as by-products of antigen receptor rearrangement during V(D)J recombination2,3. However, current dogma states that ESCs are progressively lost through cell division[4]. Here we show that ESCs replicate and persist through many cell generations and share many properties in common with circular extrachromosomal DNAs. Increased ESC copy numbers at diagnosis of B cell precursor acute lymphoblastic leukaemia were highly correlated with subsequent relapse. By taking advantage of the matching recombination footprint that is formed upon the generation of each ESC, we measured ESC persistence and replication and found increased ESC replication in patients who later relapsed. This increased replication is controlled by cell-intrinsic factors and corresponds to increased expression of DNA replication- and repair-associated genes. Consistent with high ESC levels having a role in disease progression, the number of mutations typical of those caused by the V(D)J recombinase–ESC complex was significantly increased at diagnosis in patients who later relapsed. The number of such mutations in genes associated with relapse increased between diagnosis and relapse, and corresponded to clonal expansion of cells with high ESC copy numbers. These data demonstrate that the by-product of V(D)J recombination, when increased in abundance, potently associates with the V(D)J recombinase to cause adverse disease outcomes.

Similar content being viewed by others

Main

Circular extrachromosomal DNAs (ecDNAs) are present in most cancer types and are associated with poor patient outcomes[1]. ecDNAs typically span 50 kb to 1 Mb and have low nucleosome densities and high levels of transcription, resulting in increased expression of oncogenes when they are present5,6. This confers a growth advantage to recipient cells and preferential retention of oncogene-expressing ecDNAs. ecDNAs replicate autonomously, approximately once per cell cycle[7]; however, the absence of a centromere results in their unequal segregation at mitosis8,9, driving cancer heterogeneity and oncogene amplification in daughter cells[10]. This contributes to tumour evolution, treatment resistance and increased ecDNA copy numbers as the cancer progresses[11]. Consistent with this, ecDNAs predict 43% of high-grade oesophageal cancers and persist from early-stage to late-stage cancers[12].

V(D)J recombination is vital to generate diversity of immunoglobulin and T cell receptor (TCR) genes. It is catalysed by the recombination-activating gene (RAG) proteins RAG1 and RAG2, which bring complementary V, D or J gene segments into a synaptic complex by binding to their adjacent recombination signal sequences (RSSs)[2]. The RSSs consist of conserved heptamer and nonamer sequences separated by a non-conserved spacer of 12 ± 1 or 23 ± 1 bp, with recombination almost exclusively occurring between RSSs of different spacer lengths[13]. Following cleavage at gene segment–RSS boundaries, gene segments are joined to generate the variable exons of immunoglobulins or TCRs, whereas the intervening DNA is normally excised2,3. The signal sequences on the excised DNA are joined together, generating a signal joint (SJ) on an ESC2,3 (Fig. 1a). ESCs from immunoglobulin light chain loci are typically 50 kb to 1 Mb in size.

Fig. 1: RAG-generated extrachromosomal circular DNAs persist throughout mouse B cell development.

a, Schematic of the mouse immunoglobulin kappa (Igk) locus, highlighting the gene segments studied: Vκ16-104, Vκ3-1 and Vκ11-125, which undergo deletional recombination to generate an ESC. All Igl recombination reactions are deletional. Grey and blue triangles represent 12- and 23-RSSs, respectively; blue and purple rectangles represent V and J gene segments, respectively; the orange rectangle represents the constant region exon; the RS element is depicted by a green rectangle. b, Ratio of SJs to recombination junctions (Rec) at sequential stages of B cell development as determined by absolute qPCR for Jκ5-Vκ3-1, Jκ5-Vκ16-104 and Jλ1-Vλ1 and compared with the ratio in pre-B cells, which was set at 1:1 for ease of comparison. n = 3 samples. BM, bone marrow. c, Schematic of the isolation of ESCs from mouse mature B cells. Splenocytes were isolated from six-week-old mice and purified by flow cytometry to obtain IgM+ and IgG+ B cells (Supplementary Fig. 1); genomic DNA (gDNA) was extracted and digested with RecBCD to remove linear DNA. d, Jκ5-Vκ11-125 and Jκ5-Vκ16-104 ESCs persist as circles in mouse mature B cells (IgM+, upper and IgG+, lower). The amount of undigested DNA was determined by qPCR. Gapdh (encoded by linear, genomic DNA) was used as a negative control; untreated DNA was a further control (Ctrl). P values were determined by an unpaired, two-tailed Student’s t-test. Comparison versus Gapdh, 95% confidence interval: IgM+ Jκ5-Vκ11-125, −71.36 to −13.20; IgM+ Jκ5-Vκ16-104, −79.49 to −25.81; IgG+ Jκ5-Vκ11-125, −80.44 to −10.43; IgG+ Jκ5-Vκ16-104, −88.83 to −37.15. n = 3 samples. e, Rag1 expression levels at different stages of mouse B cell development as determined by quantitative PCR with reverse transcription (RT–qPCR). Data are normalized to Hprt expression levels. NIH3T3 cDNA is a negative control. n = 3 samples. Mean values are shown; error bars represent s.d.

Source Data

Initially, ESCs were thought to be inert, non-replicative entities that become diluted through cell division[4]. However, ESCs are now known to trigger genome instability through two related mechanisms. First, RAGs reassociate with the ESC SJ to catalyse ESC reintegration at RSS-like sequences known as cryptic RSSs (cRSSs), in a reaction that requires cleavage of both the ESC SJ and a genomic cRSS14,15,16. Although the frequency of reintegration is not known, it can cause insertional mutagenesis at tumour suppressor gene hotspots in T cell acute lymphoblastic leukaemia (T-ALL)[17]. Second, the RAG–ESC complex triggers double strand DNA breaks (DSBs) at cRSSs via a ‘cut-and-run’ reaction. In this reaction, the RAG–ESC complex synapses with a genomic cRSS, but unlike in reintegration, only the cRSS is cut[18]. The cleaved cRSS is released as a DSB, whereas the RAG–ESC complex remains intact to potentially trigger further DSBs[18]. Crucially, the DSBs caused by the cut-and-run reaction colocalize with many structural variants (SVs) found in ETV6–RUNX1 acute lymphoblastic leukaemia (ALL)[19] and map to frequently mutated genes in B cell precursor ALLs (BCP-ALLs)[18], implying that cut-and-run contributes to the development of BCP-ALL.

Current dogma states that ESCs are diluted during cell division and gradually decrease in number to negligible levels20,21. This, together with the downregulation of RAG proteins following productive immunoglobulin light chain (IgL)[22] or TCRα/γ recombination was believed to limit the potential harmful effects of the RAG–ESC complex. However, we show here that ESCs replicate and persist through multiple cell divisions. Moreover, similar to ecDNAs, high ESC copy numbers correlate with poor cancer prognosis, indicating that ESCs also have a pivotal role in cancer progression.

ESCs persist to mature B cells in mice

ESCs, in the form of TCR excision circles, are present in naive thymic emigrants and persist in circulating lymphocytes for approximately two weeks in chickens and potentially much longer in primates23,24,25. Similarly, kappa-deleting recombination excision circles, generated by recombination between the Jκ–Cκ intron RSS and kappa-deleting element (KDE in humans, RS in mice), are found in about 30% of Igκ+ B cells and nearly all newly generated Igλ+ B cells[4]. RAG gene expression is downregulated following productive TCRα/γ and IgL rearrangement and editing[22], and therefore ESC production outside the thymus and bone marrow is negligible. Furthermore, ESCs are believed to be non-replicative[4] and lost via cell division. However, to test whether, like ecDNAs, ESCs are replicated and inherited, we purified genomic DNA from pre-B cells and IgM+ B cells from mouse bone marrow, as well as IgM+ and IgG+ B cells from mouse spleen.

Several IgL recombination products were examined from both immunoglobulin kappa (Igk) and lambda (Igl) loci, together with their corresponding ESCs, via quantitative PCR (qPCR) using standards with known numbers of copies of the PCR product under investigation. The Igk locus undergoes both deletional recombination, where the SJ is found on the extrachromosomal ESC, and inversional recombination, where SJs are retained in the genome; our analyses focussed solely on deletional events (Fig. 1a). Remarkably, the SJ:recombination junction ratio shows only modest differences across all stages of B cell maturation and even appears to increase in IgG+ cells for Jκ5-Vκ3-1 and Jκ5-Vκ16-104 ESCs (Fig. 1b and Extended Data Fig. 1a). This increase cannot be explained by removal of the recombination junction via secondary recombination, as the ratio of the recombination junction to other genomic regions is maintained throughout B cell development (Extended Data Fig. 1b). Given that at least six cell divisions are required for maturation from IgM+ to IgG+ cells[26], these data imply that SJs on ESCs are replicated and inherited. Indeed, in the absence of replication, ESCs would be diluted to 1.6% or less of their corresponding recombination junction in IgG+ cells.

It remains possible, however, that ESCs have reintegrated into the genome and been replicated as part of genomic DNA. Reintegration cannot have occurred via opening of the SJ, as the assay to detect ESCs involves amplification of intact SJs. However, in principle, reintegration could occur via recombination between an RSS on the ESC (Fig. 1a) and one in the genome, resulting in the insertion of an intact SJ. The frequency of such events is expected to be low15,16,17, but to address this possibility, we tested whether ESCs remain as extrachromosomal circles in IgM+ and IgG+ B cells.

High-molecular-mass genomic DNA was prepared from IgM+ and IgG+ B cells using conditions that minimize DNA shearing. Following exonuclease V (RecBCD) treatment to digest linear DNA but leave closed circular or nicked DNA intact[27] (Fig. 1c), we measured the amounts of residual Jκ5-Vκ11-125 and Jκ5-Vκ16-104 SJs by qPCR, using standards with known copy numbers. Remarkably, both SJs were present at more than 50% of the undigested level, whereas the Gapdh control from linear genomic DNA was nearly completely lost (Fig. 1d). The presence of significantly higher fractions of ESCs compared with Gapdh following treatment strongly indicates that ESCs are circular in mouse splenic IgM+ and IgG+ B cells. Moreover, very low Rag1 expression in IgG+ cells implies that the circular ESCs have replicated and persisted from earlier stages, rather than being newly generated (Fig. 1e).

ESCs are present in BCP-ALL samples

In principle, the presence of ESCs in mature lymphocytes is unlikely to have functional consequences, owing to their very low RAG gene expression. However, RAGs are aberrantly expressed in most BCP-ALL subtypes28,29,30 (Extended Data Fig. 1c), and analysis of cDNA from more than 85 patient samples shows that expression of RAG1, but not RAG2, is significantly increased at diagnosis in patients who subsequently relapse (Extended Data Fig. 1d; RAG1: P = 0.0022). Therefore, the presence of RAGs and ESCs in these cancers could increase RAG–ESC complex formation and the risk of genome instability via cut-and-run or reintegration reactions. To investigate whether ESCs are detectable in primary BCP-ALL samples, we first determined the major recombination event(s) in nine ETV6–RUNX1 BCP-ALL samples using degenerate primer sets[31] to amplify rearrangements at the human IGK and IGL light chain loci. The resulting PCR products were cloned and sequenced, followed by sequence alignment to the IGK and IGL loci (Extended Data Fig. 2a).

The presence of the corresponding ESC SJs was then investigated using primers specific to each sample. Using this strategy, SJs with the predicted sequences were detected in six out of nine patients analysed (Extended Data Fig. 2b), with between one and three distinct SJs per patient. Since each recombination event generates just a single ESC and there are millions of cells in these malignancies, the ability to detect SJs in these samples suggests that these ESCs have replicated and persisted through many cell divisions.

Similar analyses (and high-throughput analyses, discussed below) using samples from patients with BCR–ABL1, CRLF2-r and low-hypodiploid BCP-ALL showed that SJs from deletional recombination events are also present in other BCP-ALL subtypes (Extended Data Fig. 2c).

To verify that SJs in BCP-ALL are present as extrachromosomal circles, high-molecular-mass DNA was prepared from patient samples using conditions that minimize DNA shearing. Following RecBCD treatment to remove linear DNA, SJs were amplified by droplet digital PCR (ddPCR). Consistent with their presence on extrachromosomal circles, SJs were amplified to a similar level with or without RecBCD treatment; by contrast, RecBCD reduced control linear DNA (GAPDH) to around 7% of untreated DNA levels (Extended Data Fig. 2d).

To better determine the fraction of patients with BCP-ALL carrying ESCs, we next capitalized on available whole-genome sequencing (WGS) data from patients with ETV6–RUNX1 BCP-ALL and re-analysed them for the presence of ESCs. DNA is prepared for WGS by shearing into fragments that average 500 bp, and approximately 35–50 bp at each end is sequenced. If the sequenced fragment includes an ESC SJ, the corresponding paired-end reads are flagged as ‘discordant’ when mapped to the genome, because the reads map much further away from each other than expected and appear to point towards each other, rather than away from each other. To detect ESCs, we therefore aligned WGS data from 61 patients with ETV6–RUNX1 BCP-ALL (European Genome-phenome Archive: EGAD00001000116) to the human genome and filtered for reads that fit the above criteria. We detected ESCs in 51 out of 61 patients, with between 1 and 27 different ESCs per patient (Extended Data Fig. 2e and Supplementary Table 1). Owing to low sequencing depth and the fact that an ESC will be identified only if a split read is positioned exactly across the SJ, these data cannot quantify ESCs. Nevertheless, they fully support the presence of ESCs in the majority of patients with ETV6–RUNX1 BCP-ALL and demonstrate that multiple ESCs can be present in each individual.

The coexistence of ESCs and RAGs in BCP-ALL could lead to increased RAG–ESC-mediated mutations and disease progression. However, the potential effect of the increased RAG–ESC activity depends on the quantity of ESCs and the timeframe over which ESCs are present. To investigate this, we established assays to detect all IGK and IGL recombination events and all IGK and IGL SJs. These assays, linear amplification-mediated (LAM)-recombination and LAM-ESC, are derived from LAM-high-throughput genome-wide translocation sequencing (LAM-HTGTS)[32] and involve linear amplification with biotinylated primers against J regions across VJ coding junctions or ESC SJs (Extended Data Fig. 3a,b). The biotinylated products are then selected, adapters are ligated and the coding junctions or SJs are amplified by PCR. Following amplicon sequencing of the products, the resulting sequences are mapped to bespoke reference databases that include all possible IGK/IGL recombination events or IGK/IGL SJs[33] (https://github.com/Boyes-Lab/LAM-ESC-Recombination) but exclude intra-KV region recombination events[34] and their SJs.

Using the LAM-recombination and LAM-ESC assays, we analysed 71 samples, taken at diagnosis, from patients with BCP-ALL, 34 of whom subsequently relapsed. In addition to the primary recombination event, many secondary recombination events were present, indicating continued RAG activity[29] (Supplementary Table 2). Complementary LAM-ESC data show multiple ESCs per patient and that ESC copy numbers varied widely (Fig. 2a and Supplementary Table 3). Remarkably, comparison of normalized LAM-ESC sequencing reads between patients who did and who did not subsequently relapse shows that significantly more ESCs were present at increased levels in patients who later relapsed (Fig. 2a,b; P = 0.00017). By contrast, in most patients who did not relapse, ESC copy numbers were close to those in healthy blood or bone marrow (Fig. 2a). Given that absolute ESC copy numbers, determined by ddPCR, correlated well with the number of normalized sequencing reads (Extended Data Fig. 4a) and that ddPCR experiments independently confirmed a similar fold increase of SJ levels in patients who later relapsed (Extended Data Fig. 4b), these data imply that there was increased ESC replication and/or persistence in patients who subsequently relapsed. No correlation was observed between RAG1 or RAG2 expression and ESC copy numbers (Extended Data Fig. 4c) and even in BCP-ALL samples in which RAG1 expression was very similar, increased ESC copy numbers were observed in patients who later relapsed but not in those who did not (Fig. 2c; P = 0.0156). Differences in tumour infiltration also do not explain altered ESC levels, as leukaemic blast levels were similar (greater than 90%) in both patient groups (Supplementary Table 4).

Fig. 2: High SJ copy numbers at diagnosis correlate with subsequent relapse.

a, Total IGK/IGL SJ levels were determined in samples from patients with BCP-ALL (from VIVO Biobank) at diagnosis using LAM-ESC. Normalized copy number of each SJ at diagnosis for patients who later relapsed (n = 34) and those who remained in remission (non-relapse; n = 37) are plotted. Normalized reads were calculated by dividing the reads obtained per SJ by the total LAM-ESC reads in that experiment. A threshold (horizontal line) was set at the highest normalized ESC level detected in healthy blood (HB, n = 2). SJ levels in a bone marrow sample taken at remission (REM) are shown for comparison. Only SJs resulting from deletional recombination events are shown. b, A significantly higher number of distinct SJs is present at levels above the threshold in patients who subsequently relapse compared with those who remain in remission. P value was determined by a two-tailed Fisher’s exact test. n = 34 (relapse) and 37 (non-relapse). c, Left, expression of RAG1 and RAG2 mRNA at diagnosis in patients who later relapsed (n = 5) and those who did not (n = 6); comparable RAG1 expression levels were observed in both groups. Right, normalized SJ copy numbers. The P value was determined by a two-tailed Fisher’s exact test.

Source Data

High ESC replication coupled to relapse

The increased ESC copy numbers in patients who later relapse implies that ESCs have replicated. Consistent with this, we identified seven SJs that were more abundant than their corresponding recombination junction using ddPCR (Extended Data Fig. 4d). Similarly, comparison of numbers of SJs and recombination junctions from KDE-KV2-30 and KDE-KV3-20 rearrangements across 48 samples shows that SJ numbers were significantly higher in patients who later relapsed (KDE-KV2-30: P = 0.0461, KDE-KV3-20: P = 9.25 × 10−5). By contrast, a much smaller increase (KDE-KV2-30: P = 0.0756, KDE-KV3-20: P = 0.0173) was observed in the corresponding recombination junctions (Extended Data Fig. 4e,f).

To investigate the extent of ESC replication, we capitalized on the fact that when each ESC is generated, a corresponding recombination ‘footprint’ is formed in the genome. If cells undergo multiple divisions following generation of an ESC, there will be multiple copies of the corresponding recombination junction. By contrast, if an ESC was generated recently, fewer copies of its recombination junction will be present (Fig. 3a). To measure ESC replication when the influence of ESC persistence is minimal, we focussed on recently generated ESCs. To this end, we examined ESCs corresponding to the lower limits of detectable LAM-recombination reads (≤0.2 normalized reads); as shown in Fig. 3b, the ratio of these SJs to the corresponding recombination junction was significantly higher in patients who later relapsed compared with those who did not (P = 0.004), implying increased ESC replication in patients prone to relapse. Notably, of the recently generated ESCs, 11 were identical in both patient groups (Extended Data Fig. 5a). After verifying that these ESCs were indeed recently generated by measuring the corresponding recombination junction by ddPCR, we quantified the SJ levels. Recently generated SJs were present at significantly higher levels in patients who later relapsed (Fig. 3c; P = 0.001). Given that the exact same SJ sequence was examined in the two patient groups, this increased replication cannot be due to the ESC sequence. Instead, it is likely that cell-intrinsic factors that are present at diagnosis trigger increased ESC replication in patients who later relapse.

Fig. 3: Increased ESC replication in patients with BCP-ALL who later relapse.

a, Schematic highlighting that multiple copies of a recombination junction (white and pink) are present if recombination took place many cell divisions ago. b, SJs corresponding to very recent recombination events (≤0.2 normalized LAM-recombination reads) were identified. Normalized SJ reads were divided by corresponding normalized recombination reads. P value for the increase in patients who later relapsed determined by two-tailed Mann–Whitney U test; n = 74 SJs from 12 patients (relapse) and 51 SJs from 8 patients (non-relapse). c, Eleven SJs corresponding to ≤0.2 normalized recombination reads are in both patient groups. SJ levels were measured by ddPCR for patients who later relapsed (red) or remained in remission (blue). Data are mean observed/predicted SJ values, assuming a twofold SJ dilution at each cell division (Methods). Black dots indicate values for individual patients. P values determined using a two-tailed Wilcoxon signed-rank test. n = 11 pairs. SJ levels only shown for HeLa controls (orange dots; n = 2). d, Enrichment plot for DNA repair genes from GSEA of RNA-seq data from 123 patients at diagnosis, 74 of whom relapsed. Significance determined as described53,54 with corrections for multiple comparisons. e, RT–qPCR analysis of expression of genes associated with DNA replication and repair in patients who later relapse (for patients with high (H-) or low (L-) SJ levels) or remain in remission (non-relapse). n = 11 for each group except L-relapse: n = 8 (PCNA) and 10 (POLE3); and non-relapse: n = 12 (RBX1). Data are normalized to HPRT expression. P values determined using an unpaired, two-tailed Student’s t-test. The 95% confidence interval is presented in Methods. Data are mean ± s.d. f, GSEA of RNA-seq data (EGAS00001006863) from patients with known SJ levels. Enrichment plot for DNA repair genes for patients with high versus low SJ levels (n = 4 and n = 3, respectively). P values determined as in d.

Source Data

To investigate what these cell-intrinsic factor(s) might be, we capitalized on available RNA sequencing (RNA-seq) data (https://www.cancer.gov/ccg/research/genome-sequencing/target, dbGaP sub-study ID: phs000464) obtained at diagnosis from 123 patients with BCP-ALL, 74 of whom later relapsed. Using DESeq2, followed by gene set enrichment analysis (GSEA), we found significantly increased expression of DNA repair genes (P = 0.0095; Fig. 3d) in patients who were prone to relapse. Published single-cell RNA-seq data from neuroblastoma cell lines similarly showed increased expression of the replication-associated genes PCNA, POLE3 and RPA2 corresponding to high ecDNA levels[35]. It is therefore plausible that replication and repair-associated gene products enhance ESC replication; consistent with this, significantly increased expression of PCNA, RBX1, POLE3 and POLE4 was observed in patients with high levels of SJs who later relapsed (Fig. 3e), but not in those with low levels of SJs, regardless of whether they relapsed (Fig. 3e). Furthermore, analysis of RNA-seq data (EGAS00001006863) from seven patients with known SJ levels (Fig. 2a) using DESeq2 and GSEA showed that expression of PCNA, RBX1, POLE3 and POLE4 was significantly increased in patients with high SJ levels compared with those with low SJ levels (Extended Data Fig. 5b) and that there was a significant increase in expression of DNA repair genes in patients with high SJ levels (Fig. 3f). These data therefore link higher expression of replication and repair-associated genes with increased ESC copy numbers, although a causal relationship with ESC replication has yet to be established. Nonetheless, previously identified replication initiation sites[36] are present within IGK and IGL ESC sequences (Extended Data Fig. 6), suggesting that ESCs may replicate via eukaryotic replication origins.

ESCs persist through many cell divisions

The effects of an ESC are dependent not only on how many copies there are, but also on the timeframe during which it co-exists in cells with RAG proteins. Therefore, we investigated the extent of ESC persistence by measuring how many ESCs correspond to recombination events that took place many cell divisions ago—that is, where the corresponding recombination junction was present at a high copy number (Fig. 3a). These were categorized as ‘major’ recombination events and were distinguished from other events by the maximal change in the gradient on plots of the distribution of sequencing reads[37] (Extended Data Fig. 7a). Although we detected many ESCs corresponding to such major recombination events, implying that ESCs persist, there was no significant difference in the percentage of major recombination events with a corresponding SJ (or SJs) between patients who later relapsed and those who did not (relapse: 25.85%, non-relapse: 28.3%). However, SJs that corresponded to major recombination events were present with higher copy numbers in patients who later relapsed (Fig. 4a; P = 0.011). Moreover, when only SJs with increased copy numbers (above the threshold in Fig. 2a) were considered, almost half corresponded to major recombination events (Fig. 4b, left). This is consistent with persistence of high-copy ESCs through multiple cell divisions, increasing the risk that they will trigger mutations.

Fig. 4: ESCs persist at higher copies in patients who subsequently relapse.

a, Major recombination signifies multiple cell divisions since the recombination event (Fig. 3a and Extended Data Fig. 7a). Normalized sequencing reads for SJs corresponding to major recombination events are plotted for each patient group. P value for the increase in patients who later relapse versus those who do not determined by a two-tailed Mann–Whitney U test; n = 40 from 23 patients (relapse) and n = 25 from 20 patients (non-relapse). b, Pie chart showing percentage of SJs with normalized sequencing reads above or below the threshold in healthy blood (Fig. 2a) that correspond to major recombination events versus other recombination events. P value for the difference determined by a two-tailed Fisher’s exact test. n = 23 high-copy SJs from 7 patients and 124 low-copy SJs from 12 patients. Recomb, recombination events. c, Representative DAPI-stained metaphase chromosome spreads from BCP-ALL samples with ESC levels similar to patients who remain in remission (left; n = 29 images) or who later relapse (right; n = 26 images). Red arrows indicate non-chromosomal DNAs. Images deconvoluted using CellSens Dimension software. d, ESCs detected by interphase FISH in patients with ESC levels similar to those who relapse (patient P, n = 108 images) or remain in remission (patient M, n = 101 images; patient N, n = 127 images). e, Schematic showing ESC and control FISH probes to IGK and IGL loci. Blue and grey triangles represent 12- or 23-RSSs. f, Representative interphase FISH image. Control (ctrl) probes against IGK and IGL are in green; the regions excised to generate ESCs are in red (IGL) or magenta (IGK). n = 99. g, IGK (magenta) and IGL (red) ESCs in the same cell. n = 10. h, Multiple ESCs detected per cell using IGK control probe (green) and KDE probe (magenta). n = 8. All images obtained at 60× magnification.

Source Data

In control experiments, we considered the possibility that rather than persisting, identical ESCs could have been generated by more recent, secondary recombination events38,39. However, by capitalizing on the presence of ESCs that correspond to the primary recombination event (that is, those with the most sequencing reads) in three patients and analysing the clonotypes of the respective recombination junctions, our data indicate that it is very likely that the ESCs persisted from the primary recombination event in at least two cases (Extended Data Fig. 7b–g).

ESC distribution in BCP-ALL

BCP-ALL progression is also likely to be influenced by the number of ESCs per cell and their intratumoral heterogeneity. To explore this possibility, we performed DNA fluorescence in situ hybridization (FISH) using probes that detect all ESCs from IGL and IGK loci. Actively cycling cells were blocked in mitosis and the presence of non-chromosomal DNAs was confirmed by DAPI staining (Fig. 4c). Since ecDNAs were not detectable in primary BCP-ALL samples by AmpliconArchitect[40] in this and a separate study[41] (20 and 44 patients[41], respectively), these non-chromosomal DNAs are likely to be ESCs. To further test this and more accurately determine ESC distribution, we screened interphase nuclei for ESC FISH signals that were distinct from control (chromosomal) signals. For a patient with ESC levels similar to those in patients who later relapsed (patient P; Extended Data Fig. 8a), ESCs were observed in around 50% of cells, with a noticeable clustering of 3–7 ESCs in some cells (Fig. 4d–f and Extended Data Fig. 8b). By contrast, for patients with ESC levels similar to those in patients who remained in remission (patients M and N; Extended Data Fig. 8a), ESCs were detected in fewer cells, with only one or occasionally two ESCs per cell (Fig. 4d). Notably, these interphase FISH signals showed high correspondence with the relative levels of DAPI-stained non-chromosomal DNAs (Extended Data Fig. 8c), and, when present at increased levels, ESCs exhibited remarkable intratumoral heterogeneity (Fig. 4d). We also detected the presence of IGK and IGL ESCs in the same cell (Fig. 4g). Given that simultaneous recombination of both loci is highly unlikely, the coexistence of three IGK ESCs and one IGL ESC supports the idea that ESCs replicate and persist.

Similarly, seven ESCs resulting from recombination to KDE were found within a single cell (Fig. 4h). There are only two KDE RSSs; therefore, the maximum number of ESCs that could be generated by recombination to KDE is two. Thus, the presence of seven ESCs in one cell was a strong indication of ESC replication. To verify this, we prepared metaphase chromosome spreads from BCP-ALL cells that were cultured in the presence of bromodeoxyuridine (BrdU) and then blocked in mitosis. Following hybridization with BrdU antibodies, we observed signals coinciding with DAPI-stained non-chromosomal DNAs, confirming ESC replication (Extended Data Fig. 8d).

ESC copy number and BCP-ALL progression

The presence of high ESC copy numbers over multiple generations increases the cumulative risk of DNA damage and may lead to cells with high ESC copy numbers undergoing clonal expansion. Consistent with this, SJs with high copy numbers were associated with a larger fraction of cells that had undergone many divisions (major recombination events; Fig. 4b, left) than those with low copy numbers (below threshold) (Fig. 4b, right). Next, we aimed to determine how ESC copy number at diagnosis influenced BCP-ALL progression. In other cancers, ecDNAs lead to a worse prognosis by increasing oncogene copy numbers1,42, acting as mobile enhancers[43], or by ecDNA integration into a tumour suppressor gene[44]. There are no known oncogenes on ESCs from the IGK–IGL or TCRA–TCRG loci and no known enhancers in the excised V-J regions of human loci. Similarly, although recombination to KDE generates ESCs that incorporate two strong enhancers—iEκ and 3′Eκ45,46—and such ESCs are significantly enriched and found in patients who later relapse (Extended Data Fig. 8e–g), patients who lack KV-KDE ESCs nonetheless relapse (Supplementary Table 3). Therefore, although ESCs may promote malignancy by acting as mobile enhancers, ESCs are likely to influence disease progression by other mechanisms.

ESCs cause increased mutations when complexed with RAG proteins, triggering either ESC reintegration at cRSSs or the cut-and-run reaction that generates DSBs at cRSSs. Both reactions produce SVs that have a cRSS on only one side of the breakpoint14,18. RAGs also trigger genome alterations that are independent of ESCs via off-target recombination between two cRSSs, leading to insertion–deletion mutations or chromosome translocations with cRSSs on both sides of the breakpoint19,47. To test whether the RAG–ESC complex contributes significantly to the mutations found in BCP-ALL, we examined the SVs in WGS data of patients with BCP-ALL using Therapeutically Applicable Research to Generate Effective Treatments (TARGET) data (https://www.cancer.gov/ccg/research/genome-sequencing/target; dbGaP sub-study ID: phs000464). Using 150 patient sequences obtained at diagnosis across all BCP-ALL subtypes, we first calculated the fraction of SVs with one or two cRSSs at the breakpoint. Consistent with previous data[19], cRSSs were present at nearly 40% of breakpoints (38.4%); of these, nearly 62% had a single cRSS and 36.4% had two cRSSs (Extended Data Fig. 9a). To determine the probable cause of the breaks at single cRSSs, we used an in-house script[48] (https://github.com/Boyes-Lab/NGS-Analysis), which showed that cut-and-run[18] occurs more than 60-fold more frequently than either reintegration14,15,16 or RAG-mediated insertions[49] (Extended Data Fig. 9a).

Next, we compared the numbers of SVs in patients, and found a significant increase in SVs with cRSSs on only one side of the breakpoint in patients who subsequently relapsed compared with those who did not (Fig. 5a, left). Moreover, consistent with the above analysis, the frequency of SVs with a single cRSS at the breakpoint (Fig. 5a, left) was much higher than those with cRSSs on both sides of the breakpoint (Fig. 5a, right; mean relapse: 27.19 versus 8.27, mean non-relapse: 23.48 versus 4.635), suggesting a greater role for RAG–ESC-mediated mutations.

Fig. 5: Association between increased ESC-mediated mutations and relapse.

a, SVs per patient at diagnosis with a single cRSS (left) or two cRSSs (right) at the breakpoints plotted for patients who later relapsed (121 patients) versus those who remained in remission (29 patients). P value for the difference determined by a two-tailed Mann–Whitney U test. Single cRSS: P = 0.016; two cRSSs: P = 0.0006. SVs are from the TARGET study. Breakpoint junctions within antigen receptor loci are omitted. b, Right, pie chart showing all SVs at relapse with one cRSS at the breakpoint, two cRSSs or no cRSS for 83 matched patient samples; SVs at diagnosis were subtracted from those at relapse. Left, bar chart showing SVs at genes commonly mutated at relapse. P value for increased SVs involving single cRSSs at relapse-associated genes compared with all SVs involving a single cRSS calculated using a one-sided hypergeometric distribution; P = 0.0001. c, Frequency of breaks in 10 genes that most often acquire somatic mutations in relapsed BCP-ALL[51] in the presence of the ESC (SJ) versus 12-RSS and 23-RSS controls (RSS) in a LAM-HTGTS experiment[18]. P value for co-localization of breaks detected by LAM-HTGTS and frequently mutated genes in relapsed ALL versus all genes mutated in ALL calculated using a one-sided hypergeometric distribution; P = 0.00077. n = 4. d, ddPCR of selected recombination junctions at diagnosis and relapse. Cell numbers normalized using GAPDH. Bars show mean values. n = 10 recombination junctions from four patients. e, ddPCR analysis of selected SJs at diagnosis and relapse for the indicated patients. Black dots show technical repeats. Bars show mean values. n = 10 SJs from 4 patients. f, Copy numbers of individual SJs at diagnosis for patients with ETV6–RUNX1 BCP-ALL (n = 16) who later relapsed or remained in remission. The horizontal line shows the highest normalized SJ copy number detected in healthy blood.

Source Data

Increased ESCs in patients at diagnosis imply that the RAG–ESC complex continues to cause damage between diagnosis and relapse. We therefore compared WGS data from 83 matched samples taken at diagnosis and relapse. By focusing on SVs near genes that are frequently mutated at relapse50,51, we observed significantly more SVs with cRSSs on one side of the breakpoint that are specifically present at relapse compared with other SVs (Fig. 5b). Likewise, re-analysis of available LAM-HTGTS data[18] (NCBI SRA: PRJNA483469) showed a significant increase in targeting of relapse-associated genes by the RAG–ESC complex compared with the RAG–RSS complex in cells derived from a patient with relapsed ETV6–RUNX1 BCP-ALL (Fig. 5c). Together, these data imply that ongoing activity of the RAG–ESC complex triggers mutations at genes that are associated with relapse.

