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- China is leading the world on AI governance: other countries must engage

- The Indian Ocean disaster is a climate tragedy — and needs more attention

EDITORIAL 10 December 2025

China is leading the world on AI governance: other countries must engage

The nation’s regulators are attempting to match the rapid pace at which AI is evolving. That needs to become a global initiative.

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China has been forging its own path on the regulation of technologies based on artificial intelligence.Credit: Hector Retamal/AFP/Getty

The past few years have seen no shortage of international dialogues, white papers and recommendations from advisory groups on the development and use of artificial intelligence. Yet when it has come to turning these into globally agreed rules to maximize the benefits and minimize the harm of AI, there has been a leadership vacuum.

As Nature reported last week (Nature https://doi.org/qhbv; 2025), one country is pushing forwards with plans to change that. China is proposing to set up a global body to coordinate the regulation of AI, to be known as the World Artificial Intelligence Cooperation Organization (WAICO). Establishing such a body is in all countries’ interests, and governments around the world should get on board.

AI models have astounding power, and abilities that could supercharge science and boost economic growth. But they do not fully understand the world, and can fail in unpredictable ways. There are many ways in which they could cause harm, including exacerbating inequality, aiding criminality and assisting the spread of mis- and disinformation. Some prominent researchers even argue that superintelligent AI could one day destroy humanity.

So far, such risks have not been given due attention in the breakneck race to develop AI — a race that many fear has created an economic bubble that is on the brink of bursting. The United States, which is home to many of the companies making the most powerful and widely used models, has no national AI regulations, just a patchwork of state-level laws. On the whole, companies in the United States are expected to police themselves and establish their own internal guardrails — while also being in relentless competition.

The latest assessment of large technology companies’ safety and risk policies — the AI Safety Index — by the Future of Life Institute, based in Campbell, California, was published on 3 December. On a scale from A to F, no US firm scores higher than a C+ (see go.nature.com/48ikyhv). Yet last month, US President Donald Trump launched an initiative dubbed the Genesis Mission, which will give companies and researchers developing AI models unprecedented access to government data sets. The administration has compared it to the Apollo programme to reach the Moon.

In the European Union, the AI Act, introduced last year, requires the makers of the most powerful advanced AI systems to strengthen their analyses of the threats their models pose. The act is being implemented in stages, and it is not yet clear what effect the threat of substantial fines for non-compliance will have. Media reports suggest that companies are pressuring the EU to water down its laws.

China, meanwhile, has charted its own course. Its government is pushing hard to embed AI across society, from local government chatbots to factory robots that can accelerate production. But its regulators have also been pushing for AI outputs to be traceable and companies to be accountable (prominent China-based AI companies score even lower on the AI Safety Index than do their Western counterparts, partly, according to the Future of Life Institute, owing to failure to address catastrophic misuse).

Since 2022, the country has introduced an array of laws and technical standards that require developers to submit generative AI models to regulators for pre-deployment safety assessments and to include visible, indelible watermarks on AI-generated content, in a bid to prevent fraud and misinformation. That push is accelerating: China issued as many national requirements on AI in the first half of 2025 as it did in the previous three years, according to the Beijing-based consultancy Concordia AI.

Chinese officials want to prevent AI from rocking political stability, but still allow it to be used to boost economic growth, says Angela Zhang, a law researcher and technology-regulation specialist at the University of Southern California in Los Angeles. Any attempt to control the outputs of AI models in the name of safety, whether for political purposes or to align outputs with social values, remains fraught. But, as neuroscientist and AI entrepreneur Gary Marcus told reporters at an event in London in October, in many respects China’s motivations are “pretty similar” to those of other countries. “They don’t want to be annihilated by robots.”

Understanding China’s standards on AI is important for everyone. The country’s policy of producing free or cheap-to-access ‘open weight’ models means that companies around the world are increasingly building their services on Chinese AI. At the same time, it’s important that China’s researchers engage multilaterally to help assess what kind of global governance would be both effective and realistic.

Existing efforts to oversee AI at the global level — for example, the Organisation for Economic Co-operation and Development’s AI Principles and the Council of Europe’s Framework Convention on AI — are either non-binding or not enforced. To effectively regulate AI, unique solutions will be required, but one model that WAICO could learn from is that used by the International Atomic Energy Agency in Vienna to regulate nuclear energy. This involves countries agreeing to limits on development and to opening nuclear facilities for inspection, which allows nations to verify that others are adhering to the system.

Much of the rhetoric surrounding AI frames it as a geopolitical contest, whereby a country’s safety is guaranteed by technological dominance. But ‘winning’ is not an option for most nations, and an AI arms race won’t guarantee that people will be safer or wealthier. A better plan would be for everyone to come together to agree on what is safe and how the world wants to harness AI. China’s initiative should be welcomed, and researchers and authorities around the world should engage.

Nature 648, 251 (2025)

doi: https://doi.org/10.1038/d41586-025-03972-y

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WORLD VIEW 05 December 2025

The Indian Ocean disaster is a climate tragedy — and needs more attention

A region unused to tropical cyclones has had three in a week. The world needs to ask why this happened, not look away.

By

Dyna Rochmyaningsih

Residents remove their belongings from flood-damaged homes in Meureudu, Indonesia.Credit: Hotli Simanjuntak/EPA/Shutterstock

In late November, three tropical cyclones — Senyar, Ditwah and Koto — devastated cities and villages in countries around the Indian Ocean. In Indonesia’s Sumatra, Malaysia, Vietnam, Thailand, India’s Andaman and Nicobar Islands, the Philippines and Sri Lanka, torrential rains, high winds, landslides and flash floods killed at least 1,000 people, buried homes beneath metres of mud and destroyed roads and bridges.

The storms’ destructive scale is close to that of the 2004 Indian Ocean tsunami, as Muzakir Manaf, the governor of Aceh, Indonesia, said in a statement. However, the world has mostly overlooked this emergency. Millions of people have been displaced, and many are sick or starving, yet aid has been slow to arrive. Few people have recognized the cyclones’ unusual nature and what they herald for the world’s future.

The rainfall was so intense that it created ‘a rough sea on the land’, as my friend in the Sumatran city of Langsa told me before we lost contact. One week of non-stop deluges induced a powerful tsunami-like river current that washed away concrete bridges, dragged giant timber trees from encroached forests and inundated people in their homes.

But with these horrifying scenes also comes frustration. Some countries, such as Sri Lanka, have declared a national emergency and asked for international help. Others, including Indonesia, have not even acknowledged that this is a crisis. Indonesia’s President Prabowo Subianto held his first cabinet meeting about the disaster on 27 November, ten days after the first heavy rains and landslides in North Sumatra. As this article went to press, the government has still not declared a national emergency.

I’m baffled by the slow response. Many villages and cities in West Sumatra, North Sumatra and Aceh are disconnected from the rest of the world. Food is scarce and prices are soaring; hospitals have collapsed. Local governments have sent some aid, but damaged infrastructure has hampered the process.

Indonesia not declaring this to be a national emergency means international aid is slow in coming. The issue is exacerbated by the silence of much of the international community. Some world leaders have expressed condolences and the United Nations has offered help. But no word has yet come from the European Union or United States.

Perhaps one reason for the delays is the sparse coverage of the crisis in the global media, which has failed to portray the vast scale of this catastrophe. Initially, news outlets reported a series of floods on a country-by-country basis, ignoring the connection between them. The disaster is now being reported as ‘southeast Asia floods’, a shift that is welcome, but that still misses the root of the problem.

The Indian Ocean region is especially vulnerable to extreme weather, owing to a combination of climate change and severe environmental degradation, including from deforestation and mining. The fact that most international climate activists are also failing to call the situation out as a climate tragedy is another troubling omission.

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Nature 648, 252 (2025)

doi: https://doi.org/10.1038/d41586-025-03973-x

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Competing Interests

The author declares no competing interests.

News in Focus

- Trump’s AI ‘Genesis Mission’: what are the risks and opportunities?

- ‘Fire amoeba’ survives in hotter conditions than any other complex cell

- Major AI conference flooded with peer reviews written fully by AI

- Has the mysterious ‘compass’ organ of birds been found at last?

- AlphaFold is five years old — these charts show how it revolutionized science

- Is your brain tired? Researchers are discovering the roots of mental fatigue

NEWS 26 November 2025

Trump’s AI ‘Genesis Mission’: what are the risks and opportunities?

National laboratories have been instructed to broaden access to their data sets to accelerate research as part of the federal government’s AI platform. But who stands to benefit?

By

Elizabeth Gibney,

Alexandra Witze &

Jenna Ahart

The Genesis Mission aims to provide researchers with the computing power and data sets necessary to train artificial-intelligence models.Credit: William Potter/iStock via Getty

The White House has launched a plan to accelerate research in the United States, by building artificial intelligence (AI) models on the rich scientific data sets held by the country’s 17 national laboratories, as well as harnessing their enormous computing resources.

An executive order issued on 24 November instructs the US Department of Energy (DoE) to create a platform through which academic researchers and AI firms can create powerful AI models using the government’s scientific data. Framed as part of a race for global technology dominance, it lists collaborations with technology firms including Microsoft, IBM, OpenAI, Google and Anthropic, as well as quantum-computing companies such as Quantinuum. Such a vast public–private partnership would give companies unprecedented access to federal scientific data sets for AI-driven analysis.

The effort, dubbed the Genesis Mission, aims to “double the productivity and impact of American research and innovation within a decade”, in a variety of fields from fusion energy to medicine. The project expects to “unlock breakthroughs in medicine, energy, materials science and beyond”, says Michael Kratsios, the US president’s science adviser. It also aims to build AI agents — general models with the ability to harness tools such as specialized software and coding suites — that can generate hypotheses and automate research workflows.

Labs around the world are already training AI systems on scientific data, to boost their capabilities in scientific domains and attempting to use AI models to make discoveries. But some researchers remain sceptical that general AI tools are capable of making truly fresh insights, and warn that their inherent flaws make the value of agents unclear.

The new US initiative formalizes and expands ongoing AI research efforts by the administration of President Donald Trump. “The impact is that it enables many more scientists and researchers to have access to all of the infrastructure that they need to explore important scientific questions that the country cares about,” says Lynne Parker, a robotics engineer at the University of Tennessee, Knoxville, who led AI-policy initiatives for the administrations of Trump and his predecessor, Joe Biden, but was not involved in the current initiative. “That really has not been possible before.”

Supercomputers at national laboratories, including the Argonne National Laboratory in Illinois, will probably be used as part of the Genesis Mission.Credit: Argonne National Laboratory/Getty

Trump’s team has been working to funnel money and attention to AI projects even as it tries to gut federal research spending more broadly. The White House has the power to shape the direction of research at the DoE’s network of national laboratories. It did not give an estimated price tag for the AI initiative; any extra funding beyond the laboratories’ normal budgets would have to be approved by the US Congress.

Nature looks at how the project might affect researchers and AI companies, and its promises and risks.

What are government-funded scientists being asked to do?

The scale and timeline of the plan is ambitious. In 60 days, the DoE is expected to create a list of 20 potential science and technology challenges for the project to tackle, in areas of national priorities such as nuclear fusion, quantum information science and crucial materials. The agency is supposed to create a full inventory of available federal computing resources and identify initial data assets to use, then work out how to safely include external data sets. The administration expects to demonstrate the platform’s capability for one of these research challenges in nine months.

These early steps will probably build on projects that are already under way at the national laboratories. For instance, Oak Ridge National Laboratory in Tennessee has been working on advancing AI research using a hybrid approach that uses both quantum and classical computing. Lawrence Berkeley National Laboratory in California is using AI to find ways to speed up network traffic.

The “DoE has been making a case for ‘AI for science’ for over seven years, and this executive order is the starting pistol to get on with it”, says Michael Norman, an astrophysicist at the University of California, San Diego, and former director of the San Diego Supercomputer Center. “It is an exciting direction indeed.”

What are companies being asked to do?

The project has named more than 50 collaborating companies, including some that have already been working on their own ‘AI scientists’. FutureHouse, a start-up based in San Francisco, California, for instance, launched a commercially available, AI-driven research platform earlier this month.

The precise role of these private companies in the Genesis plan remains unclear — although Trump’s executive order says the project will entail “collaboration with external partners possessing advanced AI, data, or computing capabilities or scientific domain expertise”. Such partnerships could include research agreements to jointly develop technologies, or a user-facility agreement for external researchers to conduct work in government facilities. Chip-manufacturing and computer companies such as NVIDIA, Advanced Micro Devices and Hewlett Packard Enterprise have reportedly agreed to build facilities in national labs, according to a report by The New York Times.

Some partnerships are already under way. In October, for instance, Argonne National Laboratory in Illinois announced a partnership with NVIDIA and technology firm Oracle to build two next-generation AI supercomputing systems. At least two national laboratories already have arrangements with the company OpenAI, based in San Francisco, California, to host local AI models that can process classified data on computers in the facilities. In February, the company held an ‘AI jam session’ with researchers from nine US national labs that allowed scientists to test the use of OpenAI’s reasoning models in their specific domains.

What are the opportunities?

The new Genesis Mission is meant to provide “secure access to appropriate datasets, including proprietary, federally curated, and open scientific datasets, in addition to synthetic data generated through DOE computing resources”, according to the executive order. Creating a national-scale platform that harnesses rich data sets usually housed in the walls of the national laboratories could be a boon for researchers. Although task-specific models such as the protein-folding model AlphaFold were built on open scientific data sets, general-purpose AI systems such as OpenAI’s GPT-5 are thought to be largely built on data scraped from the Internet.

It isn’t yet clear which data sets would be involved, but possible candidates include information gathered at facilities such as the Spallation Neutron Source at Oak Ridge National Laboratory. That facility collects neutron-scattering data, which illuminate how materials behave at the atomic scale, says Georgia Tourassi, the lab's associate director for computing and computational sciences. “From atomistic measurements to exascale simulations, such data sets can immediately accelerate the development of trustworthy, science-capable AI models,” she says.

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Nature 648, 253-255 (2025)

doi: https://doi.org/10.1038/d41586-025-03890-z

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NEWS 02 December 2025 Correction 02 December 2025

‘Fire amoeba’ survives in hotter conditions than any other complex cell

The single-celled organism can grow at 63 °C, a record for eukaryotic life.

By

Ewen Callaway

Hot springs at Lassen Volcanic National Park in California, where the heat-tolerant amoeba was discovered.Credit: Kelly Vandellen/iStock via Getty

This cell likes it hot. A tiny, single-celled amoeba that can thrive at temperatures that kill all other known complex life — organisms whose cells contain a nucleus and internal structures — has been found.

The discovery questions the notion that such ‘eukaryotic’ life — which includes all animals and plants — is not suited to the kind of extreme conditions that can be tolerated by bacteria and other organisms lacking a cell nucleus.

“We need to rethink what’s possible for a eukaryotic cell in a significant way,” says Angela Oliverio, a microbiologist at Syracuse University in New York. The work, which has not yet been peer reviewed, was described in a preprint[1] published on 24 November.

Oliverio and fellow Syracuse microbiologist Beryl Rappaport were part of a team that discovered the organism at Lassen Volcanic National Park in northern California’s Cascade mountain range. They named it Incendiamoeba cascadensis, which translates to ‘fire amoeba from the cascades’.

Incendiamoeba cascadensis can thrive at temperatures that would kill other complex cells.Credit: Image taken by Natalie Petek-Seoane from the preprint by H. Beryl Rappaport et al./bioRxiv

The park is famous for gurgling acid lakes and incandescent geothermal pools, but I. cascadensis comes from a pH-neutral ‘hot stream’. “It’s the most uninteresting geothermal feature you’ll find in Lassen,” says Rappaport.

Water samples from the stream looked devoid of life under a microscope, but after culturing them with nutrients, the researchers spotted the amoeba growing at 57 °C, within the stream’s temperature range. The scientists slowly raised the temperature, sailing past the previous eukaryote record of 60 °C. I. cascadensis was still able to divide at 63 °C and was still moving around at 64 °C. Even at 70 °C, the cells could form dormant ‘cysts’ that were capable of reactivating at cooler temperatures.

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Nature 648, 255-256 (2025)

doi: https://doi.org/10.1038/d41586-025-03933-5

Updates & Corrections

- Correction 02 December 2025: In an earlier version of this article Incendiamoeba cascadensis was spelled incorrectly. This has now been updated.

References

1. Rappaport, H. B. et al. Preprint at bioRxiv https://doi.org/10.1101/2025.11.24.690213 (2025).

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NEWS 27 November 2025 Correction 01 December 2025

Major AI conference flooded with peer reviews written fully by AI

Controversy has erupted after 21% of manuscript reviews for an international AI conference were found to be generated by artificial intelligence.

By

Miryam Naddaf

An AI-detection tool developed by Pangram labs found that peer reviewers are increasingly using chatbots to draft responses to authors.Credit: breakermaximus/iStock via Getty

What can researchers do if they suspect that their manuscripts have been peer reviewed using artificial intelligence (AI)? Dozens of academics have raised concerns on social media about manuscripts and peer reviews submitted to the organizers of next year’s International Conference on Learning Representations (ICLR), an annual gathering of specialists in machine learning. Among other things, they flagged hallucinated citations and suspiciously long and vague feedback on their work.

Graham Neubig, an AI researcher at Carnegie Mellon University in Pittsburgh, Pennsylvania, was one of those who received peer reviews that seemed to have been produced using large language models (LLMs). The reports, he says, were “very verbose with lots of bullet points” and requested analyses that were not “the standard statistical analyses that reviewers ask for in typical AI or machine-learning papers.”

But Neubig needed help proving that the reports were AI-generated. So, he posted on X (formerly Twitter) and offered a reward for anyone who could scan all the conference submissions and their peer reviews for AI-generated text. The next day, he got a response from Max Spero, chief executive of Pangram Labs in New York City, which develops tools to detect AI-generated text. Pangram screened all 19,490 studies and 75,800 peer reviews submitted for ICLR 2026, which will take place in Rio de Janeiro, Brazil, in April. Neubig and more than 11,000 other AI researchers will be attending.

Pangram’s analysis revealed that around 21% of the ICLR peer reviews were fully AI-generated, and more than half contained signs of AI use. The findings were posted online by Pangram Labs. “People were suspicious, but they didn’t have any concrete proof,” says Spero. “Over the course of 12 hours, we wrote some code to parse out all of the text content from these paper submissions,” he adds.

The conference organizers say they will now use automated tools to assess whether submissions and peer reviews breached policies on using AI in submissions and peer reviews. This is the first time that the conference has faced this issue at scale, says Bharath Hariharan, a computer scientist at Cornell University in Ithaca, New York, and senior programme chair for ICLR 2026. “After we go through all this process … that will give us a better notion of trust.”

AI-written peer review

The Pangram team used one of its own tools, which predicts whether text is generated or edited by LLMs. Pangram’s analysis flagged 15,899 peer reviews that were fully AI-generated. But it also identified many manuscripts that had been submitted to the conference with suspected cases of AI-generated text: 199 manuscripts (1%) were found to be fully AI-generated; 61% of submissions were mostly human-written; but 9% contained more than 50% AI-generated text. Pangram described the model in a preprint[1].

For many researchers who received peer reviews for their submissions to ICLR, the Pangram analysis confirmed what they had suspected. Desmond Elliott, a computer scientist at the University of Copenhagen, says that one of three reviews he received seemed to have missed “the point of the paper”. His PhD student who led the work suspected that the review was generated by LLMs, because it mentioned numerical results from the manuscript that were incorrect and contained odd expressions.

When Pangram released its findings, Elliott adds, “the first thing I did was I typed in the title of our paper because I wanted to know whether my student’s gut instinct was correct”. The suspect peer review, which Pangram’s analysis flagged as fully AI-generated, gave the manuscript the lowest rating, leaving it “on the borderline between accept and reject”, says Elliott. “It’s deeply frustrating”.

Repercussions

The ICLR 2026 team permitted authors and reviewers to use AI tools to polish text, generate experiment codes or analyse results, but mandated disclosure of such uses. It also prohibited AI use that would have breached the confidentiality of manuscripts or produced falsified content.

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Nature 648, 256-257 (2025)

doi: https://doi.org/10.1038/d41586-025-03506-6

Updates & Corrections

- Correction 01 December 2025: This story has been amended to clarify how Pangram described the model in a preprint.

References

1. Thai, K., Emi, B., Masrour, E. & Iyyer, M. Preprint at arXiv https://doi.org/10.48550/arXiv.2510.03154 (2025).

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NEWS 20 November 2025

Has the mysterious ‘compass’ organ of birds been found at last?

Multiple lines of evidence suggest that pigeons sense magnetic fields by detecting electric currents in their inner ears.

By

Davide Castelvecchi

Credit: Suriya Silsaksom/Alamy

Pigeons can sense Earth’s magnetic field by detecting tiny electric currents in their inner ears, a team of researchers suggests. Such an inner compass could help to explain how certain animals can achieve astonishing feats of long-distance navigation.

The team performed advanced brain mapping as well single-cell RNA sequencing of pigeon inner-ear cells. Both lines of evidence point to the inner ear as the birds’ ‘magnetoreception’ organ. The results were published in Science on 20 November [1].

“This is probably the clearest demonstration of the neural pathways responsible for magnetic processing in any animal,” says Eric Warrant, a sensory biologist at Lund University in Sweden. Studies have suggested that various animals, including turtles, trout and robins, can sense the direction and strength of magnetic fields, although the evidence has sometimes been contested — and the mechanisms have remained controversial.

Bird-brained navigation

Two leading hypotheses have guided research into how birds sense magnetic fields. One is based on a quantum-physics effect in retinal cells in which birds ‘see’ magnetic fields. The other hypothesis is that microscopic iron oxide particles in the beak could act as tiny compass needles. However, it’s largely unknown where magnetic information is sensed in animals’ brains and how sensory neurons confer sensitivity to electromagnetic changes.

In 2011, researchers found hints that magnetic fields triggered pigeons’ vestibular system, which enables vertebrates to sense accelerations (including gravity) and helps them to stay balanced[2]. The structure is made of three fluid-filled loops which are mutually perpendicular, so they can communicate the direction of an acceleration to the brain by breaking it down into three x, y and z components.

In the present study, David Keays, a neuroscientist at Ludwig Maximilian University of Munich in Germany, and his colleagues designed an experiment that could reveal how pigeons’ brains respond to magnetic fields.

Keays’ team exposed pigeons to a magnetic field slightly stronger than Earth’s for more than an hour. The birds’ heads were immobilized and the magnetic field was continually rotated to simulate the heads’ motions with respect to Earth’s geomagnetic field.

Next, the team used a method for measuring activation patterns of neurons across the brain — by measuring a genetic marker of cell activity in pigeon brains, which were made transparent by a technique called clearing. Maps of brain activity in birds that had been exposed to magnetic fields were compared with a control group that had not been exposed to magnetic fields.

The results showed neuronal activity related to magnetic fields in the brain region that receives input from the vestibular system, as well as in regions that help to integrate various sensory stimuli. This result narrowed down the list of potential compasses to one — the vestibular system — although it did not explain how pigeon neurons can physically sense magnetic fields.

A magnetic sense organ

In principle, a conducting material in an organism could produce electric currents in response to magnetic fields, giving an animal a ‘magnetic sense’ — a mechanism that was proposed as early as 1882 by French zoologist Camille Viguier[3].

In previous research, Keays had looked for a molecular mechanism of this magnetoreception by following inspiration from the biophysics of sharks and skates, which have organs that sense minute electric fields to help them find prey[4]. These animals express a protein that is sensitive to changes in neurons’ electrical activity. They have a 10-amino-acid-long insertion that allows them to sense electric currents that are generated from magnetic fields.

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Nature 648, 257-258 (2025)

doi: https://doi.org/10.1038/d41586-025-03798-8

References

1. Nordmann, G. C. et al. Science https://doi.org/10.1126/science.aea6425 (2025).

2. Wu, L.-Q. & Dickman, J. D. Curr. Biol. 21, 418–423 (2011).

3. Viguier, C. Rev. Phil. France Etranger 14, 1–36 (1882).

4. Bellono, N. W., Leitch, D. B. & Julius, D. Nature 558, 122–126 (2018).

5. Nimpf, S. et al. Curr. Biol. 29, 4052–4059 (2019).

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NEWS 26 November 2025 Correction 27 November 2025

AlphaFold is five years old — these charts show how it revolutionized science

Since it was unveiled in 2020, Google DeepMind’s game-changing AI tool has helped researchers all over the world to predict the 3D structures of hundreds of millions of proteins.

By

Ewen Callaway

An AlphaFold model of Tmem81, a membrane protein involved in the fusion of egg and sperm.Credit: Google DeepMind/EMBL-EBI (CC-BY-4.0)

For nearly a decade, Andrea Pauli, a biochemist at the Research Institute of Molecular Pathology in Vienna, has been trying to work out how sperm and egg get together.

In 2018, her laboratory found a protein on the surface of zebrafish (Danio rerio) eggs, called Bouncer, that was essential for fertilization. But Pauli’s team and others struggled to show how Bouncer recognized sperm cells. Then a revolution happened.

Five years ago, in late November 2020, researchers at London-based Google DeepMind unveiled AlphaFold2. The artificial-intelligence tool for predicting protein structures generated stunningly accurate 3D models that, in some cases, were indistinguishable from experimental maps, dominating a long-running structure-prediction challenge. The first version of AlphaFold was announced in 2018, but its predictions weren’t nearly as good as its successor, which limited its impact.

The 2021 release of AlphaFold2’s code and a database that has swelled to hundreds of millions of predicted structures mean that scientists can now get a reliable prediction for almost any protein.

“Having models for anything has had a huge impact,” says Janet Thornton, a bioinformatician at the European Bioinformatics Institute in Hinxton, UK, part of the European Molecular Biology Laboratory (EMBL–EBI). “It’s like the second coming of structural biology.”

Rapid discovery

For Pauli’s team, the software shone a light on a path they might otherwise never have found. The model predicted that a protein, called Tmem81, stabilizes a complex of two other sperm proteins, creating a pocket for Bouncer to bind to[1]. Experiments backed up the tool’s predictions. AlphaFold “speeds up discovery”, says Pauli. “We use it for every project.”

Source: OpenAlex/Google DeepMind

Her team’s paper about this, published in 2024, is one of nearly 40,000 journal articles to cite the 2021 Nature paper describing AlphaFold2[2]. Unlike many other highly cited life-sciences and biomedical papers from the same period, including seminal reports about the COVID-19 pandemic, interest in AlphaFold doesn’t seem to be slowing down (see ‘Peak citations’).

DeepMind’s John Jumper — who shared half of the 2024 Nobel Prize in Chemistry with chief executive Demis Hassabis for developing AlphaFold — says he is “deeply proud” of how useful the tool has been for scientists such as Pauli. “When will someone win one of these major awards because they used AlphaFold?” he wonders.

Part of AlphaFold2’s rapid impact is down to its accessibility, say researchers. Google DeepMind made the underlying code and other parameters freely available to scientists, and it quickly became possible for them to run the software themselves at scale: this is what Pauli’s team did.

Source: AlphaFold Protein Structure Database

Some 3.3 million users in more than 190 countries have accessed the AlphaFold database (AFDB), which is hosted by EMBL–EBI and contains more than 240 million structural predictions, encompassing most known proteins. More than one million AFDB users come from low- and middle-income countries, including China and India (see ‘Global appeal’).

Protein-structure revolution

The field in which AlphaFold seems to have made its biggest impact is structural biology. Researchers who used AlphaFold submitted around 50% more protein structures to a repository of experimental models, called the Protein Data Bank (PDB), than did a non-AlphaFold-using ‘baseline’ of structural-biology researchers, finds a Google DeepMind-funded study of AlphaFold’s impacts released this week. AlphaFold2 use was also associated with higher rates of PDB submissions than those of researchers using other ‘frontier’ methods in AI, structural biology and protein structure prediction (see ‘Protein pile-up’).

Source: AI in science: Emerging evidence of impact from AlphaFold2

Jumper says he is especially gratified that AlphaFold2 — which was trained using PDB data — has proved so useful for deducing protein structures. The predicted structures can help researchers to make sense of raw data generated by X-ray crystallography and cryo-electron microscopy. “I love that it helps the people that gave us the data,” Jumper adds.

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Nature 648, 258-259 (2025)

doi: https://doi.org/10.1038/d41586-025-03886-9

Updates & Corrections

- Correction 27 November 2025: A previous version of this article misstated the number of studies and scientists included in the Innovation Growth Lab’s analysis of AlphaFold’s impacts. These figures have now been corrected.

References

1. Deneke, V. E. et al. Cell 187, 7066–7078 (2024).

2. Jumper, J. et al. Nature 596, 583–589 (2021).

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NEWS FEATURE 10 December 2025

Is your brain tired? Researchers are discovering the roots of mental fatigue

Better ways to measure cognitive exhaustion could point to treatments for long COVID and other debilitating disorders.

By

Lynne Peeples

Illustration by Patrycja Podkościelny

Near the end of his first series of chess matches against IBM’s Deep Blue computer in 1996, the Russian grandmaster Garry Kasparov lamented what he saw as an unfair disadvantage: “I’m really tired. These games took a lot of energy. But if I play a normal human match, my opponent would also be exhausted.”

Whereas machine intelligence can keep running as long as it has a power supply, a human brain will become fatigued — and you don’t have to be a chess grandmaster to understand the feeling. Anyone can end up drained after a long day of work, at school or juggling the countless decisions of daily life. This mental exhaustion can sap motivation, dull focus and erode judgement. It can raise the odds of careless mistakes. Especially when combined with sleep loss or circadian disruption, cognitive fatigue can also contribute to deadly medical errors and road traffic accidents.

It was partly Kasparov’s weary comments that inspired Mathias Pessiglione, a cognitive neuroscientist and research director at the Paris Brain Institute, to study the tired brain. He wanted to know: “Why is this cognitive system prone to fatigue?”

Researchers and clinicians have long struggled to define, measure and treat cognitive fatigue — relying mostly on self-reports of how tired someone says they feel. Now, however, scientists from across disciplines are enlisting innovative experimental approaches and biological markers to probe the metabolic roots and consequences of cognitive fatigue.

The efforts are getting a boost in attention and funding in large part because of long COVID, which afflicts roughly 6 in every 100 people after infection with the coronavirus SARS-CoV-2, says Vikram Chib, a biomedical engineer at Johns Hopkins University in Baltimore, Maryland. “The primary symptom of long COVID is fatigue,” says Chib. “I think that has opened a lot of people’s eyes.”

Chib and others hope that a fundamental understanding of cognitive fatigue will help the billions of people who face it from time to time, as well as the tens of millions who carry it as a more extreme and chronic companion. As well as being common in long COVID, debilitating fatigue is a symptom of chronic fatigue syndrome, also known as myalgic encephalomyelitis (ME/CFS), post-traumatic stress disorder, multiple sclerosis, depression and Parkinson’s disease. Extreme mental exhaustion can also follow cancer treatment, head injury, stroke or exposure to certain toxins.

“Fatigue is a really big problem,” says Chib. “We really need to figure this out — how to study it and how to intervene.”

What is cognitive fatigue?

At the start of a chess match, a professional player might rely on well-rehearsed openings. “The first five, six or seven moves can be done without thinking,” says Pessiglione. But when there’s an unfamiliar position on the board, the player no longer has a ready routine. They are “required to think”, he says. The same is true for a driver who turns on to an unfamiliar street. On roads they’ve been down hundreds of times, mental autopilot can kick in. But if they take an unknown route, Pessiglione says, the demands on the brain intensify.

Cognitive control is the term that scientists give to this effortful directing and regulating of thought. Over time, as a leading theory goes, maintaining control becomes costly for the brain, and fatigue emerges. Scientists aren’t entirely sure why. Some think it is related to how cells cope when their energy supply is strained; others point to a build-up of toxins from neural activity[1]. But researchers tend to agree that the sensation of fatigue is protective — a warning that the brain is nearing a physiological boundary and it’s time to rest.

During chess matches in 1996 and 1997, Russian grandmaster Garry Kasparov grew tired, unlike his opponent, IBM’s Deep Blue computer.Credit: Stan Honda/AFP via Getty

Molecular players across several brain regions might be involved, scientists say. Researchers have found potential links between cognitive fatigue and changing levels of metabolites such as glucose and lactate, neurochemical messengers such as glutamate and adenosine, and a protein involved in learning and memory called brain-derived neurotrophic factor[2]. Even amyloid-β, a protein fragment associated with Alzheimer’s disease, might contribute by disrupting synapses, interfering with the clearance of glutamate or increasing neuroinflammation[3]. But it is uncertain what is a marker and what is a cause.

Cognitive neuroscientist Clay Holroyd at Ghent University in Belgium is among the researchers who favour the toxic-build-up theory of cognitive fatigue. This idea has been gaining traction over the past five years or so, although it’s not yet clear what the waste metabolite is. He likens the sensation of fatigue to pain: both have a role in protecting the body from accumulating damage.

But even if a person ignores the sensation at first, he says, there’s little risk of real metabolic harm in most cases. “We have an automatic fail-safe,” he says. “You can work really, really, really hard for a time, but eventually you’re going to need to go to sleep.” Although taking a break from a task can offer temporary relief, sleep has a much more restorative role. Sleep, especially slow-wave deep sleep, acts as the brain’s nightly maintenance. It clears out metabolic debris and recalibrates circuits and cells so that they can best use energy reserves.

Seeking better measures

Conventionally, cognitive fatigue has been quantified either by asking a person to report their own levels of fatigue or by detecting a change in their performance on working-memory tests or other tasks. These are not great measurements, scientists say. Drops in performance can be obscured by factors such as motivation, boredom and frustration. Performance can also be offset by training, such as when a chess player automates a sequence of moves.

Self-reports, meanwhile, are subjective and unreliable. “People are terrible judges of their own fatigue,” says Daniel Forger, a researcher in computational medicine at the University of Michigan in Ann Arbor, who is investigating new ways to assess cognitive fatigue.

To better understand fatigue, Pessiglione, Chib and other researchers are trying to bridge an understanding of its biochemical workings with how it affects motivation[4]. The current hypothesis: cognitive fatigue arises from metabolic changes in parts of the brain that are responsible for cognitive control. And those changes, whether resulting from depleted energy stores or amassed waste, alter how brain circuits weigh the costs and benefits of exerting mental effort — nudging decisions towards easier options that are more immediately rewarding[1].

In a 2022 study[5], Pessiglione and his team simulated a workday by asking otherwise healthy participants to spend several hours on either easy or hard versions of the same cognitive tasks. In one task, participants viewed letters appearing one after another on a screen and had to decide whether each new letter matched one a certain number of letters earlier. Recalling whether the letter on screen matched the third letter back, for example, would be much more difficult than recalling whether it matched the first letter back.

After this simulated workday, participants made choices between smaller immediate rewards and larger delayed ones. Those who had completed the harder tasks were more likely to opt for instant gratification. That preference was also consistent with greater accumulation of glutamate — one of the metabolites suspected to build up with cognitive exertion — in the lateral prefrontal cortex. This brain region is involved in executive functions, such as working memory and decision-making, and has been found to have lower activity after a hard day of simulated work[6].

Matthew Apps, a cognitive neuroscientist at the University of Birmingham, UK, says that the dynamics of dopamine — which interacts closely with adenosine, glutamate and other metabolic players in the brain — might help to explain the connection between neurometabolic strain and the experience of fatigue. Because dopamine enhances the perceived value of rewards, it typically boosts motivation to invest effort. He proposes that sustained effort might cause dopamine levels to drop, leaving people less willing to work for the same pay-off.

Together, these and similar lines of research are starting to reveal how levels of these molecules and measures of brain activity align with fatigue.

The bottom line, says Chib, is that there is “something happening with the chemistry of your brain” that changes your calculation on whether you should exert cognitive effort. He says that baseline chemistry will differ between people: “You and I might have different concentrations of neurotransmitters in our brain, and that inherent difference could make me feel very tired, whereas you’re able to persist.”

These, or similar differences in chemistry, might help to explain chronic and other extreme fatigue. In people with long COVID or ME/CFS, a small mental task can feel as intimidating as performing brain surgery.

For Ana Lia Tamariz, an artist and health-and-wellness coach in Miami, Florida, who has ME/CFS, simply listening to music or reading a book often requires immense effort. “Sometimes, I cannot read one more word,” she says. “Imagine coming out of anaesthesia from a surgical procedure groggy. Imagine you never exit that state.”

For her, the cognitive and physical fatigue can be hard to separate. Any cognitively demanding task can make her physically drained, she says. And anything physically demanding can leave her mentally spent. Tamariz says she is constantly doing the calculation: “Is this worth my energy?”

Research supports the idea that some shared mechanisms might drive both physical and cognitive fatigue, and that the two interact[7]. “If you run a marathon, yes, there is physical fatigue in your body,” says Apps. “But by God, you’re going to feel all kinds of cognitive fatigue as well from the strain and the concentration that’s required to maintain your performance.”

The reverse also seems to be true. In a preprint from last year, Chib’s team found that otherwise healthy participants were less willing to exert physical effort after performing a mentally taxing task[8].

Other researchers are studying the roles of stress, sleep, circadian rhythms and inflammation in cognitive fatigue, as well as the consequences. When the brain doesn’t get restorative sleep, small clusters of neurons can go briefly offline. These local sleep-like episodes can cause momentary lapses in attention and other slips in performance.

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Nature 648, 262-264 (2025)

doi: https://doi.org/10.1038/d41586-025-03974-w

References

1. Pessiglione, M., Blain, B., Wiehler, A. & Naik, S. Trends Cogn. Sci. 29, 730–749 (2025).

2. ElGrawani, W. et al. Cell Rep. 43, 114500 (2024).

3. Aschenbrenner, A. J. et al. Psychol. Aging 38, 428–442 (2023).

4. Steward, G., Looi, V. & Chib, V. S. J. Neurosci. 45, e1612242025 (2025).

5. Wiehler, A., Branzoli, F., Adanyeguh, I., Mochel, F. & Pessiglione, M. Curr. Biol. 32, 3564–3575 (2022).

6. Blain, B., Hollard, G. & Pessiglione, M. Proc. Natl Acad. Sci. USA 113, 6967–6972 (2016).

7. Hogan, P. S., Chen, S. X., Teh, W. W. & Chib, V. S. Nature Commun. 11, 4026 (2020).

8. Dryzer, M. & Chib, V. S. Preprint at bioRxiv https://doi.org/10.1101/2024.12.06.627274 (2024).

9. Mayer, C. et al. Cell Rep. Med. 6, 102001 (2025).

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Books & Arts

- What we eat is making us obese and sick — but science shows solutions are within reach

- Of masks and Mayans: Books in brief

- How the Royal Institution made science a seasonal spectacle

BOOK REVIEW 09 December 2025 Correction 09 December 2025

What we eat is making us obese and sick — but science shows solutions are within reach

An ambitious book challenges long-held assumptions on diet and nutrition and exposes gaps in public-health guidance.

By

Tim Spector

Research shows that many ultra-processed foods can hijack satiety signals and promote overeating. Credit: Violeta Stoimenova/Getty

Food Intelligence: The Science of How Food Both Nourishes and Harms Us Julia Belluz & Kevin Hall Avery (2025)

In 2019, Kevin Hall, a physicist turned nutrition researcher, published a landmark study[1]. In it, 20 adults ate one of two diets, which were identical in nutrients and differed only in their level of processing. Participants who ate ultra-processed foods (UPFs) consumed about 500 kilocalories more per day and gained weight, whereas those on a minimally processed diet lost weight. The results offered strong evidence that many industrially produced foods can override satiety signals and drive overeating. And it made Hall one of the most influential figures in nutritional science.

Understandably, expectations were high for his book, Food Intelligence, co-written with Canadian journalist Julia Belluz. It digs deeper into the implications of the 2019 study — that the harms of processed foods can’t be reduced to their fat, sugar or salt content alone, and that the prevalent government strategy of politely asking companies to tweak their recipes by cutting salt or sugar content, say, is unlikely to address rising obesity rates. Unfortunately, the execution only partly lives up to the promise.

In this wide-ranging primer on food science, Hall and Belluz revisit many food-related misconceptions. They debunk the idea that cutting 500 kilocalories a day reliably leads to the loss of half a kilogram a week and that “broken metabolism” explains obesity — as Hall showed in his studies on contestants who participated in The Biggest Loser, a reality television programme built around extreme weight loss.

The authors challenge the current obsession with protein, noting that most people already consume enough through ordinary diets. They are equally dismissive of the booming supplements industry, arguing that many products lack clinical evidence or have been shown to offer no real benefit. Their scepticism extends to continuous glucose monitoring in people without diabetes, which they warn might provoke needless anxiety without providing clear advantages. The critique culminates in a forceful take down of the personalized-nutrition industry — diet plans based on genetics, which they argue have no solid scientific basis.

Limited legislation

By tracing the origins of the limited control the US Food and Drug Administration (FDA) exerts over food additives and supplements, the authors provide valuable context for why the US food environment is particularly problematic. The Dietary Supplement Health and Education Act of 1994 ensured that dietary supplements do not require premarket approval. The FDA also allows companies to introduce additive chemicals into food if these are merely ‘generally recognized as safe’.

This lax regulatory framework, shaped heavily by food-industry lobbying, stands in stark contrast to the stricter regimes in much of Europe and Latin America. Some countries now warn the public about highly processed foods, yet nutrition-guideline committees in the United States and United Kingdom still decline to mention them as potentially harmful, even as the FDA has been asked to consider the issue in its upcoming review. The status quo persists despite multiple observational studies, Hall’s influential 2019 clinical trial and studies that have replicated his findings.

Nutrition researcher Kevin Hall dispels widely held misconceptions about food.Credit: Mark Schiefelbein/AP Photo/Alamy

In terms of solutions, the book argues that “personal responsibility” plays little part in nutrition — a point that, if pushed too rigidly, can feel disempowering. The authors insist that the real challenge lies in reshaping the “toxic food environment” that drives overconsumption. They call for tighter regulation and greater transparency on additives, reformulation of industrial products, and taxes on ultra-processed foods to shift diets towards whole foods, fruit and vegetables.

It’s a powerful message, and one that deserves wider attention, even if the book’s practical diet suggestions are underwhelming: eat less meat, eat more fruit and vegetables, and store junk food out of sight.

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Nature 648, 265-266 (2025)

doi: https://doi.org/10.1038/d41586-025-03977-7

Updates & Corrections

- Correction 09 December 2025: In a previous version of this story, Kevin Hall was described as an adviser on The Biggest Loser. This has now been corrected.

References

1. Hall, K. D. et al. Cell Metab. 30, 67–77 (2019).

2. Sclafani, A. & Springer, D. Physiol. Behav. 17, 461–471 (1976).

3. Gardner, C. D. et al. JAMA 319, 667–679 (2018).

Competing Interests

Tim Spector is the co-founder of a science and nutrition company called ZOE. He has also published books on related topics, such as Food for Life: The New Science of Eating Well.

BOOK REVIEW 21 November 2025

Of masks and Mayans: Books in brief

Andrew Robinson reviews five of the best science picks.

By

Andrew Robinson

The Mask

Bruno J. Strasser & Thomas Schlich Yale Univ. Press (2025)

“Masks have signified hope and despair, courage and cowardice, a sense of community and a sense of selfishness.” All of these emotions — known to those who experienced the COVID-19 pandemic — underpin this engrossing, finely illustrated account by historians Bruno Strasser and Thomas Schlich (who was previously a physician). Their discussions cover theatrical performances in ancient Greece, plagues and gas attacks in the First World War and present-day urban smog and surgery, while addressing the crucial issue of mask efficacy.

The Maya Myths

Mallory E. Matsumoto Thames & Hudson (2025)

Deciphering Mesoamerica’s ancient Maya hieroglyphs was a fascinating achievement of the twentieth century. But “about one-third” of some 1,000 distinct hieroglyphs “remain to be deciphered”, notes anthropologist Mallory Matsumoto in her intriguing book about ancient Maya myths. The logical structure of the Maya calendar, which could accurately predict astronomical phenomena such as eclipses, is clear, as is the Maya’s preoccupation with the natural world. But their beliefs — which included human sacrifice — are not.

Outcast

Oliver Basciano Faber (2025)

Leprosy has had a complex, confusing history even after its causative bacterium was identified in 1873. In this gripping account, journalist Oliver Basciano quotes a 1960 novel by Graham Greene, A Burnt-Out Case: “What strange ideas people have about leprosy, doctor.” “They learn about it from the Bible, like sex.” Basciano journeys from Brazil to Japan and Mozambique in search of insights. He concludes that today’s grim image of leprosy stems from a nineteenth-century myth created to justify outcasting those affected.

Irrational Together

Adam S. Hayes Univ. Chicago Press (2025)

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Nature 648, 269 (2025)

doi: https://doi.org/10.1038/d41586-025-03868-x

Competing Interests

The author declares no competing interests.

ESSAY 08 December 2025

How the Royal Institution made science a seasonal spectacle

From flaming raisins to robots and rockets, the institution’s Christmas Lectures have educated and entertained for two centuries.

By

Philip Ball

Space scientist Maggie Aderin-Pocock helped to develop the James Webb Space Telescope. Credit: Tristan Bejawn/Guardian/eyevine

For science enthusiasts in the United Kingdom, the Christmas Lectures at the Royal Institution (RI) are as much a part of the season’s celebration as are Christmas trees and carol singing. These iconic talks for a young audience, celebrating their 200th anniversary this year, have introduced many people to the delights of science through captivating demonstrations. Space scientist Maggie Aderin-Pocock is the next speaker to take to the floor, delivering this historic lecture series this week.

Held in the RI’s famous lecture theatre on Albemarle Street in London, the lectures began in 1825 as one of London’s most fashionable educational spectacles. In theory, the lectures were open to anyone “who wanted to improve their minds”, says Charlotte New, the RI’s head of heritage and collections. But, although the ticket price wasn’t prohibitively high, it was enough to ensure a well-heeled and genteel audience. As the writer George Eliot observed in 1851, the lectures were “as fashionable an amusement as the Opera”.

The RI was founded in 1799 by scientist Benjamin Thompson and botanist Joseph Banks as an organization to introduce new technologies and teach science to the general public through lectures and demonstrations. It soon also became a research institution with its own laboratories, in which chemist Humphry Davy, who was appointed director of the chemical laboratory in 1801, made groundbreaking discoveries about new chemical elements. Davy also presented many of the public lectures, and his flamboyant style brought them wide renown.

When Davy’s former assistant Michael Faraday took over as laboratory director in 1825, he faced the formidable task of living up to his mentor’s legacy. Once a bookbinder’s apprentice, Faraday had already come to rival Davy as a researcher, notably through his work on electromagnetic induction, which led to the invention of the electric motor. Soon enough, he proved himself to be his predecessor’s equal behind the lecture podium, too.

“Very little information exists in the archives to describe why the lectures were developed,” says New. The first series was delivered in 1825 by John Millington, the RI’s professor of mechanics. Originally, the series were much more extensive than today’s, comprising a set of 22 lectures on natural philosophy that were, according to the institute’s management minutes, “suited to a juvenile auditory, during the Christmas, Easter, and Whitsuntide recesses”. (Here, ‘juvenile’ probably referred to people aged 15 to 20 — older than the current target audience of schoolchildren, typically aged 11 to 17.)

Science in action

Initially, Faraday tried to avoid getting roped in as a speaker, but in 1827 he relented, delivering his first series on the topic of chemistry. Before long, he became the default Christmas lecturer, presenting 19 series over the next four decades and shaping the format that persists today. He mastered the art of live demonstration. “He never told his listeners of an experiment, he always showed it,” wrote Lovell Reeve, a dealer of natural-history objects, in 1863. The Illustrated London News declared in 1861: “There can be no greater treat to any one fond of scientific pursuits than to attend a course of these lectures.”

“If you look at his lecture notes, they are laid out almost like a theatre script,” says Katy Duncan, a postdoctoral research fellow at the RI. “Demonstrations like stage directions on the left leaf, and the script on the right.”

Faraday’s most famous series, The Chemical History of a Candle (delivered between 1860 and 1861), turned an everyday object into a profound exploration of combustion, capillary action and electrolysis. His playful use of the party game snapdragon — in which players are dared to snatch flaming raisins from a bowl of brandy and eat them without getting burned — perfectly embodied his belief that science should inspire wonder.

The lectures were soon published in Chemical News by chemist William Crookes, and subsequently as a book with elegant illustrations, which was received as an exemplar of popular science. The Chemical History of a Candle, wrote the Glasgow Herald in 1861, “will be eagerly welcomed by many readers who turn in despair from the dry chronicles of scientific terms called popular works, but which, in many instances, are about as interesting as street directories”.

Over the following decades, RI professors such as John Tyndall, James Dewar and William Henry Bragg continued the tradition, although wartime interruptions paused the series between 1939 and 1942 — for safety reasons and because evacuations meant there were few children in London to attend.

Although the initial lectures reflected the RI’s focus on chemistry, by the early twentieth century topics had broadened — evolutionary biologist Edwin Ray Lankester gave lectures on ‘extinct animals’, physicist William Henry Bragg on ‘the world of sound’ and physiologist Archibald Hill on ‘nerves and muscles’.

The 1932 Christmas Lectures were given by physicist Alexander Rankine.Credit: Daily Herald Archive/SSPL/Getty

In 1949, one of the lectures was televised for the first time, delivered by psychologist Frederic Bartlett. Despite occasional tension with the British Broadcasting Corporation (BBC) — especially after a financial scandal involving the laboratory director Edward Andrade in the early 1950s — the televised lectures (filmed live) soon became a national institution. “The RI’s attitude to working with the BBC on these broadcasts was generally cooperative so long as the BBC did not inconvenience the day-to-day running of the institution as a social club for its members,” says Rupert Cole, a former curator at the Science Museum in London.

The postwar years brought cultural tensions to the RI, because the atomic bomb and rising environmental fears made the public adopt a more sceptical view of science’s role in society. Such tensions came to the fore in the Christmas Lectures of 1974, given by electrical engineer Eric Laithwaite. Framed around an Alice-in-Wonderland theme and infused with a then-fashionable dose of Eastern philosophy, the series culminated in Laithwaite’s demonstration of an alleged ‘anti-gravity’ device based on gyroscopes. The response from other scientists was predictably hostile, and Laithwaite was subsequently ostracized from the scientific establishment.

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Nature 648, 267-269 (2025)

doi: https://doi.org/10.1038/d41586-025-03976-8

Competing Interests

The author declares no competing interests.

Opinion

- Darleane C. Hoffman obituary: chemist who expanded the periodic table

- Food will be more affordable — if we double funds for agriculture research now

- How to get science back into policymaking

OBITUARY 03 December 2025

Darleane C. Hoffman obituary: chemist who expanded the periodic table

Her experiments on the heaviest elements deepened our understanding of radioactivity.

By

Dawn Shaughnessy

Credit: Lawrence Berkeley National Laboratory

Darleane Hoffman was a trailblazing nuclear chemist whose work helped to extend the periodic table and deepen our understanding of the heaviest elements. The transuranic elements — those with an atomic number higher than uranium’s 92 — are all unstable and radioactive. Her discovery of naturally occurring plutonium-244 overturned the long-held premise that uranium-238 was the heaviest element found in nature. Her research influenced our understanding of nuclear fission, advanced cancer therapies and improved nuclear-waste-management protocols. She has died aged 98.

One of her proudest achievements was validating the discovery of element 106, later named seaborgium in honour of her friend and mentor, Glenn Seaborg. Beyond her landmark discoveries, Hoffman will also be remembered for her advocacy for women in science.

Born in Terril, Iowa, Hoffman developed an early fascination with science — encouraged by her father, a school principal who taught mathematics. She began studying applied art at Iowa State College in Ames, but switched to chemistry, inspired by her teacher Nellie Naylor and physicist Marie Curie, who attained global renown for her work on radioactivity. Hoffman was drawn to nuclear chemistry and the excitement of a field still in its infancy. Later, she would tell her students that she was often the only woman in her university chemistry classes.

After earning her doctorate in nuclear chemistry in 1951, Hoffman began her career at Oak Ridge National Laboratory in Tennessee, before joining the Los Alamos National Laboratory in New Mexico, where she became the first female division leader in 1979. Her husband Marvin Hoffman, a nuclear physicist, had been a fellow graduate student and collaborated in her early research. She detected plutonium-244 in 1971 while analysing rock samples from California’s Mountain Pass mine. Before this discovery, scientists thought that all elements heavier than uranium had to be created artificially in particle accelerators.

Hoffman further advanced the field by isolating fermium-257 and showing that it could split into two fragments of similar size — an unexpected result at the time, because fission was thought to produce uneven fragments. Her findings, initially met with scepticism, forced scientists to rethink how fission works.

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Nature 648, 270 (2025)

doi: https://doi.org/10.1038/d41586-025-03969-7

Competing Interests

The author declares no competing interests.

COMMENT 09 December 2025

Food will be more affordable — if we double funds for agriculture research now

A global drop in public and private investment in agricultural science in the past four decades is partly to blame for high food prices, an analysis reveals.

By

Philip G. Pardey,

Connie Chan-Kang,

Gert-Jan Stads,

Yuan Chai,

Julian M. Alston,

Jan Greyling &

…

Hernán Muñoz

Terraced rice fields in Thailand. Credit: Narathip Ruksa/Getty

Food prices are increasing almost everywhere. Disruptions and declines in food production owing to climate extremes are part of the reason[1],[2]. But our analysis of global spending on the innovations that underpin food production and the processes that get it to people’s tables shows major shifts in investment in agricultural science. These could help to explain why demand for food is getting out of balance with supply — and why things are likely to get worse.

From 1980 to 2021, the world’s population increased by almost 80% (by 3.5 billion people). Owing to agricultural science, food and other farm products have become more plentiful over this period for most people on the planet — by no means all.

Our analysis of public and private spending on research and development in agriculture and food (agrifood R&D) for 150 countries from 1980 until 2021 shows an alarming trend, however. Between 2015 and 2021, the annual average rate of growth in total ‘real spending’ on agrifood R&D over 6 years was one-third less than it was during the 35 years between 1980 and 2015. (Real spending refers to spending adjusted for differences in the purchasing power of money among countries and over time; see also Supplementary information.) When comparing these two time periods, growth in absolute spending has slowed for more than half of the world’s countries. In one-third of them, spending has even declined. This has happened even though demand for food and other agricultural products continues to increase, thanks to growing populations and rising incomes[3].

The countries and sectors that are investing most in agrifood R&D are changing, too. In 1980, the public sector, including government agencies and universities, was responsible for two-thirds of the world’s spending on this research area. By 2021, private-sector spending had caught up with that from the public sector. And whereas high-income countries were the top spenders in 1980, by 2021, middle-income countries had overtaken high-income ones. Today, the Asia-Pacific region is responsible for half of the world’s spending on agrifood R&D (see ‘Changing spending habits’).

Source: Analysis by P. G. Pardey et al.

Early signs of these shifts were evident in 2016 when we conducted a similar analysis of R&D spending from 1980 to 2011 in 130 countries[4]. Still, we were surprised by the extent and speed of the changes since then — particularly the widespread slowdown in spending.

It generally takes years or decades until spending on agrifood R&D widely benefits farmers and consumers. So a slowdown in the growth of R&D funding, or an overall decline, will eventually mean higher food prices for decades to come and increased pressures on the natural resources that underpin food production. Likewise, the shifting balance in spending by the public and private sector and by high- and middle-income countries will affect what kind of research gets done, and which producers and consumers around the world benefit from the resulting innovations.

Some of these trends must be reversed — fast — if the world’s farmers are to have any chance of sustainably meeting the expected growth in demand for food, animal feed, textile fibres and agriculturally sourced fuel by 2050 (the relevant timeline given the R&D lags that are at play[5]).

Three seismic shifts

Although the growth has come with important environmental and societal downsides as well as upsides, the real value of agricultural output increased by 137% — from $1.69 trillion to $4.15 trillion (in international dollars)[6] between 1980 and 2021.

The rise in agricultural output over the past 40 years comes mainly from improved production systems, such as those for cotton in China (left) and milk in Austria.Credit: Tao Weiming/VCG via Getty; Simone Padovani/Getty

Around 96% of this increase in production has come from increasing the amounts of crops, meat, milk and other agricultural outputs produced per unit of land. (The other 4% is from expanding how much land is used.) And these productivity gains are mostly the result of increasing the amounts of fertilizers, seeds, machinery and other inputs used per unit of land; improving the quality of such inputs; and increasing the size and specialization of farms. All of those changes have been enabled by public and private investment in agrifood R&D[7].

Three shifts in the global investment in agricultural science are changing the picture, however.

Spending slowdown

Our analysis of statistical reports, studies of R&D investments, company annual reports, government-agency databases and other sources show that between 2015 and 2021, the growth in real public and private sector spending on agrifood R&D combined was around 1.9% per year. From 1980 to 2015, it was 2.7% per year.

Comparing these two time periods, for the 38 high-income countries in our analysis (as a group), the growth rate in R&D spending has fallen from 2% to around 1% per year (see ‘Slowdown in global spending on agricultural science’). As with the worldwide pattern, rates of growth in spending have slowed in nearly half of these countries, and almost one-quarter of them have reduced their public spending on agrifood R&D.

Source: Analysis by P. G. Pardey et al.

In the 67 middle-income countries, the rate of growth in spending was 3.8% per year in 1980–2015. In 2015–21, it was just 2.7% per year. Of these countries, 39 (58%) have slowed their rates of growth in spending and 19 (28%) have reduced their spending. Meanwhile, for the 21 low-income countries in our analysis, growth in spending on agrifood R&D dropped from 2.3% per year before 2015 to 1.7% per year afterwards. More than half (57%) of these countries have reduced their real spending since 2015.

Rise of middle-income countries

In 2021, middle-income countries produced about 73% of the world’s agricultural output (up from around 56% in 1980), with China, India and Brazil accounting for 41% of the 2021 total[6]. Today, these three nations are among the top five agrifood R&D spenders. The United States now lags well behind China on this metric[8]. For public-sector research, the United States is behind India, too.

Also, fewer countries are now responsible for a larger share of the total (public and private) spend on agrifood R&D. And the difference in spending between low-income countries and the rest of the world is increasing. In 2021, the top ten countries in R&D spending accounted for 69% of the global total — up from 66% in 1980. Meanwhile, the share of spending for the bottom 50 countries fell from around 1% in 1980 to 0.5% in 2021.

Rise of the private sector

The global slowdown in public agrifood R&D spending growth has coincided with a larger contribution from the private sector, including many small and all the large agrifood corporations. In 2021, private firms accounted for nearly 50% of the global spend on agrifood R&D, up from around 32% in 1980. And this trend is not confined to high-income countries. Private R&D spending now makes up 54% of the total R&D spend in upper-middle-income countries — up from 15% in 1980.

All of these changes are happening because of multiple political and socio-economic influences.

Spending on agrifood R&D has increased in upper-middle-income countries probably because food insecurity is a high policy priority for these economies, with their vast populations and relatively recent experiences of widespread hunger. Conversely, complacency and shifting priorities are probably what’s causing spending in many high-income nations, particularly by the public sector, to stagnate or shrink.

This complacency seems to be setting in even though, on average, each dollar invested in agrifood R&D yields a total social return of $10 (in present value terms and counting benefits to both producers and consumers), and often much more[9],[10]. But agricultural R&D is slow to take effect and most people and their political representatives are impatient. Certainly, in the United States, agrifood R&D tends to receive less political support compared with farm subsidy or other programmes that have more immediate impacts on farmers and consumers[11].

As economies develop, farms become more reliant on technology and less reliant on labour. Also, people’s diets change as their incomes increase, with processed food or restaurant food often being favoured over meals prepared at home. These changes incentivize private-sector investment in R&D across the entire food-supply chain, but especially for innovations related to transporting, processing or retailing food and new food products. In 2021, R&D related to food processing, storage and logistics made up 58% of all agrifood R&D in high- and upper-middle-income countries. In fact, in the United States today, 90 cents of every dollar spent on food pays for these post-farm activities[6].

Trouble ahead

So what do these trends mean for the future?

It generally takes decades for the benefits from investments in agrifood R&D to be fully realized[5]. After the 6–10 years it takes to breed new varieties of wheat or soya beans, for instance, several more years are needed to produce enough seed to sell them commercially. It can then take years or decades for the new varieties to be adopted at scale across farmers’ fields for a host of reasons. These include a lack of economic incentives or transportation infrastructure, and underdeveloped links between farms, suppliers of inputs (seeds and fertilizer) and downstream food transporters, processors and traders.

Also, because of biological and physical constraints, such as limits to how efficiently plants can convert sunlight, water and other crop inputs into biomass, humanity has generally managed to increase crop and livestock yields only linearly, not exponentially. This means that any absolute increase in crop or animal yields (such as milk or meat production per animal) as a proportion of current yield or current production shrinks over time.

For example, our analysis shows that in 1961, it took just 12 years to increase global average wheat yields by 50%. Looking back from 2022, increasing global average wheat yields by 50% took 31 years. For rice yields, it took 40 years (compared with 20 in the 1960s). For soya bean yields, it took 34 years (compared with 16 in the 1960s; see go.nature.com/3m7fp2t). And today, owing to climate change and depleted natural resources, it is becoming increasingly difficult to sustain yields, let alone achieve even a constant absolute annual increase in agricultural productivity.