To test whether there is a direct link between increased ESC levels and SVs at single cRSSs, we analysed WGS (EGAS00001006863) and whole-exome sequencing (WES) data of patients with BCP-ALL for whom we had measured SJ and RAG gene expression levels (Fig. 2a and Extended Data Fig. 1d). Consistent with the idea that the RAG–ESC complex triggers relapse-associated mutations, we observed a significant increase in SVs with a single cRSS at the breakpoint at relapse-associated genes in patients with high SJs plus high RAG1 expression compared with those with high RAG1 expression plus low SJs or low RAG1 expression plus low SJs (Extended Data Fig. 9b–d). Moreover, in a patient with high SJs, we observed clonal expansion of an SV at a single cRSS in the spleen tyrosine kinase (SYK) gene between diagnosis and relapse (Extended Data Fig. 9e).

If reactions involving the ESC truly underpin the mutations that lead to relapse, the presence of sufficient copies of ESCs at or before diagnosis would be expected to lead to expansion of the ESC-harbouring cells by relapse. To test this, we capitalized on the ability to trace cells in which ESCs have been generated by virtue of their corresponding recombination junction. We therefore performed LAM-recombination on samples taken at relapse, in cases where patients have high ESC copies at diagnosis. The frequencies of some recombination junctions stayed the same or even decreased between diagnosis and relapse, possibly owing to treatment-mediated loss of the corresponding cells (Supplementary Table 2). However, others showed marked increases in normalized sequencing reads (Extended Data Fig. 10a), an observation that was confirmed for ten cases by ddPCR (Fig. 5d).

We next tested whether clonal expansion, measured by the increase in recombination junctions, was linked to the presence of a matching ESC at diagnosis. Remarkably, a corresponding ESC was detected in every case of clonal expansion, but in only 58% of cases where no expansion of recombination junctions was observed, and in these latter cases, ESC copy numbers were often lower (Extended Data Fig. 10b). This correlation is notable and consistent with the idea that ESC-mediated mutagenesis promotes disease progression to relapse.

A further prediction is that if ESCs indeed replicate and persist, the same ESCs should be detectable at both diagnosis and relapse. Remarkably, we found that all ESCs persisted (Fig. 5e), in one case for more than seven years and in two cases for more than four years. Quantification of SJs at diagnosis and at relapse showed that some increased, whereas others decreased slightly, supporting the idea that the SJ is on an extrachromosomal circle rather than integrated into the genome.

Finally, if ESC activity causes disease progression, high SJ copy numbers at diagnosis should predict disease outcome. We therefore re-analysed the data showing SJ levels at diagnosis (Fig. 2) according to BCP-ALL subtype (Supplementary Table 4). Although genomic integration of SJs in some DUX4-r samples (Extended Data Fig. 10c,d) precluded such analyses for this subtype, there was a good correlation between the SJ copy number above the threshold and subsequent relapse for subtypes that usually have a good prognosis (ETV6–RUNX1 and high hyperploid (HeH) BCP-ALL) or an intermediate prognosis (TCF3::PBX BCP-ALL) (Fig. 5f and Extended Data Fig. 10e). Moreover, in BCP-ALLs where PAX5 was altered or mutated, SJ levels were higher overall, but were noticeably different between patients who relapsed and those who did not, suggesting that a higher threshold may better identify patients who are at risk of relapse (Extended Data Fig. 10e). Our data therefore imply that the presence of ESCs at diagnosis above subtype-specific threshold levels is frequently associated with subsequent relapse. This strongly suggests a central role for ESCs in disease progression.

Discussion

ESCs were long believed to be inert and diluted during cell division. However, it is now clear that ESCs have biological activity and replicate and persist in healthy lymphocytes and in BCP-ALL. In BCP-ALL, persistence of increased copy numbers of ESCs is strongly linked with worse disease outcomes, thereby resembling ecDNAs. ESCs and ecDNAs are both extrachromosomal circles; IGK/IGL ESCs are a similar size to ecDNAs; and ESCs and ecDNAs replicate and persist through multiple cell divisions and both confer a growth advantage to cancer cells when present at elevated levels5,6. However, there are key differences. Whereas ecDNAs often confer a growth advantage by increasing oncogene copy numbers[10], ESCs trigger mutations, including at cancer driver genes and relapse-associated genes, via the cut-and-run reaction[18]. These mutations accumulate through time and are inherited by all daughter cells, regardless of whether those cells inherit the ESC. Similarly, once the RAG–ESC complex has triggered sufficient mutations in key genes, the continued presence of the ESC may not be required. By contrast, continued oncogene amplification via ecDNAs is required for a growth advantage. This may explain why ecDNA levels gradually increase as cancers progress[12], whereas ESC levels are lower overall and may increase or decrease between diagnosis and relapse. Moreover, the stochastic nature by which the recombinase, and thus the RAG–ESC complex, finds its targets means that different mutations will be triggered in each cell. This may explain why some cells with high ESC copy numbers expand between diagnosis and relapse whereas others, possibly those in which fewer cancer driver genes have been mutated, either respond better to treatment or become diluted. Although high ESC copy numbers correlate with subsequent relapse in around 50% of cases, some patients with low ESC levels at diagnosis nonetheless go on to relapse. In these cases, other mutations, such as deletion of IKZF1[52] or initiating mutations that alter signalling to dysregulate multiple pathways[50], may predispose the patient to relapse. Nonetheless, the good correlation between high ESC levels and poor prognosis, particularly for ETV6–RUNX1 and HeH BCP-ALL, may be of clinical utility. Collectively, our data demonstrate that ESCs are replicated and inherited and form a complex with RAG proteins that can lead to relapse-associated mutations and clonal expansion (Extended Data Fig. 11).

Methods

Purification of mouse B cells

Non-transgenic CBA/C57BL/6 J mice were obtained from the University of Leeds animal facility, which is a full barrier facility, with a light/dark cycle of 12 h on/12 h off, an ambient temperature of 21 °C (range 20–22 °C) and 45–65% humidity. No more than six animals are housed per cage and all mice are free of common pathogens, including murine norovirus, Pasteurella and Helicobacter. Animal procedures were performed under Home Office licence P3ED6C7F8, following review by the University of Leeds ethics committee. Mouse femurs and spleens were collected from 5- to 7-week-old mice, using 12 mice in total to minimize animal numbers used, according to 3Rs principles. Roughly equal numbers of male and female mice were used; randomization and blinding were not necessary, as all mice were wild type. Bone marrow cells were flushed from femurs with PBS whereas splenocytes were prepared by flushing cells from finely diced pieces of spleen with PBS through a 50-µm cell strainer. Following preparation of single-cell suspensions in PBS, bone marrow cells and splenocytes were centrifuged at 600g for 3 min and resuspended in 10 ml of 0.168 M NH_4Cl to lyse erythrocytes. After 10 min, cells were washed with 40 ml PBS and resuspended in 1 ml staining buffer (2% FCS, 1 mM EDTA, 25 mM HEPES-KOH pH 7.9 in PBS).

Cells were stained with the appropriate antibodies prior to purification by flow cytometry. For bone marrow pre-B cells, cell suspensions were stained with 6 μl each (6:1,000 dilution) of FITC anti-CD19 (BD Pharmingen, 553785) and PE anti-CD43 (BD Pharmingen, 553271). Bone marrow or spleen IgM+ cells were stained with 10 μl (1:100 dilution) FITC anti-IgM (BD Pharmingen, 553408) whereas spleen IgG+ cells were stained with 15 μl PE (3:200 dilution) anti-IgG (eBioscience, 12-4010-82). Following incubation at room temperature for 10 min, cells were washed with PBS and resuspended in 0.5 ml staining buffer prior to purification using a FACSMelody (BD) cell sorter running BDFACSChorus 3.0 software. CD19+/CD43− cells were isolated as the pre-B population whereas cells stained with anti-IgM+ or anti-IgG+ were isolated as their respective populations.

Patient samples

Patient samples, taken as part of routine diagnostics, were supplied by VIVO Biobank, HMDS or a hospital in the Czech Republic. Collection and use of patient samples were approved by the appropriate institutional review board (IRB). Each organization obtained informed patient consent for anonymized samples to be used by third parties for research. The use of surplus diagnostic material for research by HMDS and collaborators was approved by the Health Research Authority (HRA): 04_Q1205_125. Local ethics approval was obtained from the Biological Sciences Research Ethics Committee, University of Leeds: BIOSCI 18-031 & 2308 and CCR 2285, Royal Marsden Hospital NHS Foundation Trust.

Cell culture

hTERT-RPE-1 cells were from ATCC where they were authenticated by morphology, STR profiling and karyotyping and verified mycoplasma-free. NIH3T3 cells were from the laboratory of C. Bonifer, whereas HeLa cells were from the laboratory of T. Enver. Both cell types were authenticated using species-specific PCR primers. They were verified free from mycoplasma using MycoAlert Mycoplasma Detection Kit (LT07-318). HeLa cell contamination has caused misidentification of other cell lines. However, HeLa cells were used here only to prepare human DNA and we verified that the DNA was human using human-specific PCR primers. hTERT-RPE-1, NIH3T3 and HeLa cells were maintained in Dulbecco’s modified Eagle’s medium (DMEM) supplemented with 10% fetal calf serum, 4 mM l-glutamine, 50 U ml−1 penicillin and 50 μg ml−1 streptomycin in a humidified incubator at 37 °C with 5% CO_2.

Preparation of genomic DNA

Genomic DNA from mouse B cells, NIH3T3 cells, HeLa cells and patient samples was prepared by gently resuspending 1 × 10^6 to 5 × 10^6 cells in a 200 µl digestion buffer (200 mM NaCl, 10 mM Tris-HCl pH 7.5, 2 mM EDTA, 0.2% SDS). Proteinase K was added to a final concentration of 0.4 mg ml−1, followed by incubation at 56 °C overnight, with rotation. The next day, an equal volume of isopropanol was added and the sample mixed thoroughly but gently by inversion to precipitate the DNA. The DNA pellet was recovered by centrifugation at 20,000g for 5 min at room temperature and washed twice with 70% ethanol. DNA was then resuspended in 100 µl TE and incubated at 56 °C for at least 3 h to ensure complete resuspension; the concentration was measured using a DeNovix DS-11 spectrophotometer.

High-molecular-mass genomic DNA was prepared from fresh BCP-ALL bone marrow aspirates (that were surplus to diagnostic needs and that had been maintained at 4 °C), using a Promega Wizard HMW DNA extraction kit according to the manufacturer’s instructions for whole blood. Samples were resuspended in TE at room temperature overnight prior to measuring the concentration as above.

Isolation of total RNA and reverse transcription

Two million mouse B cells, NIH3T3 cells, HeLa cells or BCP-ALL cells were resuspended in 500 µl of TRIzol (Invitrogen, 3289) and total RNA was isolated according to the manufacturer’s instructions. DNA contaminants were removed by treatment with 2 U DNase I (Thermo Scientific, EN0521) for 45 min at 37 °C in 100 µl of 1× DNase I buffer (10 mM Tris-HCl pH 7.5, 2.5 mM MgCl_2, 0.1 mM CaCl_2). Following phenol-chloroform extraction and ethanol precipitation, total RNA was resuspended in 20 µl of ddH_2O and the concentration was determined using a DeNovix DS-11 spectrophotometer.

One microgram of total RNA was reverse transcribed with M-MuLV reverse transcriptase (Invitrogen, 28025-013). In brief, 1 µg of RNA was added to 2.5 µM oligo dT primer, 500 µM dNTPs and ddH_2O to give a total volume of 12 µl. This was incubated at 65 °C for 5 min and immediately placed on ice before addition of 4 µl first strand buffer (Invitrogen), 10 mM DTT and 1 µl RNase inhibitor (PCRBIO, PB30.23-02). The reaction was incubated at 37 °C for 2 min, followed by addition of 1 µl M-MuLV and incubation at 37 °C for 50 min prior to heat inactivation at 70 °C for 15 min.

Exonuclease V treatment of genomic DNA

Linear DNA was removed from genomic DNA using Exonuclease V (RecBCD, NEB M0345S). Reactions comprised 1 µg genomic DNA, 1× NEBuffer 4, 1 mM ATP and 10 U RecBCD in 100 µl total volume. Negative control reactions were identical except RecBCD was omitted. Following incubation at 37 °C for 1 h (mouse DNA) or 3 h (BCP-ALL DNA), EDTA was added to a final concentration of 11 mM and reactions were heat inactivated at 70 °C for 30 min. DNA was then ethanol precipitated and resuspended in 50 µl ddH_2O; 5 µl (100 ng) was used directly for PCR.

Quantitative PCR

qPCR was performed using a Rotor-Gene 6000 cycler (Corbett) and analysed using the Corbett Rotor-Gene 6000 Series Software (v.1.7, build 87). All reactions were carried out in a final volume of 10 µl, containing 1× qPCRBIO SyGreen Mix (PCRBIO, PB20.14), 400 nM each primer and 100 ng genomic DNA, 1–5 ng cDNA or 1 µl first round PCR product (for nested PCR). All reactions were performed in duplicate. In each case, a standard curve of the amplicon was analysed concurrently to evaluate the amplification efficiency and to calculate the relative amount of amplicon in unknown samples. R^2 values were 1 ± 0.1. A typical cycle consisted of: 95 °C for 3 min, followed by 40 cycles of 95 °C for 5 s, Tm for 10 s and extension at 72 °C for 10 s, where Tm = melting temperature of the primers (Supplementary Table 5). A melt curve, to determine amplicon purity, was produced by analysis of fluorescence as the temperature was increased from 72 °C to 95 °C. Amplicons were 100–200 bp.

Standard curves for absolute quantification were generated by 35 cycles of conventional PCR and purification of the desired product via a 1.2% agarose gel and a QIAquick gel extraction kit, (QIAGEN, 28704). Following measurement of the concentration via absorbance at 260 nm (using a DeNovix DS-11 spectrophotometer), DNA was diluted to 1–10 ng/μl before more accurate concentration determination using a QuantiFluor dsDNA kit (Promega, E2670) and a FLUOstar OPTIMA plate reader (BMG Labtech). An appropriate range of each standard was used in qPCR, ensuring that all unknown samples were within the standard curve.

Primers and melting temperatures are shown in Supplementary Table 5 for quantitative analysis of recombination, SJs and Rag1 expression in mouse bone marrow and spleen, and for quantitative (qPCR) analysis of recombination, SJ levels, RAG1 and RAG2 expression as well as PCNA, POLE3, POLE4 and RBX1 expression in BCP-ALL patient samples. BLAST was used to check primer specificity. HPRT was used as a reference gene for expression studies, using primers that span an intron. Genomic GAPDH sequences were used to normalize for cell numbers. These housekeeping genes were chosen for their widespread expression (HPRT) and low likelihood of mutation.

Detection of recombination in BCP-ALL patient samples

PCR was performed using Taq DNA polymerase (NEB, M0267) in reactions comprising 1× ThermoPol buffer, 200 µM dNTPs, 0.5 µM each primer, 1.25 U Taq DNA polymerase and 100 ng genomic DNA template in a final volume of 50 µl. Primers for recombination at the immunoglobulin kappa and lambda loci were as described by the BIOMED-2 consortium[31]. Cycling conditions involved initial denaturation at 95 °C for 5 min, followed by 95 °C for 30 s, 60 °C for 30 s and 68 °C for 30 s for 35 cycles, followed by a final extension of 5 min at 68 °C. PCR products were separated by gel electrophoresis; products of the expected sizes[31] were excised and cloned prior to Sanger sequencing.

Nested PCR of recombination junctions and SJs in mouse and patient samples

To achieve sufficient specificity and sensitivity, nested PCR was performed using Taq DNA polymerase (NEB, M0267). First round reactions consisted of 1× ThermoPol buffer, 200 µM dNTPs, 0.5 µM each primer, 1.25 U Taq DNA polymerase and 20–100 ng genomic DNA template in a final volume of 50 µl. To detect mouse recombination and SJs, thermocycling conditions involved denaturation at 94 °C for 3 min, followed by 18 cycles of 94 °C for 20 s, Tm for 20 s and 72 °C for 20 s. A 7 min of final extension was performed. One microlitre of 1:10 diluted first round PCR product was used as the template for a second round of qPCR using the primers shown in Supplementary Table 5.

As the BIOMED-2 primers to detect human SJs do not robustly identify specific J gene segments, nested PCRs were carried out with a mixture of first round primers that bind upstream of all five KJ RSSs or LJ1, LJ2 and LJ3 RSSs, which account for ~99% of IGL recombination events[31], followed by second round PCRs specific for each individual J RSS. First round reactions were set up as described above with 50–100 ng template DNA, followed by denaturation at 95 °C for 5 min, and 25 cycles of 95 °C for 30 s, Tm for 30 s and 68 °C for 30 s, and a final extension of 5 min at 68 °C. Second round reactions were identical except 1 µl first round PCR product was used as template and the number of cycles was optimized for each amplicon, which was typically 36 cycles. Primers and melting temperatures are shown in Supplementary Table 5.

Sequencing of PCR products

PCR products were separated on a 1.2% agarose gel; DNA was purified from the gel using a QIAquick gel extraction kit (QIAGEN, 28704) and cloned into a T-tailed pBluescript II SK (+) vector (Stratagene, 212205) that had been digested with EcoRV-HF (NEB, R3195). Positive clones were sent for Sanger sequencing (Eurofins Genomics, LightRun Tube) using a M13 forward sequencing primer.

Sequencing traces (in .ab1 format) were aligned using SnapGene (v4; GSL Biotech). For recombination, sequences were aligned against the human immunoglobulin kappa (NCBI Gene ID: 50802) or lambda loci (NCBI Gene ID: 3535), as appropriate. For ESCs, the possible head-to-head SJ sequence was assembled from the appropriate genomic sequence and sequences were aligned to this. All alignments were verified by BLASTN (NCBI; accessed at https://blast.ncbi.nlm.nih.gov), where the search set was limited to the Homo sapiens (taxid: 9606) RefSeq Genome Database (refseq_genomes).

ddPCR

ddPCR reactions were conducted in a total volume of 20 µl with 1× ddPCR Supermix for probes (Bio-Rad 1863026), 900 nM of each primer, 250 nM probe and 63 ng template DNA. Droplets were generated in an 8-well droplet generation plate using a Bio-Rad QX100 droplet generator. Nanodroplets were carefully transferred to a 96-well plate, which was sealed with foil prior to thermocycling. The latter involved an initial denaturation at 95 °C for 10 min, followed by 40 cycles of 94 °C for 30 s and 60 °C for 1 min, followed by 98 °C for 10 min and 4 °C for 30 min to allow droplets to equilibrate. The presence of amplified products was determined using the Bio-Rad QX100 Droplet Reader and QuantaSoft v1.7.4 software. For positive droplet identification, a manual threshold (2000) was applied to 1D amplitude data to minimize the occurrence of false positives. Primers are shown in Supplementary Table 5, for absolute quantitative analysis of GAPDH, recombination junctions and SJs in BCP-ALL samples.

Targeted sequencing of recombination and SJs (LAM-ESC and LAM-recombination)

Targeted sequencing of light chain recombination and SJs was performed using modified versions of the LAM-HTGTS technique[32] with bespoke analysis pipelines. Recombination junctions were detected using LAM-recombination, where bait primers (Supplementary Table 5) were designed against regions adjacent to J gene segments, allowing recombination to V gene segments to be determined. SJs were detected via LAM-ESC where bait primers (Supplementary Table 5) were designed against regions adjacent to J segment RSSs, allowing any sequence (for example, V RSSs) joined to J RSSs to be determined.

Libraries were generated as described[32] with minor modifications. Specifically, 500 ng genomic DNA was used as template in 90 cycles of the initial Bio-PCR. For the final PCR step (Tagged PCR), primers were used to add sequencing adaptors (Amplicon-EZ-I7-blue and Amplicon-EZ-I5-nested; Supplementary Table 5). Following library generation, samples were sent for 2× 250 bp paired-end sequencing using the Amplicon-EZ service (Azenta).

To analyse the data, FASTQ files were initially demultiplexed using each J gene segment or J RSS nested primer, for recombination and SJ libraries, respectively. The paired-end reads were then combined into a single read, using the overlap at the 3′ end of read 1 and 5′ end of read 2. If reads could not be combined, read 1 only was analysed. A custom Python script was used to automate BLAST searches against a custom BLAST database, consisting of all V-J recombination events or all head-to-head RSS combinations from the immunoglobulin kappa and lambda loci, for recombination and SJ libraries, respectively https://github.com/Boyes-Lab/LAM-ESC-Recombination[33].

Clonotype determination

Recombination junctions were amplified using LV3-1_REC_F, LV5-45_REC_F or LV2-11_REC_F with LJ2/3_REC_R (Supplementary Table 5). Following gel purification of the amplified products using the QIAquick gel extraction kit (QIAGEN, 28704), samples were sent for 2 ×250 bp paired-end sequencing using the Amplicon-EZ service (Azenta) that included addition of Amplicon-EZ-I7 and Amplicon-EZ-I5 sequencing adaptors. Paired-end reads in the .fastq format were combined by overlapping the 3′ end of read 1 with the 5′ end of read 2 (EGAD50000001518). The reads were compared to the reference motifs near the breakpoint junction of interest using the script Clonotype_analysis.py (https://github.com/Boyes-Lab/NGS-Analysis)[48], which identified each unique clonotype and the frequency at which it occurred. The reference motifs consisted of 5 bp from each of the respective V and J motifs, derived from sequences that lie 20 bp from the V-J junction that would be formed in the absence of processing. Specifically, the reference motifs were: 5 bp of V gene reference sequence; omit 20 bp of V gene sequence to the boundary; omit 20 bp of J gene sequence; use 5 bp of J gene sequence as reference. If the amplified sequence contained both of the 5bp motifs, then the code identifies each unique sequence that intervenes. The identified sequences were then inputted into IgBlast[55] which determined if the insert at the V-J junction was derived from elsewhere in the genome. The number of unique clonotypes was determined from these inserts: two sequences with the same V-J insert were classed as being the same clonotype.

The number of recombination copies attributable to each distinguishable minor clonotype was determined by calculating the absolute copy number of the recombination event by ddPCR and multiplying that by the percentage of each minor clonotype. Assuming each recombination is present on a single allele, the number of cells harbouring the recombination event was then estimated (that is, one recombination copy equates to one cell harbouring the recombination). The number of cell divisions (n) required to generate the recombination levels measured for each minor clonotype was subsequently calculated using the formula for cell population doublings: N_2 = N_1(2n) where N_1 = number of cells at beginning (that is, 1 cell) and N_2 = number of cells at end (that is, the estimated number of cells). From this, the minor clonotypes were calculated to be present at copies equivalent to 0.81–3.69 relative cell divisions (patients R-8 and R-13).

To investigate if the SJ levels observed via ddPCR (Extended Data Fig. 7c) could have resulted from replication of SJs from the minor clonotypes, the number of SJs predicted to remain if ESCs are diluted at each cell division were calculated using the formula for exponential decay: xt = x_0/2t where xt = predicted SJ level, x_0 = initial SJ level (that is, 1) and t = number of cell divisions (calculated above). Theoretically, the SJ measured by ddPCR could correspond to one or more of the minor clonotypes; we therefore took a conservative approach and summed the predicted SJ values for all the distinguishable clonotypes. We then divided the observed SJ value (Extended Data Fig. 7c) by the predicted SJ levels for the minor clonotypes. This observed/predicted value was compared to the observed/predicted values for SJs generated a similar number of relative cell divisions ago, using the values shown in Fig. 3c, where the SJs were estimated to result from 0.33–6.32 relative cell divisions. The SJ copies found in patient R-8 are substantially higher than those generated by replication of SJs from similarly recent recombination events (Extended Data Fig. 7d), implying that at least some of the SJs have persisted from the primary recombination event. Similar analyses cannot discount the possibility that replication of recently generated SJs generated the SJs observed in patients R-13 and R-9.

Calculation of observed/predicted ESC levels

The observed SJ/predicted SJ ratio provides a more accurate measure of ESC replication as it takes the extent of cell division into account. It ensures that ESCs from cells that have undergone marked differences in cell division do not artefactually show the same level of replication. Predicted SJ levels were calculated using the formula for exponential decay given above. For Fig. 3c, only recombination junctions that had undergone ≤6 cell relative divisions per ddPCR sample were examined.

Phi29 amplification

Freeze-thawing of cells causes DSBs56,57 and depletion of circular DNAs in patient samples. Phi29 was therefore used to amplify remaining circular DNAs in BCP-ALL samples via rolling circle replication, using the Illustra TempliPhi 500 Amplification kit (Cytiva 25640010) according to the manufacturer’s protocol. Specifically, 10 ng of DNA was diluted with 50 μl of sample buffer, incubated at 95 °C for 3 min and cooled to 4 °C. The reaction was then incubated in 1× Phi29 reaction buffer (50 mM Tris-HCl pH 7.5, 10 mM MgCl_2, 10 mM (NH_4)2SO_4, 4 mM DTT) with 2 μl of enzyme mix at 30 °C for 18 h (human DNA) or 6 h (mouse DNA), followed by 65 °C for 10 min to inactivate the enzyme. DNA was precipitated with isopropanol, washed with 70% ethanol and resuspended in 25 μl ddH_2O. Control experiments omitted the enzyme. Sample concentrations were determined via absorbance at 260 nm (using a DeNovix DS-11 spectrophotometer) and diluted to 7 ng/µl. SJs were quantified by ddPCR and the SJ/GAPDH ratio of treated versus untreated sample determined.

Fluorescence in situ hybridization

DNA-FISH was performed as described[58]. Fosmid clones targeting IGK (ABC10-44246300H4), IGK-JK-KDE (ABC8-2123240B1) and IGL (ABC10-44455600K21) ESCs as well as IGK and IGL control regions (ABC10-43608900D2 and ABC10-44444000A2, respectively) were gifts from E. Eichler. Each fosmid probe was directly labelled by nick translation as described[59], except the amount of DNA labelled was reduced to 1 μg and both aminoallyl-dUTP and aminoallyl-dCTP were incorporated, followed by coupling to fluorescent dyes (Alexa Fluor 488/555/647, Invitrogen). Fosmid probes were purified using a QIAquick PCR purification kit and elution in 10 mM Tris-HCl pH 8.5. Patient bone marrow samples were cultured in StemSpan SFEMII medium (Stem Cell Technologies) supplemented with 20% fetal calf serum, 1% l-glutamine, 100 μg ml−1 Primocin (InvivoGen), 20 ng ml−1 IL-3 and 20 ng ml−1 IL-7 (Cell Guidance Systems) in a 37 °C humidified incubator, 5% CO2, prior to Colcemid treatment (0.2 µg ml−1, KaryoMAX, ThermoFisher) for 2 h. hTERT-RPE-1 cells were maintained in supplemented DMEM and treated with Colcemid as described above. Cells were then centrifuged and resuspended in prewarmed 75 mM KCl, followed by incubation at 37 °C for 20 min. After further centrifugation, cells were resuspended in Carnoy’s fixative (methanol: glacial acetic acid 3:1) and dropped onto humidified microscope slides. Slides were incubated in 2× SSC/RNase A 100 µg ml−1 at 37 °C for 1 h, followed by successive dehydration in 70%, 90%, and 100% ethanol. Slides were heated to 70 °C for 5 min on a hot plate, followed by DNA denaturation in preheated denaturant (2× SSC/70% formamide) at 70 °C for 30 min. Subsequently, slides were placed in ice-cold 70% ethanol, then 90% and 100% ethanol at room temperature before air-drying. For each slide, 100 ng of fosmid probe was combined with 6 µg human Cot-1 DNA (Invitrogen) and 5 µg single stranded DNA from salmon testes (Invitrogen), followed by ethanol precipitation. The DNA pellet was washed with 70% ethanol and resuspended in hybridization buffer (2× SSC, 50% deionized formamide, 10% dextran sulfate, 1% Tween-20). FISH probes were denatured at 92 °C for 5 min, pre-annealed at 37 °C for 15 min and then were immediately hybridized with DNA on slides overnight at 37 °C in a light-tight humidified chamber. Slides were washed in 2× SSC at 45 °C, 0.1× SSC at 60 °C, 1× PBS with 10 µg ml−1 DAPI at room temperature and finally mounted with SlowFade Gold antifade reagent (Invitrogen). Slides were imaged using an Olympus IX83 widefield fluorescence microscope with a 60× (60×/1.4 Oil, Plan Apo (oil)) objective and a Photometrics Prime BSI CMOS camera with a motorized xyz stage. Filter sets are DAPI (excitation 365/10 nm) emission 440/40 nm, GFP (excitation 482/24 nm) emission 530/40 nm, RFP (excitation 545/10 nm) emission 600/50 nm, Cy5/A647 (excitation 628/40 nm) emission 692/40 nm. Images were acquired using Olympus CellSens Dimension 3.2 (Build 23706) software and analysed using FIJI 2.16.0 software.

BrdU immunofluorescence

Bone marrow cells were resuspended in StemSpan SFEMII medium, supplemented as described above, and labelled with 10 µM BrdU (Merck B5002) for 28 or 48 h in a 37 °C humidified incubator, 5% CO_2. Primary BCP-ALL cells[60] have a doubling time of 26 to 240 h. Therefore, for cells incubated with BrdU for 28 h, incorporation should be limited to a single S phase for any cells in metaphase. Chromosome spreads were prepared as described for DNA-FISH. DNA was denatured by incubating the slides in 1 M HCl for 40 min at room temperature, followed by neutralization in 0.1 M Borate buffer pH 8.5 for 15 min at room temperature. Slides were then washed in 0.1% Triton X-100/PBS and blocked in 0.1% Triton X-100/PBS/5% goat serum (Merck G9023) for 1 h at room temperature. Following immunostaining with a 1:500 dilution of anti-BrdU antibody (BD Pharmingen, 555627) for 1 h at room temperature, cells were incubated with goat anti-mouse secondary antibody (Jackson ImmunoResearch, 115-001-003) at a 1:1,000 dilution for 1 h at room temperature, followed by incubation with Alexa Fluor Plus 488 labelled donkey anti-goat antibody (ThermoFisher, A32814), also at 1:1,000 dilution for 1 h at room temperature. Following counterstaining with DAPI (10 µg ml−1, Invitrogen), images were captured using an Olympus IX83 widefield fluorescent microscope and CellSens software and analysed using FIJI 2.16.0 software as above.

PCR amplification of the SYK gene

PCR was performed using Taq DNA polymerase (NEB, M0267) using the conditions described above for BIOMED-2 primers except the final volume was 25 µl. Primers are given in Supplementary Table 5. Cycling conditions involved initial denaturation at 95 °C for 3 min, followed by 95 °C for 20 s, 64 °C for 30 s and 68 °C for 30 s for 39 cycles, followed by a final extension of 5 min at 68 °C. PCR products were separated by gel electrophoresis.

Analysis of ETV6–RUNX1 BCP-ALL WGS data for ESCs

WGS datasets from patients with BCP-ALL (downloaded from the European Genome-phenome Archive (EGA), dataset ID: EGAD00001000116) were analysed for SJs using an in-house Python script (https://github.com/Boyes-Lab/NGS-Analysis)[48]. In brief, paired-end sequencing data was aligned to the hg19 build of the human genome using Bowtie2 in local alignment mode. Following alignment to the genome, the data were filtered for discordant reads at the immunoglobulin and TCR loci using Samtools. Reads were further filtered (using the above in-house Python script) to extract divergent reads, indicative of SJs. Similar tools that capitalize on discordant paired-end reads have been developed to map ecDNAs. However, AmpliconArchitect[40] also requires increased circular DNA copy number whereas CircleSeq involves removal of linear DNA prior to sequencing and analysis44,61. AmpliconArchitect[40] did not detect circular DNAs in WGS from 20 patient samples where ESCs were detected by LAM-ESC (Fig. 2; EGA accession code: EGAS00001006863). This is likely because unlike ecDNAs, individual ESC sequences do not undergo copy number amplification that is required for detection by AmpliconArchitect[40].

Identification of differentially expressed genes and GSEA analysis

RNA-seq data of patients at diagnosis were downloaded from the TARGET database (dbGaP Sub-study ID: phs000464; Fig. 3d) or EGA (Accession Code EGAS00001006863; Fig. 3f). Differentially expressed genes were identified using DESeq2 with |logFC| > 0.585 and FDR < 0.05. Adjustment for multiple comparisons was performed via the DESeq2 programme. Gene set enrichment analysis (GSEA) was carried out according to the user guide provided by the BROAD Institute (https://docs.gsea-msigdb.org/#GSEA/GSEA_User_Guide/).

Whole-exome sequencing

DNA was prepared from germline and BCP-ALL patient samples taken at diagnosis and relapse, using the Promega Wizard HMW DNA extraction kit. The concentration was measured via Qubit and whole-exome paired-end read sequencing was performed at 100× depth by Azenta.

Analysis of SVs

SV data of patients at diagnosis and relapse were downloaded from Complete Genomics (CGI, from within the TARGET database: dbGaP Sub-study ID: phs000464; Fig. 5a,b). For Extended Data Fig. 9d, WGS of patients with BCP-ALL in the VIVO Biobank cohort was downloaded from EGA under the Accession Code EGAS00001006863. The analysis used similar numbers of WGS and WES where WES from germline and BCP-ALL samples are available from EGA (dataset ID: EGAD50000001519). Breakpoints of SVs were analysed using a bespoke Python program, SVs_near_RSSs.py, which creates an analysis window spanning 50 bp either side of each breakpoint (https://github.com/Boyes-Lab/Structural-Variants)[62]. The presence of an RSS within the window is then analysed using the DNAGrep algorithm, via RSSsite[63].

The relative impact of cut-and-run, ESC reintegration and RAG-mediated insertion was determined as follows: SVs were defined as either deletions, insertions, translocations or complex insertions based on the source of the DNA strand on either side of an SV breakpoint. The DNA damage occurring near RSS sites was analysed, as RAG-mediated DSBs are required for both reintegration and cut-and-run-mediated DNA damage. ESC reintegration events are defined by the reinsertion of ESC DNA into the genome. Thus, insertions were considered to be reintegration-derived where the inserted DNA came from immunoglobulin or TCR loci. The proportion of these events near RSS sites was then compared with other types of DNA damage. Open-source scripts to analyse potential cut-and-run events compared to reintegration are provided at https://github.com/Boyes-Lab/Structural-Variants[62].

Analysis of ecDNAs using AmpliconArchitect[40]

In silico experiments to detect ecDNAs were carried out using AmpliconArchitect[40] according to the AmpliconSuite pipeline (https://github.com/AmpliconSuite/AmpliconSuite-pipeline/blob/master/documentation/GUIDE.md) using WGS BAM files from VIVO Biobank patient samples available from EGA (Accession Code EGAS00001006863).

Statistics

All statistical analyses were performed using GraphPad Prism v9. Statistical test results are provided as P values in the figures. Detailed descriptions of error bars and the number replicates and/or cells analysed are reported in the figure legends. Biological replicates are shown unless otherwise indicated. Analyses of fold changes between biological replicates were performed using a two-tailed Student’s t test or Mann–Whitney U test (depending on data distribution) where *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001. The 95% confidence intervals are given in the figure legends where possible. The 95% confidence intervals for the difference of mean gene expression (H-relapse versus non-relapse) in Fig 3e: PCNA: −2.007 to −0.1691; POLE3: −2.206 to −0.1488; POLE4: −4.910 to −0.8914; RBX1: −2.206 to −0.6157. The Kolmogorov–Smirnov test was used to determine whether the data followed a Gaussian distribution. GSEA uses the statistical test described53,54 with corrections for multiple comparisons. DeSeq2 analysis used the Wald statistical test with the Benjamini–Hochberg correction for multiple testing. Statistical analyses with two categorical variables were performed using a two-way ANOVA. Statistical analyses of the proportion of ESCs above the threshold in patients who relapse versus those who do not were determined using a two-tailed Fisher’s exact test. The significance of the difference between matched ESCs in relapse and non-relapse groups was determined using a two-tailed Wilcoxon signed-rank test. Pearson correlation coefficients (r values) were computed for scatter plots and tested (null r = 0) with a standard two-tailed test. The significance of SVs involving single cRSSs occurring more frequently at relapse-associated genes was calculated using the hypergeometric distribution (Fig. 5b and Extended Data Fig. 9d) to analyse the number of SVs involving single cRSSs within relapse-associated genes compared to SVs involving single cRSSs in the whole dataset. The significance of the co-localization of breaks detected by LAM-HTGTS and genes that are frequently mutated in relapsed ALL (Fig. 5c) was calculated by using the hypergeometric distribution (implemented in the R software, https://www.r-project.org) to test whether the number of genes which were more commonly mutated with SJ partner versus 12-RSS or 23-RSS partners (controls) occurred more frequently in the relapse-associated genes versus the whole gene list. A power calculation, taking an alpha value of 0.05 and a desired power of 80% was used to initially estimate the sample size in which to analyse ESC levels.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

WGS datasets from 61 patients with ETV6–RUNX1 BCP-ALL were downloaded from the European Genome-phenome Archive (EGA) (dataset ID: EGAD00001000116). The human genome sequence hg19, (GCA_000001405.14) release GRCh37.p13, was downloaded from https://hgdownload.soe.ucsc.edu/goldenPath/hg19/bigZips/. SV data for patients with BCP-ALL at diagnosis and relapse were downloaded from Complete Genomics (CGI, from within the TARGET database; dbGaP sub-study ID: phs000464). RNA-seq data of patients with BCP-ALL at diagnosis were downloaded from the TARGET database (dbGaP sub-study ID: phs000464). RNA-seq and WGS datasets from patients with BCP-ALL in the VIVO Biobank cohort were downloaded from EGA under the accession code EGAS00001006863. Raw LAM-ESC and LAM-recombination sequences are available from the European Genome-phenome Archive (EGA) under the dataset ID EGAD50000000597. The extracted recombination junctions and ESCs are given in Supplementary Tables 2 and 3. WES data from patients with BCP-ALL in the VIVO Biobank cohort are available from EGA via the dataset ID EGAD50000001519. Amplicon sequencing data of the recombination junctions used for clonotype analysis are available from EGA under the dataset ID EGAD50000001518. Source data for all graphs is available as Excel spreadsheets for main figures, extended data and supplementary figures. FISH data are available via Research Data Leeds (https://doi.org/10.5518/1693 (ref. [64])). The sample cohort used for each figure is given in Supplementary Table 6. Source data are provided with this paper.

Code availability

A custom Python script to analyse LAM-ESC and LAM-recombination data, together with a custom database is available at https://github.com/Boyes-Lab/LAM-ESC-Recombination[33]. The script automates BLAST searches against a custom BLAST database, consisting of all V-J recombination events or all head-to-head RSS combinations from the immunoglobulin kappa and lambda loci, for recombination and SJ libraries, respectively. A custom Python script to analyse SJs in WGS datasets is available at https://github.com/Boyes-Lab/NGS-Analysis[48]. A bespoke Python programme to analyse breakpoints of SVs, SVs_near_RSSs.py, is available at https://github.com/Boyes-Lab/Structural-Variants[62]. This creates an analysis window spanning 50 bp either side of each breakpoint; the presence of an RSS within the window is then analysed using the DNAGrep algorithm, via RSSsite. A custom Python script to analyse potential cut-and-run events compared to reintegration events is provided at https://github.com/Boyes-Lab/Structural-Variants[62]. The programme to determine the clonotypes present in sequencing reads compared to the reference motifs near the breakpoint junction of interest, Clonotype_analysis.py, is available at https://github.com/Boyes-Lab/NGS-Analysis[48].

References

1. Kim, H. et al. Extrachromosomal DNA is associated with oncogene amplification and poor outcome across multiple cancers. Nat. Genet. 52, 891–897 (2020).

2. Gellert, M. V(D)J recombination: RAG proteins, repair factors, and regulation. Annu. Rev. Biochem. 71, 101–132 (2002).

3. Bassing, C. H., Swat, W. & Alt, F. W. The mechanism and regulation of chromosomal V(D)J recombination. Cell 109, S45–S55 (2002).

4. van Zelm, M. C., Szczepanski, T., van der Burg, M. & van Dongen, J. J. Replication history of B lymphocytes reveals homeostatic proliferation and extensive antigen-induced B cell expansion. J. Exp. Med. 204, 645–655 (2007).

5. Noer, J. B., Horsdal, O. K., Xiang, X., Luo, Y. & Regenberg, B. Extrachromosomal circular DNA in cancer: history, current knowledge, and methods. Trends Genet. 38, 766–781 (2022).

6. Yi, E., Chamorro Gonzalez, R., Henssen, A. G. & Verhaak, R. G. W. Extrachromosomal DNA amplifications in cancer. Nat. Rev. Genet. 23, 760–771 (2022).

7. Itoh, N. & Shimizu, N. DNA replication-dependent intranuclear relocation of double minute chromatin. J. Cell Sci. 111, 3275–3285 (1998).

8. Yi, E. et al. Live-cell imaging shows uneven segregation of extrachromosomal dna elements and transcriptionally active extrachromosomal DNA hubs in cancer. Cancer Discov. 12, 468–483 (2022).

9. Shoshani, O. et al. Chromothripsis drives the evolution of gene amplification in cancer. Nature 591, 137–141 (2021).

10. Turner, K. M. et al. Extrachromosomal oncogene amplification drives tumour evolution and genetic heterogeneity. Nature 543, 122–125 (2017).

11. Lange, J. T. et al. The evolutionary dynamics of extrachromosomal DNA in human cancers. Nat. Genet. 54, 1527–1533 (2022).

12. Luebeck, J. et al. Extrachromosomal DNA in the cancerous transformation of Barrett’s oesophagus. Nature 616, 798–805 (2023).

13. Tonegawa, S. Somatic generation of antibody diversity. Nature 302, 575–581 (1983).

14. Arnal, S. M. & Roth, D. B. Excised V(D)J recombination byproducts threaten genomic integrity. Trends Immunol 28, 289–292 (2007).

15. Curry, J. D. et al. Chromosomal reinsertion of broken RSS ends during T cell development. J. Exp. Med. 204, 2293–2303 (2007).

16. Vanura, K. et al. In vivo reinsertion of excised episomes by the V(D)J recombinase: a potential threat to genomic stability. PLoS Biol. 5, e43 (2007).

17. Balducci, E. et al. TREC mediated oncogenesis in human immature T lymphoid malignancies preferentially involves ZFP36L2. Mol. Cancer 22, 108 (2023).

18. Kirkham, C. M. et al. Cut-and-run: a distinct mechanism by which V(D)J recombination causes genome instability. Mol. Cell 74, 584–597.e589 (2019).

19. Papaemmanuil, E. et al. RAG-mediated recombination is the predominant driver of oncogenic rearrangement in ETV6–RUNX1 acute lymphoblastic leukemia. Nat. Genet. 46, 116–125 (2014).

20. Geenen, V. et al. Quantification of T cell receptor rearrangement excision circles to estimate thymic function: an important new tool for endocrine-immune physiology. J. Endocrinol. 176, 305–311 (2003).

21. van Zelm, M. C., van der Burg, M., Langerak, A. W. & van Dongen, J. J. PID comes full circle: applications of V(D)J recombination excision circles in research, diagnostics and newborn screening of primary immunodeficiency disorders. Front. Immunol. 2, 12 (2011).

22. Grawunder, U. et al. Down-regulation of RAG1 and RAG2 gene expression in preB cells after functional immunoglobulin heavy chain rearrangement. Immunity 3, 601–608 (1995).

23. Kong, F. K., Chen, C. L., Six, A., Hockett, R. D. & Cooper, M. D. T cell receptor gene deletion circles identify recent thymic emigrants in the peripheral T cell pool. Proc. Natl Acad. Sci. USA 96, 1536–1540 (1999).

24. Sodora, D. L. et al. Quantification of thymic function by measuring T cell receptor excision circles within peripheral blood and lymphoid tissues in monkeys. Eur. J. Immunol. 30, 1145–1153 (2000).

25. Livak, F. & Schatz, D. G. T-cell receptor α locus V(D)J recombination by-products are abundant in thymocytes and mature T cells. Mol. Cell. Biol. 16, 609–618 (1996).

26. Hodgkin, P. D., Lee, J. H. & Lyons, A. B. B cell differentiation and isotype switching is related to division cycle number. J. Exp. Med. 184, 277–281 (1996).

27. Palas, K. M. & Kushner, S. R. Biochemical and physical characterization of exonuclease V from Escherichia coli. Comparison of the catalytic activities of the RecBC and RecBCD enzymes. J. Biol. Chem. 265, 3447–3454 (1990).

28. Swaminathan, S. et al. Mechanisms of clonal evolution in childhood acute lymphoblastic leukemia. Nat. Immunol. 16, 766–774 (2015).

29. Bashford-Rogers, R. J. et al. Eye on the B-ALL: B-cell receptor repertoires reveal persistence of numerous B-lymphoblastic leukemia subclones from diagnosis to relapse. Leukemia 30, 2312–2321 (2016).

30. Dong, Y. et al. Illegitimate RAG-mediated recombination events are involved in IKZF1 Δ3–6 deletion in BCR–ABL1 lymphoblastic leukaemia. Clin. Exp. Immunol. 185, 320–331 (2016).

31. van Dongen, J. J. et al. Design and standardization of PCR primers and protocols for detection of clonal immunoglobulin and T-cell receptor gene recombinations in suspect lymphoproliferations: report of the BIOMED-2 Concerted Action BMH4-CT98-3936. Leukemia 17, 2257–2317 (2003).

32. Hu, J. et al. Detecting DNA double-stranded breaks in mammalian genomes by linear amplification-mediated high-throughput genome-wide translocation sequencing. Nat. Protoc. 11, 853–871 (2016).

33. Boyes-Lab. LAM-ESC-Recombination: Initial release (v1.0). Zenodo https://doi.org/10.5281/zenodo.15412315 (2025).

34. Shinoda, K. et al. Intra-Vκ cluster recombination shapes the Ig kappa locus repertoire. Cell Rep. 29, 4471–4481.e4476 (2019).

35. Chamorro Gonzalez, R. et al. Parallel sequencing of extrachromosomal circular DNAs and transcriptomes in single cancer cells. Nat. Genet. 55, 880–890 (2023).

36. Akerman, I. et al. A predictable conserved DNA base composition signature defines human core DNA replication origins. Nat. Commun. 11, 4826 (2020).

37. Whyte, W. A. et al. Master transcription factors and mediator establish super-enhancers at key cell identity genes. Cell 153, 307–319 (2013).

38. Alpar, D. et al. Clonal origins of ETV6-RUNX1+ acute lymphoblastic leukemia: studies in monozygotic twins. Leukemia 29, 839–846 (2015).

39. van Delft, F. W. et al. Clonal origins of relapse in ETV6–RUNX1 acute lymphoblastic leukemia. Blood 117, 6247–6254 (2011).

40. Deshpande, V. et al. Exploring the landscape of focal amplifications in cancer using AmpliconArchitect. Nat. Commun. 10, 392 (2019).

41. Zhang, H. et al. Characterization and integrated analysis of extrachromosomal DNA amplification in hematological malignancies. Neoplasia 56, 101025 (2024).

42. Wu, S. et al. Circular ecDNA promotes accessible chromatin and high oncogene expression. Nature 575, 699–703 (2019).

43. Zhu, Y. et al. Oncogenic extrachromosomal DNA functions as mobile enhancers to globally amplify chromosomal transcription. Cancer Cell 39, 694–707.e697 (2021).

44. Koche, R. P. et al. Extrachromosomal circular DNA drives oncogenic genome remodeling in neuroblastoma. Nat. Genet. 52, 29–34 (2020).

45. Meyer, K. B. & Neuberger, M. S. The immunoglobulin kappa locus contains a second, stronger B-cell-specific enhancer which is located downstream of the constant region. EMBO J. 8, 1959–1964 (1989).

46. Das, S., Nikolaidis, N. & Nei, M. Genomic organization and evolution of immunoglobulin kappa gene enhancers and kappa deleting element in mammals. Mol. Immunol. 46, 3171–3177 (2009).

47. Teng, G. et al. RAG represents a widespread threat to the lymphocyte genome. Cell 162, 751–765 (2015).

48. Boyes-Lab. NGS-analysis: Initial release (v1.0). Zenodo https://doi.org/10.5281/zenodo.15412502 (2025).

49. Rommel, P. C., Oliveira, T. Y., Nussenzweig, M. C. & Robbiani, D. F. RAG1/2 induces genomic insertions by mobilizing DNA into RAG1/2-independent breaks. J. Exp. Med. 214, 815–831 (2017).

50. Waanders, E. et al. Mutational landscape and patterns of clonal evolution in relapsed pediatric acute lymphoblastic leukemia. Blood Cancer Discov. 1, 96–111 (2020).

51. Woo, J. S., Alberti, M. O. & Tirado, C. A. Childhood B-acute lymphoblastic leukemia: a genetic update. Exp. Hematol. Oncol. 3, 16 (2014).

52. Mullighan, C. G. et al. Deletion of IKZF1 and prognosis in acute lymphoblastic leukemia. N. Engl. J. Med. 360, 470–480 (2009).

53. Subramanian, A. et al. Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles. Proc. Natl Acad. Sci. USA 102, 15545–15550 (2005).

54. Mootha, V. K. et al. PGC-1alpha-responsive genes involved in oxidative phosphorylation are coordinately downregulated in human diabetes. Nat. Genet. 34, 267–273 (2003).

55. Ye, J., Ma, N., Madden, T. L. & Ostell, J. M. IgBLAST: an immunoglobulin variable domain sequence analysis tool. Nucleic Acids Res. 41, W34–W40 (2013).

56. Marino, M. et al. Impact of 12-month cryopreservation on endogenous DNA damage in whole blood and isolated mononuclear cells evaluated by the comet assay. Sci. Rep. 11, 363 (2021).

57. Rocheteau, P. et al. Cryopreserved stem cells incur damages due to terrestrial cosmic rays impairing their integrity upon long-term storage. Cell Transplant. 31, 9636897211070239 (2022).

58. Jubb, A. & Boyle, S. Visualising genome reorganisation using 3D DNA FISH. Methods Mol. Biol. 2148, 85 (2020).

59. Bolland, D. J., King, M. R., Reik, W., Corcoran, A. E. & Krueger, C. Robust 3D DNA FISH using directly labelled probes. J. Vis. Exp. 78, 50587 (2013).

60. Cooperman, J., Neely, R., Teachey, D. T., Grupp, S. & Choi, J. K. Cell division rates of primary human precursor B cells in culture reflect in vivo rates. Stem Cells 22, 1111–1120 (2004).

61. Moller, H. D., Parsons, L., Jorgensen, T. S., Botstein, D. & Regenberg, B. Extrachromosomal circular DNA is common in yeast. Proc. Natl Acad. Sci. USA 112, E3114–E3122 (2015).

62. Boyes-Lab. Structural-Variants: initial release (v.10). Zenodo https://doi.org/10.5281/zenodo.15412565 (2025).

63. Merelli, I. et al. RSSsite: a reference database and prediction tool for the identification of cryptic Recombination Signal Sequences in human and murine genomes. Nucleic Acids Res. 38, W262–W267 (2010).

64. Gao, Z. et al. Circular Extra-chromosomal DNA in BCP-ALL [Dataset]. Univ. of Leeds https://doi.org/10.5518/1693 (2025).

65. Ramsden, D. A. & Wu, G. E. Mouse kappa light-chain recombination signal sequences mediate recombination more frequently than do those of lambda light chain. Proc. Natl Acad. Sci. USA 88, 10721–10725 (1991).

Acknowledgements

The authors acknowledge funding from the Little Princess Trust and Harley Staples Cancer Research Trust, via the Children’s Cancer and Leukaemia Group (CCLGA 2019 15; CCLGA 2020 12 and CCLGA 2023 06), Blood Cancer UK (grant 15042), a Wellcome Trust ISSF award (to J.N.F.S.; institutional grant 204825/Z/16/Z), a China Scholarship Council studentship (to X.W.), a Mary and Alice Smith Research Scholarship (to M.P.E.) and a Leeds Doctoral Scholarship (to D.C.). D.R.W. is supported in part by the National Institute for Health and Care Research (NIHR) Leeds Biomedical Research Centre (BRC) (NIHR203331). The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care. Primary childhood leukaemia samples and data were provided by VIVO Biobank supported by Cancer Research UK & Blood Cancer UK (grant CRCPSC-Dec21\100003). Further samples were provided by J. Zuna. We also gratefully acknowledge E. Eichler for fosmid clones. The results presented here are in part based upon data generated by the Therapeutically Applicable Research to Generate Effective Treatments (https://www.cancer.gov/ccg/research/genome-sequencing/target) initiative, phs000218; the data used for this analysis are available at the Genomic Data Commons (https://portal.gdc.cancer.gov). We thank the Sanger Cancer Genome Project, primarily funded by the Wellcome Trust, for making available the EGA dataset (ID: EGAD00001000116). Those who carried out the original analyses and collection of dataset ID EGAD00001000116 bear no responsibility for the data presented here. We also thank W. Bickmore, K. Purshouse and S. Boyle, A. Corcoran, C. Bassi and S. Horsley for advice on FISH experiments; staff in the flow cytometry and bioimaging facility, University of Leeds, for advice on microscopy; and J. Ladbury for comments on the manuscript.

Author information

Author notes

1. Matthew P. Edwards

Present address: Pathology Sciences, Southmead Hospital, Bristol, UK

2. Xiaoling Wang

Present address: State Key Laboratory of Experimental Hematology, National Clinical Research Center for Blood Diseases, Haihe Laboratory of Cell Ecosystem, Institute of Hematology and Blood Diseases Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Tianjin, China

3. Andrew D. Gillen

Present address: School of Molecular Biosciences, College of Medical, Veterinary and Life Sciences, University of Glasgow, Glasgow, UK

4. These authors contributed equally: James N. F. Scott, Matthew P. Edwards

Authors and Affiliations

1. School of Molecular and Cellular Biology, Faculty of Biological Sciences, University of Leeds, Leeds, UK

Zeqian Gao, James N. F. Scott, Matthew P. Edwards, Dylan Casey, Xiaoling Wang, Andrew D. Gillen & David R. Westhead

2. Wolfson Childhood Cancer Centre, Newcastle University, Newcastle upon Tyne, UK

Sarra Ryan & Lisa J. Russell

3. Leukaemia Research Cytogenomics Group, Translation and Clinical Research Institute, Newcastle University, Newcastle upon Tyne, UK

Anthony V. Moorman

4. Haematological Malignancy Diagnostic Service (HMDS), St James’s University Hospital, Leeds, UK

Ruth de Tute & Catherine Cargo

5. Centre for Evolution and Cancer, The Institute of Cancer Research, London, UK

Anthony M. Ford

6. Leeds Institute of Data Analytics, University of Leeds, Leeds, UK

David R. Westhead

7. School of Molecular and Cellular Biology, Astbury Centre for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds, Leeds, UK

Joan Boyes

Contributions

Z.G. performed the LAM-ESC experiments, qPCR analyses of SJ and recombination junctions, DESeq2, GSEA analyses, in depth analyses of LAM-ESC and LAM-recombination data, FISH experiments (with R.d.T., C.C. and L.J.R.), WES, analysis of the VIVO Biobank patient WGS and WES (with data from S.R. and A.V.M.), and with M.P.E., RT–qPCR analyses of gene expression levels in patients and bioinformatic analyses of SVs in the TARGET database. J.N.F.S. developed the LAM-ESC and LAM-recombination assays, performed the mouse RecBCD experiments as well as bioinformatic analyses of SJs in patients with ETV6–RUNX1 BCP-ALL using the EGA data and, with A.M.F., C.C. and R.d.T., analysed recombination events and SJs by PCR plus amplicon sequencing. M.P.E. performed the LAM-recombination experiments, clonotype analyses, amplification of ESCs by Phi29 and examined SJ and recombination levels by ddPCR. ddPCR experiments to measure SJ and recombination levels for matched ESCs in patients who relapsed and those who did not relapse were performed by M.P.E. and D.C. D.C. measured high copy SJ levels by ddPCR, analysed SJs corresponding to recent recombination events, determined mouse recombination to Gapdh ratios, performed control ddPCR and qPCR assays, identified SJs that are frequently present at higher copies in LAM-ESC data and compared mapped replication initiation sites with ESC sequences. X.W. determined the SJ/recombination junction ratio at different stages of mouse B cell development and analysed Rag1 expression in mouse B cells by RT–qPCR. A.D.G. wrote the code to analyse SVs with cRSSs at their breakpoints. J.B. performed RecBCD experiments for BCP-ALL samples with C.C. and R.d.T. A.V.M. provided detailed genomic subtype annotation for patient samples. Z.G. produced all figures and schematic images. D.R.W. advised on statistics and bioinformatic analyses. All authors analysed the data. J.B., D.R.W. and A.M.F. devised the overall study and wrote the manuscript with Z.G. and J.N.F.S.

Corresponding author

Correspondence to Joan Boyes.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Basil el Jundi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer review reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Elevated RAG1 expression at diagnosis correlates with subsequent relapse.

a, Control qPCR experiments showing amplification of recombination and SJ junctions using pre-B and NIH3T3 (non-RAG-expressing) DNA. n = 3 samples. Igλ recombination accounts for only ~5% of mouse IgL recombination[65]; this reduces the difference between specific Vλ1-Jλ1 amplification using pre-B DNA and non-specific amplification (as determined by melt curve analysis) using NIH3T3 DNA. Gel electrophoresis (lower) confirms only minimal amplification of the correct product in NIH3T3 compared to pre-B DNA. For source gel data, see Supplementary Fig. 2a. Mean values are shown ± s.d. b, Recombination junction levels were determined by qPCR and normalised to genomic Gapdh in mouse B cells at the stages of development shown. The ratio in pre-B cells was set at one and other ratios are plotted against this. Mean values are plotted. n = 2 samples. c, Levels of RAG1 (upper) and RAG2 (lower) expression in different BCP-ALL subtypes using samples taken at diagnosis and determined by RT-qPCR. Data are normalised to HPRT expression levels. Mean values are plotted; black dots indicate values for individual patients. n = 121 (RAG1) and n = 92 (RAG2). Samples provided by VIVO Biobank. d, Analysis of RAG1 (upper) and RAG2 (lower) expression by RT-qPCR in BCP-ALL patient samples (from VIVO Biobank). Samples from patients who subsequently relapse are shown in red whereas those who are not known to have relapsed are in blue. Data are normalized to HPRT expression. For RAG1 expression, n = 44 (Relapse) and 77 (Non-relapse). For RAG2 expression, n = 50 (Relapse) and 42 (Non-relapse). HeLa cDNA is a negative control. Mean values are shown ± s.d. The significance of the difference in expression between patients who later relapse and those who do not was determined by a two-tailed Mann-Whitney U test.

Source Data

Extended Data Fig. 2 ESCs are present as non-chromosomal DNA in BCP-ALL patients.

a, Sequences of recombination events in each ETV6::RUNX1 + BCP-ALL sample were determined via PCR (using degenerate primers from the BIOMED-2 consortium[31]) and sequencing of the amplified products. The SJ of the corresponding ESC was amplified and sequenced. b, Sequences of SJs from ETV6::RUNX1 + BCP-ALL patients (lower), aligned to the sequences surrounding the respective 12- and 23-RSS in the genome (upper, bold). Individual patients (n = 6) are denoted by letters A-F. The SJs detected per patient are numbered. All SJs result from deletional recombination. Samples from a hospital in the Czech Republic with informed consent[19]. c, SJs are present in different BCP-ALL subtypes. The SJs in low-hypodiploid (patient G), CRLF2-r (patient H) and BCR::ABL1 (patient I) BCP-ALL samples were detected as above. The SJs detected per patient are numbered 1, 2, 3, etc. n = 3 patients. Patient samples provided, with consent, by the Haematological Malignancy Diagnostic Service, Leeds. d, ESCs persist as circles in BCP-ALL samples. The level of undigested DNA following RecBCD treatment was determined by ddPCR; GAPDH (linear, genomic DNA) is a negative control. Untreated DNA is a further control (Ctrl). n = 3 BCP-ALL samples. Mean values are shown ± s.d. Black dots show the mean of 3-4 technical repeats. The significance of the difference between RecBCD-treated GAPDH and SJs was determined by an unpaired, two-tailed Student’s t-test. 95% CI: GAPDH vs KDE-KV2-28: 98.59 to 169.2; GAPDH vs LJ2-LV3-10: 46.30 to 90.86; GAPDH vs KDE-KV1-8: 63.22 to 180.3; GAPDH vs KDE-KV3-20: 44.64 to 197.5. e, The total number of SJs identified in WGS data of 61 ETV6::RUNX1 + BCP-ALL patients. The x-axis shows the number of SJs identified per patient whereas the y-axis shows the number of patients with that number of SJs. NGS data from the European Genome-phenome Archive (EGAD00001000116).

Source Data

Extended Data Fig. 3 Schematic of LAM-ESC and LAM-recombination methods.

a, LAM-ESC and LAM-recombination are based on LAM-HTGTS that was originally described by Hu et al.[32]. LAM-ESC and LAM-recombination directly amplify SJ and coding junctions from sonicated genomic DNA using linear amplification-mediated PCR, followed by bead enrichment and on-bead bridge adapter ligation. This enables exponential PCR amplification and labelling of the enriched PCR products with MiSeq (AmpEZ I5 and I7) adapters. Cas9-mediated blocking is introduced to remove germline sequences from amplified LAM-ESC products. The purified Cas9/sgRNA (RNP) complex is targeted by sgRNAs specific to the IGK and IGL loci. b, Schematic of the designed biotinylated oligo, nested primer and a Cas9 targeting site for LAM-ESC for a given J gene segment. The amplified libraries are sequenced via Amplicon sequencing and the reads mapped to the IGL and IGK loci using a custom Python script (https://github.com/Boyes-Lab/LAM-ESC-Recombination)[33]. ESCs resulting from inversional recombination events are excluded from our analyses. Likewise, ESCs from intra-KV recombination, between bona fide 12-RSSs and flipped 23-RSSs at a subset of KV gene segments[34], are not detected, since LAM-ESC involves amplification from J regions. The specificity of the pipeline was verified via control experiments with HeLa genomic DNA that generated only negligible background reads for LAM-ESC or LAM-recombination.

Extended Data Fig. 4 Comparison of SJ, RAG gene expression and recombination levels.

a, The levels of 27 SJs that are frequently detected by LAM-ESC were determined by ddPCR using samples from 11 patients and plotted against the normalised levels of the respective SJs determined by LAM-ESC. A strong positive correlation (Pearson, r) is observed between the normalised SJ reads determined by NGS and the absolute SJ copies/μl as determined by ddPCR (statistical significance from a two-sided test). b, The levels of 12 SJs found above the threshold in healthy blood (Fig. 2a) were measured by ddPCR. Levels in patients who later relapse (n = 7) are shown in red; the levels of the same ESCs in patients who did not relapse (n = 10) are shown in blue. SJs in healthy blood (n = 2) are shown in pink whereas control amplifications with HeLa DNA (n = 2) are shown in black. Levels were normalised to the GAPDH gene. Complementary clonotype analyses of SJs shown in Fig. 2a are given in Supplementary Fig. 3. c, The number of SJ copies that are above the threshold found in healthy blood are plotted per patient against the corresponding expression levels of RAG1 (n = 26) or RAG2 (n = 36). No significant correlation is found between RAG1 (left) or RAG2 (right) expression and high SJ copies per patient following calculation of a two-tailed Pearson correlation coefficient. d, Absolute copies of the SJ and corresponding recombination junction determined by ddPCR in cases where the normalised SJ reads exceed the normalised recombination reads in LAM-ESC and LAM-recombination experiments. Black dots indicate technical repeats. Mean values are plotted. n = 3 technical repeats for six patients. e, f, qPCR analysis of the levels of (e) KDE-KV2-30 SJ and the corresponding recombination event (REC) and (f) KDE-KV3-20 SJ and the corresponding recombination event in BCP-ALL patients. Subsequent relapse status is plotted (red – relapse; blue – non-relapse). The levels relative to GAPDH (genomic DNA) control are shown. The significance of differences in levels was calculated by a two-tailed Mann-Whitney U test. For (e), SJ: n = 23 (Relapse) and n = 26 (Non-relapse); REC: n = 25 (Relapse) and n = 26 (Non-relapse). For (f), SJ: n = 22 (Relapse) and n = 23 (Non-relapse); REC: n = 25 (Relapse) and n = 26 (Non-relapse). Since recombination to KDE precludes further recombination (Fig. 1a), recombination junctions cannot be lost via secondary recombination but instead, these data imply that there is increased ESC replication in patients who later relapse.

Source Data

Extended Data Fig. 5 ESC sequences are identical regardless of subsequent relapse.

a, Alignment of LAM-ESC reads for the SJs examined in Fig. 3c. The schematic above each plot shows the position of the 12- and 23-RSS; the reference (expected) SJ sequence is shown at the top of each alignment. LAM-ESC sequences from the patients indicated to the left, are aligned and confirm that the RSSs are from identical recombination events. Differences in linear amplification during LAM-ESC results in variability in sequence length. Processing of the SJ junction is observed for some SJs, potentially due to SJ reopening by RAGs. These small changes are negligible within 20 kb to 1 Mb of the whole ESC. b, Differential gene expression of PCNA, RBX1, POLE3 and POLE4 determined by DESeq2 for patients who later relapse with high SJ levels (n = 4) and with low SJ levels (n = 3) where the SJ levels were determined in Fig. 2a. Significance of the difference determined by a (two-sided) Wald test with the Benjamini-Hochberg correction for multiple testing (padj).

Extended Data Fig. 6 Eukaryotic replication origins map to ESC sequences.

Mapping of proposed eukaryotic replication origins and ESC sequences to the IGK (upper) and IGL (lower) loci. n = 35 SJs (IGK) and n = 20 SJs (IGL). Maps of the IGK and IGL loci are shown with key V and J regions indicated in red. Human replication origins were previously mapped by short nascent strand isolation coupled with next generation sequencing[36]. The activity of these origins was split into 10 quantiles according to mean origin activity where quantile 1 (Q1) represents the top 10% activity. Only Q1 and Q2 replication origins (defined as core replication origins) are shown (light blue) as these account for the majority (70–85%) of replication initiation events. ESCs that were observed at least once above the threshold level found in healthy blood are mapped (in purple) as these ESCs are most likely to have replicated. ESCs below the threshold could have resulted from recent recombination events or have persisted from much earlier recombination events and therefore their level of replication is more difficult to predict.