Workers check harvested carrots on a sorting line in Laixi, China.Credit: Zhang JinGang/Feature China/Future Publishing via Getty

Countries need to be increasing their rates of annual investment in agrifood R&D just to sustain the current rates of growth in farm productivity. It will take decades for the harmful consequences of current R&D spending slowdowns to be realized, including increased environmental damage, poverty, malnutrition and civil or military strife. And it will take many more years to undo the damage from the recent slowdowns in R&D spending.

A slowdown in agrifood innovation —whether it entails developing better ways of managing water, soil health or pests, developing crop varieties, animal breeds or better systems for storing, processing and transporting food — is already driving up food prices. Further cutbacks in science and technology that result from governments ramping up their spending in other areas, such as defence, or looking to trim their overall budgets following heightened spending during the COVID-19 pandemic, will eventually result in a resurgence of hunger and malnutrition and further undermine the health of the environment.

The increased contribution by the private sector to total global spending on agricultural science is encouraging. But private companies cannot fill the gap in public spending. Corporations tend to focus on the patentable farming and food-manufacturing technologies that they can sell to farmers and those engaged in supply-chain activities and processes. Such technologies, developed on the back of fundamental discoveries made through publicly funded research, are more directly linked to the commercialization of farm products. Consequently, cutting publicly funded R&D slows overall progress and reduces the effectiveness of private innovation.

The shifts in where agrifood R&D is being done are concerning, too, because technologies developed in one country are not necessarily deployed in another as effectively or easily. Also, it is unclear whether past patterns of technology transfer between countries will be sustained going forward.

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Nature 648, 271-274 (2025)

doi: https://doi.org/10.1038/d41586-025-03970-0

References

1. Kotz, M., Kuik, F., Lis, E. & Nickel, C. Commun. Earth Environ. 5, 116 (2024).

2. Rosegrant, M. W., Bryan, E., Thomas, T. S. & Wiebe, K. in Food Policy: Lessons and Priorities for a Changing World (eds Swinnen, J. & Barrett, C. B.) Ch. 4 (International Food Policy Research Institute, 2025).

3. Alston, J. M., Beddow, J. M. & Pardey, P. G. Science 325, 1209–1210 (2009).

4. Pardey, P. G., Chan-Kang, C., Dehmer, S. P. & Beddow, J. M. Nature 537, 301–303 (2016).

5. Wang, S., Alston, J. M. & Pardey, P. G. Econ. Innov. N. Technol. 34, 842–862 (2024).

6. Pardey, P. G., Alston, J. M., Greyling, J. C., Joglekar, A. B. & Chan-Kang, C. 2025 Agri-Food Innovation: From Ideation to Impact. ATIO Background Paper (UN Food and Agriculture Organization, in the press).

7. Pardey, P. G. & Alston, J. M. J. Econ. Hist. 8, 114–155 (2021).

8. Chai, Y. et al. Food Policy 86, 101729 (2019).

9. Alston, J. M., Pardey, P. G. & Rao, X. Am. J. Agric. Econ. 104, 502–529 (2022).

10. Rao, X., Hurley, T. M. & Pardey, P. G. Aus. J. Agric. Res. Econ. 64, 977–1001 (2020).

11. Pardey, P. G. & Smith, V. H. Waste Not, Want Not: Transactional Politics, Research and Development Funding, and the US Farm Bill (American Enterprise Institute, 2017).

12. Qaim, M. Appl. Econ. Perspect. Policy 42, 129–150 (2020).

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1. Contents

2. Methodology and raw data

Competing Interests

The authors declare no competing interests.

COMMENT 08 December 2025

How to get science back into policymaking

Misunderstanding and hubris have broken public trust in governments’ use of science, but it can be restored.

By

Diane Coyle &

Michael Kenny

Medical students talk to patients during a health screening event in California. Credit: Marcus Yam/Los Angeles Times via Getty

The idea that science should shape public policy is under serious attack. The massive funding cuts requested this year by the administration of US President Donald Trump, affecting US universities and leading scientific and research institutions, is one drastic demonstration. But there have been straws in the wind for some time.

Conspiracy theories spread by people opposed to vaccines and 5G mobile phone networks, and claims that the COVID-19 pandemic and climate change are hoaxes, tell us that scientific evidence has lost its standing among parts of the public and some politicians. This trend threatens to derail the contributions science can make to improving people’s lives. Think, for example, of the announcement in August that US funding for mRNA vaccine research would be slashed.

How to meet this challenge must be a priority for researchers and the institutions of science in 2026. Rebuilding support for evidence-based policymaking among voters and political decision makers will require researchers and universities to change their outlook and ethos. Academics must recognize that the importance of science is not self-evident, and that part of the blame for the erosion of trust in science lies with scientists themselves.

Here, we offer four recommendations for the scientific community and one for policymakers.

Mixed results

‘Evidence-based policymaking’ is talked about and championed by many policymakers and scientists. Yet, the process it entails and its limitations remain widely misunderstood. In public policy, solutions to the problems society faces are rarely, if ever, purely technical. People’s values and interests often conflict, and scientific studies do not always provide direct answers to the questions that politicians and officials must grapple with, such as how to reduce crime rates or respond to a disease outbreak.

The idea of evidence-based policy was taken forward vigorously after the end of the Second World War, especially in the United States, following the wartime success of science and operations research[1]. An influential 1945 report called ‘Science, The Endless Frontier’, by engineer and science administrator Vannevar Bush, put science at the heart of shaping government priorities[2]. Since then, most policy professionals have been trained to accept that good public policy is the outcome of the rational analysis of a robust evidence base. But that’s not as straightforward as it sounds.

Government decisions around the timing, design and implementation of policies are infused with political considerations. And those political choices can often override the science — a truth laid bare during the pandemic. For example, the UK COVID-19 inquiry summarized last month how scientific advice had little influence on the chaotic decisions being made by the then government. The US Centers for Disease Control and Prevention’s decision to post on its website that “the claim ‘vaccines do not cause autism’ is not an evidence-based claim” is another (ironic) example of politics trumping science.

In reality, the ‘truth’ around a policy problem can be uncertain. It will be contested in good faith by experts and in bad faith by lobbyists, in high stakes contexts such as whether and when to introduce a lockdown during a pandemic or mandate a switch to electric vehicles.

And it’s not always straightforward to know which kind of evidence matters most. For instance, policies that aim to address climate change by making fossil fuels more costly might disadvantage poorer people and add to inequality. How should the relevant social, economic and climate evidence be given their due weight? Science alone won’t answer this dilemma.

Many policymakers also kid themselves that they are making objective decisions by using quantitative tools to evaluate options. Take cost-benefit analysis, for example. The UK Treasury ‘Green Book’ offers guidance for evaluating whether a government programme is good value for money by using modelling to predict costs and benefits over many years.

The resulting figure for the ‘net present value’ of a project is used to make policy choices. But it is based on a limited set of data and leaves much out. It doesn’t tell you about the value judgements that went in, such as whether and how to include the costs of environmental damage and impacts on health, or what assumptions were made around different population groups and future generations, for example.

Target-setting is another way to make policy choices seem more objective than they are. Since the 1990s, some governments, including those of the United Kingdom, United States, Australia and Sweden, have broadly followed ‘new public management’ theory in an attempt to make their operations more efficient. Efforts are focused by setting numerical outcomes for public services, such as the proportion of pupils attaining specified grades, or the length of waiting lists for treatments.

Unfortunately, such targets often turn out to be counterproductive; they can be gamed and don’t necessarily reflect what’s actually important. For example, in 1999, the UK government set an 8-minute target for ambulance response times for the most serious calls; it was met, although through tactics such as changing the definition of calls received or altering the times that calls were recorded[3].

US workers protest against cuts to federal health-research budgets and staffing levels.Credit: Bryan Dozier/NurPhoto/Reuters

Now, the allure of big data and artificial intelligence as potential sources of public-sector efficiency is driving interest in the concept of ‘deliverology’[4] — the latest variant of the illusion that better data ensure better policy. The cuts in federal-agency spending introduced by the US Department of Government Efficiency this year are a drastic example of the thinking that technology can optimize decisions. But many other governments, including the United Kingdom’s, are embracing similar ideas around data-driven policy.

On the face of it, it’s hard to argue with the claim that policy choices should follow the evidence. But the emphasis on defined metrics has clearly not delivered for the public, and this failure has helped to fuel public disenchantment with science. And, still, the underlying flaw of technocratic policymaking remains unaddressed: conflicts of values and interests do not have a numerical or technical answer.

Scientific evidence clearly does have a lot to offer well-informed policymaking, and the anti-science backlash needs to be addressed. The lesson from policy failures across countries since the 1990s is that the way in which scientists and suppliers of evidence and expertise engage with policy needs to change.

A deeper look

Until a decade ago, most elected politicians did generally pay lip service to the idea of policy informed by rigorous evidence. But this idea is increasingly called into question, as exemplified by the Trump administration’s policies against vaccination and against measures to tackle climate change. Like Trump, Argentinian president Javier Milei has also asserted that climate change is a “hoax” and made large cuts in research funding.

One of the main explanations for this shift, which deserves greater recognition in our view, is the chasm that has opened up between people who have attended university, and thrived economically as a result, and those who have not. Put bluntly, evidence-based policy has not delivered for the latter, despite the massive resources that governments have poured into scientific research over many decades. And that fact affects public views about science.

For example, in the United States, people with at least a four-year university degree have experienced higher income growth since 1980, with a wage premium over those without a degree climbing from 40% to about 75% by 2000[5]. Better-educated people experience better health outcomes for illnesses such as diabetes and heart disease[6].

Inequality affects places, too. In rural parts of the United States, poverty is growing and social mobility declining among people who lack degrees[7]. Graduates have increasingly been moving to fast-growing cities such as San Francisco in California and Boston in Massachusetts, where plenty of professional jobs are located[8].

As a result of this deep polarization, which is apparent in many democracies, the very idea of ‘the public interest’ — a shared understanding of what will benefit the majority — is fragmenting. People’s values or beliefs about issues such energy or migration policy, as reflected in opinion polling, are diverging to such an extent that the very idea of policies designed to serve the public good prompts widespread scepticism.

Academics such as us, based in an elite higher-education institution, must ask ourselves whether the reasoned, evidence-based approach is more likely to serve the interests of some social groups and demographics over others.

Although it is tempting to blame increased political polarization on social-media bubbles or biased mass media, beneath this trend sits the erosion of shared experiences and common values, observed by Robert Putnam in his 2000 book Bowling Alone, for example. So although trust in science remains moderately high — for example, a large multicountry survey in 2022–23 found that 57% of respondents agreed that most scientists are honest[9] — trust in the institutions that make policy decisions is in decline, especially among those with less formal education. A 2023 survey across the Organisation for Economic Co-operation and Development found that just 40% trusted their government to use the best evidence in decision-making[10], and general trust in government has been declining since about 2000 (see go.nature.com/4ryvpdw).

There has been a good deal of soul-searching in the scientific community about such issues. But, rather than hoping that politicians and the public will see the error of their ways and rediscover the merits of evidence-based policymaking, we suggest that scientists and universities need to respond to these dynamics in proactive and creative ways.

Scientists and researchers must recognize that the evidence they produce can be only part of what policymakers must take into account, and we should all be more open about this. A better understanding of the societal and political context for policy decision-making would make for greater humility, improved communication and a more effective role for research and evidence.

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Nature 648, 275-277 (2025)

doi: https://doi.org/10.1038/d41586-025-03978-6

References

1. Berman, E. P. Thinking Like an Economist: How Efficiency Replaced Equality in U.S. Public Policy (Princeton Univ. Press, 2022).

2. Bush, V. Science: The Endless Frontier (National Science Foundation, 1945).

3. Bevan, G. & Hamblin, R. J. R. Stat. Soc. Ser. A. 172, 161–190 (2009).

4. Barber, M., Kihn, P. & Moffitt, A. Deliverology 101: A Field Guide for Educational Leaders (SAGE Publications, 2010).

5. McKay, L. C. What Happened to the College Wage Premium (Federal Reserve Bank of Minneapolis, 2025).

6. Brooks, R. et al. Degrees of Difference (Sutton Trust, 2025).

7. Connor, D. S. et al. Popul. Space Place 30, e2802 (2024).

8. Autor, D. H. AEA Pap. Proc. 109, 1–32 (2019).

9. Cologna, V. et al. Nature Human Behav. 9, 713–730 (2025).

10. OECD. OECD Survey on Drivers of Trust in Public Institutions – 2024 Results: Building Trust in a Complex Policy Environment (OECD Publishing, 2024).

11. Fourcade, M. & Healy, K. The Ordinal Society (Harvard Univ. Press, 2024).

12. Fabian, M., Alexandrova, A. & Nair, Y. J. Happiness Stud. 24, 2309–2330 (2023).

13. Valero, A. & Van Reenen, J. Econ. Educ. Rev. 68, 53–67 (2019).

14. Royal Society. Science and the Economy: Policy Briefing (Royal Society, 2024).

15. UPP Foundation Civic University Commission. Truly Civic: Strengthening the Connection Between Universities and Their Places (UPP Foundation, 2019).

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Competing Interests

D.C. and M.K. give occasional unpaid expert advice to government, public sector or intergovernmental bodies on various aspects of policies.

Work

- Five important financial moves for PhD students

- Home-field advantage: how local research leads to new discoveries

CAREER FEATURE 08 December 2025

Five important financial moves for PhD students

Students and a financial planner give their advice on budgeting, saving and investing during doctoral studies.

By

Maddi Langweil

Find a new job

PhD students can live on a modest stipend and still save for the future, financial planners say.Credit: Images By Tang Ming Tung/Getty

At a mellow surf spot near the campus of the University of California, Santa Barbara, Paige Hoel smiled to herself; as an oceanographer, she understood why the waves were breaking just so. Between 2014 and 2024, she had earned her undergraduate degree, a master’s and a doctorate. But her passion for the field did not come without financial strain.

“I spent my 20s pursuing this,” says Hoel, who adds that her father lived on a “shoestring budget” during his own time as a PhD student. “I knew I had to hustle to support myself.”

PhD candidates do not just commit to long hours and intense research, but also to the financial uncertainty that comes with low stipends relative to high costs of living, especially in urban locations. As a PhD student at the University of California, Hoel earned US$30,000–36,000 per year, along with the benefits of waived tuition, health care and a gym membership. The financial strain can persist into early-career training and result in a limited capacity to save and invest in the future.

“This is the time to plan and build a foundation for yourself, one that sticks,” says Brian Skinner, a financial planner at Skinner Wealth Strategies in Milford, Connecticut. Specialists such as Skinner say that completing a PhD and feeling financially stable are not mutually exclusive. Here are five personal financial strategies for before, during and after a PhD programme that students and financial advisers say could help individuals to feel more secure.

Create and stick to a budget

Financial management begins with identifying your goals, then creating a budget that reflects them. Generally, a well-planned budget is a blueprint for how to control costs and make informed decisions each month as income arrives and expenses flow out.

First, identify all regular costs, such as rent, food, debt and savings. The rule of thumb, according to financial advisers, is to allocate up to 50% of your take-home pay to essential expenses, 15–20% to retirement funds and savings accounts, and 5% to an emergency fund. PhD students should focus on covering fixed expenses and building accessible savings, financial planners say.

“You need to break down what your priorities are and then budget to live within your means,” Skinner says.

When Rodrigo Dios completed his PhD in zoology in 2020 at the University of São Paulo, he was living in one of the most expensive cities in Brazil. (During his master’s studies, he lived in his family home to save money.) “I received one of the biggest grants in Brazil and things were really tight,” he says.

Dios received a monthly stipend of about 3,600 reais (the equivalent of around US$553 at that time) — for comparison, the average monthly income for 2024 in the state of São Paulo was 2,662 reais. Roughly 50% of his income went towards rent and utilities, including water, electricity and access to the Internet, 30% went towards food and 10% to other essential items, such as transport. Anything that was left, he tried to put into savings. Although Dios could have earned a higher salary after his master’s, he says that taking the lower pay as a PhD student is worth it in the long run because of the skills acquired. “You might feel undervalued, but you are investing in yourself,” Dios says.

During his studies, Dios maintained an ‘essentials only’ lifestyle, which felt a little restrictive at the time — he didn’t go out to eat and avoided impulse buys— but it meant he had financial wiggle room. For Dios, every Brazilian real had a purpose, which follows the popular zero-based budgeting strategy. As part of this mindful method, individuals assign all their income to financial goals, such as paying off debt or saving for a house deposit. Every dollar, or real, is ‘spent’ but not wasted.

When making a budget, ask the question: will it actually work? Before starting a PhD, financial advisers suggest that individuals try to live off their potential income for a month or two to see whether they can stick to it.

Several online budgeting tools can help, including Monarch, EveryDollar, Rocket Money and, often, banking apps. Breaking down a budget using a pen and paper or on a spreadsheet also works. But remember to stay balanced — it is important to go out for dinner or to see a film with friends occasionally.

Create a savings safety net

Rules around saving for retirement vary between countries, but setting up an account early on means that researchers can put a small amount of money aside each month for when they retire. The European Union, for example, offers plans such as the Pan-European Personal Pension Product (PEPP). Those under 30 can contribute up to 15% of their annual income to this voluntary scheme. In the United States, a Roth IRA — a personal after-tax account that grows investments tax free — is open to PhD students with an income. In 2025, those under the age of 50 can make maximum annual contributions of $7,000. However, depositing as little as $100 a month at age 22 until 65 years old would lead to a sum of more than $250,000, assuming a 7% rate of return. “If you’re a PhD student, especially full time, you’re probably at a very low tax bracket,” in countries with progressive tax systems, such as the United States, the Netherlands and Brazil, Skinner says. Saving modestly now means “you will be better off down the road”.

Some types of savings account, such as a money market or high-yield, enable you to earn interest but with the convenience of being able to withdraw funds before retirement age.

“You want to be building your foundation of strong financial habits like maintaining your credit and even automating your savings and retirement accounts to stash some money away,” Skinner says. Whether it’s $1,000 or $10, putting away a little each month can help with large purchases in the future, such as a car.

Manage debt

Education is an investment in the future, so taking out loans to pay for undergraduate, master’s and PhD courses or living expenses, is not necessarily a bad idea — but proceed with caution and borrow only what is needed, Skinner says.

Graduate students should investigate whether they are eligible for subsidized government loans, for which interest might not accrue until after courses have finished. If they are not, they might need an unsubsidized government or private loan, which accrue interest right away. “You need to choose what you are comfortable with,” says Karim El Khaldi, who finished his master’s in global health at the University of Barcelona in Spain in July.

Karim El Khaldi had to work while studying.Credit: Karim El Khaldi

Many PhD programmes offer free tuition, including in Europe, South America and the United States. But not all of them pay a stipend. “I’m from Lebanon and I’ve been actively seeking PhD positions [in places] like Belgium that will pay me because I simply cannot pay for a programme myself,” says Khaldi.

For students who begin a PhD programme in considerable debt from their undergraduate or master’s studies, Skinner advises them to develop a plan based on expected income, field and type of employer. For example, if a student is not going to be working in the US public sector or in underserved areas in education and health care for which loan forgiveness is an option, then they might opt to pay back the interest-only portion of their loan while they are pursuing a PhD.

Online tools such as a student-loan planner can help individuals to navigate current or future debt. Students should also plan for extra costs, such as visa application fees, travel and relocation costs that could increase debt.

“I hustled to manage my expenses and avoid coming out of school with debt,” Hoel says. “I graduated with some savings, but I am still living on a tight budget.”

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Nature 648, 489-490 (2025)

doi: https://doi.org/10.1038/d41586-025-03979-5

WHERE I WORK 08 December 2025

Home-field advantage: how local research leads to new discoveries

By studying caves near his home in Johannesburg, South Africa, geologist Tebogo Makhubela ventures into places people have never been before.

By

Nikki Forrester

Tebogo Makhubela is a geologist and lecturer at the University of Johannesburg, South Africa. Credit: Marco Longari/AFP/Getty

“The Cradle of Humankind is a complex system of limestone caves that has the world’s highest concentration of ancient human fossils. It’s located about 50 kilometres northwest of Johannesburg, South Africa. When I started working there as a PhD student ten years ago, I never thought that I would be the person making discoveries. I always saw myself as a support person who helped the palaeontologists and archaeologists.

Now, I work as a senior geologist at four sites in the Cradle of Humankind, and the more time I spend there, the more I realize how much is still unknown in the field of geology. Before 2013, none of the geology research here was done by local researchers. Instead, people would fly in from the United States, Australia and France for a week, map a section of cave where fossils were excavated, collect samples and then do their analyses abroad.

This photo was taken in the Rising Star Cave, which was mined heavily from around the early 1900s until the late 1940s. Researchers typically look for blocks of rock left over from mining activity, because that’s where the fossils tend to be, but one day my team and I decided to investigate what we thought was the bedrock. We eventually broke through to discover some of the best fossils we’ve found so far, along with missing skeletal elements from other fossil pieces that had been found closer to the surface.

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Nature 648, 492 (2025)

doi: https://doi.org/10.1038/d41586-025-03980-y

This interview has been edited for length and clarity.

Research

- Laser-based conversion electron Mössbauer spectroscopy of 229ThO2

- Observation of deuteron and antideuteron formation from resonance-decay nucleons

- Discovering state-of-the-art reinforcement learning algorithms

- Direct deaminative functionalization with N-nitroamines

- Origins of chromosome instability unveiled by coupled imaging and genomics

- Thiorphan reprograms neurons to promote functional recovery after spinal cord injury

- Synthetic α-synuclein fibrils replicate in mice causing MSA-like pathology

- Viral NblA proteins negatively affect oceanic cyanobacterial photosynthesis

- Mapping Plasmodium transitions and interactions in the Anopheles female

- A skin-permeable polymer for non-invasive transdermal insulin delivery

Article Open access Published: 10 December 2025

Laser-based conversion electron Mössbauer spectroscopy of 229ThO_2

Ricky Elwell,

James E. S. Terhune,

Christian Schneider,

Harry W. T. Morgan,

Hoang Bao Tran Tan,

Udeshika C. Perera,

Daniel A. Rehn,

Marisa C. Alfonso,

Lars von der Wense,

Benedict Seiferle,

Kevin Scharl,

Peter G. Thirolf,

Andrei Derevianko &

…

Eric R. Hudson

Nature volume 648, pages 300–305 (2025)

Abstract

The exceptionally low-energy 229Th nuclear isomeric state is expected to provide several new and powerful applications1,2, including the construction of a robust and portable solid-state nuclear clock[3], perhaps contributing to a redefinition of the second[4], exploration of nuclear superradiance5,6 and tests of fundamental physics7,8,9,10. Further, analogous to the capabilities of traditional Mössbauer spectroscopy, the sensitivity of the nucleus to its environment can be used to realize laser Mössbauer spectroscopy and, with it, new types of strain and temperature sensors3,11 and a new probe of the solid-state environment12,13, all with excellent sensitivity. However, current models for examining the nuclear transition in a solid require the use of a high-bandgap, vacuum ultraviolet (VUV) transmissive host, severely limiting the applicability of these techniques. Here we report the first, to the authors’ knowledge, demonstration of laser-induced conversion electron Mössbauer spectroscopy (CEMS) of the 229Th isomer in a thin ThO_2 sample whose bandgap (approximately 6 eV) is considerably smaller than the nuclear isomeric state energy (8.4 eV). Unlike fluorescence spectroscopy of the 229Th isomeric transition, this technique is compatible with materials whose bandgap is less than the nuclear transition energy, opening a wider class of systems to study and the potential of a conversion-electron-based nuclear clock.

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Main

The recent observation14,15 of direct laser excitation of the 229Th isomeric state in high-bandgap crystals has, after almost 50 years of work, opened the door to a laser-accessible nuclear transition and driven rapid progress in the development of solid-state optical clocks. Already, the nuclear transition frequency has been compared with an atomic clock and its linewidth studied[16], and work has begun to optimize the clock performance by developing both a theoretical understanding of nuclear quenching mechanisms[12] and using them to shorten the clock interrogation cycle17,18. Similarly, excitation of the nuclear transition in a VUV transmissive thin film has opened the door to integrated-photonic-based nuclear clocks and sensors[19]. Further, new high-bandgap materials have been analysed that could provide considerable simplification of the clock by, for example, doping 229Th into a nonlinear optical crystal[20] and, by using principles of molecular design, provide a system with the potential for performance orders of magnitude beyond any current or planned optical clock4,21.

Because the 229Th nucleus provides a highly controllable system that can be deployed into various hosts, it is expected, in analogy to Mössbauer spectroscopy, that these same techniques can also be used as new probes of the solid-state chemical and nuclear environment. However, in all studies so far, 229Th nuclear excitation is detected by observing the resulting nuclear fluorescence. This leads to the requirement that the host material has a bandgap larger than the isomeric transition energy (>Eiso), as the large internal conversion (IC) coefficient of the isomeric state (roughly 10^8–10^9 (refs. 22,23)) extinguishes the nuclear fluorescence. This requirement severely limits the material hosts available for study and, therefore, it is highly desirable to extend the spectroscopy of the isomeric transition to low-bandgap (<Eiso) environments by means of a new method for nuclear excitation detection.

CEMS, which has been used for decades as an important materials probe24,25,26 and was recently used to detect the 12.4-keV nuclear clock transition in 45Sc (ref. [27]), has been proposed for detection of 229Th nuclear excitation28,29. CEMS of the 229Th isomer uses the fact that, if the nuclear energy is larger than the material bandgap, the IC relaxation process is possible by promoting an electron across the bandgap23,30. If this promoted IC electron originates in a shallow enough state in the valence band, the electron can overcome the ionization energy barrier (that is, the difference between the top of the valence band and the vacuum[31]) and emerge from the material surface. By detecting these conversion electrons, nuclear spectroscopy can be recorded and, as a result, the technique of tabletop laser-based nuclear spectroscopy can be extended to low-bandgap materials28,29 through this laser-based CEMS.

As well as providing a means to study low-bandgap materials containing 229Th, CEMS could also allow marked improvements in nuclear clock stability, as the IC decay rate is roughly 10^8 times faster than the radiative decay rate, enabling a much faster clock interrogation rate. This rapid interrogation reduces the stability demands on the local oscillator while providing a projected clock instability as low as about 10−18 at 1 s. Further, a CEMS-based nuclear clock could operate by simply reading out the CEMS photocurrent, providing a means to greatly simplify and miniaturize future nuclear clocks[32].

Here we report the first demonstration of laser-based CEMS of any nucleus. Specifically, a VUV laser system is used to excite 229Th nuclei in a thin sample of thoria (ThO_2). 229ThO_2 was chosen as the first host as it has a low bandgap (about 6 eV (ref. [33])) and is readily available as a stoichiometric Th compound. Conversion electrons from the 229ThO_2 are detected as a function of laser excitation energy providing the first laser-based CEMS nuclear spectrum, which determines the 229Th nuclear transition frequency as 2,020,407.5(2)stat(30)sys GHz, consistent with previously reported values of the transition14,15,16,19 and whose width is consistent with the laser linewidth of our system reported in previous studies15,19. Further, the IC lifetime is measured as approximately 10 μs, which is consistent with that measured in 229Th implantation studies[34] and theoretical calculations of the IC lifetime described below. In what follows, we describe the 229ThO_2 target, experimental apparatus and the spectroscopic protocol, before presenting the results of the CEMS spectroscopy. Next, we present calculations of the isomer shift and IC lifetime in 229ThO_2 using a theoretical approach that combines solid-state density functional theory (DFT) and relativistic atomic many-body perturbation theory methods. Following these results, we use the measured lifetime of the IC decay of the isomeric state in 229ThO_2 to evaluate the ideal performance of a 229ThO_2 conversion electron clock and find its projected instability to be about 2 × 10−18 at 1 s.

229ThO_2 target and apparatus

The CEMS target was constructed by electrodepositing 229ThO_2 onto a stainless steel disc (see Fig. 1 for an image of the target, procured from Eckert & Ziegler Analytics, Inc.). Although other oxide and hydroxide compounds of Th may be present in the target, this paper assumes that the predominant chemical form of 229Th in the target is 229ThO_2, based on the method of target preparation (see Methods for details). The diameter of the 229ThO_2 is about 5 mm and its thickness is estimated from the width of the α-particle spectrum as approximately 10 nm (Fig. 1c), which is consistent with a measured total activity of about 6.3 kBq. The VUV absorption of ThO_2 is estimated as α ≈ 0.1 nm−1 (ref. [35]), implying that 229Th nuclei within a depth of about 10 nm can be efficiently excited by the laser. Also, the inelastic mean free path of electrons in solids at the eV energy scale is typically about 10 nm (ref. [36]), meaning that an IC electron generated at greater depths probably scatters before extraction from the surface. As such, further 229ThO_2 thickness primarily contributes to the background in the form of electrons produced through radioactive decays[37] and thus a thickness of about 10 nm is probably optimal for CEMS.

Fig. 1: CEMS target set-up and characterization.

a, Cutaway rendering of the 229ThO_2 target mount. Arrows denote front aperture, window, target and pyroelectric detector. b, Rendering of the spectroscopy chamber. Magenta arrow, direction of VUV laser propagation. Yellow arrows, IC electron trajectories from target to detection MCP. Blue arrows, background photoelectrons generated from VUV scatter diverted to the secondary electrode. Green arrow, direction of static B-field used to guide IC electrons. c, α-spectrum of the 229ThO_2 target. Inset, photograph of 229ThO_2 target used in this study. The peak indicated at 4,845 keV corresponds to the dominant α-decay mode of 229Th. The other large peaks correspond to the α-decays of daughter nuclei. The 229Th peak had a full width at half maximum (FWHM) of about 22 keV, consistent with energy loss through an approximately 10-nm sample, as estimated with SRIM[56]. a.u., arbitrary units.

CEMS spectroscopy is recorded by directing a tunable VUV laser onto the 229ThO_2 target. Briefly, VUV radiation was produced by means of resonance-enhanced four-wave mixing of two pulsed dye lasers in Xe gas. The frequency of the first pulsed dye laser, ωu, was locked to the \({5{\rm{p}}}^{6}\,\genfrac{}{}{0ex}{}{1}{}{S}_{0}\to 5{{\rm{p}}}^{5}\,\left(\,\genfrac{}{}{0ex}{}{2}{}{P}_{3/2}^{^\circ }\right)\,6{{\rm{p}}}^{2}\,{[1/2]}_{0}\) two-photon transition of Xe at about 249.63 nm. The frequency of the second pulsed dye laser, ωv, was scanned to produce VUV radiation in the Xe cell given by the difference mixing relation ω = 2ωu − ωv. All three laser beams then impinge off-axis with respect to a MgF_2 lens, whose chromatic dispersion is used with downstream pinholes to spatially filter the VUV beam and pass it towards the 229ThO_2 spectroscopy chamber. The laser system delivers 30 pulses per second to the target with a typical VUV pulse energy of about 6–8 μJ per pulse (see refs. 15,38 for details). For these experiments, N_2 gas is added to the Xe cell to quench an amplified spontaneous emission (ASE) process at 147 nm (see Methods for details), which occurs on a timescale similar to IC decay and otherwise contributes to the photoelectron background.

The 229ThO_2 target is held in a custom mount (see Fig. 1a) that provides the ability to electrically bias the sample, as well as VUV laser monitoring capabilities. Biasing the target is necessary as the VUV laser causes a prompt burst of photoelectrons when it impinges on the 229ThO_2 target, which will overwhelm the electron detector. These initial photoelectrons are suppressed for approximately the first 100 ns after the laser pulse by positively biasing the 229ThO_2 target to 135 V, before the bias voltage is changed to −405 V to aid the extraction of IC electrons from the surface; at all times, the front aperture of the mount is held at 100 V. The mount also houses a fused silica target that fluoresces under VUV illumination aiding alignment and a pyroelectric crystal to provide in situ monitoring of the VUV laser pulse energy. The target chamber is mounted on a combined lever arm–stepper motor system that allows it to be raised and lowered, causing the VUV laser to illuminate either the 229ThO_2 target or the laser energy monitor. To limit hydrocarbon build-up on the target and to limit scattering of the IC electrons owing to background gases, the target chamber was ozone plasma cleaned before baking and operated at a pressure of about 10−7 Pa.

In principle, IC electron detection can be accomplished by simply positively biasing, for example, a multichannel plate (MCP) detector held near the 229ThO_2. However, it was found that scattered light from the VUV laser generated a large afterglow of photoelectrons originating at positions dispersed throughout the chamber, which lasted tens of microseconds—presumably because of the fluorescence of components within the beamline and chamber. To overcome this background, a combination of electric and magnetic fields was used that focused electrons originating from the 229ThO_2 target onto a detection MCP, while diverting electrons generated elsewhere to another region of the chamber (see Methods). Finally, as an extra layer of protection for the detection MCP, its front plate voltage was controlled so that it had no gain during the initial burst of photoelectrons from the target.

Spectroscopy

Using this apparatus, CEMS was performed by recording the number of detected electrons in the window between 6 and 40 μs after each laser pulse as a function of VUV laser wavelength; this window was chosen on the basis of previous theoretical estimates[23] and observations of IC decay[39] following 233U decay. The electron signal, normalized by the laser pulse energy, is shown in Fig. 2a as a function of frequency for a region roughly 100 GHz wide and centred on the 229Th nuclear transition energy. These data were recorded by first measuring the pulse energy and then detecting the total number of electrons emitted after 36,000 pulses (20 min) before measuring the pulse energy again. This process was repeated to record a laser CEMS spectrum. The data in Fig. 2a are the average of four spectra, with the vertical error bars representing the standard error. Owing to differences in system alignment between campaigns, the photoelectron background varied slightly between different spectra. Therefore, a Lorentzian with a background fit was used to determine and subtract the photoelectron background before the data are combined. Further, because the laser frequency is not perfectly controlled, these spectra are binned in frequency and the horizontal error bars are the standard deviation of the frequency. Each data point represents the average of at least 140,000 laser pulses.

Fig. 2: Nuclear spectroscopy of the 229Th transition in ThO_2.

a, The laser-based CEMS spectra of 229ThO_2 is shown in black with a fit of a Lorentzian profile. Each point is an average of ≥140,000 laser pulses. A constant baseline of about 75 e− per laser pulse has been subtracted. The vertical error bars denote the standard error and the horizontal error bars are the standard deviation of the laser frequency for the points in the bin. For comparison, the radiative decay spectrum of 229Th:LiSrALF_6, taken from ref. [15], is shown in blue. b, The IC decay rate as a function of time is shown in black, alongside a fit of a decaying exponential with a background, leading to an IC lifetime of 12.3(3) μs. a.u., arbitrary units.

A nonlinear least-squares fit of a Lorentzian to the spectrum yields a central value of 2,020,407.5(2)stat(30)sys GHz and full width at half maximum linewidth of 12.4(4) GHz, both consistent with our observations in LiSrAlF_6 (ref. [15]) and ThF_4 (ref. [19]). Here statistical error is the 68% confidence interval and the systematic uncertainty is predominantly because of the accuracy of the wavemeter and probably conservative. On resonance, an average of 0.41(5) e μJ−1 per laser pulse is detected. The expected signal can be estimated as \({\eta }_{{\rm{e}}}{\eta }_{{\rm{c}}}{N}_{{\rm{e}}}\times {{\rm{e}}}^{-{t}_{{\rm{i}}}/{\tau }_{{\rm{IC}}}}\), in which ηe is the extraction of efficiency of IC electrons from the sample, ηc is the collection efficiency of electrons emitted from the sample, Ne is the number of excited 229Th nuclei and ti is the time that electron counting begins after the laser pulse. On the basis of calibrations of the apparatus (see Methods), the expected signal is found as \(0.1{5}_{-0.09}^{+0.25}\,{{\rm{e}}}^{-}\,{{\rm{\mu }}{\rm{J}}}^{-1}\), in reasonable agreement with the recorded spectrum.

Using the same system, the lifetime of the IC decay is measured by comparing the time-binned electron counts collected on resonance in the first 190 μs after laser excitation. Specifically, the average number of time-binned electron counts per μJ of laser energy is obtained for both the on-resonant and off-resonant (about 100 GHz detuning) illumination periods. The average off-resonance counts are then subtracted from the average on-resonance counts to remove any photoelectron background and the result is plotted in Fig. 2b. A background-free nonlinear least-squares fit of a decaying exponential reveals an IC lifetime of 12.3(3) μs, as shown in Fig. 2b. As discussed later, the IC decay rate is sensitive to the local chemical environment, so a range of decay rates is possible and this lifetime should be interpreted as an estimate.

Calculation of isomer shifts and IC lifetime

The measured isomer energy is in agreement with the earlier spectroscopic experiments in three wide-bandgap hosts14,15,19. Theoretically, this is supported by the calculations[40] of isomer shifts for a large variety of 229Th solid-state hosts and by our 229ThO_2-specific calculations presented in Methods. For example, we expect that the isomer shift between bulk 229ThO_2 and 229Th:LiSrAlF_6 is on the order of 100 MHz, well below the approximately 3 GHz reported experimental accuracy. Our calculations predict the nuclear transition frequency for bulk 229ThO_2 to be 2,020,407,338(70) MHz.

In the IC process, the energy of the excited nucleus is transferred to the electrons. In a crystalline solid, that means promoting a valence band electron |vkσv⟩ into a conduction band state |ckσc⟩ and creating a hole in the valence band (Fig. 3a). The process is mediated by the hyperfine interaction (HFI) W, which, for periodic lattices, conserves the electronic crystal momentum k but can connect electronic states of different spin projections σv,c. We derived the rate for the described IC process (see Methods) as

$${\varGamma }_{{\rm{IC}}}=\frac{2{\rm{\pi }}}{\hbar }\frac{1}{2{I}_{{\rm{e}}}+1}\sum _{{M}_{{\rm{g}}}{M}_{{\rm{e}}}}\sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}\overline{| {W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}}){| }^{2}}{G}_{{\rm{cv}}}(\hbar {\omega }_{{\rm{nuc}}}).$$

(1)

Fig. 3: Calculation of the IC rate in ThO_2.

a, Feynman diagram of the IC process. Single black strokes represent the electron lines and the double blue ones denote the nuclear lines. The interaction is mediated by a virtual photon exchange, corresponding to the HFI W. The crystal momentum k is conserved in this process. b, Conventional unit cell of ThO_2, with Th atoms in green and O atoms in red. c, Th PDOS computed with G_0W_0. The horizontal dashed line denotes the Fermi level. d, Th PJDOS computed with G_0W_0. The vertical dashed line denotes the nuclear isomeric energy.

Here |e⟩ and |g⟩ are the isomer and ground nuclear states with spins Ie,g and magnetic quantum numbers Me,g. The HFI W connects the two nuclear states and the valence and conduction band electronic states. Gcv(ħωnuc) is the conventional[41] joint density of states (JDOS) at the nuclear transition energy ħωnuc. The bar denotes averaging over a surface of constant energy in k-space.

The same JDOS appears in the theory of electromagnetic interband absorption[41] and is clearly a highly material-dependent quantity. Therefore, to understand the physics of the IC process, and in particular its rate, we calculated the properties of 229ThO_2 with periodic electronic structure theory (GW and DFT). The calculations used the G_0W_0 approximation for the electronic self-energy and the Bethe–Salpeter equation (BSE) for optical properties (see Methods for details). The fundamental bandgap computed with G_0W_0 is 6.20 eV, in reasonable agreement with experimental measurements of 5.9 eV (refs. 42,43) (calculation details provided in Methods). The absorption spectrum, computed with G_0W_0 + BSE, agrees with the measurements in ref. [35], supporting our estimation of α ≈ 0.1 nm−1.

ThO_2 crystallizes in the fluorite structure (space group \(Fm\bar{3}m\), #225), in which each Th atom is coordinated by eight oxygen atoms in a cubic arrangement (Fig. 3b). The Th4+–O2− bonding is predominantly ionic, with a modest covalent admixture arising from overlap of Th 6d/5f and O 2p orbitals. That Th is in the +4 oxidation state may be verified from the projected density of states (PDOS) on Th, in which the 5f and 6d components in the valence band are nearly empty. By contrast, the Th 5f and 6d valence orbitals form large peaks in the conduction band, indicating the transfer of an electron from an O2− anion to form Th3+. Both the valence and conduction bands contain small contributions from Th-projected p orbitals. As it turns out, the IC process primarily involves transferring electrons between these p-orbital components.

In computing the HFI matrix element in equation (1), it is convenient to project the valence and conduction band states |vkσv⟩ and |ckσc⟩ onto the basis of Th atomic orbitals. The matrix element \({W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})\) may then be expressed as a sum over different HFI matrix elements connecting atomic orbitals of definite angular momenta, weighted by the expansion coefficients of |vkσv⟩ and |ckσc⟩. To the lowest order, cross terms arising when squaring the expansion of \({W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})\) are neglected. This allows the expression of the IC rate in terms of the nuclear ground state HFI constants A and the ‘projected joint density of states’ (PJDOS) in Th. The PJDOS is a JDOS weighted by the projections of the crystal electronic states onto the thorium atomic orbitals that allows us to describe the character of the delocalized crystal orbitals close to the thorium nucleus (see Methods). The HFI A constants for Th3+ are known from experiments and high-precision relativistic atomic-structure calculations[12]. The PJDOS of transitions with the largest contributions to the IC rate are shown in Fig. 3c. Using these values, we arrive at an estimate for the IC rate of ΓIC ≈ 1.3 × 10^4 s−1, corresponding to an IC lifetime of about 80 μs.

Sources of the disparity between the measured and theoretical lifetimes could be because of cross-order and higher-order expansion terms neglected in our evaluation of the rate (equation (1)) and errors in the local projections of the plane-wave orbitals done by VASP[44]. For example, adding the cross terms coherently may increase the IC rate and thus reduce the estimated IC lifetime to approximately 30 μs. Relativistic contraction approximately (Zα)2 may increase the non-relativistic PDOS computed with VASP as much as 40%, so the increase in the IC rate may be up to a factor of 1.4^2 ≈ 2, further reducing the estimated IC lifetime to about 15 μs. See Methods for more details. Small changes to the valence and conduction states expected with the addition of spin–orbit coupling in solid-state calculations and deviations of the sample from bulk 229ThO_2 owing to both surface and self-radiation damage effects may further affect the IC rate. Compared with the pristine 229ThO_2, the IC rate for 229Th adjacent to point defects can be enhanced by the electric quadrupole HFI contribution[45] owing to symmetry breaking. Evaluating these uncertainties requires a much more comprehensive study that will be carried out in future work. Here we simply note that the order-of-magnitude experiment–theory agreement supports the physical interpretation that observed IC decay results from the nucleus relaxing by means of transferring an electron from an oxide anion into the Th 6p component of the conduction band.

Projected clock performance

As well as its use as a new chemical probe, laser-based CEMS may allow the construction of a new type of nuclear clock with several advantages over crystal-based clocks[46]. Chief among these advantages are a greatly reduced clock interrogation time, as the IC decay rate is about 10^8 times faster than radiative decay, and the potential for clock readout by simply monitoring the current leaving the target, which could facilitate substantial miniaturization.

For such a clock, assuming that 229ThO_2 is produced from 16O, the largest sources of instability would be broadening owing to magnetic dipole interactions between the 229Th nuclei and lifetime broadening. Given that the Th–Th distance in ThO_2 is 3.96 Å (ref. [47]), the expected Zeeman broadening owing to neighbouring 229Th nuclei is about 10 Hz. The next largest sources of broadening would be the varying intrinsic isomeric shift and second-order Doppler shift arising from temperature gradients across the ThO_2 sample. Drawing estimates from other Mössbauer experiments, typical intrinsic isomeric shifts range from 0.1 to 5.0 kHz K−1 (refs. 48,49,50,51), as supported by recent measurements of the intrinsic isomeric shift in 229Th:CaF_2 at 0.4 kHz K−1 (ref. [11]). Within the Debye model, the second-order Doppler shift can be estimated to be ≲1 Hz K−1 at 4 K, using the lowest reported value of 236 K for the Debye temperature of ThO_2 (ref. [52]). With temperature gradients stabilized across the sample to ≤0.1 mK, the intrinsic isomeric and second-order Doppler shifts result in a broadening of roughly 0.5 Hz. Thus, the primary source of instability is the lifetime broadening of Γ ≈ 2π × 16 kHz.

Assuming that a polished face of an approximately 10-nm-thick single crystal is prepared and realizes an electron extraction efficiency ηe ≈ 0.5 (ref. [36]) and that the photoelectron background is eliminated by material purification and baffling, a 100-μW laser leads to a projected clock instability of about 2 × 10−18 at 1 s averaging (see Methods for details). Notably, it is possible that the electric current from the IC process could also be used as a form of readout, as it would generate a current of about 300 nA, providing a simple means for clock operation and locking[32]. It may also be possible to further enhance this performance by purposefully exciting defect or conduction band electrons to realize an ‘on-demand’ quench of the nuclear excitation17,18.

Discussion and outlook

With this first demonstration of laser-based CEMS, an entirely new class of materials is now compatible with laser nuclear spectroscopy. By implanting 229Th into low-bandgap materials and observing both the lifetime of the IC decay channel and the isomer shift of the transition, detailed information can be gathered about the local phononic, electronic and nuclear structure. This in turn allows the isomeric transition to serve as a sensor of strain and temperature in the solid11,3. Further, at the energy scale of the IC electrons, their inelastic mean free path is a sensitive function of their energy relative to the Fermi level[36]. In the future, it may be possible to relate the efficiency with which IC electrons emerge from a surface with both the surface quality and the band structure local to the implanted 229Th. Looking further forward, off-resonant excitation of 229Th nuclei through a combined nuclear and phononic transition in the solid could enable laser-based nuclear resonance vibrational spectroscopy53,54. This could allow measurement of the local phonon density of states with sub-μeV precision, considerably beyond what is possible with conventional Mössbauer spectroscopy[54].

Given our previous work in 229ThF_4 films[19], it can be concluded that, as the 229Th is converted from the oxide to the fluoride state, the 229Th isomer will convert from decaying by IC to decaying by the emission of a VUV photon. Thus, the relative ratio of radiative decay to conversion electron decay following laser excitation could provide a new set of methods to characterize the chemical state of Th compounds, perhaps aiding studies of nuclear power generation[55].

Furthermore, laser-based CEMS provides a new platform to realize a solid-state Th clock that benefits from the inherent ease of a production of stoichiometric Th compounds, a 10^8 reduction in clock interrogation cycle and the potential for a current-based readout, allowing simplification and miniaturization of future nuclear clocks.

Methods

Expected IC signal

The incident VUV flux is attenuated, so that it follows φ_0e−αz, in which α is the VUV attenuation coefficient. The number of excited  229Th nuclei in a target of length L should go as[57]

$${N}_{{\rm{e}}}\approx \frac{4}{6}\frac{{\lambda }^{2}}{2{\rm{\pi }}}\frac{{n}_{{\rm{Th}}}}{{\varGamma }_{{\rm{L}}}}\frac{T|\widetilde{n}{|}^{2}}{{\rm{Re}}[\widetilde{n}]}\frac{{\varphi }_{0}(1-{{\rm{e}}}^{-\alpha L})}{\alpha }\times \frac{1}{1+4{\left(\frac{\delta }{{\varGamma }_{{\rm{L}}}}\right)}^{2}}\times \left(\frac{{t}_{{\rm{e}}}}{{\tau }_{{\rm{rad}}}}\right),$$

(2)

in which λ is the vacuum transition wavelength, nTh is the density of 229Th in the 229ThO_2 target, Γrad = 1/τrad is the vacuum radiative decay rate, ΓL is the VUV laser bandwidth, ΓIC = 1/τIC is the IC decay rate, δ is the laser detuning, φ_0 is the incident laser photon flux, L is the target thickness, T is the transmission of the VUV laser into the target and \(\widetilde{n}=n-{\rm{i}}\kappa \) is the complex index of refraction with κ = λα/4π. The target was produced using a 0.75:0.25 229Th:232Th isotope mix from Oak Ridge National Laboratory, leading to an effective 229Th density of nTh = 0.75 × 2.28 × 10^22 cm−3 (ref. [47]).

From the number of excited 229Th nuclei, the number of detected IC electrons is given by

$${N}_{\det }={\eta }_{{\rm{e}}}{\eta }_{{\rm{c}}}{N}_{{\rm{e}}}\times {{\rm{e}}}^{-{t}_{{\rm{i}}}/{\tau }_{{\rm{IC}}}}$$

(3)

in which ηe is the extraction efficiency from the 229ThO_2 target, ηc is the collection efficiency and ti is the start of the acquisition time window. The extraction efficiency represents the probability that an IC electron is able to leave the 229ThO_2 target and combines many physical processes, such as whether the electron is promoted high enough into the conduction band to overcome the ionization energy barrier (either by being in a state above the ionization energy or tunnelling), whether the electron inelastically scatters, whether surface conditions are favourable and so on. Owing to all of these confounding factors, theoretical calculation of ηe is difficult and it must be estimated from experiments. To do this, we make the assumption that the probability for a photoelectron promoted by a VUV photon to leave the target is the same as an IC electron promoted by an excited 229Th nucleus. By making this assumption, we are able to use the efficiency with which photoelectrons are generated by our VUV laser system to obtain an estimate of Tηe. The collection efficiency ηc is simply the efficiency with which electrons that leave the target are detected on the MCP given the voltage biasing and magnetic field configuration used in the experiment. This can be readily determined by measuring the ratio of the number of photoelectrons collected on the MCP front plate relative to the number of photoelectrons leaving the target.

Using the values listed in Extended Data Table 1, the expected on-resonance IC signal was estimated to be \({N}_{{\rm{\det }}}/(\hbar {\omega }_{0}{\varphi }_{0}{t}_{{\rm{e}}})\,=\) \(0.1{5}_{-0.09}^{+0.25}\,{{\rm{e}}}^{-}\,{{\rm{\mu }}{\rm{J}}}^{-1}\) per shot.

Quenching of ASE in Xe four-wave mixing

The four-wave mixing process can produce a beam of ASE along the beam axis, complicating detection. The origin of the ASE is resonant excitation by the 249.6-nm laser of the \(5{{\rm{p}}}^{6}\,\genfrac{}{}{0ex}{}{1}{}{S}_{0}\to 5{{\rm{p}}}^{5}\,\left(\,\genfrac{}{}{0ex}{}{2}{}{P}_{3/2}^{^\circ }\right)\,6{{\rm{p}}}^{2}\,{[1/2]}_{0}\) transition. Any Xe population not participating in the four-wave mixing process will be left in the excited two-photon state. This \(5{{\rm{p}}}^{5}\,\left(\,\genfrac{}{}{0ex}{}{2}{}{P}_{3/2}^{^\circ }\right)\,6{{\rm{p}}}^{2}\,{[1/2]}_{0}\) (abbreviated as 6p^2 [1/2]0) state will then decay to the \(5{{\rm{p}}}^{5}\,\left(\,\genfrac{}{}{0ex}{}{2}{}{P}_{3/2}^{^\circ }\right)\,6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\) (abbreviated as \(6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\)) state by 828-nm emission in about 30 ns and the \(6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\) state will decay to the 1S_0 ground state by emission of a 147-nm photon in about 3.7 ns. If the Xe pressure is in the several hundred Pa range, as it is for efficient four-wave mixing, there are enough nearby Xe atoms that they may reabsorb these 828-nm and 147-nm photons. Effectively, this leads to radiation trapping, which extends the effective fluorescence lifetime of the Xe spontaneous emission[58]. At the same time, the 828-nm/147-nm spontaneous emission will experience gain as it stimulates Xe in the excited 6p^2 [1/2]0 and \(6{{\rm{s}}}^{2}\,{[3/2]}_{1}^{^\circ }\) to emit, yielding ASE. This gain will be highly directional, as the excited Xe will essentially lie in a column defined by the propagation of the 249.6-nm pulse of the pump laser. This interplay between radiation trapping and ASE will then yield bidirectional emission from the Xe cell along the pumping axis, which will have a timescale much longer than the spontaneous emission lifetime of the excited states[59].

To mitigate this effect, we introduce N_2 gas in the Xe, which quenches the excited state Xe population through collision.

Simulation of electron trajectories

SIMION[60] simulations were carried out to determine a combination of voltage biasing and static magnetic field that would guide IC electrons to our detector while diverting background photoelectrons to a secondary electrode. The voltage biasing chosen during the IC observation period was to have the target at −405 V, the front aperture of the target mount at +135 V, the front of the detection MCP at +140 V and the secondary electrode at +2,500 V. The magnetic field was set to about 3–5 G. As can be seen in Extended Data Fig. 1a, under the voltage biasing described, there is a ‘saddle’ in the potential through which the IC electrons that have been accelerated by our target mount system can be made to travel through by the magnetic field. Meanwhile, as can be seen in Extended Data Fig. 1b, electrons that are generated randomly throughout the chamber with about 8 eV of kinetic energy either crash into the chamber wall or fall into the sacrificial electrode.

Preparation of the target

The target used in this study was prepared in an electrodeposition buffer solution of NaOH and sulfuric acid. 229Th material was deposited onto the stainless steel disc until target activity was reached, at which a quench was performed with ammonium hydroxide. The disc was then heated overnight at 200–300 °C in ambient atmosphere.

Although the electrodeposited target is probably a mixture of Th hydroxides, oxides and metal impurities, the use of low-impurity (>99.99% grade) chemicals during electrodeposition and heat treatment in air lead us to assume that it is predominantly Th in an oxidized state. As the most stable oxide form, we assume that the target is predominately 229ThO_2.

IC rate derivation

We consider the IC processes in an insulator, when the bandgap Δ is smaller than the nuclear isomer energy ωnuc. In the IC process, the nuclear excitation is transferred to the electrons, spawning a particle–hole pair, with a valence band electron promoted into the conduction band, leaving behind a hole in the valence band; see Fig. 3a.

The 229Th nuclear subsystem is modelled as two distinct energy levels: the ground state |g⟩ with nuclear spin Ig = 5/2 and the excited (isomeric) state |e⟩ with Ie = 3/2, separated by the energy gap ωnuc.

The IC process is mediated by the HFI. In a crystal, containing \({\mathcal{N}}\) 229Th nuclei with one 229Th per unit cell, HFI reads

$$W({\bf{r}})=\mathop{\sum }\limits_{\nu =1}^{{\mathcal{N}}}{\mathcal{M}}({{\bf{R}}}_{\nu })\cdot {\mathcal{T}}\,({\bf{r}}-{{\bf{R}}}_{\nu }),$$

(4)

in which we sum over unit cells, \({\mathcal{M}}({{\bf{R}}}_{\nu })\) is a 229Th nuclear magnetic moment operator and the 229Th-centred \({\mathcal{T}}\) is a rank-1 tensor acting on the electronic degrees of freedom. The nuclear electric-quadrupolar and higher-rank HFI interactions can be added in a similar fashion. For 229ThO_2, owing to the cubic symmetry, the electric-quadrupole contribution vanishes.

To compute the IC rate, we use Fermi’s golden rule. The initial state of the electron subsystem is a fully occupied valence band \(| \mathop{0}\limits^{ \sim }\rangle \) and the final state is the particle–hole excitation \({a}_{c{\bf{k}}{\sigma }_{{\rm{c}}}}^{\dagger }{a}_{v{\bf{q}}{\sigma }_{{\rm{v}}}}|\widetilde{0}\rangle \) with energy εck − εvq, in which εck and εvq are the band functions of the conduction (c) and the valence (v) bands. Then, the final state quantum numbers are spanned by crystal momenta k, q and two electron spin projections. We also sum over the nuclear ground state magnetic quantum numbers Mg and average over the nuclear isomer state magnetic quantum numbers Me,

$$\begin{array}{c}{\varGamma }_{{\rm{IC}}}^{({\mathcal{N}}\,)}=\frac{2{\rm{\pi }}}{\hbar }\frac{1}{2{I}_{{\rm{e}}}+1}\sum _{{M}_{{\rm{g}}}{M}_{{\rm{e}}}}\sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}{\int }_{{\rm{BZ}}}{d}^{3}k{\int }_{{\rm{BZ}}}{d}^{3}q|\langle c{\bf{k}}{\sigma }_{{\rm{c}}}|{W}^{{\rm{ge}}}|v{\bf{q}}{\sigma }_{{\rm{v}}}\rangle {|}^{2}\\ \,\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{q}}}-{\omega }_{{\rm{nuc}}}).\end{array}$$

(5)

The integrations are carried over the Brillouin zone (BZ). We use the conventions from ref. [41] in our derivation.

The HFI (equation (4)) is cell-periodic and its matrix element ⟨ckσc|Wge∣vqσv⟩ between Bloch functions can be reduced from an integration over the entire crystal to an integration over a single unit cell. The result reads

$$\langle c{\bf{k}}{\sigma }_{{\rm{c}}}|{W}^{{\rm{ge}}}|v{\bf{q}}{\sigma }_{{\rm{v}}}\rangle =\delta ({\bf{k}}-{\bf{q}}){W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})$$

(6)

with

$${W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})\equiv \frac{{(2{\rm{\pi }})}^{3}}{\varOmega }\langle g|{\mathcal{M}}|e\rangle \cdot {\int }_{\varOmega }{d}^{3}r{u}_{c{\bf{k}}}^{* }({\bf{r}}){\chi }_{{\sigma }_{{\rm{c}}}}^{\dagger }{\mathcal{T}}({\bf{r}}){\chi }_{{\sigma }_{{\rm{v}}}}{u}_{v{\bf{k}}}({\bf{r}}).$$

(7)

Here Ω is the unit cell volume, u…(r) are cell-periodic envelopes of Bloch functions[41] and χ are the conventional electron spinors. Note that the cell-periodicity imposes conservation of crystal momentum, k = q.

Now, with this matrix element, we evaluate the IC rate.

$$\begin{array}{c}{\varGamma }_{{\rm{IC}}}^{({\mathcal{N}}\,)}=\frac{2{\rm{\pi }}}{\hbar }\frac{1}{2{I}_{{\rm{e}}}+1}\sum _{{M}_{{\rm{g}}}{M}_{{\rm{e}}}}\sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}\int {d}^{3}k\int {d}^{3}q|{W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}}){|}^{2}\\ \,\delta ({\bf{k}}-{\bf{q}})\delta ({\bf{k}}-{\bf{q}})\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{q}}}-{\omega }_{{\rm{nuc}}}).\end{array}$$

(8)

There is a product of two identical delta functions. q is replaced by k while integrating over q, but we encounter \(\delta ({\bf{0}})={\mathrm{lim}}_{\Delta {\bf{q}}\to 0}\delta (\Delta {\bf{q}})\). Using the following identity for each component of Δq:

$$\mathop{\mathrm{lim}}\limits_{\Delta {q}_{x}\to 0}\delta (\Delta {q}_{x})=\mathop{\mathrm{lim}}\limits_{{L}_{x}\to \infty }\mathop{\cos }\limits_{\Delta {q}_{x}\to 0}\frac{1}{2{\rm{\pi }}}{\int }_{-{L}_{x}/2}^{{L}_{x}/2}{{\rm{e}}}^{{\rm{i}}\Delta {q}_{x}x}{\rm{d}}x=\frac{{L}_{x}}{2{\rm{\pi }}},$$

in which Lx is the crystal size in the x-direction, we can show that

$$\mathop{\mathrm{lim}}\limits_{\Delta {\bf{q}}\to 0}\delta (\Delta {\bf{q}})=\frac{{V}_{{\rm{xtal}}}}{{(2{\rm{\pi }})}^{3}},$$

in which the crystal volume Vxtal = LxLyLz. This is similar to the formal time-domain limit in deriving Fermi’s golden rule; see, for example, p. 72 of ref. [61].