Extended Data Fig. 7 Clonotype analyses imply ESCs persist from early recombination events.

a, To identify major recombination events, all recombination events in a patient (Supplementary Table 2) were ranked by decreasing number of reads and plotted against the individual events. This reveals a point in the distribution of sequencing reads where levels begin increasing rapidly. To define this point, we followed the methodology described[37]. We then found the x-axis point for which a line with a slope of ~1 was tangent to the curve. We define recombination events above this point to be major recombination events, and those below, minor recombination events. Two sets of plots are shown: Left: Data from four patients where high numbers (left) or lower numbers (right) of sequencing reads were detected. In each case, there is a clear point where the sequencing reads begin to increase rapidly. b, SJs that correspond to the primary recombination event (i.e. most sequencing reads) were identified in three patients (R-8 – DUX4-r; R-13 – ETV6::RUNX1+ and R-9 – DUX4-r). Here, an identical ESC can be generated only if the second allele undergoes the same recombination event. The extensive addition and deletion of bases upon formation of VJ coding junctions2,3 means that the chances of two independent recombination events generating exactly the same coding junction are negligible. To determine the number of clonotypes for each SJ, the corresponding recombination junctions were amplified and subjected to Amplicon sequencing. The levels of the distinguishable clonotypes are shown to the right of the respective junction sequences. For LV2-11-LJ2, and LV5-45-LJ2, 99.42% and 99.64%, respectively of coding junctions have the same sequence with only 2-3 distinguishable minor clonotypes. The dominance of a single clone in each case suggests it is very likely that each ESC persisted from the major recombination event. c, To test if SJs corresponding to the primary recombination event could have arisen from minor clonotypes, total SJ copies, total recombination junctions and GAPDH (genomic DNA) were measured via ddPCR and plotted. The number of recombination copies attributable to each clonotype was calculated by multiplying the absolute copy number of the recombination event by the proportion of each clonotype. From this, the levels of minor clonotypes equate to those expected from 0.81-3.69 relative cell divisions following recombination (see Methods). Mean values are plotted. n = 2 or 3 technical repeats for three patients. d, Comparison of the measured SJ copies (b) to those observed for other SJs generated a similar number of cell divisions ago (<6 relative cell divisions – Fig. 3c; n = 77): the observed LJ2-LV2-11 SJ copies are substantially higher than those found for all other recently generated SJs (see Methods), implying that at least some of the observed LJ2-LV2-11 SJs persist from the primary recombination event. e, Control experiments to test if ESCs remain circular. Schematic of ESC amplification via rolling circle amplification using Phi29 polymerase. f, Samples from patients with known SJs were amplified with Phi29 polymerase whereas the enzyme was omitted from control (untreated) samples. The levels of the SJs shown were determined by ddPCR in treated (amplified; orange bars) and control samples (blue bars). Following normalisation to GAPDH, the significance of the increase of the Phi29-treated samples compared to the untreated samples was determined by a two-way Anova test. Mean values are plotted. Black dots indicate technical repeats. n = 3 patients. g, Verification that Phi29 amplifies circular DNA. Mouse IgG+ samples with known circular ESCs (Fig. 1d) were treated as in f. Levels of treated (orange bars) and untreated products (blue bars) are shown, following normalisation to Gapdh and as determined by ddPCR. Black dots indicate technical repeats. Mean values are plotted. n = 3 IgG+ samples. Brief sonication of DNA prior to Phi29 treatment eliminated ddPCR amplification of the SJ but Gapdh amplification was not significantly altered. Amplification of circular DNA by Phi29 implies that SJ persistence cannot be explained by their reintegration.

Source Data

Extended Data Fig. 8 ESCs replicate and are non-chromosomal.

a, ddPCR measurements of the levels of five frequently observed SJs, normalised to GAPDH, in patients M, N and P, without (-) or with (+) prior RecBCD treatment of the DNA. Individual SJs are shown by distinct colours. Mean values of three or more technical repeats are shown. n = 3 patients. The median of normalised, elevated SJ levels in patients who later relapse is 4 copies/µl (Extended Data Fig. 4b); the high copy SJ detected for patient P (normalised value: 2.3 copies/µl) is therefore at the lower end of elevated SJ levels. b, Representative interphase FISH images. Control probes against IGK and IGL are in green; the regions that are excised to generate ESCs are in red (IGL) or magenta (IGK). Upper: Cell where neither IGK nor IGL ESCs are present. n = 200. The overlapping IGL control and ESC signals indicate no IGL recombination. The overlapping IGK control and ESC signals implies no recombination to KDE but one or both of the IGK loci may have recombined to the JK RSSs, with loss of the resulting ESC. Middle: Cell with one ESC.  n = 99. Lower: Cell with two ESCs. n = 27. Controls for FISH probe hybridisation to metaphase chromosome spreads are given in Supplementary Fig. 4. c, Total non-chromosomal DNAs detected in DAPI stained metaphase chromosome spreads versus interphase FISH per 100 cells for patients with ESC levels similar to those who later relapse (patient P; n = 26 metaphase & 108 interphase images) and those who remain in remission (patients M and N; n = 29 & 127 and 24 & 101 images, respectively). Fewer ESCs are detected by DAPI staining compared to interphase FISH due to losses and/or inefficient DAPI staining of small circular DNAs. d, Metaphase chromosomes from cells grown with BrdU for 28 or 48 h, followed by hybridisation of the chromosomes to anti-BrdU antibodies. The labelled non-chromosomal DNA is indicted by a red arrow. Images were deconvoluted using CellSens Dimension software. Magnification of all images is 60x. e, f, g, The percentage of times the (e) V gene segment (f) J gene segment or (g) SJ shown is found in the population of SJs above the threshold level in healthy blood (Fig. 2a) compared to the percentage of times it is found in the whole population (n = 1585 total SJs from 71 patients). The significance of the difference was calculated by one-sided hypergeometric distribution. P = 0.045 (IGKV1-17), 0.00007 (IGKV1-8), 0.044 (IGKV3-20), 0.048 (LV4-3), 0.0110 (KDE), 0.0345 (IGLJ2), 0.0287 (IGKJ3), 0.0010 (IGKV1-8-KDE), 0.0050 (IGKV1-17-KDE), and 0.0423 (IGKV1-8-KJ2).

Source Data

Extended Data Fig. 9 Increased mutations at relapse-associated genes correlate with high ESC levels.

a, Characterisation of SVs with cRSS(s) at the breakpoint(s). Pie chart showing fraction of SVs that have two cRSSs at the breakpoints (consistent with cryptic recombination19,47) or one cRSS at the breakpoint, consistent with cut-and-run[18], reintegration14,15,16 or RAG-mediated insertion[49]. Further breakpoint characteristics at single cRSSs (cut-and-run, reintegration or RAG-mediated insertion) were determined using a custom programme available from https://github.com/Boyes-Lab/Structural-Variants[62]. SVs from the TARGET study. n = 150 patients. b, RAG1 expression levels determined by RT-qPCR for BCP-ALL patients shown in Fig. 2a. Three patient groups were identified according to RAG1 expression and total normalised SJ reads: (i) High RAG1, high SJs (n = 14); (ii) High RAG1, low SJs (n = 15) and (iii) low RAG1, low SJs (n = 12). RAG expression data are normalised to HPRT expression levels. Data are presented as mean values ± s.d. The significance of the difference in expression levels was determined by a two-tailed Student’s t-test. 95% CI: 0.3122 to 1.360 (high RAG1 expression, high SJs versus low RAG1 expression, low SJs); 0.2294 to 0.9355 (high RAG1 expression, low SJs versus low RAG1 expression, low SJs) c, Total normalised SJ levels for the patient groups given in (b). Data are presented as mean values ± s.d. The significance of the differences was determined by a two-tailed Student’s t-test. 95% CI: 4.675 to 21.12 (high RAG1 expression, high SJs versus low RAG1 expression, low SJs); 5.431 to 19.94 (high RAG1 expression, high SJs versus high RAG1 expression, low SJs). d, SVs at genes that are commonly mutated in BCP-ALL or at relapse with a cRSS on one side of the breakpoint (blue), both sides (orange) or no cRSS (grey) for the patient groups given in (b) using WGS or WES compared to the corresponding germline sequence. The significance of increased SVs involving single cRSSs at relapse-associated or frequently mutated genes compared to all SVs involving a single cRSS was calculated using a one-sided hypergeometric distribution; P = 9.44×10−7 for the high RAG1, high SJ group (bottom panel). e, PCR amplification of the SYK gene using template DNA from patient samples taken at diagnosis or at relapse (indicated above the gel) as well as the BCP-ALL cell line, REH. R and NR indicate samples taken from patients who did, and who did not, later relapse. ddH_2O indicates no template control. A 67 bp insertion in one allele of the SYK gene in patient R-8 increases between diagnosis and relapse. Quantification of the 272 and 339 bp bands is shown beneath the gel. For source gel data, see Supplementary Fig. 2b.

Source Data

Extended Data Fig. 10 ESCs are associated with clonal expansion between diagnosis and relapse.

a, Changes in normalised LAM-recombination sequencing reads for individual recombination junctions between diagnosis and relapse. n = 27. For clarity, only junctions where the levels have increased at relapse are plotted. The changes in all junctions where LAM-recombination reads are detected at both diagnosis and relapse are given in Supplementary Table 2, final tab. b, SJ levels at diagnosis when the corresponding recombination junction is increased at relapse (Expansion) or shows no increase between diagnosis and relapse (No expansion). The SJ/GAPDH ratio is shown, using levels determined by ddPCR. n = 10 ESCs (Expansion) and n = 12 (No expansion), from eight patients. A range of ESC levels correspond to expansion of cells with the corresponding recombination junction. This may be because ESCs can trigger mutations at different times prior to diagnosis and therefore some of the ESCs that triggered damaging mutations may have been diluted; likewise, ESCs from other recombination events may contribute to disease-causing mutations and thus expansion may be influenced by a combination of ESCs. c, Total SJ levels plotted for five DUX4-r patients who did not subsequently relapse. The exceptionally high SJ reads in these patients is anomalous and similar to the levels for SJs that are integrated in the genome following inversional recombination events. In three cases, NR-39, NR-40 and NR-42, SJs involving the same sequences, KV1-17/KV1-5 or KV1-8 are present that are 10- to 60-fold higher than the SJs typically observed in patients who later relapse. LAM-ESC reads for KV1-17 and KV1-5 SJs are identical. KV1-8 differs from KV1-17/KV1-5 by just 2 bp. All sequences differ from their corresponding inversional recombination event (KVD1-17/1-5 or KVD1-8) by just a single bp, suggesting that these SJs may have resulted from inversional events. d, ddPCR analysis of samples that had, or had not, been treated with Phi29 to amplify circular DNA. The mean fold-change in PCR product is plotted following treatment with Phi29 compared to untreated sample. The plots to the left (in red; n = 4 SJs) show fold-change for SJs that appear to be present on ESCs; the plots to the right (in blue; n = 4 SJs) show the fold-change for SJ sequences from DUX4-r patients. The low amplification is consistent with these SJs being integrated into the genome. The LAM-ESC data for these five patients were therefore omitted from Fig. 2a. It was not possible to obtain a ddPCR amplification product for the high copy SJ from patient NR-40. e, Total SJs in BCP-ALL samples at diagnosis were replotted according to the BCP-ALL subtype: High hyperdiploidy (left; n = 15), TCF3::PBX1 (middle; n = 5) and PAX5 altered/mutated (right; n = 8). For each BCP-ALL subtype, the normalised number of copies of each SJ for patients who later relapse (red) and those who remain in remission (blue) is plotted. A threshold is set at the value equivalent to the highest normalised SJ level detected in healthy blood (horizontal line).

Source Data

Extended Data Fig. 11 Model outlining the impact of increased ESC levels on BCP-ALL progression.

In patients prone to relapse (left), increased RAG1 expression will lead to increased secondary recombination and the generation of new ESCs. This, combined with cell-intrinsic factors that cause increased ESC replication, results in higher ESC levels. These ESCs can combine with RAG proteins to trigger DSBs at cRSSs in the genome via the cut-and-run reaction. Ongoing mutations, including those at frequently mutated and relapse-associated genes, lead to an increased mutational burden that is inherited by all daughter cells, promoting treatment resistance and relapse. In patients who are unlikely to relapse (right), although new ESCs are generated, the absence of significant ESC replication results in a lower mutational burden and a decreased likelihood of treatment resistance.

Supplementary information

Supplementary Information

This file contains Supplementary Figs. 1–4

Reporting Summary

Supplementary Table 1

SJs detected in WGS of ETV6::RUNX1+ patients in the EGA database (EGA: EGAD00001000116).

Supplementary Table 2

The number of sequencing reads across each coding junction, as determined by LAM-recombination is shown. The patient numbers are given in each tab. R and NR denote patient samples taken at diagnosis for patients who did, and who did not, later relapse, respectively. Rel denotes patient samples taken at relapse. The final tab compares normalized LAM-recombination reads between diagnosis and relapse.

Supplementary Table 3

The number of sequencing reads across each SJ, as determined by LAM-ESC is shown. SJs resulting from inversional recombination events were removed from all plots and analyses. LAM-ESC amplifies SJs by priming from J regions and therefore SJs resulting from intra-KV recombination[34] will not be detected. The patient numbers are given in each tab. R and NR denote patient samples taken at diagnosis for patients who did, and who did not, later relapse, respectively. Rel denotes patient samples taken at relapse.

Supplementary Table 4

The BCP-ALL subtype is shown for each patient used in the analyses. Relapse and no relapse denote patient samples taken at diagnosis for patients who did, and who did not, later relapse, respectively. Bone marrow (BM) blasts shows the percent of leukaemic cells at diagnosis.

Supplementary Table 5

List of oligos used by type of experiment.

Supplementary Table 6

Summary of cohorts and source data used in each figure.

Peer Review File

Source data for Supplementary Fig. 3

Source data

Source Data Figs. 1–5

Source Data Extended Data Figs. 1, 2, 4, 7–10

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Gao, Z., Scott, J.N.F., Edwards, M.P. et al. Excised DNA circles from V(D)J recombination promote relapsed leukaemia. Nature 645, 774–783 (2025). https://doi.org/10.1038/s41586-025-09372-6

- Received: 26 June 2024

- Accepted: 08 July 2025

- Published: 06 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09372-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Multi-omic characterization of genome-wide abnormal DNA methylation reveals diagnostic and prognostic markers for esophageal squamous-cell carcinoma

Article Open access 25 February 2022

Encoding gene RAB3B exists in linear chromosomal and circular extrachromosomal DNA and contributes to cisplatin resistance of hypopharyngeal squamous cell carcinoma via inducing autophagy

Article Open access 22 February 2022

Comprehensive analysis of clinical features, mRNA splicing, and immunological role of REEP5 in esophageal squamous cell carcinoma

Article Open access 27 October 2024

High levels of circular DNA made as immune cells develop increases the risk of leukaemia relapse

- Karla K. Rodgers

Nature News & Views 06 Aug 2025

Article Open access Published: 30 July 2025

Programmable protein ligation on cell surfaces

Christian Kofoed,

Girum Erkalo,

Nicholas E. S. Tay,

Xuanjia Ye,

Yutong Lin &

…

Tom W. Muir

Nature volume 645, pages 793–800 (2025)

Abstract

The surface landscapes of cells differ as a function of cell type and are frequently altered in disease contexts1,2,3. Exploiting such differences is key to many therapeutic strategies and is the basis for developing diagnostic and basic-science tools. State-of-the-art strategies typically target single surface antigens, but each individual receptor rarely defines the specific cell type4,5. The development of programmable molecular systems that integrate multiple cell-surface features to convert on-target inputs to user-defined outputs is therefore highly desirable. Here we describe an autonomous decision-making device driven by proximity-gated protein trans-splicing that allows local generation of an active protein from two otherwise inactive polypeptide fragments. We show that this protein-actuator platform can perform convergent protein ligation on designated cell surfaces, allowing highly selective generation of active proteins, which can either remain physically associated with the cell surface on which they were manufactured or be released into the surrounding milieu. Because of its intrinsic modularity and tunability, we demonstrate that the technology is compatible with different types of input, targeting modality and functional output, allowing for the localized interrogation or manipulation of cellular systems.

Similar content being viewed by others

Main

Cell-surface heterogeneity is exploited in nature as a central strategy for discrimination in multicellular systems with the purpose of modulating biological functions in time and space. Designing protein tools that emulate this paradigm with new and highly selective stimulus–response functions provides opportunities to study complex cell biochemistry and to create sophisticated synthetic biology outputs. Current synthetic systems use macromolecular targeting modalities, such as antibodies, to selectively deliver activities that affect downstream cellular function6,7. Despite the notable successes of this strategy, it is limited by the fact that single antigens rarely define cell or tissue types, and the wrongful commitment of these agents can therefore complicate their use in more complex settings4,5. Protein Boolean logic gates8,9 have been implemented to define targeting more finely10,11, whereby engineered antibody-based platforms or synthetic protein switches use the concurrent binding of two or more targeting vectors to recruit a third effector modality12,13,14. Although these are exciting developments, many effector modalities (such as cytokines and enzymes) are highly active in ways that are independent of any Boolean-based recruitment, and they will therefore exert activities unconstrained by target binding. It therefore remains an outstanding challenge to turn on protein function in situ from an inactive state in response to cell-surface cues. Developing a system that allows for the local generation of effector proteins is one way of achieving this goal. Fragmented proteins are often inactive but their function can be gained by proximity-induced complementation or ligation15,16,17. Thus, a control strategy could be devised that uses the identity of cell-surface antigens to recruit inactive precursor polypeptides, which in proximity would template the reconstitution of an effector molecule on a target cell by in situ protein ligation. In this scenario, activation of the desired protein function occurs only on the subset of target cells displaying the predefined antigen combination, in essence making the effector activity stringently cell selective.

Conditional protein splicing (CPS) is an attractive strategy to control protein structure and function because it uses the autocatalytic excision–ligation reaction of split inteins to synthesize functional proteins on demand from precursor polypeptides[16] (Supplementary Fig. 2a,b). We previously engineered the conditional reactivity of the ultra-efficient split inteins Npu, gp41-1, gp41-8 and NrdJ-1 (ref. [18]). This was done by caging each split intein fragment with a truncated segment of the matching partner (Supplementary Fig. 2c), thereby strongly inhibiting the initial fragment–fragment complexation required for splicing. However, because each caged split-intein fragment exists in an incomplete and therefore semi-frustrated structural state, the pair will readily undergo a spontaneous intermolecular domain-swapping event to produce the functional intein fold when colocalized[19] (Supplementary Fig. 2c). Any input that induces such colocalization can in principle program this strategy, theoretically limited only by which targeting vectors can be appended onto the caged split-intein fragment pair. Importantly, CPS serves as a broadly applicable control strategy for the on-demand generation of a wide array of protein functions[20], with the caged split intein thereby functioning as an actuator of a rewired stimulus–response relationship. We therefore proposed an approach that uses the unique features of a cell-surface landscape to conditionally template in situ protein trans-splicing, thereby achieving cell-selective protein function.

Here, we develop a protein actuator system called splicing-modulated actuation upon recognition of targets (SMART), which discriminates between various cell populations on the basis of their surface landscapes, such that cells with correct antigen combinations template protein trans-splicing on their surface (Fig. 1a). We show that the system is compatible with a wide variety of targeting modalities, from antibody fragments to small molecules that drive the cell-selective ligation of proteins. The localized activities of these proteins can be used in applications as varied as gated-proximity labelling and the induction of localized cellular signalling outputs.

Fig. 1: A protein actuator that computes Boolean logic on live-cell surfaces using conditional protein splicing.

a, Complementary caged split intein fragments (IntNcage and IntCcage) are fused to targeting vectors (anti-Ag_1 and anti-Ag_2) to different cell-surface antigens (Ag_1 and Ag_2). Colocalization on the cell surface leads to protein trans-splicing and generation of a functional protein nested between anti-Ag_1 and anti-Ag_2. The system works as an AND-gated input-to-output actuator. b, As a functional output, SMART-SpyCatcher was designed by splitting SpyCatcher003 at residues 73–74 and fusing the fragments to IntNcage and IntCcage. The reconstituted SpyCatcher003 binds covalently to SpyTag003 through an isopeptide bond. c, Live-cell imaging of individual K562 cell lines (wild type, HER2+, EGFR+ and HER2+/EGFR+) treated with anti-HER2–SpyN and SpyC–anti-EGFR (100 nM each, 2 h) followed by SpyTag003 labelled with Alexa Fluor 594 (SpyTag003–AF594, 100 nM, 20 min). Cells were stained with Hoechst; HER2 and EGFR expression were visualized by eGFP and iRFP, respectively. Scale bar, 20 μm. d, Schematic of SMART-SpyCatcher operating through [HER2 AND EGFR] logic on a mixed population of the four K562 cell lines. e, Flow cytometry analysis of the mixed K562 population (combined at equal amounts) either treated with SpyTag003–AF594 alone (top) or following treatment with SMART-SpyCatcher (bottom, [HER2 AND EGFR] logic). The four cell types were gated based on HER2–eGFP AND EGFR–iRFP expression and each cell type is plotted as number of cells versus AF594 relative fluorescence units (RFU); histograms are normalized to the mode. f, Dose–response experiment on the mixed K562 population with a dilution series of SMART-SpyCatcher (1 µM to 1 nM) and excess SpyTag003–AF594 (100 nM). Fold change in AF594 median fluorescence intensity (MFI) were calculated relative to untreated cells. Data shown in panels c,e,f are representative of three independent experiments. All other data are presented as mean ± s.e.m. (n = 3 independent biological replicates).

Engineering a protein actuator

Although CPS can in principle generate any desired protein output, we initially focused our efforts on designing a SMART protein that would convert two antigen inputs presented on the same cell into a unique protein recruitment dock. This would allow us to monitor and characterize the protein design using fluorescence-based methods and later deliver a broader arsenal of functionalities. To achieve this, we concentrated on developing a SMART version of SpyCatcher003 (ref. [21]), a protein superglue that spontaneously forms an isopeptide bond with the 16-amino-acid peptide SpyTag003 (Fig. 1b).

We began by systematically screening multiple potential split sites in SpyCatcher003 (designated SpyN and SpyC) for compatibility with CPS (Extended Data Fig. 1a), initially using the caged Npu split intein (NpuNcage and NpuCcage) in conjunction with the FKBP/rapamycin/FRB three-hybrid system (Supplementary Fig. 3 and Supplementary Table 1). To simulate cell-surface colocalization, we induced in-solution dimerization of SpyN–NpuNcage–FKBP and FRB–NpuCcage–SpyC by adding rapamycin (Extended Data Fig. 1b). Our screening process revealed several pairs with the ability to fully recapitulate SpyCatcher003–SpyTag003 reactivity after splicing (Extended Data Fig. 1c and Supplementary Fig. 4). We chose the SpyN1–73–SpyC74–113 pair, because this combination had minimal background reactivity with the peptide probe before splicing, that is, spontaneous complementation was minimal (Extended Data Fig. 1c). The Npu split intein contains four cysteines in its structure and leaves a cysteine substitution in the spliced product. Anticipating that these features could be deleterious to applications in the oxidizing environment of the cell surface, we exchanged Npucage for a caged version of the NrdJ-1 split intein[22], which leaves a serine at the splice site. The resulting constructs SpyN–NrdJ-1Ncage–FKBP and FRB–NrdJ-1Ccage–SpyC yielded almost complete splicing when rapamycin was added (Extended Data Fig. 1d), whereas no splicing or reactivity with SpyTag003 was observed when the caged split intein was inactivated (Extended Data Fig. 1e). To enable further engineering of this system, we generated a fusion of NrdJ-1 and solved its structure at 1.95 Å by X-ray crystallography (Protein Data Bank (PDB): 8UBS; Extended Data Fig. 1f, Supplementary Fig. 5 and Supplementary Table 2). Using this structural information, we were able to design a fully active mutant of NrdJ-1cage in which the non-catalytic Cys76 is replaced by a valine (Extended Data Fig. 1f–j and Supplementary Fig. 6). We expected that this mutant would be better suited to applications on the cell surface. We refer hereafter to the individual components SpyN–NrdJ-1N(C76V)cage and NrdJ-1Ccage(C76V)–SpyC as SpyN and SpyC, respectively, and their sum as SMART-SpyCatcher.

On-cell performance of SMART-SpyCatcher

Next, SMART-SpyCatcher was refitted for on-cell activation by removing both FKBP and FRB and installing DARPins23,24,25 targeting the two model antigens HER2 and EGFR, thereby generating anti-HER2–SpyN and SpyC–anti-EGFR (Supplementary Fig. 3 and Supplementary Table 1). The ability of SMART-SpyCatcher to perform [HER2 AND EGFR] logic was assessed on K562 leukaemia cells coexpressing HER2–eGFP and EGFR–iRFP[12]. Treatment of these cells with anti-HER2–SpyN and SpyC–anti-EGFR followed by a SpyTag003 Alexa Fluor 594 conjugate (SpyTag003–AF594) resulted in the expected fluorescence signal, albeit a weak one, on the cell surface (Extended Data Fig. 2a); using Npucage as the actuator component also led to the expected output (Supplementary Fig. 7). With the aim of improving the reaction, we tested an enhanced version of NrdJ-1(C76V)cage (referred to as eNrdJ-1cage) with re-engineered cages to improve the recruitment of SpyTag003–AF594 (Supplementary Fig. 6). This strategy afforded noticeably brighter AF594 fluorescence on the cell surface (Fig. 1c and Extended Data Fig. 2a). We therefore continued to use this actuator variant for all subsequent experiments unless otherwise stated. To exclude in-solution or at-solution-surface interphase activation, we also evaluated the activity of SMART-SpyCatcher on K562 cell lines naive (wild type) or single positive for either HER2–eGFP or EGFR–iRFP, all of which failed to elicit any response (Fig. 1c and Extended Data Fig. 2b,c). We further tested the on-target/off-target specificity of SMART-SpyCatcher when presented simultaneously with multiple decisions, and applied a mixed-population flow cytometry assay for quantification (Fig. 1d and Supplementary Figs. 8 and 9). When incubated concurrently with equal amounts of the four cell lines in a mixture, SMART-SpyCatcher retained its target specificity (Fig. 1e, Extended Data Fig. 2d and Supplementary Fig. 9), even over a broad concentration range (nanomolar to micromolar), producing a sigmoidal dose–response curve only for K562HER2+/EGFR+ (Fig. 1f). Further experimental evidence supports a three-step mechanism of action: first, anti-HER2–SpyN and SpyC–anti-EGFR bind to the target cell; second, SpyCatcher003 is spliced, owing to colocalization; and third, SpyCatcher003 reacts with SpyTag003. Blocking any of these steps leads to a complete loss of the AF594 signal (Extended Data Fig. 3a–c). Furthermore, although SMART-SpyCatcher worked under various conditions (Extended Data Fig. 3d) and was AND gated (Extended Data Fig. 3e), its decision-making ability was lost when the cages were omitted from NrdJ-1, instead inducing massive crosslinking between single- and double-positive K562 cells (Extended Data Fig. 3f).

We also generated SpyN and SpyC constructs that target epithelial cell adhesion molecule (EpCAM; Supplementary Fig. 3 and Supplementary Table 1). When tested on mixed K562 cell lines expressing either low endogenous or high ectopic levels of EpCAM in combination with different profiles of HER2 and EGFR (Supplementary Figs. 9–11), we found that SMART-SpyCatcher computed AND functions on cells that fulfilled the assigned logic gates (Extended Data Fig. 4a). This observation held true when SMART-SpyCatcher was evaluated on a variety of cancer cell lines with endogenous levels of HER2, EGFR and EpCAM (Extended Data Fig. 4b,c and Supplementary Tables 3 and 4). Furthermore, we found that the responsiveness of SMART-SpyCatcher, as measured by the magnitude of SpyTag003–AF594 recruitment, was correlated with the quantity of the less-expressed antigen used in each AND gate (Extended Data Fig. 4d). This implies that the level of SMART actuation is predominantly dictated by the quantities of each target antigen. Finally, with multiple antigen inputs available, we could also use SpyN–anti-Ag_1/SpyN–anti-Ag_2/SpyC–anti-Ag_1/SpyC–anti-Ag_2 in OR and SpyN–anti-Ag_1/SpyC–anti-Ag_2/SpyC–anti-Ag_3 in AND/OR targeting strategies (Extended Data Fig. 4e–h).

Tuning SMART response dynamics

Encouraged by the ability of our protein device to make correct decisions, we created a suite of SMART-SpyCatcher pairs with a dynamic response range. Guided by the crystallographic information on NrdJ-1 (Fig. 2a), we manipulated the cage of eNrdJ-1Ncage while maintaining unaltered eNrdJ-1Ccage as a constant. This afforded multiple pairs with increased or decreased activities (Fig. 2b, Extended Data Fig. 5, Supplementary Fig. 12 and Supplementary Tables 5 and 6), without any compromise in target specificity. For instance, introducing K114A and K116A mutations in the cage sequence increased SpyTag003–AF594 recruitment by 150%, whereas A119K led to a 25% drop. Alternatively, elongating or shortening the cage length of eNrdJ-1Ncage resulted in variants with activities ranging between 13% and 150% of that of the standard 35-amino acid toehold.

Fig. 2: Tuning SMART actuation and logic operations.

a, Summary of the diverse interactions between NrdJ-1N and NrdJ-1C forming the hedgehog–intein fold (PDB: 8UBS). Electrostatic surface potential mapping (PyMOL, adaptive Poisson–Boltzmann solver; kB = Boltzmann constant; T = temperature (K) and ec = elementary charge (C)) reveals an electrostatic interface between the basic N terminus of NrdJ-1C and an acidic groove of NrdJ-1N (i); further inserts detail electrostatic interactions (ii), residue hydrogen bonding (iii,iv), backbone hydrogen bonding (v) and hydrophobic packing (vi) stabilizing the complex. b, The eNrdJ-1Ncage variants were tested on K562HER2+/EGFR+ cells using anti-HER2–SpyN (variant indicated), SpyC–anti-EGFR (eNrdJ-1Ccage) and SpyTag003–AF594 (100 nM each). The AF594 MFI values were normalized to the response with standard eNrdJ-1Ncage. c, Anti-EGFR-Decoy was introduced as a NOT operator to obstruct AND logic output on HER2+/EGFR+/EpCAM+ cells by splicing with SpyC to generate defective SpyCatcher003. d, A SMART-SpyCatcher implementing [HER2 AND EpCAM NOT EGFR] logic was tested on mixed K562 cells (phenotypes indicated). Cells were treated with anti-EGFR–Decoy (concentrations indicated), anti-HER2–SpyN/SpyC–anti-EpCAM/SpyTag003–AF594 (100 nM each) and analysed by flow cytometry. The AF594 MFI is plotted relative to control cells lacking anti-EGFR–Decoy. e, Schematic of AND-gated cell depletion. Cells are decorated with SpyTag003-biotin via SMART-SpyCatcher enabling recruitment of a Streptavidin–Saporin disulfide conjugate (Strep–Saporin), leading to cell death upon internalization. f, Mixed K562 cells (phenotypes indicated) were treated with a two-dose regimen of SMART-SpyCatcher/SpyTag003-biotin ([HER2 AND EGFR] logic, 100 nM each) and Streptavidin–Saporin (20 nM) at a 24-h interval. Cell viability was assessed after 72 h by flow cytometry and normalized to untreated wild-type cells. g, A431 cells (HER2low, EGFRhi and EpCAMhi) were treated as in f, using the indicated SMART-SpyCatcher system (eNrdJ-1cage(K114A/K116A)). Cell viability was determined by XTT assay. Data are mean ± s.e.m. (n = 3 independent biological replicates). Statistical analysis: unpaired two-sided t-test (b). NS, not significant; *P < 0.05; **P < 0.01; ***P < 0.001; ****P < 0.0001.

The ability to tune the responsiveness of the SMART system by engineering the caging element expands the types of application possible using the approach. Notably, we were able to perform more logic operations, including a NOT gate, where we exploited a decoy protein featuring a weakened cage (Fig. 2c,d, Extended Data Fig. 6a and Supplementary Fig. 13), and for selectively targeting breast cancer cell lines based on their surface antigen presentations (Extended Data Fig. 6b–f and Supplementary Figs. 14–16).

Cell-selective killing

The ability to stringently deliver a payload to cells has many applications. Interestingly, when K562HER2+/EGFR+ cells were treated with anti-HER2–SpyN/SpyC–anti-EGFR/SpyTag003-biotin, it allowed for the cell-selective recruitment and endosomal internalization of a NeutrAvidin Rhodamine Red-X conjugate (Extended Data Fig. 7a–c). We reasoned that targeted cell tagging with a protein toxin (such as Saporin)[26] could allow for selective depletion in a heterogeneous population (Fig. 2e). To test this, mixed K562 cells were first treated with SMART-SpyCatcher assigned for [HER2 AND EGFR] logic and SpyTag003-biotin, then cultured with a Streptavidin–Saporin disulfide conjugate, and subsequently sampled for variations in cell composition after 72 h (Extended Data Fig. 7d,e). A one-dose regimen led to a 53% reduction of K562HER2+/EGFR+ cells (Extended Data Fig. 7f and Supplementary Fig. 17), and a two-dose regimen gave a 78% depletion of the subpopulation (Fig. 2f and Supplementary Fig. 18). Importantly, the wild type, K562HER2+ and K562EGFR+ cell lines were not depleted to a similar extent in the mixed population. We also tested the depletion of A431 cells (HER2low, EGFRhi and EpCAMhi) and used SMART-SpyCatcher with eNrdJ-1cage(K114A/K119A) to enhance the recruitment of SpyTag003-biotin. Compared with an untreated control, A431 cells were depleted by 92% when using the two-dose regimen with SpyTag003-biotin, Streptavidin–Saporin and SMART-SpyCatcher operating by [EGFR AND EpCAM] logic (Fig. 2g). As expected, an identical workflow with SMART-SpyCatcher acting by [HER2 AND EGFR] or [HER2 AND EpCAM] logic failed to achieve a comparable reduction in the cell viability of this cell line, and no reduction was observed when the toxin conjugate was omitted. Thus, SMART-SpyCatcher enables logic-gated cell-depletion strategies27,28,29.

Diversifying vector modalities

Many modalities including antibody fragments and mimetics, peptides and small molecules can be used to target cell-surface receptors (Fig. 3a). The ability to use these unlocks new potential targets of SMART. For instance, while we earlier fused SpyN and SpyC to DARPins, we found that single-domain antibody (sdAb)[30] and single-chain fragment variable (scFv)[12] fusions could easily be produced by recombinant bacterial expression (Supplementary Fig. 3 and Supplementary Table 1). Furthermore, introducing a carboxy-terminal cysteine in eNrdJ-1Ccage (which lacks any other cysteines) provided facile chemical installation of synthetic ligands (Supplementary Figs. 19–21). For example, we conjugated SpyC to the peptidyl antagonist BKT140 (ref. [31]) of the cytokine receptor CXCR4, and to the small-molecule antagonist SCH58261 (ref. [32]) that targets the G-protein-coupled receptor ADORA2A, correspondingly making SpyC–anti-CXCR4 and SpyC–anti-A2A. To test the generated sdAb and scFv fusions, as well as the synthetic ligand conjugates, we used K562HER2+/EGFR+, wild-type OE19 cells (HER2hi, EGFRlow, EpCAMhi, CEACAM6hi, CXCR4low and ADAORA2Alow), and the two stable cell lines OE19CXCR4DOX and OE19A2ADOX made for the doxycycline-inducible expression of either CXCR4 or ADORA2A, respectively (Supplementary Fig. 22). Without altering our previous SMART-SpyCatcher protocol, we found these new vectors to be fully compatible with our previous DARPin variants, in each case affording the expected logic-gated outputs (Fig. 3b–d, Supplementary Fig. 23 and Supplementary Table 4). Thus, the SMART platform is highly modular with respect to targeting vector modalities.

Fig. 3: Diverse SMART targeting enables AND-gated proximity labelling.

a, SMART targeting modalities encompass antibody fragments (AbFs), antibody mimetics (AbMs) and synthetic ligands (peptides and small molecules). b–d, SMART-SpyCatcher was tested with an anti-CEACAM6 single-domain antibody, a CXCR4-targeting cyclic peptide BKT140, an ADORA2A-targeting small molecule SCH58261 and the DARPins anti-HER2, anti-EGFR and anti-EpCAM. OE19 (HER2hi, EGFRlow and EpCAMhi; b) or derivatives stably expressing CXCR4 (OE19CXCR4DOX; c) or ADORA2A (OE19A2ADOX; d) were treated with SMART-SpyCatcher and fluorescently labelled SpyTag003 (100 nM each), followed by flow cytometry. e, Schematic of AND-gated protein proximity labelling by the delivery of a SpyTag003 catalyst. f, K562HER2+/EGFR+, OE19, A431 and OE19CXCR4DOX were treated with SMART-SpyCatcher (100 nM), SpyTag003–APEX2 (300 nM) and then biotin-phenol (250 μM) and H_2O_2 (100 mM, 2 min) before western blot analysis. AND gates predicted to enable labelling are shown in red; asterisks indicate endogenously biotinylated proteins. g, Densitometry analysis was done using FIJI (National Institutes of Health). Signals were normalized to tubulin (loading control). a.u., arbitrary units. h, Schematic of cell-selective photocatalytic proximity labelling using SMART-SpyCatcher and a SpyTag003-Ir conjugate. i, Mixed K562 cells (phenotypes indicated) were treated with SMART-SpyCatcher (100 nM) and SpyTag003-Ir (200 nM). After washing, cells were incubated with biotin-diazirine (100 μM), irradiated with 450-nm light (5 min), stained with Streptavidin-Alexa Fluor 546 and analysed by flow cytometry; histograms are normalized to the mode. j, Quantification of the data in i; mean ± s.e.m. (n = 3 independent biological replicates). Statistical analysis: applied unpaired two-sided t-test (b–d); applied one-way analysis of variance (ANOVA) followed by Dunnett’s test (j) (Supplementary Tables 7 and 8).

Logic-gated proximity labelling

Many surface proteins localize into specialized networks, the biological functions of which are often difficult to discern. With our diverse set of SMART-SpyCatcher pairs in hand, we reasoned that logic operations could be coupled to protein proximity labelling strategies to elucidate such microenvironments (Fig. 3e). We initially established a workflow that involves the delivery of SpyTag003–APEX2 for the APEX2/H_2O_2-catalysed generation of long-lived phenoxyl radicals (a t½ of milliseconds)[33]. First, we treated K562HER2+EGFR+ cells with SMART-SpyCatcher for [HER2 AND EGFR] logic, followed thereafter with SpyTag003–APEX2 (Extended Data Fig. 8a, Supplementary Fig. 3 and Supplementary Table 1). After washing out excess SpyTag003–APEX2, a biotin-phenol probe was added and activated by H_2O_2, which led to robust cell biotinylation (Extended Data Fig. 8b). Importantly, no labelling was observed in the various controls (Extended Data Fig. 8b). We validated these results on various cell lines by performing several AND-gated logic combinations involving HER2, EGFR, EpCAM, CEACAM6, CXCR4 and ADORA2A for the delivery of SpyTag003–APEX2 before proximity labelling. Only when SMART-SpyCatcher was matched with the correct antigen profile of the individual cell line did we observe APEX2-dependent biotinylation (Fig. 3f,g and Extended Data Fig. 8c–j).

Our ability to conduct AND-gated proximity labelling was extended to the photocatalytic proximity labelling platform μMap[34], which uses an iridium-centred photocatalyst to activate an aryl diazirine by blue-light irradiation for the generation of short-lived singlet carbene species (t½ = 2 ns). In this case, K562 cells expressing HER2 and EGFR were treated with anti-HER2–SpyN and SpyC–anti-EGFR followed by SpyTag003 conjugated to the iridium photocatalyst (Extended Data Fig. 9a–d and Supplementary Table 1). These initial studies confirmed that treatment of these cells with the diazirine-biotin probe followed by blue-light irradiation led to robust cellular labelling that was dependent on the SMART reaction (Extended Data Fig. 9e,f and Supplementary Fig. 24). Encouraged by this, we then performed a similar photocatalytic proximity labelling experiment using mixtures of K562 cell lines expressing different receptor combinations and used flow cytometry as the read-out (Fig. 3h). We found that labelling occurred only on cells for which the SMART-SpyCatcher was programmed to react with the assigned antigen profile (Fig. 3i,j and Supplementary Fig. 25). Collectively, these data demonstrate that the SMART system can be used to conduct photocatalytic proximity labelling experiments in a context-specific manner, potentially creating new opportunities for proteomics mapping of cell surfaces in complex settings such as tissues.

Developing SMART-IL-1β

The SMART platform has the potential to respond to antigen inputs with different protein functional outputs through their templated trans-splicing. To examine this further, we next focused on generating a new SMART protein. Cytokines are a potent class of immune-system modulators, and their on-demand function has become a pursuit of protein design[13]. Interleukin-1β (IL-1β) is a key pro-inflammatory cytokine with a broad range of immune activities, including the stimulation of antigen-presenting cells, natural killer cells and CD4+/CD8+ T cells[35] (Extended Data Fig. 10a). We explored whether SMART could be used as a platform to generate IL-1β in response to a combination of surface antigens with the spliced cytokine being released into the surrounding microenvironment (Fig. 4a). Because IL-1β represents a challenging target for SMART, owing to its complex β-barrel structure, we first systematically screened for potential split sites using the FKBP/rapamycin/FRB three-hybrid system (Extended Data Fig. 10b–f, Supplementary Fig. 3 and Supplementary Table 1). This revealed IL-1βN1–44 and IL-1βC45–153 as a candidate pair, with IL-1β activity on cultured HeLa cells only when spliced. Specifically, we found that NF-κB localized to the nucleus (Extended Data Fig. 10g,h), a clear sign of activated IL-1 receptor 1/IL-1 receptor accessory protein (IL-1R1/IL-1RAcP) signalling induced by biologically active IL-1β. We therefore refer to the individual components IL-1βN1–44-eNrdJ-1Ncage and eNrdJ-1Ccage-IL-1βC45–153 as IL-1βN and IL-1βC, respectively, and their sum as SMART-IL-1β.

Fig. 4: Development of a smart cytokine.

a, Colocalization of SMART-IL-1β (IL-1βN–anti-Ag_1/anti-Ag_2–IL-1βC) on a target-cell template ligation and release of the cytokine IL-1β, which activates IL-1R1/IL-1RAcP on neighbouring cells. b, OE19 cells (HER2hi, EGFRlow and EpCAMhi) were treated with SMART-IL-1β (eNrdJ-1cage, 20 nM) and the conditioned media supplemented to HeLa cells to stimulate IL-1R1 receptor signalling (top). Control experiments included: adding anti-HER2/anti-EpCAM DARPins (500 nM); use of splicing-deficient SMART-IL-1β (eNrdJ-1N(C1A)cage, 20 nM); and IL-1RA (IL-1R1 antagonist) pretreatment of HeLa cells. NF-κB localization was assessed by immunofluorescence imaging. c–f, HEK-Blue IL-1β cells, reporting IL-1β stimulation by SEAP, were exposed to conditioned media. SMART-IL-1β was supplied to OE19 (**P = 0.0072) (c), K562HER2+/EGFR+ (d) and individual cultures of the specified K562 cell lines (e) at the indicated concentrations. The conditioned media were then transferred to HEK-Blue IL-1β cells for 24 h before SEAP quantification. Controls are as in b. K562HER2+/EGFR+ cells were used in dose–response experiments with SMART-IL-1β using eNrdJ-1cage, eNrdJ-1cage_1–38 (strengthened cage) or eNrdJ-1cage_1–27 (weakened cage) (f). g, OE19 cells were co-cultured with HeLaeGFP+ cells, stably expressing eGFP, and treated with SMART-IL-1β (eNrdJ-1cage, 20 nM). IL-1R1 pathway signalling was determined as in b. h, HEK-Blue IL-1β cells co-cultured with K562HER2+/EGFR+ cells were treated with SMART-IL-1β (eNrdJ-1cage, 20 nM) and SEAP activity determined after 24 h (***P = 0.0003). Controls are as in b. Data are mean ± s.e.m. (n = 3 independent biological replicates). Statistical analysis: unpaired two-sided t-test. Data in b and g are representative of two independent experiments. Scale bars: b, 40 μm; g, 20 μm.

SMART-IL-1β actuation on cells

Our original SMART mechanism retains the spliced product on the cell surface by having targeting vectors fused onto the N and C termini of the ExtN and ExtC fragments, respectively (anti-Ag_1–ExtN-IntNcage and IntCcage-ExtN–anti-Ag_2). For SMART-IL-1β, however, we wanted to release IL-1β after its antigen-templated ligation to mimic the natural release of a cytokine in a real biological context (Fig. 4a). We therefore rearranged the domains of the protein chimeras by fusing the targeting vectors onto the caged split intein fragments, replacing FKBP and FRB, thus generating the general designs ExtN-IntNcage–anti-Ag_1 and anti-Ag_2–IntCcage-ExtN. Based on this, we proceeded by making IL-1βN–anti-HER2 and anti-EpCAM–IL-1βC. We then incubated these with an OE19 (HER2hi, EGFRlow or EpCAMhi) culture and tested the produced medium for IL-1β activity. When HeLa cells were supplemented with this medium, we found that IL-1R signalling was activated, indicated by the nuclear translocation of NF-κB (Fig. 4b and Extended Data Fig. 10i); by contrast, no activation was seen when SMART-IL-1β was blocked from binding to the OE19 cells, when the splicing-deficient mutant eNrdJ-1N(C1A)cage was used, or when the HeLa cells were pretreated with IL-1 receptor 1 antagonist (IL-1RA), which blocks IL-1β binding. SMART-IL-1β therefore actuates the ligation and release of functional IL-1β in response to defined antigen inputs. We quantified this further using a cell reporter line (HEK-Blue IL-1β), which produces secreted embryonic alkaline phosphatase (SEAP) when stimulated with IL-1β and IL-1R1/IL-1RAcP activation. Robust SEAP activity was detected when the reporter cell line was supplemented with medium produced from a combination of OE19/IL-1βN–anti-HER2/anti-EpCAM–IL-1βC (Fig. 4c) or K562HER2+/EGFR+/IL-1βN–anti-HER2/anti-EGFR–IL-1βC (Fig. 4d). Importantly, no-to-low signal was measured in control experiments. SEAP activity was furthermore detectable over a broad concentration range of SMART-IL-1β (Fig. 4e), with little activity related to medium from control K562 cell lines. By tuning the cage of eNrdJ-1cage, we could adjust the effective concentration of SMART-IL-1β needed on K562HER2+/EGFR+ cells to yield a 50% response on HEK-Blue IL-1β cells (Fig. 4f).

Finally, we also tested SMART-IL–1β in co-culture experiments. First, we co-cultured HeLaeGFP+ with OE19 cells (which importantly do not respond to IL-1β; Extended Data Fig. 10j) and then treated these with IL-1βN–anti-HER2/anti-EpCAM–IL-1βC. This led to the nuclear localization of NF-κB in the HeLaeGFP+ cells (Fig. 4g). When we co-cultured HEK-Blue IL-1β with K562HER2+/EGFR+ and treated these with IL-1βN–anti-HER2/anti-EGFR–IL-1βC, we measured robust SEAP activity, which was absent in control experiments (Fig. 4h). We believe that SMART-IL-1β constitutes the first example of an on-demand system capable of post-translationally generating an active cytokine (IL-1β) in response to local stimuli and mediating its release into the cell microenvironment.

Discussion

In this study, we present a synthetic biology platform we call SMART that, at its core, functions as a protein actuator based on conditional protein trans-splicing with tunable responsiveness to cellular inputs. SMART can sense multiple cell surface features and converts these to a user-defined functional output based on Boolean logic operations. Specifically, we show that programmable protein ligation is achievable on cell surfaces in response to the presence of two receptors. A key attribute of our SMART system is its modularity in terms of possible inputs and outputs. We have demonstrated that the platform is compatible with a variety of protein, peptide and small-molecule targeting agents, enabling SMART activation following the co-engagement of a range of surface proteins, such as growth-factor receptors, cell-adhesion molecules and G-protein-coupled receptors.

In principle, SMART can generate many types of output, leveraging the broad sequence tolerance of the NrdJ-1 split intein that functions as the protein ligase in the system. In the present work, we have illustrated this through the generation of a functional SpyCatcher003 protein and the cytokine IL-1β. SpyCatcher003 serves as a protein dock that allowed us to recruit a variety of activities to designated cells. These two examples also illustrate another feature of the SMART system, namely the ability to control whether the reaction product remains associated with the manufacturing cells (as in the SpyCatcher example) or is released into the extracellular environment (as shown for IL-1 β) through a ligation-and-retain and ligation-and-release mechanism. The latter represents a unique feature of SMART that distinguishes the approach from other protein logic devices that rely on the recruitment of pre-existing factors to a location of interest. By coupling protein trans-splicing to the localized release of an active protein, we can achieve exquisite control over protein activation. We imagine that the scope of SMART will be expanded by implementing efficient screening approaches to identify split sites in target proteins[36], in combination with the use of orthogonal inteins from expanded libraries37,38. Finally, although we so far focused on cell-surface applications of SMART, we expect that the platform will find applications in other contexts, including logic-gated imaging, proximity proteomics and possibly even genomics in permeabilized cells.

Methods

General materials

Common reagents and chemicals were purchased from MilliporeSigma unless stated otherwise. The 2,4-dinitrochlorobenzene (CAS number 97-00-7), tert-butyl bromoacetate (CAS 5292-43-3), N-hydroxysuccinimide (CAS 6066-82-6), N,N′-dicyclohexylcarbodiimide (CAS 538-75-0), Celite 545 (CAS 68855-54-9), ethyl 2-bromoacetate (CAS 105-36-2) and 1-(2-aminoethyl)maleimide hydrochloride (CAS 134272-64-3) were purchased from MilliporeSigma. The 2-[2-(2-aminoethoxy)ethoxy]ethanol (CAS 86770-74-3), biotin-PEG3-amine (CAS 359860-27-8), 2-(furan-2-yl)-7H-pyrazolo[4,3-e][1,2,4]triazolo[1,5-c]pyrimidin-5-amine (CAS. 288-13-1) and 4-[3-(trifluoromethyl)-3H-diazirine-3-yl]benzylamine hydrochloride (CAS 1258874-29-1) were purchased from Ambeed. Triethylamine (CAS 121-44-8) was purchased from Thermo Fischer Scientific. Dithiothreitol (DTT, CAS 3483-12-3), isopropyl-β-thiogalactopyranoside (IPTG, CAS 367-93-1) and bovine serum albumin (BSA) were obtained from Gold Biotechnology. Alexa Fluor 594 C5 maleimide, biotin-PEG3-NHS ester (CAS 1253286-56-4), hydroxy-PEG10-tert-butyl ester (CAS 778596-26-2) and chloroacetamido-PEG4-NHS ester (CAS 1353011-95-6) were purchased from BroadPharm. Biotin maleimide (CAS 116919-18-7) was purchased from MilliporeSigma. Alexa Fluor 568 DBCO was purchased from Lumiprobe.

Oligonucleotide primers were purchased from MilliporeSigma. The gBlock gene fragments were purchased from Integrated DNA Technologies. PrimeSTAR HS DNA polymerase was purchased from Takara Bio. Gibson Assembly Master Mix and the restriction enzymes NheI, NotI and T7 DNA Ligase were purchased from New England Biolabs. DNA purification kits were purchased from Qiagen. PCR purification and gel extract columns were purchased from Thomas Scientific. All the plasmid sequencing was done by GENEWIZ or Plasmidsaurus. DH5α competent cells and One Shot Stbl3 chemically competent Escherichia coli cells were purchased from Thermo Fisher Scientific. SHuffle T7 competent E. coli cells were purchased from New England Biolabs. Plasmids for lentiviral preparations were obtained from Addgene.

Nickel nitrilotriacetic acid (Ni-NTA) resin was obtained from Thermo Fisher Scientific. MOPS-SDS running buffer was obtained from Boston Bioproducts. Criterion cassettes, acrylamide, ammonium persulfate, tetramethylethylenediamine and Econo-Pac 10DG columns were obtained from Bio-Rad. Nitrocellulose membrane (0.45 μm) for western blotting was purchased from Thermo Fisher Scientific. Empore solid-phase extraction stage tips were purchased from Thermo Fisher Scientific.

Primary antibodies were purchased from Santa Cruz Biotechnology, Abcam, Cell Signaling Technology, Thermo Fisher Scientific and MilliporeSigma. Secondary antibodies were purchased from LI-COR Biotechnology.

NeutrAvidin Rhodamine Red-X and Streptavidin-Alexa Fluor 546 conjugates were purchased from Thermo Fischer Scientific. Streptavidin–Saporin (Streptavidin-ZAP) was purchased from Advanced Targeting Systems.

Dulbecco’s Modified Eagle medium (Gibco), RPMI-1640 medium (Gibco), McCoy’s 5a medium modified (Gibco), F-12K medium (Gibco), Dulbecco’s phosphate-buffered saline (DPBS, Gibco), Penicillin-Streptomycin (5,000 U ml−1), trypsin-EDTA (0.25%), trypsin-EDTA (0.05%), Lipofectamine 3000 transfection reagent, l-glutamine (200 mM), puromycin dichloride (10 mg ml−1) and Falcon standard tissue culture dishes were purchased from Thermo Fisher Scientific. A mammary epithelial cell growth medium kit was purchased from MilliporeSigma. Fetal bovine serum (heat inactivated) was purchased from Bio-Techne. Doxycycline (hyclate) was purchased from StemCell Technologies. An XTT cell viability kit was purchased from Cell Signal Technologies. Hoechst 33342 solution was obtained from Invitrogen. Glass-bottom plates were purchased from Cellvis. QUANTI-Blue solution was purchased from InvivoGen.

Human cell lines K562EpCAMlow (wild type, CCL-243), K562HER2+, K562EGFR+, K562HER2+/EGFR+, K562HER2+/EpCAMhi and K562HER2+/EGFR+/EpCAMhi were gifts from D. Baker. Human cell lines MCF-10a (CRL-10317), MCF-7 (HTB-22), LoVo (CCL-229), A594 (CCL-185) were gifts from Y. Kang. Human cell line Sk-br-3 (HTB-30) was a gift from S. Lipkowitz. Human cell line OE19 (JROECL19) was purchased from MilliporeSigma. Human cell lines HCT-116 (CCL-247) and A431 (CRL-1555) were purchased from ATCC. Human cell line HEK-Blue IL-1β was purchased from Invivogen. The PiggyBac transposase plasmid was a gift from C. Kadoch.

Coomassie-stained SDS–PAGE gels and western blots were imaged on an Odyssey system (LI-COR). See Supplementary Fig. 1 for uncropped source data. Densitometry measurements were performed using FIJI (National Institutes of Health)[39]. Molecular graphics and analyses were performed with PyMOL v.2.5, developed by Schrödinger. Graph plots and statistical analysis were made in GraphPad Prism v.9.2.0 (121).

High-performance liquid chromatography

Analytical-scale reverse-phase high-performance liquid chromatography (RP-HPLC) was done on an Agilent 1100 series or an Agilent 1260 Infinity system equipped with a C18 Vydac column (5 mM, 4.6 × 150 mm) at a flow rate of 1 ml min−1. Semi-preparative RP-HPLC was done on an Agilent 1260 Infinity system equipped with a Waters XBridge BEH C18 column (5 mM, 10 × 250 mm) at a flow rate of 4 ml min−1. Preparative-scale RP-HPLC was done on a Waters prep LC system consisting of a Waters 2545 binary gradient module and a Waters 2489 ultraviolet (UV)-visible detector equipped with a C18 Vydac column (10 mM, 22 × 250 mm). The HPLC solvents were H_2O with 0.1% TFA (solvent A) and 90% acetonitrile in water with 0.1% trifluoroacetic acid (TFA) (solvent B). Applied solvent gradients are specified in detail in the relevant sections.

Mass spectrometry

Proteins and peptides were characterized by electrospray ionization mass spectrometry (ESI-MS) on a Bruker Daltonics MicroTOF-Q II mass spectrometer by direct injection after isolation by RP-HPLC.

Peptide synthesis

The CXCR4 antagonist peptide ligand BTK140 was synthesized manually using a standard Fmoc solid-phase peptide synthesis method on a 0.2 mmol scale using H-Rink Amide resin (ChemMatrix). The solid-phase synthesis cycle included Fmoc deprotection at room temperature for 20 min with 20% v/v piperidine in dimethylformamide (DMF) containing 0.1 M 1-hydroxybenzotriazole hydrate and coupling at room temperature for 30 min using 5 equivalents of Fmoc protected amino acid in DMF with 5 equivalents of hexafluorophosphate azabenzotriazole tetramethyl uronium (HATU) and 10 equivalents of N,N-diisopropylethylamine (DIPEA). All couplings were performed twice. For non-proteogenic amino acids and for coupling of the Arg–Arg junction, the coupling step was performed with 3 equivalents of the specific Fmoc protected amino acid in DMF with 3 equivalents of (7-azabenzotriazol-1-yloxy)tripyrrolidinophosphonium hexafluorophosphate (PyAOP) and 10 equivalents of DIPEA for 3 h (if the coupling step was done once) or 2 × 2 h (if double couplings were done). D-Lys(Dde) deprotection was done on resin at room temperature for 30 min by adding 2% v/v hydrazine in DMF under N_2 agitation. Two successive coupling steps were done at room temperature for 1 h with 5 equivalents of azido-PEG3-acid, or alternatively azido-PEG10-acid, in DMF with 5 equivalents of HATU and 10 equivalents of DIPEA. Deprotection of Cys(Acm) was done on resin using either thallium triflate or in solution phase with I_2. Final peptide cleavage and side-chain deprotection was done at room temperature for 3 h using a cleavage cocktail of 95% v/v TFA, 2.5% v/v triisopropyl silane, 2.5% v/v H_2O. The peptide was pelleted by adding ice-cold diethyl ether and subsequent centrifugation at 4,000g for 10 min at 4 °C. The crude peptide was then dissolved in aqueous acetonitrile 0.1% v/v TFA and purified by preparative RP-HPLC using aqueous 0.1% v/v TFA as solvent A and 90% v/v acetonitrile, 0.1% v/v TFA as solvent B, with a gradient of 0–73% over 40 min. Pure fractions were identified by analytical RP-HPLC and ESI-TOF MS, and pooled and lyophilized.

Peptide conjugation

To BTK140-PEG3-azide (370 µg, 123 nmol) dissolved in 1 ml MeCN we added a slight excess of AF568-DBCO (124 nmol) dissolved in DMSO to 1 mM, and the reaction was left overnight at room temperature away from light. The crude mixture was analysed by RP-HPLC and diluted with 9 ml of solvent A (aqueous 0.1% v/v TFA) on full conversion to BTK-AF568, which was further purified by preparatory-scale RP-HPLC (0–73% solvent B for 40 min). The collected product fractions were combined and lyophilized away from light. The peptide was redissolved in 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA and 10% v/v glycerol to a final concentration of 100 µM when used for cell-phenotyping experiments.

Chemical synthesis

Synthetic protocols of SCH58261 and its maleimide functionalization, the azido-PEG10-acid linker, the iridium photocatalyst and its chloroalkane functionalization, and the biotin-phenol and biotin-diazirine probes are provided in the Supplementary Methods.

DNA cloning

All bacterial expression vectors were based on a pET backbone vector with a gene for kanamycin resistance. DNA fragments amplified by PCR were inserted into a gene cassette using Gibson Assembly. The gene cassette included an upstream T7 promoter under regulation of a lac operator, an ATG start codon in frame with an N-terminal His_6-SUMO fusion tag when specified and ended with a TAA stop codon and a T7-terminator sequence.

Site-directed mutagenesis (including missense substitutions, insertions and deletions), as well as amplifications of gene inserts and plasmid backbones, was done using PCR. To a solution of 10 µl of 1 ng µl−1 plasmid, 1 µM forward primer and 1 µM reverse primer we added 10 µl 2× PrimeSTAR DNA polymerase master mix. The mixture was used in a PCR reaction. The completed PCR reaction was restriction digested with 20 units of DpnI for 1 h at 37 °C before the PCR amplicon was isolated by a general PCR clean-up protocol. The purified PCR amplicon was then used in a Gibson assembly reaction (see below). Alternatively, full plasmid amplicons from site-directed mutagenesis were used directly in heat-shock transformations of chemically competent E. coli DH5α cells, which were plated on LB-agar plates supplemented with 50 µg ml−1 kanamycin. Single colonies were picked, grown and the plasmid isolated before being verified by Sanger sequencing.

DNA components prepared by PCR using primers designed to have 15–20 base pair overlaps were used in Gibson Assembly reactions. Gibson Assembly reactions were set up by mixing 2 µl of DNA fragments (100 ng plasmid backbone amplicon, 3–5 molar excess gene insert amplicon) with 2 µl 2× NEBuilder HiFi DNA Assembly master mix. The reaction was incubated for 15 min at 50 °C, cooled and thereafter used in a heat-shock transformation of chemically competent E. coli DH5α, which was plated on LB-agar plates supplemented with 50 µg ml−1 kanamycin. Single colonies were picked, grown and the plasmid isolated before being verified by Sanger sequencing.

The PiggyBac transposon plasmids used in the generation of stable cell lines were generated by standard restriction cloning. Gene fragments containing the desired transgene sequence were synthesized to contain NheI and NotI restriction sites. Separate restriction digest reactions with NheI and NotI were prepared for the plasmid backbone and the two gene inserts encoding SPHA-Flag-CXCR4-GFP and SPHA-Flag-ADORA2A-mCherry. Reactions were done for 1 h at 37 °C and the digest products isolated. The linearized plasmid backbone was mixed with either of the digested gene inserts and T7 DNA ligase and the reactions incubated for 1 h at 37 °C. The ligation reactions where then used to transform One Shot Stbl3 chemically competent E. coli cells, which were plated on LB-agar plates supplemented with ampicillin (100 µg ml−1). Single colonies were picked, grown and the plasmid isolated before being verified by either Sanger sequencing or full plasmid sequencing.

Recombinant protein expression and purification

Chemically competent E. coli BL21(DE3) cells were heat-shock transformed with a pET vector carrying the gene cassette for the protein of interest. Cells were grown overnight at 37 °C in 8 ml LB medium supplemented with 50 µg ml−1 kanamycin. This overnight culture was used to inoculate an expression culture of 1 l LB medium supplemented with 50 µg ml−1 kanamycin. In general, the expression culture was incubated at 37 °C until it reached an optical density at 600 nm (OD_600) of 0.4, after which it was cooled for 20 min at 18 °C. Protein expression was then induced by the addition of 0.1 ml 1 M IPTG and the culture was left overnight at 18 °C. For expression of full-length NrdJ-1, used in the crystallography study and for any SpyTag003 and stand-alone DARPin constructs, the expression culture was incubated at 37 °C until it reached an OD_600 of 0.6. The expression was then induced by the addition of 0.1 ml 1 M IPTG and the culture was left for 4 h at 37 °C. In all cases, cells were collected by centrifugation at 3,500g at 18 °C for 20 min and suspended in lysis buffer containing 20 ml 50 mM NaH_2PO_4 (pH 8.0), 300 mM NaCl, 20 mM imidazole, supplemented with 1 mM DTT and 1 mM phenylmethylsulfonyl fluoride (PMSF). Cell suspensions were then either stored at −20 °C until further use or used directly. Soluble protein was extracted by subjecting the cell suspension to sonication using a duty cycle of 20 s on, 30 s off at 30% amplitude while cooled on an ice bath, after which a cleared lysate was produced by centrifugation at 35,000g at 4 °C for 20 min. The cleared lysate was passed through a pre-equilibrated Ni2+-nitrilotriacetic acid (NTA) column (2 ml resin slurry per litre of culture) and the flow-through discarded. The column was then washed with 50 ml lysis buffer, before the protein was eluted using 6 ml lysis buffer supplemented with 250 mM imidazole. His_6–SUMO tagged proteins were treated overnight with His_6–Ulp1 protease while being dialysed against lysis buffer supplemented with 1 mM DTT. The dialysed sample was then passed through a pre-equilibrated Ni2+-NTA column to remove any cleaved His_6–SUMO tag and His_6–Ulp1 protease. The flow-through and an additional 6 ml lysis buffer passed through the column was collected, combined and concentrated to 0.5 ml. The concentrated sample was filtered through a 0.22 μm spin filter. Size-exclusion chromatography was done at 4 °C with a flow rate of 0.5 ml min−1 on an ÄKTA Fast Performance liquid chromatography (GE Healthcare) system using a Superdex 200 10/300 GL (Cytiva Life Sciences) column with 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA and 1 mM DTT as the eluent. Pure fractions were identified by SDS–PAGE, validated by analytical RP-HPLC and the protein mass was confirmed by ESI-TOF MS. Pure fractions were supplemented with 10% v/v glycerol, aliquoted and flash-frozen in liquid nitrogen before being stored at −80 °C until further use. Analytical data for all proteins is shown in Supplementary Fig. 3, Extended Data Fig. 9 and Supplementary Table 1. The fully annotated amino acid sequences of overexpressed constructs used in this study are given in Supplementary Table 9.

SHuffle T7 competent E. coli cells were used for the cytosolic expression of His_6–SUMO–anti-HER2scFv–SpyN. Chemically competent cells were heat-shock transformed with a pET vector carrying the gene cassette for the protein of interest. Cells were grown overnight at 37 °C in 8 ml LB medium supplemented with 50 µg ml−1 kanamycin. This overnight culture was used to inoculate an expression culture of 1 l LB medium supplemented with 50 µg ml−1 kanamycin. The culture was incubated at 37 °C until it reached an OD_600 of 0.4, after which it was cooled for 30 min at 16 °C. Protein expression was then induced by the addition of 0.3 ml 1 M IPTG and the culture was expressed overnight at 16 °C. Cells were collected and the protein purified from the soluble fraction as mentioned above.

Western blotting

Samples were run on an SDS–PAGE gel. For western blotting, the gel was used for a transfer reaction onto a nitrocellulose membrane, which was subsequently blocked with TBS-T (25 mM Tris, 150 mM NaCl, 0.1% v/v Tween-20, pH 7.7) supplemented with 4% w/v skimmed-milk powder for 1 h at room temperature. The membrane was washed 3 times for 5 min with TBS-T and incubated with primary antibodies at specified dilution (Supplementary Table 10) on an orbital shaker for 1 h at room temperature or alternatively overnight at 4 °C. After washing 3 times for 5 min with TBS-T, the IRDye secondary antibody or alternatively IRDye Streptavidin was applied for 30 min to 1 h at room temperature, before imaging on a Li-Cor Odyssey imager (Li-Cor).

X-ray crystallography

Crystallography studies used a fused version of NrdJ-1 containing C1A and N145A inactivating mutations and SGG and SEI as N- and C-terminal extein sequences, respectively. The protein was dialysed against a buffer containing 25 mM HEPES (pH 7.5), 150 mM NaCl, then concentrated to 40 mg ml−1, and finally flash-frozen as aliquots in liquid nitrogen before being stored at −80 °C for further use. Initial crystallization conditions were established using a SaltRx HT screen (Hampton Research) with a Phoenix crystallization robot (Art Robbins). Crystals were grown at 4 °C by the sitting-drop vapour-diffusion method. A focused screen was centred on conditions with increasing concentrations of sodium formate at various pH values. Optimal crystals were obtained after one week using a solution of 4.5 M sodium formate (pH 7.0). Diffraction data were obtained at the National Synchrotron Light Source II (Brookhaven National Laboratory), beamline 17-ID-1. The data were processed using the XDS package[40]. The phase information was determined by molecular replacement using PHASER in the CCP4 suite[41] and using an in silico AlphaFold2 (refs. 42,43) model of full-length NrdJ-1 as input. Iterative rounds of model building in Coot[44] and refinements in PHENIX Refine (v.1.17_3644)[45] were performed to obtain the final structure. Data collection and refinement statistics are displayed in Supplementary Table 2.

Protein conjugation reactions

Purified protein containing a C-terminal cysteine (SpyTag003-Cys, SpyTag003D117A-Cys, anti-HER2-Cys DARPin, anti-EGFR-Cys DARPin, anti-EpCAM-Cys DARPin, anti-CEACAM6-Cys single-domain antibody and SpyC-Cys) or catalytic cysteine (anti-HER2-SpyN-eNrdJ-1Ncage) was reduced with 1 mM DTT for 20 min on ice to prepare it for conjugation chemistry. The sample was washed with buffer (100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA) using spin-filtration to remove small-molecule thiols. The reduced protein was either flash-frozen in liquid nitrogen and stored at −80 °C for later use or used directly in conjugation reactions as described in the following sections.