Thereby, the IC rate per crystal volume

$$\begin{array}{c}{\varGamma }_{{\rm{IC}}}^{({\mathcal{N}}\,)}/{V}_{{\rm{xtal}}}=\frac{2{\rm{\pi }}}{\hbar }\frac{1}{{(2{\rm{\pi }})}^{3}}\frac{1}{2{I}_{{\rm{e}}}+1}\sum _{{M}_{{\rm{g}}}{M}_{{\rm{e}}}}\sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}{\int }_{{\rm{BZ}}}{d}^{3}k|{W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}}){|}^{2}\\ \,\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{k}}}-\hbar {\omega }_{{\rm{nuc}}})\end{array}$$

(9)

The assumption made during the derivation was that all \({\mathcal{N}}\) 229Th nuclei were initially in the excited (isomer) state. Consider an ensemble of quantum emitters, with N(t) being the number of emitters in the excited state at time t, with a single emitter decay rate γ and

$$\begin{array}{l}{\rm{d}}N/{\rm{d}}t\,=\,-\gamma N(t)\Rightarrow N(t)=N(0)\exp -\gamma t\\ \,\,\,\Rightarrow \,{\rm{ensemble}}\,{\rm{decay}}\,{\rm{rate}}\,\varGamma \\ \,\,\,=\,-{\rm{d}}N/{\rm{d}}t\\ \,\,\,=\,\gamma N(0)\exp -\gamma t.\end{array}$$

(10)

We see that the ensemble decay rate Γ at t = 0 is γN(0). The experimentally relevant excited state population, however, decays as exp−γt. On the basis of this discussion, we define the experimentally measured IC decay rate

$${\varGamma }_{{\rm{IC}}}={\varGamma }_{{\rm{IC}}}^{({\mathcal{N}}\,)}/{\mathcal{N}}=\varOmega {\varGamma }_{{\rm{IC}}}^{({\mathcal{N}}\,)}/{V}_{{\rm{xtal}}}.$$

(11)

Following the derivation of interband electromagnetic absorption rates[41], we define a surface SE of constant energy in k-space through an implicit relation εck − εvk = ħωnuc. If the matrix element remains reasonably constant on SE, the rate simplifies to

$${\varGamma }_{{\rm{IC}}}=\frac{1}{{\tau }_{{\rm{IC}}}}=\frac{2{\rm{\pi }}}{\hbar }\frac{1}{2{I}_{{\rm{e}}}+1}\sum _{{M}_{{\rm{g}}}{M}_{{\rm{e}}}}\sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}\overline{|{W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}}){|}^{2}}{G}_{{\rm{cv}}}(\hbar {\omega }_{{\rm{nuc}}}).$$

(12)

with the JDOS

$${G}_{{\rm{cv}}}(E)=\frac{\varOmega }{{(2{\rm{\pi }})}^{3}}{\int }_{{\rm{BZ}}}{d}^{3}k\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{k}}}-E)=\frac{\varOmega }{{(2{\rm{\pi }})}^{3}}\int \frac{d{S}_{{\rm{E}}}}{|{\nabla }_{{\bf{k}}}{({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{k}}})}_{E}|}.$$

(13)

With this simplification, \(\overline{|{W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}}){|}^{2}}\) has the meaning of \(|{W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}}){|}^{2}\) averaged over the surface of constant energy SE.

This concludes the derivation of the IC rate (equation (1)).

Also worthy of mention, note that the electromagnetic absorption coefficient at laser frequency ωnuc is proportional to the same JDOS Gcv(ħωnuc). This can be used to back out the JDOS value from the laser absorption measurements at a frequency slightly detuned away from ωnuc.

To proceed with the computation of the hyperfine matrix element, we expand the functions u⁎ck(r) in terms of the Th atomic states. Owing to the short-range nature of the HFI, relativistic effects play an important role. As a result, we use relativistic Dirac spinors for the Th atomic states. However, equation (7) is given in terms of nonrelativistic (or scalar relativistic[62]) two-component spinors. Here, for simplicity, we replace equation (7) with

$${W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})\equiv \frac{{(2{\rm{\pi }})}^{3}}{\varOmega }\langle \,g|{\mathcal{M}}|e\rangle \cdot {\int }_{\varOmega }{d}^{3}r{u}_{c{\bf{k}}{\sigma }_{{\rm{c}}}}^{\dagger }({\bf{r}}){\mathcal{T}}\,({\bf{r}}){u}_{v{\bf{k}}{\sigma }_{{\rm{v}}}}({\bf{r}}),$$

(14)

in which \({u}_{n{\bf{k}}{\sigma }_{{\rm{n}}}}({\bf{r}})\) is now a four-component Dirac spinor with momentum k and spin projection σn.

The crystal function \({u}_{c{\bf{k}}{\sigma }_{{\rm{c}}}}({\bf{r}})\) (and similarly \({u}_{v{\bf{k}}{\sigma }_{{\rm{v}}}}({\bf{r}})\)) may be expanded in terms of the Th atomic states of definite principle and angular momentum quantum numbers φnjlm(r)

$${u}_{c{\bf{k}}{\sigma }_{{\rm{n}}}}({\bf{r}})=\sqrt{\frac{\varOmega }{{(2{\rm{\pi }})}^{3}}}\sum _{njlm}{a}_{njlm}(c{\bf{k}}{\sigma }_{{\rm{n}}}){\varphi }_{njlm}({\bf{r}})+\ldots ,$$

(15)

in which the ellipsis denotes contributions from O atomic states, which, owing to their small overlap with the Th nucleus, do not affect the HFI matrix element. Using the expansion (14), we may write

$${W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})=\sum _{njlm}\sum _{{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}{a}_{njlm}^{* }(c{\bf{k}}{\sigma }_{{\rm{c}}}){a}_{{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}(v{\bf{k}}{\sigma }_{{\rm{v}}}){\widetilde{W}}_{njlmn{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}^{{\rm{ge}}},$$

(16)

in which \({\widetilde{W}}_{njlmn{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}^{{\rm{ge}}}=\langle g|{\mathcal{M}}|e\rangle \cdot {\int }_{\varOmega }{d}^{3}r{\varphi }_{njlm}^{\dagger }({\bf{r}}){\mathcal{T}}({\bf{r}}){\varphi }_{{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}({\bf{r}})\).

Given the crystal functions and the atomic wavefunctions, the expansion coefficients anjlm(kσn) may be computed and the total HFI matrix element obtained. Here we make a simplifying assumption that only a few terms contribute substantially to the sum in equation (15). Furthermore, we shall neglect the contribution from cross terms in \({|{W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})|}^{2}\). With these simplifications, the IC rate may be written as

$$\begin{array}{l}{\varGamma }_{{\rm{IC}}}\,\approx \,\frac{{\rm{\pi }}}{\hbar }\frac{1}{2{I}_{{\rm{e}}}+1}\sum _{{M}_{{\rm{g}}}{M}_{{\rm{e}}}}\sum _{njlm}\sum _{{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}{|{\widetilde{W}}_{njlm{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}^{{\rm{ge}}}|}^{2}\\ \,\,\times \,\sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}\frac{2\varOmega }{{(2{\rm{\pi }})}^{3}}{\int }_{{\rm{BZ}}}{d}^{3}k{|{a}_{njlm}(c{\bf{k}}{\sigma }_{{\rm{c}}})|}^{2}{|{a}_{{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}(v{\bf{k}}{\sigma }_{{\rm{v}}})|}^{2}\\ \,\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{k}}}-\hbar {\omega }_{{\rm{nuc}}}).\end{array}$$

(17)

Let us now consider the matrix element \({W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})\) in more detail. Using the Wigner–Eckart theorem, we may write

$$\begin{array}{l}{\widetilde{W}}_{njlmn{j}^{{\prime} }{l}^{{\prime} }{m}^{{\prime} }}^{{\rm{ge}}}=\mathop{\sum }\limits_{\nu =-1}^{1}{(-1)}^{\nu +{I}_{{\rm{g}}}-{M}_{{\rm{g}}}+j-m}\left(\begin{array}{ccc}{I}_{{\rm{g}}} & 1 & {I}_{{\rm{e}}}\\ -{M}_{{\rm{g}}} & \nu & {M}_{{\rm{e}}}\end{array}\right)\\ \,\,\,\,\left(\begin{array}{ccc}j & 1 & {j}^{{\prime} }\\ -m & -\nu & {m}^{{\prime} }\end{array}\right)\langle g||{\mathcal{M}}||e\rangle \langle njl||{\mathcal{T}}||{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }\rangle .\end{array}$$

(18)

Here \(\langle g||{\mathcal{M}}||e\rangle \approx 0.84{\mu }_{{\rm{N}}}\) (μN is the nuclear magneton) is the reduced matrix element of the nuclear magnetic moment operator (see, for example, ref. [12]) and \(\langle njl||{\mathcal{T}}||{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }\rangle \) is the reduced matrix element of the rank-1 electronic HFI tensor. Th off-diagonal HFI matrix elements are at least two orders of magnitude smaller than the diagonal ones, so the most important contributions to the IC rate come from terms with (njl) = (n′j′l′). The reduced matrix element \(\langle njl||{\mathcal{T}}||njl\rangle \) may be related to the ground state HFI constant Anjl through[63]

$${A}_{njl}=\frac{{\mu }_{{\rm{g}}}}{{I}_{{\rm{g}}}\,j}\frac{(2j)!}{\sqrt{(2j-1)!(2j+2)!}}\langle njl||{\mathcal{T}}||njl\rangle ,$$

(19)

in which μg = 0.360(7)μN is the magnetic moment of the ground nuclear state[64]. With this, the summations over Mg and Me in equation (16) may be carried out, giving

$$\sum _{{M}_{{\rm{g}}}{M}_{{\rm{e}}}}{|{\widetilde{W}}_{njlmnjl{m}^{{\prime} }}^{{\rm{ge}}}|}^{2}=\frac{1}{3}\left[\mathop{\sum }\limits_{\nu =-1}^{1}{\left(\begin{array}{ccc}j & 1 & j\\ -m & \nu & {m}^{{\prime} }\end{array}\right)}^{2}\right]{\langle g||{\mathcal{M}}||e\rangle }^{2}{\langle njl||{\mathcal{T}}||njl\rangle }^{2}.$$

(20)

To proceed, we make a further assumption that the quantity in the second line of equation (16) does not depend strongly on the magnetic quantum numbers m and m′, that is,

$$\begin{array}{rcl} & & \sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}\frac{2\varOmega }{{(2{\rm{\pi }})}^{3}}{\int }_{{\rm{BZ}}}{d}^{3}k{|{a}_{njlm}(c{\bf{k}}{\sigma }_{{\rm{c}}})|}^{2}{|{a}_{njl{m}^{{\prime} }}(v{\bf{k}}{\sigma }_{{\rm{v}}})|}^{2}\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{k}}}-\hbar {\omega }_{{\rm{nuc}}})\\ & & \,\approx \sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}\frac{2\varOmega }{{(2{\rm{\pi }})}^{3}}{\int }_{{\rm{BZ}}}{d}^{3}k{|{a}_{njl}(c{\bf{k}}{\sigma }_{{\rm{c}}})|}^{2}{|{a}_{njl}(v{\bf{k}}{\sigma }_{{\rm{v}}})|}^{2}\\ & & \,\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{k}}}-\hbar {\omega }_{{\rm{nuc}}}),\end{array}$$

(21)

then the summation over m and m′ may be carried out analytically, finally giving

$$\begin{array}{l}{\varGamma }_{{\rm{IC}}}\,\approx \,\frac{{\rm{\pi }}}{3\hbar }\frac{1}{2{I}_{{\rm{e}}}+1}{\langle g||{\mathcal{M}}||e\rangle }^{2}\sum _{njl}{\langle njl||{\mathcal{T}}||njl\rangle }^{2}\\ \,\,\times \,\sum _{{\sigma }_{{\rm{c}}}{\sigma }_{{\rm{v}}}}\left[\frac{2\varOmega }{{(2{\rm{\pi }})}^{3}}{\int }_{{\rm{BZ}}}{d}^{3}k{|{a}_{njl}(c{\bf{k}}{\sigma }_{{\rm{c}}})|}^{2}{|{a}_{njl}(v{\bf{k}}{\sigma }_{{\rm{v}}})|}^{2}\right.\\ \,\delta ({\varepsilon }_{c{\bf{k}}}-{\varepsilon }_{v{\bf{k}}}-\hbar {\omega }_{{\rm{nuc}}})].\end{array}$$

(22)

We recognize the quantity in the square bracket as the (twice) PJDOS, which counts the number of allowed transitions at energy ħωnuc between the atomic component |njl⟩ of |vkσv⟩ and the atomic component |njl⟩ of |ckσc⟩. In Fig. 3c, we present the most relevant PJDOS. These PJDOS were computed using VASP (see the next section) and use the scalar relativistic approximation of Koelling and Harmon[62]. To obtain the relativistic PJDOS, we use the procedure developed in ref. [12], that is, for any l > 0, \({|{a}_{n(l-1/2)l}(c{\bf{k}}{\sigma }_{{\rm{c}}})|}^{2}={|{a}_{n(l+1/2)l}(c{\bf{k}}{\sigma }_{{\rm{c}}})|}^{2}={|{a}_{nl}|}^{2}/2\), in which |anl|2 is the VASP projection. As a result, for l > 0, the relativistic (njl) → (njl) PJDOS is a quarter of the scalar relativistic value. On the other hand, because the VASP calculation was independent of spin, the double summation over σc and σv in equation (21) results in a factor of 2 × 2 = 4. In Extended Data Table 2, we list the HFI constants A, the corresponding ‘diagonal’ values of the PJDOS at the nuclear energy for various Th atomic states and the contributions to the IC rate. Using these values, we arrive at an estimate for the IC rate of

$${\varGamma }_{{\rm{IC}}}\approx 1.2\times 1{0}^{4}\,{{\rm{s}}}^{-1},$$

(23)

corresponding to an IC lifetime of 80 μs.

In obtaining the estimate in equation (22), we have neglected the contribution from the cross terms in the expansion of \({|{W}_{c{\sigma }_{{\rm{c}}}v{\sigma }_{{\rm{v}}}}^{{\rm{ge}}}({\bf{k}})|}^{2}\). Neglecting off-diagonal HFI matrix elements, the contribution from these terms reads

$$\begin{array}{c}{\varGamma }_{{\rm{I}}{\rm{C}}}^{{\rm{cross\; terms}}}\,\approx \,\frac{{\rm{\pi }}}{3{\hbar }}\frac{1}{2{I}_{{\rm{e}}}+1}{\langle g||{\mathcal{M}}||e\rangle }^{2}\\ \times \sum _{njl\ne {n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }}\langle njl||{\mathcal{T}}\,||njl\rangle \langle {n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }||{\mathcal{T}}\,||{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }\rangle \\ \times \,\sum _{{{\sigma }}_{{\rm{c}}}{{\sigma }}_{{\rm{v}}}}\left[\frac{2{\Omega }}{{(2{\rm{\pi }})}^{3}}{\int }_{{\rm{B}}{\rm{Z}}}{d}^{3}k{a}_{njl}^{\ast }(c{\bf{k}}{{\sigma }}_{{\rm{c}}}){a}_{njl}(v{\bf{k}}{{\sigma }}_{{\rm{v}}}){a}_{{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }}(c{\bf{k}}{{\sigma }}_{{\rm{c}}}){a}_{{n}^{{\prime} }{j}^{{\prime} }{l}^{{\prime} }}^{\ast }(v{\bf{k}}{{\sigma }}_{{\rm{v}}})\delta ({{\varepsilon }}_{c{\bf{k}}}-{{\varepsilon }}_{v{\bf{k}}}-{\hbar }{\omega }_{{\rm{n}}{\rm{u}}{\rm{c}}})\right].\end{array}$$

(24)

Heuristically, we expect the different terms in equation (23) to have different phases and, thus, their total sum to be small. A more detailed calculation in which the expansion coefficients anjl(ckσc) and anjl(vkσv) are computed explicitly is needed to precisely gauge the accuracy of this approximation. This is the subject of a future work. Here we assume that the expansion coefficients have the same phase (and may thus be taken as all real) and estimate the maximum contributions from the cross terms. In this case, the quantity in the square bracket of equation (23) is a ‘cross-PJDOS’, which is obtained by summing over the delta functions weighted by the product of square roots of |anjl|2. The maximum values for the cross terms are listed in Extended Data Table 3. The sum of these cross contributions amounts to

$${\varGamma }_{{\rm{IC}}}^{\max \,{\rm{cross}}\,{\rm{terms}}}\approx 2.6\times 1{0}^{4}\,{{\rm{s}}}^{-1}.$$

(25)

The estimated maximum IC rate is therefore

$${\varGamma }_{{\rm{IC}}}^{\max }\approx 3.8\times 1{0}^{4}\,{{\rm{s}}}^{-1},$$

(26)

corresponding to an IC lifetime of 30 μs.

A further reduction in the IC lifetime is very plausible if we that the relative error in making the non-relativistic approximation |an(l−1/2)l(ckσc)|2 = |an(l+1/2)l(ckσc)|2 = |anl|2/2 is approximately (αZ)2, that is, about 40% for Z = 90 of Th. Because relativistic contraction generally increases the electron density near the origin, the IC rate including relativistic effects may be larger than its non-relativistic counterpart by a factor of about 1.4^2 = 2, thus further reducing the estimated IC lifetime to 15 μs.

Computational methods for electronic structure theory

Calculations were performed with VASP version 6.4.2 (ref. [65]) using the PAW[66] method. The structure of ThO_2 was optimized with DFT in the conventional unit cell using the PBE[67] functional, 6-6-6 Γ-centred k-mesh and a 500-eV plane wave cut-off. Our computed lattice parameter is 5.617 Å, which matches very well with experimental measurements of 5.597 Å (ref. [68]). Subsequent electronic structure calculations used the optimized structure in the primitive cell representation.

Parameters for G_0W_0 calculations69,70,71, specifically the k-mesh, plane wave cut-off energy and the number of frequency grid points (NOMEGA tag in VASP), were tested for convergence of the bandgap. The k-mesh was tested with a 400-eV cut-off and NOMEGA = 80, the cut-off was tested with a 6-6-6 k-mesh and NOMEGA = 80 and NOMEGA was tested with a 400-eV cut-off and a 4-4-4 k-mesh. The number of unoccupied bands was 812 (there are 12 occupied bands). The results of these tests are shown in Extended Data Tables 4–6. On the basis of these results, further G_0W_0 calculations were done with an 8-8-8 k-mesh, a 500-eV plane wave cut-off and 80 frequency grid points.

Our converged bandgap of 6.20 eV agrees well with single-crystal and thin-film measurements of 5.9 eV (refs. 42,43), although we note that a range of bandgaps has been reported on the basis of a range of experimental samples (thin films, nanoparticles, single crystals)72,73,74,75,76 because the measured absorption spectrum can be strongly influenced by morphology, defects and the effects of irradiation.

The BSE is a two-particle Green’s function formalism to explicitly account for electron–hole interactions in electronic excited states77,78. The G_0W_0 + BSE parameters were converged with respect to the predicted absorption spectrum. The tested parameters were the highest excitation energy (OMEGAMAX) and the number of occupied and unoccupied bands (NBANDSO and NBANDSV, respectively) considered in the BSE calculation. Absorption spectra computed with various settings for these methods are shown in Extended Data Fig. 2a,b. On the basis of these tests, further G_0W_0 + BSE calculations were carried out with OMEGAMAX = 20 eV and (NBANDSO, NBANDSV) = (8, 16).

We can validate our method against published experimental data by computing the dielectric function with G_0W_0 + BSE. Our computed data, shown in Extended Data Fig. 2c,d, are a good match with the spectroscopic data in ref. [72]. Some differences in the imaginary part of the dielectric function ε_2, namely the rate at which ε_2 increases with increasing energy from 5 to 8 eV and the low-energy non-zero ‘tail’ in the experimental spectrum, we attribute to the presence of defects in the real crystal, as noted by the authors of the experimental study.

We also compute the absorption spectrum of ThO_2 with G_0W_0 + BSE, as shown in Extended Data Fig. 2e. The value at the nuclear transition energy is 1 × 10^6 cm−1 ≡ 0.1 nm−1, in agreement with ellipsometric measurements[35].

Absorption spectra and dielectric functions were processed from VASP output with VASPKIT[79].

Isomer shift

The isomer shift originates from differences in the nuclear charge distribution between the ground and excited nuclear states. The value of the shift depends on the local electronic environment of 229Th. Here we follow the formalism[40] that combines relativistic many-body atomic-structure methods with periodic DFT to evaluate the isomer shifts in 229ThO_2. The scalar relativistic periodic DFT reproduces valence band properties, whereas relativistic atomic-structure methods capture the essential core-electron relaxation effects. The valence band contribution to the isomer shift in 229Th solid-state hosts is expressed as[40]

$$\delta {E}_{{\rm{iso}}}^{{\rm{VB}}}=\sum _{{\ell }}{{\rm{IPDOS}}}_{{\ell }}\delta {\varepsilon }_{{\ell }}^{{\rm{iso}}}({{\rm{Th}}}^{3+}),$$

(27)

in which IPDOSℓ denotes the integrated projected (on 229Th) valence band density of states for angular momentum ℓ and \(\delta {\varepsilon }_{{\ell }}^{{\rm{iso}}}({{\rm{Th}}}^{3+})\) is the isomer shift for the lowest-energy valence orbitals of Th3+ of angular momentum ℓ. The valence band isomer shift is to be added to the isomer shift in 229Th4+ ions; this contribution remains constant across a wide range of materials. Extended Data Table 7 presents the calculated isomer shifts for 229ThO_2 for three different methods. Compared with the PBE and MBJ80,81 methods, the G_0W_0 method includes self-energy correction and, as discussed earlier, we consider it of a higher quality.

Extended Data Table 8 presents the calculated isomer shifts \(\delta {E}_{{\rm{iso}}}^{{\rm{VB}}}\), the corresponding nuclear clock frequencies ν of 229Th and their offsets Δν relative to the ThO_2 reference for a range of solid-state hosts.

Determination of clock stability

We estimate the clock stability by[82]

$$\sigma =\frac{1}{2{\rm{\pi }}QS}\sqrt{\frac{{T}_{{\rm{e}}}+{T}_{{\rm{c}}}}{\tau }},$$

(28)

in which Q = f_0/Δf is the transition quality factor, S is the signal-to-noise ratio, Te is the excitation time, Tc is the electron collection time and τ is the averaging time. As stated in the text, we assume that Δf is dominated by the homogeneous lifetime broadening owing to IC and use Δf = 16 kHz. For our analysis, we assume Te = Tc = 12 μs and a shot-noise-limited signal-to-noise ratio given by \(S=\sqrt{{N}_{\det }}\), in which Ndet is given by

$${N}_{\det }={N}_{{\rm{e}}}\times (1-{{\rm{e}}}^{-{T}_{{\rm{c}}}/{\tau }_{{\rm{IC}}}}),$$

(29)

Ne (≈2.5 × 10^7) is the total number of 229Th nuclei excited, η = 0.5 is the electron detection efficiency in the clock system and τIC = 12 μs. Ne is calculated assuming that the probe laser linewidth is much smaller than the lifetime-limited transition linewidth, and the probe laser power is 100 μW. From this, we obtain a projected clock performance of about \(2\times 1{0}^{-18}/\sqrt{\tau }\).

Data availability

The data that support the findings of this study are available from the corresponding author on request.

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Acknowledgements

This work was supported by NSF awards PHYS-2013011, PHY-2412869, PHY-2513134, and PHY-2207546 and ARO award W911NF-11-1-0369. P.G.T. and K.S. acknowledge support by BaCaTeC (grant 7 [2029-2]) and funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program (‘ThoriumNuclearClock’, Grant Agreement No. 856415). E.R.H. acknowledges institutional support by the NSF QLCI award OMA-2016245. This work used Bridges-2 at Pittsburgh Supercomputing Center through allocation PHY230110 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) programme, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603 and #2138296. H.B.T.T. and D.A.R. acknowledge support from the Laboratory Directed Research and Development programme under projects 20258345CT-IMS and 20260021DR, as well as computational resources provided by the Institutional Computing Program through the Center for Integrated Nanotechnologies, a DOE BES user facility, at Los Alamos National Laboratory.

Author information

Author notes

1. These authors contributed equally: Ricky Elwell, James E. S. Terhune, Christian Schneider

Authors and Affiliations

1. Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, CA, USA

Ricky Elwell, James E. S. Terhune, Christian Schneider & Eric R. Hudson

2. Department of Chemistry, University of Manchester, Manchester, UK

Harry W. T. Morgan

3. Department of Physics, University of Nevada, Reno, Reno, NV, USA

Hoang Bao Tran Tan, Udeshika C. Perera & Andrei Derevianko

4. Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM, USA

Hoang Bao Tran Tan & Daniel A. Rehn

5. Eckert & Ziegler Analytics, Inc., Atlanta, GA, USA

Marisa C. Alfonso

6. Department of Physics, Johannes Gutenberg-Universität Mainz, Mainz, Germany

Lars von der Wense

7. Faculty of Physics, Ludwig-Maximilians-Universität München, Garching, Germany

Benedict Seiferle, Kevin Scharl & Peter G. Thirolf

8. Challenge Institute for Quantum Computation, University of California, Los Angeles, Los Angeles, CA, USA

Eric R. Hudson

9. Center for Quantum Science and Engineering, University of California, Los Angeles, Los Angeles, CA, USA

Eric R. Hudson

Contributions

R.E., J.E.S.T., C.S. and E.R.H. constructed the experimental chamber and performed the spectroscopy measurement. H.W.T.M., H.B.T.T., U.C.P., D.A.R. and A.D. performed theory calculations. M.C.A. produced and characterized the sample. L.v.d.W., B.S., K.S. and P.G.T. calibrated and provided detectors. All authors contributed to the manuscript.

Corresponding author

Correspondence to Eric R. Hudson.

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Competing interests

E.R.H. declares a provisional patent (U.S. provisional patent application no. 63/814,873) related to the findings presented in this work.

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Nature thanks Olga Kocharovskaya, who co-reviewed with Xiwen Zhang, Xu Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Electron trajectory simulations.

SIMION simulations of electron trajectories under the voltage biasing and static magnetic field used in the experiment. a, Trajectories of IC electrons from the target region. The magnetic field bends them towards the detection MCP through a saddle in the electric potential. b, The trajectories of photoelectrons generated by VUV scattered light at random locations in the chamber. Most either crash into the chamber walls or end up falling into the electrode biased at +2,500 V.

Extended Data Fig. 2 ThO[2] optical properties through DFT.

a,b, Absorption spectra of ThO_2 computed with G_0W_0 + BSE using different OMEGAMAX (a) and (NBANDSO, NBANDSV) (b) settings. The meanings of these parameters are given in the text. c,d, Real (ε_1) and imaginary (ε_2) parts of the frequency-dependent dielectric function for bulk ThO_2 computed with G_0W_0 + BSE. e, Absorption spectrum of bulk ThO_2 computed with G_0W_0 + BSE.

Extended Data Table 1 Parameter values and estimated relative errors used in the calculation of expected IC signal

Extended Data Table 2 Magnetic dipole A HFI constants for low-lying levels of 229Th3+, the corresponding values of PJDOS at the nuclear energy about 8.35 eV and the contributions to the IC rate

Extended Data Table 3 Maximum contributions to the IC rate from cross terms arising from the expansion in equation (15), assuming that all of the expansion coefficients are in phase

Extended Data Table 4 Convergence of the G_0W_0 bandgap with respect to k-mesh

Extended Data Table 5 Convergence of the G_0W_0 bandgap with respect to plane wave cut-off

Extended Data Table 6 Convergence of the G_0W_0 bandgap with respect to frequency grid points (NOMEGA)

Extended Data Table 7 Integrated partial densities of states, IPDOSℓ, and the products, \({\boldsymbol{\delta }}{{\boldsymbol{E}}}_{{\bf{iso}}{\boldsymbol{,}}{\boldsymbol{\ell }}}^{{\bf{VB}}}{\boldsymbol{=}}{{\bf{IPDOS}}}_{{\boldsymbol{\ell }}}{\boldsymbol{\delta }}{{\boldsymbol{\varepsilon }}}_{{\boldsymbol{\ell }}}^{{\bf{iso}}}{\boldsymbol{(}}{{\bf{Th}}}^{{\bf{3}}{\boldsymbol{+}}}{\boldsymbol{)}}\), obtained with the three electronic structure methods

Extended Data Table 8 Nuclear clock frequencies ν obtained from the isomer shifts \({\boldsymbol{\delta }}{{\boldsymbol{E}}}_{{\bf{iso}}}^{{\bf{VB}}}\) and their offsets Δν relative to ThO_2 computed with MBJ

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Elwell, R., Terhune, J.E.S., Schneider, C. et al. Laser-based conversion electron Mössbauer spectroscopy of 229ThO_2. Nature 648, 300–305 (2025). https://doi.org/10.1038/s41586-025-09776-4

- Received: 30 May 2025

- Accepted: 20 October 2025

- Published: 10 December 2025

- Version of record: 10 December 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09776-4

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Observation of deuteron and antideuteron formation from resonance-decay nucleons

The ALICE Collaboration

Nature volume 648, pages 306–311 (2025)

Abstract

High-energy hadronic collisions generate environments characterized by temperatures above 100 MeV (refs. 1,2), about 100,000 times hotter than the centre of the Sun. At present, it is therefore unclear how light (anti)nuclei with mass number A of a few units, such as the deuteron, 3He or 4He, each bound by only a few MeV, can emerge from these collisions3,4. Here, the ALICE Collaboration reports that deuteron–pion momentum correlations in proton–proton (pp) collisions provide model-independent evidence that about 90% of the observed (anti)deuterons are produced in nuclear reactions[5] following the decay of short-lived resonances, such as the Δ(1232). These findings, obtained by the ALICE Collaboration at the Large Hadron Collider, resolve a gap in our understanding of nucleosynthesis in ultrarelativistic hadronic collisions. Apart from offering insights on how (anti)nuclei are formed in hadronic collisions, the results can be used in the modelling of the production of light and heavy nuclei in cosmic rays[6] and dark-matter decays7,8.

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Main

Nuclear physicists have long been intrigued by the microscopic mechanism behind the formation of light nuclei and antinuclei in hadron–hadron collisions3,4. In ultrarelativistic heavy-ion collisions with energies per nucleon up to a few TeV (10^12 eV), the study of particle production is directly connected to the confinement of colour charge in colour-neutral hadrons. These collisions produce a quark–gluon plasma, a state in which quarks and gluons are deconfined, and as the system evolves, they bind into hadrons and light (anti)nuclei1,9. As the binding energies of light (anti)nuclei are substantially lower (2.23 MeV for deuteron, 7.72 MeV for 3He; ref. [10]) than the average kinetic energy of hadrons in these energetic collisions (of the order of 100 MeV; ref. [1]), the question is about both the formation of loosely bound nuclei and their survival through the hadronic phase that follows the hadronization of the quark–gluon plasma. This issue is also relevant in ultrarelativistic proton–proton (pp) and proton–nucleus (p–A) collisions, in which the formation of a quark–gluon plasma remains under experimental and theoretical scrutiny and average kinetic energies above 100 MeV can still be achieved[2].

The study of (anti)nucleus formation in hadronic collisions is of importance in astrophysics. On one front, the precise composition of ultrahigh-energy (>PeV) cosmic rays, particularly their heavier elements (A > 50) component, remains an open question[6]. A microscopic modelling of nucleus formation in ultrarelativistic hadron collisions is an essential ingredient for understanding the composition of these cosmic rays and for uncovering the origin of particle acceleration mechanisms in the Universe[11]. On another front, antinuclei formation—whether from cosmic-ray interactions with the interstellar medium or as potential products of dark-matter decay—plays a pivotal part in indirect searches for dark matter7,8,12. Experimental investigations into the microscopic processes underlying light nucleus and antinucleus formation thus offer a dual benefit: they advance the knowledge of the strong interaction in the non-perturbative regime and provide the quantitative framework needed to decode the spectra of cosmic rays and their origins.

The yields of nuclei such as deuterons (p–n bound system), 3H (p–n–n), 3He (p–p–n), 4He (p–p–n–n), \(\genfrac{}{}{0ex}{}{3}{\Lambda }{\rm{H}}\) (Λ–p–n) and their corresponding antinuclei have been precisely measured at the Relativistic Heavy Ion Collider in Au–Au collisions at centre-of-mass energies per nucleon pair (√sNN) across an energy range of 7.7–200 GeV (refs. 13,14,15,16) and at the Large Hadron Collider (LHC) for pp collisions at √s ranging from 0.9 TeV to 13 TeV, as well as for p–Pb and Pb–Pb collisions at √sNN = 2.76–8.16 TeV (refs. 17,18,19,20). Current understanding suggests that nuclei can be produced either through direct emission as multi-quark states following a collision, similar to other hadrons such as protons or pions, or through a secondary binding mechanism of nucleons.

Two types of models have been used to study these mechanisms. Statistical hadronization models describe the direct production and assume that hadrons and nuclei are directly emitted from a source in thermal and chemical equilibrium, with abundances determined by the particle mass, the system temperature, volume and quantum number conservation9,21,22. This work uses the canonical statistical model (CSM)[23], which is better suited for pp collisions. Although CSMs predict yields effectively, they do not provide insights into the microscopic mechanisms driving (anti)nucleus formation. By contrast, coalescence models12,24,25,26,27 emulate binding mechanisms and they assume that (anti)nucleons form independently before binding to create (anti)nuclei. This approach incorporates microscopic parameters, such as the spatial proximity of nucleons alongside their strong interactions, allowing for a satisfactory description of yields and momentum distributions25,28.

Microscopic calculations implemented in event generators for heavy-ion collisions5,29 include pion-catalysed reactions—both formation and disintegration (for example, π + p + n ⇔ π + d)—and successfully describe measured nuclear yields. The important aspect of these models is that a third body, such as a meson, aids the binding process by carrying away the excess energy.

Overall a direct experimental evidence for the microscopic mechanisms of (anti)nucleus formation remains unknown. Femtoscopy provides a complementary approach by examining pion–(anti)deuteron (π–d) momentum correlations and offers direct insights into the microscopic processes underlying (anti)deuteron formation. This technique has been effectively used by the ALICE Collaboration to study various hadron pairs produced in pp and p–Pb collisions at the LHC, see for example, ref. [30] and the references therein, shedding light on their residual strong interactions.

Using π–d femtoscopy correlations, the study presented in this paper shows, in a model-independent manner, that (anti)deuterons are formed following the decay of strong resonances, such as the Δ(1232) (hereafter Δ). Considering the possible contribution to all produced resonances, we estimate that 88.9 ± 6.3% of the observed (anti)deuterons are generated through binding processes. These findings resolve a longstanding puzzle regarding the formation of light (anti)nuclei in collider experiments and provide a robust foundation for further modelling of nucleosynthesis from hadronic collisions, both in accelerators and in the Universe.

Resonances and correlation function

As a bound state of a proton and a neutron, the deuteron may inherit correlations developed by its constituent nucleons during the evolution of the collision. The study of π–d correlations offers a sensitive probe of this process. If deuterons are produced thermally alongside pions, any correlation signal between them would arise solely from final-state interactions. By contrast, if deuterons form through the coalescence of nucleons originating from the decay of an intermediate resonance, the resulting π–d correlation function could retain the signatures of that resonance.

The correlation function C(k*) is the key experimental observable, and k* is the single-particle momentum in the pair rest frame (PRF). Experimentally, \(C({k}^{* })={\mathcal{N}}\,[{N}_{{\rm{same}}}({k}^{* })/{N}_{{\rm{mixed}}}({k}^{* })]\), where Nsame(k*) (same-event sample) is the distribution of relative momenta between the π–d pair measured for pions and deuterons stemming from the same collision[31]. Equivalently, Nmixed(k*) (mixed-event sample) is an uncorrelated reference obtained by building the distribution through the combination of pions and deuterons originating from different collisions. Finally, \({\mathcal{N}}\) is a normalization factor ensuring the proper convergence of C(k*) to unity at large k*. In the case of non-interacting particles, the correlation function is equal to unity for all k* as the relative momentum distribution is purely governed by the underlying single-particle phase space, which is the same for Nsame(k*) and Nmixed(k*) distributions. An attractive interaction enhances the correlation function above unity at low k* ≲ 200 MeV c−1, whereas a repulsive interaction leads to a depletion below unity. A resonance that decays into the hadron pair of interest would produce a peak in the k* spectrum.

Figure 1 shows three scenarios of (anti)deuteron production mechanisms and interactions and the resulting π±–d correlations. Simulations were performed to quantify the effects of the different production scenarios, and details are provided in the Methods. All scenarios include repulsive (red curves) and attractive (green curves) Coulomb interactions for the π+–d and π−–d systems, respectively. The strong interaction contribution is minimal because of the small scattering parameters of the π±−d system and is hence neglected32,33. In the first two scenarios (Fig. 1a,b), directly produced deuterons and pions are considered. The simulation results shown on the right were obtained assuming that pions and (anti)deuterons are produced following a canonical statistical hadronization scheme, ThermalFIST[34]. The obtained correlation functions are multiplied by the Coulomb correlation function. The results indicate a depletion in the correlation function at low k* for π+–d and an enhancement for π−–d because of the Coulomb interaction.

Fig. 1: (Anti)deuteron production scenarios.

Illustration of three scenarios for deuteron production and interaction with pions (left) and the resulting π±–d correlation functions (right). All scenarios include Coulomb attraction between π−–d (green curves) and Coulomb repulsion between the π+–d (red curves). The dashed lines always show the correlation function using Coulomb interaction. a,b, Thermally produced deuterons with only Coulomb (a) and Coulomb + elastic + inelastic (b) interactions, respectively. c, Deuteron formation by nuclear binding following Δ-resonance decays. All the simulations include the charge conjugates (\({{\rm{\pi }}}^{+}-{\rm{d}}\equiv {{\rm{\pi }}}^{+}-{\rm{d}}\oplus {{\rm{\pi }}}^{-}-\overline{{\rm{d}}}\) and \({{\rm{\pi }}}^{-}-{\rm{d}}\equiv {{\rm{\pi }}}^{-}-{\rm{d}}\oplus {{\rm{\pi }}}^{+}-\overline{{\rm{d}}}\)). The bandwidths corresponds to the statistical uncertainties of the models.

In Fig. 1b, the elastic and inelastic scattering of pions and deuterons is considered. This is tested by using the hadronic transport model SMASH[35] as an afterburner to ThermalFIST to simulate inelastic and elastic rescattering according to the experimental cross-sections. The elastic processes do not modify the shape of the correlation function, as both the incoming and outgoing π±–d pairs must conserve energy, ensuring that their relative momentum k* remains unchanged. The same holds for pseudo-elastic processes, in which an intermediate Δ resonance is formed, as in π + (pn) → pΔ → π + (pn).

By contrast, inelastic π±–d scattering leads to deuteron destruction, reducing the number of measurable pairs in the k* region in which the inelastic cross-section reaches its maximum. Both elastic and inelastic cross-sections peak at the nominal Δ mass (k* ≈ 240 MeV c−1), and the inelastic one is three times larger than the elastic contribution[36]. Figure 1b (right) shows the results of these simulations for the π+–d and π−–d cases. As expected, a depletion at the relative momentum k* ≈ 240 MeV c−1, corresponding to the peak of the inelastic cross-section, is observed.

In Fig. 1c, a deuteron forms when a primordial nucleon binds with one from a Δ decay. These resonances are very short-lived excited states of nucleons and decay after approximately 1.5 fm c−1 into π–nucleon pairs. Considering all charge states (Δ++,+,0,−), they are expected to contribute 43% of the nucleon yield in pp collisions at the LHC34,37. Measurements of the π±–p femtoscopy correlations by ALICE[38] have already shown the presence of the Δ resonances, modified by rescattering and regeneration effects (Methods). For the formation of deuterons, the possible combinations include neutron–proton binding from Δ++ → π+–p or Δ^0 → π−–p, proton–neutron binding from Δ± → π±–n, and binding of two nucleons from separate Δ decays. This scenario was simulated by exploiting a state-of-the-art coalescence afterburner[25] combined with the EPOS 3 event generator39,40. The latter accounts for resonance production and their decays, whereas the aforementioned rescattering and regeneration effects are not included in the simulations. The results are shown in the right panel, and a clear peak appears in correspondence with the Δ resonance nominal mass. The observed peak is due to the residual correlation between the pion and an (anti)nucleon from the Δ decay during the (anti)deuteron formation process.

The three patterns in the correlation function correspond to different physics scenarios and are easily distinguishable from one another. The observed patterns remain unchanged across different models: although model parametrization may shift or rescale the structures, their shapes are preserved. This constitutes a solid reference to proceed with the interpretation of the experimental data.

Discussion

The experimental π+–d and π−–d correlation functions have been measured in pp collisions at √s = 13 TeV. Charged pions (π±), deuteron (d) and antideuteron (\(\overline{{\rm{d}}}\)) tracks are reconstructed with the ALICE detector, and their momentum transverse to the beam direction (pT) is measured in the range pT ∈ [0.14, 4.0] GeV c−1 for pions and pT ∈ [0.8, 2.4]  GeV c−1 for deuterons. The excellent particle identification and tracking abilities of the ALICE detector provide samples of π+ (π−) and d (\(\overline{{\rm{d}}}\)) with a purity of 99% and 100%, respectively. Further details on the particle selection and evaluation of the systematic uncertainties are described in the Methods. After the selection of pions and (anti)deuterons, the correlation functions for pairs of particles (π+–d and π−–d) and their charge conjugates (\({{\rm{\pi }}}^{+}-\overline{{\rm{d}}}\) and \({{\rm{\pi }}}^{-}-\overline{{\rm{d}}}\)) are obtained. As the same interaction governs hadron–hadron and antihadron–antihadron pairs[31], the sum of particles and antiparticles is considered (\({{\rm{\pi }}}^{+}-{\rm{d}}\equiv {{\rm{\pi }}}^{+}-{\rm{d}}\oplus {{\rm{\pi }}}^{-}-\overline{{\rm{d}}}\) and \({{\rm{\pi }}}^{-}-{\rm{d}}\equiv {{\rm{\pi }}}^{-}-{\rm{d}}\oplus {{\rm{\pi }}}^{+}-\overline{{\rm{d}}}\)) in the following. The resulting π−–d and π+–d correlation functions are shown by the open markers in Fig. 2a,b. The grey boxes around the markers represent the systematic uncertainties, and the vertical bars show the statistical uncertainties. The fit results for the π−–d and π+–d correlation functions are shown in Fig. 2a,b, respectively.

Fig. 2: Experimental π−–d and π+–d correlation functions.

The data are obtained from high-multiplicity pp collisions at √s = 13 TeV. a, The measured π−–d correlation function together with the corresponding fit function (magenta). The brown cross-hatched band represents contributions from the Δ resonance, the blue band denotes the Coulomb and strong FSI interactions, and the teal diagonally hatched band corresponds to the residual background. The widths of the bands indicate the fit uncertainty. b, In the same representation, the π+–d correlation function. However, the strong FSI interaction is neglected for this system. The χ^2 per degree of freedom is 14/15 for both correlations.

The measured π±–d correlation functions are modelled and fitted using a decomposition approach summarized by the relation \({C}_{{\rm{fit}}}({k}^{* })=\varepsilon ({k}^{* })\otimes B({k}^{* })[{\lambda }_{{\rm{gen}}}{C}_{{\rm{gen}}}({k}^{* })+(1-{\lambda }_{{\rm{gen}}})]\) (Methods). Here, ε(k*) represents a correction for momentum resolution effects, and B(k*) is a baseline accounting for residual background correlations. The latter arise mainly from non-primary pions produced in weak decays of long-lived resonances, as well as from secondary particles originating from interactions with the detector material. These contributions can mimic correlated pairs and must be accounted for in the modelling. The parameter λgen quantifies the fraction of genuine π±–d pairs, with the non-genuine component primarily arising from the feed-down of long-lived resonances into pions[41] with a lifetime τ > 5 fm c−1. The term Cgen(k*) denotes the corresponding genuine correlation function that contains Coulomb and strong interactions, alongside contributions from the Δ resonance. The interaction components are modelled using the CATS (Correlation Analysis Tool using the Schrödinger equation) framework[42]. Theoretically, \(C({k}^{* })=\int {{\rm{d}}}^{3}{r}^{* }S({r}^{* })\times {| \psi ({{\bf{k}}}^{* },{{\bf{r}}}^{* })| }^{2}\), where r* is the relative distance (in the PRF) between the particles at the time of their effective emission, ψ(k*, r*) is the wavefunction of the pair relative motion, and S(r*) is the source function corresponding to the probability to emit the pair at a certain relative distance r* (ref. [43]). Dedicated studies of the source function in pp collisions at √s = 13 TeV performed by the ALICE Collaboration showed a common emission source for all hadrons38,41,44. This source is typically modelled by a Gaussian function with a standard deviation (an effective size of the source) of reff ≈ 1.5 fm, obtained by accounting for the contribution of short-lived resonances (see Methods for details).

For the source, an effective Gaussian distribution with reff = 1.51 ± 0.12 fm was used (Methods). The real part of the π−–d potential is included in the fit. However, owing to the small scattering parameters of the π±–d system, the contribution is negligible32,33. To gauge the influence of the resonance decays on the π±–d correlations, the contributions of the Δ resonances extracted from the measured π±–p correlations are modified assuming that the nucleon emerging from the Δ decay coalesces with an additional nucleon to form a deuteron. The assumption is that the two nucleons have similar momenta (see Methods for details). Finally, the relative momentum k* between the pion from the Δ decay and the deuteron is evaluated. All charge states Δ++,+,0,− are considered, assuming the Δ+,− peak has the same shape as Δ++,0 from π±–p correlations. The experimental correlation functions are well described, confirming the scenario in which the deuteron is formed after the decay of the Δ by a fusion process as assumed in Fig. 1c. An excellent description (Fig. 2) of the measured correlation function is obtained by adopting the data-driven shape of the Δ derived from π±–p correlations[38]. The Δ shape in the π±–d correlation function exhibits a shift towards lower masses due to rescattering effects, consistent with the displacement observed in Fig. 2 relative to the nominal Δ position at k* ≈ 240 MeV c−1. The simulations obtained with the EPOS 3 event generator at present do not include the rescattering of the Δ decay products, resulting in no shift of the Δ peak in Fig. 1c.

The evidence of Δ decay in the π±–d correlation function is model-independent, as freeing the radius parameter does not affect the results, the Coulomb interaction is inherently model-independent and the residual background is accounted for in the systematic uncertainties of the fit.

Furthermore, the fraction of deuterons produced following a resonance decay is extracted. The contribution from Δ resonances is evaluated by integrating the peak in the π±–d correlation functions corresponding to these resonances, subtracting the number of π±–d pairs expected in the same k* region without a nucleon originating from the Δ resonance (Coulomb + background) and dividing the result by the total number of detected deuterons. The result is corrected for combinatorial effects, reconstruction efficiency and the non-measured π^0 final state. With these corrections, the fraction of deuterons produced by a Δ resonance is calculated to be 60.6 ± 4.1% (Methods). To test the compatibility of this measurement with expectations from event generators, the EPOS 3 model is used. For this, the yield of baryonic resonances in EPOS 3 was adjusted to match the predictions of the CSM ThermalFIST for pp collisions at √s = 13 TeV. Furthermore, the change in the pion detector acceptance resulting from the shift in the experimentally observed Δ spectral shape is taken into account. In this simulation, the fraction of deuteron for which at least one of the nucleons stems from any Δ resonance and both the deuteron and the π are found within the acceptance is determined to be 53.8 ± 3.1% (more details in the Methods). The fact that these two fractions are in agreement within 1.32 standard deviations demonstrates that the survival probability of deuterons produced in pp collisions at the LHC is very high. This is the case because (anti)nuclei are produced after the resonance decays, in which spectral temperatures of about 20 MeV (see the Methods for details) have been evaluated, much lower than the average kinetic energy of hadrons (about 100 MeV) in pp collisions at the LHC.

Deuterons can form through fusion after any strong resonance decay, with Δ resonances accounting for 77.3 ± 1.2% of all cases. Moreover, considering that 15.5 ± 0.5% of Δ resonances are not properly reconstructed because of the detector acceptance effects, the experimental fraction of deuterons from Δ can be scaled up to a total fraction of deuterons originating from all resonances of 88.9 ± 6.3%. These results indicate not only that the presence of resonances can contribute to the (anti)deuteron production but also that it is the dominant process responsible for the creation of deuterons.

Summary

In this work, π±–d correlation functions measured in pp collisions at √s = 13 TeV by the ALICE Collaboration at the LHC are used to study the (anti)deuteron production mechanism. It is demonstrated that (anti)deuteron formation by nucleonic fusion follows the strong decay of short-lived resonances. Model-independent evidence is provided by observing the residual correlation of pion–nucleon pairs stemming from the same Δ decay in the pion–deuteron correlation function. This effect can be explained only assuming that (anti)deuteron formation occurs after the Δ decay and the measured correlation is interpreted by a data-driven method based on the independent measurement of the Δ in the π±–p final state. The residual signal in the π±–d correlations can be used to evaluate the fraction of (anti)deuterons produced following Δ decays, which is found to be 60.6 ± 4.1%. Extending this reasoning to all strong resonances produced in pp collisions at √s = 13 TeV, it is found that 88.9 ± 6.3% of (anti)deuterons are formed through binding processes involving nucleons originating from strongly decaying resonances. This large fraction demonstrates that most of the (anti)nuclei are produced through secondary binding processes in pp collisions at the LHC and not by direct emission as other hadrons. A large survival probability is expected for (anti)deuterons as the low spectral temperature of Δ (about 20 MeV) reflects that the environment in which (anti)nuclei are created is characterized by a much lower kinetic energies than the hadronization phase (around 100 MeV) in pp collisions at the LHC. These findings solve a longstanding puzzle in nuclear physics, providing insight into the microscopic mechanism that leads to (anti)nuclei formation in pp collisions at the LHC. These insights can now be used for a more realistic microscopic modelling of (anti)nuclei production, for example, in reactions induced by cosmic ray.

Methods

Event selection

The results are based on the analysis of a dataset comprising inelastic pp collisions at √s = 13 TeV, recorded with the ALICE detector45,46 during the LHC run 2 (2015–2018). The events are selected using a high-multiplicity (HM) trigger, which captures the highest multiplicity events—specifically, the top 0.17% of all inelastic collisions that include at least one charged particle within the pseudorapidity interval |η| < 1 (denoted as 0.17% INEL > 0). This approach ensures a statistically rich sample, as a five-fold increase in the production of (anti)deuteron candidates has been observed in HM pp collisions compared with minimum bias pp collisions[47]. The sample of HM-triggered collisions considered for this analysis corresponds to 1 × 10^9 events. On average, 31 charged tracks are found within |η| < 0.5 (ref. [48]) for the HM-triggered collisions. Detailed descriptions of the event selection criteria, pileup rejection techniques, primary-vertex reconstruction methods and the HM trigger procedure are provided in ref. [49].

Tracking and particle identification

Particle identification and momentum measurement of charged particles are performed using the inner tracking system (ITS)[50], time projection chamber (TPC)[51] and time-of-flight (TOF)[52] detectors of ALICE covering the whole azimuthal angle and the pseudorapidity interval |η| < 0.9. These detectors are located within a uniform magnetic field of 0.5 T along the beam axis, generated by the ALICE solenoid magnet, which causes the trajectories of particles to bend. The curvature of the charged-particle tracks is used to measure the particle momenta. The transverse momentum for pion and deuteron candidates is determined with a resolution ranging from approximately 2% for tracks with pT ≈ 10 GeV c−1 to below 1% for pT < 1 GeV c−1. Particle identification is performed by measuring the energy loss per unit track length (dE/dx) in the TPC detector and the particle velocity (β) in the TOF detector. For tracks in the TPC detector, the signal is obtained from the nσTPC distribution, where nσTPC represents the deviation of the measured signal from the expected value for a given particle hypothesis, normalized by the detector resolution. Similarly, for the TOF detector, the resolution is defined by nσTOF, which quantifies the difference between the measured and expected time of flight, also normalized by the resolution. Further experimental details are discussed in ref. [46]. The selection criteria for pion and deuteron tracks used in this work are described in refs. 30,41.

Pions are identified by the measurement of the specific energy loss within |nσTPC| < 3 in a transverse momentum range pT ∈ [0.14, 4.0] GeV c−1. This information is combined with the TOF measurement by taking the geometric sum, \(\sqrt{n{\sigma }_{{\rm{TPC}}}^{2}+n{\sigma }_{{\rm{TOF}}}^{2}} < 3\), for track momentum p > 0.5 GeV c−1. Similarly, the deuteron candidates are selected within a transverse momentum range pT ∈ [0.8, 2.4] GeV c−1. They are identified by using |nσTPC| < 3 for candidate tracks with momentum p < 1.4 GeV c−1, whereas both TPC and TOF information are required, \(\sqrt{n{\sigma }_{{\rm{TPC}}}^{2}+n{\sigma }_{{\rm{TOF}}}^{2}} < 3\), for candidates with p > 1.4 GeV c−1. Moreover, for (anti)deuteron candidate selections, electrons are rejected by the condition nσTPC,e > 6 for p < 1.4 GeV c−1 and pions are rejected by the condition nσTPC,π > 3 for the tracks with momentum p > 1.4 GeV c−1. Overall, using these methods, a purity of 99% for π± and 100% for (anti)deuterons is achieved.

The selection criteria of pions and deuterons constitute the primary source of systematic uncertainties associated with the measured correlation function. All particle selection criteria are varied from their default values. To account for the effect of possible correlations, the analysis of π+–d and π−–d pairs is repeated 44 times using random combinations of these selection criteria. The total systematic uncertainties are extracted by first randomly selecting a correlation function from the 44 systematic variations. For each sampled function, a bootstrap method is applied by randomly varying the C(k*) values in the individual k* bins according to their statistical uncertainties, assuming Gaussian errors. This results in a distribution of values for each k* bin, which is then fitted to determine the total uncertainty. As the statistical and systematic uncertainties are independent, the total uncertainty is obtained by adding them in quadrature. The systematic component is then determined by subtracting the known statistical uncertainty. The systematic uncertainties are largest at low k* ≈ 10 MeV c−1, reaching 1%. The same procedure is applied to extract the uncertainties of the fitted parameters and propagated to the final results on the fraction of deuterons stemming from resonance-assisted fusion processes.

Characterization of the particle-emitting source

A standard approach to evaluate the source function, used by ALICE in pp collisions, is the resonance source model (RSM)41,44. In these publications, the ALICE Collaboration measured the source size for baryon–baryon, meson–baryon and meson–meson pairs, demonstrating a common emission source of all particles and resonances produced directly in the collision. These are described as primordial particles, whereas the short-lived resonances that decay into the pairs of interest on the timescale of fm c−1 will lead to an increase in the effective source size. If this increase in the source size is properly modelled by Monte Carlo simulations, the underlying primordial source has a Gaussian profile of width rcore, and scales as a function of the pair transverse mass \({m}_{{\rm{T}}}=({k}_{{\rm{T}}}^{2}+{m}^{2}{)}^{1/2}\), where m is the average mass, the average of the masses of the two particles constituting the pair and kT =  |pT,1 + pT,2|/2 is the average transverse momentum of the pair41,44. The scaling of the primordial source size follows a power law \({r}_{{\rm{core}}}=a{\langle {m}_{{\rm{T}}}\rangle }^{b}+c\), where the parameters for the high-multiplicity pp collisions at √s = 13 TeV used for the present π–d analysis are provided in ref. [44]. The knowledge of both the pair average mT and the cocktail of contributing resonances allows us to evaluate both the rcore and subsequently the total source distribution S(r*). The present analysis incorporates the resonances decaying into pions from the ThermalFIST model34,37, as already performed in the ALICE π–π and p–π analyses38,41. From the study of p–d and K+–d correlations in pp collisions at √s = 13 TeV (ref. [30]), it has been shown that in pp collisions, the hadron–deuteron pairs follow the same transverse mass scaling as other hadron–hadron pairs, allowing to constrain the π–d emission source using the RSM. The deuterons are not produced directly by resonances. Nevertheless, the present work demonstrates that resonances decaying into nucleons are an important step in the production mechanism. This will lead to an effective delay in the deuteron production, an effect already described in a previous analysis of the K+–d analysis[53]. The present analysis adopts a conservative approach and integrates two extreme scenarios for the deuteron production as part of the systematic uncertainties, namely, assuming either that all deuterons are primordial or that the deuteron formation is delayed based on the amount of emission delay by which their constituent nucleons are affected[44]. This variation, which affects the effective source size, reff of up to 0.08 fm, is included in the systematic uncertainties on the modelling of the correlation functions. The final values for the reff, after the inclusion of resonances, are summarized in the Extended Data Table 1, along with the total uncertainties.

Corrections of the correlation function

The experimental correlation function, defined as \(C({k}^{* })=\)\({\mathcal{N}}\,[{N}_{{\rm{same}}}({k}^{* })/{N}_{{\rm{mixed}}}({k}^{* })]\) is only corrected by a normalization constant \({\mathcal{N}}\), by ensuring that the correlation becomes unity for k* ∈ (400, 600) MeV c−1. The remaining corrections are included in the fit function

$${C}_{{\rm{fit}}}({k}^{* })=\varepsilon ({k}^{* })\otimes B({k}^{* })[{\lambda }_{{\rm{gen}}}{C}_{{\rm{gen}}}({k}^{* })+(1-{\lambda }_{{\rm{gen}}})].$$

(1)

The parameter ε(k*) incorporates momentum resolution effects, which are included by obtaining a transformation matrix that can be used to apply resolution effects to the correlation functions. Details on the procedure are provided in the supplemental materials in ref. [44]. The required experimental inputs are the matrix itself and the experimental mixed-event sample, both of which are provided in the HEPData entry related to this work. The baseline \(B({k}^{* })=a+b{k}^{* 2}+c{k}^{* 3}\) accounts for any remaining long-range correlations[54]. These correlations do not contribute as an additive contamination to the correlations as misidentified particles do, but rather stem from the kinematics of the collision event. These long-range correlations are not correlated to the final-state interaction and can therefore be factorized and included as a multiplicative factor in the correlation. All the parameters of the baseline are left free in the fit procedure. The final correction to the correlation function is λgen, which represents the amount of genuine π–d pairs. In the context of the source, a genuine particle is either a primordial or the decay product of a short-lived resonance of lifetime cτ < 5 fm c−1. Details on the extraction of these parameters for the pions and deuterons are provided in ref. [41] and ref. [30], respectively. Combining the information for the two species, the correction obtained for π±–d is summarized in Extended Data Table 1. The (1 − λgen) factor in the definition of Cfit(k*) reflects the remaining non-genuine correlations, which are assumed to produce a flat correlation signal. These non-genuine correlations stem from misidentified particles, as well as feed-down from long-lived resonances. Owing to the high purity in the present analysis, the non-genuine correlations are predominantly linked to the feed-down into pions from non-strong decays, such as decays of kaons[41]. There is no contribution to the non-genuine correlation from feed-down into deuterons, as these decay processes do not exist, except for the weak decay of the hypertriton \((\genfrac{}{}{0ex}{}{3}{\Lambda }{\rm{H}}\to {{\rm{\pi }}}^{-}+{\rm{p}}+{\rm{d}})\), which has a negligible effect.

Spectral shape of Δ

In the measurement of the π±–p correlation functions[38], a prominent peak around k* = 211 MeV c−1 can be seen, associated with the Δ resonances (Δ++ for π+–p and Δ^0 for π−–p). In the decay of a Δ resonance into a pion–nucleon pair, the Δ is at rest in the centre-of-mass frame of the decay products. By applying energy and momentum conservation for this two-body decay, the invariant mass of the Δ is related to the relative momentum k* of the decay products by

$${m}_{\Delta }=\sqrt{{({k}^{* })}^{2}+{m}_{{\rm{\pi }}}^{2}}+\sqrt{{({k}^{* })}^{2}+{m}_{{\rm{N}}}^{2}}.$$

(2)

Inverting this expression yields the expected relative momentum k* associated with a given Δ mass

$${k}^{* }=\frac{\sqrt{{({m}_{\Delta }^{2}-{m}_{{\rm{\pi }}}^{2}-{m}_{{\rm{N}}}^{2})}^{2}-4{m}_{{\rm{\pi }}}^{2}{m}_{{\rm{N}}}^{2}}}{2{m}_{\Delta }}.$$

(3)

For the nominal Δ mass of MΔ = 1.215 GeV c−2, this corresponds to a relative momentum of k* = 211 MeV c−1 for the pion–nucleon pair. The peak position observed in the π±–p correlations is shifted to lower values than the nominal Δ mass because of the rescattering of the decay products and regeneration of the resonances55,56,57.

Following ref. [38], the Δ spectral shape is modelled as \({C}_{\Delta }({k}^{\ast })={{\mathcal{N}}}_{\Delta }\times PS({p}_{{\rm{T}},\Delta },T)\times Sill({M}_{\Delta },{{\Gamma }}_{\Delta })\). The first term \({{\mathcal{N}}}_{\Delta }\) is a normalization constant, whereas the undisturbed spectral shape of the resonances is described usingthe Sill distribution[58], which depends on the resonance mass MΔ and width ΓΔ. As the Sill is expressed as a function of k*, it is essential to account for the Jacobian factor \(| {\rm{d}}{m}_{\Delta }/{\rm{d}}{k}^{* }| \) in the change of variables, where mΔ is given by equation (2). Modifications of the spectral shape due to rescattering and resonance regeneration effects are incorporated by a multiplicative PS(pT,Δ, T) term56,57, a Boltzmann-like phase space factor,

$$PS({p}_{{\rm{T}},\Delta },T)\propto \frac{M}{\sqrt{{M}^{2}+{p}_{{\rm{T}},\Delta }^{2}}}\exp \left[-\frac{\sqrt{{M}^{2}+{p}_{{\rm{T}},\Delta }^{2}}}{T}\right],$$

(4)

acting as a weight for the emission of the resonance with certain transverse momentum pT,Δ at a temperature T. The latter is referred to as the ‘Δ spectral temperature’ in ref. [38].

To obtain the corresponding spectral shape in the π–d correlation, a simple approach is adopted by assuming that each measured deuteron consists of two nucleons of equal momenta. In this way, the Δ spectral shape in the π–N system (equation (3)) can be transformed into the π–d PRF. For a nominal Δ mass of MΔ = 1.215 GeV c−2 leads to k* = 237 MeV c−1 in the pion–deuteron system.

A final systematic check was performed by allowing a non-zero relative momentum between the two nucleons forming a deuteron. For this, a relative momentum sampled from a distribution, which was obtained from a coalescence model[59], was used. The relative momentum is, on average, about 100 MeV c−1 (ref. [59]). The final shape of the Δ peak in the π–d correlation remains identical regardless of the assumption of the relative momenta between the nucleons. Thus, the simpler approach of identical nucleon momenta was used in the analysis.

Fitting the π–d correlation

The fit function is defined by equation (1). The genuine correlation Cgen(k*) encapsulates Coulomb and strong interactions alongside contributions from the Δ resonance. The interaction components were modelled using the CATS framework[42], which uses the Schrödinger equation and requires as input the source function and the strong interaction potential. The contribution of the strong interaction is minimal because of the small scattering parameters of the π–d system, as the scattering length is cancelled for π–p and π–n pairs32,33. The real part of the π−–d potential was included in the fit32,33. To account for the Δ resonance, a phenomenological approach was adopted, expressing the genuine correlation as

$${C}_{{\rm{gen}}}({k}^{* })={C}_{{\rm{interaction}}}({k}^{* })[{F}_{\Delta }{{\mathcal{A}}}_{\Delta }{C}_{\Delta }({k}^{* })+(1-{F}_{\Delta }{{\mathcal{A}}}_{\Delta })],$$

(5)

where FΔ is a free parameter representing the number of Δ resonances contributing to deuteron production divided by the number of all measured deuterons. The parameter \({{\mathcal{A}}}_{\Delta }\) is an arbitrary normalization constant, introduced to keep the physically motivated definition of FΔ intact. The term CΔ(k*) reflects the spectral shape of the Δ resonance measured and fitted in the π–p analysis by ALICE (see previous section)[38], transformed to the π–d system. The mass (MΔ = 1,215 MeV c−2) and width (ΓΔ) of the Δ resonance in the present analysis are fixed to the values extracted from the measured π–p correlations, whereas the Δ spectral temperature T is fitted. The width ΓΔ is dependent on mT, for the mT-integrated data shown in Fig. 2, the value is 95 MeV c−2.

The fit to the data is performed in the range k* ∈ (0, 500) MeV c−1, with a systematic variation of k* ∈ (0, 600) MeV c−1. As a systematic check, a 5% variation in λgen is considered, accounting for the uncertainties arising in the determination of secondary contributions and purities due to systematic variations in the particle candidate selection criteria. As the parameters FΔ and \({{\mathcal{A}}}_{\Delta }\) are maximally correlated, the fit is performed using the effective parameter \({F}_{\Delta }^{{\prime} }={F}_{\Delta }{{\mathcal{A}}}_{\Delta }\). The parameter \({F}_{\Delta }^{{\prime} }\) represents the fraction of π–d pairs in which the pion and at least one of the nucleons within the deuteron originate from a Δ. This can be expressed as

$${F}_{\Delta }^{{\prime} }=\int {C}_{\Delta }({k}^{* }){N}_{{\rm{mixed}}}({k}^{* }){\rm{d}}{k}^{* }\,/\,\int {N}_{{\rm{mixed}}}({k}^{* }){\rm{d}}{k}^{* }.$$

(6)

As the key parameter in this study is FΔ, establishing a relationship with \({F}_{\Delta }^{{\prime} }\) is necessary. A straightforward analytical transformation can be derived under the assumption that most recorded collisions containing a reconstructed deuteron include only one. This implies that no additional Δ signal is introduced in the peak region because of combinatorial effects, and the number of Δ resonances associated with deuteron production becomes equal to the number of pairs (peak amplitude) linked to a Δ. This results in

$${F}_{\Delta }\approx \int {C}_{\Delta }({k}^{* }){N}_{{\rm{mixed}}}({k}^{* }){\rm{d}}{k}^{* }/{N}_{{\rm{d}}},$$

(7)

where Nd is the total number of reconstructed deuterons used in the analysis. Given the fraction of events containing more than one deuteron, the uncertainty associated to equation (7) is estimated to be negligible (≲0.03%). Using equations (6) and (7)

$${F}_{\Delta }=\frac{\int {N}_{{\rm{mixed}}}({k}^{* })}{{N}_{{\rm{d}}}}{F}_{\Delta }^{{\prime} }=0.533\pm 0.035,$$

(8)

where both Nmixed(k*) and Nd are measured, whereas \({F}_{\Delta }^{{\prime} }\) is extracted from the fit. The quoted uncertainty combines the statistical and systematic errors of the data and the fit. The fit results for the phase space parameters (equation (4)) are pT,Δ = 985 ± 171  MeV c−1 and T = 20 ± 2 MeV.

Deuteron and proton fraction from resonances

Relating FΔ to the probability PΔ of producing a single nucleon from a Δ resonance requires accounting for the reconstruction efficiency. Although the efficiency of deuterons cancels out because of the definition of FΔ, the pion reconstruction efficiency, επ, must be included. The pion efficiencies are obtained using Monte Carlo simulations produced with PYTHIA 8.2 (ref. [60]), tuned to reproduce pp collisions at 13 TeV, and filtered through the ALICE detector and reconstruction algorithm[45].

The following calculations are based purely on combinatorial considerations, without explicitly accounting for the microscopic or kinematical properties of the resonances. The probability of producing exactly one of the two nucleons within the deuteron from a Δ resonance and detecting the decay pion is 2επPΔ(1 − PΔ). The probability of having both nucleons within the deuteron originating from a Δ resonance and detecting both decay pions is \({\varepsilon }_{{\rm{\pi }}}^{2}{P}_{\Delta }^{2}\), whereas the probability for the same production scenario when failing to detect one of the pions is \(2{\varepsilon }_{{\rm{\pi }}}(1-{\varepsilon }_{{\rm{\pi }}}){P}_{\Delta }^{2}\). Note that in the case in which both nucleons in the deuteron stem from a Δ, the final state contains a single deuteron and two pions, resulting in two entries in the peak region of the correlation function. As FΔ is defined as the ratio of the number of π–d pairs to single deuterons, the corresponding term, \({\varepsilon }_{{\rm{\pi }}}^{2}{P}_{\Delta }^{2}\), contributes with twice the number of pairs. Taking all these considerations into account and adding all of the terms together leads to

$${F}_{\Delta }=2{\varepsilon }_{{\rm{\pi }}}{P}_{\Delta }.$$

(9)

Owing to the effect of double counting some of the pairs, the result must be transformed into the fraction of (single) deuterons, fΔ, produced by a Δ resonance. The definition of fΔ is similar to FΔ, but it removes the double-counting effect by taking the pure term \({\varepsilon }_{{\rm{\pi }}}^{2}{P}_{\Delta }^{2}\) without additional multiplication by 2. This leads to the expression

$${f}_{\Delta }=2{\varepsilon }_{{\rm{\pi }}}{P}_{\Delta }(1-\frac{{\varepsilon }_{{\rm{\pi }}}{P}_{\Delta }}{2}).$$

(10)

Equations (9) and (10) account for the pion reconstruction efficiency, επ, in correcting the single-particle purities. Consequently, fΔ is evaluated after applying this efficiency correction. The efficiency-independent result, \({f}_{\Delta }^{{\rm{true}}}\), is obtained by setting επ = 1 and expressing it in terms of the measured FΔ

$${f}_{\Delta }^{{\rm{true}}}=2{P}_{\Delta }\left(1-\frac{{P}_{\Delta }}{2}\right)=\frac{{F}_{\Delta }}{{\varepsilon }_{{\rm{\pi }}}}\left(1-\frac{{F}_{\Delta }}{4{\varepsilon }_{{\rm{\pi }}}}\right).$$

(11)

Considering the experimental result FΔ = 0.533 ± 0.035 and a pion reconstruction efficiency of επ = 71.53 ± 0.65%, evaluated using Monte Carlo simulation and averaged over the transverse momentum range for the pion candidates considered in the analysis, the true fraction is calculated as \({f}_{\Delta }^{{\rm{true}}}=60.6\pm 4.1 \% \). The uncertainty is propagated by treating the errors of FΔ and επ as independent.

It should be noted that this value must be considered a lower limit, as it is possible for the pion from the Δ decay to escape the detector acceptance, while the associated nucleus is still reconstructed. This loss of Δ resonances can be estimated only in a model-dependent manner using Monte Carlo event generators. Using EPOS 3 and PYTHIA 8.3, the loss of Δ particles due to η acceptance effects of the pion is estimated to be 15.5 ± 0.5%, implying that the value of FΔ is underestimated by a similar amount. This number is obtained by calculating the acceptance as a function of k* folded with the measured k* distribution of the delta resonance. Re-evaluating \({f}_{\Delta }^{{\rm{true}}}\) using equation (11) by including in addition the acceptance effect, the result becomes \({f}_{\Delta }^{{\rm{true}}}=68.7\pm 4.6 \% \).

Similar relations apply to deuterons produced from any resonance. However, the corresponding value is experimentally inaccessible because of the large spectral widths and small individual contributions of the other resonances. By defining the total fraction as fR and assuming that the ratio fΔ/fR = 0.773 ± 0.012, as predicted by the CSM models, holds for the experimental data, it is possible to extrapolate the acceptance corrected \({f}_{\Delta }^{{\rm{true}}}\) to \({f}_{{\rm{R}}}^{{\rm{true}}}=88.9\pm 6.3 \% \).

The fraction of deuterons from Δ resonances was also obtained using the EPOS event generator. For this, all resonances included in EPOS were reweighted using the CSM ThermalFIST with the settings shown in the Extended Data Table 2. The deuteron formation is simulated using a coalescence afterburner[25] in which the information about the mother particles of the nucleons is conserved. For each nucleon in the deuteron, the potential resonance mother is identified and it is checked, whether the nucleon and the corresponding π fall within the pT and η acceptance. If at least one nucleon in the deuteron fulfils this criterion, the deuteron is counted as stemming from a resonance. Finally, the η-acceptance of π is expected to be different in EPOS compared with the measurement, as the spectral shape of the Δ in the experiment is shifted towards lower k* values. Losses due to this η-acceptance increase for increasing k*, and thus are lower in reality than in the simulation. For this, the acceptance as a function of k* is averaged using the experimental Δ spectral shape. The resulting acceptance is 83.6%, whereas a similar study with PYTHIA 8.3 gives 85.4%. Averaging these values and taking the variance as an uncertainty, the Monte Carlo yields \({f}_{\Delta }^{{\rm{true,MC}}}=53.8\pm 3.1 \% \), a result compatible with the experimental value of 60.6 ± 4.1%.

Although removing the model dependence of this estimation is not feasible, a validation can be performed using π–p correlation measurements[38]. For this purpose, we define the experimental fraction

$${F}_{\Delta \to {\rm{p}},\exp .}={Y}_{\exp }(\Delta )/[{Y}_{\exp }({\rm{p}}){\varepsilon }_{{\rm{\pi }}}]$$

(12)

for the π–p correlation function, where Yexp denotes the experimentally measured yields of Δ and proton candidates. Yexp(Δ) is derived from the spectral shape RΔ(k*) published in ref. [38], and the proton–pion mixed-event distribution \({N}_{{\rm{mixed}},{\rm{p}}-{{\rm{\pi }}}^{\pm }}\) using the relation

$${Y}_{\exp }(\Delta )=\int {R}_{\Delta }({k}^{* }){N}_{{\rm{mixed}},{\rm{p}}-{{\rm{\pi }}}^{\pm }}{\rm{d}}{k}^{* }.$$

(13)

This yields proton fractions of (14.2 ± 0.4)% from Δ++ decays and (5.8 ± 0.3)% from Δ^0 decays. The performance of the Monte Carlo event generators has been validated by calculating the corresponding model-based fraction FΔ→p,MC, using ThermalFIST to fix the initial yields of resonances and baryons, followed by PYTHIA or EPOS simulations within the ALICE acceptance. The change in the η-acceptance of the pion due to the shift of the experimentally observed Δ spectral shape is accounted for as described above. With this, ThermalFIST + EPOS predicts that 13.4% of the protons stem from Δ++ within the experimental acceptance and 4.6% from Δ^0. The corresponding numbers in ThermalFIST + PYTHIA are 14.6% for Δ++ and 5.0% for Δ^0.

Simulations

The simulation of the π+–d correlation function was performed for three different hypotheses. The first simulation (Fig. 1c) is done using the EPOS 3 event generator combined with a coalescence afterburner developed in ref. [25], and it is able to reproduce the total number of deuterons in the analysed dataset without any free parameters. The deuterons obtained from this coalescence afterburner are combined with all pions of the desired charge in the same event to create the same-event distribution and with a buffer of up to 50 pions from previous events to build the mixed-event distribution. The predictions using ThermalFIST use the ThermalFIST sampler34,61, which uses a Cooper-Frye particlization sampling procedure[61] and a blast-wave parameterization[62] tuned to pp collisions at √s = 13 TeV (ref. [2]) to obtain positions and momenta of the particles. In the blast-wave model, a thermalized medium expands radially with a subsequent instantaneous freeze-out. Its main parameters are the average expansion velocity ⟨β⟩, its kinetic freeze-out temperature Tkin and the velocity profile exponent n. ThermalFIST can directly produce deuterons without the need for an afterburner, and the same mixed events can be directly constructed in a similar manner as before. The last prediction obtained with ThermalFIST and SMASH uses the particles output by the ThermalFIST sampler in the kinematic region |η| < 1, including deuterons, and feeds it into the hadronic afterburner SMASH[35]. Inside SMASH, particles rescatter for up to 15 fm c−1 with a fixed timestep of Δt = 0.001 fm c−1. The stochastic collision criterion is chosen to enable deuteron production and destruction using the 3 ↔ 2 scattering processes such as p + n + π ↔ d + π. Furthermore, all 2 ↔ 2 processes included in SMASH are enabled. The parameters used in ThermalFIST and the blast-wave model are shown in Extended Data Table 2.

Resonance spectral temperature

The modifications of the Δ spectral shape in the fitting procedure are modelled with the PS term presented in equation (4). As discussed above, this function is effectively controlled by the Δ spectral temperature T. The Δ spectral temperatures for the π±–d system are shown in the Extended Data Fig. 1 as a function of the transverse mass, mT, of one nucleon in the deuteron and the pion. They are comparable for π+–d and π−–d but differ from the π±–p systems discussed in ref. [38], being lower than the spectral temperature found for Δ++ and higher than that of Δ^0. This aligns qualitatively with the resonance regeneration, Δ ↔ Nπ, and rescattering picture56,57. For π+–p, repulsive strong and Coulomb interactions stop Δ++ regeneration and rescattering earlier, whereas the attractive π−–p interaction allows extended Δ^0 regeneration and rescattering, leading to a lower Δ spectral temperature. In π+–d, the signal arises from Δ++ → π+p (with subsequent fusion with a neutron) or Δ+ → π+n (with later fusion with a proton). As π+–p interactions are repulsive and π+–n interactions attractive[63], Δ+ undergoes longer regeneration cycles than Δ++. This results in a lower spectral temperature than a pure Δ++ as reflected in the data. Similarly, the π−–d system includes contributions from Δ^0 → π−p (attractive) and Δ− → π−n (repulsive). The shorter regeneration phase of Δ− compared with Δ^0 yields a higher temperature for π−–d than a pure π−–p system, again seen in the measurements.

Dibaryon hypothesis and π–d correlations

Although no dibaryon states have been confirmed unambiguously (such as a bound NΔ), candidates have been proposed to explain anomalies in data reported by WASA-at-COSY[64], ELPH[65] and BGOOD[66]. In particular, the NΔ(2114) candidate was first observed by ELPH with a reported mass of m2B = 2,140 MeV c−2, and later by BGOOD at m2B = 2,114 MeV c−2. The expected imprint of such a state on the π±–d correlation can be evaluated using ThermalFIST. Assuming an extreme upper limit of 100% for the unknown π–d branching ratio, as much as 28.5 ± 1.5% of deuterons could originate from this decay. Adopting a more realistic branching ratio, estimated from the ratio of elastic to inelastic π–d cross–sections[67], reduces this fraction to only 9.5 ± 0.5%, far below the 60.6 ± 4.1% estimated in the present study. Furthermore, if this small contribution is taken as a template, the fit to the data is incompatible with the observed correlation. When the amplitude is left unconstrained, the measured signal remains consistent with at most 1% of deuterons being produced through these decays. Hence, the experimental data strongly disfavour dibaryon decays as a notable source of the observed signal in the measured π±–d correlation.

Data availability

This study has associated data in a HEPData repository at https://www.hepdata.net/record/ins2907586.

Code availability

This study has associated code/software in a data repository. The code/software used for the analysis is publicly available at GitHub (https://github.com/alisw/AliRoot, https://github.com/alisw/AliPhysics and https://github.com/dimihayl/DLM/tree/master/CATS).

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Acknowledgements

We thank E. Bratkovskaya, J. Aichelin, K. Sun, A. Kievsky, M. Viviani, C.-M. Ko, S. Mrówczński, and S. König for the fruitful discussions on the pion–deuteron interactions and light (anti)nuclei production. We thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. We gratefully acknowledge the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. We acknowledge the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research ∣ Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency – BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; The Research Council of Norway, Norway; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Romania; Ministerstvo skolstva, vyskumu, vyvoja a mladeze SR, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and US Department of Energy, Office of Nuclear Physics (DOE NP), the United States. Moreover, individual groups or members have received support from Czech Science Foundation (grant no. 23-07499S), Czech Republic; FORTE project, reg. no. CZ.02.01.01/00/22_008/0004632, Czech Republic, co-funded by the European Union, Czech Republic; European Research Council (grant no. 950692), European Union; Deutsche Forschungs Gemeinschaft (DFG, German Research Foundation) ‘Neutrinos and Dark Matter in Astro- and Particle Physics’ (grant no. SFB 1258), Germany; ICSC - National Research Center for High Performance Computing, Big Data and Quantum Computing and FAIR – Future Artificial Intelligence Research, funded by the NextGenerationEU program (Italy); The National Recovery and Resilience Plan of the Republic of Bulgaria (project no. SUMMIT BG-RRP-2.004-0008-C01), funded by the European Union - NextGenerationEU (Bulgaria).

Author information

Author notes

1. E. S. Chizzali

Present address: Max-Planck-Institut fur Physik, Munich, Germany

2. G. Clai

Present address: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy

3. G. G. A. de Souza

Present address: Instituto de Fisica da Universidade de São Paulo, São Paulo, Brazil

4. C. Ferrero & U. Follo

Present address: Dipartimento DET del Politecnico di Torino, Turin, Italy

5. M. Mohisin Khan

Present address: Department of Applied Physics, Aligarh Muslim University, Aligarh, India

6. K. Redlich

Present address: Institute of Theoretical Physics, University of Wroclaw, Wrocław, Poland

7. L. Serkin

Present address: Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico

8. Deceased: R. C. Lemmon, A. Vasiliev

Authors and Affiliations

1. INFN Sezione di Bari, Bari, Italy

S. Acharya, A. R. Altamura, M. T. Camerlingo, F. Colamaria, G. de Cataldo, D. Elia, S. Kumar, V. Manzari, A. Mastroserio, E. Nappi, A. Palasciano, R. N. Patra & C. Terrevoli

2. Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India

A. Agarwal, Z. Ahammed, P. P. Bhaduri, S. Chandra, S. Chattopadhay, C. Ghosh, S. K. Giri, D. Kumar, S. Muhuri, B. Paul, J. Saini, V. K. Singh, V. Singhal & A. K. Yadav

3. European Organization for Nuclear Research (CERN), Geneva, Switzerland

G. Aglieri Rinella, A. Augustinus, K. Barth, L. Betev, P. M. Bond, F. Carnesecchi, M. Castoldi, F. Catalano, S. Chapeland, V. Chibante Barroso, P. Chochula, M. Concas, F. Costa, P. Das, L. Dello Stritto, A. Di Mauro, B. Diab, R. Divià, G. Eulisse, M. Faggin, M. B. Ferrer, U. Fuchs, C. Gargiulo, C. Grigoras, O. S. Groettvik, F. Grosa, J. F. Grosse-Oetringhaus, E. Hellbär, H. Hillemanns, P. Hristov, J. M. Jowett, A. Junique, A. Kalweit, M. Keil, J. Kim, J. Klein, A. Kluge, P. J. Konopka, L. Krcal, S. Kundu, M. Lamanna, P. Larionov, E. Laudi, M. Mager, P. Martinengo, M. P. P. Martins, F. Mazzaschi, M. W. Menzel, A. Morsch, T. Mrnjavac, L. Musa, J. E. Parkkila, O. Pinazza, C. Pinto, S. Politano, M. Puccio, I. Ravasenga, F. Reidt, W. Riegler, M. V. Rodriguez, D. Rohr, F. Ronchetti, I. Sanna, M. H. P. Sas, H. S. Scheid, F. Schlepper, M. O. Schmidt, J. Schukraft, R. Shahoyan, C. Sonnabend, A. Suiu, M. Suljic, A. Tauro, N. Tiltmann, A. S. Triolo, S. Tripathy, B. Volkel, B. vonHaller, I. Vorobyev, A. Wegrzynek, S. C. Wenzel, C. Zampolli & N. Zardoshti

4. Dipartimento di Fisica dell’Università and Sezione, INFN, Turin, Italy

L. Aglietta, G. Alocco, S. Beole, L. Bianchi, E. Botta, R. Cerri, F. Chinu, G. Cimador, A. Ferretti, M. Gagliardi, B. Lim, M. Masera, L. Mattei, M. Pennisi, S. Perciballi, S. Politano, S. Pucillo, L. Quaglia, A. G. Riffero, L. Terlizzi, D. Thakur, S. Trogolo & E. Vercellin

5. Dipartimento DISAT del Politecnico and Sezione, INFN, Turin, Italy

M. Agnello, S. Bufalino, M. Ciacco, M. Di Costanzo & G. Gioachin

6. Dipartimento di Fisica e Astronomia dell’Università and Sezione, INFN, Bologna, Italy

N. Agrawal, A. Alici, S. Arcelli, F. Bellini, M. Colocci, F. Ercolessi, N. Jacazio, G. Malfattore, G. Romanenko, G. Scioli, S. Strazzi & S. Tomassini

7. Department of Physics, Aligarh Muslim University, Aligarh, India

S. Ahmad, B. Ali, M. D. Azmi, S. Khan, N. Malik, M. Mohisin Khan & S. Singh

8. Korea Institute of Science and Technology Information, Daejeon, Republic of Korea

S. U. Ahn

9. Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic

I. Ahuja, V. Barbasova, M. Bombara, A. Kravčáková, K. Sajdakova, L. A. Tarasovicova, M. Vala & J. Vrláková

10. Affiliated with an institute formerly covered by a cooperation agreement with CERN, Geneva, Switzerland

A. Akindinov, D. Aleksandrov, E. Andronov, D. Averyanov, S. Belokurova, Y. Berdnikov, D. Blau, A. Borissov, D. Budnikov, N. Burmasov, U. Dmitrieva, S. Evdokimov, G. Feofilov, D. Finogeev, S. Fokin, P. Gordeev, V. Grigoriev, R. Ilkaev, M. Ippolitov, S. Iurchenko, V. Ivanov, O. Karavichev, T. Karavicheva, E. Karpechev, A. Khanzadeev, Y. Kharlov, S. Kiselev, N. Kondratyeva, V. Kovalenko, E. Kryshen, A. B. Kurepin, A. Kuryakin, V. Kuskov, M. Malaev, V. Manko, K. Mikhaylov, I. Morozov, S. Nikolaev, V. Nikulin, V. A. Okorokov, D. Peresunko, Y. Pestov, V. Petrov, B. Polichtchouk, I. Pshenichnov, A. Riabov, V. Riabov, R. Rogalev, E. Ryabinkin, Y. Ryabov, S. Sadovsky, D. Serebryakov, A. Shangaraev, S. Shirinkin, Y. Sibiriak, M. Sukhanov, R. Sultanov, A. Tikhonov, N. Topilskaya, A. Tumkin, A. Vasiliev, V. Vechernin, A. Vinogradov, N. Vozniuk, M. Zhalov & V. Zherebchevskii

11. Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

V. Akishina, N. Bluhme, G. Dange, J. de Cuveland, H. M. Gaur, D. Hutter, I. Kisel, G. Kozlov, S. L. LaPointe, V. Lindenstruth, A. R. Redelbach, A. Schröter & F. Weiglhofer

12. Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany

M. Al-Turany, R. Averbeck, P. Becht, M. B. Blidaru, P. Braun-Munzinger, M. R. Ciupek, A. Dubla, C. Garabatos, P. Gasik, P. Giubellino, R. Grosso, M. Ivanov, J. M. Jowett, T. Kollegger, C. Lippmann, P. Lu, A. Marn, S. Masciocchi, D. Miśkowiec, C. A. Reetz, A. Schmah, C. Schmidt, K. Schweda, I. Selyuzhenkov, R. Singh, C. Sonnabend, J. Wilkinson & S. Zhu

13. INFN Sezione di Torino, Turin, Italy

B. Alessandro, R. Arnaldi, L. Barioglio, P. Cortese, N. DeMarco, C. Ferrero, U. Follo, P. Giubellino, L. Micheletti, C. Oppedisano, F. Prino, L. Ramello, E. Scomparin, M. Sitta & S. C. Zugravel

14. Central China Normal University, Wuhan, China

H. M. Alfanda, M. N. Anaam, T. Cheng, Y. Ding, F. Fan, T. Fang, W. Guo, Y. Hou, M. Li, D. H. Liu, W. Lu, Y. Mao, H. Pei, Y. Wang, R. Xu, J. Yi, Z. Yin, M. Zhang, M. Zhang, X. Zhang, Z. Zhang, D. Zhou, J. Zhu & Y. Zhu

15. Instituto de Fsica, Universidad Nacional Autónoma de México, Mexico City, Mexico

R. Alfaro Molina, V. Grabski, F. V. Lugo & A. Menchaca-Rocha

16. University of Houston, Houston, TX, USA

N. Alizadehvandchali, R. Bellwied, A. Bensaoula, M. F. T. Cabrera, D. R. Gangadharan, S. G. Hernandez, A. Hutson, I. Likmeta, M. Mazzilli, A. S. Menon, L. Pinsky, A. R. Timmins & O. Vazquez Rueda

17. Sungkyunkwan University, Suwon City, Republic of Korea

A. Alkin, J. Bae, Y. Bae, B. Kim, D. Kim, H. Lee & S. Park

18. Department of Physics and Technology, University of Bergen, Bergen, Norway

J. Alme, T. Bodova, A. Bylinkin, Ø. Djuvsland, I. M. Lofnes, A. U. Mikalsen, J. Nystrand, M. P. Rauch, A. Rehman, M. Richter, D. Röhrich, J. Saetre, K. Ullaland, S. Yang & S. Yuan

19. Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

T. Alt, H. Appelshäuser, R. Bailhache, E. Bartsch, C. Blume, Y. E. M. Bouziani, L. Bratrud, H. Buesching, J. Ditzel, B. Dönigus, F. Eisenhut, T. Gündem, M. V. Hartung, M. Hemmer, B. Heybeck, P. Huhn, J. Jung, M. Jung, J. Keul, Z. Khuranova, S. Kirsch, M. Kleiner, J. Konig, M. Krüger, R. H. Munzer, H. S. Scheid, J. Schoengarth, N. J. Strangmann, A. Toia & J. Wiechula

20. Physik Department, Technische Universität München, Munich, Germany

I. Altsybeev, D. Battistini, A. Bilandzic, E. S. Chizzali, R. DelGrande, L. Fabbietti, H. Fribert, R. A. Gernhaeuser, T. Klemenz, S. A. Konigstorfer, M. Korwieser, L. Lautner, M. M. Lesch, M. Mahlein, G. Mantzaridis, D. L. Mihaylov, A. A. Riedel, I. Sanna, V. M. Sarti, L. Šerkšnytė, B. Singh, S. F. Taghavi & B. Ulukutlu

21. High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

J. R. Alvarado, Y. A. V. Beltran, A. Fernández Téllez, J. M. Garcia, T. García Chávez, M. A. T. Johnson, M. I. Martínez, S. Paisano-Guzmán, I. Y. Pozos, C. O. Ramírez-Álvarez, H. D. Regules-Medel, M. Rodríguez Cahuantzi, D. Rosales Herrera & G. Tejeda Muñoz

22. Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania

C. Andrei, I. Legrand, M. Petrovici, A. Pop, C. Schiaua & M. G. Tarzila

23. University of Derby, Derby, UK

N. Andreou & L. S. Barnby

24. Institut für Kernphysik, Universität Münster, Münster, Germany

A. Andronic, A. D. C. Bell Hechavarria, A. R. Dash, T. M. Eder, C. Klein-Bösing, G. Legras, D. A. Moreira DeGodoy, T. Stellhorn, P. Stratmann, N. Tiltmann, J. P. Wessels & G. A. Willems

25. Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

V. Anguelov, A. Berdnikova, L. Bergmann, A. G. Borquez Carcamo, M. C. Danisch, V. J. G. Feuillard, I. Fokin, P. Glässel, N. A. Grunwald, M. W. Menzel, A. Nath, K. Reygers, R. Schicker, F. Schlepper, J. J. Seo, G. Skorodumovs, J. Stachel, S. F. Stiefelmaier, C. A. vanVeen, B. Windelband, A. Yuncu, F. Zanone & B. Zhang

26. INFN Sezione di Padova, Padova, Italy

F. Antinori, A. Dainese, A. Rossi, H. Sharma, R. Singh, R. Turrisi & J. Zhu

27. INFN Sezione di Bologna, Bologna, Italy

P. Antonioli, F. Cindolo, G. Clai, M. Giacalone, D. Hatzifotiadou, G. Malfattore, A. Margotti, R. Nania, F. Noferini, O. Pinazza, R. Preghenella, R. Rath, N. Rubini, B. Sabiu & E. Scapparone

28. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

N. Apadula, I. Chakaberia, R. J. Ehlers, W. Fan, B. Jacak, P. M. Jacobs, F. Jonas, S. Klein & M. Płoskoń

29. Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

C. Arata, G. Conesa Balbastre, J. Faivre, C. Furget, R. Guernane & A. R. Landou

30. Universidade de São Paulo (USP), São Paulo, Brazil

J. G. M. C. A. Arneiro, L. Barreto, M. Bregant, F. D. M. Canedo, L. A. D. Carvalho, G. G. A. de Souza, L. Ferrandi, M. P. P. Martins, M. Melo, M. G. Munhoz, T. B. Saramela, T. F. Silva & A. A. P. Suaide

31. Department of Physics, University of Oslo, Oslo, Norway

I. C. Arsene, A. Neagu, S. Nese, K. Røed, T. B. Skaali, E. H. Solheim, I. Storehaug, M. Thogersen, C. Tsolanta, T. S. Tveter & J. Wikne

32. Yale University, New Haven, CT, USA

M. Arslandok, H. Caines, S. L. Cantway, F. Flor, J. W. Harris, L. B. Havener, A. Rai, N. Smirnov & Z. Varga

33. University of Tokyo, Tokyo, Japan

H. Baba, T. Gunji, R. Kohara, H. Murakami, Y. Sekiguchi & D. Sekihata

34. INFN Sezione di Catania, Catania, Italy

A. Badalà, G. Mandaglio, A. Sturniolo, A. Trifiró & A. S. Triolo

35. Gangneung-Wonju National University, Gangneung, Republic of Korea

Y. W. Baek

36. University of Science and Technology of China, Hefei, China

X. Bai, A. M. Khan, P. Lu, Z. Tang, Y. Wu, Z. Xiong, Y. Zhang & S. Zhu

37. Indian Institute of Technology Indore, Indore, India

Y. Bailung, D. Behera, K. Goswami, R. Gupta, S. S. Khade, A. K. Manna, K. K. Pradhan, S. Prasad, A. M. K. Radhakrishnan, A. Roy, B. Sahoo, R. Sahoo, D. Sahu & K. Singh

38. Physics Department, University of Jammu, Jammu, India

R. Bala, Z. Banoo, A. Bhasin, A. Gupta, R. Gupta, F. U. Haider, N. M. Malik, S. K. Malik, S. Sambyal, B. Sharma, M. Sharma, S. Sharma, U. Sharma, B. Singh, V. Sumberia & M. Vaid

39. IRFU Départment de Physique Nucléaire (DPhN), Centre d’Etudes de Saclay (CEA), Université Paris-Saclay, Saclay, France

A. Baldisseri, H. Borel, J. Castillo Castellanos, A. Ferrero, A. M. C. Glaenzer, S. Panebianco, A. Rakotozafindrabe, P. Veen, M. Winn & C. Zhang

40. AGH University of Krakow, Cracow, Poland

B. Balis, M. Gorgon, A. Horzyk, M. Jablonski, S. D. Koryciak, T. M. Lelek, E. M. Majerz, R. W. Marcjan, D. K. Plociennik, P. G. Russek & P. K. Wiacek

41. University of Kansas, Lawrence, KS, USA

S. Bangalia, S. Bhattarai, A. Binoy, A. Gautam, T. Isidori, A. Khatun, N. Minafra, P. Paudel, L. C. V. Ryder & J. D. Tapia Takaki

42. Dipartimento Interateneo di Fisica, ‘M. Merlin’ and Sezione INFN, Bari, Italy

F. Barile, G. E. Bruno, D. Colella, A. Colelli, D. DiBari, N. Nicassio & G. Volpe

43. National and Kapodistrian University of Athens, School of Science, Department of Physics, National and Kapodistrian University of Athens, Athens, Greece

M. Barlou, P. Ganoti & M. Vasileiou

44. Department of Physics, Gauhati University, Guwahati, India

B. Barman, B. Bhattacharjee, D. Choudhury, P. Sarma & T. Sharma

45. HUN-REN Wigner Research Centre for Physics, Budapest, Hungary

G. G. Barnaföldi, G. Bencedi, G. Biro, L. Boldizsár, E. Frajna, L. Gyulai, P. Lévai, D. Varga & R. Vértesi

46. SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France

E. Barreau, G. Batigne, N. Bize, M. L. Coquet, B. Erazmus, M. Germain, M. Guilbaud, S. Lambert, G. Martínez García, P. Pillot, A. Shabetai, D. Stocco & V. V. Torres

47. Université Clermont Auvergne, CNRS/IN2P3 LPC, Clermont-Ferrand, France

V. Barret, N. Bastid, P. Crochet, P. Dupieux, X. Lopez, F. Manso, L. Mattei, S. Porteboeuf-Houssais, T. Tripathy & M. Zhang

48. Department of Physics, Lund University, Lund, Sweden

S. Basu, P. Christiansen, J. Hansen, K. E. Iversen, R. Nepeivoda, A. Ohlson, I. Panasenko, D. Silvermyr & J. Staa

49. Affiliated with an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland

B. Batyunya, R. A. Diaz, S. Grigoryan, A. Kondratyev, A. Kuznetsov, K. Mikhaylov, P. Nomokonov, E. Rogochaya & A. Vodopyanov

50. Indian Institute of Technology Bombay (IIT), Mumbai, India

D. Bauri, S. Dash, T. Gahlaut, M. S. Islam, B. K. Nandi, S. Padhan, P. Panigrahi, Y. Patley, S. Roy, D. Sharma & R. Verma

51. Sección Fsica, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru

J. L. Bazo Alba, E. Calvo Villar & A. M. Gago

52. Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

I. G. Bearden, C. H. Christensen, J. J. Gaardhøje, K. Gulbrandsen, N. F. Nathanson, B. S. Nielsen, E. G. Nielsen, D. Sarkar & Y. Zhou

53. Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France

I. Belikov, A. P. Bigot, B. Hippolyte, C. Kuhn, A. Maire & S. Senyukov

54. Universidad Autónoma de Sinaloa, Culiacán, Mexico

L. G. E. Beltran, J. C. Cabanillas Noris, J. M. M. Camacho, C. D. Galvan, R. A. N. Laveaga & I. León Monzón

55. Dipartimento di Fisica dell’Università and Sezione, INFN, Trieste, Italy

L. Bernardinis, P. Camerini, S. Cannito, S. Cattaruzzi, G. Contin, C. De Martin, G. V. Margagliotti, R. Rui, M. Urioni, A. Villani & V. Zaccolo

56. Physics Department, Panjab University, Chandigarh, India

T. Bhalla, L. Kumar, N. Kumar & J. Tanwar

57. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic

J. Bielčk, M. Broz, J. G. Contreras, V. Filova, D. Grund, S. Haidlova, T. Herman, A. Khuntia, K. Krizkova Gajdosova, D. M. Krupova, A. M. Lejeune & S. Rojas Torres

58. Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež, Czech Republic

J. Bielčková, E. Grecka, A. Kotliarov, F. Krizek & S. Kushpil

59. Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Bose Institute, Kolkata, India

S. Biswas, S. Das, M. Haldar, S. K. Prasad & S. Thakur

60. Oak Ridge National Laboratory, Oak Ridge, TN, USA

F. Bock, M. Fasel, C. Loizides, N. Novitzky, M. G. Poghosyan, K. F. Read, J. Schambach & N. V. Schmidt

61. Department of Physics, Pusan National University, Pusan, Republic of Korea

J. Bok, S. Ji, C. Kim, H. Lim, S. H. Lim, J. Ryu & I.-K. Yoo

62. Università di Brescia, Brescia, Italy

G. Bonomi, R. Deb, R. Lea, A. Modak, D. Pagano & N. Zurlo

63. INFN Sezione di Pavia, Pavia, Italy

G. Bonomi, R. Lea, D. Pagano, N. Valle & N. Zurlo

64. Institute of Space Science (ISS), Bucharest, Romania

D. C. Brandibur, A. Danu, A. Dobrin, A. Manea, C. Ristea, A. Sevcenco & I. Stan

65. Politecnico di Bari and Sezione INFN, Bari, Italy

G. E. Bruno & T. Triloki

66. Faculty of Physics, Sofia University, Sofia, Bulgaria

V. D. Buchakchiev, V. Kozhuharov, M. V. Makariev, D. L. Mihaylov, M. N. Naydenov & R. Simeonov

67. Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, UK

M. D. Buckland & R. C. Lemmon

68. Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

P. Buhler, D. D. Chinellato, J. K. Gumprecht, R. Lavicka, E. Meninno, D. Samitz & R. Schotter

69. iThemba LABS, National Research Foundation, Somerset West, South Africa

Z. Buthelezi, S. Foertsch & T. J. Shaba

70. University of the Witwatersrand, Johannesburg, South Africa

Z. Buthelezi, B. Naik & Z. Vilakazi

71. The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland

S. A. Bysiak, M. Kowalski, S. Lokos, A. Matyja, J. Otwinowski, A. Rybicki, I. Sputowska & S. Upadhyaya

72. Dipartimento di Fisica ‘E.R. Caianiello’, Università degli Studi di Salerno and Gruppo Collegato INFN, Salerno, Italy

A. Caliva, A. De Caro, D. De Gruttola, S. DePasquale, N. Funicello, R. Ricci, C. Ripoli & T. Virgili

73. Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Bucharest, Romania

M. Carabas, D. Mihai, V. Nastase, A. Suiu & N. Tapus

74. Warsaw University of Technology, Warsaw, Poland

P. Chakraborty, Z. A. Chochulska, M. M. Czarnynoga, J. M. Dubinski, L. K. Graczykowski, K. Gwizdziel, M. J. Jakubowska, M. A. Janik, M. J. Karwowska, A. Kisiel, G. Kornakov, M. Kutyla, S. Monira, J. W. Myrcha, J. Oleniacz, P. S. Rokita, K. Roslon, D. Ruggiano, W. Rzesa & T. P. Trzcinski

75. University of Liverpool, Liverpool, UK

M. Chartier, D. M. Jones, J. Liu, J. Norman & M. R. Ockleton

76. Fudan University, Shanghai, China

M. Chen, J. Luo, Y. G. Ma, Q. Shou, R. Tu, J. Wan, C. Wang, D. Wang, Y. Wang, Z. Wang, W. Wu, K. Xiong, L. Zhang & S. Zhang

77. Institut de Physique des 2 Infinis de Lyon, Université de Lyon, CNRS/IN2P3, Lyon, France

C. Cheshkov, S. Herrmann, C. Lotteau, N. Ramasubramanian & A. Uras

78. Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy

D. Chiappara, P. Giubilato, S. Mattiazzo, C. Pantouvakis, M. Rignanese, F. Soramel & M. Zhang

79. Inha University, Incheon, Republic of Korea

J. Cho, S. Cho, G. Kim, H. Kim, J. Kim, V. Kučera, M. J. Kweon, S. Yang & J. H. Yoon

80. Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India

S. Choudhury & T. Sinha

81. Nikhef National institute for Subatomic Physics, Amsterdam, The Netherlands

P. Christakoglou, I. P. M. Hobus, A. Isakov, C. Koster, P. G. Kuijer, J. A. Rudolph, R. Russo, M. Selina, J. M. Sonneveld, R. Spijkers, C. P. Stylianidis, M. van Leeuwen & R. J. G. van Weelden

82. University of Tsukuba, Tsukuba, Japan

T. Chujo, M. Inaba, T. Kumaoka, M. Kuo, H. Park, J. Park & S. Sakai

83. INFN Sezione di Cagliari, Cagliari, Italy

C. Cicalo, F. M. Fionda, A. Masoni & S. Siddhanta

84. School of Physics and Astronomy, University of Birmingham, Birmingham, UK

J. S. Colburn, D. Evans, A. Jusko, N. Karatzenis, M. Krivda, R. Lietava, O. Villalobos Baillie & M. A. Völkl

85. IJCLab, Université Paris-Saclay, CNRS/IN2P3, Orsay, France

Z. Conesa del Valle, B. Espagnon, S. Garetti, C. Hadjidakis, D. Mallick, L. Massacrier, A. Shatat, C. Suire & A. Tavira García

86. Università del Piemonte Orientale, Vercelli, Italy

P. Cortese, L. Ramello & M. Sitta

87. Universidade Federal do ABC, Santo Andre, Brazil

M. R. Cosentino & C. Reckziegel

88. Dipartimento di Fisica, Università di Pavia, Pavia, Italy

S. Costanza

89. Dipartimento di Fisica dell’Università and Sezione, INFN, Cagliari, Italy

A. De Falco, A. Mulliri, V. Sarritzu & G. L. Usai

90. Department of Physics, University of California Berkeley, Berkeley CA, USA

P. Dhankher, M. C. Hwang, B. Jacak, M. Kim, B. E. Liang-Gilman, A. I. Nambrath, K. Naumov & E. R. Yeats

91. Università degli Studi di Foggia, Foggia, Italy

B. Di Ruzza & A. Mastroserio

92. Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Bratislava, Slovak Republic

N. Dzalaiova, M. Ivanov, M. Meres, M. Pikna & B. Sitar

93. Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, Hiroshima, Japan

R. Ejima, K. Kimura, M. Oya, K. Shigaki, R. Tokumoto, K. Tomohiro, Y. Yamaguchi & S. Yano

94. Laboratori Nazionali di Frascati, INFN, Frascati, Italy

A. Fantoni, V. Muccifora, S. Pisano, M. Toppi & O. Vázquez Doce

95. The University of Texas at Austin, Austin, TX, USA

A. N. Flores, R. Hannigan, C. Markert, D. Thomas & J. R. Wright

96. Sezione di Trieste, INFN, Trieste, Italy

E. Fragiacomo, G. Luparello, A. Modak & S. Piano

97. Saga University, Saga, Japan

T. Fusayasu

98. National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India

S. Gami, B. Mohanty, M. M. Mondal, S. Saha, S. Sawan, R. Singh & G. J. Tambave

99. Chicago State University, Chicago, IL, USA

E. Garcia-Solis & A. Harton

100. Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

M. B. Gay Ducati & C. Krug

101. University of Tennessee, Knoxville, TN, USA

E. Glimos, C. Nattrass, K. F. Read & A. R. Schmier

102. Wayne State University, Detroit, MI, USA

V. Gonzalez, B. G. Hanley, C. A. Pruneau, O. Sheibani & S. A. Voloshin

103. Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia

S. Gotovac & L. Vickovic

104. Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands

A. Grelli, B. Hofman, J. Lömker, O. Massen, N. B. Sundstrom, T. Peitzmann, R. J. M. Snellings, L. V. R. van Doremalen & M. Verweij

105. A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia

S. Grigoryan

106. China Nuclear Data Center, China Institute of Atomic Energy, Beijing, China

J. Guo, S. Jia, T. Jiang, S. Jin, P. Li, X. Li, S. Lin, Z. Lu, M. Zhao & Y. Zhi

107. Nagasaki Institute of Applied Science, Nagasaki, Japan

H. Hamagaki, M. Ogino & K. Oyama

108. Yonsei University, Seoul, Republic of Korea

Y. Han, J. Kim, T. Kim & Y. Kwon

109. University of Jyväskylä, Jyväskylä, Finland

H. Hassan, L. M. Huhta, D. J. Kim, N. Mallick, C. Mordasini, W. H. Trzaska & M. M. O. Virta

110. Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany

P. Hauer, B. Ketzer, S. Sadhu & A. Yadav

111. Faculty of Technology, Environmental and Social Sciences, Bergen, Norway

H. Helstrup, K. F. Hetland, B. Kileng & H. A. Reme-Ness

112. Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico

G. Herrera Corral

113. Fachbereich Informatik und Mathematik, Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Frankfurt, Germany

F. W. Hoffmann & U. Kebschull

114. Ohio State University, Columbus OH, USA

T. J. Humanic & A. B. Soto-Hernandez

115. Technical University of Košice, Košice, Slovak Republic

S. Jadlovska, J. Jadlovsky, D. Liskova & M. Tkacik

116. National Research and Innovation Agency - BRIN, Jakarta, Indonesia

S. Jaelani & S. Sumowidagdo

117. Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

C. Jahnke, G. S. S. Liveraro & J. Takahashi

118. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico

A. A. P. Jimenez, J. E. M. Mendez, L. Nellen, A. Ortiz Velasquez, G. Paić, E. D. Rosas, L. Serkin & P. Vargas Torres

119. Suranaree University of Technology, Nakhon Ratchasima, Thailand

J. Kaewjai, C. Kobdaj, A. Lakrathok & T. Simantathammakul

120. Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic

P. Kalinak, I. Králik, M. Krivda & J. Musinsky

121. Yildiz Technical University, Istanbul, Turkey

A. Karasu Uysal

122. Jeonbuk National University, Jeonju, Republic of Korea

E. J. Kim & J. Kim

123. Department of Physics, Sejong University, Seoul, Republic of Korea

S. Kim, A. F. Nassirpour & S. Oh

124. California Polytechnic State University, San Luis Obispo CA, USA

J. L. Klay

125. Physics Department, Faculty of Science, University of Zagreb, Zagreb, Croatia

N. Kovacic, M. Planinic & N. Poljak

126. National Centre for Nuclear Research, Warsaw, Poland

P. Kurashvili, S. K. Mandal, K. Redlich, T. Siemiarczuk & G. Wilk

127. Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy

P. LaRocca & M. Rasa

128. University of South-Eastern Norway, Kongsberg, Norway

R. Langoy & J. Lien

129. Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba

E. López Torres, G. M. Perez & L. H. Tabares

130. Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

G. Mandaglio, A. Sturniolo, A. Trifiró & A. S. Triolo

131. Helsinki Institute of Physics (HIP), Helsinki, Finland

Y. Melikyan, M. A. Molander & S. S. Räsänen

132. Chungbuk National University, Cheongju, Republic of Korea

S. Noh & H. Yu

133. China University of Geosciences, Wuhan, China

X. Peng

134. Creighton University, Omaha, NE, USA

S. Ragoni & J. E. Seger

135. National Nuclear Research Center, Baku, Azerbaijan

A. Rustamov

136. Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

P. K. Sahu

137. Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany

M. Schmidt

138. Nara Women’s University (NWU), Nara, Japan

M. Shimomura

139. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine

V. Trubnikov

140. Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

P. Závada

Consortia

The ALICE Collaboration

- S. Acharya

- , A. Agarwal

- , G. Aglieri Rinella

- , L. Aglietta

- , M. Agnello

- , N. Agrawal

- , Z. Ahammed

- , S. Ahmad

- , S. U. Ahn

- , I. Ahuja

- , A. Akindinov

- , V. Akishina

- , M. Al-Turany

- , D. Aleksandrov

- , B. Alessandro

- , H. M. Alfanda

- , R. Alfaro Molina

- , B. Ali

- , A. Alici

- , N. Alizadehvandchali

- , A. Alkin

- , J. Alme

- , G. Alocco

- , T. Alt

- , A. R. Altamura

- , I. Altsybeev

- , J. R. Alvarado

- , M. N. Anaam

- , C. Andrei

- , N. Andreou

- , A. Andronic

- , E. Andronov

- , V. Anguelov

- , F. Antinori

- , P. Antonioli

- , N. Apadula

- , H. Appelshäuser

- , C. Arata

- , S. Arcelli

- , R. Arnaldi

- , J. G. M. C. A. Arneiro

- , I. C. Arsene

- , M. Arslandok

- , A. Augustinus

- , R. Averbeck

- , D. Averyanov

- , M. D. Azmi

- , H. Baba

- , A. Badalà

- , J. Bae

- , Y. Bae

- , Y. W. Baek

- , X. Bai

- , R. Bailhache

- , Y. Bailung

- , R. Bala

- , A. Baldisseri

- , B. Balis

- , S. Bangalia

- , Z. Banoo

- , V. Barbasova

- , F. Barile

- , L. Barioglio

- , M. Barlou

- , B. Barman

- , G. G. Barnaföldi

- , L. S. Barnby

- , E. Barreau

- , V. Barret

- , L. Barreto

- , K. Barth

- , E. Bartsch

- , N. Bastid

- , S. Basu

- , G. Batigne

- , D. Battistini

- , B. Batyunya

- , D. Bauri

- , J. L. Bazo Alba

- , I. G. Bearden

- , P. Becht

- , D. Behera

- , I. Belikov

- , A. D. C. Bell Hechavarria

- , F. Bellini

- , R. Bellwied

- , S. Belokurova

- , L. G. E. Beltran

- , Y. A. V. Beltran

- , G. Bencedi

- , A. Bensaoula

- , S. Beole

- , Y. Berdnikov

- , A. Berdnikova

- , L. Bergmann

- , L. Bernardinis

- , L. Betev

- , P. P. Bhaduri

- , T. Bhalla

- , A. Bhasin

- , B. Bhattacharjee

- , S. Bhattarai

- , L. Bianchi

- , J. Bielčk

- , J. Bielčková

- , A. P. Bigot

- , A. Bilandzic

- , A. Binoy

- , G. Biro

- , S. Biswas

- , N. Bize

- , D. Blau

- , M. B. Blidaru

- , N. Bluhme

- , C. Blume

- , F. Bock

- , T. Bodova

- , J. Bok

- , L. Boldizsár

- , M. Bombara

- , P. M. Bond

- , G. Bonomi

- , H. Borel

- , A. Borissov

- , A. G. Borquez Carcamo

- , E. Botta

- , Y. E. M. Bouziani

- , D. C. Brandibur

- , L. Bratrud

- , P. Braun-Munzinger

- , M. Bregant

- , M. Broz

- , G. E. Bruno

- , V. D. Buchakchiev

- , M. D. Buckland

- , D. Budnikov

- , H. Buesching

- , S. Bufalino

- , P. Buhler

- , N. Burmasov

- , Z. Buthelezi

- , A. Bylinkin

- , S. A. Bysiak

- , J. C. Cabanillas Noris

- , M. F. T. Cabrera

- , H. Caines

- , A. Caliva

- , E. Calvo Villar

- , J. M. M. Camacho

- , P. Camerini

- , M. T. Camerlingo

- , F. D. M. Canedo

- , S. Cannito

- , S. L. Cantway

- , M. Carabas

- , F. Carnesecchi

- , L. A. D. Carvalho

- , J. Castillo Castellanos

- , M. Castoldi

- , F. Catalano

- , S. Cattaruzzi

- , R. Cerri

- , I. Chakaberia

- , P. Chakraborty

- , S. Chandra

- , S. Chapeland

- , M. Chartier

- , S. Chattopadhay

- , M. Chen

- , T. Cheng

- , C. Cheshkov

- , D. Chiappara

- , V. Chibante Barroso

- , D. D. Chinellato

- , F. Chinu

- , E. S. Chizzali

- , J. Cho

- , S. Cho

- , P. Chochula

- , Z. A. Chochulska

- , D. Choudhury

- , S. Choudhury

- , P. Christakoglou

- , C. H. Christensen

- , P. Christiansen

- , T. Chujo

- , M. Ciacco

- , C. Cicalo

- , G. Cimador

- , F. Cindolo

- , M. R. Ciupek

- , G. Clai

- , F. Colamaria

- , J. S. Colburn

- , D. Colella

- , A. Colelli

- , M. Colocci

- , M. Concas

- , G. Conesa Balbastre

- , Z. Conesa del Valle

- , G. Contin

- , J. G. Contreras

- , M. L. Coquet

- , P. Cortese

- , M. R. Cosentino

- , F. Costa

- , S. Costanza

- , P. Crochet

- , M. M. Czarnynoga

- , A. Dainese

- , G. Dange

- , M. C. Danisch

- , A. Danu

- , P. Das

- , S. Das

- , A. R. Dash

- , S. Dash

- , A. De Caro

- , G. de Cataldo

- , J. de Cuveland

- , A. De Falco

- , D. De Gruttola

- , N. DeMarco

- , C. De Martin

- , S. DePasquale

- , R. Deb

- , R. DelGrande

- , L. Dello Stritto

- , G. G. A. de Souza

- , P. Dhankher

- , D. DiBari

- , M. Di Costanzo

- , A. Di Mauro

- , B. Di Ruzza

- , B. Diab

- , R. A. Diaz

- , Y. Ding

- , J. Ditzel

- , R. Divià

- , Ø. Djuvsland

- , U. Dmitrieva

- , A. Dobrin

- , B. Dönigus

- , J. M. Dubinski

- , A. Dubla

- , P. Dupieux

- , N. Dzalaiova

- , T. M. Eder

- , R. J. Ehlers

- , F. Eisenhut

- , R. Ejima

- , D. Elia

- , B. Erazmus

- , F. Ercolessi

- , B. Espagnon

- , G. Eulisse

- , D. Evans

- , S. Evdokimov

- , L. Fabbietti

- , M. Faggin

- , J. Faivre

- , F. Fan

- , W. Fan

- , T. Fang

- , A. Fantoni

- , M. Fasel

- , G. Feofilov

- , A. Fernández Téllez

- , L. Ferrandi

- , M. B. Ferrer

- , A. Ferrero

- , C. Ferrero

- , A. Ferretti

- , V. J. G. Feuillard

- , V. Filova

- , D. Finogeev

- , F. M. Fionda

- , F. Flor

- , A. N. Flores

- , S. Foertsch

- , I. Fokin

- , S. Fokin

- , U. Follo

- , E. Fragiacomo

- , E. Frajna

- , H. Fribert

- , U. Fuchs

- , N. Funicello

- , C. Furget

- , A. Furs

- , T. Fusayasu

- , J. J. Gaardhøje

- , M. Gagliardi

- , A. M. Gago

- , T. Gahlaut

- , C. D. Galvan

- , S. Gami

- , D. R. Gangadharan

- , P. Ganoti

- , C. Garabatos

- , J. M. Garcia

- , T. García Chávez

- , E. Garcia-Solis

- , S. Garetti

- , C. Gargiulo

- , P. Gasik

- , H. M. Gaur

- , A. Gautam

- , M. B. Gay Ducati

- , M. Germain

- , R. A. Gernhaeuser

- , C. Ghosh

- , M. Giacalone

- , G. Gioachin

- , S. K. Giri

- , P. Giubellino

- , P. Giubilato

- , A. M. C. Glaenzer

- , P. Glässel

- , E. Glimos

- , V. Gonzalez

- , P. Gordeev

- , M. Gorgon

- , K. Goswami

- , S. Gotovac

- , V. Grabski

- , L. K. Graczykowski

- , E. Grecka

- , A. Grelli

- , C. Grigoras

- , V. Grigoriev

- , S. Grigoryan

- , O. S. Groettvik

- , F. Grosa

- , J. F. Grosse-Oetringhaus

- , R. Grosso

- , D. Grund

- , N. A. Grunwald

- , R. Guernane

- , M. Guilbaud

- , K. Gulbrandsen

- , J. K. Gumprecht

- , T. Gündem

- , T. Gunji

- , J. Guo

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Extended data figures and tables

Extended Data Fig. 1 Extracted Δ spectral temperature.

The Δ spectral temperature is derived from π±–p and π±−d correlation functions measured in high-multiplicity pp collisions at \(\sqrt{{s}}\) = 13 TeV. The bands correspond to the uncertainties obtained by fits to the correlation functions, incorporating systematic uncertainties on the measured data, as well as those arising from variations in the source size and the λ parameter for the genuine interaction.

Extended Data Table 1 Parameters used in the measured correlation function

Extended Data Table 2 Parameters used in the π+–d correlation function predictions for thermal production

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The ALICE Collaboration. Observation of deuteron and antideuteron formation from resonance-decay nucleons. Nature 648, 306–311 (2025). https://doi.org/10.1038/s41586-025-09775-5

- Received: 07 May 2025

- Accepted: 20 October 2025

- Published: 10 December 2025

- Version of record: 10 December 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09775-5

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David Silver

Nature volume 648, pages 312–319 (2025)

Abstract

Humans and other animals use powerful reinforcement learning (RL) mechanisms that have been discovered by evolution over many generations of trial and error. By contrast, artificial agents typically learn using handcrafted learning rules. Despite decades of interest, the goal of autonomously discovering powerful RL algorithms has proven to be elusive1,2,3,4,5,6. Here we show that it is possible for machines to discover a state-of-the-art RL rule that outperforms manually designed rules. This was achieved by meta-learning from the cumulative experiences of a population of agents across a large number of complex environments. Specifically, our method discovers the RL rule by which the agent’s policy and predictions are updated. In our large-scale experiments, the discovered rule surpassed all existing rules on the well-established Atari benchmark and outperformed a number of state-of-the-art RL algorithms on challenging benchmarks that it had not seen during discovery. Our findings suggest that the RL algorithms required for advanced artificial intelligence may soon be automatically discovered from the experiences of agents, rather than manually designed.

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Main

The primary goal of artificial intelligence is to design agents that, like humans, can predict and act in complex environments to achieve goals. Many of the most successful agents are based on reinforcement learning (RL), in which agents learn by interacting with environments. Decades of research have produced ever more efficient RL algorithms, resulting in numerous landmarks in artificial intelligence, including the mastery of complex competitive games such as Go[7], chess[8], StarCraft[9] and Minecraft[10], the invention of new mathematical tools[11], or the control of complex physical systems[12].

Unlike humans, whose learning mechanism has been naturally discovered by biological evolution, RL algorithms are typically manually designed. This is usually slow and laborious, and limited by reliance on human knowledge and intuition. Although a number of attempts have been made to automatically discover learning algorithms1,2,3,4,5,6, none have proven to be sufficiently efficient and general to replace hand-designed RL systems.

In this work, we introduce an autonomous method for discovering RL rules solely through the experience of many generations of agents interacting with various environments (Fig. 1a). The discovered RL rule achieves state-of-the-art performance on a variety of challenging RL benchmarks. The success of our method contrasts previous work in two dimensions. First, whereas previous methods searched over narrow spaces of RL rules (for example, hyperparameters13,14 or policy loss1,6), our method allows the agent to explore a far more expressive space of potential RL rules. Second, whereas previous work focused on meta-learning in simple environments (for example, grid-worlds3,15), our method meta-learns in complex and diverse environments at a much larger scale.

Fig. 1: Discovering an RL rule from a population of agents.

a, Discovery. Multiple agents, interacting with various environments, are trained in parallel according to the learning rule, defined by the meta-network. In the meantime, the meta-network is optimized to improve the agents’ collective performances. b, Agent architecture. An agent produces the following outputs: (1) a policy (π), (2) an observation-conditioned prediction vector (y), (3) action-conditioned prediction vectors (z), (4) action values (q) and (5) an auxiliary policy prediction (p). The semantics of y and z are determined by the meta-network. c, Meta-network architecture. A trajectory of the agent’s outputs is given as input to the meta-network, together with rewards and episode termination indicators from the environment (omitted for simplicity in the figure). Using this information, the meta-network produces targets for all of the agent’s predictions from the current and future time steps. The agent is updated to minimize the prediction errors with respect to their targets. LSTM, long short-term memory. d, Meta-optimization. The meta-parameters of the meta-network are updated by taking a meta-gradient step calculated from backpropagation through the agent’s update process (θ_0 → θN), where the meta-objective is to maximize the collective returns of the agents in their environments.

To choose a general space of discovery, we observe that the essential component of standard RL algorithms is a rule that updates one or more predictions, as well as the policy itself, towards targets that are functions of quantities such as future rewards and future predictions. Examples of RL rules based on different targets include temporal-difference learning[16], Q-learning[17], proximal policy optimization (PPO)[18], auxiliary tasks[19], successor features[20] and distributional RL[21]. In each case, the choice of target determines the nature of the predictions, for example, whether they become value functions, models or successor features.