The reduced protein was mixed with a molar excess of the required alkylating agent (iodoacetamide, Alexa Fluor 594 maleimide, Alexa Fluor 568 maleimide, Alexa Fluor 488 maleimide, biotin-maleimide, DBCO-maleimide or SCH58261-maleimide) and incubated for 20 min at room temperature in the dark. Reactions were monitored by RP-HPLC and ESI-TOF MS and quenched with 1 mM DTT when completed. The reaction mixture was then passed over an Econo-Pac 10DG column using 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 10% v/v glycerol as the eluent. The product was characterized by RP-HPLC and ESI-TOF MS, flash-frozen and stored at −80 °C. Analytical data for protein conjugations are provided in Supplementary Fig. 3 and Supplementary Table 1, and for the SpyC-anti-A2A conjugate in Supplementary Fig. 21 and Supplementary Table 1.

SpyC-DBCO was generated by reacting SpyC-Cys with DBCO-maleimide according to the protocol described above and used subsequently in a strain-promoted alkyne-azide cyclo-addition reaction with the synthetically prepared CXCR4 antagonist peptide BTK140 functionalized with an azide. SpyC-DBCO (1.7 mg, 94 nmol) was reacted with BTK-PEG10-azide (4.4 mg, 133 nmol) in 100 µl of 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 10% v/v glycerol. The reaction was incubated at 4 °C and monitored by RP-HPLC and ESI-TOF MS. When full conversion was observed, the reaction was washed with buffer (100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 10% v/v glycerol) by spin filtration to remove excess peptide and then finally concentrated to 1 ml. Size-exclusion chromatography was done at 4 °C at a flow rate of 0.5 ml min−1 on an ÄKTA Fast Performance liquid chromatography (GE Healthcare) system using a Superdex 200 10/300 GL (Cytiva Life Sciences) column with 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 10% v/v glycerol as the eluent. Pure fractions were identified by SDS–PAGE, validated by analytical RP-HPLC and the protein mass was confirmed by ESI-TOF MS. Pure fractions were flash-frozen in liquid nitrogen before being stored at −80 °C until further use. Analytical data for the final SpyC–anti-CXCR4 conjugate are provided in Supplementary Fig. 21 and Supplementary Table 1.

Anti-CEACAM6–AF594 was prepared by reacting anti-CEACAM6–SpyCatcher003 (0.33 mg, 12.3 nmol) with SpyTag003–AF594 (0.2 mg, 12.5 nmol) in 100 µl of 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 10% v/v glycerol. The reaction was incubated away from light at room temperature and monitored by RP-HPLC and ESI-TOF MS. When full conversion was observed, the reaction was washed with buffer (100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 10% v/v glycerol) by spin filtration to remove excess peptide and then finally concentrated to reach 100 µM of the conjugate. The product was validated by RP-HPLC and ESI-TOF MS, flash-frozen and stored at −80 °C.

SpyTag003-HaloTag13 was used in reactions with the iridium catalyst functionalized with a chloroalkane linker (Ir-PEG4-C_6H_12Cl). Specifically, one equivalents of SpyTag003-HaloTag13 (585 µg, 15 nmol) was reacted with three equivalents of Ir-PEG4-C_6H_12Cl (62 µg, 50 nmol) in 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 1 mM DTT for 1 h at room temperature. The reaction was monitored by RP-HPLC. When all the protein had been consumed to generate the SpyTag003–HaloTag13-Ir conjugate (referred to as SpyTag003-Ir), the reaction was washed in 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 1 mM DTT by spin filtration to remove excess Ir-PEG4-C_6H_12Cl. The conjugate was then aliquoted, flash-frozen and stored at −80 °C.

Rapamycin-induced protein trans-splicing reactions

Screening for the optimal split site within SpyCatcher003 was done in splicing buffer (100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 1 mM DTT, 10% v/v glycerol) by combining complementary protein chimeras Flag-SpyN1−x-NpuNcage-FKBP and FRB-NpuCcage-SpyCy-113–Myc (1 µM of each), with x and y denoting the last and first residue of the two fragments (the split site). When indicated, samples were supplemented with SpyTag003 or conjugates thereof (2 µM) and either rapamycin (a final concentration of 10 µM from a 50 µM DMSO stock) or TEV protease (10 units). Reaction mixtures were incubated for 24 h at 37 °C before being analysed by SDS–PAGE or western blotting.

Screening for the optimal split site in IL-1β was done in splicing buffer (100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA, 1 mM DTT, 10% v/v glycerol) by combining complementary protein chimeras Flag-IL-1βN1−x-eNrdJ-1Ncage-FKBP and FRB-eNrdJ-1Ccage-IL-1βCy−153–Myc (1 µM of each), with x and y denoting the last and first residue of the two fragments (the split site). When indicated, samples were supplemented with rapamycin (final concentration of 10 µM from a 50 µM DMSO stock). Reaction mixtures were incubated at 37 °C before being analysed by SDS–PAGE or western blotting.

Generation of stable cell lines

To generate stable cell lines expressing CXCR4- and ADORA2A-related constructs, low-passage OE19 cells were transfected with a PiggyBac transposon plasmid encoding for the desired transgene under the control of a doxycycline-inducible promoter and a PiggyBac transposase plasmid (2:1 ratio). Lipofectamine 3000 transfection reagent was used for the transfection according to the manufacturer’s instructions. The transfected cells were allowed to recover in RPMI-1640 supplemented with 2 mM l-glutamine, 10% v/v FBS, 100 U ml−1 penicillin/streptomycin for 30 h after transfection. The cells were then cultured for 5 days in RPMI-1640 supplemented with 2 mM l-glutamine, 10% v/v FBS, 100 U ml−1 penicillin/streptomycin and 1 µg ml−1 puromycin. Transfected OE19 cells that survived puromycin selection were further expanded and maintained in RPMI-1640 supplemented with 2 mM l-glutamine, 10% v/v FBS, 100 U ml−1 penicillin/streptomycin and 1 µg ml−1 puromycin, with cultures being discarded after 30 passage cycles. Transgene expression was achieved by supplementing the culture with 400 ng ml−1 doxycycline for 24 h. Protein expression was confirmed by western blot, immunofluorescence microscopy and flow cytometry. The primary structures of the CXCR4- and ADORA2A-related constructs are given in Supplementary Table 11.

Lenti-X 293 T cells (Takara Bio, 632180) were cultured in DMEM supplemented with 10% (v/v) FBS and 100 U ml−1 penicillin/streptomycin in 6-well plates to approximately 70% confluency. The cells were then transfected in culture medium without penicillin/streptomycin using Lipofectamine 2000 with: a transfer plasmid encoding the genes for HER2Δ-eGFP and blasticidin resistance (4 µg); the envelope plasmid pMD2.G (1.2 µg); and the packaging plasmid psPAX2 (3.6 µg). After 24 h, the culture was aspirated and DMEM supplemented with 10% (v/v) heat FBS and 100 U ml−1 penicillin/streptomycin added. Lentivirus was collected the following day by isolating and filtering (0.45 µm) the culture supernatant. The lentivirus preparation was stored at −80 °C until further use. Wild-type HeLa cells were cultured in DMEM supplemented with 10% (v/v) FBS and 100 U ml−1 penicillin/streptomycin to a confluency of 50% in a 6-well plate. Then, 1 ml of the produced lentivirus preparation was added along with 1 ml of fresh medium and further supplemented with 4 µg ml−1 polybrene. After 24 h, an extra 1 ml of virus was added to the HeLa cells. The following day, the medium was changed and the cells were allowed to recover for another 24 h. The day after that, selection was initiated by adding 1 µg ml−1 blasticidin. After several passages, the cells were sorted by fluorescence-activated cell sorting on a BD FACSymphony A3 Cell Analyzer using the eGFP signal for gating to isolate the HeLaeGFP+ population. The primary structure of HER2Δ-eGFP is given in Supplementary Table 11.

Mammalian cell culture

Mammalian cell lines were cultured in media as detailed in the Supplementary Table 12 in an incubator at 37 °C and 5% CO_2. All cell lines were regularly tested free of mycoplasma.

Confocal microscopy

Suspension cell lines

The specific cell line or mixture was treated as specified in the relevant section. After treatment, cells were suspended in DBPS, 1% w/v BSA, 2 mM CaCl_2 supplemented with Hoechst 33342 (10 µg ml−1) and incubated for 30 min at room temperature before being washed twice in buffer. The cells were then transferred to a glass-bottom plate and allowed to settle before being imaged using 40× magnification on a Nikon A1/HD25 microscope (Nikon Instruments). Processing of fluorescence microscopy images was done using FIJI (National Institutes of Health)[39].

Adherent cell lines

The specific cell line was plated on a glass-bottom plate, cultured and then treated as specified in the relevant section. After treatment, DBPS, 1% w/v BSA, 2 mM CaCl_2 supplemented with Hoechst 33342 (10 µg ml−1) was added to the plate and the adherent cells incubated for 30 min at room temperature before being washed twice in buffer. The cells were then imaged as described above.

Flow cytometry

Cell lines were suspended as 1,000,000 cells per ml in cold DBPS, 1% w/v BSA, 2 mM CaCl_2 (supplemented with 50 mM EDTA for adherent cell cultures), filtered through a cell strainer and kept on ice. Flow cytometry data acquisition was obtained on a BD LSR II flow cytometer and the results were analysed using FlowJo 10.8.1. Single-colour controls were included for compensation adjustments. Examples for the gating strategy used for flow cytometry analysis of mixed K562 populations are given in Supplementary Figs. 8–11. Examples for the gating strategy used for flow cytometry analysis of mixed mammary populations are given in Supplementary Figs. 14–16.

Cell surface labelling using SMART-SpyCatcher

Suspension cell lines

Individually cultured K562 cell lines were spun down and counted to estimate the cell concentration. Then approximately 200,000 cells of an individual K562 cell culture were isolated, washed twice with a buffer containing DPBS, 1% w/v BSA and 2 mM CaCl_2 and then suspended in 0.4 ml of the same buffer or in an appropriate medium. To this sample was added the specified SMART-SpyCatcher system at the stated concentration by adding each individual component (SpyN and SpyC) from stock solutions dissolved in 100 mM NaH_2PO_4 (pH 7.2), 150 mM NaCl, 1 mM EDTA and 1 mM DTT. The sample was then incubated for 2 h at 37 °C in 5% CO_2 to allow for cell-surface receptor binding and protein trans-splicing. The specified SpyTag003 conjugate was then added (100 nM final concentration) and the SpyTag003–SpyCatcher003 reaction was allowed to proceed in the dark at room temperature for 20 min. The cells were then washed twice with cold DPBS, 1% w/v BSA, 2 mM CaCl_2 and incubated on ice until further analysis by confocal microscopy or flow cytometry. Samples subjected to SDS–PAGE or western blotting were washed twice with DPBS alone to remove excess BSA. Control experiments examining the mechanism of action in Extended Data Fig. 3a–c included the following steps before the addition of SpyTag003–AF594: first, addition of competing DARPins (500 nM) blocking SMART-SpyCatcher binding; second, addition of the Cys1-alkylated eNrdJ-1Ncage component, unable to perform protein trans-splicing; or third, pre-addition of unlabelled SpyTag003 (500 nM) to block the reaction with SpyTag003–AF594. In reactions with SpyTag003D117A–AF594, the mutation D117A disables the formation of an isopeptide bond with SpyCatcher003.

Adherent cell lines

Individually cultured adherent cell lines were lifted using trypsin, washed with complete medium and counted to estimate the cell concentration. Then 200,000 cells were seeded in 24-well plates and allowed to attach and recover for 24 h in complete media. The assay protocol for SMART-SpyCatcher actuation and SpyTag003 recruitment followed that outlined above for the suspension cell lines. After treatment, the adherent cells were washed twice with DPBS, 1% w/v BSA, 2 mM CaCl_2 and then lifted with a non-enzymatic solution of DPBS, 1% w/v BSA, 50 mM EDTA and incubated on ice before analysis by flow cytometry. For SDS–PAGE or western blotting, cells were lifted as described and then washed with DPBS alone to remove excess BSA.

Mixed-population experiments using SMART-SpyCatcher

Suspension cell lines

Two distinct mixed populations of K562 cell lines were generated (K562 expresses low endogenous levels of EpCAM):

- Mixed K562 population 1

- K562 (wild-type cell line)

- K562EGFR+

- K562HER2+

- K562HER2+/EGFR+

- Mixed K562 population 2

- K562 (wild-type cell line)

- K562EGFR+

- K562HER2+/EpCAMhi

- K562HER2+/EGFR+/EpCAMhi

The mixed populations were generated by combining the specified four cell lines (50,000 cells each) in a reaction tube. The SMART-SpyCatcher system (SpyN and SpyC) was then added at the specified concentration and the sample was incubated for 2 h at 37 °C and 5% CO_2 to allow for cell-surface receptor binding and protein trans-splicing. In experiments involving NOT gating, the decoy was added at 100 nM just before the addition of SMART-SpyCatcher. The required SpyTag003 conjugate was then added (100 nM final concentration) and the SpyTag003–SpyCatcher003 reaction was allowed to proceed in the dark at room temperature for 20 min. The cells were then washed twice with cold DPBS, 1% w/v BSA, 2 mM CaCl_2 and incubated on ice until further analysis by confocal microscopy or flow cytometry. When appropriate for data representation, the individual data sets from the two distinct mixed populations were combined into one common bar graph.

Adherent cell lines

The three adherent cell lines MCF-10a, MCF7 and Sk-br-3 were cultured individually. Each cell line was lifted with a non-enzymatic solution of DPBS, 1% w/v BSA, 50 mM EDTA and counted to estimate the cell concentrations. MCF-10a was then mixed in equal numbers with either MCF-7 or Sk-br-3, and the two mixed mammary populations washed with either complete DMEM medium (MCF-10a + MCF-7) or complete McCoy’s 5a Medium Modified medium (MCF-10a + Sk-br-3) before being aliquoted at 200,000 cells per well in a 24-well plate. The cells were incubated for 6 h at 37 °C and 5% CO_2. The assay protocol for SMART-SpyCatcher actuation and SpyTag003 recruitment follows that outlined above for the suspension cell lines. After treatment, the adherent cells were washed twice with DPBS, 1% w/v BSA, 2 mM CaCl_2 and then lifted with a non-enzymatic solution of DPBS, 1% w/v BSA, 50 mM EDTA and incubated on ice before analysis by flow cytometry.

Cell antigen phenotyping

Suspension cell lines

Individually cultured K562 cell lines were spun down and counted to estimate the cell concentration. Then approximately 200,000 cells of an individual K562 cell culture were isolated, washed with DBPS, 1% w/v BSA, 2 mM CaCl_2 and incubated for 30 min at room temperature in the same buffer supplemented with 100 nM Alexa Fluor 594 DARPin conjugate targeting the antigen EpCAM. The cells were washed twice with DBPS, 1% w/v BSA, 2 mM CaCl_2 and incubated on ice until further analysis by flow cytometry.

Adherent cell lines

Plated cells were lifted with trypsin, washed with complete medium and counted to estimate the cell concentration. Then 200,000 cells were seeded in a 24-well plate format and allowed to recover and attach for 24 h in complete media. The cells were then washed with DBPS, 1% w/v BSA, 2 mM CaCl_2 and incubated for 30 min at room temperature in the same buffer supplemented with 100 nM Alexa Fluor 594 DARPin conjugate targeting one of the three antigens HER2, EGFR or EpCAM, or alternatively 100 nM Alexa Fluor 594 single-domain antibody conjugate targeting CEACAM6. The doxycycline-inducible cell lines OE19CXCR4DOX and OE19A2ADOX were incubated with 100 nM of the synthetic conjugates BTK140-PEG3-AF568 or SCH58261-AF488 respectively. The cells were washed twice with DBPS, 1% w/v BSA, 2 mM CaCl_2 before being lifted with a non-enzymatic solution of DPBS, 1% w/v BSA, 50 mM EDTA and incubated on ice until further analysis by flow cytometry.

NeutrAvidin Rhodamine Red-X recruitment assay

The cell sample was prepared following the assay protocol detailed for single population or mixed populations of suspension cells described above. After incubation with SMART-SpyCatcher (SpyN and SpyC each at 100 nM final concentration) for 2 h, SpyTag003 labelled with biotin (SpyTag003-Biotin, 100 nM) was added to the cells and the SpyTag003–SpyCatcher003 reaction allowed to proceed for 20 min at room temperature in the dark. The cells were then washed twice with cold DPBS, 1% w/v BSA, 2 mM CaCl_2 and then incubated with NeutrAvidin Rhodamine Red-X (1:500) for 30 min. The cells were then washed with DBPS, 1% w/v BSA, 2 mM CaCl_2 before being imaged by confocal microscopy or analysed by flow cytometry. For the experiment studying the intake of NeutrAvidin Rhodamine Red-X, the sample was imaged immediately and after an extra incubation period of 4 h at the specified temperature.

Cell-depletion assay

Mixed K562 population depletion

The sample was prepared following the assay protocol detailed for mixed populations of suspension cells described above. After incubation with SMART-SpyCatcher (SpyN and SpyC each at 100 nM final concentration) for 2 h, SpyTag003 labelled with biotin (SpyTag003-biotin, 100 nM) was added to the cells and the SpyTag003–SpyCatcher003 reaction allowed to proceed for 30 min at room temperature. The cells were washed with complete RPMI-1640 medium. Cells were then aliquoted into a 96-well plate (12,500 cells per well) and an extra 100 μl of complete RPMI-1640 media containing Streptavidin–Saporin (20 nM final concentration) was added. The cells were then cultured for 72 h for the single-dose regimen. For the two-dose regimen, the cells were cultured for 24 h before being subjected to the treatment described above a second time and then cultured for an extra 72 h. Samples were then analysed by flow cytometry.

Subpopulation percentages obtained from the flow cytometry analysis were normalized using the following formula: percentage viability = X_1/(X_0 × (WT_1/WT_0)) × 100, where X_0 is the percentage of the specific subpopulation in the negative untreated sample, X_1 is the percentage of the specific subpopulation, the relevant sample, WT_0 is the percentage of the wild-type subpopulation in the negative untreated sample, and WT_1 is the percentage of the wild-type subpopulation in the relevant sample. The derived percentage is taken to be the viability of the specified subpopulation.

Single A431 population depletion

For the A431 cell-depletion assay, the cultured cells were lifted with trypsin, counted and then seeded at 5,000 cells per well in a 96-well plate before further culturing for 24 h at 37 °C and 5% CO_2. The cells were then washed with DPBS, 1% w/v BSA, 2 mM CaCl_2 and incubated with the indicated SMART-SpyCatcher (SpyN and SpyC, each at 100 nM final concentration) for 2 h at 37 °C and 5% CO_2. SpyTag003-biotin (100 nM) was added and the sample was incubated for 30 min at room temperature. The cells were gently washed with complete DMEM medium before being suspended in 200 μl DMEM medium containing 20 nM Streptavidin–Saporin conjugate as indicated. The cells were cultured for 24 h at 37 °C and 5% CO_2 before the complete treatment described above was repeated to give a two-dose regimen. Finally, the cells were cultured for an extra 72 h. Each well was then washed twice with complete DMEM medium and 200 μl of complete DMEM medium added. An XTT cell viability assay was used to quantify the metabolic activity of each sample according to the protocol prescribed by the manufacturer. The conversion of XTT to formazan was measured on a SpectraMax iD5 Multi-Mode Microplate Reader (Molecular Devices) using well-scan mode at 465 nm at room temperature. The obtained absorbance values were normalized to the negative untreated control.

Protein proximity labelling

APEX2 proximity labelling

The cell sample, prepared following the assay protocol detailed for single populations, was treated with the SMART-SpyCatcher reactants (SpyN and SpyC each at 100 nM final concentration) for 2 h. The cells were then incubated with SpyTag003-APEX2 (300 nM) for 30 min at room temperature before being washed twice with DPBS. To initiate APEX proximity labelling, the cells were treated with 1 ml DPBS containing biotin-phenol (250 µM final concentration) followed by the addition of 10 µl of freshly prepared DPBS containing 100 mM H_2O_2, and the reaction was allowed to proceed at room temperature under gentle swirling for the indicated time. The reaction was quenched by the addition of 200 µl DPBS, 10 mM sodium ascorbate and 5 mM Trolox, and the cells washed twice with 1 ml of the same buffer. The cells were lifted (when necessary) by the addition of 1 ml DPBS, 50 mM EDTA, pelleted and suspended in 200–500 µl 50 mM Tris-HCl (pH 8.0), 150 mM NaCl, 1% v/v NP-40, 0.5% w/v sodium deoxycholate, 0.1% w/v sodium dodecyl sulfate supplemented with 1× Halt Protease Inhibitor Cocktail and 1 mM PMSF, then sonicated briefly and centrifuged for 20 min at 15,000g at 4 °C. The supernatant was isolated and analysed by SDS–PAGE/western blotting.

AND-gated μMap photocatalytic proximity labelling

For the mixed-cell experiment, the mixed K562 population 1 was prepared as described above in DPBS, 1% w/v BSA, 2 mM CaCl_2. The cells were incubated with the SMART-SpyCatcher (100 nM, eNrdJ-1cage variant) in 1 ml DPBS, 1% w/v BSA, 2 mM CaCl_2 for 2 h at 37 °C, 5% CO_2. SpyTag003-Ir was added to a final concentration of 200 nM in DPBS and the cells were incubated for 30 min at room temperature. The cells were washed twice with DPBS before incubation in DPBS supplemented with 250 µM biotin-diazirine for 5 min at room temperature. The cell sample was then irradiated using a Kessil PR160L lamp (LED 440 nm) for 5 or 10 min. The cells were washed again twice with DPBS and then treated with Streptavidin–Alexa Fluor 546 (1:2,000 v/v ratio) and incubated for 30 min. Finally, the cells were washed twice with DPBS and analysed by flow cytometry.

Cell experiments using SMART-IL-1β

On-cell splicing and release

OE19 cells were cultured to full confluency on a 12-well plate and washed twice with DBPS supplemented with 1% w/v BSA and 2 mM CaCl_2. Alternatively, one million cultured K562 cells were collected and washed twice with DBPS, 1% w/v BSA, 2 mM CaCl_2. In both cases, the cells were incubated with each SMART-IL-1β fragment (at the specified concentration) in 0.5 ml with DBPS, 1% w/v BSA and 2 mM CaCl_2 for 2 h at 37 °C and 5% CO_2. The supernatant was then withdrawn, cleared of any cell debris by centrifugation and used further.

IL-1β stimulation of HeLa cultures

HeLa cells were cultured to about 30–50% confluency in a 24-well glass-bottom plate. The supernatant from OE19 or K562 cultures, prepared as described above, was applied to the cell culture with an additional 500 µl fresh DMEM supplemented with 10% v/v FBS, 100 U ml−1 penicillin/streptomycin for 30 min at 37 °C at 5% CO_2. The cells were then washed with DBPS before being fixed by incubation in 0.5 ml 5% v/v formaldehyde for 10 min at room temperature. Excess formaldehyde was quenched by the addition of 0.5 ml 150 mM glycine followed by washes with DPBS. The cells were subsequently permeabilized by incubation with 0.5 ml DPBS and 0.5% v/v Triton X-100. The fixed and permeabilized cell sample was then washed and blocked for 1 h at room temperature by the addition of DPBS, 4% w/v BSA and 0.1% v/v Tween-20, and then washed with DPBS, 4% w/v BSA and 0.1% v/v Tween-20. The cell sample was thereafter treated first with rabbit anti-NF-κB (p65) antibody in DPBS and 1% w/v BSA for 1 h at room temperature, washed and then incubated with goat anti-rabbit dye conjugate and Hoechst (1:2,000 dilution) in DPBS and 1% w/v BSA for 30 min in the buffer. Finally, the cell sample was subjected to immunofluorescence microscopy.

HEK-Blue IL-1β cell assay

Cultured HEK-Blue IL-1β cells were gently lifted by trypsinization, counted and plated as 100,000 cells per well in a 24-well plate, after which they were allowed to recover overnight. After aspiration, 500 µl supernatant from OE19 or K562 cultures, prepared as described above, was added with an additional 500 µl of fresh medium without Normocin/Zeocin. The cell cultures were then incubated for 24 h at 37 °C and 5% CO_2. From each of the treated HEK-Blue IL-1β cell cultures, 50  µl supernatant was transferred to a 96-well plate. To each well we added 150 µL QUANTI-Blue solution, after which the plate was incubated for 30 min at 37 °C. SEAP levels were then determined using a plate reader measuring the absorbance at 630 nm.

Mixed cells K562 and HEK-Blue

One million K562 cells and 100,000 HEK-Blue IL-1β cells were collected, mixed and washed and suspended in 0.5 ml DPBS, 1% w/v BSA and 2 mM CaCl_2. The cells were then co-incubated in a 12-well plate. SMART-IL-1β was added to the cell sample, which was further incubated for 2 h at 37 °C and 5% CO_2. Then 500 µl RPMI medium supplemented with 5% FBS, 100 U ml−1 penicillin-streptomycin and 25 mM HEPES buffer was added and the cells were co-cultured for 24 h at 37 °C and 5% CO_2. The SEAP assay was then done as described above.

Mixed cells OE19 and HeLaeGFP+

OE19 and HeLaeGFP+ cells were seeded in a 24-well glass-bottom plate in a 5:1 ratio and cultured in a mixture of 50% DMEM, 50% RPMI media supplemented with 2 mM l-glutamine, 10% w/v FBS and 100 U ml−1 penicillin-streptomycin. When nearly confluent, the cells were washed with DPBS, 1% w/v BSA and 2 mM CaCl_2 and incubated with SMART-IL-1β for 2 h at 37 °C and 5% CO_2. The cells were then washed, fixed, permeabilized and analysed by fluorescence microscopy as described above.

Statistics and reproducibility

All statistical analyses were done in GraphPad Prism v.9.2.0. P-values were determined by either two-sided t-test or one-way ANOVA followed by Dunnett’s test, as listed in the figure legends. The statistical significances of differences (NS, not significant; *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001) are specified throughout the figures and legends. Heatmaps were generated using GraphPad Prism v.9.2.0. All experiments analysed by SDS–PAGE/western blotting and/or flow cytometry were repeated at least 2–3 times (independent biological replicates). All experiments analysed by microscopy were repeated at least twice (independent biological replicates). All results were reproducible.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

All the data supporting the findings of this study are available in the paper and the Supplementary Information. Coordinates and structure files have been deposited to the Protein Data Bank (PDB: 8UBS).

References

1. Bausch-Fluck, D. et al. The in silico human surfaceome. Proc. Natl Acad. Sci. USA 115, E10988–E10997 (2018).

2. Dannenfelser, R. et al. Discriminatory power of combinatorial antigen recognition in cancer T cell therapies. Cell Syst. 11, 215–228 (2020).

3. Hu, Z. et al. The Cancer Surfaceome Atlas integrates genomic, functional and drug response data to identify actionable targets. Nat. Cancer 2, 1406–1422 (2021).

4. Kichloo, A. et al. Systemic adverse effects and toxicities associated with immunotherapy: a review. World J. Clin. Oncol. 12, 150–163 (2021).

5. Tarantino, P., Ricciuti, B., Pradhan, S. M. & Tolaney, S. M. Optimizing the safety of antibody–drug conjugates for patients with solid tumours. Nat. Rev. Clin. Oncol. 20, 558–576 (2023).

6. Porta, C., Paglino, C. & Mutti, L. Ranpirnase and its potential for the treatment of unresectable malignant mesothelioma. Biologics 2, 601–609 (2008).

7. Tsuchikama, K., Anami, Y., Ha, S. Y. Y. & Yamazaki, C. M. Exploring the next generation of antibody–drug conjugates. Nat. Rev. Clin. Oncol. 21, 203–223 (2024).

8. Chen, Z. et al. De novo design of protein logic gates. Science 368, 78–84 (2020).

9. Vishweshwaraiah, Y. L., Chen, J., Chirasani, V. R., Tabdanov, E. D. & Dokholyan, N. V. Two-input protein logic gate for computation in living cells. Nat. Commun. 12, 6615 (2021).

10. MacKay, M. et al. The therapeutic landscape for cells engineered with chimeric antigen receptors. Nat. Biotechnol. 38, 233–244 (2020).

11. Savanur, M. A., Weinstein-Marom, H. & Gross, G. Implementing logic gates for safer immunotherapy of cancer. Front. Immunol. 12, 780399 (2021).

12. Lajoie, M. J. et al. Designed protein logic to target cells with precise combinations of surface antigens. Science 369, 1637–1643 (2020).

13. Quijano-Rubio, A. et al. A split, conditionally active mimetic of IL-2 reduces the toxicity of systemic cytokine therapy. Nat. Biotechnol. 41, 532–540 (2023).

14. Oostindie, S. C. et al. Logic-gated antibody pairs that selectively act on cells co-expressing two antigens. Nat. Biotechnol. 40, 1509–1519 (2022).

15. Shekhawat, S. S. & Ghosh, I. Split-protein systems: beyond binary protein-protein interactions. Curr. Opin. Chem. Biol. 15, 789–797 (2011).

16. Shah, N. H. & Muir, T. W. Inteins: nature’s gift to protein chemists. Chem. Sci. 5, 446–461 (2014).

17. Dagliyan, O. et al. Computational design of chemogenetic and optogenetic split proteins. Nat. Commun. 9, 4042 (2018).

18. Gramespacher, J. A., Stevens, A. J., Nguyen, D. P., Chin, J. W. & Muir, T. W. Intein zymogens: conditional assembly and splicing of split inteins via targeted proteolysis. J. Am. Chem. Soc. 139, 8074–8077 (2017).

19. Gramespacher, J. A., Burton, A. J., Guerra, L. F. & Muir, T. W. Proximity induced splicing utilizing caged split inteins. J. Am. Chem. Soc. 141, 13708–13712 (2019).

20. Lee, G. & Muir, T. W. Distinct phases of cellular signaling revealed by time-resolved protein synthesis. Nat. Chem. Biol. 20, 1353–1360 (2024).

21. Keeble, A. H. et al. Approaching infinite affinity through engineering of peptide-protein interaction. Proc. Natl Acad. Sci. USA 116, 26523–26533 (2019).

22. Carvajal-Vallejos, P., Pallissé, R., Mootz, H. D. & Schmidt, S. R. Unprecedented rates and efficiencies revealed for new natural split inteins from metagenomic sources. J. Biol. Chem. 287, 28686–28696 (2012).

23. Stefan, N. et al. DARPins recognizing the tumor-associated antigen EpCAM selected by phage and ribosome display and engineered for multivalency. J. Mol. Biol. 413, 826–843 (2011).

24. Steiner, D., Forrer, P. & Plückthun, A. Efficient selection of DARPins with sub-nanomolar affinities using SRP phage display. J. Mol. Biol. 382, 1211–1227 (2008).

25. Zahnd, C. et al. A designed ankyrin repeat protein evolved to picomolar affinity to Her2. J. Mol. Biol. 369, 1015–1028 (2007).

26. Polito, L., Bortolotti, M., Mercatelli, D., Battelli, M. G. & Bolognesi, A. Saporin-S6: a useful tool in cancer therapy. Toxins 5, 1698–1722 (2013).

27. Bolshakov, A. P., Stepanichev, M. Y., Dobryakova, Y. V., Spivak, Y. S. & Markevich, V. A. Saporin from Saponaria officinalis as a tool for experimental research, modeling, and therapy in neuroscience. Toxins 12, 546 (2020).

28. Dittel, B. N. Depletion of specific cell populations by complement depletion. J. Vis. Exp. https://doi.org/10.3791/1487 (2010).

29. Lee, D. S. W., Rojas, O. L. & Gommerman, J. L. B cell depletion therapies in autoimmune disease: advances and mechanistic insights. Nat. Rev. Drug Discov. 20, 179–199 (2021).

30. Baral, T. N., Murad, Y., Nguyen, T.-D., Iqbal, U. & Zhang, J. Isolation of functional single domain antibody by whole cell immunization: implications for cancer treatment. J. Immunol. Methods 371, 70–80 (2011).

31. Tamamura, H. et al. Enhancement of the T140-based pharmacophores leads to the development of more potent and bio-stable CXCR4 antagonists. Org. Biomol. Chem. 1, 3663–3669 (2003).

32. Zocchi, C. et al. The non-xanthine heterocyclic compound SCH 58261 is a new potent and selective A2a adenosine receptor antagonist. J. Pharmacol. Exp. Ther. 276, 398–404 (1996).

33. Lam, S. S. et al. Directed evolution of APEX2 for electron microscopy and proximity labeling. Nat. Methods 12, 51–54 (2015).

34. Geri, J. B. et al. Microenvironment mapping via Dexter energy transfer on immune cells. Science 367, 1091–1097 (2020).

35. Garlanda, C., Dinarello, C. A. & Mantovani, A. The interleukin-1 family: back to the future. Immunity 39, 1003–1018 (2013).

36. Ho, T. Y. H. et al. A systematic approach to inserting split inteins for Boolean logic gate engineering and basal activity reduction. Nat. Commun. 12, 2200 (2021).

37. Pinto, F., Thornton, E. L. & Wang, B. An expanded library of orthogonal split inteins enables modular multi-peptide assemblies. Nat. Commun. 11, 1529 (2020).

38. Palei, S., Becher, K. S., Nienberg, C., Jose, J. & Mootz, H. D. Bacterial cell-surface display of semisynthetic cyclic peptides. ChemBioChem. 20, 72–77 (2019).

39. Schindelin, J. et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012).

40. Kabsch, W. XDS. Acta Crystallogr. D 66, 125–132 (2010).

41. Winn, M. D. et al. Overview of the CCP4 suite and current developments. Acta Crystallogr. D 67, 235–242 (2011).

42. Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–589 (2021).