In our framework, an RL rule is represented by a meta-network that determines the targets towards which the agent should move its predictions and policy (Fig. 1c). This allows the system to discover useful predictions without pre-defined semantics, as well as how they are used. The system may in principle rediscover past RL rules, but the flexible functional form also allows the agent to invent new RL rules that may be specifically adapted to environments of interest.

During the discovery process, we instantiate a population of agents, each of which interacts with its own instance of an environment taken from a diverse set of challenging tasks. Each agent’s parameters are updated according to the current RL rule. We then use the meta-gradient method[13] to incrementally improve the RL rule such that it could lead to better-performing agents.

Our large-scale empirical results show that our discovered RL rule, which we call DiscoRL, surpasses all existing RL rules on the environments in which it was meta-learned. Notably, this includes Atari games[22], arguably the most established and informative of RL benchmarks. Furthermore, DiscoRL achieved state-of-the-art performance on a number of other challenging benchmarks, such as ProcGen[23], that it had never been exposed to during discovery. We also show that the performance and generality of DiscoRL improves further as more diverse and complex environments are used in discovery. Finally, our analysis shows that DiscoRL has discovered unique prediction semantics that are distinct from existing RL concepts such as value functions. To the best of our knowledge, this is the empirical evidence that surpassing manually designed RL algorithms in terms of both generality and efficiency is finally within reach.

Discovery method

Our discovery approach involves two types of optimization: agent optimization and meta-optimization. Agent parameters are optimized by updating their policies and predictions towards the targets produced by the RL rule. Meanwhile, the meta-parameters of the RL rule are optimized by updating its targets to maximize the cumulative rewards of the agents.

Agent network

Much RL research considers what predictions an agent should make (for example, values), and what loss function should be used to learn those predictions (for example, temporal-difference (TD) learning) and improve the policy (for example, policy gradient). Instead of hand-crafting them, we define an expressive space of predictions without pre-defined semantics and meta-learn what the agent needs to optimize by representing it using a meta-network. It is desirable to maintain the ability to represent key ideas in existing RL algorithms, while supporting a large space of novel algorithmic possibilities.

To this end, we let the agent, parameterized by θ, output two types of predictions in addition to a policy (π): an observation-conditioned vector prediction y(s) ∈ ℝn of arbitrary size n and an action-conditioned vector prediction z(s, a) ∈ ℝm of arbitrary size m, where s and a are an observation and an action, respectively (Fig. 1b). The form of these predictions stems from the fundamental distinction between prediction and control[16]. For example, value functions are commonly divided into state-value functions v(s) (for prediction) and action-value functions q(s, a) (for control), and many other concepts in RL, such as rewards and successor features, also have an observation-conditioned version  and an action-conditioned version. Therefore, the functional form of the predictions (y, z) is general enough to represent, but is not restricted to, many existing fundamental concepts in RL.

In addition to the predictions to be discovered, in most of our experiments the agent makes predictions with pre-defined semantics. Specifically, the agent produces an action-value function q(s, a) and an action-conditional auxiliary policy prediction p(s, a)[8]. This encourages the discovery process to focus on discovering new concepts through y and z.

Meta-network

A large proportion of modern RL rules use the forward view of RL[16]. In this view, the RL rule receives a trajectory from time step t to t + n, and uses this information to update the agent’s predictions or policy. They typically update the predictions or policy towards bootstrapped targets, that is, towards future predictions.

Correspondingly, our RL rule uses a meta-network (Fig. 1c) as a function that determines targets towards which the agent should move its predictions and policy. To produce targets at time step t, the meta-network receives as input a trajectory of the agent’s predictions and policy as well as rewards and episode termination from time step t to t + n. It uses a standard long short-term memory[24] to process these inputs, although other architectures may be used (Extended Data Fig. 3).

The choice of inputs and outputs to the meta-network maintains certain desirable properties of handcrafted RL rules. First, the meta-network can deal with any observation and with discrete action spaces of any size. This is possible because the meta-network does not receive the observation directly as input, but only indirectly via predictions. In addition, it processes action-specific inputs and outputs by sharing weights across action dimensions. As a result it can generalize to radically different environments. Second, the meta-network is agnostic to the design of the agent network, as it sees only the output of the agent network. As long as the agent network produces the required form of outputs (π, y, z), the discovered RL rule can generalize to arbitrary agent architectures or sizes. Third, the search space defined by the meta-network includes the important algorithmic idea of bootstrapping. Fourth, as the meta-network processes both policy and predictions together, it can not only meta-learn auxiliary tasks[25] but also directly use predictions to update the policy (for example, to provide a baseline for variance reduction). Finally, outputting targets is strictly more expressive than outputting a scalar loss function, as it includes semi-gradient methods such as Q-learning in the search space. While building on these properties of standard RL algorithms, the rich parametric neural network allows the discovered rule to implement algorithms with potentially much greater efficiency and contextual nuance.

Agent optimization

The agent’s parameters (θ) are updated to minimize the distance from its predictions and policy to the targets from the meta-network. The agent’s loss function can be expressed as:

$$L(\theta )={{\mathbb{E}}}_{s,a\sim {{\boldsymbol{\pi }}}_{\theta }}[D(\hat{{\boldsymbol{\pi }}},{{\boldsymbol{\pi }}}_{\theta }(s))+D(\hat{{\bf{y}}},{{\bf{y}}}_{\theta }(s))+D(\hat{{\bf{z}}},{{\bf{z}}}_{\theta }(s,a))+{L}_{{\rm{a}}{\rm{u}}{\rm{x}}}]$$

where s and a are distributed according to the policy πθ, and D(p, q) is a distance function between p and q. We chose the Kullback–Leibler divergence as the distance function, as it is sufficiently general and has previously been found to make meta-optimization easier[3]. Here πθ, yθ, zθ and \(\hat{{\boldsymbol{\pi }}}\), \(\hat{{\bf{y}}}\), \(\hat{{\bf{z}}}\) are the outputs of the agent network and the meta-network, respectively, with a softmax function applied to normalize each vector.

The auxiliary loss Laux is used for predictions with pre-defined semantics: action values (q) and auxiliary policy predictions (p) as follows: Laux = D(\(\hat{{\bf{q}}}\), qθ(s, a)) + D(\(\hat{{\bf{p}}}\), pθ(s, a)), where \(\hat{{\bf{q}}}\) is an action-value target from Retrace[26] projected to a two-hot vector[8], and \(\hat{{\bf{p}}}\) = πθ(s′) is the policy at the one-step future state. To be consistent with the rest of losses, we use the Kullback–Leibler divergence as the distance function D.

Meta-optimization

Our goal is to discover an RL rule, represented by the meta-network with meta-parameters η, that allows agents to maximize rewards in a variety of training environments. This discovery objective J(η) and its meta-gradient ∇ηJ(η) can be expressed as:

$$J(\eta )={{\mathbb{E}}}_{{\mathcal{E}}}{{\mathbb{E}}}_{\theta }[\,J(\theta )],{\nabla }_{\eta }\,J(\eta )\approx {{\mathbb{E}}}_{{\mathcal{E}}}{{\mathbb{E}}}_{\theta }[{\nabla }_{\eta }\theta {\nabla }_{\theta }\,J(\theta )],$$

where \({\mathcal{E}}\) indicates an environment sampled from a distribution and θ denotes agent parameters induced by an initial parameter distribution and their evolution over the course of learning with the RL rule. \(J(\theta )={\mathbb{E}}\left[{\sum }_{t}{{\gamma }}^{{t}}{r}_{{t}}\right]\), where γ is the discount factor and rt is the reward at step t, is the expected discounted sum of rewards, which is the typical RL objective. The meta-parameters are optimized using gradient ascent following the above equations.

To estimate the meta-gradient, we instantiate a population of agents that learn according to the meta-network in a set of sampled environments. To ensure this approximation is close to the true distribution of interest, we use a large number of complex environments taken from challenging benchmarks, in contrast to previous work that focused on a small number of simple environments. As a result the discovery process surfaces diverse RL challenges, such as the sparsity of rewards, the task horizon, and the partial observability or stochasticity of environments.

Each agent’s parameters are periodically reset to encourage the update rule to make fast learning progress within a limited agent lifetime. As in previous work on meta-gradient RL[13], the meta-gradient term ∇ηJ(η) can be divided into two gradient terms by the chain rule: ∇ηθ and ∇θJ(θ). The first term can be understood as a gradient over the agent update procedure[27], whereas the second term is the gradient of the standard RL objective. To estimate the first term, we iteratively update the agent multiple times and backpropagate through the entire update procedure, as illustrated in Fig. 1d. To make it tractable, we backpropagate over 20 agent updates using a sliding window. Finally, to estimate the second term, we use the advantage actor–critic method[28]. To estimate the advantage, we train a meta-value function, which is a value function used only for discovery.

Empirical result

We implemented our discovery method with a large population of agents in a set of complex environments. We call the discovered RL rule DiscoRL. In evaluation, the aggregated performance was measured by the interquartile mean (IQM) of normalized scores for benchmarks that consist of multiple tasks, which has proven to be a statistically reliable metric[29].

Atari

The Atari benchmark[22], one of the most studied benchmarks in the history of RL, consists of 57 Atari 2600 games. They require complex strategies, planning and long-term credit assignment, making it non-trivial for AI agents to master. Hundreds of RL algorithms have been evaluated on this benchmark over the past decade, which include MuZero[8] and Dreamer[10].

To see how strong the rule can be when discovered directly from this benchmark, we meta-trained an RL rule, Disco57, and evaluated it on the same 57 games (Fig. 2a). In this evaluation, we used a network architecture that has a number of parameters comparable to the number used by MuZero. This is a larger network than the one used during discovery; the discovered RL rule must therefore generalize to this setting. Disco57 achieved an IQM of 13.86, outperforming all existing RL rules8,10,14,30 on the Atari benchmark, with a substantially higher wall-clock efficiency compared with the state-of-the-art MuZero (Extended Data Fig. 4). This shows that our method can automatically discover a strong RL rule from such challenging environments.

Fig. 2: Evaluation of DiscoRL.

a–f, Performance of DiscoRL compared to human-designed RL rules on Atari (a), ProcGen (b), DMLab (c), Crafter (d; figure inset shows results for 1 million environment steps), NetHack (e), and Sokoban (f). The x axis represents the number of environment steps in millions. The y axis represents the human-normalized IQM score for benchmarks consisting of multiple tasks (Atari, ProcGen and DMLab-30) and average return for the rest. Disco57 (blue) is discovered from the Atari benchmark and Disco103 (orange) is discovered from Atari, ProcGen and DMLab-30 benchmarks. The shaded areas show 95% confidence intervals. The dashed lines represent manually designed RL rules such as MuZero[8], efficient memory-based exploration agent (MEME) [30], Dreamer[10], self-tuning actor-critic algorithm (STACX)[14], importance-weighted actor-learner architecture (IMPALA)[34], deep Q-network (DQN) [51], phasic policy gradient (PPG)[52], proximal policy optimization (PPO)[18], and Rainbow[53].

Generalization

We further investigated the generality of Disco57 by evaluating it on a variety of held-out benchmarks that it was never exposed to during discovery. These benchmarks include unseen observation and action spaces, diverse environment dynamics, various reward structures and unseen agent network architectures. Meta-training hyperparameters were tuned on only training environments (that is, Atari) to prevent the rule from being implicitly optimized for held-out benchmarks.

The result on the ProcGen[23] benchmark (Fig. 2b and Extended Data Table 2), which consists of 16 procedurally generated two-dimensional games, shows that Disco57 outperformed all existing published methods, including MuZero[8] and PPO[18], even though it had never interacted with ProcGen environments during discovery. In addition, Disco57 achieved a competitive performance on Crafter[31] (Fig. 2d and Extended Data Table 5), where the agent needs to learn a wide spectrum of abilities to survive. Disco57 reached the third place on the leaderboard of NetHack NeurIPS 2021 Challenge[32] (Fig. 2e and Extended Data Table 4), where more than 40 teams participated. Unlike the top submitted agents in the competition[33], Disco57 did not use any domain-specific knowledge for defining subtasks or reward shaping. For a fair comparison, we trained an agent with the importance weighted actor-learner architecture (IMPALA) algorithm[34] using the same settings as Disco57. IMPALA’s performance was much weaker, suggesting that Disco57 has discovered a more efficient RL rule than standard approaches. In addition to environments, Disco57 turned out to be robust to a range of agent-specific settings such as network size, replay ratio and hyperparameters in evaluation (Extended Data Fig. 1).

Complex and diverse environments

To understand the importance of complex and diverse environments for discovery, we further scaled up meta-learning with additional environments. Specifically, we discovered another rule, Disco103, using a more diverse set of 103 environments consisting of the Atari, ProcGen and DMLab-30[35] benchmarks. This rule performs similarly on the Atari benchmark while improving scores on every other seen and unseen benchmark in Fig. 2. In particular, Disco103 reached human-level performance on Crafter and neared MuZero’s state-of-the-art performance on Sokoban[36]. These results show that the more complex and diverse the set of environments used for discovery, the stronger and more general the discovered rule becomes, even on held-out environments that were not seen during discovery. Discovering Disco103 required no changes to the discovery method compared with Disco57 other than the set of environments. This shows that the discovery process itself is robust, scalable and general.

To further investigate the importance of using complex environments, we ran our discovery process on 57 grid-world tasks that are extended from previous work[3], using the same meta-learning settings as for Disco57. The new rule had a significantly worse performance (Fig. 3c) on the Atari benchmark. This verifies our hypothesis about the importance of meta-learning directly from complex and challenging environments. While using such environments was crucial, there was no need for a careful curation of the correct set of environments; we simply used popular benchmarks from the literature.

Fig. 3: Properties of discovery process.

a, Discovery efficiency. The best DiscoRL was discovered within 3 simulations of the agent’s lifetimes (200 million steps) per game. b, Scalability. DiscoRL becomes stronger on the ProcGen benchmark (30 million environment steps for all methods) as the training set of environments grows. c, Ablation. The plot shows the performances of variations of DiscoRL on Atari. ‘Without auxiliary prediction’ is meta-learned without the auxiliary prediction (p). ‘Small agents’ uses a smaller agent network during discovery. ‘Without prediction’ is meta-learned without learned predictions (y, z). ‘Without value’ is meta-learned without the value function (q). ‘Toy environments’ is meta-learned from 57 grid-world tasks instead of Atari games.

Efficiency and scalability

To further understand the scalability and efficiency of our approach, we evaluated multiple Disco57s over the course of discovery (Fig. 3a). The best rule was discovered within approximately 600 million steps per Atari game, which amounts to just 3 experiments across 57 Atari games. This is arguably more efficient than the manual discovery of RL rules, which typically requires many more experiments to be executed, in addition to the time of the human researchers.

Furthermore, DiscoRL performed better on the unseen ProcGen benchmark as more Atari games were used for discovery (Fig. 3b), showing that the resulting RL rule scales well with the number and diversity of environments used for discovery. In other words, the performance of the discovered rule is a function of data (that is, environments) and compute.

Effect of discovering new predictions

To study the effect of the discovered semantics of predictions (y, z in Fig. 1b), we compared different rules by varying the outputs of the agent, with and without certain types of prediction. The result in Fig. 3c shows that the use of a value function markedly improves the discovery process, which highlights the importance of this fundamental concept of RL. However, the result in Fig. 3c also shows the importance of discovering new prediction semantics (y and z) beyond pre-defined predictions. Overall, increasing the scope of discovery compared with previous work1,2,3,4,5,6 was essential. In the following section, we provide further analysis to uncover what semantics have been discovered.

Analysis

Qualitative analysis

We analysed the nature of the discovered rule, using Disco57 as a case study (Fig. 4). Qualitatively, the discovered predictions spike in advance of salient events such as receiving rewards or changes in the entropy of the policy (Fig. 4a). We also investigated which features of the observation cause the meta-learned predictions to respond strongly, by measuring the gradient norm associated with each part of the observation. The result in Fig. 4b shows that meta-learned predictions tend to pay attention to objects that may be relevant in the future, which is distinct from where the policy and the value function pay attention to. These results indicate that DiscoRL has learned to identify and predict salient events over a modest horizon, and thus complements existing concepts such as the policy and value function.

Fig. 4: Analysis of DiscoRL.

a, Behaviour of discovered predictions. The plot shows how the agent’s discovered prediction (y) changes along with other quantities in Ms Pacman (left) and Breakout (right). ‘Confidence’ is calculated as negative entropy. Spikes in prediction confidence are correlated with upcoming salient events. For example, they often precede large rewards in Ms Pacman and strong action preferences in Breakout. b, Gradient analysis. Each contour shows where each prediction focuses on in the observation through a gradient analysis in Beam Rider. The predictions tend to focus more on enemies at a distance, whereas the policy and the value tend to focus on nearby enemies and the scoreboard, respectively. c, Prediction analysis. Future entropy and large-reward events can be better predicted from discovered predictions. The shaded areas represent 95% confidence intervals. d, Bootstrapping horizon. The plot shows how much the prediction target produced by DiscoRL changes when the prediction at each time step is perturbed. The individual curves correspond to 16 randomly sampled trajectories and the bold curve corresponds to the average over them. e, Reliance on predictions. The plot shows the performance of the controlled DiscoRL on Ms Pacman without bootstrapping when updating predictions and without using predictions at all. The shaded areas represent 95% confidence intervals.

Information analysis

To confirm the qualitative findings, we further investigated what information is contained in the predictions. We first collected data from the DiscoRL agent on 10 Atari games and trained a neural network to predict quantities of interest from either the discovered predictions, the policy or the value function. The results in Fig. 4c show that the discovered predictions contain greater information about upcoming large rewards and the future policy entropy, compared with the policy and value. This suggests that the discovered predictions may capture unique task-relevant information that is not well captured by the policy and value.

Emergence of bootstrapping

We also found evidence that DiscoRL uses a bootstrapping mechanism. When the meta-network’s prediction input at future time steps (zt+k) is perturbed, it strongly affects the target \({\hat{{\bf{z}}}}_{t}\) (Fig. 4d). This means that the future predictions are used to construct targets for the current predictions. This bootstrapping mechanism and the discovered predictions turned out to be critical for performance (Fig. 4e). If the y and z inputs to the meta-network are set to zero when computing their targets \(\hat{{\bf{y}}}\) and \(\hat{{\bf{z}}}\) (thus preventing bootstrapping), performance degrades substantially. If the y and z inputs are set to zero for computing all targets including the policy target, the performance drops even further. This shows the discovered predictions are heavily used to inform the policy update, rather than just serving as auxiliary tasks.

Previous work

The idea of meta-learning, or learning to learn, in artificial agents dates back to the 1980s[37], with proposals to train meta-learning systems with backpropagation of gradients[38]. The core idea of using a slower meta-learning process to meta-optimize a fast learning or adaptation process39,40 has been studied for numerous applications in various contexts, including transfer learning[41], continual learning[42], multi-task learning[43], hyperparameter optimization[44] and automated machine learning[45].

Early efforts to use meta-learning for RL agents comprised attempts to meta-learn information-seeking behaviours[46]. Many later works have focused on meta-learning a small number of hyperparameters of an existing RL algorithm13,14. Such approaches have produced promising results but cannot markedly depart from the underlying handcrafted algorithms. Another line of work has attempted to eschew inductive biases by meta-learning entirely black-box algorithms implemented, for example, as recurrent neural networks[47] or as a synaptic learning rule[48]. Although conceptually appealing, these methods are prone to overfit to tasks seen in meta-training[49].

The idea of representing knowledge using a wider class of predictions was first introduced in temporal-difference networks[50] but without any meta-learning mechanism. A similar idea has been explored for meta-learning auxiliary tasks[25]. Our work extends this idea to effectively discover an entire loss function that the agent optimizes, covering a much broader range of possible RL rules. Furthermore, unlike previous work, the discovered knowledge can generalize to unseen environments.

Recently, there have been growing interests in discovering general-purpose RL rules1,3,4,5,6,15. However, most of them were limited to small agents and simple tasks, or the scope of discovery was limited to a partial RL rule. Therefore, their rules were not extensively compared with state-of-the-art rules on challenging benchmarks. In contrast, we search over a larger space of rules, including entirely new predictions, and scale up to a large number of complex environments for discovery. As a result, we demonstrate that it is possible to discover a general-purpose RL rule that outperforms a number of state-of-the-art rules on challenging benchmarks.

Conclusion

Enabling machines to discover learning algorithms for themselves is one of the most promising ideas in artificial intelligence owing to its potential for open-ended self-improvement. This work has taken a step towards machine-designed RL algorithms that can compete with and even outperform some of the best manually designed algorithms in challenging environments. We also showed that the discovered rule becomes stronger and more general as it gets exposed to more diverse environments. This suggests that the design of RL algorithms for advanced AI may in the future be led by machines that can scale effectively with data and compute.

Methods

Meta-network

The meta-network maps a trajectory of agent outputs along with relevant quantities from the environment to targets: \({m}_{\eta }:{f}_{\theta }({s}_{t}),{f}_{{\theta }^{-}}({s}_{t}),\) \({a}_{t},{r}_{t},{b}_{t},\ldots ,{f}_{\theta }({s}_{t+n}),{f}_{{\theta }^{-}}({s}_{t+n}),{a}_{t+n},{r}_{t+n},{b}_{t+n}\mapsto \hat{{\boldsymbol{\pi }}},\hat{{\bf{y}}},\hat{{\bf{z}}},\) where η represents meta-parameters, and fθ = [πθ(s), yθ(s), zθ(s), qθ(s)] is the agent output with parameters θ. a, r and b are an action taken by the agent, a reward and an episode termination indicator, respectively. θ− is an exponential moving average of parameters θ. This functional form allows the meta-network to search over a strictly larger space of rules compared with meta-learning a scalar loss function. This is further discussed in Supplementary Information.

The meta-network processes the inputs by unrolling a long short-term memory (LSTM) backwards in time as illustrated in Fig. 1c. This allows it to take into account n-step future information to produce targets, as in multi-step RL methods such as temporal-difference methods TD(λ)[54]. We found that this architecture is computationally more efficient than alternatives such as transformers, while achieving a similar performance, as shown in Extended Data Fig. 3b.

The action-specific inputs and outputs are processed in the meta-network using shared weights over the action dimension, and an intermediate embedding is computed by averaging across it. This allows the meta-network to process any number of actions. More details about it can be found in Supplementary Information.

To allow the meta-network to discover a wider class of algorithms, such as reward normalization, that require maintaining statistics over an agent’s lifetime, we add an additional recurrent neural network. This ‘meta-RNN’ is unrolled forward across agent updates (from θi to θi+1), rather than across time steps in an episode. The core of the meta-RNN is another LSTM module. For each of the agent updates, the whole batch of trajectories is embedded into a single vector that is passed to this LSTM. The meta-RNN can potentially capture the learning dynamics throughout the agent’s lifetime, producing targets that are adaptive to the specific agent and the environment. The meta-RNN slightly improved the overall performance, as shown in Extended Data Fig. 3a. Further details are described in Supplementary Information.

Meta-optimization stabilization

A number of challenges arise when we discover at a large scale, mainly because of unbalanced gradient signals coming from agents in different environments and myopic gradients caused by long lifetimes of agents. We introduce a few methods to alleviate these problems.

First, when estimating the advantage term in the advantage actor–critic method to estimate ∇θJ(θ) in the meta-gradient, we normalize the advantage term as follows: \(\bar{A}\) = (A − μ)/σ, where \(\bar{A}\) is a normalized advantage and μ and σ are the exponentially moving average and standard deviation of advantages accumulated over the agent’s lifetime. We found that this makes the scale of the advantage term balanced across different environments. In addition, when aggregating the meta-gradient from the population of agents, we take the average of the meta-gradients over all agents after applying a separate Adam optimizer to the meta-gradient calculated from each agent: \(\eta \leftarrow \eta +\frac{1}{n}{\sum }_{i=1}^{n}\mathrm{ADAM}({g}_{i})\), where gi is the meta-gradient estimation from the ith agent in the population. We found that this helps to normalize the magnitude of the meta-gradients from each agent.

We add two meta-regularization losses (Lent and LKL) to the meta-objective J(η) as follows: \({{\mathbb{E}}}_{{\mathcal{E}}}{{\mathbb{E}}}_{\theta }[\,J(\theta )-{L}_{\mathrm{ent}}(\theta )-{L}_{\mathrm{KL}}(\theta )]\).\({L}_{\mathrm{ent}}(\theta )=-{{\mathbb{E}}}_{s,a}\) \([H({{\bf{y}}}_{\theta }(s))+H({{\bf{z}}}_{\theta }({\rm{s}},a))]\) is an entropy regularization of predictions y and z, where H(⋅) is the entropy of the given categorical distribution. We found that this helps prevent the predictions from converging prematurely. \({L}_{{\rm{K}}{\rm{L}}}(\theta )={D}_{{\rm{K}}{\rm{L}}}({{\boldsymbol{\pi }}}_{{\theta }^{-}}||\hat{{\boldsymbol{\pi }}})\) is the Kullback–Leibler divergence between the policy of a target network with an exponential moving average of the agent parameters (θ−) and the meta-network’s policy target (\(\hat{{\boldsymbol{\pi }}}\)). This prevents the meta-network from proposing excessively aggressive updates that could lead to collapse.

It is noted that these methods are used only to stabilize meta-optimization, and they do not determine how the agents are updated. The meta-learned rule still solely determines how the agents are updated.

Implementation details

We developed a framework that uses JAX library55,56 and distributes computation across tensor processing units (TPUs)[57] inspired by the Podracer architectures[58]. In this framework, each agent is simulated independently, with the meta-gradients of all agents being calculated in parallel. The meta-parameters are updated synchronously by aggregating meta-gradients across all agents. We used MixFlow-MG[59] to minimize the computational cost of the runs.

For Disco57, we instantiate 128 agents by cycling through the 57 Atari environments in lexicographic order. For Disco103, we instantiate 206 agents, with two copies of each environment from Atari, ProcGen and DMLab-30. Disco57 was discovered using 1,024 TPUv3 cores for 64 hours, and Disco103 was discovered using 2,048 TPUv3 cores for 60 hours.

The meta-value function used to calculate the meta-gradient is updated using V-Trace[34], with a discount factor of 0.997 and a TD(λ) coefficient of 0.95. The meta-value function and agent networks are optimized using an Adam optimizer with a learning rate of 0.0003. For meta-parameter updates, we use the Adam optimizer with a learning rate of 0.001 and gradient clipping of 1.0. Each agent is updated based on a batch of 96 trajectories with 29 time steps each. In each batch, on-policy trajectories and trajectories sampled from the replay buffer are mixed, with replay trajectories accounting for 90% of each batch. At each meta-step, 48 trajectories are generated to calculate the meta-gradient and update the meta-value function.

Each agent’s parameters are reset after it has consumed its allocated experience budget. When resetting, a new experience budget is sampled from the categories (200 million, 100 million, 50 million, 20 million) with a weight inversely proportional to the budget, such that the same amount of total experience is sampled in each category. This was based on our observation that much of learning happens early in the lifetime and demonstrated a marginal improvement in our preliminary small-scale investigation.

Hyperparameters and evaluation

For evaluation on held-out benchmarks, we only tuned the learning rate from {0.0001, 0.0003, 0.0005}. The rest of the hyperparameters were selected based on baseline algorithms from the literature.

The evaluation on Atari games (shown in Fig. 2a and Extended Data Table 1) used a version of the IMPALA[34] network with an increased parameter count that matches the agent network size used by MuZero[8]. Specifically, we used a network with 4 convolutional residual blocks with 256, 384, 384 and 256 filters, a shared fully connected final layer of 768 dimensions, and an LSTM-based action-conditional predictions component that is composed of an LSTM with a 1,024 hidden state dimension and a 1,024-dimensional fully connected layer. DMLab-30 evaluations (Fig. 2c and Extended Data Table 3) use the same action space discretization and agent network architecture as used in IMPALA. See Extended Data Table 6 for the list of hyperparameters. To verify the statistical significance of our evaluations, we used two random seeds for initialization on each environment from Atari, ProcGen and DMLab, three seeds on Crafter and NetHack, and five seeds on Sokoban.

Analysis details

For the prediction analysis in Fig. 4c, we train multiple 3-layer perceptrons (MLPs) with 128, 64 and 32 hidden units for each layer respectively. The MLPs are trained to predict quantities such as future entropy and rewards from the outputs of an agent that has been trained on different Atari games using Disco57. We use 10 Atari games (Alien, Amidar, Battle Zone, Frostbite, Gravitar, Qbert, Riverraid, Road Runner, Robotank and Zaxxon). The values shown in Fig. 4c are R^2 scores for future entropy and test accuracy for large-reward events using fivefold cross-validation. Extended Data Fig. 2 provides an additional prediction analysis for more quantities. For high-dimensional outputs (y, z, za), we used a larger 3-layer MLP with 256 hidden units each.

Data availability

No external data were used for the results presented in the article.

Code availability

We provide the meta-training and evaluation code, with the meta-parameters of Disco103, under an open source licence at https://github.com/google-deepmind/disco_rl. All of the benchmarks presented in the article are publicly available.

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Acknowledgements

We thank S. Flennerhag, Z. Marinho, A. Filos, S. Bhupatiraju, A. György and A. A. Rusu for their feedback and discussions about related ideas; B. Huergo Muñoz, M. Kroiss and D. Horgan for their help with the engineering infrastructure; R. Hadsell, K. Kavukcuoglu, N. de Freitas and O. Vinyals for their high-level feedback on the project; and S. Osindero and D. Precup for their feedback on an early version of this work.

Author information

Author notes

1. These authors contributed equally: Junhyuk Oh, Gregory Farquhar, Iurii Kemaev, Dan A. Calian

Authors and Affiliations

1. Google DeepMind, London, UK

Junhyuk Oh, Gregory Farquhar, Iurii Kemaev, Dan A. Calian, Matteo Hessel, Luisa Zintgraf, Satinder Singh, Hado van Hasselt & David Silver

Contributions

J.O., I.K., G.F. and D.A.C. contributed equally. J.O., G.F., I.K., D.A.C. and L.Z. developed and analysed the method with advice from H.v.H., S.S. and D.S. J.O., G.F., M.H., D.A.C. and I.K. evaluated the method. I.K. led engineering with contributions from J.O., D.C. and G.F. J.O. and G.F. wrote the paper with contributions from L.Z. and D.A.C. H.v.H., S.S. and D.S. advised the team. J.O. and D.S. led the project.

Corresponding authors

Correspondence to Junhyuk Oh or David Silver.

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A patent application(s) directed to aspects of the work described has been filed and is pending as of the date of manuscript submission. Google LLC has ownership and potential commercial interests in the work described.

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Extended data figures and tables

Extended Data Fig. 1 Robustness of DiscoRL.

The plots show the performance of Disco57 and Muesli on Ms Pacman by varying agent settings. ‘Discovery’ and ‘Evaluation’ represent the setting used for discovery and evaluation, respectively. (a) Each rule was evaluated on various agent network sizes. (b) Each rule was evaluated on various replay ratios, which define the proportion of replay data in a batch compared to on-policy data. (c) A sweep over optimisers (Adam or RMSProp), learning rates, weight decays, and gradient clipping thresholds was evaluated (36 combinations in total) and ranked according to the final score.

Extended Data Fig. 2 Detailed results for the regression and classification analysis.

Each cell represents the test score of one MLP model that has been trained to predict some quantity (columns) given the agent’s outputs (rows).

Extended Data Fig. 3 Effect of meta-network architecture.

(a) The x-axis represents the number of environment steps in evaluation and the y-axis the IQM on the Atari benchmark. All methods are discovered from 16 randomly selected Atari games. The meta-RNN component slightly improves performance. The shaded areas show 95% confidence intervals. (b) The x-axis represents the number of environment steps in evaluation and the y-axis the IQM on the Atari benchmark. All methods are discovered from 16 randomly selected Atari games. Each curve corresponds to a different meta-network architecture, with varying number of LSTM hidden units, or its LSTM component is replaced by a transformer. The choice of the meta-net architecture minimally affects performance. The shaded areas show 95% confidence intervals.

Extended Data Fig. 4 Computational cost comparison.

The x-axis represents the amount of TPU hours spent for evaluation. The y-axis represents the performance on the Atari benchmark. Each algorithm was evaluated on 57 Atari games for 200 M environment steps. DiscoRL reached MuZero’s final performance with approximately 40% less computation.

Extended Data Table 1 Atari57 result

Extended Data Table 2 ProcGen result

Extended Data Table 3 DMLab-30 result

Extended Data Table 4 NetHack result

Extended Data Table 5 Crafter result

Extended Data Table 6 Hyperparameters of agents in evaluation

Supplementary information

Supplementary Information

This Supplementary Information file contains three sections: (1) Design of meta-learned rule; (2) Meta-network details; and (3) Meta-optimization details. It includes 4 Supplementary figures, 1 Supplementary table and Supplementary references.

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Oh, J., Farquhar, G., Kemaev, I. et al. Discovering state-of-the-art reinforcement learning algorithms. Nature 648, 312–319 (2025). https://doi.org/10.1038/s41586-025-09761-x

- Received: 11 December 2024

- Accepted: 15 October 2025

- Published: 22 October 2025

- Version of record: 26 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09761-x

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Direct deaminative functionalization with N-nitroamines

Guangliang Tu,

Ke Xiao,

Xiaoping Chen,

Haoran Xu,

Haifeng Zeng,

Fangjiang Zhang,

Xiao-Song Xue &

…

Xiaheng Zhang

Nature volume 648, pages 341–348 (2025)

Abstract

Amines are among the most common functional groups in bioactive molecules[1]. Despite this prevalence, conventional means of converting aromatic amines rely heavily on diazonium intermediates[2], which pose significant safety risks due to the explosive nature of these salts3,4. Here we report a direct deaminative strategy through the formation of N-nitroamines, allowing the direct conversion of inert aromatic C−N bonds into an array of other functional groups, including C−X (C−Br, C−Cl, C−I, C−F, C−N, C−S, C−Se, C−O) and C−C bonds. This operationally simple, general protocol establishes a unified strategy for one-pot deaminative cross-couplings by integrating deaminative functionalization with transition-metal-catalysed arylation, thereby streamlining synthesis and late-stage functionalization. The key advantage of this transformation over other deaminative functionalization methods lies in its versatility across nearly all classes of medicinally relevant heteroaromatic amines, as well as electronically and structurally diverse aniline derivatives, regardless of the position of the amino group. Mechanistic studies, supported by both experimental observations and theoretical analysis, suggest that the aryl cation equivalent reactivity of N-nitroamines is generally favoured in this deaminative process. This study highlights the potential of the direct deamination approach in synthetic chemistry, offering a safer alternative to the traditionally explosive and hazardous aryldiazonium chemistry.

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Main

For decades, aryl halides and phenols have dominated as privileged arylating agents5,6, serving as fundamental building blocks for transformations such as transition-metal-catalysed cross-coupling reactions (Fig. 1a). By contrast, aromatic amines—structural cornerstones of natural products and medicinal compound libraries7,8—remain severely under-used as reactive species. Although stepwise functionalization strategies emerged as early as 1884 with the copper-mediated Sandmeyer reaction via diazonium intermediates, subsequent developments expanded this reactivity largely through free-radical pathways3,9. In general, conventional diazotization protocols require the use of explosive diazonium salts, introducing safety concerns. Accordingly, the Ritter group devised an elegant safer varianet of the Sandmeyer reaction that generates transient aryldiazonium through nitrate-reduction chemistry (Fig. 1b)[10]. However, these aryldiazonium-based processes still suffer from stoichiometric copper consumption and restrictive substrate compatibility. The Cornella group recently disclosed an innovative deaminative strategy in which electron-deficient (hetero)aromatic systems, following in situ generation of pyridinium intermediates, undergo substitution via an SNAr pathway11,12. In parallel, the Levin group demonstrated a promising radical-based deamination approach that uses anomeric amide reagents to generate carbon-centred radical species13,14. Yet these reactions often rely on reagents with poor atom economy and are typically restricted to either electron-deficient or -rich aromatic systems, thereby limiting their broader applicability. Building on these advances, we set out to investigate whether an alternative activation mode could enable direct deaminative functionalization and thus provide access to previously unexplored reaction manifolds.

Fig. 1: Direct deaminative functionalization of aromatic amines.

a, Relative commercial availability of common aryl donors used in cross-coupling reactions (data retrieved from the Reaxys database). b, Recent advances in deaminative functionalization of aromatic amines10,11,14. c, Aromatic amines as direct precursors to aryl donors with in situ rapid diversification (this work). Het., heterocycle.

Our direct deaminative strategy makes use of the distinct reactivity of N-nitroamines through nitric acid-mediated extrusion of nitrous oxide (N_2O), enabling direct conversion of aromatic C−N bonds into an array of C−X (C−Br, C−Cl, C−I, C−F, C−N, C−S, C−Se, C−O) and C−C bonds. This approach establishes a route for one-pot deaminative cross-couplings that merges deaminative functionalization with transition-metal-catalysed arylation, offering expeditious access to complex pharmacophores from ubiquitous aromatic amine precursors under mild conditions (Fig. 1c). Moreover, the process is readily scalable to kilogram-scale synthesis.

Reaction development

The direct substitution of amino groups within aromatic frameworks presents a formidable synthetic challenge due to the poor leaving-group capability of NH_2 moieties2,15. Building on established deamination strategies for prefunctionalized aliphatic amines16,17,18, we hypothesized that installing dual electron-withdrawing groups (for example, acyl, sulfonyl) on the amino group could substantially weaken the C(sp^2)−N bond, thereby promoting subsequent nucleophilic substitution. In pursuit of suitable precursors for this transformation, we synthesized various substrates bearing different electron-withdrawing groups on the amino group (trifluorosulfonyl-, acetyl-, benzoyl- and so on; see Supplementary Section 3 for full details). Unfortunately, these substrates proved ineffective in our initial investigations; our exploration thus shifted towards introducing two nitro groups via the nitration process, which unexpectedly led us to the identification of N-pyridylnitroamine 1 and N-(4-cyanophenyl)nitroamine S122, which were presumably formed through the dehydration of aromatic amines with nitric acid (see Supplementary Section 7.1 for full experimental details). The structures of these compounds were elucidated through X-ray crystallographic analysis (Supplementary Figs. 41–43). Despite their earliest discovery in 189319,20,21, the reactivity potential of heteroaromatic and aniline-derived nitroamines have remained largely unexplored.

A pivotal discovery emerged when N-pyridylnitroamine was treated with magnesium chloride/nitric acid, aluminium trichloride, or thionyl dichloride, each of which efficiently yielded the deaminative chlorination product 2 (Supplementary Figs. 1 and 2). Mechanistic studies unveiled an unprecedented N_2O extrusion pathway accompanying this transformation, as confirmed by gas chromatography-mass spectrometry (GC-MS) analysis (Fig. 2a and Supplementary Figs. 25–28). This serendipitous result uncovered an operationally mild protocol for the deaminative chlorination of aminoheterocycles. The observed reactivity motivated us to streamline the process. We envisioned a practical protocol that involves the in situ generation of reactive N-nitroamine intermediates through nitric-acid-mediated nitration of aromatic amines, followed by tandem deaminative chlorination, thereby eliminating the need for nitroamine isolation. Indeed, we successfully detected the formation of N-pyridylnitroamine upon the exposure of 2-aminopyridine to nitric acid (Supplementary Figs. 16 and 17). After an extensive optimization, subjecting 2-aminopyridine to just 1.2 equivalents of nitric acid under the optimized conditions successfully afforded the corresponding chlorination product 2 in good yield (Fig. 2b and Supplementary Figs. 3–10). These results suggest that the deamination process is initiated by the formation of N-pyridylnitroamine (1). It is worth noting that 4-dimethylaminopyridine (DMAP) is critical for increasing the efficiency of this reaction, probably due to its dual role as a base and as an activator of SOCl_2, thereby facilitating the generation of nucleophilic chloride anions. Next we conducted kinetics experiments, which suggest that the formation of the N-nitroamine intermediate might be the rate-determining step (Supplementary Figs. 18–22). Notably, direct exposure of preformed nitroamines to chlorination conditions resulted in complete conversion within 1.5 min. These findings support our hypothesis that the N-nitroamine might act as a transient intermediate that, once formed, rapidly collapses to the final product.

Fig. 2: Reaction development and proposed mechanism.

a, Unexpected finding. b, Standard conditions. c, Mechanistic hypothesis. See Supplementary Section 3 for full experimental details. LG, leaving group.

Building on these observations, a plausible mechanistic hypothesis for the deaminative process is depicted in Fig. 2c. The sequence initiates with the nitration of the aromatic amine to form an N-nitroamine 1, which undergoes tautomerization to generate intermediate 4. Following treatment with the appropriate reagents, this species is converted to a labile intermediate 5. Intermediate 5 then extrudes N_2O and is subsequently intercepted by a nucleophile, thereby delivering the deaminative functionalization product and driving the reaction to completion.

Substrate scope exploration

With the established deaminative chlorination procedure in hand, we systematically explored its generality. This transformation demonstrates exceptional versatility across a diverse range of medicinally relevant aminoheterocyclic scaffolds. As depicted in Fig. 3, both ortho- and para-aminopyridines bearing electronically varied substituents—including trifluoromethyl, nitro, cyano, ester, halogen, ether, phenyl and alkyl groups—underwent successful conversion to provide the corresponding chlorinated products in moderate to good yields (6–20, 55–96% yield). Notably, the protocol accommodates synthetically valuable functional handles such as alkenes (6), alkynes (14) and aryl boronates (7), which are particularly advantageous for downstream derivatization. A long-standing challenge in deaminative halogenation has been the functionalization of meta-aminopyridines, which typically suffer from poor reactivity under conventional conditions10,11,14. We found that our methodology successfully addresses this limitation, enabling efficient chlorination of meta-aminopyridines (24–27, 46–64% yield). The scope further extends to five-membered heteroaromatic amines, including thiazole, isothiazole and 1,3,4-thiadiazole, delivering chlorinated products with useful levels of efficiency (21–23, 28; 36–87% yield). Moreover, multinitrogen-containing heterocycles, such as pyrazole, imidazole, pyrimidine, pyrazine and pyridazine, were all well-tolerated (29–33, 50–83% yield). The protocol is also compatible with fused polycyclic aromatics (34, 40% yield). Comparative studies with classical Sandmeyer conditions revealed the superior performance of our protocol, particularly in multi-nitrogen systems. Although conventional copper-mediated aryldiazonium-based chemistry typically results in low (often undetectable) yields, our approach reliably achieves satisfactory efficiency (Fig. 3, grey highlights). This enhanced reactivity is attributed to our unique mechanistic pathway, which circumvents traditional radical intermediates. This deaminative transformation exhibits good electronic tolerance and positional generality, enabling efficient chlorination of structurally diverse aniline derivatives. The protocol successfully accommodates substituents across the entire electronic spectrum, electron-donating, -neutral and -withdrawing groups at all aromatic positions, furnishing chlorinated arenes in synthetically useful yields (35–47, 40–77% yield).

Fig. 3: Scope of direct deaminative chlorination.

Isolated yields. aYield (1H NMR). See Supplementary Sections 4–6 for full experimental details. DMAP, 4-dimethylaminopyridine; Bpin, bispinacolboronate; Bn, benzyl; TMS, tetramethylsilane; Ph, phenyl; Bz, benzoyl; Piv, pivaloyl; Ac, acetyl; Sandm., Sandmeyer conditions; n.d., not detected.

Given the importance of late-stage functionalization in drug discovery, we explored the applicability of our approach to more structurally complex bioactive molecules. The deaminative chlorination of procaine, a local anaesthetic, proceeded smoothly in a yield of 45% (42), even with the presence of a tertiary amine fragment. Interestingly, the anti-inflammatory agents amlexanox and deuterated-amlexanox yielded the corresponding products in good yields (48, 68% yield; 49, 60% yield). Using starane, an agrochemical, as the substrate, the yield of 50 improved significantly to 95%. Moreover, the fused heterocyclic compound imiquimod, an immunomodulator, was also tolerated, yielding product 51 in 42% yield. Notably, the substrate trimethoprim, an antibacterial bearing two NH_2 groups, underwent smooth double deaminative chlorination (52, 30% yield). Chlorination of acid-sensitive, purin-based compounds such as adefovir (anti-hepatitis B) and famciclovir (anti-viral) delivered 53 and 56 in moderate yields. Benzothiazole derivative from fasudil (anti-angina) and riluzole (anti-glutamate) were successfully converted with yields of 41% and 82%, respectively (54 and 55). This performance stands in stark contrast to Sandmeyer conditions, which largely failed for these complex architectures. Our protocol thus represents a robust method for late-stage diversification of drug molecules. An additional 51 examples in Extended Data Fig. 1 further highlight the generality of this protocol.

The integration of diverse aromatic amines into chlorination reactions demonstrated the operational efficiency of our deaminative strategy, thus motivating us to systematically explore the reactivity with alternative nucleophiles. We initiated our investigation by exploring a range of deaminative transformations using N-nitroamines (Supplementary Fig. 29). The N-nitroamine intermediates consistently afforded the desired products in good yields, indicating their pivotal role as reactive species in the deamination process. Building on the established protocol for deaminative chlorination, wherein minimal quantities of nitric acid were introduced to activate amino moieties, this strategy exhibited remarkable versatility, enabling facile construction of an array of carbon−heteroatom bonds (C−Br, C−I, C−F, C−N, C−S, C−Se, C−O) and C−C bonds directly from aromatic amines (Fig. 4). Deaminative halogenation proceeded smoothly when using simple halogenation reagents such as SOBr_2, LiBr and KI. For example, aromatic amines with five- or six-membered heterocycles, and benzene rings bearing electronically diverse array of functional groups, reacted efficiently to provide the halogenated products (57–66 and 70–76; 43–87% yield). Notably, a range of di- and tri-halogenated aromatic amines proved competent in this transformation (57–60, 64 and 70). No halogen scrambling was observed, which represents a valuable feature with respect to further derivatization. Minor over-halogenated side products were also detected with electron-rich arenes in deaminative halogenation (Cl, Br, I), presumably due to NOx-induced oxidation of halide anions to the corresponding electrophilic equivalents. The incorporation of fluorinated groups into aromatic rings is particularly important, as they can considerably alter their physical and biological properties[22]. We were delighted to find that 2-aminopyridines successfully underwent deaminative fluorination (67–69, 35–45% yield). We next further examined the compatibility of our new method towards other common nucleophiles. To our delight, the strategy demonstrated versatile engagement with N-, S- and Se-centred nucleophiles, allowing access to a broad array of chemical diversity (77–83, 38–69% yield). However, the current nucleophile scope remains limited for species with low basicity. Significantly, the protocol proved productive in C−O bond formation, demonstrating its potential for facilitating further cross-coupling reactions and late-stage modification of bioactive molecules5,23,24,25. Oxygen-centred reagents—including Ts_2O, Tf_2O, H_2O, EtOH and HFIP—exhibited excellent tolerance with the system, successfully accommodating a wide range of aromatic compounds, including pyridazine, quinoline, pyrazine, pyrimidine, purine, pyridine and benzene derivatives (84–96, 38–88% yield). To comprehensively illustrate the compatibility of this method, several examples were tested under standard aryldiazonium-based conditions. As highlighted in Fig. 4, most cases provided significantly lower yields (often undetectable) compared with our protocol. The construction of carbon–carbon bonds is pivotal in organic synthesis and industrial production[26]. Encouraged by the preceding outcomes, we extended the scope to C-nucleophiles. Importantly, the direct use of C(sp^2)−H or C(sp^3)−H bonds as latent nucleophiles enabled streamlined access to both C(sp^2)−C(sp^2) and C(sp^2)−C(sp^3) bonds, potentially accelerating the synthesis of a myriad of organic compounds (97–99, 101, 123 and 125; 40–71% yield). A further 29 examples for this deaminative functionalization are detailed in Extended Data Fig. 2. The bar graph in Extended Data Fig. 3 demonstrates an enhanced yield of our method for several representative substrates over conventional Sandmeyer or diazonium salt pathways.

Fig. 4: Scope of deaminative functionalization with other nucleophiles.

Isolated yields. aYield (1H NMR). See Supplementary Sections 4–6 for the full experimental details. General halogenation conditions: amine (0.5 mmol), SOBr_2 (1.25 mmol) as a bromine source, HNO_3 (2.0 equiv.), DMAP (2.5 equiv.), DCE (5.0 ml), 70 °C, 1 h; amine (0.5 mmol), KI (2.0 mmol) as an iodine source, HNO_3 (6.0 equiv.), DCE (5.0 ml), 70 °C, 1 h; amine (0.2 mmol), AgF_2 (0.6 mmol) as a fluorine source, HNO_3 (3.0 equiv.), DCE (2.0 ml), 70 °C, 2.5 h. Nuc, nucleophiles; Piv, pivaloyl; Ph, phenyl; Ac, acetyl; Tf, trifluoromethanesulfonyl; Ts, tosyl; Sandm., Sandmeyer conditions; Diaz.s., diazonium salts; n.d., not detected.

One-pot strategy and application

We sought to improve operational simplicity further by developing a one-pot deaminative cross-coupling sequence. This makes use of in situ-generated aryl (pseudo)halides in subsequent transition-metal-catalysed coupling or nucleophilic substitution reactions without the need for intermediate isolation, enhancing its synthetic usefulness. Although there have been some instances of one-pot cross-coupling protocols27,28, methods with broad applicability are still lacking.

The deaminative halogenation products require no purification and could be directly subjected to cross-coupling reactions by simply adding the appropriate coupling reagents under standard transition-metal catalysis (102–108, 38–52% yield) (Extended Data Fig. 4). Notably, a range of transformations—including Negishi coupling (102), reductive cross-coupling (104), Ullmann–Ma reaction (105), Buchwald–Hartwig amination (106), Hirao reaction (107), and sulfonylation (108)—were all compatible with this one-pot deaminative cross-coupling sequence29,30,31,32,33,34. Furthermore, metallaphotoredox catalysis[35] was successfully integrated into the one-pot sequence, delivering azetidine product 103. A further 16 examples using other coupling reagents are detailed in Extended Data Fig. 5. The broad compatibility of this one-pot protocol with diverse transition-metal-catalysed couplings, and its good tolerance towards multifunctional coupling partners, offers distinct retrosynthetic disconnections for the expedient synthesis of complex molecules from widely available native functionalities, thereby underscoring its significance for advancing medicinal chemistry. Encouraged by these results, we also initiated a preliminary exploration into direct deaminative cross-coupling and were pleased to achieve a direct deaminative Suzuki coupling (109, 47% yield) of aromatic amines.

To further showcase the applicability of this method, we explored its capacity to efficiently construct drug-like molecular complexity in a highly expedient yet modular fashion through chemoselective, sequential deaminative functionalization (Fig. 5a). To this end, compound 110, which contains two NH_2 groups of similar reactivity, was chosen as the starting material. Encouragingly, deaminative chlorination occurred at the isoquinolinyl aromatic ring, delivering mono-chlorinated product 111 in 60% yield with high regioselectivity by simply controlling the reaction temperature. Interestingly, increasing the amount of chlorinating reagents smoothly facilitated a double deaminative chlorination to product 112 in 51% yield. Subjection of the resulting chloride 111 to a stepwise Chan–Lam coupling followed by a Suzuki–Miyaura coupling afforded the diarylation product 117. Alternatively, treatment of 111 under Suzuki–Miyaura coupling conditions followed by our newly developed deaminative cross-coupling sequence provided the drug-like compound 115 with good efficiency. Remarkably, the reaction of the substrate 5-bromopyridin-2-amine (118) was successfully scaled up to 1 kg, yielding the product 119 in a high yield of 90% with simple recrystallization (Fig. 5b). This operational robustness offers distinct industrial advantages, particularly for discovery chemistry and process development across other industries[36].

Fig. 5: Synthetic applications.

a, Chemoselective deamination towards divergent synthesis of complex molecules. b, Kilogram-scale synthesis. c, Efficient synthesis of etoricoxib. aThe product was purified by simple recrystallization. bSee ref. [37] for the previous route. All yields are isolated. See Supplementary Section 8 for full experimental details. r. r., regioselective ratio.

Moreover, our one-pot methodology enables streamlined synthesis of multifunctional (hetero)arenes but typically necessitates overcoming multiple challenges, including the electronic and steric properties of electrophiles and nucleophiles, choice of catalysts, ligands, additives and solvents. We then investigated the selective and sequential functionalization of three sites on a pyridine ring. The iterative conversion of C−Br, C−Cl and C−NH_2 bonds in a commercially available starting material was achieved successively[37] to deliver etocoxib 121 in a three-step, one-pot operation with a synthetically useful yield of 28% (Fig. 5c).

Mechanistic studies

On the basis of our proposed mechanism (Fig. 2c), we conducted a series of experiments to gain some mechanistic insights into the key product-forming step of this deaminative transformation (see Supplementary Section 3 for full experimental details). Whether the transformation proceeds through an aryl cation intermediate38,39 or a direct nucleophilic aromatic substitution (SNAr) pathway remains a subject of ongoing discussion. Past literature has extensively documented the Mascarelli-type reaction as a classical example of intramolecular C–H insertion mediated via aryl cation intermediates[40]. Notably, substrates 100 and 122 underwent smooth deamination, yielding the corresponding C−H insertion products in 43% and 40% isolated yields, respectively. Furthermore, treatment of substrate 124 under nitric acid conditions afforded intramolecular electrophilic substitution product 125 in 60% yield. These initial results support the possible formation of aryl cation intermediates during the reaction (Extended Data Fig. 6a). We then performed further experiments to investigate the nature of the reactive species. ortho-n-Butyl aniline 126 underwent intramolecular C–H insertion in ethyl acetate under nitric acid conditions, affording the deaminative cyclization product 127, whereas selective deaminative arylation product 128 was obtained when benzene was used as solvent (Extended Data Fig. 6b). Alternatively, when meta-n-butyl aniline was used as the precursor under identical conditions, arylation product was obtained in 36% yield, probably occurring through an electrophilic aromatic substitution process (Supplementary Fig. 32). These findings further corroborate the intermediacy of aryl cations in these transformations[39]. Moreover, under Ritter-type conditions, the formation of deaminoamidation product 130 provides additional support for the aryl cation intermediate acting as the key electrophilic species (Extended Data Fig. 6c). A Hammett analysis was also conducted with a series of para-substituted aniline derivatives under standard deaminative chlorination conditions. Plotting log(kX/kH) against the substituent parameter σ resulted in a linear correlation with the negative slope (ρ = −0.229), consistent with the proposed aryl cation intermediate in the transition state (Extended Data Fig. 6d). Although these results collectively support the involvement of aryl cation intermediates in the deaminative reaction, we recognize that the electronic properties of the substrates may significantly influence the stability of these intermediates, potentially leading to divergent mechanistic pathways.

We performed density functional theory (DFT) calculations to gain a deeper mechanistic insight (see Supplementary Section 3.8 for full computational analysis; see also Supplementary Figs. 39 and 40). The DFT results suggest that the reaction proceeds through the energetically favoured pathway a, which aligns with experimental observations. As depicted in Extended Data Fig. 6e, loss of chloride anions from intermediate 131 affords intermediate 5, which then undergoes N_2O extrusion to form aryl cation 133 (ΔG = 11.1 kcal mol–1). This highly reactive electrophilic species is then captured by nucleophiles to furnish the deaminative functionalization product. Unlike the stable aryldiazonium intermediate, intermediate 5 could not be isolated due to the rapid elimination of N_2O. As N_2O is a superior leaving group, its extrusion from 5 occurs readily via transition state 132, requiring only 7.3 kcal mol–1 (overall ΔG‡ = 17.0 kcal mol–1). However, we cannot rule out the possibility that a competing SNAr process (pathway b) operates in parallel. It is likely that the reaction mechanism may depend on the nature of the substrate and nucleophile. To investigate this, DFT calculations were performed using seven different nucleophiles (Cl, Br, I, OTf, OCH(CF_3)2, SCN, NTf_2) across a variety of electronically diverse (hetero)arylamines for both the aryl cation and SNAr pathways (Supplementary Fig. 40). When using strongly electron-deficient aromatic amines in deaminative halogenation (Cl, Br, I), the SNAr pathway via intermediate 134 was favoured over the aryl cation route[41]. Conversely, in other deaminative functionalizations, the aryl cation mechanism was generally preferred regardless of the electronic nature of the arylamine substrates, including electron-donating (S114), neutral (S117, S118) and electron-withdrawing (S115, S116) substituents.

Data availability

All data supporting the findings of this study are available within the Article and its Supplementary Information. The supplementary crystallographic data for this paper are available free of charge from the Cambridge Crystallographic Data Centre (CCDC) under accession nos. CCDC 2328567 (1), CCDC 2474737 (S120) and CCDC 2474761 (S122). Copies of the data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/.

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Acknowledgements

We are grateful for financial support from the National Natural Science Foundation of China (grant nos. 22171049 and 22122104), the Natural Science Foundation of Zhejiang Province (grant no. LDQ23B020001), the Hangzhou leading innovation and entrepreneurship team project (grant no. TD2022002), the CAS Project for Young Scientists in Basic Research (YSBR-095) and the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB0590000). We thank D. W. C. MacMillan (Princeton University), R. R. Knowles (Princeton University), Y. Liang (AstraZeneca), M. Chen and C. Liu for helpful discussions. We thank H. Wang and B. Zhou from the laboratory of mass spectrometry analysis at Shanghai Institute of Organic chemistry for their support with facility access.

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Author notes

1. These authors contributed equally: Guangliang Tu, Ke Xiao, Xiaoping Chen, Haoran Xu

Authors and Affiliations

1. School of Chemistry and Materials Science, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, China

Guangliang Tu, Ke Xiao, Xiaoping Chen, Xiao-Song Xue & Xiaheng Zhang

2. State Key Laboratory of Fluorine and Nitrogen Chemistry and Advanced Materials, Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai, China

Haoran Xu & Xiao-Song Xue

3. Heilongjiang Record New Materials, Jixi, China

Haifeng Zeng & Fangjiang Zhang

Contributions

X.Z. and F.Z. conceived the project. X.Z. designed and supervised the project. G.T., K.X., X.C. and H.Z. conducted the experimental work and analysed the data. H.X. and X.X. performed the computational studies. G.T., K.X., X.C. and X.Z. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to Xiao-Song Xue or Xiaheng Zhang.

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Competing interests

H.Z., F.Z., X.Z., X.C., G.T. and K.X. are inventors on Chinese patent applications (application nos. CN 2023118572004 and 2024101567075). The other authors declare no competing interests.

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Extended data figures and tables

Extended Date Fig. 1 Additional 51 substrates as extended scope (deaminative chlorination).

Isolated yields. a1H NMR yield. See Supplementary Information Sections 4–6 for full experimental details. DMAP, 4-dimethylaminopyridine; Ph, phenyl; Bn, benzyl; Sandm., Sandmeyer conditions.

Extended Data Fig. 2 Additional 29 substrates as extended scope (deaminative functionalization).

Isolated yields. a1H NMR yield. See Supplementary Information Sections 4–6 for full experimental details. General halogenation conditions: amine (0.5 mmol), SOBr_2 (1.25 mmol) as a bromine source, HNO_3 (2.0 equiv.), DMAP (2.5 equiv.), DCE (5.0 mL), 70 °C, 1 h; amine (0.5 mmol), KI (2.0 mmol) as an iodine source, HNO_3 (6.0 equiv.), DCE (5.0 mL), 70 °C, 1 h. Nuc, nucleophiles; Ph, phenyl; Tf, trifluoromethanesulfonyl; Sandm., Sandmeyer conditions; n.d., not detected.

Extended Data Fig. 3 Improved yields of representative substrates compared to Sandmeyer or diazo methods.

a1H NMR yield.See sections 4–6 for full experimental details. Nuc, nucleophiles; Sandm., Sandmeyer conditions; Diaz.s., diazonium salts; n.d., not detected.

Extended Data Fig. 4 One-pot deaminative cross-coupling reactions.

All yields are isolated. See Supplementary Information Sections 4 and 8 for full experimental details. Boc, tert-butyloxy carbonyl; Ph, phenyl.

Extended Data Fig. 5 Additional 16 examples for one-pot cross-coupling.

All yields are isolated. See Supplementary Information Sections 4 and 8 for full experimental details. Ph, phenyl; Ac, acetyl; tBu, tert-butyl; Boc, tert-butyloxy carbonyl.

Extended Data Fig. 6 Mechanistic studies.

(A) C − H insertion and electrophilic substitution. (B) Control experiments. (C) Ritter-type reaction. (D) Hammett analysis. (E) Proposed mechanism. See Supplementary Information Section 3 for full experimental details.

Supplementary information

Supplementary Information

Supplementary Sections 1–10 and Figs. 1–293.