43. Varadi, M. et al. AlphaFold Protein Structure Database: massively expanding the structural coverage of protein-sequence space with high-accuracy models. Nucleic Acids Res. 50, D439–D444 (2022).

44. Emsley, P., Lohkamp, B., Scott, W. G. & Cowtan, K. Features and development of Coot. Acta Crystallogr. D 66, 486–501 (2010).

45. Liebschner, D. et al. Macromolecular structure determination using X-rays, neutrons and electrons: recent developments in Phenix. Acta Crystallogr. D 75, 861–877 (2019).

46. Kirsten, D. & Kritzer, J. A. HaloTag forms an intramolecular disulfide. Bioconjug. Chem. 32, 964–970 (2021).

Acknowledgements

This work was funded by NIH-GMS grant R01 GM086868 and by funds from the Ludwig Institute for Cancer Research. C.K. was supported by EMBO (ALTF 1189-2020). N.E.S.T. is supported by an NIH postdoctoral fellowship (GM149123). X.Y. was supported by a graduate fellowship from the China Scholarship Council (CSC). We thank members of the Muir laboratory for discussions and support; P. Jeffrey for technical assistance with setting up crystal trays, looping, data collection and data processing; C. DeCoste and K. Rittenbach for technical assistance with flow cytometry and cell sorting, and instrument use (Princeton University Flow Cytometry Resource Facility, Department of Microbiology, supported, in part, with funding from NCI-CCSG P30CA072720-5921 and 1S10OD028592-01A1); S. Wang and G. Laevsky for technical assistance with confocal microscopy and instrument use; D. Baker for sharing K562 cell lines; Y. Kang for sharing MCF-10a, MCF-7, LoVo and A594 cell lines; S. Lipkowitz for sharing the Sk-br-3 cell line; and C. Kadoch for sharing the PiggyBac transposon system.

Author information

Author notes

1. These authors contributed equally: Girum Erkalo, Nicholas E. S. Tay

Authors and Affiliations

1. Department of Chemistry, Princeton University, Princeton, NJ, USA

Christian Kofoed, Girum Erkalo, Nicholas E. S. Tay, Xuanjia Ye, Yutong Lin & Tom W. Muir

Contributions

C.K. and T.W.M. conceived the work. C.K., N.E.S.T., G.E., X.Y., Y.L. and T.W.M. designed and executed the experiments. C.K. and T.W.M. wrote the manuscript.

Corresponding author

Correspondence to Tom W. Muir.

Ethics declarations

Competing interests

T.W.M. is a scientific founder, scientific advisory board member and shareholder of SpliceBio and is a consultant for Merck. T.W.M., C.K., N.E.S.T., X.Y. and G.E. have filed a provisional US patent based on this work. Y.L. declares no competing interests.

Peer review

Peer review information

Nature thanks Baojun Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Systematic screening to identify SpyCatcher003 split site and optimization of SMART-SpyCatcher.

a, SpyCatcher003 was split at various sites and the cognate pairs used to generate FLAG-SpyN1-x-NpuNcage-FKBP and FRB-NpuCcage-SpyCy-113-Myc, with x and y denoting the last and first residue of the two fragments (i.e., the split site). The isopeptide bond (formed between D117 of SpyTag003 and K31 of SpyCatcher003) is shown in sticks in the structure of SpyTag-SpyCatcher (PDB: 4MLI). The primary structure of SpyCatcher003 is shown with split sites indicated. b, Schematic of the cell-free in vitro screen used to identify the optimal split site. Conditional protein splicing (CPS) was induced either by proteolytic decaging using TEV protease or through chemically induced FKBP/rapamycin/FRB hybridization, which simulates ideal colocalization on a target cell surface. c, The result of screening FLAG-SpyN1-73-NpuNcage-FKBP and FRB-NpuCcage-SpyC74-113-Myc generated from splitting SpyCatcher003 at position 73-74. Reactions were performed with FLAG-SpyN1-73-NpuNcage-FKBP (1 μM), FRB-NpuCcage-SpyC74-113-Myc, (1 μM) and His_6-SpyTag003 (2 μM). CPS was induced by the addition of either TEV protease (10 units) or rapamycin (10 μM). The reactions were analyzed by Western blot after 24 hr incubation at 37 °C. FLAG-SpyCatcher003-Myc was used as a size standard for the spliced product; FLAG-SpyCatcher003-Myc (1 μM) reacted with His_6-SpyTag003 (2 μM) was used as a size standard for the covalent complex between the two. The legend and experimental conditions apply for subsequent panels with alterations when noted. d, Npucage was swapped with NrdJ-1cage in SMART-SpyCatcher thereby giving FLAG-SpyN1-73-NrdJ-1Ncage-FKBP and FRB-NrdJ-1Ccage-SpyC74-113-Myc. A SpyTag003 Alexa Fluor 594 conjugate (SpyTag003-AF594) was used as the activity probe. The reactions were analyzed by Western blot. e, SpyN1-73-NrdJ-1Ncage-FKBP with the wildtype (WT) or a catalytically dead C1A mutant of NrdJ-1Ncage was mixed with FRB-NrdJ-1Ccage-SpyC74-113-Myc and SpyTag003-AF594. The reactions were analyzed by Western blot. f, The crystal structure of fusion NrdJ-1 (PDB: 8UBS), with sequences corresponding to NrdJ-1N and NrdJ-1C colored in cyan and orange respectively. A schematic representation of the fusion protein and the caged split intein is shown as well to indicate relevant domains in addition to their N- and C-termini and the position of the non-catalytic Cys76. g-h, A structural analysis was performed to predict the impact of introducing a C76V mutation in fusion NrdJ-1. g, The backbone of wildtype NrdJ-1 (crystal structure) and that of the NrdJ-1C76V mutant (in silico AlphaFold2 model) are superimposable with a root mean square deviation (RMSD) of 0.56 Å. h, Residue sidechains of Cys76 and Leu2 are shown as sticks and cavities in solid grey. The experimentally determined local environment of Cys76 is shown on the left, whereas the in silico predicted local environment of C76V is shown on the right and changes between the two are indicated with arrows. i, Combinations of FLAG-SpyN1-73-NrdJ-1Ncage-FKBP or FLAG-SpyN1-73-NrdJ-1NC76Vcage-FKBP with FRB-NrdJ-1Ccage-SpyC74-113-Myc or FRB-NrdJ-1Ccage(C76V)-SpyC74-113-Myc were tested as indicated using the reaction conditions described above. The reactions were analyzed by Western blot. j, Electrospray ionization time-of-flight mass spectrometry (ESI-TOF MS) characterization of the SpyCatcher003 spliced product produced by rapamycin triggered CPS between FLAG-SpyN1-73-NrdJ-1NC76Vcage-FKBP and FRB-NrdJ-1Ccage(C76V)-SpyC74-113-Myc. Reaction conditions followed those described above. Data shown in panels c-e, and i are representative of two independent experiments.

Extended Data Fig. 2 Confocal microscopy of K562 cell lines treated with SMART-SpyCatcher for [HER2 AND EGFR] logic.

a, K562HER2+/EGFR+ cells were treated with αHER2-SpyN (100 nM) and SpyC-αEGFR (100 nM) for 2 hr, followed by SpyTag003 labeled with Alexa Fluor 594 (SpyTag003-AF594, 100 nM) for 20 min. SMART-SpyCatcher employed either NrdJ-1N(C76V)cage/NrdJ-1Ccage(C76V) or NrdJ-1N(C76V)cage(K109EK119A)/NrdJ-1Ccage(C76VD66K) (referred to as eNrdJ-1cage). Following washing, the live cells were analyzed by confocal microscopy. Cell nuclei were stained with Hoechst, while HER2 and EGFR were tagged with eGFP and iRFP, respectively. Scale bar equals 20 μm. All subsequent panels apply similar reaction and analysis conditions as in panel a using the SMART-SpyCatcher (eNrdJ-1cage) [HER2 AND EGFR] system. b, K562HER2+, K562EGFR+, and K562HER2+/EGFR+ cells were treated and analyzed individually. Scale bars equal 10 µm. c, To determine the colocalization of HER2, EGFR and SpyTag003-AF594 the signal intensities of eGFP, iRFP, and AF594 derived from the cells in panel b were plotted (yellow dotted lines). d, A mixed population consisting of equal amounts of K562 (wildtype), K562HER2+, K562EGFR+, and K562HER2+/EGFR+ cells were treated and imaged. Representative single cells of each cell line from the treated mixture and their associated fluorescence signals are shown on the right. Scale bar equals 20 μm. Data are representative of two independent experiments.

Extended Data Fig. 3 The mechanism of action of SMART-SpyCatcher.

a, K562HER2+/EGFR+ cells were treated with αHER2-SpyN (100 nM) and SpyC-αEGFR (100 nM) for 2 hr, followed by SpyTag003 labeled with Alexa Fluor 594 (SpyTag003-AF594, 100 nM) for 20 min. SMART-SpyCatcher employed eNrdJ-1cage. Following washing, the live cells were analyzed by confocal microscopy. Cell nuclei were stained with Hoechst, while HER2 and EGFR were tagged with eGFP and iRFP, respectively. The cells in row 1 were treated as described above, whereas reaction conditions in the subsequent experiments were supplemented with DARPins targeting HER2 and EGFR (500 nM each, row 2), used an inactivated version of NrdJ-1Ncage (Cys1-alkylated, row 3), or were supplemented with unlabeled SpyTag003 (500 nM, row 4). Scale bar equals 20 μm. All subsequent panels apply similar reaction and analysis conditions as in panel a (row 1) using the SMART-SpyCatcher (eNrdJ-1cage) system with any alterations as noted. b, Western blot analysis of K562HER2+/EGFR+ cells treated with αHER2-SpyN and SpyC-αEGFR (identified by FLAG and Myc respectively), and SpyTag003 labeled with biotin (SpyTag003-biotin; identified by Strep-800). The inactivated version of NrdJ-1Ncage (Cys1-alkylated) was used as a negative control. c, Experiments were performed on K562HER2+/EGFR+ cells with the SMART-SpyCatcher (eNrdJ-1cage) [HER2 AND EGFR] system, and either SpyTag003-AF594 or inactive SpyTag003D117A labeled with Alexa Fluor 594 (SpyTag003D117A-AF594). Scale bar equals 20 μm. d, K562HER2+/EGFR+ cells were treated with SMART-SpyCatcher (100 nM, eNrdJ-1cage) in buffer (DPBS, 1% w/v BSA, 2 mM CaCl_2), RPMI 1640 medium (cystine-free), or in medium supplemented with 5% v/v fetal bovine serum (5% v/v FBS) for 2 hr, followed by SpyTag003-AF594 for 20 min. Further image analysis was performed as described above. Scale bar equals 20 μm. e, Flow cytometry analysis of a mixed population consisting of equal amounts of K562 (wildtype), K562HER2+, K562EGFR+, and K562HER2+/EGFR+ cells following treatment with SMART-SpyCatcher (eNrdJ-1cage) operating through the AND logic indicated. The added SpyN and SpyC pairs (i.e., the targeting DARPins employed in the constructs) are indicated at the bottom. Data are presented as the mean of the AF594 median fluorescence intensities (MFI) from flow cytometry analysis with error bars signifying the standard error mean (n = 3 independent biological replicates; see Supplementary Table 13 for statistical one-way ANOVA followed by Dunnett’s test). f, The mixed K562 population described above were treated with αHER2-SpyN (100 nM) and SpyC-αEGFR (100 nM) employing eNrdJ-1cage or the uncaged split intein NrdJ-1, for 2 hr, followed by SpyTag003-AF594 (100 nM) for 20 min. Further image analysis was performed as described above. Scale bars are equal to 20 μm. Data shown in panels a-d, and f are representative of two independent experiments.

Extended Data Fig. 4 Extended SMART logic and three-input systems.

a, SMART-SpyCatcher (i.e., SpyN and SpyC) was assigned to operate through AND logic involving combinations of EpCAM with HER2 and EGFR. Two combinations of K562 cell lines were used to test for the actuation of SMART-SpyCatcher and thereby recruitment of SpyTag003-AF594. Anticipated target cells are highlighted in red. Mixed-population 1 consisted of equal amounts of K562 (wildtype), K562EGFR+, K562HER2+, and K562HER2+/EGFR+, whereas mixed-population 2 consisted of equal amounts of K562 (wildtype), K562EGFR+, K562HER2+/EpCAMhigh, and K562HER2+/EGFR+/EpCAMhigh. The antigen profile of each cell line is indicated below each bar plot (L and H designates low endogenous and high ectopic levels respectively for EpCAM), whereas the antigens targeted by the added SpyN and SpyC pairs (i.e. the targeting DARPins employed in the constructs) are indicated at the bottom. Experiments were performed with SMART-SpyCatcher (100 nM, eNrdJ-1cage), 100 nM SpyTag003-AF594. Data are presented as the mean of the AF594 median fluorescence intensities (MFI) from flow cytometry analysis with error bars signifying the standard error mean (n = 3 independent biological replicates; see Supplementary Table 13 for statistical one-way ANOVA followed by Dunnett’s test). b, Target cells were profiled for their relative surface levels of HER2, EGFR, and EpCAM. Cells were treated with DARPins labeled with AF594 followed by flow cytometry analysis. In parallel, combinations of SpyN and SpyC linked to targeting DARPins were used to solve the AND logic matrix for a given cell line. c, Top: Single cells lines were profiled for their relative surface levels of HER2, EGFR, and EpCAM using the three DARPin Alexa Fluor 594 conjugates αHER2-AF594, αEGFR-AF594, and αEpCAM-AF594. Cells were treated with the indicated DARPin-AF594 conjugate and analyzed by flow cytometry analysis. Bottom: Single cell lines were also treated with variations of SMART-SpyCatcher003 (100 nM, eNrdJ-1cage) operating through different combinations of AND logic targeting HER2, EGFR, and EpCAM. The heatmaps represents the mean MFI of the AF549 signal from three independent replicates (see Supplementary Tables 3 and 4 for individual values). The cell lines are categorized as displaying low (MFI < 1000) or high (MFI ≥ 1000) levels of the three antigens. d, The quantity of the lesser-expressed antigen used in each AND gate and the resulting recruitment of SpyTag003-AF594 is plotted for the data from panel c. Errors = standard error mean (n = 3 independent biological replicates). e, Schematic illustrating SMART-SpyCatcher operating through [(HER2 OR EGFR) AND (HER2 OR EGFR)] logic on a mixed K562 population; sets of SpyN and SpyC are used to achieve [HER2 AND HER2], [EGFR AND EGFR], [HER2 AND EGFR], and [EGFR AND HER2] gating, essentially resulting in OR logic. f, The SMART-SpyCatcher [HER2 OR EGFR] logic operation was tested on mixed K562 cell population 1. Cells were treated with SMART-SpyCatcher (i.e. αHER2-SpyN/αEGFR-SpyN/SpyC-αHER2/SpyC-αEGFR, each at 100 nM, employing eNrdJ-1cage), and SpyTag003-AF594 (100 nM) and analyzed by flow cytometry. Error bars signify the standard error mean (n = 3 independent biological replicates; see Supplementary Table 14 for statistical one-way ANOVA followed by Dunnett’s test). g, Schematic illustrating a 3-input logic operation, where SMART-SpyCatcher acts through the use of αAg_1-SpyN/SpyC-αAg_2/SpyC-αAg_2 to achieve [Ag_1 AND either Ag_2 OR Ag_3] cell targeting strategy. h, SMART-SpyCatcher (i.e. αAg_1-SpyN/SpyC-αAg_2/SpyC-αAg_2) was used in mixed K562 cell experiments to evaluate its AND/OR logic function involving combinations of HER2, EGFR and EpCAM. The two mixed populations of K562 cell lines described above were used to test for the actuation of SMART-SpyCatcher and thereby recruitment of SpyTag003-AF594. Experiments were performed with SMART-SpyCatcher (100 nM, employing eNrdJ-1cage), and SpyTag003-AF594 (100 nM). Data are presented as AF594 MFI from flow cytometry analysis with error bars signifying the standard error mean (n = 3 independent biological replicates; see Supplementary Table 15 for statistical one-way ANOVA followed by Dunnett’s test).

Extended Data Fig. 5 Tuning SMART for an adjustable stimulus-response.

Several eNrdJ-1Ncage variants were made either by mutating ionizable sidechain residues (a-c) or adjusting the cage length (d-f); these were tested in standard mixed K562 cell experiments followed by flow cytometry analysis. Data are presented as the mean of the AF594 median fluorescence intensities (MFI) from flow cytometry analysis with error bars signifying the standard error mean (n = 3 independent biological replicates). Panels b and e: A mixed population consisting of equal amounts of K562 (wildtype), K562HER2+, K562EGFR+, and K562HER2+/EGFR+ cells was treated with αHER2-SpyN (using the indicated eNrdJ-1Ncage variant at 100 nM), SpyC-αEGFR (using the standard eNrdJ-1Ccage variant at 100 nM), and SpyTag003-AF594 (100 nM). The experimental median fluorescence intensity (MFI) values were normalized to those obtained employing eNrdJ-1Ncage for comparison (n = 3 independent biological replicates). The normalized AF594 MFI associated with the individual four cell lines across the different experiments are summarized in the form of two heatmaps (see Supplementary Table 13 for statistical one-way ANOVA followed by Dunnett’s test and Supplementary Tables 5 and 6 for individual values). Panels c and f: The most active variants from the two ways of cage tuning were tested in dose-response experiments.

Extended Data Fig. 6 Employing tuned SMART-SpyCatchers.

a, SpyCatcher003 utilizes its residue K31 to form an isopeptide bond with D117 of SpyTag003 upon binding. A mutant of SpyN carrying K31E was evaluated for its abilty to recruit SpyTag003-AF594 upon SMART actuation of SpyCatcher003. The data represent the flow cytometry analysis of K562HER2+/EGFR+ cells left untreated or treated with either SMART-SpyCatcher or SMART-SpyCatcherK31E (both at 100 nM, employing eNrdJ-1cage and operating through [HER2 AND EGFR] gating). RFU denotes relative fluorescence units. The relative mean AF594 MFI is given in the bar graph on the right with error bars signifying the standard error mean (n = 3 independent biological replicates) and statistical significance evaluated using an unpaired two-sided t-test (ns = not significant; ****P < 0.0001). b, The total cellular levels of HER2 and EpCAM for MCF-10a, MCF-7, and Sk-br-3 cell lines were determined by Western blotting (left) and quantified (right). Intensity values were corrected against the GAPDH signal for each cell line and further normalized to the overall highest level (Sk-br-3 for HER2, MCF-7 for EpCAM). c, The endogenous surface levels of HER2 and EpCAM on mammary cell lines MCF-10a, MCF-7, and Sk-br-3 were furthermore profiled and categorized as low (MFI < 1000) or high (MFI ≥ 1000). Errors = standard error mean (n = 3 independent biological replicates). d, MCF-10a cells either unstained or stained with the cell-permeable dye 5-Chloromethylfluorescein diacetate (CMFDA) were also phenotyped to determine any differences in the levels of surface HER2 and EpCAM. Errors = standard error mean (n = 3 independent biological replicates). Statistical significance was evaluated using an unpaired two-sided t-test (ns = not significant). e, SMART-SpyCatcher assigned for [HER2 AND EpCAM] logic was tested in flow cytometry experiments using mixed mammary cell population 1 (equal amounts of MCF-10aHER2low/EpCAMlow and MCF-7HER2low/EpCAMhigh) and mixed mammary population 2 (equal amounts of MCF-10aHER2low/EpCAMlow and Sk-br-3HER2high/EpCAMhigh). MCF-10a cells were pre-stained with CMFDA, which labels intracellular proteins. Each population was incubated with 100 nM SpyTag003-AF594 in the absence or presence of 100 nM αHER2-SpyN and SpyC-αEpCAM (employing eNrdJ-1cage with K114AK116A). Shown are representative flow cytometry plots of the recruitment of SpyTag-AF594 by the subpopulations under the different conditions. f, SMART-SpyCatcher003 using different versions of eNrdJ-1cage were tested on the cell lines (color coded as in panel e) and the quantified data presents the mean of the individual median fluorescence intensities (MFI) of the AF594 signal with error bars signifying the standard error mean (n = 3 independent biological replicates). Statistical analysis using paired two-sided t-test.

Extended Data Fig. 7 Targeted cell depletion using Boolean logic.

a, K562HER2+/EGFR+ cells were treated with SMART-SpyCatcher (100 nM, employing eNrdJ-1cage) for [HER2 AND EGFR] logic and SpyTag003 labeled with biotin (SpyTag003-biotin, 100 nM). Following washing, the cells were treated with a NeutrAvidin Rhodamine Red-X conjugate (NA-RRx, magenta) and then either visualized by confocal microscopy immediately or after further incubation for 4 hr at 37 °C or 4 °C. Cell nuclei were stained with Hoechst, while lysosomal compartments were stained with LysoTracker. Scale bar equals 20 μm. b, Schematic illustrating the proposed recruitment and internalization of NA-RRx enabled by the SMART-SpyCatcher system. c, A mixed population consisting of equal amounts of K562 (wildtype), K562EGFR+, K562HER2+, and K562HER2+/EGFR cells was used to test for the selective recruitment of SpyTag003-biotin and subsequent recruitment of NA-RRx. The cell mixture was treated as in panel b. The NA-RRx signal associated with the individual subpopulations was quantified by flow cytometry with the data presented as the mean of the NA-RRx median fluorescence intensities (MFI) with error bars signifying the standard error mean (P(WT vs HER2+) = 0.9950; P(WT vs EGFR+) = 0.9950; P(WT vs HER2+/EGFR+) < 0.0001; see Supplementary Table 13 for further statistical one-way ANOVA followed by Dunnett’s test). d, Schematic illustrating the selective cell depletion of a HER2/EGFR positive K562 cell line in a complex cell mixture using SMART-SpyCatcher, SpyTag003-biotin and a Streptavidin-Saporin disulfide conjugate. e, Summary of how the one-dose and two-dose regimens were performed. f, The mixed K562 cell population employed in panel c was treated with SMART-SpyCatcher (100 nM, employing eNrdJ-1cage and [HER2 AND EGFR] logic), SpyTag003-biotin (100 nM), and Streptavidin-Saporin (20 nM). Cells were then analyzed by flow cytometry and the data presented as percentage viability relative to untreated wildtype cells (ns = not significant; ****P < 0.0001). All flow cytometry data are presented as the mean with error bars signifying standard error mean (n = 3 independent biological replicates). Statistical significance in panel f was evaluated using an unpaired two-sided t-test. Data shown in panel a is representative of two independent experiments.

Extended Data Fig. 8 AND-gated proximity labeling.

a, Western blot analysis of K562HER2+/EGFR+ treated with αHER2-SpyN (100 nM, eNrdJ-1cage) and SpyC-αEGFR (100 nM) for 2 hr at 37 °C, followed by HA-tagged SpyTag003-APEX2 (300 μM) for 20 min. b, K562 (wildtype), K562HER2+, K562EGFR+, and K562HER2+/EGFR+ cells were treated individually as described in panel a. Following washing, APEX2 proximity labeling was induced by the addition of biotin-phenol (250 μM) and H_2O_2 (1 mM). The reactions were quenched with sodium ascorbate (10 mM) and Trolox (5 mM) at room temperature after two minutes. Samples were then analyzed by Western blot using Strep-800 to detect biotinylation. c-e, Time-course study of APEX2 labeling. The cells were treated as in panel b with labeling quenched at the indicated time points. αHER2-SpyN/SpyC-αEGFR was used with the K562HER2+/EGFR+ cells; αHER2-SpyN/SpyC-αEpCAM was used with the OE19 cells; αEGFR-SpyN/SpyC-αEpCAM was used with the A431 cells. SMART-SpyCatcher employed eNrdJ-1cage in all cases. f, Displayed are the employed AND gates used in the following experiments (note, lettering differs from that in Fig. 3). Each AND gate constitute a pair of SpyN and SpyC protein fusions and/or synthetic ligand conjugates; for instance, AND gate D is generated by αCEACAM6-SpyN and SpyC-αHER2. g-j, AND-gated proximity labeling using the described AND gates, SpyTag003-APEX2 and the workflow described under panels a-e. In each case, the lane expected to give proximity labeling is indicated in red. When applicable, cells were treated for 12 hr beforehand with doxycycline (DOX, 200 ng/mL) to induce the expression of FLAG-CXCR4-eGFP (OE19CXCR4DOX) or FLAG-ADORA2A-mCherry (OE19A2ADOX). SpyC-Cys indicates the unconjugated variant. Asterisks indicate endogenously biotinylated proteins. Data shown in panels a-e, and g-j are representative of two and three independent experiments, respectively.

Extended Data Fig. 9 Optimization of AND-gated μMap photocatalytic proximity labeling.

a, Illustration of the principle of AND-gated photocatalytic proximity labeling achieved using SMART-SpyCatcher targeting two cell surface antigens and the subsequent delivery of SpyTag003 conjugated to an iridium photocatalyst. Iridium enables the blue light activation of a biotin diazirine probe, which reacts with nearby proteins. b, Schematic of the preparation of SpyTag003-Ir from the precursors SpyTag003-HaloTag13 and the iridium photocatalyst Ir-PEG4-C_6H_12Cl. HaloTag13 is based on HaloTag9 with the additional mutations C61S and C262S to improve recombinant expression and solubility[46]. c, d, The protein preparation of SpyTag003-HaloTag13 and its conjugate with Ir-PEG4-C_6H_12Cl (i.e. SpyTag003-Ir) were analyzed by SDS-PAGE (left), RP-HPLC (0-70% B gradient over 30 min, middle), and ESI-TOF MS (right). e, The K562HER2+/EGFR+ cell line was treated with SMART-SpyCatcher (100 nM, eNrdJ-1cage) operating by [HER2 AND EGFR] logic and subsequently supplemented with SpyTag003-Ir (200 nM). Following a wash, the culture was incubated with biotin-diazirine (250 µM) and irradiated with blue light (LED 440 nm) for 5 min or 10 min. The cells were thereafter analyzed by flow cytometry using Streptavidin conjugated to Alexa Fluor 546 (AF546) to detect biotinylation. f, Quantification of the flow cytometry data from panel e for the samples irradiated for 5 min (****P < 0.0001). Data are presented as the mean of the AF546 median fluorescence intensities (MFI) with error bars signifying the standard error mean (n = 3 independent biological replicates). See Supplementary Table 16 for individual values. Statistical significance was evaluated using an unpaired two-sided t-test.

Extended Data Fig. 10 Systematic screen to make SMART-IL-1β.

a, The X-ray crystal structure (PDB: 4DEP) of interleukin 1β (IL-1β) bound to interleukin 1 receptor, type 1 (IL-1R1). b, IL-1β was split at various sites and the cognate pairs used to generate FLAG-IL-1βN1-x-eNrdJ-1Ncage-FKBP and FRB-eNrdJ-1Ccage-IL-1βCy-153–Myc, with x and y respectively denoting the last and first residue of the two fragments (i.e., the split site). Shown is the X-ray crystal structure (PDB: 9ILB) and primary structure of IL-1β with tested split sites indicated. c, Schematic of the in vitro screen used to identify the optimal split site that would render a conditional version of IL-1β: (i) The screen relied on chemically induced FKBP-rapamycin-FRB heterodimerization to trigger conditional protein splicing (CPS) with analysis by Western blotting to identify spliced IL-1β; (ii) spliced IL-1β variants were subsequently tested on cells to determine biological activity using immunofluorescence imaging to determine NF-κB localization. d, Western blot of reactions performed with FLAG-IL-1βN1-x-eNrdJ-1Ncage-FKBP (0.5 μM), FRB-eNrdJ-1Ccage-IL-1βCy-153–Myc (0.5 μM) and rapamycin (10 μM) for 2 hr at 37 °C. The expected mass of spliced IL-1β is 20.5 kDa. e-f, Additional experiments for the two pairs FLAG-IL-1βN1-44-eNrdJ-1Ncage-FKBP/FRB-eNrdJ-1Ccage-IL-1βC45-153-Myc and FLAG-IL-1βN1-69-eNrdJ-1Ncage-FKBP/FRB-eNrdJ-1Ccage-IL-1βC70-153-Myc to validate splicing of IL-1β being rapamycin- and CPS-dependent (the latter experiment used the splicing-deficient eNrdJ-1N(C1A)cage mutant). g, Cultured HeLa cells were incubated with recombinantly expressed IL-1β for 20 min at 37 °C to induce IL-1R1 signaling and NF-κB nuclear localization. Cells were then fixed (5% formaldehyde), permeabilized (0.5% Triton X100), and analyzed by confocal imaging using a primary rabbit anti-NF-κB (p65) antibody and a secondary goat anti-rabbit antibody Alexa Fluor 488 conjugate. Scale bar equals 100 μm. Subsequent experiments followed a similar analytical procedure. h, Cultured HeLa cells were treated with reaction mixtures of the pair FLAG-IL-1βN1-44-eNrdJ-1Ncage-FKBP/FRB-eNrdJ-1Ccage-IL-1βC45-153-Myc and analyzed as described above to determine IL-1R1 signaling activation. Scale bar equals 50 μm. i, HeLa cells were left untreated or incubated with recombinant IL-1β (0.5 nM). In experiments with SMART-IL-1β (i.e. IL-1βN/IL-1βC), HeLa cells were treated with a medium produced by incubating OE19 cells (HER2high, EGFRlow, EpCAMhigh) with IL-1βN-αHER2 (20 nM) and αEpCAM-IL-1βC (20 nM) for 2 hr at 37 °C. In all cases, HeLa cells were incubated for 30 min at 37 °C, before being collected and analyzed by Western blotting to determine the phosphorylation of NF-κB (pNF-κB) and IκB (pIκB). j, The localization of NF-κB was examined for OE19 cells untreated or incubated with recombinant IL-1β. Scale bar equals 40 μm. Data shown are representative of two independent experiments.

Supplementary information

Supplementary Information

Reporting Summary

Supplementary Fig. 1

Uncropped western blots.

Supplementary Table 2

Data collection and refinement statistics (molecular replacement).

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Kofoed, C., Erkalo, G., Tay, N.E.S. et al. Programmable protein ligation on cell surfaces. Nature 645, 793–800 (2025). https://doi.org/10.1038/s41586-025-09287-2

- Received: 24 September 2023

- Accepted: 13 June 2025

- Published: 30 July 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09287-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

- Improving CAR-T cell function through a targeted cytokine delivery system utilizing car target-modified extracellular vesicles

- Yuanyuan Zhang

- Meijuan Huang

- Jue Wang

Experimental Hematology & Oncology (2025)

- SMART tool builds proteins on cell surfaces

- Gemma Conroy

Nature (2025)

Targeting protein–ligand neosurfaces with a generalizable deep learning tool

Article Open access 15 January 2025

Spatiotemporal functional assembly of split protein pairs through a light-activated SpyLigation

Article 17 April 2023

Induced proximity at the cell surface

Article 26 March 2025

‘Smart’ tool pieces together proteins in response to combinations of cell-surface cues

Nature Research Briefing 30 Jul 2025

Amendments & Corrections

- Author Correction: Macrophages excite muscle spindles with glutamate to bolster locomotion

- Author Correction: Disease-associated astrocyte epigenetic memory promotes CNS pathology

- Author Correction: Complex genetic variation in nearly complete human genomes

- Author Correction: Endophilin marks and controls a clathrin-independent endocytic pathway

- Author Correction: Dual neuromodulatory dynamics underlie birdsong learning

- Publisher Correction: Multiple oestradiol functions inhibit ferroptosis and acute kidney injury

Author Correction Open access Published: 21 August 2025

Author Correction: Macrophages excite muscle spindles with glutamate to bolster locomotion

Yuyang Yan,

Nuria Antolin,

Luming Zhou,

Luyang Xu,

Irene Lisa Vargas,

Carlos Daniel Gomez,

Guiping Kong,

Ilaria Palmisano,

Yi Yang,

Jessica Chadwick,

Franziska Müller,

Anthony M. J. Bull,

Cristina Lo Celso,

Guido Primiano,

Serenella Servidei,

Jean François Perrier,

Carmelo Bellardita &

…

Simone Di Giovanni

Nature volume 645, page E4 (2025)

The Original Article was published on 04 December 2024

Correction to: Nature https://doi.org/10.1038/s41586-024-08272-5 Published online 4 December 2024

In the version of the article initially published, in Fig. 2j, the 0.5 mm light stimulation trace was inadvertently a duplicate of the 0.5 mm control trace. The figure has now been corrected in the HTML and PDF versions of the article.