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Tu, G., Xiao, K., Chen, X. et al. Direct deaminative functionalization with N-nitroamines. Nature 648, 341–348 (2025). https://doi.org/10.1038/s41586-025-09791-5

- Received: 08 September 2025

- Accepted: 21 October 2025

- Published: 27 October 2025

- Version of record: 03 December 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09791-5

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Abstract

Somatic chromosome instability results in widespread structural and numerical chromosomal abnormalities (CAs) during cancer evolution1,2,3. Although CAs have been linked to mitotic errors resulting in the emergence of nuclear atypia4,5,6,7, the underlying processes and rates of spontaneous CA formation in human cells are underexplored. Here we introduce machine-learning-assisted genomics and imaging convergence (MAGIC)—an autonomously operated platform that integrates live-cell imaging of micronucleated cells, machine learning on-the-fly and single-cell genomics to systematically investigate CA formation. Applying MAGIC to near-diploid, non-transformed cell lines, we track de novo CAs over successive cell cycles, highlighting the common role of dicentric chromosomes as initiating events. We determine the baseline CA mutation rate, which approximately doubles in TP53-deficient cells, and observe that chromosome losses arise more frequently than gains. The targeted induction of DNA double-strand breaks along chromosome arms triggers distinct CA processes, revealing stable isochromosomes, coordinated segregation and amplification of isoacentric segments in multiples of two, as well as complex CA outcomes, influenced by the chromosomal break location. Our data contrast de novo CA spectra from somatic mutational landscapes after selection occurred. The experimentation enabled by MAGIC advances the dissection of DNA rearrangement processes, shedding light on fundamental determinants of chromosomal instability.

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Main

Cancer genomes are shaped profoundly by somatic chromosomal abnormalities (CAs)1,2,3. According to pan-cancer studies, CA driver events outnumber base substitution drivers in cancer genomes, and the cumulative burden of CAs is linked strongly to adverse clinical outcomes2,3,8,9. Recent studies have shed light on patterns and classes of CAs present in cancer genomes10,11,12,13. However, unlike for base substitutions10,14, specific contributions of CA formation processes to the mutational spectrum in cancer, as well as the baseline rate at which CAs emerge, are poorly understood. Consequently, our understanding of the role of CA formation in driving karyotype evolution in cancer remains incomplete.

Recent reports have established that a single DNA lesion can trigger a cascade of alterations, resulting in chromosomal instability and promoting complex CA formation processes5,6,15. Mitotic errors serve as intermediate steps for these cascades4,5,6,7, resulting in nuclear atypia such as micronuclei and chromatin strings2,16. Live-cell microscopy combined with (semi)-manual cell selection and single-cell sequencing, has causally linked nuclear atypia to the formation of complex CAs, and shed light on mechanisms underlying chromothripsis4,5,6,15,17,18. Yet, owing to their labour-intensive nature, only a limited number of single-cell genomes have been investigated, leaving important gaps in our understanding of chromosomal instability processes linked to aberrant mitoses.

To address these limitations, we devised a platform that couples autonomous confocal microscopy in live cells, machine learning for on-the-fly assessment of nuclear atypia, targeted cell photolabelling and cell sorting. Through automated imaging-based cell selection, target cells are isolated precisely from a heterogeneous cell population. The isolated cells are then subjected to single-cell sequencing and systematic phenotype analyses, thus enabling investigation of the cellular context, mutation rates and triggers of spontaneous CA formation in cell line models that mimic particularly early steps in tumour evolution.

Investigating de novo CA formation with MAGIC

Mitotic error profiles in non-transformed cells

To investigate de novo CAs arising in a human cell, we devised MAGIC—a platform coupling automated microscopy with targeted photolabelling and single-cell genomics to gain insights into CA formation from studying nuclear atypia (Fig. 1a; Methods). To investigate CA formation landscapes during an initial stage of tumorigenesis, we selected two non-transformed cell lines maintaining a relatively stable karyotype4,5,19,20: MCF10A cells, derived from normal breast tissue and spontaneously immortalized; and hTERT RPE-1 cells (RPE-1) of retinal pigment epithelial origin. During mitosis, both cell lines occasionally form micronuclei21,22,23, the collapse of which can result in complex CAs, including chromothripsis2,4,6.

Fig. 1: MAGIC enables characterization of de novo CAs at scale.

a, Overview of MAGIC. Left to right, automated microscope analyses of a cell population with a heterogeneous morphology, performing targeted photolabelling using a machine-learning-based (ML-based) classifier that outputs a micronuclei detection probability for each cell, identification of areas for targeted photolabelling and automatic microscope laser photolabelling of target cells. The steps are repeated to reach a desired yield. Photolabelled cells are then isolated for further analysis. b, Annotation strategy for long-term live-cell imaging of MCF10A H2B-Dendra2 cells. Anaphase and nuclear phenotypes were assessed over two generations, to observe at least one cell cycle; first generation cells are referred to as parents, and second generation cells as daughters. A total of 821 genealogies were annotated, 765 of which generated progeny. c,d, Overall frequency of anaphase (c) and nuclear (d) phenotypes over all genealogies; 1,750 mitoses and 1,795 nuclei were annotated, respectively. e, Frequency of daughter micronucleation associated with different anaphase phenotypes (Fisher’s exact test). f, MCF10A cells constitutively expressing H2B-Dendra2 before in its native state (left, green) and after photolabelling (right, magenta). g, FACS profile of control (left) and photolabelled (right) cell conditions. Native (green) versus photolabelled (red) fluorescence is plotted. The sorting gate is represented by a dashed line. h, Frequency of Chr. X CAs after targeted DSB induction in randomly sampled single cells, or in cells selected using MAGIC (Fisher’s exact test). On-breakpoint CAs (green bar) refer to the HPRT1 locus. i, Examples of CAs involving a breakpoint at the HPRT1 locus. Grey shading, acentric fragment created through targeted DSBs (*P < 0.05, **P < 0.01, ***P < 0.001; Methods). Scale bar, 10 μm.

To generate pilot data for setting up MAGIC, we manually annotated nuclear and mitotic phenotypes across two generations in MCF10A cells (Fig. 1b). We find that spontaneously arising anaphase bridges and lagging chromosomes are the predominant type of mitotic error, occurring in 5.1% and 6.2% of all mitoses, respectively (Fig. 1c). During interphase, 6.2% of cells have nuclear atypia, with micronuclei (5.8%) being by far the most common type (Fig. 1d). We find that mitotic errors result in the formation of at least one micronucleated daughter cell in 32.3% and 17.2% of cases for lagging chromosomes and chromatin bridges, respectively, demonstrating that both types of mitotic error converge on micronucleation (Fisher’s exact test, Fig. 1e). Furthermore, micronucleated cells are around 9.5 times more likely to generate a micronucleated daughter cell, compared with cells with normal nuclei (Supplementary Fig. 1a). Accordingly, we detect widespread anaphase defects in daughter cells originating from abnormal anaphases (Supplementary Fig. 1b). This ‘self-propagating’ nature of micronucleated cells implies that mitotic errors can result in nuclear atypia formation over consecutive cell cycles, which could trigger episodic chromosomal instability.

We examined micronucleated MCF10A cells also with respect to their propensity to generate viable daughters. Micronucleated cells exhibit a significantly longer cell cycle duration, and a notably delayed cell cycle compared with normal cells (Supplementary Fig. 1c–e). Irrespectively, relevant subsets of micronucleated cells continue dividing, and some eventually regain normal nuclear morphology, facilitating the automated isolation of viable cells subject to de novo CAs.

Machine-learning-enabled adaptive feedback loop

MAGIC systematically selects micronucleated cells using adaptive feedback microscopy (‘smart microscopy’), driven by a computational loop integrating machine learning, image analysis and photolabelling (Fig. 1a and Supplementary Fig. 2a). In brief, a confocal image is acquired and examined on-the-fly by machine learning; if a cell of interest is identified, information on its location is used to photolabel its nucleus automatically with the microscope laser. Then, the next image is assessed, re-initiating the adaptive feedback loop. MAGIC operates autonomously for up to 24 h, examining tens of thousands of cells to photolabel hundreds of live cells exhibiting the desired nuclear morphology for downstream investigation.

We trained machine-learning-classifiers for micronuclei using manually annotated images. We used an extreme gradient boosting-based machine learning framework (XGBoost; Methods) for its model explainability, streamlined implementation, and the relatively few training examples it requires. The whole classification pipeline achieves a precision of at least 90% and a recall of 50%, offering an acceptable balance between specificity and sensitivity (Supplementary Fig. 2b and Supplementary Methods).

Photolabelling dyes and cell sorting

Photolabelling leverages fluorescent markers with unique characteristics. The expression of the Dendra2 protein allows tagging cells of interest through the stable transition of emitted fluorescence from green to red7,24, upon gentle and targeted illumination with a 405 nm laser. We engineered MCF10A and RPE-1 cells to stably express H2B-Dendra2, facilitating nuclear morphology visualization and allowing photolabelling (Fig. 1f). The photolabelling efficiency increases with the illumination up to a maximum dependent on the amount of H2B-Dendra2 expression (Supplementary Fig. 2c,d). We fine-tuned photolabelling conditions to achieve a red fluorescence increase of roughly 22-fold after illumination, without any detectable phototoxicity (Supplementary Fig. 2e,f). As an alternative dye, we synthesized DACT-1 (Supplementary Methods)—a small molecule used for cell tracking[25]—allowing for photo-activation under similar conditions (Supplementary Fig. 2g) while bypassing the need for genetic manipulation. Using fluorescence-activated cell sorting (FACS), we observe distinct populations that represent photolabelled cells with either dye (Fig. 1g and Supplementary Fig. 2h), confirming that target cells are sorted efficiently.

Targeted CRISPR–Cas9 manipulation reveals de novo CAs

Having demonstrated the effectiveness of MAGIC in cell sorting, we next explored its utility for identifying de novo CAs. To verify experimentally that discovered CAs originate from chromosomes entrapped in micronuclei, we generated DNA double-strand breaks (DSBs) at the HPRT1 locus on Chr. X, by applying CRISPR–Cas9 in MCF10A cells (Methods). Cas9-mediated DSBs have been reported previously to result in acentric fragments incorporated into micronuclei[26] (Supplementary Fig. 3a). Quantifying nuclear defects upon targeted DSB generation, we find that micronucleation rises by approximately 4.8-fold, indicating an increase in CA formation.

To enable the discovery of de novo CAs resulting in copy-number imbalances, we coupled MAGIC with single-cell template-strand sequencing (Strand-seq)[27]. We performed single-cell genomic sequencing on 85 and 93 cells, respectively, with and without (‘control’) automated selection for micronucleated cells. We identified CAs using the strandtools algorithm (Methods). We observe a strong increase in CAs in the selected cell fraction (Supplementary Fig. 3b), with 37 (45%) of micronucleated cells showing at least one CA on the X chromosome, corresponding to a fivefold enrichment over the control. Moreover, 24 of 37 (64.9%) of the CAs in the enriched sample contain a breakpoint at the HPRT1 locus (Fig. 1h), consistent with CAs arising directly at the cut site.

Notably, we find that the cut site gives rise to a diversity of CA classes (Fig. 1i and Supplementary Fig. 3c). Within the micronucleated cells, 18 of 37 (48.6%) CAs show an isolated loss or gain of the cut fragment, indicating abnormal segregation of the acentric fragment. Moreover, 12 CAs comprise terminal deletions from 18 Mb to 70 Mb in size, and 6 are terminal duplications ranging from 22 Mb to 76 Mb in size. We also find evidence for complex CAs in nine cases, all mapping to a single homologue as resolved by haplotype analysis[27], and observe amplifications of the cut acentric fragment in a further nine cases (Supplementary Fig. 3c–e). These data demonstrate the capability of MAGIC to selectively isolate cells undergoing de novo CAs.

Verification of de novo CAs from sister cell pairs

Reciprocal template-strand inheritance and sister chromatid-exchange (SCE) events[27] from Strand-seq offer uniquely identifiable records of sister cell relationship (Supplementary Fig. 3f). Harnessing these records, we devised an approach to confidently identify sister cell pairs directly from single-cell sequencing data (Supplementary Methods). Using this approach, we find two sister cell pairs in the enriched sample. In one of these pairs, we observe directly a de novo CA. Analysis of this pair reveals a cut fragment inherited asymmetrically in the sisters, thus verifying CA formation (Supplementary Fig. 3g).

Spontaneous CA formation landscapes

CA formation in spontaneously micronucleated cells

Whereas biochemically or genetically induced micronuclei have been used to study CA formation4,5,6,15, how spontaneously arising micronuclei may trigger distinct classes of CAs is underexplored. Addressing this gap, we used MAGIC to isolate spontaneously micronucleated cells and investigate CAs landscapes. We first focused on MCF10A, sequencing 142 single-cell genomes from micronucleated cells. Single-cell genome analysis (Methods) revealed 124 CAs, with 54.9% micronucleated cells exhibiting at least one CA (Fig. 2a). When compared with 115 cells with a normal nucleus (‘control’), we observe a threefold enrichment in CAs (P = 1.75 × 10−9; Fisher’s exact test), indicating widespread CA formation in micronucleated MCF10A cells. We also investigated RPE-1 cells, sequencing the genomes of 166 micronucleated cells and 68 controls. Unlike for MCF10A, we find a non-significant enrichment of CAs in micronucleated cells (P = 0.69; Fig. 2a), indicating that RPE-1 exhibits a more stable karyotype.

Fig. 2: CA landscape of spontaneous micronucleated cells in near-diploid human cell lines.

a, CAs detected per cell (P values on the basis of Fisher’s exact test). NS, not significant. b, Reciprocal CAs between sister cells. Segment annotation: dashed lines indicate an SCE, and demarcate shared and reciprocal segments. Red ticks mark points of inferred complex CA formation. NA, not available. c, Mitotic history reconstruction for reciprocal CAs in b. Orange and teal colours correspond to Watson and Crick template-strand orientations, respectively. d,e, Breakdown of CA classes in micronucleated MCF10A (d) and RPE-1 (e) cells, class percentage over all CAs. See Methods for CA classification criteria. f,g, CA count per chromosome in micronucleated MCF10A (f) and RPE-1 (g) cells (binomial testing was used to identify enrichments). In RPE-1, the highest CA counts are seen for Chr. 10 and Chr.  X engaging in an unbalanced der(X) t(X;10) translocation—a derivative chromosome that could be particularly susceptible to inclusion in micronuclei—in this cell line[29]. h, Scheme showing mitosis with a dicentric chromosome. Sister chromatid fusion generates a dicentric. During anaphase, the dicentric chromosome forms a bridge, which can rupture and potentially form micronuclei in daughter cells. i, Chromothripsis affecting Chr. 13, with reciprocal segment inheritance into sister cells seen for a large fraction of the affected homologue. Top, Strand-seq data. Bottom, smoothened, normalized read counts along chromosomal positions.

Reconstructing de novo CAs over consecutive cell cycles

To further corroborate CA formation, we focused on the sister cell pairs found among 142 micronucleated MCF10A cells (Extended Data Fig. 1a). Out of 12 sister pairs, 7 (58%) show reciprocal CA segregation, consistent with de novo CAs (Extended Data Fig. 1b). We identify three sister pairs with shared CAs; in two cases, these are also accompanied by reciprocal CAs, indicating CA formation across several recent divisions (Fig. 2b and Extended Data Fig. 1b). By contrast, among ten sister pairs of micronucleated RPE-1 cells, only two (20%) show reciprocal CAs and one pair shares a common CA (Extended Data Fig. 1a,b), consistent with a lower spontaneous CA rate in this cell line.

The concomitant presence of shared and reciprocal CAs affecting a single haplotype implies a multi-step process extending over successive cell cycles. To exemplify this, Fig. 2b depicts reciprocal CAs that, on the basis of our genomic reconstruction, arose over two consecutive breakage-fusion-bridge (BFB)28,29 cycles. In the first cell cycle, sister chromatid fusion followed by bridge breakage gave rise to two cells carrying an inverted duplication on Chr. 14 along with a terminal deletion on the same homologue (Fig. 2c). In the second cell cycle, the cell carrying the terminal deletion underwent a second fusion and bridge breakage on this homologue. We also find evidence for complex CAs arising during the most recent cell cycle near the second bridge-breakage site (Fig. 2b; addressed further below). These data show how MAGIC enables reconstruction of CA processes over successive cell cycles.

De novo CA landscapes in near-diploid cell lines

We next performed a comprehensive analysis of the CA landscape of spontaneously micronucleated cells, initially focusing on MCF10A (Fig. 2d and Extended Data Fig. 1c). We find that the most common CA class comprises a simple gain or loss of terminal chromosome segments (‘terminal CAs’), representing 21.8% and 19.4% of CAs, respectively. By comparison, simple, interstitial CAs represent only 4% of the CAs detected. Whole-chromosome aneuploidies represent 16.9% of all CAs, with chromosomal losses (N = 19) being significantly more frequent than gains (N = 2; P = 0.007, permutation test; Supplementary Table 10). We also find 29 CAs (23.4%) that seem to have arisen from multi-step rearrangements affecting terminal segments of a single homologue (Fig. 2d and Extended Data Fig. 1b). Furthermore, we find 18 examples of clustered CAs unrelated to terminal multi-step events. Leveraging the haplotype resolution of Strand-seq, we confirm that the respective CAs are on the same homologue in line with complex CA formation, except for one instance where both homologues are affected. These complex CAs include four chromothripsis cases30,31 with extensive rearrangements spread across the respective homologues (Extended Data Fig. 1e).

Analysis of the CA landscape in micronucleated RPE-1 cells revealed a similar range of CAs, with terminal CAs occurring most frequently. Yet, unlike in micronucleated MCF10A, we observe that complex CAs are essentially absent in RPE-1 cells (Fig. 2e and Extended Data Fig. 1d). Application of MAGIC to two more non-transformed cell lines—BJ-5ta and IMR-90 (Methods)—confirm widespread terminal CA formation in spontaneously micronucleated cells, with complex CAs remaining comparably infrequent (Extended Data Fig. 2a–f). Furthermore, we compared these data with CA landscapes from MCF10A and RPE-1 cells exposed to the mitotic kinase MPS1 inhibitor reversine (Methods), which exhibit pervasive whole-chromosome aneuploidies both in the presence and absence of micronucleation32,33,34, alongside a relatively low frequency of terminal CAs (Extended Data Fig. 3a–f). These data show that CA landscapes can vary substantially depending on whether CAs are induced biochemically, or arise spontaneously in non-transformed cells, highlighting the utility of MAGIC in distinguishing specific sources of chromosomal instability.

Genomic contexts associated with spontaneous CAs

We next examined the genomic features of spontaneously arising de novo CA across the chromosome sets of MCF10A and RPE-1. Although we do not observe recurrent CA breakpoints, we find an uneven density of CAs across each karyotype. Analysing region-specific properties associated previously with somatic structural variants (Supplementary Notes), we observe significant overrepresentation of regions forming G4-quadruplexes, as well as both early and late-replicating regions (Extended Data Fig. 4a; adjusted P < 0.05; permutation test). Furthermore, under the assumption that each homologue acquires CAs with equal probability, we observe an enrichment of CAs on chromosome 19 in MCF10A (adjusted P < 0.05, binomial test; Fig. 2f). As most CAs are terminal to a chromosome arm and thus comprise the telomeres, we conducted long-read sequencing on an MCF10A-derived clone (‘clone 7’) to infer arm-specific telomere lengths (Methods). We observe a significant inverse correlation between the chromosomal arm CA frequency and telomere length estimates (Pearson’s R = −0.39; P = 0.0073; Extended Data Fig. 4b), indicating that shortened telomeres5,35,36,37 can foster mitotic errors resulting in CA formation.

By comparison, RPE-1 Chr. 2, Chr. 6, Chr. 10 and the X chromosome each exhibit elevated CAs (Fig. 2g, adjusted P < 0.05). Overall, we note a bias towards CAs affecting larger chromosomes in RPE-1, but not in MCF10A (P < 0.05; Extended Data Fig. 4c). This trend in RPE-1 is consistent with an earlier report using this cell line[32] (Extended Data Fig. 4d) and might originate from differences in the tendency of large versus small chromosomes32,38,39 to be included in micronuclei in both cell line models.

Post-selection CA landscape

CAs contributing to tumorigenesis must be maintained in the cell population. To investigate the potential of CAs to propagate clonally, we used MAGIC to isolate micronucleated cells and test their clone-forming capability. We observe a significantly reduced success rate in generating clones from micronucleated compared to normal cells (MCF10A: 0.73-fold reduced; RPE-1: 0.41-fold reduced; P < 0.001, Fisher’s exact test; Extended Data Fig. 5a). We subjected 27 single-cell-derived clones from MCF10A (18 from micronucleated and 9 from control cells) and 11 RPE-1 clones (all from micronucleated cells) to low-pass whole-genome sequencing (WGS) (Methods). We find 13 clonally propagated CAs in the clones seeded from micronucleated MCF10A cells (Supplementary Table 1), with 9 out of 18 expanded cultures containing at least one CA (Extended Data Fig. 5b). These CAs compromise both simple (N = 12) and putatively complex (N = 1) events (Methods). By comparison, three clones grown from the controls each contain one simple CA. In RPE-1, none of the 11 micronucleated cell-derived clones exhibited CAs (Extended Data Fig. 5b; P < 0.0052, Fisher’s Exact test versus MCF10A). Furthermore, we note reciprocal CAs are less frequent in RPE-1 sister cells with spontaneous micronuclei (Extended Data Fig. 5b), indicating that selective constraints limit CA propagation in the RPE-1 cell line.

We compared clonally propagated CAs with the de novo CA landscape of MCF10A cells. Notably, we observe a prevalence of losses on the 7q arm including simple and complex events, affecting 5 of 13 (38.5%) of all propagated CAs—a fourfold enrichment compared with the de novo CAs (P = 0.0043; Bonferroni-corrected Chi-square test; Extended Data Fig. 5c,d). Although 7q-losses are common in breast cancer8,40 (Supplementary Note), these CAs may either be subject to positive selection or could have persisted as selectively neutral events during clonal expansion, implying selective pressures[2] influence genomic CA landscapes. To investigate clonally maintained 7q events in a specific case, we analysed the long-read sequencing data generated for MCF10A clone 7, for which low-pass WGS indicated complex CA formation involving Chr. 7. Long-read analysis confirmed the existence of these complex CAs, uncovering a chromothripsis event accompanied by isochromosome formation, which ultimately resulted in 7q loss (Extended Data Fig. 5e,f). These data illustrate how MAGIC can be used to select cells undergoing CAs for phenotypic analyses and clone-based sequencing.

CA processes acting in micronucleated cells

Pivotal role of dicentric chromosomes

Harnessing the combined Strand-seq data generated for MCF10A and RPE-1, we next systematically inferred de novo CA processes. We first investigated terminal CAs, which represent 64.6% and 75.5% of all CAs seen in MCF10A and RPE-1, respectively. Out of the 49 terminal gains observed in both cell lines involving either parts of or an entire chromosomal arm, 42 (85.7%) show a configuration where the segment gained at the terminus has a strand-state opposite to that of its homologue (Extended Data Fig. 6a). This karyotypic pattern could arise from a terminal inverted duplication arising during a BFB cycle (Fig. 2h), yet may alternatively reflect acentric fragments entering mitosis unrepaired and undergoing asymmetric segregation (Extended Data Fig. 6c).

Although both scenarios would yield reciprocal gain–loss in sister cells, BFB cycles typically result in sequential CAs affecting the same homologue. Among several CAs mapping to the same chromosome, where at least one involves a terminal segment, 86.2% can be traced back to the same homologue, consistent with BFBs (Fig. 2h and Extended Data Fig. 6b). These data are further bolstered by our analysis of three sister cell pairs harbouring at least one shared and one reciprocal CA on the same homologue, in each case supporting the occurrence of multi-step BFBs (Fig. 2b and Extended Data Fig. 1b). These data highlight the pivotal role of dicentrics in facilitating spontaneous CA formation.

Complex CAs

We next focused on other CA processes. We observe two distinct types of complex CA implicating chromothripsis. Among all 54 CAs involving a terminal deletion or inverted duplication in spontaneously micronucleated MCF10A cells, 11 (20.4%) exhibit a localized copy-number oscillation pattern near the internal breakpoint (Extended Data Fig. 6d,e). This pattern is further corroborated by its similar occurrence frequency in MCF10A control cells, and is likewise detected in RPE-1 cells (Extended Data Fig. 6e). Pooling examples of this pattern across all examined conditions, we observe a single oscillation in most cases (11 of 16), characterized by troughs and crests of similar size (averaging 1.6 Mb, with the whole oscillation pattern spanning from 2 to 7 Mb; Extended Data Fig. 6f–h). Assuming chromatin bridge breakage as the source of this pattern, the location of these complex CAs corresponds to the point of rupture, indicating a link to bridge resolution. The position and oscillatory characteristics of this pattern resemble previously described instances of chromothripsis associated with dicentric breakage, mediated by cytosolic enzyme activity[5], implicating this mechanism in spontaneous complex CA formation.

Chromosome pulverization

In MCF10A cells, but not in RPE-1, we observed four instances of whole-chromosome or whole-arm-level chromothripsis that we subjected to more detailed analysis. The respective rearrangements are confined to a single homologue and show evidence for random fragmentation, in line with established chromothripsis criteria[30] (Fig. 2i and Extended Data Figs. 1e and 5i). In two instances, we identified the corresponding sister cell from the Strand-seq data (this included a single sister cell not initially passing quality control). In both instances, we observe anti-correlated read counts (Fig. 2i and Extended Data Fig. 5g–i), in line with the reciprocal segregation of pulverized chromosome fragments. These CA patterns closely mirror previous reports of chromothripsis linked to micronucleus entrapment, observed in TP53-depleted RPE-1 cells following monastrol washout[4]. Altogether, up to 13% of CAs in spontaneously micronucleated MCF10A cells can be attributed to chromothripsis, considering both focal and chromosome-wide patterns.

TP 53 status affects de novo CA formation

Analysis of TP53 −/− cells

Disruption of TP53, causing loss of the p53 tumour suppressor, is the most common driver mutation in cancer, and associated with a range of genomic instability patterns41,42,43,44. Yet, the potential roles of TP53 deficiency in CA mutational rates and in determining the de novo CA landscape remains underexplored. By performing single-cell transcriptomics coupled with MAGIC in MCF10A and RPE-1, we find strong evidence for cell cycle arrest and over-expression of TP53 or its targets in micronucleated as opposed to normal cells (Supplementary Note and Extended Data Fig. 7a–c), indicating the DNA damage response may constrain CA formation. To explore the effect of TP53 in CA formation, we used isogenic TP53−/− models of MCF10A and RPE-1 (Supplementary Fig. 4a; Methods). Using microscopy, we find a general increase in nuclear atypia in both of these TP53−/− cell lines compared with their unmutated (‘wild-type’) counterparts (Supplementary Fig. 4b,c). For example, about one-third of TP53−/− MCF10A cells exhibit micronuclei (Fig. 3a)—an increase accompanied by a high frequency of anaphase bridges (36.8%; Fig. 3b). Moreover, the probability of anaphase errors to result in a micronucleated daughter is increased to 73.3% and 69.7% for anaphase lagging chromosomes and chromatin bridges, respectively (Supplementary Fig. 4d). Similar to their wild-type counterparts, micronucleated TP53−/− cells are prone to generate a micronucleated daughter cell (Supplementary Fig. 4e,f). Yet, unlike wild-type cells, the duration of the cell cycle is not prolonged and TP53−/− cells do not effectively enter cell cycle arrest[42] (Supplementary Fig. 4g,h). These observations hint at an elevated rate of spontaneous CAs in TP53−/− cells, with the absence of efficient cell cycle arrest potentially promoting CA formation.

Fig. 3: Effect of TP53 disruption on de novo CA formation, and modelling basal CA rates.

a,b, Frequency of nuclear (a) and anaphase (b) phenotypes in MCF10A TP53−/− cells from long-term live-cell imaging. c, Observed CA frequency by cell (Fisher’s exact test). d, Fold change in CA numbers per cell for TP53−/− versus the respectively matched wild-type cell line model, shown across cell line models and nuclear phenotypes. e,f, Breakdown of CA classes in micronucleated MCF10A TP53−/− (e) and RPE-1 TP53−/− (f) cells, class percentage over all CAs. g, Agent-based model for estimating the de novo CA rate. Scheme representing available states (numbers in teal circles; 1, normal cell; 2, normal mitosis; 3, laggard mitosis; 4, bridge mitosis; 5, micronucleated cell) and available transitions (arrows) between states, with Pij being the empirically measured transition probabilities. Parameters are estimated for three mitosis types with R representing estimated CA rates. h, Mitosis type-specific CA rate estimations in MCF10 wild-type (WT) and TP53−/− models. Each data point represents the estimated value from an optimization run. Black lines represent the average weighted by the residual error of each optimized simulation.

To investigate the effect of TP53 disruption on CAs, we subjected both TP53−/− cell lines to MAGIC. Analysis of 300 single-cell genomes indicates a marked increase in de novo CAs (Fig. 3c), with TP53−/− micronucleated cells exhibiting significantly more CAs than wild-type micronucleated cells (Fig. 3d; P < 2.65 × 10−10 for MCF10A; P < 9.36 × 10−6 for RPE-1). We next conducted an analysis of CA classes arising in both TP53−/− cell lines (Fig. 3e,f and Supplementary Fig. 5a,b). Although the CA spectra seem very similar between TP53−/− and wild-type cells (Supplementary Fig. 5c), a notable exception is the marked increase in complex CAs seen in micronucleated TP53−/− RPE-1 cells compared with wild type (from 2.7% to 16.5%; P < 0.05 Fisher’s exact test; cf. Fig. 2e and Fig. 3f), which includes chromothripsis events. This finding is consistent with TP53 status exerting a particularly strong effect on complex CA formation[41].

CA mutation rates

Accurately estimating the baseline mutational rate of somatic CAs was previously unfeasible due to technological limitations[2]. Harnessing the imaging and genomic data generated in our study, we devised a statistical agent-based model (Methods) where simulated cells transition between nuclear atypia and normal mitoses on the basis of probabilities derived from live-cell long-term imaging (Figs. 1b and 3g). This model allows simulating the CA rate associated with three mitosis types: normal (with lagging chromosomes (‘laggard’)) and with chromatin bridges (‘bridge’). We selected MCF10A, given that CAs arise in both TP53−/− and wild-type contexts in this line. The simulation closely recapitulates our empirical data (Supplementary Fig. 6a,b), enabling estimation of the mitosis type-specific CA rate (Supplementary Methods). We calculated that 3.7% of normal cell divisions result in a CA for wild-type cells, whereas this value increases to 92.5% and 84.4% for laggard and bridge mitoses in wild-type cells, respectively (Fig. 3h). In TP53−/− cells, mitosis type-specific CA rate estimates are very similar—2.9% for normal, 82.8% for laggard and 83.2% for bridge mitoses per cell division—indicating that the underlying processes by which CAs form through nuclear atypia are not affected by TP53 deficiency. Finally, by considering the relative contribution of mitosis types, we estimate the basal CA rate for MCF10A, which is 13.3 % in wild-type cells per cell division, and approximately doubles to 30.4% in TP53−/− cells. This increase seems to be driven particularly by the higher proportion of chromatin bridges in TP53−/− cells (Fig. 3b), consistent with dicentrics representing an important trigger for CA formation.

Chromosome region determinants for de novo CAs

Modelling CA formation with targeted DSBs

Understanding the mechanistic origins of chromosomal instability requires clarifying how CAs arise from initial DNA lesions, particularly DSBs. Considering the patterns observed in our data, we reasoned that following an initial DSB trigger, the size and nature of fragments generated and whether they result in a dicentric or acentric chromosome (Fig. 2h and Extended Data Fig. 6c) are likely to influence their fate, implying that the chromosomal DSB location could have an important role in determining CA processes. Reanalysis of X chromosomal HPRT1 data reveals that most segmental CAs (53.5%; 23 of 43) involve centrally oriented alterations near the cut site, indicating that BFB cycles are triggered frequently by CRISPR–Cas9 treatment at this locus. To explore the potential relationship between DSB location and CA process, we devised a MAGIC experiment generating DSBs on Chrs. 2 and 7 (Methods), with each chromosome targeted at specific sub-centromeric, sub-telomeric and central sites of the q arm (Fig. 4a and Supplementary Table 2). After subjecting MCF10A cells to targeted DSBs, we sequenced 361 single-cell genomes from micronucleated cells. Although we observe different CA induction efficiencies for each targeted DSB (from 20% to 60%), in each case most CAs originate from the gRNA-directed DSB sites (Fig. 4b).

Fig. 4: CA landscape following targeted DSB induction along chromosome arms.

a, Scheme showing the locations of targeted DSBs. b, CA frequency per cell across the different chromosomal cut sites. c, Frequency of CA types for different cut sites on the Chr. 7 q arm (Fisher’s exact test). SV, structural variant. d, Overview of CAs for the Chr. 7 q arm, expressed as copy-number states. Sub-centromere, central and sub-telomere target loci are depicted from top to bottom. (Note the consensus copy number for Chr. 7 in MCF10A H2B-Dendra2 cells is three—trisomy). e,f, Enrichment for bridge-mediated CAs (e) and coupled p arm gain/q arm loss indicative for isochromosome formation (f) (Fisher’s exact test). Only terminal and complex CAs were considered in this analysis. g,h, Sister cells showing one-sided (g) and asymmetric (h) inheritance of the acentric fragment in multiples of two. The sister cell examples shown here are from the Chr. 2 central cut and HPRT1 datasets, respectively.

Analysing the CA spectra separately by DSB site, we observe a wide diversity of CA classes (Fig. 4c,d), including cases of chromothripsis (Extended Data Fig. 8f). However, the relative proportions of CA classes differ substantially by cut location, with patterns largely consistent between 7q and 2q (Fig. 4c,d and Extended Data Fig. 8a,b). For example, we find terminal CAs affecting the q arm—seen with 29.4% and 80.0% for 7q—when targeting the central and sub-telomeric site, respectively, whereas whole-arm CAs arise exclusively from sub-centromeric DSBs. Furthermore, when focusing on those CAs initially annotated as either terminal or complex, we find several cases of terminal deletions with an inverted duplication centrally located relative to the DSB (Fig. 4d and Extended Data Fig. 8a,c), consistent with BFBs; these bridge-related CAs are enriched more than eightfold in central and sub-telomeric cuts compared with sub-centromeric cuts (Fig. 4e and Extended Data Fig. 8d).

Moreover, when targeting the sub-centromeres, we observe a notable frequency (10.5% and 9.1% for 7q and 2q, respectively) of whole-arm CAs sharing a distinctive pattern characterized by a p arm gain in inverted orientation coupled with q arm loss (Fig. 4d and Extended Data Fig. 8a,g). This pattern is indicative of isochromosome formation, reflecting a derivative chromosome structure recurrent in different cancer types8,45. By comparison, neither central nor sub-telomeric cuts result in isochromosomes (Fig. 4f and Extended Data Fig. 8e). Taken together, these data provide strong evidence that different DSB sites can promote distinct CA processes.

Acentric fragments result in distinctive CA patterns

Across cut sites, we also observe several cases of amplification of the generated acentric fragment. This pattern accounts for up to 40% of all CAs, depending on the cut site (Supplementary Fig. 7a–c), and is characterized by the simultaneous gain of both Watson and Crick templates[27] in the Strand-seq data (Supplementary Fig. 7d): particularly, among 18 acentric gains with a copy-number increment of two, the Watson/Crick ratio remains 1:1 in all 18 cases, with Crick/Crick and Watson/Watson configurations missing entirely (P < 7.63 × 10−6, binomial test; Supplementary Methods). This peculiar strand pattern implies that these duplicated acentric segments are integrated into the same derivative chromosome, promoting their co-segregation in multiples of two, with the segments arranged in inverted orientation (Supplementary Fig. 7e). This inference is corroborated by sister cell pair analysis demonstrating the joint segregation of gains in multiples of two (Fig. 4g,h). In summary, coupling MAGIC with targeted DSBs provides evidence for a CA process that enables the co-segregation of amplified acentrics.

Verification by fluorescent in situ hybridization

To further investigate these reconstructed CA patterns, we conducted a further round of targeted DSB experiments, this time coupled with fluorescent in situ hybridization (FISH). We used a two-probe strategy labelling the sub-centromeric regions of 7p and 7q, respectively. The gRNA cut site, thereby, is located within our designed q-arm FISH probe, facilitating the analysis of CA outcomes (Fig. 5a). Following centromeric cuts, we find that 28% of metaphases have an abnormal sub-centromeric probe signal indicative for CAs, an outcome not observed for sub-telomeric cuts (Supplementary Fig. 8a).

Fig. 5: Isodicentric and isoacentric derivative chromosome generation through targeted DSBs.

a, Scheme depicting hybridization sites for sub-centromeric p-arm and q-arm FISH probes. The targeted DSB site, ‘splitting’ one of the FISH probe locations to facilitate the examination of chromosome rearrangement outcomes, is indicated by an arrowhead. b, FISH-based quantification of Chr. 7 abnormalities showing an abnormal probe pattern in metaphase spreads. A total of 69 abnormal Chr. 7s were analysed over 155 metaphases. c, Metaphase spread example revealing different derivative chromosomes. Left, regions of interest (ROIs) are marked by yellow squares. Right, magnified ROIs, with breakdown per fluorescent channel and putative chromosomal structures. ROI (i), normal Chr. 7; ROI (ii), isodicentric chromosome with a q-arm signal surrounded by two p-arm signals, indicating the presence of two adjacent centromeres and duplication of 7q; ROI (iii), isoacentric derivative chromosomes with signs of premature chromatin condensation. d, Metaphase spread example with amplified isoacentrics. ROI (i) shows visibly clustering and amplified isoacentrics, with several interspersed q-arm signals clearly visible. Scale bars, 5 µm.

Systematic analysis of metaphase spreads reveals CA patterns confirming those identified through Strand-seq. Following sub-centromeric cutting, we observe loss of the long arm at the DSB site in 33.3% of all spreads with an abnormal Chr. 7 (centric fragment; Fig. 5b). Isochromosomes account for 11.6% of all abnormalities, as visualized by two sub-centromeric p-arm signals surrounding a single sub-centromeric q-arm signal (Fig. 5b,c). These data validate isochromosome formation following targeted DSB generation, resulting in a derivative chromosome that, despite comprising two centromeres, seems to represent a chromosomally stable structure.

Notably, these FISH experiments also highlight abnormalities affecting acentrics. Acentrics appear as isolated chromosome fragments, with a q-arm signal at one extremity, in 30.4% of spreads with an abnormal Chr. 7 (Fig. 5b and Supplementary Fig. 8b). In 18.8% of cases, we detect 7q acentric fragments that have doubled in size, bearing a sub-centromeric q-arm probe signal located at the middle (Fig. 5b,c and Supplementary Fig. 8c). These visualized chromosomal derivatives represent isoacentrics, characterized by two inverted acentric arms fused at the cut site, thus confirming our Strand-seq based genome reconstructions. Notably, the isoacentrics occasionally appear thin and elongated, indicating that they could be subject to abnormal chromatin condensation (Fig. 5c). Such morphology has been associated previously with premature chromatin condensation46,47, and could reflect under-replication due to micronucleus entrapment[47]. Furthermore, in 5.8% of metaphase spreads with an abnormal sub-centromeric probe signal, we observe further amplified isoacentrics, which present as clusters of condensed DNA with interspersed sub-centromeric q-arm signals (Fig. 5b,d). It is intriguing to speculate that these condensed DNA structures might promote the co-segregation of highly amplified genetic material in multiples of two. These observations support the utility of MAGIC in leveraging targeted DSBs to dissect the origins of CA formation.

Discussion

We show that MAGIC facilitates investigating spontaneously arising CAs, providing a representative view of the de novo CA landscape linked to micronucleation in non-transformed cell lines. Dicentric chromosomes represent key drivers of karyotypic diversification, capable of triggering homologue-specific changes across successive cell divisions. Similarities between the CA patterns identified here and those reported in advanced cancer stages[13] (Supplementary Fig. 9 and Supplementary Notes) imply a potentially significant role of micronuclei in shaping cancer genome evolution; however, our data also show marked differences between spontaneously arising CAs and the post-selection CA landscape.

Analysis of our dataset as a whole reveals a distinct bias for de novo whole-chromosome losses compared with chromosome gain, observed under different experimental conditions (Supplementary Table 10). These data are supported by recent findings implicating CRISPR-based genome manipulation specifically in the induction of chromosome losses48,49. Furthermore, in an analysis of 2,600 cancer genomes[8] we observe that chromosome losses predominate markedly (81.5%) over chromosome gains, even when excluding cases subject to whole-genome duplication (Extended Data Fig. 9a). The mechanism underlying this marked bias towards chromosome losses remains unclear. Although proteotoxic stress linked to trisomy can select against chromosome gains50,51, our data indicate that the bias is established during CA formation, preceding proteotoxic effects. Furthermore, MPS1 inhibition, which can induce missegregation in the presence and absence of micronucleation[34], yields balanced chromosome gains and losses (Extended Data Fig. 3a–f), arguing against immediate proteotoxic selection. It therefore seems likely that micronucleus-specific processes, such as DNA replication defects and DNA damage[22] as well as micronucleus elimination52,53, or dicentric segregation into a single daughter[54], contribute to the chromosome loss bias observed in our study.

MCF10A and RPE-1 cells show certain differences in their CA formation patterns. MCF10A cells frequently develop complex CAs and even chromothripsis, despite TP53 wild-type status. This is potentially facilitated by immortalizing events that occurred on MCF10A, including gain of MYC and loss of CDKN2A and CDKN2B[55]. By contrast, RPE-1 cells maintain a relatively stable karyotype, and only rarely exhibit complex CAs unless TP53 is lost. Irrespective of this, our sister cell analyses indicate that RPE-1 cells occasionally tolerate de novo CAs, implying p53 surveillance can be bypassed (Fig. 2e). Tolerance of de novo CAs is similarly observed following biochemical perturbation of chromosome segregation (Extended Data Fig. 3d–f). These findings indicate that MAGIC could provide a framework for uncovering how cell-intrinsic factors, including DNA repair activity and cell cycle regulation, influence chromosome instability and context-specific determinants of CA formation and tolerance.

Integrating CRISPR–Cas9 and MAGIC, we show that the location of initiating DSBs distinctly influences CA outcomes, resulting either in stable derivative chromosomes (particularly isochromosomes) or facilitating further chromosomal instability. Our data support a single-DSB U-type exchange mechanism for isochromosome formation, initiated by a sub-centromeric DSB, and followed by DNA replication and subsequent sister chromatid end fusion[56]. Compared with a process involving two independent DSBs, this mechanism offers a simpler, and thus more parsimonious, model.

With respect to isochromosomes, our results underscore the significance of the inter-centromeric distance of fused chromatids in determining CA outcomes (Fig. 5c and Supplementary Fig. 8d). Longer inter-centromeric distances enable dual kinetochore attachments, causing chromatin bridges and further chromosomal instability. By comparison, shorter distances can result in a single kinetochore attachment enabling stable mitotic segregation of dicentric isochromosomes (isodicentrics). Indeed, cancer genome analysis demonstrates isodicentrics are widespread in tumours (31% of samples in the Cancer Genome Atlas dataset; 55% in the Pan-Cancer Analysis of Whole Genomes dataset; Extended Data Fig. 9b,c and Supplementary Notes), with inter-centromeric distances occasionally exceeding 20 Mb in length.

Our targeted DSB experiments also reveal asymmetric segregation of acentric segments amplified in inverted orientation (isoacentrics). These derivative chromosomes probably form through fusion of an acentric fragment with its sister chromatid or by aberrant replication. They may facilitate rapid DNA segment amplification, and potentially explain the recurrent inheritance of chromosomal segments in multiples of two, observed recently from in vitro screens[57]. In spontaneously micronucleated MCF10A and RPE-1 cells, we detect isoacentric formation in up to 3% (Supplementary Fig. 7f,g). Upon targeted DSB induction, their relative frequency increases by approximately tenfold (Supplementary Fig. 7h). Likewise, we find that isochromosome formation is relatively frequent following targeted sub-centromeric DSBs, but occurs only occasionally in spontaneously micronucleated cells (Supplementary Fig. 7i). This indicates that chromosomal fragments emerging from internal unrepaired DSBs do not represent primary drivers of spontaneous CA formation in these cell lines, with a larger fraction of CAs appearing to spontaneously arise from lesions at (or near) the telomeres.

Furthermore, the inverted duplication architecture of isoacentrics observed in our study implies that fold-back inversions11,58 may occasionally result from CA processes independent of classical BFB cycles, with implications for interpreting rearrangement patterns in cancer genomes. Mitotic clustering of isoacentric derivative chromosomes could facilitate their asymmetric segregation after subsequent rounds of isoacentric amplification17,18. It is intriguing to speculate that this might promote oncogene amplification, extrachromosomal DNA (ecDNA) formation, or complex rearrangements in cancer genomes when coupled with other CA processes.

MAGIC enables automated analysis of several tens of thousands of cells per experiment, permitting the isolation of rare cell morphologies at large numbers, and thus overcoming previous limitations in studying nuclear atypia. In total, we isolated 2,898 single cells and sequenced 2,192 single-cell genomes in this study, generating an unprecedented dataset for investigating de novo CAs. Nevertheless, methodological constraints remain: due to the intermediate coverage achieved, the single-cell sequencing approach we coupled with MAGIC (Strand-seq) is limited to detecting CAs larger than 200 kb. Furthermore, because Strand-seq requires BrdU incorporation, only dividing cells are sequenced, potentially underrepresenting CAs leading to immediate cell cycle arrest. Coupling MAGIC with complementary single-cell sequencing approaches4,59,60 could allow studies of CA formation in non-dividing cells, enhance sensitivity for smaller genetic variants and ecDNAs and improve CA breakpoint-resolution to inform mechanistic analyses[2] of underlying CA formation processes.

Looking ahead, MAGIC holds promise for versatile future applications. Future studies could exploit MAGIC to target other nuclear atypia, or expand analyses to primary cell types. Integration of advanced deep learning-based nuclear segmentation approaches61,62 would broaden morphological classification capabilities. The openly accessible computational workflows accompanying MAGIC (Methods) thereby allow optimization of resolution, experimental duration and cell yield. Further method advancements, including enrichment of sister cell pairs or linking single-cell sequencing data directly to cell images through automated cell picking, could facilitate the investigation of particular CA processes, albeit with potential trade-offs in throughput. Realization of such further method developments could facilitate comprehensive delineation of CA-associated mutational processes arising before Darwinian selection acts (Supplementary Note), enhancing our understanding of cancer evolutionary mechanisms.

In conclusion, MAGIC enables systematic investigation of sporadic CAs in non-transformed cells. Our results demonstrate that dicentrics drive chromosome instability, DSB location influences CA outcomes and TP53 status shapes the CA mutation rate. These insights lay the groundwork for future research aimed at explaining tumorigenesis driven through somatic karyotype evolution.

Methods

Statistical analysis

Unless otherwise stated, we used the following system to indicate significance levels in the figure panels: *P < 0.05; **P < 0.01; ***P < 0.001. Statistical tests used are indicated in the main text or figure caption, with specific tests for chromosome biases and breakpoint as well as SCE locations detailed in the Supplementary Methods.

Cell culture and cell line development

MCF10A (CRL-10317, American Type Culture Collection) and RPE-1 (CRL-4000, American Type Culture Collection) cell line and their TP53−/− derivatives were cultured at 37 °C with 5% CO_2 atmosphere and 100% humidity, in DMEM/F12 medium (1:1) without phenol red (Gibco), supplemented as follows: RPE-1 medium was further supplemented with 10% FCS, 2 mM l-glutamine (Gibco) and antibiotics; MCF10A medium with 5% horse serum (Thermo Fisher Scientific), 2 mM l-glutamine (Gibco), 20 ng ml−1 human EGF (Biotrend), 0.5 mg ml−1 hydrocortisone (Sigma-Aldrich), 100 ng ml−1 cholera toxin (Sigma-Aldrich), 10 μg ml−1 recombinant human insulin (Sigma-Aldrich) and antibiotics. BJ-5ta (CRL-4001, American Type Culture Collection) were cultured at 37 °C with 5% CO_2 atmosphere and 100% humidity in a 4:1 ratio of DMEM (Gibco) and Medium 199 (Gibco) without phenol red, supplemented with 10% FCS, 2 mM l-glutamine (Gibco) and antibiotics. IMR-90 (CCL-186, American Type Culture Collection) were cultured at 37 °C with 5% CO_2 atmosphere and 100% humidity in Minimum Essential Medium containing Earle’s salts and without phenol red (Gibco), supplemented with 10% FCS, 2 mM l-glutamine (Gibco), 1 mM sodium pyruvate (Gibco), 1× NEAA (Gibco) and antibiotics; cells were discarded after 15 population doublings. MCF10A TP53−/− cells were kindly provided by C. Scholl (Laboratory of Applied Functional Genomics, DKFZ), whereas RPE-1 TP53−/− variants were generated in a previous study from our laboratory[63]. All cell lines tested negative for mycoplasma contamination.

For experiments using H2B-Dendra2 as photolabelling strategy, a plasmid carrying H2B-Dendra2 (ref. [64]) (Addgene, plasmid no. 75283) was introduced by transfection: 20,000 cells were seeded in a glass-bottom slide (Nunc LabTek eight-well) and transfected with 20 µl of transfection mixture at 4:1 ratio of Fugene HD (Promega) to DNA in Opti-MEM (Thermo Fisher Scientific). Transfection success was assessed 48 h later by fluorescence microscopy, cells were transferred into two 10-cm dishes and G418 antibiotic was added at 200 µg ml−1 (MCF10A) or 400 µg ml−1 (RPE-1) for selection. Two weeks later, well separated, fluorescent colonies were visible and were isolated by pipetting, transferred to 24-well plates and grown into stable cell lines. Stable-transfectants for RPE-1 wild-type and RPE-1 TP53−/− were instead collected in pool and isolated by single-cell sorting using a BD FACSAria at 1.0 flow rate, with a 130 µm nozzle, dispensed in a flat-bottom, 96-well plate (Thermo Fisher, Nunc plates) with normal growth medium. In experiments designed to induce micronucleus formation biochemically, MCF10A and RPE-1 cells were treated with 0.5 µM of reversine (Sigma), a potent MPS1 inhibitor[65], 1 day after seeding. After 24 h of treatment, cells were washed gently four times with 1× PBS before being released into fresh medium.

MAGIC: autonomous platform for de novo CA formation studies

MAGIC leverages machine learning and automated microscopy to perform targeted photolabelling of cells of interest, for subsequent fluorescence-activated cell sorting and downstream analysis, building on approaches coupling the imaging of visual phenotypes with precise optical tagging66,67,68. An MAGIC experiment with this adaptive feedback microscopy (Smart Microscopy) system comprises three phases: (1) the preparation phase of MAGIC, where cells are seeded and other treatments, such as targeted DSB induction or staining by DACT-1, can take place; (2) the photolabelling phase of MAGIC, where targeted illumination66,67,69 takes place using automated microscopy and (3) the cell collection phase of MAGIC, when cells are collected and isolated by FACS. These steps are outlined below, accompanied by further details presented in the Supplementary Methods.

Preparation

During this phase cells are prepared to undergo the targeted photolabelling procedure. Further treatments, such as targeted DSB induction, staining with live-cell dyes and adding BrdU for Strand-seq, can take place. To enable photolabelling, we engineered MCF10A and RPE-1 cell line models to constitutively express H2B-Dendra2—a monomeric fluorescent protein that undergoes irreversible photoconversion with 405 nm light, which also enables the visualization of nuclear atypia without affecting mitotic fidelity[70]. As an alternative, for RPE-1 wild-type cells, as well as BJ-5ta and IMR-90, we also used DACT-1—a photo-activatable cell tracking dye—that converts to a bright red-fluorescent state upon 405 nm light exposure (further details are available in the Supplementary Methods). Neither H2B-Dendra2 nor DACT-1 significantly altered micronucleus frequency in MCF10A cells (Supplementary Fig. 1f), indicating that these labelling approaches, by themselves, do not induce chromosomal instability under the conditions used.

Cells were seeded in up to four wells of a µ-slide eight-well dish (Ibidi). Seeding density was adjusted to have about 40,000 cells 1 day before experiment start. In the case of Strand-seq downstream analysis, BrdU (40 µM final concentration) was added to the cells before the start of photolabelling (a concentration previously reported not to cause genomic instability[71]). One control slide without BrdU was also prepared to adjust gating strategies during single-cell sorting. In the case of targeted DSB induction experiments, ribonucleoprotein (RNP) complexes were delivered by electroporation 48 h before the start of the experiment and up to two different sgRNAs were examined during a single experiment.

Photolabelling

Living cells were then transferred to an LSM 900 microscope (Zeiss) with confocal and widefield imaging capabilities, and an environmental chamber with temperature and CO_2 control. MAGIC relies on full microscope automation and computer vision for laser-assisted, phenotype-driven targeted illumination of single cells at scale. The system includes three software components: a microscope control script, an image analysis manager on the basis of AutoMicTools and a Python package, magic_tools, which we designed for advanced image processing.

The microscope control script automates autofocusing, micronuclei identification and photoconversion of target nuclei across several positions. Autofocus is achieved by detecting the glass-bottom dish reflection using a 639 nm laser and AutoMicTools analysis. For micronuclei identification, a Z stack image centred on the focused slice is analysed on an image analysis server driven by magic_tools. Photoconversion involves using micronuclei coordinates to define ROIs of the corresponding parental nuclei, which are then photolabelled selectively with a 405 nm laser. Pre- and post-experiment images are acquired before the microscope moves to the next position.

We ran the photolabelling experiment overnight and up to 24 h, to achieve a yield of 700 to 2,000 photolabelled cells, depending on the experimental conditions. A detailed description of the automation software and the image analysis pipeline can be found in Supplementary Methods.

Cell collection

Following photolabelling, cells were collected and target cells were isolated by single-cell sorting. In case of Strand-seq experiments, at the end of the photolabelling phase, cells were stained for 1 h with Hoechst 33342 at 5 µg ml−1. Cells were collected with 0.25% trypsin (Gibco) and resuspended in buffer (8% FBS in 1× PBS, supplemented with Hoechst 33342 5 μg ml−1 and BrdU 40 µM). Single cells were sorted using a BD FACSAria in purity mode with a 100-µm or 130-µm nozzle and dispensed into lysis buffer or fresh medium in a flat-bottom 96-well plate (Thermo Fisher, Nunc plates). We used the following gating strategy: we selected first the general population in forward and side scatter and we excluded doublets. Then, cells were sub-gated for photolabelled cells as shown in Fig. 1g for H2B-Dendra2 or Supplementary Fig. 2h for DACT-1. When using Strand-seq, the singlet population was further filtered to select cells with a quenched Hoechst signal that had thus incorporated BrdU[72]. Cells collected from control slides were used to optimally adjust gates to exclude false positives.

Long-term live-cell imaging

The live-imaging experiment for nuclear and mitotic phenotype16,73 scoring was carried out over the course of 72 h. MCF10A cells stably expressing H2B-Dendra2 were seeded at a 15–25% confluence on µ-slide eight-well dishes (catalogue no. 80806; Ibidi), and images were acquired every 10 min with a Plan-Apochromat ×20/0.8 M27 air objective using the LSM 900 confocal microscope (Zeiss). Manual annotation was performed with the assistance of a customized tool written in Python. Mitotic phenotype and nuclear morphology for parental cells and the first generation of daughter cells were annotated as described in Fig. 1b.

Optimization of photolabelling parameters

MCF10A cells stably expressing H2B-Dendra2 were seeded on μ-slides (Ibidi) and imaged on an LSM 900 confocal microscope (Zeiss). To determine Dendra2 photoconversion dynamics, we performed five bleaching rounds, each with ten laser-scanning iterations with a ×20 objective and 405-nm laser, at scanning speed 8 and power at 0.5% in the low-intensity power range. Images in green and red channels were acquired at the beginning and end of each round. The fluorescence intensity of ten photoconverted nuclei and five non-photoconverted control nuclei per field of view was quantified on manually defined ROIs with ImageJ. Data were then processed and analysed with custom Python scripts. To assess phototoxicity from targeted illumination, MCF10A and RPE-1 cells seeded on μ-slides (Ibidi) were photoconverted with settings used in the MAGIC pipeline and followed by confocal microscopy. Images for native and photoconverted Dendra2 fluorescence channels were acquired with a ×20 objective over the course of 24 h. Cells were tracked manually and their fate annotated. No cell death was detected for the photoconverted cells within the timeframe analysed.

Single-cell genomic sequencing with Strand-seq

Unlike other single-cell genomic techniques, Strand-seq uniquely preserves haplotype identity across an entire homologue27,29, which enables sensitive detection of simple and complex CA classes at intermediate sequence coverage29,74. We performed cell sorting as in the original procedure[27] with important adjustments to accept whole cells as input, to avoid loss of cytoplasmic DNA material and micronuclei during nuclei isolation. Cells were incubated with Hoechst 33342 (5 μg ml−1) for 60 min, as it is cell membrane-permeable. Cells were then collected with 0.25% trypsin (Gibco) and resuspended in buffer (8% FBS in 1× PBS, supplemented with Hoechst 33342 5 μg ml−1 and BrdU 40 µM). Single cells were sorted using a BD FACSAria in purity mode with a 100 or 130 µm nozzle, and dispensed into a flat-bottom 96-well plate (Thermo Fisher Scientific, Nunc plates) containing freeze buffer supplemented with 0.2% NP-40 (Thermo Fisher Scientific) to ensure membrane lysis and DNA accessibility in subsequent protocol steps. Strand-seq libraries were prepared at large-scale using a liquid handling robotic platform as described previously[29]. Libraries were sequenced on a NextSeq5000 (MID-mode, 75 bp paired-end) followed by demultiplexing. Reads were aligned to GRCh38 reference assembly with BWA-MEM v.0.7.17, yielding a median of ~285,000 mapped unique fragments per cell, and further processed as described below.

Single-cell de novo CA discovery and classification

We discovered a wide variety of de novo CA classes leading to chromosomal or segmental copy-number imbalances by integrating read coverage and Watson/Crick template ratios[29], enabling high-resolution CA calling in Strand-seq data. Extending the functionality of the previously released MosaiCatcher tool[29], we designed strandtools, which is tailored for the specific task of handling de novo CA discovery in single cells under diverse ploidy backgrounds (Supplementary Methods). To achieve high confidence CA classification, we integrated read depth, strand orientation and haplotype information in each cell[29], to characterize segmental alterations and assign them to one of the following CA classes: chromosome loss, chromosome gain, interstitial loss, interstitial gain, terminal loss, terminal gain, terminal multi-step, complex CA and chromothripsis (a complex CA subclass). Chromosome gains and losses affect a whole chromosome, from p-ter telomere to q-ter telomere. Interstitial gains and losses are isolated CAs between two breakpoints, within one chromosome arm. As terminal alterations, we refer to all CAs that involve a portion of a chromosome, from a breakpoint anywhere along a chromosome arm to the telomere of that same arm. Therefore, terminal gains and losses are simple CAs, with one isolated, altered segment spanning from a breakpoint to the telomere of one chromosome arm. Terminal gains are annotated as inverted duplications if the gained segment is in opposite strand orientation compared with that of the original homologue with the same haplotype[29]. Terminal multi-step CAs are a sequential combination of gains and losses that are affecting the terminal portion of a chromosome arm. The terminal multi-step class also includes all cases of localized oscillations arising alongside terminal gains and losses.

Complex CAs are defined as events that include more than two breakpoints, can affect either one or both arms of the same homologue and can be composed of non-adjacent, altered segments. As such, complex CAs cannot be resolved as terminal multi-step. Chromothripsis events extending over large chromosomal regions, such as a chromosome arm, are included under the complex CA class. These events show characteristic copy-number oscillation between typically two copy-number states, affecting one single haplotype and with oscillating segments allowed in either strand orientation29,30. With regard to experiments on targeted DSB induction along chromosome arms, we likewise considered all copy-number imbalanced CA classes. In addition, we specified whole-arm alterations in the case of isolated gains and losses affecting more than 90% of a chromosome arm, and amplifications in case of isolated gains with a copy-number increment of two or more compared to the baseline. All single-cell CA annotations are available in Supplementary Tables 7, 8 and 9.

Targeted induction of DSBs

CRISPR components, designed as described in the Supplementary Methods, were delivered in the form of RNP complex using a Neon Electric Transfection System (10 µl kit; catalogue no.: MPK1096; Thermo Fisher). First, the RNP complex was formed by incubating 0.3 µl of Alt-R S.p. Cas9 Nuclease (catalogue no.: 1081059; IDT) with 0.2 µl Resuspension Buffer R (Neon 10 µl kit) and 1 µl of designed sgRNA for 20 min. Cells (500,000 per reaction) were prepared for electroporation as described in the manufacturer’s manual. Concentration of Cas9 nuclease in the final RNP/cell suspension was 1.5 µM, and that of sgRNA was 3.6 µM. Electroporation parameters of 1,400 V, 20 ms and two pulses were used for both RPE-1 and MCF10A cells. Transfected cells were diluted in antibiotic-free cell culture medium and different amounts (between 36,000 and 72,000) were seeded into four central wells of µ-slides containing 300 µl of antibiotic-free medium. The medium was replaced with fresh medium containing BrdU (40 µM) at 48 h post-transfection to allow cells to recover, and the slide was transferred immediately into the confocal microscope for imaging. For determining how DSB location may determine CA processes, we selected chromosome 2q due to its low average repeat content facilitating gRNA design, and 7q due to the enrichment for clonally propagated CAs we observe for this arm.

Clone generation from single cells

Cells were subjected to automated photolabelling, collected with 0.25% trypsin (Gibco) and resuspended in buffer (8% FBS in 1× PBS). Single cells were sorted using a BD FACSAria at 1.0 flow rate, with a 130-µm nozzle to minimize cell damage, and dispensed into a flat-bottom 96-well plate (Thermo Fisher, Nunc plates) with normal growth medium. Formation of viable colonies was assessed visually daily with a phase-contrast microscope from day 7 to day 14 post sorting. At the 2-week mark, clones were transferred to six-well plates, and grown to confluence to be frozen for future experiments and prepared for sequencing.

Low-pass WGS of clones

A total of 27 MCF10A cell pellets (18 clones deriving from micronucleated cells, nine control clones) and 11 RPE-1 cell pellets (11 clones deriving from micronucleated cells) were subjected to bulk-cell low-pass Illumina sequencing (NextSeq2000, P3, 100 bp paired-end sequencing) at EMBL’s Genomics Core Facility, to an approximate genomic coverage of 1× for screening purposes. Reads were aligned to the GRCh38 genome reference with BWA[75], and read depth based CA calling was determined with support of the Control-FREEC tool[76]. A single case of a potential complex CAs was inferred on the basis of the chromosomal clustering of CAs inferred by read depth analysis.

Long-read WGS of clone 7

Clone 7 was re-established to obtain 10 × 10^6 cells for Oxford Nanopore Technologies (ONT) long-read sequencing. The library was prepared using the SQK-LSK114 ligation kit, and sequencing performed on PromethION flow-cells. The obtained coverage was 16×, and the reads showed an estimated N50 of 13.97 kb. Reads were aligned to the GRCh38 genome reference with minimap2 (ref. [77]). Structural variant calling was performed with Sniffles[78] and Delly[79], and calls were curated manually to exclude false positives. Read depth profiles for the micronucleated clone 7 were generated using delly (cnv subcommand) with a window size of 25 kb and the standard GRCh38 mappability map. The read depth signal was segmented using the DNAcopy Bioconductor package. Somatic structural variants were called using sniffles2 and delly (lr subcommand). For both delly and sniffles2, we used another clone of MCF10A as a control to filter for somatic variants in the micronucleated clone 7. Subsequently, only candidate somatic structural variants called by both methods and larger than 10 kb were used. Single-nucleotide variants, as well as small insertions and deletions (indels), were called using Clair3. Haplotype phasing of the ONT reads was performed with WhatsHap to generate read depth plots by haplotype[80]. Telogator[81] was used for telomere length inference from ONT reads generated from a MCF10A-derived clone (‘clone 7’), using the suggested ‘-r ont’ parameter recommended for handling Nanopore reads.

Modelling de novo CA rates

We developed an agent-based model[82] to simulate CA acquisition in a growing population of cells, considering mitotic errors and micronuclei generation. During the simulation, cell agents are allowed to move between the states depicted in Fig. 3g. The probability Pij of transitioning from state i to state j is derived from long-term live-cell imaging experiments. Each cell agent is designed to possess three main attributes: cell cycle status, micronucleus status and CA status. The micronucleus status captures whether the cell possesses a micronucleus or not. The cell cycle status keeps track of an internal clock that simulates advancing through cell cycle until mitosis. Cell cycle duration is set at the median cell cycle duration measured in imaging experiments. The CA status captures whether the cell possesses a de novo CA. When the internal cell cycle clock reaches the end, mitosis or arrest occurs: the cell agent can move from interphase to a mitosis state (normal, laggard or bridge) or arrest. To simulate cell division, the current agent is moved to the arrest state and two new cells are generated and assigned to state 1 or 5, according to the transition probability associated with that specific mitosis type. Moreover, during mitosis, each cell has the possibility of acquiring a de novo CA according to the assigned rate R. Arrested cells are then removed from the simulation. Each simulation is initiated with an initial population of 50 cells and is stopped when the population reaches size 50,000, as we found empirically that the micronuclei and CA frequency usually stabilize by this time. Encouragingly, despite not being programmed explicitly into the model, the frequency of micronuclei stabilized at 5.0% and 38.3% for wild-type and TP53−/− cells respectively, closely mirroring our empirical data (Supplementary Fig. 6a,b). At the end of the simulation, we compute the sum of squared error between the simulated and target de novo CA frequencies. Details on how bound-constrained minimization was used to the CA rate estimation are the Supplementary Methods.

Fluorescent in situ hybridization

MCF10A cells were seeded on coverglass slides, subjected to targeted DSB induction, and allowed to recover for 48 h. Metaphase spreads were then prepared in situ directly on coverslips, as described elsewhere[83]. Sub-centromeric probes for Chr. 7 p and q arms were purchased from KromaTiD (Biocat catalogue no.: CEP-0013-C-KTD, CEP-0014-A-KTD). FISH was performed according to manufacturer instructions. After post-hybridization washes, DNA was stained with Hoechst 33342 and slides were mounted in anti-fade medium (Vectashield, Vector Laboratories). FISH images were acquired on a LSM 900 confocal microscope (Zeiss) at ×40 magnification and signals were evaluated visually.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

All genomics data generated in this study (Strand-seq, as well as short and long-read bulk WGS) are available at ENA under the following accession: PRJEB78885. Strand-seq processed count data are publicly available at Zenodo (https://doi.org/10.5281/zenodo.15262423)[84]. We re-analysed publicly available data from the PCAWG[8] and TCGA resources to compare our findings to those previously made in cancer genomes. The raw WGS data generated by TCGA can be accessed through controlled data access application using dbGAP under study accession code phs000178. Data links are available in Supplementary Table 17.

Code availability

The software automation components and step-by-step instructions for running MAGIC experiments are available in the magic_automation repository (https://git.embl.de/cosenza/magic_automation). For image analysis, computer vision, and image processing, visit the magic_tools repository (https://git.embl.de/cosenza/magic_tools). Tools for analysing Strand-seq data and single-cell copy-number calling are provided in the strandtools repository (https://git.embl.de/cosenza/strandtools). A Docker container providing a unified environment to run the main computational pipeline behind MAGIC (strandtools, magic_tools and magic_automation) is available at https://git.embl.de/tweber/magic-container. The script for estimating basal CA rates is provided at https://git.embl.de/cosenza/ca_rates_estimation. A snapshot of all software repositories for MAGIC experiments and Strand-seq data analysis has been archived and is publicly available at Zenodo (https://doi.org/10.5281/zenodo.16631215)[85]. The code used in this study to analyse WGS data is available at: https://github.com/cortes-ciriano-lab/osteosarcoma_evolution. Software repository links are available in Supplementary Table 17.

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Acknowledgements

We thank D. Pellman and C.-Z. Zhang for providing valuable comments on an advanced version of our manuscript. TP53−/− MCF10A cells are a kind gift from C. Scholl. We acknowledge support from C. Hain in the telomere length analysis. Principal funding for this work came from the European Research Council (ERC Advanced grant (SEE-MAGIC) grant no. 101098056) to J.O.K., with additional support coming from an ERC Consolidator grant (MOSAIC; no. 773026) to J.O.K, the Volkswagen Foundation (VW–95826) to J.O.K, the Health + Life Science Alliance Heidelberg Mannheim with funding approved by the State Parliament of Baden-Württemberg, and from EMBL core funding. M.R.C. received support from the EMBL Interdisciplinary Postdoc (EIPOD4) program 4 under Marie Skłodowska-Curie Actions COFUND (grant agreement no. 847543), enabling interdisciplinary studies in the Pepperkok and Korbel groups. We acknowledge the EMBL core facilities and services for support in high-performance computing (IT), sequencing (GeneCore), chemical synthesis (Chemical Biology), imaging (Advanced light microscopy) and cell sorting (Flow cytometry core facility) and the German Cancer Research Centre genomics core facility.

Funding

Open access funding provided by European Molecular Biology Laboratory (EMBL).

Author information

Authors and Affiliations

1. Genome Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany

Marco Raffaele Cosenza, Alice Gaiatto, Büşra Erarslan Uysal, Álvaro Andrades, Nina Luisa Sautter, Marina Simunovic, Michael Adrian Jendrusch, Tobias Rausch, Joshua Lucas Eigenmann, Thomas Weber, Patrick Hasenfeld, Eva Benito, Catherine Stober & Jan O. Korbel

2. Molecular Medicine Partnership Unit (MMPU), EMBL, University of Heidelberg, Heidelberg, Germany

Büşra Erarslan Uysal, Andreas E. Kulozik & Jan O. Korbel

3. Department of Pediatric Oncology, Hematology, and Immunology, University of Heidelberg, Heidelberg, Germany

Büşra Erarslan Uysal & Andreas E. Kulozik

4. CCU Pediatric Leukemia, German Cancer Research Center (DKFZ), Heidelberg, Germany

Büşra Erarslan Uysal & Andreas E. Kulozik

5. Hopp Children’s Cancer Center Heidelberg, Heidelberg, Germany

Büşra Erarslan Uysal & Andreas E. Kulozik

6. European Bioinformatics Institute (EMBL-EBI), Hinxton, UK

Sonia Zumalave, Isidro Cortes-Ciriano & Jan O. Korbel

7. Genomics Core Facility, EMBL, Heidelberg, Germany

Tobias Rausch

8. Advanced Light Microscopy Core Facility, EMBL, Heidelberg, Germany

Aliaksandr Halavatyi & Rainer Pepperkok

9. Data Science Centre, EMBL, Heidelberg, Germany

Eva-Maria Geissen & Thomas Weber

10. Cancer, Ageing and Somatic Mutation Programme, Wellcome Sanger Institute, Hinxton, UK

Isidro Cortes-Ciriano

11. Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany

Rainer Pepperkok

12. Bridging Research Division on Mechanisms of Genomic Variation and Data Science, German Cancer Research Center (DKFZ), Heidelberg, Germany

Jan O. Korbel

Contributions

M.R.C., J.O.K. and R.P. conceived the project, with J.O.K. providing scientific direction and supervision. M.R.C. and A.H. developed the microscope automation software and integration with AutoMicTools. M.R.C. developed magic_tools. T.W. integrated the software components into a Docker image. M.R.C. designed and performed the photolabelling optimization experiments. M.R.C. and A.G. designed and performed the long-term live-cell imaging experiments, M.R.C., A.G. and N.L.S. analysed the image data. N.L.S. performed Western blotting experiments. M.R.C., A.G., N.L.S. and M.S. designed and performed MAGIC experiments with support from P.H., C.S. and J.L.E. A.G. performed single-cell clone propagation experiments, low-pass WGS and long-read sequencing characterization of clones. Long-read data were analysed by A.G. and T.R. M.R.C. designed the FISH experiments, which were performed by A.G. M.A.J. developed the convolutional neural network. P.H., E.B. and C.S. prepared Strand-seq libraries. Single-cell data were analysed by M.R.C., A.G., N.L.S., A.A. and J.O.K. A.A. designed and performed copy-number pattern analysis in PCAWG data, with support from M.R.C. A.A. and S.Z. designed and performed the isochromosome analysis in primary cancer genomes, with guidance from J.O.K. and I.C.-C. B.E.U. designed and tested the CRISPR guides, under guidance of A.E.K. CRISPR experiments were performed by B.E.U. and A.G. M.R.C. developed the agent-based statistical model with support from E.-M.G. M.R.C. and J.O.K. wrote the core of the manuscript, with contributions from all authors. J.O.K., R.P., A.E.K., T.R., A.G., M.S., N.L.S., A.A., S.Z. and I.C.-C. critically reviewed and edited the manuscript.

Corresponding author

Correspondence to Jan O. Korbel.

Ethics declarations

Competing interests

J.O.K. has previously disclosed a patent application (no. EP19169090) that is relevant to the use of Strand-seq for somatic structural variation analysis. The other authors declare no competing interests.

Peer review

Peer review information

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

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Extended data figures and tables

Extended Data Fig. 1 Sister cell analysis and CA examples in near-diploid non-transformed cells.

(a) Sister cell strand-state anti-correlation analysis for MCF10A (left) and RPE-1 (right) micronucleated cells (Pearson correlation coefficient) – revealing several sister cell pairs through single-cell genomic analysis. (b) Reciprocal CA examples in MCF10A and RPE-1 cells, with annotated segment boundaries marked by dashed lines. (c,d) Breakdown of CA classes in normal MCF10A (c) and RPE-1 (d) cells, with the class percentage shown relative to all CAs. (e) Chromothripsis examples from spontaneous micronuclei in MCF10A cells.

Extended Data Fig. 2 CA landscape characterization in additional cell lines.

CAs detected per cell in BJ-5ta (a) and IMR-90 (d) cell lines (without perturbation or treatment, Fisher’s exact test). Breakdown of CA classes in the BJ-5ta (normal b, micronucleated c) and IMR-90 cell lines (normal e, micronucleated f) in absence of perturbation. See Methods section for CA classification criteria.

Extended Data Fig. 3 CA landscape characterization following perturbation of chromosome segregation.

CAs detected per cell in MCF10A (a) and RPE-1 (d) cell lines after reversine treatment (Methods). Breakdown of CA classes in the MCF10A (normal b, micronucleated c) and RPE-1 (normal e, micronucleated f) following treatment with reversine. See Methods section for CA classification criteria.

Extended Data Fig. 4 Breakpoint features of CAs and chromosome size correlation results from spontaneous micronucleation experiments.

(a) Distribution derived from permutation of breakpoint location against G-quadruplex sites (top row), early (second row) and late (third row) replicating regions, as well as BrdU fragile sites (bottom row). Red dashed line: observed statistic (see Methods). The analysis was conducted using MCF10A cells, from spontaneously micronucleated cells. (b) Correlation between CA count and ONT-sequencing based telomere length per chromosome arm for MCF10A, expressed as 90th percentile of read length (Pearson correlation; see Methods). (c) Distribution derived from permutation of determined CA numbers in spontaneously micronucleated cells against chromosome size in RPE-1 and MCF10A. Red dashed line: observed statistic. (d) Percentage of aneuploid chromosomes in RPE-1 across studies. Correlation in aneuploid chromosome percentages in RPE-1 cells as measured from spontaneous micronucleation (our study) and after chemically induced missegregation from a prior study[32]. Dots represent chromosome-specific aberration frequencies in both studies (Spearman correlation).

Extended Data Fig. 5 Analysis of chromosome-scale chromothripsis, and clonal propagation experiments.

(a) Fraction of surviving clones after MAGIC isolation (Fisher’s exact test). (b) De novo CA formation in two cell lines measured from chromosomally abnormal propagated clones as well as sister cell pairs. Left, percentage of clones carrying at least one de novo CA, originating from micronucleated cells. Right, frequency of micronucleated sister cell pairs carrying at least one de novo CA (Fisher’s exact test). (c) 7q loss enrichment in propagated clones (Fisher’s exact test). (d) Schematic of 7q hits in micronucleated clones, which include 7q-arm loss, chromosome 7 losses, and isochromosomes resulting in 7q-loss. (e) ONT long-read sequencing based copy-number plot of chromosome 7 for the micronucleated clone 7; arrows on top represent the boundaries of the different classes of SVs (DEL: deletion; DUP: duplication; INS: insertion; INV: inversion; BND: translocation, see Methods). The chromosome presents a duplication of the p-arm coupled to the deletion of the q-arm, indicating isochromosome formation; in addition, a chromothripsis event is identified based on the presence of an oscillating copy-number pattern (in this case, between copy-number 3 (CN3) and CN4) and on the simultaneous occurrence of multiple SVs on the affected chromosome arm consistent with randomness of DNA fragment joins. As a consequence of isochromosome formation followed by chromothripsis, three copy-number states are seen across the chromosome 7 genomic coordinates. (f) Copy-number plot of chromosome 7 of the micronucleated clone 7, resolved by haplotype. The copy-number alterations seen are confined to haplotype 2 (see Methods). (g,h) Sister cell read-count anti-correlation for chromosome 13 (g) and chromosome 1 q-arm (h) (Pearson correlation coefficient), verifying the reciprocal segregation of shattered DNA fragments. (i) Chromothripsis in a sister cell pair, affecting chromosome 1, q-arm, determined in a complex ploidy background. Top, Strand-seq plots with oscillatory copy-number pattern. Bottom, smoothened and normalised counts along chromosomal positions.

Extended Data Fig. 6 Analysis of spontaneous bridge-mediated CAs.

(a,b) Strand-seq based haplotype-resolved examples of terminal inverted duplications (a) and terminal multi-step alterations (b). For each example, we depict at the top: Strand-seq plot, bottom: haplotag[29] localisation. In (a), inverted terminal duplications are characterised by the presence of haplotype 2 (H2) haplotags on the W strand for both chromosome 6 and 12 examples. In the (b) upper panel, chromosome 4 carries two adjacent copy-number gains, affecting haplotype 1 (H1) and both strands. In the lower panel, chromosome 12 carries one inverted duplication on H2, with an adjacent terminal deletion of the sample haplotype. (c) Scheme showing mitosis entry with unrepaired DSB leading to micronucleus formation. (d) Localised copy-number oscillation examples indicative for small to intermediate scale complex SVs. Arrow: oscillation peak. (e) Frequency of the localised oscillation pattern in MCF10A and RPE-1 cells. (f,g,h) Features of the localised oscillation pattern: number of segments composing the oscillation (f), overall oscillation (g), trough and crest (h) oscillation size. The data depicted includes cases from both WT and TP53-/- cell line models. Center line, median; box limits, upper and lower quartiles; whiskers, 1.5x interquartile range; points, outliers.

Extended Data Fig. 7 Differential expression analysis of micronucleated cells.

(a) Volcano plots of differentially-expressed genes identified by coupling the MAGIC platform with single-cell RNA sequencing, contrasting normal vs. micronucleated cells in MCF10A (left panel) and RPE-1 (right panel) wild-type cells. Differentially expressed (DE) genes are in blue if down-regulated or red if up-regulated. (b) Enrichment analysis for Hallmark gene sets from the Human Molecular Signatures Database (MSigDB). Upper panel MCF10A, lower panel RPE-1. (c) Heatmap plot summarizing gene ontology (GO) enrichment for MCF10A (left panel) and RPE-1 (right panel). Redundant GO terms were clustered by semantic similarity, indicated by the blue to red heatmap gradient.

Extended Data Fig. 8 Detailed characterisation of CAs arising from targeted DSB induction.

(a) Overview of copy-number changes for chromosome 2 q-arm CAs, shown for sub-centromere (top), central (middle) and sub-telomere (bottom) target loci. (b) Types of CA observed for different cut sites on the chromosome 2 q-arm (Fisher’s exact test). (c) Terminal multi-step CAs on targeted chromosomal arms. (d,e) Significant enrichment for bridge-mediated (d) and isochromosome-like (e) CA patterns, depending on the cut location. We considered all terminal and complex CAs in this analysis (P-values are based on Fisher’s exact test). (f) Chromothripsis in sister cells, involving targeted DSBs at the central cut site. (g) Examples of inferred isochromosomes. Dashed lines correspond to SCEs and targeted cut sites. The chromosome 7 consensus copy-number of the MCF10 cell line is three.

Extended Data Fig. 9 Aneuploidy and isochromosome analysis in primary cancer genome datasets.

(a) Proportion of whole-chromosome losses among all whole-chromosome aneuploidy events in spontaneous micronuclei models and the PCAWG[8] dataset. The “unfiltered” PCAWG dataset includes all representative aliquots (see Supplementary Notes). The “no ambiguous ploidy” dataset only includes those aliquots in which an integer ploidy could be assigned unambiguously (see Supplementary Notes). The “no WGD” dataset excludes aliquots affected by whole genome duplication (WGD). The total number of whole-chromosome gains and losses is shown for each dataset. MNI: micronuclei; TP53KO: knockout of TP53 gene; WT: wild type, for normal TP53 status. (b,c) Number of inferred isochromosomes (b) and distribution of distances between isochromosome changepoints and centromeres (c) identified in the TCGA and PCAWG datasets, considering only non-redundant donors (see Supplementary Notes). Center line, median; inner box limits, upper and lower quartiles; whiskers, 1.5x interquartile range; gray patch, kernel density estimate.

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This file contains Supplementary Figs. 1–11, descriptions for Tables 1–17 (supplied as a separate spreadsheet), Methods and Notes.

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Cosenza, M.R., Gaiatto, A., Erarslan Uysal, B. et al. Origins of chromosome instability unveiled by coupled imaging and genomics. Nature 648, 383–393 (2025). https://doi.org/10.1038/s41586-025-09632-5

- Received: 15 August 2024

- Accepted: 15 September 2025

- Published: 29 October 2025

- Version of record: 29 October 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09632-5

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Thiorphan reprograms neurons to promote functional recovery after spinal cord injury

E. A. van Niekerk,

C. Marques de Freria,

B. O. Mancarci,

K. Groeniger,

D. Kulinich,

T. Riley,

R. Kawaguchi,

S. Okawa,

T. Vokes,

E. S. Rosenzweig,

E. Sinopoulou,

M. J. Castle,

R. Huie,

A. R. Ferguson,

N. Kfoury-Beaumont,

A. Khalessi,

P. Pavlidis &

…

M. H. Tuszynski

Nature volume 648, pages 402–408 (2025)

Abstract

We previously identified an embryonic shift in the corticospinal motor neuronal transcriptome after spinal cord injury associated with successful axonal regeneration[1]. Exploiting this transcriptional regenerative ‘signature’, here we used in silico screens to identify small molecules that generate similar shifts in the transcriptome, and identified thiorphan—a neutral endopeptidase inhibitor—as a lead candidate. In a new adult motor cortex neuronal in vitro screen[2], thiorphan increased neurite outgrowth 1.8-fold (P < 0.001). We then infused thiorphan into the central nervous system beginning 2 weeks after severe C5 spinal cord contusions and, when combined with a neural stem cell graft, thiorphan elicited significant improvements in forelimb function (P < 0.005) and corticospinal regeneration (P < 0.05). Extending clinical relevance, thiorphan significantly increased neurite outgrowth in primary cortical neuronal cultures from a 56-year-old human. These findings represent a new path for drug discovery, starting from in silico screens to proof-of-concept in adult human brain cultures.

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Main

There are no effective therapies for promoting neural repair after spinal cord injury (SCI), which represents a disorder of great unmet medical need. We reported recently that the corticospinal projection—the most important motor system for voluntary movement in humans—undergoes regression to an embryonic transcriptional state after adult SCI in mice[1]; in this state, the corticospinal axon regenerates into a neural stem cell graft placed in the site of the injury.

Taking advantage of established bioinformatics approaches, in silico screens and medium-throughput model systems of adult motor cortex neuronal cultures[2], we sought to identify drugs and small molecules that replicated the regenerative transcriptional state of the corticospinal neuron. First, we compared the injured and regenerating corticospinal transcriptome with a publicly available database of several thousand drugs and small molecules already tested in humans—the Connectivity Map[3] (CMap). This in silico screen identified several compounds that mimicked, to varying degrees, the corticospinal regenerating transcriptome. We then tested these lead compounds in a newly developed in vitro screen in cultures of adult cortical motor neurons. A lead small molecule candidate, thiorphan (253 Da), known primarily as a neutral endopeptidase inhibitor, exhibited the greatest efficacy in supporting total neurite outgrowth and longest neurite length in this medium-throughput screen. We then tested the ability of thiorphan to support axonal regeneration and functional recovery after severe, bilateral mid-cervical SCI in adult rats when delivered 2 weeks after SCI—a clinically relevant time point for intervention. Notably, thiorphan treatment combined with a neural progenitor cell (NPC) graft significantly improved functional recovery after SCI. Moreover, thiorphan administration significantly augmented corticospinal axon regeneration into stem cell grafts. Finally, pursuing the true translational potential of thiorphan, we tested its effects on primary cultures of adult cynomolgous monkey motor cortex and 56-year-old human cortex neurons: once again, thiorphan significantly increased neurite growth. Thus, a bioinformatics-driven approach combined with an in vitro screen, in vivo testing and primate in vitro confirmation represent a new pathway for drug discovery. Thiorphan previously underwent human testing for a different disease indication, enhancing its readiness for development as a therapy for SCI.

A pipeline for drug discovery

We adopted a five-step pipeline to identify candidates for enhancing neural repair with a streamlined path that could lead to human testing (Fig. 1a). Step 1 involves characterizing the transcriptomic state or ‘signature’ of a cell type that exhibits a beneficial biological effect. In this case, we used the transcriptome of corticospinal motor neurons that are capable of regeneration after SCI. We reported previously that, within 2 weeks of SCI, the corticospinal neuron undergoes transient transcriptional reversion to an embryonic state—a state in which it is capable of regenerating[1]. These data are publicly available. In Step 2, we perform an in silico screen to compare the regenerating corticospinal transcriptome with shifts in the transcriptome generated by more than 1,300 small molecules or compounds in the Broad CMap (https://bioconductor.org/packages/release/data/experiment/html/ConnectivityMap.html). Drugs and small molecules in CMap have been exposed to various cell lines in vitro, and effects of these compounds on the transcriptome of the cultured cells have been characterized[3]. Thus, we searched CMap for compounds that generated transcriptomic shifts that parallel the state of regenerating corticospinal neurons. In Step 3, we took the lead candidates from the in silico screen and applied them to a medium-throughput in vitro assay consisting of cultures of adult motor cortex neurons; this screen became available only recently[2] and provides what could be the most useful in vitro system for predicting potential in vivo effects in the mature nervous system, because the screen consists of adult rather than embryonic or postnatal neurons. To date, in vitro cellular screens of the nervous system consisted of either embryonic or early postnatal neuronal cultures, which may not accurately reflect responses of adult central nervous system (CNS) neurons. Immortalized neural cell lines[4] suffer from similar limitations. Although adult dorsal root ganglia (DRG) neurons can be cultured routinely, these cells exhibit fundamentally different transcriptomes before and after injury1,5,6 and, again, might not be accurate tools for predicting therapeutic benefits of candidate therapies for injured brain and spinal cord motor neurons. Induced pluripotent stem cells or neurons induced from other cell types also often exhibit early cellular markers[7]. Cultures of adult neurons therefore may represent the most optimal in vitro screen developed for clinical translation[2]. Step 4 consists of in vivo validation of the top drug arising from the in vitro screen in a model of SCI. Finally, Step 5 consists of validating candidate compounds in cultures of adult primate cortical neurons, including human adult cortex. This step follows rather than precedes in vivo testing because of the scarcity of the primate and human neuronal resource: normal human neurons in particular are available only occasionally from surgical specimens and in our case were obtained from an individual undergoing tumour resection through a cortical window, where pathology confirmed the cortical biopsy was normal tissue.

Fig. 1: Drug discovery pipeline, in silico analysis and in vitro validation.

a, Drug discovery pipeline consisting of five steps: (1) creation of a transcriptomic dataset; (2) in silico analysis using CMap; (3) medium-throughput in vitro screen; (4) in vivo testing of lead candidate(s); and (5) in vitro monkey and human validation. CST, corticospinal tract. b, In silico analysis shows ranking of compounds in CMap on the basis of connectivity score (left y axis), specificity score (blue, right y axis) and reliability score (green, right y axis) (see text for further detail). c, Neurite extension in composite image of cortical neurons treated with DMSO control and thiorphan (250 μM), Tuj1 labelling. d,e, In vitro screen of top three ‘hits’ from in silico screen, together with predicted negative modulator, adiphenine. Tested in cultures of adult mouse primary cortical neurons for 5 days in vitro, three independent biological replicates were performed on separate days, each using neurons from four adult mice. For each condition, data from all neurons measured across replicates were combined to yield n = 200 neurons per condition. Each neuron was spatially separated and analysed as an independent observation. Total neurite outgrowth per cell (Tuj1 labelling) is shown for each condition. Median values: DMSO (82.9); thiorphan (90.7, 99.8, 132.4, 166.1); triflusal (74.3, 61.7, 94.5, 124.5); milrinone (78.9, 77.4, 68.5, 75.5); adiphenine (74.4, 44.5, 31.7, 3) (d). Maximum neurite length per cell is shown for each condition. Median values: DMSO (93.3); thiorphan (111.1, 105.4, 122.1, 128); triflusal (84.4, 85, 104.9, 114.3); milrinone (100.6, 81.7, 79, 78.6); adiphenine (87.4, 60, 30.6, 6.23) (e). Statistical significance was determined by two-tailed Student’s t-test (**P < 0.01, ***P < 0.001). Error bars ± s.e.m. (d,e). Scale bar, 25 μm (c).

Characterizing the transcriptomic state

Step 1 was accomplished in this study by using our previous data describing the transcriptome of the regenerating corticospinal neuron[1], as referenced above.

In silico analysis

In silico analysis directly followed the original methodology of Lamb et al.[3], identifying several compounds that most closely matched the expression profile of the regenerating corticospinal system (Fig. 1b and Supplementary Fig. 1a). A ‘connectivity score’ with a value between +1 and −1 described the similarity between the corticospinal transcriptomic profile and an individual compound’s transcriptomic profile, where +1 was most similar and −1 was least similar to the corticospinal dataset (Fig. 1b). We further calculated a ‘reliability score’ for each compound that takes into account the connectivity score, P value, false detection rate (FDR), ‘instance count’ (number of experiments that include the compound), non-null score (the ratio of experiments that have a consistent score based on most experiments) and ‘specificity score’ derived from the distribution of enrichment scores for gene lists from MSigDB; see Methods for a more detailed description of the reliability score. The top compounds that met the criteria of highest enrichment, reliability and specificity scores were considered ‘hits’ in this assay and included: quinostatin (highest enrichment score +0.91 ± 0.07), thiorphan (+0.86 ± 0.11), triflusal (+0.79 ± 0.13) and milrinone (+0.78 ± 0.18), whereas adiphenine was the most negatively correlated (−0.78 ± 0.18; Fig. 1b and Supplementary Fig. 1b). Biological annotation (Methods) indicated that quinostatin inhibits PI3 kinase; thiorphan is a neutral endopeptidase inhibitor; triflusal inhibits nuclear factor κB, phosphodiesterase and COX1, and milrinone is a phosphodiesterase inhibitor (Supplementary Fig. 1a). Quinostatin was not available for purchase and attempts at synthesis did not yield adequate quality compound. Thiorphan has been characterized primarily as a neutral endopeptidase inhibitor targeting neprilysin[8]. It has also been linked to neuroprotective properties in models of perinatal excitotoxic brain lesions[9] and diabetic retinopathy[10], and has β-amyloid degrading properties[11]. Thiorphan, milrinone and triflusal were taken forward as positive candidates, and adiphenine was used as a negative control.

In vitro adult motor cortical culture screen

We assessed the lead candidate compounds in dissociated cultures of the adult (postnatal day 60) mouse motor cortex[2]. An average of 10,000 neurons per single motor cortex were obtained, and we quantified total neurite outgrowth and maximal neurite length per cell 5 days after exposure to the candidate compounds. Several drug doses were applied (Fig. 1d,e), including the predicted negative modifier of corticospinal growth, adiphenine. Significant overall differences in neurite outgrowth were present using various compounds (drug type × dose interaction generalized estimating equation for total neurite outgrowth, Wald chi-square = 60.67, P < 0.0001; drug type × dose interaction generalized estimating equation for total maximum neurite length, Wald chi-square = 227.78, P < 0.0001). Thiorphan stood out as most effective both in measures of total neurite outgrowth and neurite length: at a dose of 250 μM it increased total neurite outgrowth by 80% compared with controls (post hoc generalized estimating equation, Wald chi-square = 29.69, P < 0.001; Fig. 1d,e) and longest neurite length by 30% (post hoc generalized estimating equation, Wald chi-square = 12.62, P < 0.001; Fig. 1d,e). The effect of thiorphan was dose dependent, with peak effects occurring at doses between 100 μM and 250 μM. The effect of the next candidate drug for enhancing corticospinal regeneration, triflusal, was more modest, with an increase in neurite outgrowth of 30% at its peak dose of 250 μM with no significant change in longest neurite length; none of these changes reached statistical significance (Fig. 1e). The third candidate in rank order, milrinone, did not significantly influence either total neurite outgrowth or longest neurite length at any dose (Fig. 1d,e). Validating the in silico screening process, the predicted negative regulator of corticospinal growth, adiphenine, strongly and significantly reduced total neurite outgrowth and longest neurite length in a dose-dependent manner (post hoc generalized estimating equation, P < 0.001; Fig. 1c–e).

In vivo testing in a model of SCI

Given the success of thiorphan in demonstrating efficacy in the in vitro screen, it advanced to Step 4: in vivo testing in a clinically relevant model of SCI. Adult Fischer 344 rats underwent severe contusive bilateral cervical SCI at the C5 spinal cord segment; mid-cervical lesions are the most common levels of human injury[12] (Supplementary Fig. 2a,b). We then waited 2 weeks—a clinically relevant time to delay intervention to allow subject recovery from the acute effects of injury (Fig. 2a). Animals were then divided into one of four treatment groups: (1) lesion alone (n = 9), (2) thiorphan alone (n = 10), (3) diluent + NPC graft (n = 9) and (4) thiorphan + NPC graft (n = 9). We tested diluent + NPC grafts as a positive control in this lesion model because these cells support axonal regeneration into the lesion site, the formation of new neural relays across the injury site and partial functional recovery13,14. We also compared thiorphan alone with NPCs. The combination of thiorphan + NPCs aimed to determine whether effects of both treatments were additive, thereby representing a method of further augmenting recovery after severe cervical SCI. Thiorphan was infused continuously into the left motor cortex because it does not cross the blood–brain barrier. Infusions continued for 4 weeks starting 2 weeks after injury at a dose of 100 mM (0.25 μl h−1), based on extrapolation of in vitro dosing to in vivo dosing[15]. An in vivo neprilysin cleavage assay confirmed the bioactivity of intraparenchymal motor cortex infusions of thiorphan over 1, 2 and 4 weeks (Supplementary Fig. 2c). Spinal cord NPC grafts were obtained from Fischer 344 embryonic-day-14 (E14) spinal cords as reported previously[16] and injected through the dura into the lesion cavity 2 weeks post SCI (Fig. 2b; Methods). Two weeks before euthanasia, the corticospinal projection was traced anterogradely using an AAV9-CAG–Ruby2sm_Flag.

Fig. 2: Thiorphan improves functional outcomes after severe C5 bilateral contusion.

a, In vivo experimental outline of a clinically relevant SCI model. b, Nissl stain of a severe C5 bilateral contusion model. Sagittal section, rostral to left. Top, large contusion cavity in an ungrafted animal after 3 months. Bottom, NPC graft filling the lesion cavity and providing substrate for potential corticospinal axon regeneration. c, Skilled forelimb successful pellet retrieval with right paw on Montoya staircase[23] ± s.e.m. Animals that received thiorphan and a substrate for axonal regeneration into the lesion site—an NPC graft—exhibit significant functional recovery over time compared with lesioned controls (P = 0.005, group × time interaction, Poisson generalized linear model). Treatment with thiorphan alone also trended towards significance (P = 0.14). The lesion model applied in this experiment is the most severe that we have tested, and NPC grafts also exhibited a trend towards better outcomes than lesioned controls but this did not reach statistical significance. Grey shading, period of thiorphan infusion into cortex. d, Thiorphan + NPC graft group also exhibits significant recovery of pellet retrieval accuracy in this severe lesion model (P = 0.001). Other treated groups trend towards improved outcomes compared with lesioned controls. Accuracy represents the number of pellets eaten divided by the number of pellets displaced plus the number of pellets eaten. *P < 0.05 (c,d). Scale bar, 500 μm.

Source data

Twelve weeks after SCI, animals treated with thiorphan + NPC grafts exhibited a significant, twofold improvement in forelimb grasping success (number of pellets grasped and eaten) after severe mid-cervical SCI compared with lesioned controls (Poisson generalized linear model, Wald chi-square = 7.92, P = 0.005; Fig. 2c). Recipients of thiorphan alone or NPC grafts alone exhibited lesser degrees of forelimb recovery compared with lesioned controls that did not reach statistical significance (Poisson generalized linear model, Wald chi-square = 2.16, P = 0.14 comparing thiorphan with lesion alone, and Wald chi-square = 2.07, P = 0.15 comparing grafts-only with lesion alone; Fig. 2c). The accuracy of pellet retrieval (percentage of pellets grasped that are eaten) also improved significantly in animals that received thiorphan + NPC grafts (Gamma generalized linear model, Wald chi-square = 10.13, P = 0.001) compared with lesioned controls (60% accuracy versus 30% accuracy; Fig. 2d). Thus, as suggested by in silico and subsequent in vitro screens, thiorphan significantly improves functional outcomes when combined with neural stem cell grafts to sites of SCI by enhancing the potency of NPC grafting.

To examine anatomical mechanisms underlying beneficial effects of thiorphan infusion on functional outcomes, we assessed corticospinal axon regeneration into stem cell grafts occupying the lesion site. Previously, we have shown that corticospinal axons regenerate into NPC grafts placed into sites of SCI and form synapses. Further, grafted NPC neurons extend axons from the lesion site to host neurons below the lesion and form synapses; consequently, new neural relays are formed across the lesion that support functional improvement13,16,17,18,19. In the present experiment, thiorphan significantly increased corticospinal regeneration into grafts by 60% (P < 0.05; Fig. 3a,c,e) compared with individuals that received NPC grafts alone (Fig. 3b,d,e and Supplementary Fig. 3a,b). Thiorphan administration in the absence of NPC grafts could not promote corticospinal regeneration into the lesion cavity because there was no cellular substrate onto which injured corticospinal axons could extend. Thin plane confocal microscopy showed colocalization of corticospinal axon terminals with synaptophysin apposed onto grafted neurons, indicating putative synapse formation from regenerating host axons to grafted neurons (Fig. 3f). Nearly all grafted animals in this experiment exhibited complete graft filling of the lesion cavity (Supplementary Fig. 4a,b). Cortical infusion of thiorphan over 4 weeks caused no damage or neuronal loss in the motor cortex (Supplementary Fig. 4c,d).

Fig. 3: Thiorphan increases corticospinal axonal regeneration.

a, CST axons labelled anterogradely with Flag (red) show greater regeneration into E14 neural progenitor stem cell grafts (green (green fluorescent protein (GFP))) in animals with thiorphan cortical infusions. The white dotted line indicates the host–graft interface; the boxed region is shown at higher magnification in c. b, Fewer corticospinal axons regenerate into animals that did not receive thiorphan cortical infusions. The white dotted line indicates the host–graft interface; the boxed region is shown at higher magnification in d. c,d, Higher magnification views of the boxed regions in a (c) and b (d) showing regenerating corticospinal axons. e, Corticospinal regeneration into graft occupying lesion site is increased 1.6-fold in the presence of thiorphan infusion into the motor cortex (*P < 0.05, two-tailed t-test). In the absence of a graft, no host axons are present in the lesion site; non-grafted animals could not be quantified. f, Regenerating host corticospinal axons form putative synapses with grafted neurons, based on colocalization of regenerating CST (red) with synaptophysin (SYN, white) apposed to grafted neuron (GFP, green). DAPI in blue. Arrows indicate the exact orthogonal view intersection point, single plane. Scale bars, 500 μm (a,b); 200 μm (c,d); 5 μm (f).

Source data

We also examined whether thiorphan treatment influenced corticospinal axonal sprouting above the lesion site: there were no significant differences in corticospinal axon density among the four animal groups (Supplementary Fig. 5a,b). Although thiorphan was administered into the motor cortex, we also examined whether there was a difference in the growth of serotonergic or sensory (calcitonin gene-related-peptide-labelled) axons into the graft; as expected, there was no difference between thiorphan + NPC graft and the diluent + NPC grafted groups (Supplementary Fig. 6a–f). We further examined whether thiorphan administration into the cortex influenced the host–graft glial border (glial fibrillary acidic protein immunoreactivity); it did not (Supplementary Fig. 7a–c). Finally, we examined whether thiorphan administration into the cortex affected graft differentiation: it did not (Supplementary Fig. 7d–k); as expected, neither did it affect graft-derived axon extension into the host (Supplementary Fig. 7l,m). Thus, beneficial effects of thiorphan administration were detectable on the corticospinal system to which it was targeted.

Testing in primate systems

The final step in this process, Step 5, extended the clinical relevance of this work by determining whether thiorphan can also promote growth from adult primate motor cortex and human cortical neurons (Fig. 4a–c). This step is performed last because these samples—particularly normal human cortex samples—are highly valuable. Human participant approval was obtained for these procedures. Neurons were isolated from the monkey M1 motor cortex, dissociated and cultured, adapted from ref. [2], and treated with 100 μM thiorphan for 5 days in vitro (two replicates). These cultures are free of NPCs when assessed by markers such as Nestin and Sox2. Thiorphan treatment significantly increased total neurite outgrowth by 36% (P < 0.001) and maximum neurite length by 61% (P < 0.0001) compared with control conditions (Fig. 4a–c). We then proceeded to culture the human cortex: normal cortex from the middle temporal gyrus of a 56-year-old man was obtained from biopsy, the tissue was dissociated and neuronal cultures established (adapted from ref. [2]; Supplementary Fig. 8). Treatment with 100 μM thiorphan for 5 days in vitro (Fig. 4d–f) resulted in a significant increase in total neurite outgrowth by 30.3% ± 7.3% (P < 0.0001) compared with control conditions. Thiorphan also exhibited a significant increase in longest neurite length by 23.0% ± 9.4% (P = 0.016) compared with controls. Thus, thiorphan retains biological activity when tested in monkey and human cortical cultures, exhibiting roughly 40% of the potency exhibited in rats in effects on total neurite outgrowth and 70% of the potency exhibited in rats in terms of longest neurite length.

Fig. 4: Thiorphan increases growth of monkey and human cortical neurons and induces pro-regenerative state.

a, Thiorphan significantly increased total neurite outgrowth from primary cultures of adult cynomolgus macaque motor cortex labelled for Tuj (***P < 0.001, two-tailed t-test). Control cultures received DMSO. Each point represents the total neurite length of individual neurons. Samples were run as technical duplicates, with neurons cultured for 5 days. b, Thiorphan treatment also significantly increased the maximum neurite length per cell by 1.8-fold (****P < 0.0001, two-tailed t-test). c, Representative images of cultures of adult primate motor cortex treated with diluent or thiorphan. d, Thiorphan significantly increased total neurite outgrowth from primary cultures of normal 56-year-old human cortex neurons labelled for Tuj (****P < 0.0001, two-tailed t-test). Neurons cultured for 5 days. Each point represents the total neurite length of one neuron. e, Thiorphan treatment of human cortical neurons also significantly increased the maximum neurite length per cell (**P < 0.01, two-tailed t-test). f, Representative images of 56-year-old human cortical neurons in culture labelled for Tuj1. g, RNA sequencing was performed on cultures of adult primary motor cortex from rhesus monkeys treated for 5 days with thiorphan or vehicle (DMSO). A total of 177 genes changed ±1.5-fold on a log_2 scale. h, Gene ontology of these 177 genes demonstrates clear enrichment for developmental processes (Gene Ontology database[24], https://doi.org/10.5281/zenodo.10536401). i, To identify in vivo mechanisms recruited by thiorphan treatment, rat brains were removed after 2 weeks of thiorphan infusion and compared with diluent-infused controls. Thiorphan treatment increased immunolabelling for both BDNF and phospho-AKT in the infused motor cortex, reflecting a shift to a state that is developmental and pro-regenerative. Scale bars, 20 μm (c,f). Scale bars, 25 μm, inset scale bars, 10 μm.

Thiorphan was identified as a potential candidate for improving axonal growth after CNS injury by virtue of its ability to shift the cellular transcriptome to an embryonic, pro-growth state. To assess whether this mechanism was actually recruited in neuronal target cells, we performed RNA sequencing (RNA-seq) of macaque M1 motor cortex cells exposed to thiorphan for 5 days in vitro compared with control cultures lacking thiorphan exposure (Fig. 4g). Because we had one sample of thiorphan-treated and one sample of vehicle (dimethylsulfoxide (DMSO))-treated cells, we compared mRNA species changing ± 1.5 log_2 units between the two samples: 177 genes reached this cut-off threshold (Supplementary Fig. 1c). Gene ontology of these 177 genes identified 29 biological processes and remarkably, 16 of these 29 were related to development, including neuron development, nervous system development, and synapse assembly (Fig. 4h). To further examine mechanisms associated with thiorphan delivery, we infused it intracortically for two weeks in rats and performed immunolabelling of the infused region compared with animals that received vehicle infusions: thiorphan administration resulted in increased expression of brain-derived neurotrophic factor (BDNF) (Fig. 4i) and phospho-AKT (Fig. 4i) in the infused region, paralleling higher levels of these molecules observed both in neural development and successful regeneration. These findings support a mechanistic framework in which thiorphan modifies the developmental, metabolic and signalling state of cells to impact neuronal regeneration, consistent with its initial identification on the basis of its ability to replicate the effects of SCI in driving neurons developmentally backward towards a state of embryonic development.

Discussion

We report the identification of a new and effective drug treatment for SCI arising from an analytical pipeline that targets the regenerative transcriptome of the adult corticospinal motor system. Notably, thiorphan was selected from a database of compounds that have already been tested in human clinical trials, facilitating potential clinical translation. Direct thiorphan infusion into the motor cortex was safe and effective in this experiment, and effects on neurite outgrowth were confirmed in adult rhesus monkey and human cortical cultures. Future studies will determine whether thiorphan exhibits efficacy after intrathecal administration, or after systemic administration because there is transient breakdown of the blood–brain barrier after SCI[20]. In addition, newly synthesized derivatives of thiorphan with improved blood–brain barrier permeability can be developed to simplify administration for clinical trials.

A previous study used in silico screens to identify compounds improving neural repair after peripheral nerve injury, based on dissection of whole DRG including neurons and support cells. The compound ambroxol was identified, which exhibited relatively modest effects in improving peripheral and optic nerve regeneration and cortical sprouting in a model of stroke, without evidence of functional efficacy6,21. By contrast, the present study started with a transcriptional dataset obtained from a specific neuronal population that is critical for human voluntary movement after SCI—layer V corticospinal neurons—rather than a general neuronal and glial RNA-seq dataset. We then used a CMap enrichment method[3] to more deeply probe the CMap dataset that led to the identification of thiorphan, triflusal and milrinone as the most likely potential mimics of the specific corticospinal regeneration transcriptome. We then used a new medium-throughput assay to test candidate drugs in the most faithful potential assay of adult brain neural injury examined to date: cultures of adult motor cortex neurons. Only thiorphan resulted in consistently significant and dose-dependent improvements in motor cortex neurite outgrowth. Other lead candidates (for example, triflusal, milrinone) did not increase neurite outgrowth, suggesting that a rigorous in vitro assay is essential to validate in silico targets, as in silico models may not fully capture the complexity of cellular responses. Subsequent in vivo testing of thiorphan yielded evidence of functional CNS recovery from this type of analytical pipeline. Moreover, thiorphan exhibited significant effects on neurite outgrowth of adult human neurons, supporting clinical translation. This platform can be applied broadly to other CNS disorders, potentially yielding several new candidate drugs to treat CNS injury and neurodegenerative disorders using compounds that have already been tested in humans for other indications and have yielded evidence of safety. A lack of safety results in the failure of up to one-half of human clinical trials[22], and the current pipeline can de-risk new drug development considerably.

Thiorphan induced recovery of motor function when combined with a neural stem cell graft to a site of severe cervical SCI. This improvement occurred within 2 weeks—a timeframe in which host corticospinal axons have already regenerated into stem cell grafts[1] and stem cell grafts have extended axons into the host cord below the lesion; indeed, stem cell implants extend axons rapidly into the host beginning 3 days after implantation[16]. Without a stem cell graft in the lesion site, there would be no cellular substrate onto which axons could regenerate into the lesion site with or without thiorphan administration. But in the presence of the stem cell substrate, thiorphan increased corticospinal axon regeneration into the lesion site by 60%. This presumably supported the formation of greater numbers of neural relays across the lesion site13,16,17,18,19 that, in turn, facilitated functional recovery. The lack of statistically significant recovery in our graft-alone group (P = 0.15) highlights the challenge of achieving forelimb functional restoration in this severe model. In previous studies, we used less severe lesion models and found that stem cells alone induced significant functional recovery. Yet in the present more severe lesion, the addition of thiorphan yielded significant and meaningful functional recovery.

Administration of thiorphan in vivo to rats with SCI resulted in elevated levels of BDNF and phospho-AKT in neurons, paralleling higher levels of these molecules observed during neural development. Confirmation that thiorphan actually induces complete reversion of corticospinal neurons to an embryonic transcriptional state[1] would require RNA-seq studies after in vivo infusions, and these were not performed. RNA sequencing of adult motor cortex cultures from macaque monkeys following thiorphan exposure did indicate a development shift in transcriptional state. Nonetheless, the link between thiorphan treatment and transcriptional change is indirect.

Conclusions

A pipeline of advanced in silico analysis coupled with improved in vitro screens identify the drug thiorphan as a candidate for the treatment of SCI. This platform can be adopted across nervous system disease states to accelerate the development of new therapies for human neurological disorders.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

All code for our analysis can be found at https://github.com/oganm/regenerationCMAP. The RNA sequencing results used in this manuscript can be found at the Gene Expression Omnibus (GSE126957). Source data are provided with this paper.

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Acknowledgements

We thank T. Beaumont of UCSD for collecting human brain samples for cultures. We thank the patient who provided biopsy tissue for research. This study was supported by the Dr. Miriam and Sheldon G. Adelson Medical Research Foundation (M.H.T.), Wings for Life grants WFL-US-12-17 8980EA and WFL-US-15-23 (E.A.v.N.), Veterans Administration Gordon Mansfield Consortium for Spinal Cord Regeneration B7332R (M.H.T.), NIH R01 NS104442 (M.H.T.) and R01 NS130033 (E.S.R.), and UCSD School of Medicine Microscopy Core NS047101.

Author information

Authors and Affiliations

1. Department of Neurosciences, University of California San Diego, La Jolla, CA, USA

E. A. van Niekerk, C. Marques de Freria, K. Groeniger, D. Kulinich, T. Riley, T. Vokes, E. S. Rosenzweig, E. Sinopoulou, M. J. Castle & M. H. Tuszynski

2. Department of Psychiatry, Michael Smith Laboratories, Djavad Mowafaghian Centre for Brain Health, University of British Columbia, Vancouver, British Columbia, Canada

B. O. Mancarci & P. Pavlidis

3. David Geffen School of Medicine, University of California Los Angeles, Los Angeles, CA, USA

R. Kawaguchi

4. Vascular Medicine Institute, University of Pittsburgh, Pittsburgh, PA, USA

S. Okawa

5. Brain and Spinal Injury Center, University of California, San Francisco, CA, USA

R. Huie & A. R. Ferguson

6. San Francisco Veterans Affairs Medical Center, San Francisco, CA, USA

R. Huie & A. R. Ferguson

7. Department of Neurological Surgery, University of California San Diego, San Diego, CA, USA

N. Kfoury-Beaumont & A. Khalessi

8. Veterans Administration Medical Center, San Diego, CA, USA

M. H. Tuszynski

Contributions

Conceptualization: E.A.v.N. and M.H.T. Methodology: E.A.v.N. and M.H.T. Investigation: E.A.v.N., K.G., C.M.d.F., T.R., A.K., N.K.-B., M.J.C., T.V., E.S.R. and E.S. Formal analysis: B.O.M. and P.P. Data curation: E.A.v.N., R.K., D.K., S.O. and R.H. Funding acquisition: E.A.v.N., E.S.R. and M.H.T. Supervision: M.H.T., A.R.F. and P.P. Writing—original draft: E.A.v.N. and M.H.T. Writing—review and editing: E.A.v.N., B.O.M., P.P., J.R.H., A.R.F. M.H.T.

Corresponding authors

Correspondence to E. A. van Niekerk or M. H. Tuszynski.

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van Niekerk, E.A., de Freria, C.M., Mancarci, B.O. et al. Thiorphan reprograms neurons to promote functional recovery after spinal cord injury. Nature 648, 402–408 (2025). https://doi.org/10.1038/s41586-025-09647-y

- Received: 12 June 2024

- Accepted: 18 September 2025

- Published: 29 October 2025

- Version of record: 29 October 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09647-y

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Synthetic α-synuclein fibrils replicate in mice causing MSA-like pathology

Domenic Burger,

Marianna Kashyrina,

Lukas van den Heuvel,

Hortense de La Seiglière,

Amanda J. Lewis,

Francesco De Nuccio,

Inayathulla Mohammed,

Jérémy Verchère,

Cécile Feuillie,

Mélanie Berbon,

Marie-Laure Arotcarena,

Aude Retailleau,

Erwan Bezard,

Marie-Hélène Canron,

Wassilios G. Meissner,

Antoine Loquet,

Luc Bousset,

Christel Poujol,

K. Peter R. Nilsson,

Florent Laferrière,

Thierry Baron,

Dario Domenico Lofrumento,

Francesca De Giorgi,

Henning Stahlberg &

…

François Ichas

Nature volume 648, pages 409–417 (2025)

Abstract

Multiple-system atrophy (MSA) is a rapidly progressive neurodegenerative disease of unknown cause, typically affecting individuals aged 50–60 years and leading to death within a decade1,2,3. It is characterized by glial cytoplasmic inclusions (GCIs) composed of fibrillar α-synuclein (aSyn)4,5,6,7,8, the formation of which shows parallels with prion propagation9,10. While fibrils extracted from brains of individuals with MSA have been structurally characterized[11], their ability to replicate in a protein-only manner has been questioned[12], and their ability to induce GCIs in vivo remains unexplored. By contrast, the synthetic fibril strain 1B13,14, assembled from recombinant human aSyn, self-replicates in vitro and induces GCIs in mice[15]—suggesting direct relevance to MSA—but lacks scrutiny at the atomic scale. Here we report high-resolution structural analyses of 1B fibrils and of fibrils extracted from diseased mice injected with 1B that developed GCIs (1BP). We show in vivo that conformational templating enables fibril strain replication, resulting in MSA-like inclusion pathology. Notably, the structures of 1B and 1BP are highly similar and mimic the fold of aSyn observed in one protofilament of fibrils isolated from patients with MSA[11]. Moreover, reinjection of crude mouse brain homogenates containing 1BP into new mice reproduces the same MSA-like pathology induced by the parent synthetic seed 1B. Our findings identify 1B as a synthetic pathogen capable of self-replication in vivo and reveal structural features of 1B and 1BP that may underlie MSA pathology, offering insights for therapeutic strategies.

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Main

MSA is characterized by the rapid invasion of the brainstem, the cerebellum and/or the basal ganglia by intracellular inclusions filled with fibrillar aSyn4,5,6,7,8. These inclusions appear in neurons and in oligodendrocytes (OLs), particularly within the myelinated bundles of the white matter16,17,18. The latter inclusions are called GCIs and are specific to MSA. They are observed only rarely in other sporadic α-synucleinopathies1,2. The phenomenon of a step-by-step progression that characterizes brain invasion by GCIs, and the speed at which the GCIs induce the death of neurons in myelinated tracts[1], has led to the notion that MSA may obey a molecular mechanism analogous to that governing the intracerebral diffusion of pathogenic prions9,10. According to this hypothesis, the specific aSyn fibril strain found in GCIs has a central role as both initiator and propagator of the pathology9,10.

aSyn fibrils in GCIs were first observed in situ4,5,6,7,8, and were extracted and described using electron microscopy (EM) more than 25 years ago19,20. Such fibrils, extracted using the detergent sarkosyl, were characterized at high resolution using cryo-transmission EM (cryo-EM)[11] but, to date, it has not been demonstrated that they can self-replicate like prions or induce the formation of GCIs in animal models. The hypothesis was put forward[12] that unknown cofactors might be required for the replication of these extracted assemblies.

In parallel to the extractive approach[11], three synthetic aSyn fibril strains were obtained from recombinant aSyn, and these fibrils could self-replicate in vitro without the need for an external cofactor and induce GCIs in mice. Chronologically, the first strain was a non-helical double-filament fibrillar assembly (ribbons) composed of monomers of human aSyn, capable of inducing GCIs, but only in rats overexpressing human aSyn concomitantly[21]. The second strain corresponded to mouse synthetic aSyn fibrils, which could induce the delayed appearance of GCIs in non-transgenic mice[22]. Finally, the third case concerned a fibril strain that some of us isolated and characterized (strain 1B), formed of human recombinant aSyn and causing the rapid appearance of GCIs in interfascicular OLs of wild-type (WT) mice[15]. In contrast to the aSyn fibrils extracted from patients with MSA, a high-resolution structure of these types of synthetic aSyn fibrils was lacking. This prevented the comparison of these fibrils to the atomic models obtained from patients to understand the structural basis of their ability to induce GCIs.

Here we report the structural characterization of aSyn fibrils of strain 1B at a resolution of 1.94 Å, and compare them to the aSyn filaments extracted from the brains of 1B-injected diseased mice in which GCIs formed (1BP, resolved at 3.8 Å). The marked structural similarity between 1B and 1BP demonstrates that a conformational templating and replication process is indeed taking place in vivo and that it is responsible for fibril growth and inclusion pathology buildup. Furthermore, the structural analogy of the 1B and 1BP fold with the human MSA fold found in patient 5 of the seminal study of Goedert’s group[11] suggests that a similar conformational replication process underlies MSA in humans.

MSA-like neuropathology seeded by 1B

1B fibrils present a typical rod-like compact appearance with a width compatible to the intertwining of two protofilaments[13] and a left-handed helicoidal twist (Extended Data Fig. 1a). We observed in our founder experiments that 1B had the ability to seed a particularly strong aSyn pathology in neuronal cultures (Extended Data Fig. 1b) and in vivo in mice13,14. In this early work, we found that the pathology induced by 1B at early timepoints was made of Lewy neurites, neuronal cytoplasmic inclusions (NCIs) and, notably, neuronal intranuclear inclusions (NIIs)13,14. Together with GCIs and glial nuclear inclusions (GNIs), NIIs constitute a key feature of MSA pathology, that is, they are distinctive for MSA compared with Parkinson’s disease or dementia with Lewy bodies (DLB), in which NIIs are absent23,24. This very cytopathological feature led us to investigate the possibility that the synthetic 1B fibrils could represent an MSA-like fibril strain. Using a directed anatomical approach and later timepoints, we observed that, 6 months after intracerebral inoculation, 1B was indeed capable of also causing the appearance of GCIs in the anterior commissure (AC) of WT mice[15], that is, in a major myelinated tract containing densely packed rows of interfascicular OLs. The time course and the prominence of the GCI pathology seeded in this tract supported the notion that, like in MSA24,25, the aSyn pathology seeded by 1B fibrils originated in neurons and was secondarily propagated to OLs[15].

After 24 months, a proper invasion of the posterior limb of the AC and of the bed nucleus of the stria terminalis (BNST) by GCIs was observed (Fig. 1a–e), while IBA1+ microglia did not particularly cluster around aSyn inclusion pathology (Fig. 1c,d). Confocal three-dimensional (3D) volume reconstructions of affected OLs in the BNST showed the typical flame-like cytoplasmic distribution of phosphorylated aSyn (Fig. 1e). The global distribution of GCIs in full horizontal brain sections from animals euthanized at 1.5, 12 or 24 months after 1B fibril injection in their right caudate putamen (CP) showed generalized spread of GCIs (Fig. 1f (green markers)). This was particularly prominent in the animal euthanized at 24 months: in addition to the AC and to the BNST, GCIs were found bilaterally in deep cortical layers and the subcortical white matter, the CP and unilaterally in the globus pallidus (GP) (injection side), the internal capsule (injection side), the entopeduncular nucleus (injection side), the substantia nigra (SN) pars reticulata (injection side) and the medullary reticular nucleus (contralateral side). A hovering section overview corresponding to Fig. 1a–e is provided in Supplementary Video 1.

Fig. 1: Seeding of GCIs and fibrillar pathology in WT mice by aSyn fibrils of the 1B strain.

a, Topographic immunofluorescenceanalysis of a horizontal brain section from a WT mouse injected 24 months earlier in the right CP with 1B fibrils. aSyn inclusions are labelled with anti-phosphorylated aSyn (#64, green), OLs with anti-SOX10 (red) and nuclei with DAPI (white). The section intercepts the AC and BNST (box). b, Higher-magnification view of the boxed region in a, showing invasion of the posterior limb of the AC (magnified in c) and BNST (magnified in d) by aSyn inclusions. c, The posterior limb of the AC: most interfascicular OLs contain aSyn inclusions, that is, GCIs. Sparse IBA1+ microglia (blue) are also visible. d, BNST: SOX10+ OLs contain aSyn inclusions (GCIs); sparse IBA1+ microglia are detectable. e, Confocal 3D reconstruction centred on three OLs of the BNST bearing GCIs, from the section shown in a. See also Supplementary Video 1. f, The neuroanatomical distribution of GCIs in brains at 1.5 (left), 12 (centre) and 24 (right) months after 1B injection into the right CP. Whole-brain horizontal sections are shown with every GCI manually annotated based on pS129aSyn and SOX10. The 24-month section corresponds to the N + 1 section adjacent to a. g, CLEM analysis of pS129aSyn+ regions. From left to right, an EM overview with light-microscopy correlation inset, a closer view of the pathology and a high-magnification view used for tomography to confirm fibrillar material are shown. The white arrowheads indicate fibrils. The light-microscopy inset shows the same region as for the EM, with an IHC/Toluidine Blue overlay and inverted colour for clarity. Scale bars, 500 µm (a), 100 µm (b), 20 µm (c and d), 5 µm (e), 3 mm (f), 10 µm (g, left), 1 µm (g, middle) and 0.5 µm (g, right).