Author information

Author notes

1. These authors contributed equally: Carmelo Bellardita, Simone Di Giovanni

Authors and Affiliations

1. Faculty of Medicine, Department of Brain Sciences, Imperial College London, London, UK

Yuyang Yan, Luming Zhou, Guiping Kong, Ilaria Palmisano, Yi Yang, Jessica Chadwick, Franziska Müller & Simone Di Giovanni

2. Faculty of Natural Sciences, Department of Life Sciences, Imperial College London, London, UK

Yuyang Yan & Cristina Lo Celso

3. Department of Neuroscience, University of Copenhagen, Copenhagen, Denmark

Nuria Antolin, Irene Lisa Vargas, Carlos Daniel Gomez, Jean François Perrier & Carmelo Bellardita

4. Faculty of Engineering, Department of Bioengineering, Imperial College London, London, UK

Luyang Xu & Anthony M. J. Bull

5. Dipartimento di Neuroscienze, Organi di Senso e Torace, Fondazione Policlinico Universitario Agostino Gemelli IRCCS, Rome, Italy

Guido Primiano & Serenella Servidei

6. Dipartimento di Neuroscienze, Università Cattolica del Sacro Cuore, Rome, Italy

Guido Primiano & Serenella Servidei

Corresponding authors

Correspondence to Carmelo Bellardita or Simone Di Giovanni.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Yan, Y., Antolin, N., Zhou, L. et al. Author Correction: Macrophages excite muscle spindles with glutamate to bolster locomotion. Nature 645, E4 (2025). https://doi.org/10.1038/s41586-025-09550-6

- Published: 21 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09550-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Author Correction Published: 26 August 2025

Author Correction: Disease-associated astrocyte epigenetic memory promotes CNS pathology

Hong-Gyun Lee,

Joseph M. Rone,

Zhaorong Li,

Camilo Faust Akl,

Seung Won Shin,

Joon-Hyuk Lee,

Lucas E. Flausino,

Florian Pernin,

Chun-Cheih Chao,

Kilian L. Kleemann,

Lena Srun,

Tomer Illouz,

Federico Giovannoni,

Marc Charabati,

Liliana M. Sanmarco,

Jessica E. Kenison,

Gavin Piester,

Stephanie E. J. Zandee,

Jack P. Antel,

Veit Rothhammer,

Michael A. Wheeler,

Alexandre Prat,

Iain C. Clark &

…

Francisco J. Quintana

Nature volume 645, page E5 (2025)

The Original Article was published on 20 March 2024

Correction to: Nature https://doi.org/10.1038/s41586-024-07187-5 Published online 20 March 2024

In the published version of this article, we mistakenly provided the wrong memory transcriptional signature in Extended Data Fig. 3a and Supplementary Table 3. We have corrected this inadvertent mistake, providing additional clarity on the generation of the memory transcriptional signature in the Methods “Pathway analysis” and Code availability sections.

To improve clarity, Supplementary Table 2 has been revised to include descriptions of significant peaks. In Extended Data Fig. 3j, the graphs for CD4+ T cells and IFN-γ cells were mistakenly swapped, and Extended Data Fig. 6d included incorrect signal intensity (a.u.) data. The cluster colors in Extended Data Fig. 9d have also been corrected.

Additionally, typographical errors in the figure legends have been addressed: Fig. 5i and Extended Data Fig. 10a legends should have stated n = 9 sections in control; Extended Data Fig. 3e should have stated n = 8–12 per group; and Extended Data Fig. 6c should have stated n = 3–4 per group. The errors have been corrected in the HTML and PDF versions of the article.

Author information

Authors and Affiliations

1. Ann Romney Center for Neurologic Diseases, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA

Hong-Gyun Lee, Joseph M. Rone, Zhaorong Li, Camilo Faust Akl, Joon-Hyuk Lee, Lucas E. Flausino, Chun-Cheih Chao, Lena Srun, Tomer Illouz, Federico Giovannoni, Marc Charabati, Liliana M. Sanmarco, Jessica E. Kenison, Gavin Piester, Veit Rothhammer, Michael A. Wheeler & Francisco J. Quintana

2. Broad Institute of MIT and Harvard, Cambridge, MA, USA

Zhaorong Li, Michael A. Wheeler & Francisco J. Quintana

3. Department of Bioengineering, College of Engineering, California Institute for Quantitative Biosciences, QB3, University of California Berkeley, Berkeley, CA, USA

Seung Won Shin & Iain C. Clark

4. Neuroimmunology Unit, Montreal Neurological Institute, Department of Neurology and Neurosurgery, McGill University, Montreal, Quebec, Canada

Florian Pernin & Jack P. Antel

5. School of Computing, University of Portsmouth, Portsmouth, UK

Kilian L. Kleemann

6. Department of Pathology and Laboratory Medicine, University of Rochester Medical Center, Rochester, NY, USA

Gavin Piester

7. Neuroimmunology Research Lab, Centre de Recherche du Centre Hospitalier de l’Université de Montréal (CRCHUM), Montreal, Quebec, Canada

Stephanie E. J. Zandee & Alexandre Prat

8. Department of Neurology, University Hospital, Friedrich-Alexander University Erlangen Nuremberg, Erlangen, Germany

Veit Rothhammer

9. Gene Lay Institute of Immunology and Inflammation, Boston, MA, USA

Francisco J. Quintana

Corresponding author

Correspondence to Francisco J. Quintana.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, HG., Rone, J.M., Li, Z. et al. Author Correction: Disease-associated astrocyte epigenetic memory promotes CNS pathology. Nature 645, E5 (2025). https://doi.org/10.1038/s41586-025-09546-2

- Published: 26 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09546-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Author Correction Open access Published: 26 August 2025

Author Correction: Complex genetic variation in nearly complete human genomes

Glennis A. Logsdon,

Peter Ebert,

Peter A. Audano,

Mark Loftus,

David Porubsky,

Jana Ebler,

Feyza Yilmaz,

Pille Hallast,

Timofey Prodanov,

DongAhn Yoo,

Carolyn A. Paisie,

William T. Harvey,

Xuefang Zhao,

Gianni V. Martino,

Mir Henglin,

Katherine M. Munson,

Keon Rabbani,

Chen-Shan Chin,

Bida Gu,

Hufsah Ashraf,

Stephan Scholz,

Olanrewaju Austine-Orimoloye,

Parithi Balachandran,

Marc Jan Bonder,

Haoyu Cheng,

Zechen Chong,

Jonathan Crabtree,

Mark Gerstein,

Lisbeth A. Guethlein,

Patrick Hasenfeld,

Glenn Hickey,

Kendra Hoekzema,

Sarah E. Hunt,

Matthew Jensen,

Yunzhe Jiang,

Sergey Koren,

Youngjun Kwon,

Chong Li,

Heng Li,

Jiaqi Li,

Paul J. Norman,

Keisuke K. Oshima,

Benedict Paten,

Adam M. Phillippy,

Nicholas R. Pollock,

Tobias Rausch,

Mikko Rautiainen,

Yuwei Song,

Arda Söylev,

Arvis Sulovari,

Likhitha Surapaneni,

Vasiliki Tsapalou,

Weichen Zhou,

Ying Zhou,

Qihui Zhu,

Michael C. Zody,

Ryan E. Mills,

Scott E. Devine,

Xinghua Shi,

Michael E. Talkowski,

Mark J. P. Chaisson,

Alexander T. Dilthey,

Miriam K. Konkel,

Jan O. Korbel,

Charles Lee,

Christine R. Beck,

Evan E. Eichler &

…

Tobias Marschall

Nature volume 645, page E6 (2025)

The Original Article was published on 23 July 2025

Correction to: Nature https://doi.org/10.1038/s41586-025-09140-6 Published online 23 July 2025

In the version of the article initially published, the x-axis label for Fig. 4f was “Position (Mb)” and has now been corrected to “Position (kb)” in the HTML and PDF versions of the article.

Author information

Author notes

1. Mark Loftus

Present address: The Jackson Laboratory for Genomic Medicine, Farmington, CT, USA

2. These authors contributed equally: Glennis A. Logsdon, Peter Ebert, Peter A. Audano, Mark Loftus

Authors and Affiliations

1. Department of Genome Sciences, University of Washington School of Medicine, Seattle, WA, USA

Glennis A. Logsdon, David Porubsky, DongAhn Yoo, William T. Harvey, Katherine M. Munson, Kendra Hoekzema, Youngjun Kwon, Arvis Sulovari & Evan E. Eichler

2. Department of Genetics, Epigenetics Institute, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA

Glennis A. Logsdon & Keisuke K. Oshima

3. Core Unit Bioinformatics, Medical Faculty and University Hospital Düsseldorf, Heinrich Heine University, Düsseldorf, Germany

Peter Ebert

4. Center for Digital Medicine, Heinrich Heine University, Düsseldorf, Germany

Peter Ebert, Jana Ebler, Timofey Prodanov, Mir Henglin, Hufsah Ashraf, Stephan Scholz, Arda Söylev, Alexander T. Dilthey & Tobias Marschall

5. The Jackson Laboratory for Genomic Medicine, Farmington, CT, USA

Peter A. Audano, Feyza Yilmaz, Pille Hallast, Carolyn A. Paisie, Parithi Balachandran, Qihui Zhu, Charles Lee & Christine R. Beck

6. Department of Genetics and Biochemistry, Clemson University, Clemson, SC, USA

Mark Loftus, Gianni V. Martino & Miriam K. Konkel

7. Center for Human Genetics, Clemson University, Greenwood, SC, USA

Mark Loftus, Gianni V. Martino & Miriam K. Konkel

8. Institute for Medical Biometry and Bioinformatics, Medical Faculty and University Hospital Düsseldorf, Heinrich Heine University, Düsseldorf, Germany

Jana Ebler, Timofey Prodanov, Mir Henglin, Hufsah Ashraf, Arda Söylev & Tobias Marschall

9. Program in Medical and Population Genetics and Stanley Center for Psychiatric Research, Broad Institute of MIT and Harvard, Cambridge, MA, USA

Xuefang Zhao & Michael E. Talkowski

10. Center for Genomic Medicine, Massachusetts General Hospital, Boston, MA, USA

Xuefang Zhao & Michael E. Talkowski

11. Department of Neurology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA

Xuefang Zhao & Michael E. Talkowski

12. Medical University of South Carolina, College of Graduate Studies, Charleston, SC, USA

Gianni V. Martino

13. Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, CA, USA

Keon Rabbani, Bida Gu & Mark J. P. Chaisson

14. Pathos AI Inc., Chicago, IL, USA

Chen-Shan Chin

15. Institute of Medical Microbiology and Hospital Hygiene, Medical Faculty, Heinrich Heine University, Düsseldorf, Germany

Stephan Scholz & Alexander T. Dilthey

16. European Molecular Biology Laboratory, Wellcome Genome Campus, European Bioinformatics Institute, Cambridge, UK

Olanrewaju Austine-Orimoloye, Sarah E. Hunt & Likhitha Surapaneni

17. Department of Genetics, University of Groningen, University Medical Center Groningen, Groningen, The Netherlands

Marc Jan Bonder

18. Oncode Institute, Utrecht, The Netherlands

Marc Jan Bonder

19. Division of Computational Genomics and Systems Genetics, German Cancer Research Center, Heidelberg, Germany

Marc Jan Bonder

20. Department of Biomedical Informatics and Data Science, Yale School of Medicine, New Haven, CT, USA

Haoyu Cheng

21. Department of Biomedical Informatics and Data Science, Heersink School of Medicine, University of Alabama, Birmingham, AL, USA

Zechen Chong & Yuwei Song

22. Institute for Genome Sciences, University of Maryland School of Medicine, Baltimore, MD, USA

Jonathan Crabtree & Scott E. Devine

23. Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA

Mark Gerstein, Matthew Jensen, Yunzhe Jiang & Jiaqi Li

24. Program in Computational Biology and Bioinformatics, Yale University, New Haven, CT, USA

Mark Gerstein, Matthew Jensen, Yunzhe Jiang & Jiaqi Li

25. Department of Structural Biology, School of Medicine, Stanford University, Stanford, CA, USA

Lisbeth A. Guethlein

26. Genome Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany

Patrick Hasenfeld, Tobias Rausch, Vasiliki Tsapalou & Jan O. Korbel

27. UC Santa Cruz Genomics Institute, University of California, Santa Cruz, CA, USA

Glenn Hickey & Benedict Paten

28. Genome Informatics Section, Center for Genomics and Data Science Research, National Human Genome Research Institute, National Institutes of Health, Bethesda, MD, USA

Sergey Koren & Adam M. Phillippy

29. Department of Computer and Information Sciences, College of Science and Technology, Temple University, Philadelphia, PA, USA

Chong Li & Xinghua Shi

30. Institute for Genomics and Evolutionary Medicine, Temple University, Philadelphia, PA, USA

Chong Li & Xinghua Shi

31. Department of Data Science, Dana-Farber Cancer Institute, Boston, MA, USA

Heng Li & Ying Zhou

32. Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA

Heng Li

33. Department of Biomedical Informatics, University of Colorado School of Medicine, Aurora, CO, USA

Paul J. Norman & Nicholas R. Pollock

34. Department of Immunology and Microbiology, University of Colorado School of Medicine, Aurora, CO, USA

Paul J. Norman

35. Institute for Molecular Medicine Finland (FIMM), University of Helsinki, Helsinki, Finland

Mikko Rautiainen

36. Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI, USA

Weichen Zhou & Ryan E. Mills

37. Stanford Health Care, Palo Alto, CA, USA

Qihui Zhu

38. New York Genome Center, New York, NY, USA

Michael C. Zody

39. The University of Connecticut Health Center, Farmington, CT, USA

Christine R. Beck

40. Howard Hughes Medical Institute, University of Washington, Seattle, WA, USA

Evan E. Eichler

Corresponding authors

Correspondence to Miriam K. Konkel, Jan O. Korbel, Charles Lee, Christine R. Beck, Evan E. Eichler or Tobias Marschall.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Cite this article

Logsdon, G.A., Ebert, P., Audano, P.A. et al. Author Correction: Complex genetic variation in nearly complete human genomes. Nature 645, E6 (2025). https://doi.org/10.1038/s41586-025-09547-1

- Published: 26 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09547-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Author Correction Published: 28 August 2025

Author Correction: Endophilin marks and controls a clathrin-independent endocytic pathway

Emmanuel Boucrot,

Antonio P. A. Ferreira,

Leonardo Almeida-Souza,

Sylvain Debard,

Yvonne Vallis,

Gillian Howard,

Laetitia Bertot,

Nathalie Sauvonnet &

…

Harvey T. McMahon

Nature volume 645, page E7 (2025)

The Original Article was published on 17 December 2014

Correction to: Nature https://doi.org/10.1038/nature14067 Published online 17 December 2014

It was brought to our attention via a comment in PubPeer that images in Extended Data Fig. 1c, Extended Data Fig. 1i and Extended Data Fig. 7k in our paper contain duplicated sub-panels. After extensive internal investigation of the source data (raw, uncropped immunoblots and microscopy images), we can confirm that figure preparation errors (copy-pasting placeholder images without updating them with correct panels) were responsible for the mistakes. The errors are in presentation only, and do not affect our scientific conclusions. Specific explanations related to each duplication are described in the following sections.

1. Extended Data Fig. 1c

The immunoblots for the mAchR4 TIL R230E and the mAchR4 TIL P331E mutants were the same (see Supplementary Information: Correction Fig. 1).

The duplication was most likely introduced upon copy-pasting of a sub-panel to be used as a template/placeholder for a subsequent sub-panel. Unfortunately, the swap with the relevant image for one of the mutants was forgotten, leaving the duplication error. Inspection of the original, uncropped, immunoblot scans revealed that the one for the mAchR4 TIL R230E mutant was the duplicate, and that for the mAchR4 TIL P331E mutant was genuine (see Supplementary Information: Correction Fig. 1). The duplicate image has been replaced by a correct representative immunoblot for the mAchR4 TIL R230E mutant (Supplementary Information: Correction Figs. 1 and 2).

This correction does not affect our scientific conclusions as both mAchR4 TIL R230E and mAchR4 TIL P331E mutants were pulled down by the Endo A2 SH3 domain.

2. Extended Data Fig. 1i

The XY confocal microscopy images for control and Endo TKD were the same (Supplementary Information: Correction Fig. 3).

As above, the duplication was most likely introduced upon a similar copy-pasting of a sub-panel to be used as a template/placeholder for a subsequent one. Unfortunately, the swap with the relevant image for one of the conditions was forgotten, leaving the duplication error. Inspection of the original, uncropped, confocal microcopy images revealed that the image for the control was genuine and that of Endo TKD was the duplicate. The duplicate image has been replaced by a correct representative confocal microcopy image for Endo TKD (Supplementary Information: Correction Fig. 3).

This correction does not affect our scientific conclusions as AP2 was recruited to the plasma membrane of Endo TKD cells.

3. Extended Data Fig. 7k

The bright field microscopy images for Endo1+2+3 TKD, 2 days, –NGF and +NGF were the same, and those for Endo1+2+3 TKD, 4 days, –NGF and +NGF were also identical to each other (Supplementary Information: Correction Fig. 4).

As above, the duplication was most likely introduced upon a similar copy-pasting of a sub-panel to be used as a template/placeholder for subsequent ones. Unfortunately, the swap with the relevant images for some of the conditions (here, –NGF vs +NGF rows) was forgotten, leaving the duplication errors. Inspection of the original, uncropped, bright field micrographs revealed that the images for the Endo1+2+3 TKD +NGF (2 and 4 days) were genuine, as they showed some neurite extensions that were absent in the –NGF condition (Supplementary Information: Correction Figs. 5 and 6). Thus, the images for Endo1+2+3 TKD, –NGF after at 2 and 4 days were the duplicates. The duplicate images have been replaced by correct representative bright field microscopy images for Endo TKD, –NGF, 2 and 4 days (Supplementary Information: Correction Fig. 4).

This correction does not affect our scientific conclusions as, in absence of NGF (–NGF) after two or four days, Endo1+2+3 TKD did not affect neurite extension by PC12 cells (a process which requires +NGF).

4. Source data

The source data for all the figure panels involved contain the original, uncropped images and are available as Supplementary Information in the online version of this amendment.

5. Same image in Fig. 1e and Extended Data Fig. 2b—not a duplication error

Although not mentioned in the PubPeer comment, we also noted that the same microscopy image of a BSC1 cell from a resting (i.e., no denopamine added), control RNAi sample was present both in Fig. 1e and in Extended Data Fig. 2b (albeit at lower magnification in the latter to show the whole lamellipodia) without a specific mention in the figure legends. This was not a duplication error, but in the main figure we were showing a magnification (Fig. 1e), while in Extended Data Fig. 2b we provide a more complete image to show the context. Thus, we are using the same control BSC1 image in both places.

Supplementary information is available in the online version of this amendment.

Author information

Authors and Affiliations

1. MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge, UK

Emmanuel Boucrot, Leonardo Almeida-Souza, Yvonne Vallis, Gillian Howard & Harvey T. McMahon

2. Institute of Structural and Molecular Biology, University College London & Birkbeck College, London, UK

Emmanuel Boucrot, Antonio P. A. Ferreira & Sylvain Debard

3. Department of Biology, Ecole Normale Supérieure de Cachan, Cachan, France

Sylvain Debard

4. Institut Pasteur, Unité de Pathogenie Moleculaire Microbienne, Paris, France

Laetitia Bertot & Nathalie Sauvonnet

Corresponding authors

Correspondence to Emmanuel Boucrot or Harvey T. McMahon.

Supplementary information

Correction Figs. 1–6

Source data

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boucrot, E., Ferreira, A.P.A., Almeida-Souza, L. et al. Author Correction: Endophilin marks and controls a clathrin-independent endocytic pathway. Nature 645, E7 (2025). https://doi.org/10.1038/s41586-025-09552-4

- Published: 28 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09552-4

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Author Correction Published: 29 August 2025

Author Correction: Dual neuromodulatory dynamics underlie birdsong learning

Jiaxuan Qi,

Drew C. Schreiner,

Miles Martinez,

John Pearson &

…

Richard Mooney

Nature volume 645, page E8 (2025)

The Original Article was published on 12 March 2025

Correction to: Nature https://doi.org/10.1038/s41586-025-08694-9 Published online 12 March 2025

In the version of the article initially published, a data preprocessing error affected Fig. 2p and 2q, wherein certain duration and amplitude values were erroneously associated with the wrong dopamine trace. Figure 2 and associated source data have been updated in the HTML and PDF versions of the article. For comparison, the original Fig. 2p,q panels are available as Supplementary Information accompanying this amendment.

Supplementary information is available in the online version of this amendment.

Author information

Authors and Affiliations

1. Department of Neurobiology, Duke University School of Medicine, Durham, NC, USA

Jiaxuan Qi, Drew C. Schreiner, Miles Martinez, John Pearson & Richard Mooney

2. Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

Miles Martinez & John Pearson

3. Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, USA

John Pearson

Corresponding authors

Correspondence to John Pearson or Richard Mooney.

Supplementary information

Original, unrevised Fig. 2p, q

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qi, J., Schreiner, D.C., Martinez, M. et al. Author Correction: Dual neuromodulatory dynamics underlie birdsong learning. Nature 645, E8 (2025). https://doi.org/10.1038/s41586-025-09563-1

- Published: 29 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09563-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Publisher Correction Open access Published: 26 August 2025

Publisher Correction: Multiple oestradiol functions inhibit ferroptosis and acute kidney injury

Wulf Tonnus,

Francesca Maremonti,

Shubhangi Gavali,

Marlena Nastassja Schlecht,

Florian Gembardt,

Alexia Belavgeni,

Nadja Leinung,

Karolin Flade,

Natalie Bethe,

Sofia Traikov,

Anne Haag,

Danny Schilling,

Sider Penkov,

Melodie Mallais,

Christine Gaillet,

Claudia Meyer,

Melika Katebi,

Anushka Ray,

Louisa M. S. Gerhardt,

Anne Brucker,

Jorunn Naila Becker,

Mirela Tmava,

Lisa Schlicker,

Almut Schulze,

Nina Himmerkus,

Andrej Shevchenko,

Mirko Peitzsch,

Uladzimir Barayeu,

Sonia Nasi,

Juliane Putz,

Kenneth S. Korach,

Joel Neugarten,

Ladan Golestaneh,

Christian Hugo,

Jan Ulrich Becker,

Joel M. Weinberg,

Svenja Lorenz,

Bettina Proneth,

Marcus Conrad,

Eckhard Wolf,

Bernd Plietker,

Raphaël Rodriguez,

Derek A. Pratt,

Tobias P. Dick,

Maria Fedorova,

Stefan R. Bornstein &

…

Andreas Linkermann

Nature volume 645, page E9 (2025)

The Original Article was published on 13 August 2025

Correction to: Nature https://doi.org/10.1038/s41586-025-09389-x Published online 13 August 2025

In the version of this article initially published, due to a processing error, text from a reference title was inserted into the seventh sentence of the Discussion, which has now been amended to read “In conclusion, ferroptosis sensitivity explains the higher susceptibility of male individuals to AKI” in the HTML and PDF versions of the article.

Author information

Author notes

1. These authors contributed equally: Wulf Tonnus, Francesca Maremonti, Shubhangi Gavali

Authors and Affiliations

1. Division of Nephrology, Department of Internal Medicine 3, University Hospital Carl Gustav Carus at the Technische Universität Dresden, Dresden, Germany

Wulf Tonnus, Marlena Nastassja Schlecht, Karolin Flade, Natalie Bethe, Anne Brucker, Jorunn Naila Becker, Mirela Tmava & Christian Hugo

2. Department of Medicine V, University Medical Centre Mannheim, University of Heidelberg, Mannheim, Germany

Francesca Maremonti, Shubhangi Gavali, Florian Gembardt, Nadja Leinung, Claudia Meyer, Melika Katebi, Anushka Ray, Louisa M. S. Gerhardt & Andreas Linkermann

3. Institute of Clinical Chemistry and Laboratory Medicine, University Hospital Carl Gustav Carus at the Technische Universität Dresden, Dresden, Germany

Alexia Belavgeni, Sofia Traikov & Mirko Peitzsch

4. Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany

Sofia Traikov & Andrej Shevchenko

5. Chair of Organic Chemistry, Technische Universität Dresden, Dresden, Germany

Anne Haag & Bernd Plietker

6. Division of Redox Regulation, German Cancer Research Center (DKFZ), DKFZ-ZMBH Alliance, Heidelberg, Germany

Danny Schilling & Tobias P. Dick

7. Faculty of Biosciences, Heidelberg University, Heidelberg, Germany

Danny Schilling & Tobias P. Dick

8. Center of Membrane Biochemistry and Lipid Research, University Hospital and Faculty of Medicine Carl Gustav Carus, Technische Universität Dresden, Dresden, Germany

Sider Penkov & Maria Fedorova

9. Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario, Canada

Melodie Mallais & Derek A. Pratt

10. Equipe Labellisée Ligue Contre le Cancer, Institut Curie, CNRS, INSERM, PSL Research University, Paris, France

Christine Gaillet & Raphaël Rodriguez

11. Division of Tumor Metabolism and Microenvironment, German Cancer Research Center (DKFZ), Heidelberg, Germany

Lisa Schlicker & Almut Schulze

12. Institute of Physiology, Christian-Albrecht-University Kiel, Kiel, Germany

Nina Himmerkus

13. Max Planck Institute for Polymer Research, Mainz, Germany

Uladzimir Barayeu

14. Service of Rheumatology, Department of Musculoskeletal Medicine, Centre Hospitalier Universitaire Vaudois, University of Lausanne, Lausanne, Switzerland

Sonia Nasi

15. Clinic for Urology, University Hospital Carl Gustav Carus at the Technische Universität Dresden, Dresden, Germany

Juliane Putz

16. Laboratories of Reproductive and Developmental Toxicology, NIEHS, National Institutes of Health, Research Triangle Park, NC, USA

Kenneth S. Korach

17. Renal Division, Montefiore Medical Center, Albert Einstein College of Medicine, New York, NY, USA

Joel Neugarten & Ladan Golestaneh

18. Institute of Pathology, University Hospital of Cologne, Cologne, Germany

Jan Ulrich Becker

19. Division for Nephrology, University of Michigan Medical Center, Ann Arbor, MI, USA

Joel M. Weinberg

20. Institute of Metabolism and Cell Death, Helmholtz Zentrum München, Neuherberg, Germany

Svenja Lorenz, Bettina Proneth & Marcus Conrad

21. Chair for Molecular Animal Breeding and Biotechnology, Gene Center and Department of Veterinary Sciences, LMU Munich, Munich, Germany

Eckhard Wolf

22. Center for Innovative Medical Models (CiMM), LMU Munich, Oberschleißheim, Germany

Eckhard Wolf

23. German Center for Diabetes Research (DZD), Neuherberg, Germany

Eckhard Wolf

24. Department of Internal Medicine 3, University Hospital Carl Gustav Carus at the Technische Universität Dresden, Dresden, Germany

Stefan R. Bornstein & Andreas Linkermann

25. Diabetes and Nutritional Sciences, King’s College London, London, UK

Stefan R. Bornstein

26. Center for Regenerative Therapies, Technische Universität Dresden, Dresden, Germany

Stefan R. Bornstein

27. Paul Langerhans Institute Dresden of Helmholtz Centre Munich at University Clinic Carl Gustav Carus of TU Dresden Faculty of Medicine, Dresden, Germany

Stefan R. Bornstein

28. Division of Nephrology, Department of Medicine, Albert Einstein College of Medicine, New York, NY, USA

Andreas Linkermann

Corresponding author

Correspondence to Andreas Linkermann.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

About this article

Cite this article

Tonnus, W., Maremonti, F., Gavali, S. et al. Publisher Correction: Multiple oestradiol functions inhibit ferroptosis and acute kidney injury. Nature 645, E9 (2025). https://doi.org/10.1038/s41586-025-09562-2

- Published: 26 August 2025

- Issue Date: 18 September 2025

- DOI: https://doi.org/10.1038/s41586-025-09562-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Innovations In

- Alzheimer’s Disease

New Hope in Alzheimer’s Research

Breakthrough therapies, new diagnostics and preventive measures for fighting a devastating disease.

- Lauren Gravitz

Innovations In17 Sep 2025 Nature

Can Diet and Exercise Really Prevent Alzheimer’s?

Early studies suggest that lifestyle changes such as diet, exercise and social engagement may help slow or prevent Alzheimer’s symptoms—but the evidence is inconsistent, and many doctors remain cautious.

- Sara Harrison

Innovations In17 Sep 2025 Nature

Alzheimer’s Drugs Are Finally Tackling the Disease Itself. Here’s How

While our understanding of Alzheimer’s disease is far from complete, the latest therapies, and others in more than 100 clinical trials, offer new hope.

- Esther Landhuis

Innovations In17 Sep 2025 Nature

Controversial New Alzheimer’s Drugs Offer Hope—But at a High Cost

New Alzheimer’s drugs known as anti-amyloid therapies may slow disease progression—but they also carry serious risks, including brain bleeds and strokelike symptoms.

- Liz Seegert

Innovations In17 Sep 2025 Nature

The Vexing Promise of New Blood Tests for Alzheimer’s

A new generation of Alzheimer’s blood tests could speed up diagnosis and access to care—but they also raise thorny questions about prediction, treatment and uncertainty.

- Cassandra Willyard

Innovations In17 Sep 2025 Nature

Can We Fix America’s Dementia Care Crisis before It’s Too Late?

More than 13.8 million Americans could have Alzheimer’s by 2060, and at the rate care facilities are closing, many of them will have nowhere to go. Regina Shih of the State Alzheimer’s Research Support Center (StARS) wants to help solve that problem.

- Tara Haelle

Innovations In17 Sep 2025 Nature

The Hidden Link between Racism and Alzheimer’s Risk

Black Americans face a significantly higher risk of Alzheimer’s and other dementias than white Americans. Researchers are working to find out why that is and how to intervene.

- Jyoti Madhusoodanan

Innovations In17 Sep 2025 Nature

Neuroinflammation in Alzheimer disease

This Review provides an in-depth examination of how inflammation contributes to neurodegeneration in Alzheimer disease. The authors explore the impact of extrinsic factors, such as brain trauma, diet and infections, and host-intrinsic factors, such as the activity of microglial cells and other immune, vascular and neuronal cell populations, on disease development. They also highlight emerging drugs that target this inflammatory component for therapy of Alzheimer disease.

- Michael T. Heneka

- Wiesje M. van der Flier

- Sean-Patrick Riechers

Review Article9 Dec 2024 Nature Reviews Immunology

Integrated multimodal cell atlas of Alzheimer’s disease

The affected cellular populations during Alzheimer’s disease progression remain understudied. Here the authors use a cohort of 84 donors, quantitative neuropathology and multimodal datasets from the BRAIN Initiative. Their pseudoprogression analysis revealed two disease phases.

- Mariano I. Gabitto

- Kyle J. Travaglini

- Ed S. Lein

ArticleOpen Access14 Oct 2024 Nature Neuroscience

Systemic determinants of brain health in ageing

Peripheral organ dysfunction can have considerable effects on brain health, contributing to neurodegeneration and dementia. This Review explores how clinical and subclinical dysfunction of specific organ systems can impact brain health and discusses the implications for dementia prevention.

- Eric E. Smith

- Geert Jan Biessels

- Costantino Iadecola

Review Article7 Oct 2024 Nature Reviews Neurology

Oligodendrocytes produce amyloid-β and contribute to plaque formation alongside neurons in Alzheimer’s disease model mice

In Alzheimer’s disease, neurons are considered the sole source of amyloid-β (Aβ) peptides that form plaques. Here the authors show that oligodendrocytes, the myelinating glial cells of the brain, also contribute to Aβ plaque burden alongside neurons.

- Andrew Octavian Sasmita

- Constanze Depp

- Klaus-Armin Nave

Brief CommunicationOpen Access5 Aug 2024 Nature Neuroscience

Disentangling clinical and biological trajectories of neurodegenerative diseases

In recent years, we have seen a shift towards defining sporadic neurodegenerative diseases as a biological continuum. Here, we discuss the risks associated with this shift, emphasize the importance of maintaining a strong connection between disease definitions and subsequent clinical outcomes, and suggest clinicobiological frameworks to disentangle multiple discrete nosological entities.

- Nicolas Villain

- Vincent Planche

News & Views8 Aug 2024 Nature Reviews Neurology

APOE4 homozygosity represents a distinct genetic form of Alzheimer’s disease

The study on APOE4 homozygosity indicates a genetic variant of Alzheimer’s disease with early symptom onset and distinct biomarker progression, highlighting the need for specialized treatment approaches.

- Juan Fortea

- Jordi Pegueroles

- Víctor Montal

Article6 May 2024 Nature Medicine

Table of Contents

Nature: 2025 Sep 18

This Week

Bring us your LLMs: why peer review is good for AI models

Make trains great again — for the sake of people and the planet

Equity in science is a beautiful lie — and I’m done pretending

News in Focus

First CRISPR horses spark controversy: what’s next for gene-edited animals?

Air pollution directly linked to increased dementia risk

These nations are wooing PhD students amid US funding uncertainties

Can researchers stop AI making up citations?

Chemists cram record nine metals into trendy 2D material

‘Amazing feat’: US man still alive six months after pig kidney transplant

Newfound immune cell in mice hints at why inflammation spikes with old age

‘Brain dial’ turns food consumption on or off in mice

AI is helping to decode animals’ speech. Will it also let us talk with them?

How billions of hacked mosquitoes and a vaccine could beat the deadly dengue virus

Books & Arts

Heroes or hoarders? The strange brains of people who collect

How did assaults on science become the norm — and what can we do?

Opinion

GPS timekeeping is increasingly vulnerable: here’s how to deliver future-proofed time

Mirror of the unknown: should research on mirror-image molecular biology be stopped?

Work

‘Lipstick on a pig’: how to fight back against a peer-review bully

Sweet like chocolate: researching in the shade of a cacao tree

Research

Scaling and logic in the colour code on a superconducting quantum processor

Topological prethermal strong zero modes on superconducting processors

DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning

Supervised learning in DNA neural networks

Long-range PM2.5 pollution and health impacts from the 2023 Canadian wildfires

Flourishing chemosynthetic life at the greatest depths of hadal trenches

Whole-genome sequencing of 490,640 UK Biobank participants

A generic non-invasive neuromotor interface for human-computer interaction

Lithium deficiency and the onset of Alzheimer’s disease

Mitochondrial origins of the pressure to sleep

A gut sense for a microbial pattern regulates feeding

Driving a protective allele of the mosquito FREP1 gene to combat malaria

Fluctuating DNA methylation tracks cancer evolution at clinical scale

Excised DNA circles from V(D)J recombination promote relapsed leukaemia

Programmable protein ligation on cell surfaces

Amendments & Corrections

Author Correction: Macrophages excite muscle spindles with glutamate to bolster locomotion

Author Correction: Disease-associated astrocyte epigenetic memory promotes CNS pathology

Author Correction: Complex genetic variation in nearly complete human genomes

Author Correction: Endophilin marks and controls a clathrin-independent endocytic pathway

Author Correction: Dual neuromodulatory dynamics underlie birdsong learning

Publisher Correction: Multiple oestradiol functions inhibit ferroptosis and acute kidney injury

Innovations In

Alzheimer’s Disease