Depending on the neuroanatomical structure and the timepoint under consideration, the experimental GCIs shown in Fig. 1f coexisted with a variable load of surrounding neuronal somatic aSyn inclusions (NCIs and NIIs), which represent the forefront of the somatic aSyn pathology at earlier timepoints to progressively make way to a growing population of GCIs, as previously reported15,22 (Extended Data Fig. 2). This is supportive of a neuronal-to-oligodendroglial inclusion transfer as in MSA24,25.

Seeding of GCIs by 1B was dependent neither on the mouse strain nor on the intracerebral injection site. When C57BL/6 mice (instead of 129SV mice) were inoculated with 1B above their right SN, 17 months later, numerous aSyn inclusions could be observed on the right side (Extended Data Fig. 3a,b). Note the depletion of tyrosine hydroxylase-positive neurons also on the right side of the pars compacta of this mouse (compare with Extended Data Fig. 3b,c). Here also, the aSyn inclusions comprised numerous GCIs as demonstrated by co-staining the OL nuclei with SOX10 (Extended Data Fig. 3a,b,d,e). They were particularly obvious at the boundary in between the pars reticulata and the pars compacta and were absent on the left side (Extended Data Fig. 3a,c,d,f). IBA1+ microglial cells were also observed but without evident signs of clustering around aSyn inclusions (Extended Data Fig. 3d–f).

Ultrastructure of the neuropathology

Correlative light and electron microscopy (CLEM)26,27 was used to study inclusions in the brains of C57BL/6 mice. Consecutive brain tissue slices were imaged using fluorescence microscopy to identify inclusions positive for aSyn phosphorylated at Ser129 (hereafter, pS129aSyn). Identified sections were then resin-embedded and heavy-metal stained, and serial ultrathin sections were collected consecutively on glass slides and on EM grids. Glass slides were used for immunohistochemistry (IHC) to relocalize the pS129aSyn+ cells and stained with Toluidine Blue. The recorded images were correlated with EM images taken on the consecutive grids. We used a mouse of the 1B-injected series corresponding to Extended Data Fig. 3a–f. We imaged 30 pS129aSyn+ inclusions in a region straddling the right GP and CP and followed them throughout the brain tissue by serial sectioning. We could identify fibrillar material and membranous cytoplasmic subcompartments in the pS129aSyn-positive areas. Room-temperature electron tomography analysis of various positions within the IHC-positive regions was used to verify fibrillar morphology, which showed fibrillar morphology in a dispersed, bundled and clustered arrangement (Fig. 1g and Extended Data Fig. 4). We additionally verified that the fibrillar material in the pS129aSyn+ IHC regions corresponded to aSyn protein assemblies using immunogold labelling (Extended Data Fig. 5).

The dispersed fibrillar material correlated with the pS129aSyn-positive signal in the IHC image and could be found throughout all observed inclusions in the tissue. Six cells with nuclei of more than 8.5 µm diameter were assumed to be neurons with NCIs, and 16 pathological cells with a nucleus size of below 8.5 µm were assumed to be GCIs in OLs. In many cases, the correlated area consisted of dispersed fibrillar material within a membranous local environment with various vesicular compartments. Fibril bundles could not be observed in all inclusions. If they were present, they varied strongly in length, thickness, curvature and localization within the cell. Measurement of the identified bundles in 23 inclusions throughout 5 brain slices showed an averaged bundle length of 0.81 ± 0.41 µm. In most cases, the bundle length was of a similar size of around 0.62 ± 0.07 µm. In a few exceptional cases, we measured bundles with individual lengths of 1.08 µm up to 3.64 µm (Fig. 1g). Fibrils appeared also in bigger clusters in irregular, chaotic arrangements, with fibrils radiating outward (Extended Data Fig. 4a).

Moreover, we could observe the regular proximity or direct contact of different and morphologically distinct cells to pathological ones (Extended Data Fig. 6). The morphology of these cells is reminiscent of cells described as dark microglia in mouse models of Alzheimer’s disease28,29, as well as of cells recently described in human post-mortem MSA brain[30].

To further challenge the pathogenic impact of 1B using a humanized in vivo model, we inoculated 1B fibrils into hemizygous transgenic M83 (M83+/−) mice expressing human SNCAA53T (encoding A53T aSyn). M83+/− mice have a normal lifespan and do not spontaneously develop fibrillar aSyn inclusions, despite the presence of one copy of the human SNCAA53T transgene9,10. We found that the intracerebral injection of 1B fibrils in M83+/− mice systematically caused their rapid demise in a notably synchronized manner after only 16 weeks (Fig. 2a). Mice at death presented numerous intracerebral aSyn inclusions, in particular in the posterior limb of the AC, in which the presence of Lewy neurite bundles, GCIs and GNIs could be observed (Fig. 2b,c). Non-seeded M83+/− mice of similar age were healthy and showed no intracerebral aSyn inclusions (Fig. 2b). This indicated that, similar to in the two previous WT mouse strains, 1B fibrils were able to also cause the buildup of an inclusion pathology with cytopathological elements typical of MSA in transgenic mice expressing human A53T aSyn.

Fig. 2: 1B is rapidly lethal to humanized M83+/− mice in which it seeds GCIs and GNIs.

a, Kaplan–Meier survival curves of 28 hemizygous transgenic mice expressing human A53T aSyn (M83+/−) without (14 mice, orange curve) or after (14 mice, purple curve) a unilateral injection (right CP) of 1B fibrils (the time of injection is indicated by the arrow). b, Illustrative concatenated immunofluorescence views of coronal brain sections of a 1B-injected M83+/− mouse at the time of death (left), and of a M83+/− mouse of similar age (right). The white boxes indicate the regions magnified below, centred on the posterior limbs of the AC. aSyn inclusions are revealed using the anti-phosphorylated aSyn antibody EP1536Y (green), nuclei are revealed with DRAQ7 (blue). Note the numerous GCIs and Lewy neurites in the AC of the 1B-injected M83+/− mouse (note that the AC is a white-matter tract that does not contain neuronal somata). Scale bars, 50 µm. c, 1B fibrils seed the buildup of aSyn GCIs and GNIs in OLs of M83+/− mice. Confocal imaging of a double immunofluorescence analysis of aSyn inclusions (pS129aSyn) and of the OL-specific nuclear marker SOX10 in sections of the AC. At the time of death (4 months after injection), many commissural OLs have GCIs (bottom image row). OLs containing both a GCI and a glial intranuclear inclusion can also be observed (top image row). Scale bars, 5 μm.

Source data

1B and its in vivo seeding product 1BP

Using cryo-EM, we determined the 1B fibril structure at a resolution of 1.94 Å (Fig. 3a and Extended Data Fig. 7). Fibrils were composed of two identical, twisting amyloid protofilaments in 2_1 screw symmetry, each comprising a pseudo-Greek-key motif consisting of nine β-sheets. The map resolved residues Gly36 to Lys97, and showed additional density attached alongside the starting sequence from Gly36 to Val40 and reaching towards the inside of the protofilament interface. As that density could not be unambiguously assigned to any side chains, we did not build an amino acid sequence for this stretch. The protofilaments form their longest β-sheet secondary structure from amino acids Val52 to Lys58, which forms the site of the main protofilament–protofilament interaction, stabilizing the protofibril interaction by hydrophobic and electrostatic interactions. The main electrostatic clusters are a positive group formed by Lys43, Lys45 and His50, and a negative group formed by Glu57 and Thr59, flanking the β-sheet (Extended Data Fig. 7c). Moreover, His50 appears to make an inter-rung connection within the same protofilament to the following subunit along the z direction to Lys45 (Fig. 3b). The interaction between His50 and Glu57 causes the protofilaments to arrange in a half-step of the typical helical rise, by binding to the next aSyn subunit of the opposite strand at the 2.36 Å and a resulting twist of 179.52°.

Fig. 3: Structural organization of the 1B aSyn fibrils and of the 1BP fibrils seeded by 1B in vivo.

a, Density maps of 1B and 1BP, respectively, visualized at a local resolution range of 1.9–4.8Å. The model of 1B was built within the resolved densities starting from Val37 to Lys97 (indicated). Wrapping around the stretch starting with Val37, an additional density is present on both protofilaments, although at a lower resolution (black arrowheads), which can also be observed at different positions in 1BP. Moreover, the structure of 1BP indicates highly flexible areas that are poorly resolved at those densities and close to the N-terminal region (red arrowheads). b, Side view onto the protofilament interface (only one protofilament is shown), revealing the characteristic rise of the amyloid filament and the inter-rung connection at His50 to Lys47 of the next aSyn subunit (N and N + 1). c, Sequence overlay of 1B (blue) and 1BP (orange). One protofilament is shown as a stick representation, and one is shown with only the backbone. The overlay indicates slight alterations in the overall interface of the fibrils, with an r.m.s.d. of 1.433 Å considering Cα atoms of a single protofilament (Supplementary Table 1). The magnified views of the protofilament interface highlight changes in interaction between side chains.

To identify the conformation of aSyn fibrils in the seeded pathology, we used the fibril purification method previously developed for human MSA brain tissue[11]. The purification was successful in M83+/− mice with disease 16 weeks after inoculation with 1B. Despite the low yield of material after the extraction procedure, pS129aSyn+ fibrils were observed in negative-stain imaging (Extended Data Fig. 8a). Subsequently, the sample was vitrified for structure determination using cryo-EM.

The extracted material was heterogeneous, with a limited concentration of suitable aSyn fibrils for structure determination. We solved the structure of the extracted fibrils, here termed 1BP, out of 40 micrographs (around 0.1%) to a resolution of 3.8 Å (Fig. 3a). 1BP fibrils are composed of two identical protofilaments of which the fold is highly similar to the 1B fibril seeding them (overall root mean squared deviation (r.m.s.d.) of one protofilament: 1.433 Å), confirming a prion-like templated misfolding mechanism that underlies inclusion formation in this mouse model. At the same time, an instance of strain adaptation can be observed at the interprotofilament interface, which spans from Val52 to Lys58 in 1B but is shifted by one amino acid in 1BP, where it spans from Gly51 to Glu57. This shift, which we suppose is driven by the A53T mutation expressed by M83+/− mice, brings the side chains in the 1BP steric zipper that point towards each other into adjacent positions—as in the case of Thr53 and Val55 (Fig. 3c)—increasing the distance between Cα atoms in the backbone of the two protofilaments by more than 2 Å compared with 1B. As a result, the intercalation of small hydrophobic side chains observed in 1B is lost in 1BP, but hydrophobic interactions between opposing protofilaments are still maintained.

The fundamental organization of a single protofilament of 1B shows similarities not only to 1BP but also to already published structures as well, mainly the patient-purified MSA fibrils[11] (Protein Data Bank (PDB): 6XYQ), the corresponding amplification[12] (PDB: 7NCK), the H50Q variant[31] (PDB: 6PEO) and the WT and 1–121 aSyn variants31,32 (PDB: 80QI and 6H6B) (Fig. 4 and Supplementary Table 1). The superimposition of these structures to 1B highlights differences in the positioning of Ile88 and Phe94. The region, which was previously reported as the C-pocket and acting as the binding site for thioflavin-T (ThT)[33], is identical in arrangement for a subset of structures and particularly in MSA fibrils (PDB: 6XYQ and PDB: 7NCK) and the H50Q variant (PDB: 6PEO). This is notable because, like the 1B fibrils, the H50Q fibrils (PDB: 6PEO) are also ThT negative[31]. Consequently, the inaccessibility of the Ile88 pocket seems important to account for the ThT negativity of 1B fibrils13,14 (Fig. 4a).

Fig. 4: The C- and N-pockets are the best templated regions between 1B and 1BP, are regions where ThT would have got bound (but here they are closed) and are the regions that are also closed in MSA and amplified MSA fibrils, all of which are ThT negative.

a, The conformation of one protofilament of 1B with surface volume representation. The structural comparisons of single protofilaments with a similar fold are summarized with the respective r.m.s.d. values in Supplementary Table 1. b, Magnified view of the arrangement of the C-pocket on the example of 1B (left; PDB: 9EUU) and 1–121 aSyn (right; PDB: 6H6B) and the arrangement of the N-pocket on the example of 1B (left; PDB: 9EUU), 1–121 aSyn (centre; PDB: 6H6B) and ThT-bound (grey) aSyn (right; PDB: 7YNM). c, The full modelled sequences with transparent surface volume, as well as a ribbon representation with stick representation of Tyr39, Lys45, Glu46, His50, Ile88 and Phe94 for all compared structures. The open or closed state of either the C- or N-pocket are indicated by the green and red arrows, respectively. Structural similarities are also given as r.m.s.d. values in Supplementary Table 1.

Moreover, the other ThT-binding pocket located at the N terminus (N-pocket)[33] of the fibrils also shows a modification compared with the structure of other ThT+ fibrils. In the 1B structure, Tyr39 is shifted so that it faces Thr44 and Glu46. As a consequence, Tyr39 is not available for interaction with ThT in the N-pocket. Note that a similar conformation of the N-pocket with a shifted Tyr39 presumably preventing ThT binding is also observed in the amplified MSA fibrils (PDB: 7NCK)[12] and the H50Q mutation (PDB: 6PEO), again consistent with the parallel observation that seed amplification products templated on MSA brain extracts or on MSA cerebrospinal fluid are ThT negative[34].

Collectively, these data support the hypothesis that closure of the ThT-binding pockets at the surface of the fibrils can explain the phenomenon of ThT invisibility and, at the same time, define the pathophysiological specificity of 1B, 1BP and MSA fibrils.

Besides regions involved in ThT binding, comparison with the other aSyn fibril folds also indicates the near-identical arrangement of the H50Q variant to the 1B structure, with the exception of the His50 inter-rung side-chain orientation due to the point mutation. Whether this orientation is important and confers specific MSA-like properties to 1B is unclear, especially as the >3 Å resolutions of PDB structures 6XYQ and 7NCK do not allow for conclusions on its existence in the MSA fibrils.

The 1B fibril structure also shows an outer, non-identified density stretch interacting with Gly36 to Val40 (Fig. 3a), a feature that is also present in fibrils amplified from MSA (PDB: 7NCK), in H50Q fibrils (PDB: 6PEO) and in 1BP fibrils where poorly resolved densities flank the N terminus (Fig. 3a). This is important, because these outer stretches in 1B block access of the disaggregase complex effector-component HSC70 to its binding site at the N terminus of the fibrils, therefore most likely preventing their disassembly and clearance[35]. This structural feature might therefore represent a reason for the acute in vivo seeding ability of 1B[14].

In situ pathology characterization

Despite repeated attempts, we were not able to recover enough fibrils from the brains of WT mice seeded with 1B for cryo-EM analysis, most likely because the inclusions are much less numerous than in 1B-injected M83+/− mice. We therefore used the conformation-specific amyloid probe h-FTAA[36] to characterize the GCIs seeded by 1B directly in WT mouse brain sections without extraction and to also compare them with the inclusions present in MSA (and DLB) post-mortem brain tissue sections. Indeed, in agreement with previous work[37], we observed a clear-cut difference between the signature of GCIs in MSA and that of Lewy bodies in DLB using fluorescence lifetime imaging microscopy (FLIM) of h-FTAA (Extended Data Fig. 9). Using this in situ approach, we observed that the signature of the MSA inclusions was similar to that of the 1B brain inoculum in our mouse experiments and even closer to the signature of the inclusions seeded by 1B (Extended Data Fig. 10 and Supplementary Table 3). This was also in good agreement with the fact that the inclusion pathology seeded by 1B appeared positive to the MSA-specific silver impregnation staining technique of Gallyas[38], further suggestive of a structural analogy between 1B, 1B-seeded fibrils in WT animals and MSA fibrils in GCIs in human brain tissue sections (Extended Data Fig. 11). This is the same conclusion that we drew from the cryo-EM structural comparisons of 1B with 1BP and MSA fibrils that were extracted from brain tissue (Fig. 4 and Supplementary Table 1).

In vivo passage

Finally, given the marked similarity between 1B, 1BP and MSA filaments, we sought to determine whether 1BP raised in transgenic animals could still trigger MSA-like neuropathology in WT animals, as synthetic 1B does. To address this question, we faced the challenge of the very low yield of the sarkosyl-based purification protocol for extracting 1BP from 1B-seeded diseased mice—a yield that is insufficient to obtain the amount of intact fibrils required for in vivo reinoculation experiments. To overcome this limitation, we instead used a tenfold dilution of a total brain homogenate from a 1B-seeded diseased mouse as the inoculum, without any purification step. We also focused on early post-injection effects (6 weeks) to maximize the likelihood of detecting a seeded synucleinopathy driven by trace amounts of 1BP fibrils delivered by the inoculum (that is, 2 μl of tenfold-diluted whole-brain homogenate). Our results indicate that the amount of 1BP contained in the inoculate reached a critical value sufficient to seed anew an inclusion pathology in WT mice with the formation of NCIs, NIIs, GCIs and GNIs (Fig. 5), similar to what is observed when using synthetic 1B fibrils as seeds13,14,15.

Fig. 5: Early seeding of MSA-like pathology in WT mice by brain homogenates containing 1BP seeds.

Diluted crude brain homogenates were prepared from prematurely dying M83+/− mice injected 4 months earlier with 1B fibrils. These homogenates were injected into the right CP of WT 129SV mice. After 6 weeks, the mice were euthanized and the brains were processed for horizontal sectioning and immunofluorescence neuropathology. a–c, aSyn inclusions were revealed with anti-phosphorylated aSyn (EP1536Y, green) antibodies, the nigrostriatal tract with anti-tyrosine hydroxylase (TH, red) antibodies and nuclei with DAPI (white). a, One animal is shown with four sections spanning the nigrostriatal tract dorsoventrally. The green dots annotate aSyn inclusions (Lewy neurites, NCIs, NIIs, GCIs and GNIs). b,c, Close-up views of the different inclusion types annotated in a. d,e, Further examples of MSA-specific aSyn inclusions seeded by 1BP-containing homogenates. The sections were stained with TH (turquoise, shown only in d), SOX10 (red, OL marker) and pS129aSyn (#64, green) antibodies, and DAPI (white, shown only in e). Images are from the right SN. d, Four dopaminergic neurons (TH-positive cytoplasms) and four OLs (SOX10-positive nuclei) are visible (DAPI omitted for clarity). Three MSA-typical inclusions are present: two NIIs and one GNI. e, Among eight cells, four OLs aligned in a row and one solitary OL are visible; one OL harbours a nuclear inclusion (pS129aSyn, GNI). As control, diluted homogenates from spontaneously dying homozygous M83+/+ mice were used. Although these brains contain aSyn inclusions, they are not MSA-type, and their homogenates did not induce inclusion pathology in recipient WT mice (not shown). Scale bars, 3 mm (a) and 10 µm (b–e). 3D reconstructions and corresponding videos of selected inclusions are provided in Supplementary Videos 2–6.

Given the structural similarity of the synthetic 1B seed (which does not undergo any sarkosyl purification before cryo-EM analysis) and of 1BP (which does go through this detergent-based purification step before cryo-EM), we can deduce that the extraction procedure has no substantial impact on the structural arrangement of 1BP, which is essentially acquired by templating. Moreover, consistent with the notion that non-extracted 1BP and 1B have similar structures, the pathology seeded by brain homogenates containing 1BP is identical to the one seeded by synthetic 1B.

Together, this indicates that the 1B strain characteristics are encoded in the pseudo-Greek-key motif of the 1B/1BP fold rather than in the unattributable densities specifically observed in either 1B or in 1BP after adaptation. It also indicates that the widening and the sliding of the protofilament interface acquired in 1BP do not impinge on the MSA-like pathology-inducing characteristics of 1B/1BP.

This is in agreement with the observation that the seeding of inclusions by 1B in cultured neurons is insensitive to mutations affecting residues located at the protofilament interface (H50Q, G51D, A53T and A53E) and, instead, it is abrogated by the mutation E46K, which disrupts the Glu46–Lys80 salt bridge latch that is necessary for the stabilization of the pseudo-Greek-key motif in the 1B fold (Extended Data Fig. 12). Notably, the differential impact of the various aSyn mutations on the replication of 1B that we report here is similar to what was reported previously for MSA ‘prions’39,40.

In conclusion, the unattributed densities in 1B and 1BP, as well as the interface adaptations observed in 1BP, do not appear to have a large role in the pathogenic activity of 1B/1BP. In other words, the fold kernel shared by 1B, 1BP and MSA filaments is probably necessary and sufficient to induce both MSA and MSA-like neuropathologies.

The fold kernel of 1B, which is templated with the highest fidelity in 1BP, forms the closed N- and C-pockets (Supplementary Table 1). As previously discussed, such closure accounts for the ThT invisibility of both 1B13,14 and the amplified MSA filaments[34]. This is particularly relevant given that ThT invisibility is also observed in two other synthetic fibril assemblies of unknown structure, both of which were reported to seed GCIs in vivo21,22,41.

It is therefore tempting to speculate that closed N- and C-pockets are also present in these latter fibrils, further supporting the idea that, within the fold kernel shared by 1B, 1BP and MSA filaments, the closure of the N- and C-pockets represents the minimal common structural determinant responsible for the induction of both MSA and MSA-like pathology.

Discussion

Here we present the structures of aSyn fibrils 1B as well as of their in vivo seeding product 1BP. Indicative of a high-fidelity conformational replication process, the structures present a high similarity and can perpetuate MSA-like pathology through passage in humanized and WT mice.

This study provides evidence of a protein-only replication process occurring in vivo and evidenced at a resolution of 3.8 Å. The templating fidelity of the synthetic 1B seeds, both in vitro and in the mouse brain, is important given the difficulty of efficiently amplifying MSA brain extracts with structural preservation[12]. Although we cannot rule out the presence of additional fibril polymorphs different from 1BP in the 1B-inoculated mouse model that may have arisen through secondary nucleation and are undetectable by cryo-EM, the robust propagation of the 1B protofilament fold provides strong support for a prion-like templating mechanism.

This notion is strengthened by our observation that brain homogenates containing 1BP can trigger in WT mice the same MSA inclusion pathology as the one seen after 1B injection, indicating that untemplated secondary nucleations, if any, do not have a substantial role in the MSA pathology seeded by 1B. Instead, the kernel common to 1B and 1BP, here termed the MSA kernel, defines through a templated replication the strain characteristics of the fibrils. This MSA kernel is shared in one of the two protofilaments of MSA fibrils extracted from patient 5 in the seminal study[11], as well as the MSA fibrils resulting from the in vitro amplification of the same patient’s sample[12]. To date, it was not possible to purify the fibrils naturally occurring in homozygous M83+/+ mice to compare them with the templated structure of 1BP using cryo-EM. However, we observed that brain homogenates from dying M83+/+ mice were not capable of eliciting any synucleinopathy when injected into the brain of WT mice like it is the case for 1BP-containing brain homogenates (see also Fig. 5 legend). This suggests that either the fibrils in the brains of spontaneously dying M83+/+ mice are a different polymorph, or the fibril titre is too low for stable transmission. Notably, the templating fidelity of the MSA kernel between 1B and 1BP is most pronounced in two particular regions—the N- and C-pockets. These two regions are of particular interest because they define the binding sites for the amyloid probe ThT[33], but are closed and not accessible to the dye in the MSA kernel. Our data suggest that structural features of aSyn fibrils—specifically closed N- and C-pockets—are related to their ThT invisibility and their seeding properties, in particular their ability to seed GCIs. This is consistent with the fact that the three synthetic fibril assemblies that have been reported to induce GCIs in mice and rats are all weak ThT binders, and that the fibrils amplified from MSA patient brain samples and CSFs[34] are ThT negative as well.

This collectively points to a major pathophysiological role of C- and N-pocket closure with direct relevance to MSA.

In the MSA kernel, the specific binding site around the C-pocket of Ile88 is closed by forming a lever with Phe94, mainly caused by the outward orientation of Ile88. Compared with other aSyn fibril structures with an open C-pocket, in 1B/1BP, the inner hook of the pseudo-Greek-key motif along the stretches of Val74 to Phe94 is shifted by one amino acid position starting at Ala85. As a result, Ala85 points outwards at the most prominent position of the inner hook, which causes a consequential inversion of sidechain positioning for the remaining sequence. In 1B/1BP, this causes Ser87—a known modification site for fibril inhibition by O-Glc-N acylation[42] or by phosphorylation[43]—to be inaccessible and Ile88 to be positioned outwards, undergoing a connection with Phe94 and therefore closing the C-pocket.

Enforcing the post-translational modification of Ser87 or forcing open the C-pocket using small molecules might therefore represent promising means to derail the templating process during fibril growth, and force fibril elongation to take place on a modified template which has lost part of the MSA kernel. This would presumably not prevent fibril growth but could perhaps impinge on the acute replicative and toxic properties of MSA fibrils and slow down disease progression.

The closed N-pocket is a shared characteristic of the 1B and 1BP structures, and this was also observed in the amplified MSA filaments from patient 5 (ref. [12]). However, fibrils extracted from patients with MSA[11] did not share the closed N-pocket conformation (Fig. 4 and Supplementary Table 1). Whether this points to a dispensable pathogenic role of N-pocket closure remains to be determined.

Finally, we note that the ability of crude brain homogenates from patients with MSA to seed pathological inclusions in WT mice has, to our knowledge, not been reported to date. This may be due to a lack of systematic investigation, or it may suggest that the fibrils present in human MSA brain samples are intrinsically less aggressive than 1B or 1BP fibrils. The latter would explain why human MSA brain extracts trigger little MSA-like pathology in M83+/− animals[9]. If so, the higher infectivity of the 1B/1BP strain could result from the specific structural features not shared with patient-derived fibrils. Notably, these include (1) a closed versus open N-pocket; (2) the pseudosymmetric arrangement of two identical protofilaments in 1B/1BP, as opposed to the asymmetric fold of two distinct protofilaments in MSA fibrils; and (3) additional, unattributed densities in 1B and 1BP, which—although distinct—may obscure chaperone clearance sites in both. The relevance of these structural differences remains to be determined. Regardless of the precise mechanism underlying the high seeding efficiency, it is important to emphasize that, in the absence of previous structural knowledge of synthetic or patient-derived α-synuclein fibrils, such materials should be handled with extreme caution.

Taken together, this study demonstrates the existence of a synthetic aSyn fibril strain that is capable of inducing MSA-like pathology in WT mice and replicates in M83+/− mice through a protein-only templating process. The structures of the fibril seeds and of fibrils formed in vivo highlight the similarity of 1B and MSA fibrils, and postulate a link between fibrillar structure, assembly, mechanism of prion-like seeding and spreading, as well as animal-to-animal transmission.

Methods

aSyn expression

Escherichia coli strain BL21(DE3) was transformed with pT7-7 aSyn WT vector[43] from Addgene, (plasmid 36046) and plated onto a Luria broth (LB) agar plate containing ampicillin (100 μg ml−1) and 1 g l−1 glucose. A preculture in 5 ml of LB medium was inoculated with one clone and incubated at 37 °C under 200 rpm shaking for 4 h. Cells from the LB preculture were recovered by centrifugation (1,000g, 10 min) and used for inoculating 200 ml of LB medium. Cells were grown overnight at 37 °C under 200 rpm shaking and then diluted in 2 l of culture. Protein expression was induced by adding 0.5 mM isopropyl-β-d-thiogalactopyranoside during the exponential phase, evaluated at an optical density at 600 nm of 0.6. Cells were collected after 5 h of culture at 30 °C by centrifugation at 7,000g and 4 °C for 20 min (JLA 8.1000, Beckman Coulter), and the pellet was kept at −20 °C until purification.

aSyn purification

The pellets were resuspended in lysis buffer (10 mM Tris and 1 mM EDTA (pH 7.2) with protease inhibitor tablets (cOmplete, EDTA-free protease inhibitor cocktail, Roche)) and sonicated at 50% maximum energy, 30 s on and 30 s off for three rounds with a probe sonicator (Q-Sonica). The sonicated pellets were centrifuged at 20,000g for 30 min, and the supernatant was saved. The pH of the supernatant was then reduced to pH 3.5 using HCl, and the mixture was stirred at room temperature for 20 min and then centrifuged at 60,000g for 30 min. The pellets were discarded. The pH of the supernatant was then increased to pH 7.4 with NaOH and then dialysed against 20 mM Tris-HCl (pH 7.4) and 100 mM NaCl buffer before loading onto a 75 pg HiLoad 26/600 Superdex column equilibrated with the same buffer on the ÄKTA pure system. Monomeric fractions were collected and concentrated if needed by using the Vivaspin 15R 2 kDa cutoff concentrator (Sartorius Stedim). Purification fractions were analysed by polyacrylamide gel electrophoresis (PAGE) Tris-tricine 13% dying with ProBlue Safe Stain. The protein concentration was evaluated spectrophotometrically on the basis of the absorbance at 280 nm and an extinction coefficient of 5,960 M−1 cm−1. Quantification of the preparations using the Pierce chromogenic LAL kit indicated a low endotoxin (lipopolysaccharide, LPS) residual value of 0.03–0.06 EU μg−1 of recombinant protein.

aSyn fibrillization

Solutions of monomeric aSyn at 4 to 5 mg ml−1 in saline (H_2O, 100 mM NaCl and 20 mM Tris-HCl pH 7.40) were sterilized by filtration through 0.22-μm Millipore single-use filters and stored in sterile 15 ml conical Falcon tubes at 4 °C. Sterilized stock was then distributed into safe-lock Biopur individually sterile-packaged 1.5 ml Eppendorf tubes as 500 μl aliquots and were seeded with 1% of 1B strain fibrils13,14,15. The tubes were cap-locked and additionally sealed with parafilm. All of the previous steps were performed aseptically in a particle-free environment under a microbiological safety laminar flow hood. The samples were loaded in a ThermoMixer (Eppendorf) in a 24-position 1.5 ml Eppendorf tube holder equipped with a heating lid. The temperature was set to 37 °C with continuous shaking at 2,000 rpm for 4 days. 1B templating of the fibrillization products was quality-checked using the fibrilloscope13,14,15.

Sonication

Before intracerebral injections, 1B aSyn fibril stocks (4 mg ml−1) were distributed in cap-locked, sterile 0.5 ml PCR tubes (Thermo Fisher Scientific). Sonication was performed at 25 °C in the Bioruptor Plus water bath sonicator (Diagenode) equipped with thermostatic control and an automated tube carousel rotator. The sonication power was set to high, and 10 cycles of 30 s on followed by 10 s off were applied. In agreement with our previous quantifications[14], over 80% of the fibrils were 50-nm long or less after application of this protocol (not shown).

In vivo aSyn pathology

Adult 129SV (intrastriatal injections), C57BL/6 (nigral injections) and transgenic M83 (hemizygous, intrastriatal injections) mice were housed in a temperature-controlled (22 °C) and light-controlled environment under a 12 h–12 h light–dark cycle with forced ventilation (humidity below 50%) and with access to food and water ad libitum. All of the experimental procedures were conducted in accordance with the European Communities Council Directive (2010/63/EU) for care of laboratory animals. The study design was approved by the ethics committees of the University of Bordeaux, of the ANSES/Ecole Nationale Vétérinaire d’Alfort/Université Paris-Est Créteil and of the University of Salento, and authorized by the French Ministry of Higher Education and Research and by the Italian Ministry of Health (APAFIS 33147-2021091711598830 v6, APAFIS 37712-2022061615206629 v8, 0013178-P-17/05/2019). The mice (aged 6–8 weeks) unilaterally received 2 μl of sonicated aSyn fibrils 1B (4 mg ml−1) by stereotactic delivery at a flow rate of 0.4 µl min−1, and the pipette was left in place for 5 min after injection to avoid leakage. Delivery was performed within the right striatum (coordinates from bregma: anteroposterior (AP), −0.1; lateral (L), +2.5; dorsoventral (DV), +3.8), or above the right SN (coordinates from bregma: AP, −2.9; L, −1.3; DV, −4.5). WT mice (n = 20) and transgenic M83 hemizygous mice (n = 28) injected with either PBS, 1B fibrils or brain homogenates were euthanized after 6 weeks, 17 months, 24 months or when reaching the humane end points defined as death regarding the transgenic M83 mice, and were transcardially perfused with either Tris-buffered saline (pH 7.4) followed by 4% paraformaldehyde in PBS pH 7.4 at 4 °C, or with cacodylate buffer 0.1 M with 1 mM CaCl_2 (pH 7.4) followed by 4% paraformaldehyde plus 0.1% glutaraldehyde in 0.1 M cacodylate buffer (pH 7.4). Brains were subsequently postfixed in the same fixative. For standard neuropathology, the brains were paraffin embedded, and 10-µm-thick sections were cut using a rotative microtome (Leica). The sections of interest were deparaffinized and processed for epitope retrieval: the slides were immersed in citrate buffer pH 6 (Dako Agilent Technologies) and placed into a pressure cooker (Bio SB) at 114–121 °C for 10 min. After a cooling period of 20 min, the slides were washed twice for 5 min in PBS at room temperature. The slides were then processed for simple or double immunofluorescence using the following primary antibodies diluted at 1:500, or their combinations: EP1536Y (Abcam) or pSyn#64 (Wako) for detecting pS129aSyn-positive inclusions; LB509 for detecting human aSyn (Abcam, mouse monoclonal); anti-SOX10 (Abcam, rabbit monoclonal) for detecting OL nuclei; EP1532Y and anti-TH raised in chicken (anti-tyrosine hydroxylase, Abcam) for detecting the nigrostriatal tract; and anti-IBA1 (Abcam) for detecting microglia. DRAQ7 or DAPI were used to image the nuclei. The AlexaFluor-coupled secondary antibodies were from Thermo Fisher Scientific (Alexa 488, 568 and 674). The sections were acquired using a Pannoramic slide scanner (3D HISTECH, MM France) in epifluorescence mode, and multichannel fluorescence optical sections of the samples were performed (thickness, <0.8 µm) using either a Zeiss CD7 platform of a Leica SP5 laser-scanning confocal microscope equipped with a spectral detector, 488, 561 and 633 nm laser lines, a motorized xy stage and a mixed stepping motor/piezo z controller. The objective was ×40, and the z step size was set to 0.5 µm to produce stacks of 15 to 20 z planes. The pinhole was set to 1 airy unit. For 3D reconstructions and volume rendering/animations (corresponding to 360° tilt series of composite maximum pixel projections images), raw three-channel z-stack images were processed offline using Icy[44] (v.2.4.0.0).

HCA

Timed inbred-pregnant C57BL/6JOlaHsd (aSyn-knockout) female mice were received from Envigo 2 days before initiation of the primary culture. The pregnant mouse was euthanized by cervical dislocation, and the aSyn-knockout embryos (embryonic day 18) were surgically extracted and cold-euthanized. Cortices were collected from eight of them, pooled and dissociated enzymatically and mechanically (using a neural tissue dissociation kit, C Tubes and an Octo Dissociator with heaters; Miltenyi Biotech) to yield a homogenous cell suspension pool of eight individuals. The cells were then plated at 20,000 per well in 96-well plates (Corning, BioCoat poly-d-lysine imaging plates) in neuronal medium (MACS Neuro Medium, Miltenyi Biotech) containing 0.5% penicillin–streptomycin, 0.5 mM alanyl-glutamine and 2% NeuroBrew supplement (Miltenyi Biotech). The cultures were maintained under 5% CO_2 at 37 °C in a humidified atmosphere. The medium was changed by one-third every 3 days, until 30 days in vitro (DIV). In such cultures, and under control conditions, neurons represented approximately 85 to 95% of the cell population; thus, for simplicity, they are here referred to as neurons. After 7 DIV, vehicle and sonicated 1B aSyn fibrils were added at a final concentration of 10 nM equivalent monomeric concentration. When relevant, neurons were infected at DIV 10 with AAV (adeno-associated virus) particles (multiplicity of infection, 1,000) carrying the cDNA of aSyn and its variants under the control of the human synapsin promoter, as previously described[14]. High content analysis (HCA) was performed after fixation and double immunofluorescence staining with the conformation-dependent SynF1 antibody (mouse monoclonal, BioLegend) and the human aSyn-specific MJFR1 antibody (rabbit monoclonal, Abcam) as previously described on images acquired at ×20 using the generic analysis module of an Incucyte S3 (Sartorius) system with Top-Hat segmentation[14]. For quantifications, the signal integral of the segmented areas in each field of view was recorded. Primary neuronal cultures from C57BL/6 embryos physiologically expressing endogenous mouse aSyn and not transduced with any AAV vector (Extended Data Fig. 1) were produced and analysed similarly but after fixation at DIV 24 and after revealing pS129aSyn with EP1536Y and human aSyn with LB509 antibodies.

CLEM analysis

The CLEM protocol was performed as previously described26,27. In brief, sections (thickness, 20–40 µm) were cut from perfused mouse brain on a vibratome (Leica VT1200). Immunolabelling against aSyn pathology allowed for the identification of immunopositive sections to be used for further processing with EM. For this, the sections were incubated overnight with a primary EP1536Y (Abcam) antibody at 4 °C followed by Alexa-conjugated secondary antibody staining together with DAPI for cell nuclei identification. Fluorescence images were acquired using the Leica Thunder Tissue Imager equipped with the K8 fluorescent camera. Chosen sections with strong aSyn pathology were prepared for EM by post-fixing in reduced 2% osmium, thiocarbohydrazide and 2% osmium tetroxide, followed by contrasting in 2% uranyl acetate and lead aspartate treatment at 60 °C. The sections were dehydrated with an increasing acetone gradient, before infiltration with EMBED 812 resin for final flat embedding. The hardened sections were imaged again using light microscopy and the sections were overlayed with the overview fluorescence map by using identifiable tissue features. Regions of interest were marked and the coordinates used for laser dissection. The resulting blocks were laser cut using the Leica LMD7 system and glued onto a resin block. Serial sectioning with an ultra-microtome (Leica UC7) produced 120–200-nm-thick tissue sections that were alternatingly collected on EM grids (slot and hexagonal grids) or glass slides. The glass slides were further processed for IHC and Toluidine Blue staining.

Light-microscopy images were acquired at ×40 magnification and correlated to each other for the generation of an image overlay of pathology signal (IHC) and high-contrast tissue morphology (Toluidine Blue). The resulting overlays were then correlated to low magnification (×640 nominal magnification) EM overviews for cell identification by using identifiable tissue features both in the LM and EM images. The identified pathology was finally imaged and merged at high magnification in a tile acquisition series. For EM image acquisition, a Thermo Fisher Scientific Talos F200C with a CETA camera or a CM100 (Phillips) with a TVIPS F416 camera were used. Light-microscopy and EM images were adjusted for brightness and contrast where necessary.

On-grid immunogold labelling and analysis

EM grids with tissue sections were placed on a droplet of etching solution (1% periodic acid in water, Sigma-Aldrich), with the sections facing down, for 2.5 min. The grids were washed three times for 2 min in double-distilled H_2O, then washed twice for 2 min in washing buffer (stock solution of 10% BSA, Aurion, which was 1:50 diluted in double-distilled H_2O), and blocked in blocking solution (Aurion) for 5 min to reduce non-specific binding. The grids were then incubated with primary antibodies (EP1526Y, Abcam, 1:50 diluted in washing buffer) for 60 min, washed 6 times for 2 min in blocking buffer and then incubated in a solution of gold nanoparticles with a size of 10 nm (protein A gold, Aurion, 1:50 diluted in washing buffer) for 90 min. They were washed three times for 2 min in blocking solution, three times for 2 min in washing buffer and four times for 1 min in double-distilled H_2O. Finally, the grids were post-stained in 1% uranyl acetate for 1 min and washed three times for 10 s in double-distilled H_2O. The sections were imaged using a transmission electron microscope (Thermo Fisher Scientific, Talos L120C), operated at an operating voltage of 120 kV, and images were recorded using a Thermo Fisher Scientific Ceta camera.

Gold particles were detected automatically in the recorded EM images, using FIJI[45], by applying a difference-of-Gaussian filter (sigma1 = 10 nm, sigma2 = √2 × sigma1). The resulting image was binarized with a manually selected threshold. Particle detections with an area smaller than 25 nm^2 and a circularity (4π × area/perimeter^2) below 0.8 were excluded from analysis. The local density of gold was calculated as the decadic logarithm of the sum of a pixel’s distance to the 15 closest neighbouring gold particles. The gold particle detection was implemented as a FIJI macro and the density calculation as a Python notebook.

Electron tomography and 3D reconstruction

Electron tomography data were collected using the Tomography software (Thermo Fisher Scientific) with multisite batch acquisition on the Thermo Fisher Scientific Talos F200C system with tilt series covering −60° to +60° in 2° steps. Tomograms were reconstructed using IMOD[46] and filtered with a non-local-means filter with Amira (Thermo Fisher Scientific, Amira v.2021.2). For segmentation, nuclear membranes, fibrils and other membranous parts were manually annotated and traced throughout the tilt-series using Amira. Every few slices, the respective feature of interest was selected by drawing directly onto the image and then interpolated to generate an accurate 3D volume. The final volume was visualized directly in AMIRA.

aSyn purification from brain homogenate

Extraction of the sarkosyl-insoluble fraction of a transgenic M83+/− mouse brain 16 weeks after inoculation with 1B was done using the same procedure as was previously published for fibrils purified from a patient with MSA[11]. In brief, brain tissue was homogenized in 20 vol. (v/w) extraction buffer consisting of 10 mM Tris-HCl, pH 7.5, 0.8 M NaCl, 10% sucrose and 1 mM EGTA. Homogenates were brought to 2% sarkosyl and incubated for 30 min at 37 °C. After a 10 min centrifugation at 10,000g, the supernatants were centrifuged at 100,000g for 20 min. The pellets were resuspended in 500 μl g−1 extraction buffer and centrifuged at 3,000g for 5 min. The supernatants were diluted threefold in 50 mM Tris-HCl, pH 7.5, containing 0.15 M NaCl, 10% sucrose and 0.2% sarkosyl, and centrifuged at 166,000g for 30 min. Sarkosyl-insoluble pellets were resuspended in 100 μl g−1 of 30 mM Tris-HCl, pH 7.4.

Immunogold labelling and negative staining of sarkosyl purification

A total of 3 µl of non-diluted sample was applied to 100 mesh Ni grids with formvar support (Electron Microscopy Sciences) that were glow-discharged at 15 mA for 60 s. After a 10 min incubation time, the grid was blotted, washed three times for 5 min with incubation solution (0.2% BSA-c/PBS; Aurion) and incubated for 1 h at room temperature in a solution of pS129aSyn antibody (EP1536Y, Abcam, ab51253) diluted 1:100 in incubation solution. The grid was washed six times for 5 min and incubated for 2 h in a solution containing gold nanobeads (diameter 6 nm) coupled to an anti-rabbit antibody (Aurion), diluted 1:50 in incubation solution. After washing six times for 5 min in incubation solution and three times for 5 min in PBS, the grid was immersed in 1% uranyl acetate for 40 s, blotted and air-dried. The grid was imaged on the Talos transmission electron microscope at an operating voltage of 200 kV (Thermo Fisher Scientific).

Cryo-EM analysis

Recombinant 1B fibrils

Cryo-EM grids were prepared using the Leica GP2 plunge freezer in a BSL-2 environment at room temperature. Quantifoil 300-mesh gold grids were glow-discharged in air for 90 s. Grids were prepared using 3 µl of 1:1 and 1:2 diluted fibril samples in preparation buffer (H_2O, 100 mM NaCl and 20 mM Tris-HCl, pH 7.40) and vitrification by rapid freezing in liquid ethane. The grids were screened for the presence of non-clustered fibres and high-resolution images were acquired with an automated EPU (v3.10) setup on the Thermo Fisher Scientific Titan Krios G4 electron microscope equipped with a cold-FEG 300 kV electron source and a Falcon4i camera. In total, 11,879 dose-fractionated videos (EER) were collected with a total dose of 40 e− Å−2 at a pixel spacing of 0.66 Å at the sample level. A defocus range of between −0.8 μm and −1.8 μm was used during the acquisition.

Purified 1BP fibrils

The sarkosyl-insoluble fraction of a transgenic M83+/− mouse brain was diluted 1:3 in Tris-HCl, 50 mM, 150 mM NaCl, pH 7.4 and 2.5 µl was applied to a Quantifoil 300-mesh gold grid, coated with an additional 5-nm-thick carbon layer. The grid was not glow-discharged. Then, 30 s after applying the sample, the grid was blotted from the front side for 6 s and plunge-frozen at room temperature and 80% humidity in a Leica GP2 plunge freezer. A total of 42,812 exposures was collected on the Titan Krios (Thermo Fisher Scientific) electron microscope equipped with a cold-FEG 300 kV electron source and a Falcon4i camera. The total dose applied per video (EER) was 50 e− Å−2 and the pixel spacing was 0.732 Å. A defocus range of between −0.8 μm and −2.2 μm was used during the acquisition.

Helical reconstruction and model building of recombinant 1B fibrils

All the subsequent image processing and helical reconstruction was carried out in RELION (v.4.0)[47] (Extended Data Fig. 13). The recorded videos were gain-corrected, motion-corrected and dose-weighted using RELION’s own implementation of MOTIONCOR. The raw EER files were dose-fractionated to a total of 32 frames (1.23 e− Å−2 per frame). After CTF estimation using Ctffind (v.4.1)[48], the aligned averages that had an estimated CTF resolution of better than 5 Å were selected, resulting in a total of 11,879 micrographs. aSyn fibres were picked manually as start-to-end helical segments and extracted with an interbox distance of 19 Å. Several rounds of reference-free 2D classification were performed to exclude suboptimal 2D segments from further processing. The four best classes were selected and binned four times to re-extract the segments with a bigger box size encompassing the entire helical crossover. Clearly visible twisted class averages containing the entire crossover were used to generate initial de novo models using the relion_helix_inimodel2d program. The most likely twist was estimated from a crossover distance measured from 2D class averages and corroborated with the direct measurements from micrographs.

The helical segments (105,496) from the entire dataset were then re-extracted with a 600 pixel box size (binned by 2) comprising about 40% of the crossover. Exclusion of the suboptimal classes after 2D classification resulted in 64,889 particles. Multiple rounds of 3D autorefinement were carried out to optimize the helical twist and rise, and to check for the correct symmetry operators. This was validated from the reconstructions showing clear separation of β-strands along the helical axis. Imposing a 2_1 cork-screw symmetry (pseudo two-fold symmetry) yielded the clear separation of β-strands when compared to C_1 and C_2 symmetries. A 3D classification without image alignment was further performed to exclude the segments that gave suboptimal 3D volumes. This resulted in a final 51,272 particles. These were finally re-extracted at a 512 pixel (unbinned) box size and subjected to 3D autorefinement, followed by CTF refinement. Further iterations of Bayesian polishing coupled with CTF refinement yielded a map at 1.94 Å. The maps were sharpened using the standard post-processing procedure in RELION with an ad hoc B factor of 21 Å^2.

The atomic model for the backbone of the core of the 1B fibrils encompassing residues 34 to 95 was built de novo using Coot[49] (v.0.9.8.96) Initially, three β-rungs were modelled in coot and were refined in real-space in PHENIX[45] (v.1.21.2) Finally, these chains were extended to 9 β-rungs per protofilament and refined in tandem with phenix.real_space_refine and in coot to improve the Ramachandran and Geometric statistics. NCS and secondary structural restraints were included during the iterative refinement process.

Helical reconstruction and model building of purified 1BP fibrils

As most of the 42,812 collected videos did not contain any fibrillar material, they were first imported into cryoSPARC[50] (v.4.7.0), motion corrected and manually inspected using a manually_curate_exposures job. After manual inspection, 156 videos with intact, twisting fibrils were selected for further processing in RELION4[47]. They were dose-fractionated in RELION’s MOTIONCOR implementation with 24 frames per fraction, corresponding to a dose of 1.28 e− Å−2 per frame, and CTF-corrected using Ctffind (v.4.1)[48]. Fibrils were found to cluster into three morphological groups (Extended Data Fig. 8). Manual picking was done in three rounds, using 209, 7 and 40 videos for the three respective groups. After extraction with binning of 2 and an inter-box distance of 14.4 Å (3 asymmetrical units), several rounds of 2D classification were applied. One of the three morphological groups (40 videos) yielded 2D classes for which a clear twist and monomer separation was visible, while the other two morphological groups did not yield any interpretable result.

Using the 2D class averages of the one usable group, a de novo initial model was generated using relion_helix_inimodel2d. Particles were re-extracted with a box size of 800 and a binning of 2 and, after multiple rounds of 2D classification, 1,913 particles were retained for a 3D classification job with 1 class and the de-novo inimodel2d reconstruction as initial model. When a fibril backbone was visible, the regularisation parameter (T) was gradually increased to 12 over the course of 50 iterations, and the result was used for a 3D refinement with a tau2 fudge factor of 2 to search for the optimal helical rise and twist. After CTF refinement and postprocessing, a 3D map at a resolution of 3.8 Å was obtained.

To build the 1BP atomic model, one β-rung of the 1B model was fitted into the 1BP density using a rigid-body fit in ChimeraX[51] (v.1.10.1), followed by a jiggle-fit and all-atom refinement in Coot[49] (v.0.9.8.96). Position 53 was mutated into a threonine and the model was extended to five β-rungs, which were refined together in phenix.real_space_refine (PHENIX v.1.21.2). After refinement, the outer two β-rungs were removed in Coot. NCS and secondary structural restraints were included during the iterative refinement process.

FLIM analysis of aSyn inclusion pathology

h-FTAA was synthesized and purified as previously described[36] and paraffin-embedded sections of 1B-injected WT mouse brains (129SV) and regions from human donor brain samples were stained with h-FTAA and processed for immunofluorescence against pS129aSyn (EP1536Y) for the inclusions or against human aSyn (LB509) for the 1B inoculate and counterstained with the nuclear marker DAPI as previously described[37]. To confirm previous observations regarding the ability of h-FTAA to discriminate between Lewy bodies and GCIs using FLIM[37], human brain samples from one individual with MSA and one individual with DLB were obtained from the repository of the University Hospital of Bordeaux (CRB-BBS). Participants or a legal representative had given informed written consent for collecting and using clinical and post-mortem data, and mandatory regulatory approval for post-mortem brain tissue use was obtained from the French Ministry of Higher Education and Research (MESR AC-2024-6715, DC-2024-6714). FLIM was performed on the Leica SP8 WLL2 confocal microscope on an inverted stand DMI6000 (Leica Microsystems), using the HCX Plan Apo CS2 ×63 oil NA 1.40 objective. This microscope was equipped with a pulsed white-light laser 2 (WLL2) with freely tuneable excitation from 470 to 670 nm (1 nm steps) and a diode laser at 405 nm. A FALCON module enabled us to perform FLIM measurement based on the time correlated single photon counting technique. The FLIM analysis was done using phasor plot representation of the data and was focused on pS129aSyn-positive inclusions[37] or LB509-positive regions in the case of the 1B inoculate. Similitude analysis was performed using the Jaccard index[52]. For Gallyas silver impregnation, mouse brain sections were processed as previously described[38] using a commercial Gallyas staining kit (Morphisto).

AFM analysis

1B aSyn fibrils were deposited onto a freshly cleaved mica disk and left to adhere for 15 min in a humid chamber at room temperature. The sample was rinsed and imaged in saline buffer solution (H_2O, HEPES 20 mM, NaCl 100 mM, pH 7.4). Atomic force microscopy (AFM) imaging was performed using the Dimension FastScan setup (Bruker) operating in PeakForce Quantitative Nano-Mechanics (PF-QNM) mode in liquid at room temperature, using sharp SNL-C probes (Bruker, Silicon tips on silicon nitride cantilevers), with a nominal spring constant of 0.24 N m−1, a resonance frequency of 56 kHz and a nominal tip radius of 2 nm. Fibrils were imaged with a peak force frequency of 1 kHz, a scan rate of 0.5 Hz and a constant setpoint force of 500 pN. Image analysis was performed using Nanoscope analysis (Bruker).

Statistics and reproducibility

For all experiments/conditions without quantitative analyses, the images shown were representative of at least three independent observations. In all other cases, statistical analyses data were presented as means ± s.d. or as otherwise stated in the figure legends, and were performed using GraphPad Prism (v.9). The numbers of independent samples as well as the statistics tests used are indicated in the figure legends for each experiment. No statistical methods were used to predetermine sample size. Sample size was determined based on our previous publications. Data distribution was assumed to be normal, although this was not tested. Data assignment, organization and collection were randomized. Data collection and analysis were not performed blindly. No animals or datapoints were excluded from the analysis.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

For 1B and 1BP, the raw cryo-EM images are available at the EMPIAR database under accession numbers 12012 and 12890, respectively. The reconstructed 3D maps are available at the EMDB database under accession numbers EMD-19986 and EMD-54402. The atomic models are available at the PDB database under accession numbers 9EUU and 9RZF. Source data are provided with this paper.

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Acknowledgements

Cryo-EM data were in part collected at the Dubochet Center for Imaging (DCI) in Lausanne. The DCI-Lausanne is a joint initiative of the EPFL and the Universities of Lausanne and Geneva. We thank A. Myasnikov for expert technical assistance in cryo-EM data collection; Æ. Letourneur and F. Cavallaro for their help with primary culture and immunofluorescence; F. Serinelli for support with paraffin histology; S. Dovero and N. Biendon for support with Pannoramic slide scanning; B. Dehay for sharing the AAV-Syn mutant vectors; M. Picquemal for support with animal surgery; L. Lakhdar, A. de César and D. Gaillard for animal experiments in M83 mice; S. Lacomme and F. Cordelières from the Bordeaux Imaging Center for their help with sample fixation for CLEM and with the Zeiss CD7 platform respectively. Room-temperature EM was collected in part at the electron microscopy facility (EMF) of the University of Lausanne. We thank C. Genoud and the members of the EMF team for their assistance. This work was supported by the Swiss National Science Foundation (grants 310030_188548 and 10.002.679), the Swiss Parkinson Foundation, the Department of Excellence Initiative of the Italian Ministry of Research, the Innovative Medicines Initiative 2 Joint Undertaking under grant agreement no. 116060 (IMPRiND), supported by the European Union’s Horizon 2020 research and innovation program and EFPIA, the French Agence Nationale de la Recherche (grants ANR-21-CE18-0045-03, ANR-22-CE16-0002 and ANR-24-CE93-0003), and the Fondation pour la Recherche Médicale, grant MND202411019711.

Author information

Author notes

1. These authors contributed equally: Domenic Burger, Marianna Kashyrina, Lukas van den Heuvel

Authors and Affiliations

1. Laboratory of Biological Electron Microscopy, Institute of Physics, School of Basic Science, EPFL, Lausanne, Switzerland

Domenic Burger, Lukas van den Heuvel, Amanda J. Lewis, Inayathulla Mohammed & Henning Stahlberg

2. Department of Fundamental Microbiology, Faculty of Biology and Medicine, UNIL, Lausanne, Switzerland

Domenic Burger, Lukas van den Heuvel, Amanda J. Lewis, Inayathulla Mohammed & Henning Stahlberg

3. Institut des Maladies Neurodégénératives, UMR 5293, Univ. Bordeaux, CNRS, Bordeaux, France

Marianna Kashyrina, Hortense de La Seiglière, Marie-Laure Arotcarena, Aude Retailleau, Erwan Bezard, Marie-Hélène Canron, Wassilios G. Meissner, Florent Laferrière, Francesca De Giorgi & François Ichas

4. Laboratory of Human Anatomy, Department of Experimental Medicine, Univ. Salento, Lecce, Italy

Marianna Kashyrina & Francesco De Nuccio

5. Dubochet Center for Imaging, Lausanne, Genopode (UNIL), EPFL, Lausanne, Switzerland

Inayathulla Mohammed

6. Neurodegenerative Diseases Unit, ANSES, Univ. Lyon, Lyon, France

Jérémy Verchère & Thierry Baron

7. Institut de Chimie et Biologie des Membranes et des Nano-objets, UMR 5248, Univ. Bordeaux, CNRS, Bordeaux INP, Pessac, France

Cécile Feuillie, Mélanie Berbon & Antoine Loquet

8. Service de Neurologie des Maladies Neurodégénératives, IMNc, CHU Bordeaux, Bordeaux, France

Wassilios G. Meissner

9. Laboratoire des Maladies Neurodégénératives, UMR 9199, Univ. Paris-Saclay, CNRS, CEA, Fontenay-aux-Roses, France

Luc Bousset

10. Bordeaux Imaging Center, UAR 3420, US 4, Univ. Bordeaux, CNRS, INSERM, Bordeaux, France

Christel Poujol

11. Department of Physics, Chemistry and Biology, Linköping University, Linköping, Sweden

K. Peter R. Nilsson

12. Laboratory of Human Anatomy, Department of Biological and Environmental Sciences and Technologies, Univ. Salento, Lecce, Italy

Dario Domenico Lofrumento & François Ichas

Contributions

D.B. determined the 1B structure, performed CLEM experiments and immunogold labelling and wrote the manuscript. M.K. performed in vivo experiments in 129SV WT mice and neuropathology stainings. L.v.d.H. determined the 1BP structure, performed immunogold analysis and wrote the manuscript. H.d.L.S. produced aSyn and fingerprinted 1B, SEC-purified aSyn and performed the FLIM experiments. A.J.L. performed CLEM experiments. F.D.N. designed experiments, performed in vivo experiments in 129SV WT mice and neuropathology stainings. I.M. contributed to cryo-EM structure determination. J.V. performed the analyses of the in vivo experiments in transgenic M83 mice and purified the 1BP fibrils from brains. C.F. performed the AFM analysis of 1B fibrils. M.B. SEC-purified aSyn. M.-L.A. performed surgery on WT mice. A.R. performed post-mortem brain perfusion/fixation of C57BL/6 WT mice. E.B. participated in early characterizations of 1B. M.-H.C. and W.G.M. certified and provided the sections from patient donors with MSA and DLB. A.L. SEC-purified aSyn. L.B. participated in early characterizations of 1B. C.P. performed the FLIM experiments. K.P.R.N. synthetized h-FTAA. F.L. contributed to setting up the fibril isolation procedures from mouse brains and participated in early characterizations of 1B. T.B. designed experiments. D.D.L. designed experiments. F.D.G. designed experiments, performed the HCA experiments, as well as the confocal and slide-scanning neuropathology analyses of WT and M83 mice, and wrote the manuscript. H.S. conceived and managed the project and wrote the manuscript. F.I. conceived and managed the project, produced aSyn and fingerprinted 1B, performed the FLIM experiments, performed the HCA experiments, as well as the confocal and slide scanning neuropathology analyses of WT and M83 mice, and wrote the manuscript. All of the authors contributed to the paper and discussed the results.

Corresponding authors

Correspondence to Henning Stahlberg or François Ichas.

Ethics declarations

Competing interests

D.B. is an employee of F. Hoffmann–La Roche. The presented work was conducted before his employment and had no influence on the design, analysis, interpretation or reporting of the results of this study. E.B. is a director and shareholder and of Motac Neuroscience. The other authors declare no competing interests.

Peer review

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

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Extended data figures and tables

Extended Data Fig. 1 Atomic force microscopy (AFM) appearance of 1B fibrils and early formation of “seeding junctions” between 1B and the nascent seeded inclusions in neuronal processes.

a. Topographical (Height Sensor) and nano-mechanical mapping (Derjaguin-Müller-Toporov (DMT) Modulus, log representation) of 1B fibrils using AFM in liquid. Right panels: fibril height values (see cartoon for definitions) for n = 103 measurements (plot population statistics descriptors as shown in plot inset), and left twist periodicity for n = 12 fibrils. Scale bars = 240 nm. b. Examples of early “seeding junctions” between 1B and the nascent seeded inclusions in neuronal processes two weeks post seeding (arrowheads = seeding junctions). 96-well pooled primary cultures of cortical neurons from 8 wild-type mouse embryos (C57BL/6) were challenged at day-in-vitro 7 (DIV7) with 10 nM 1B fibrils (equivalent aSyn monomer concentration). The neurons were fixed two weeks later at DIV24 and both the 1B input fibril remnants (red) and the seeded aSyn inclusions (green) were revealed. Indeed, we took advantage of the fact that synthetic 1B is made of human aSyn and thus that it can be specifically recognized by LB509 which is a human aSyn-specific antibody. Mouse aSyn is LB509 negative. The seeded inclusions were revealed contemporary using EP1536Y against pS129 aSyn. This allowed us to observe many seeding junctions in the neuronal processes (arrows). Note that in a majority of images, and in agreement with early reports, the seed (1B in our case) is not phosphorylated, and that the growing seeded inclusions are instead pS129Syn-positive. At later time points 1B seeds get overwhelmed and are no longer discernible in the mass of the seeded inclusions (not shown). The disappearance of the 1B seeds is even faster in vivo (within a few days, not shown). (scale bars = 10 µm).

Source data

Extended Data Fig. 2 Somatic inclusions seeded by 1B in vivo observed at 3 time points.

Depending on the neuroanatomical structure and the time point under consideration, experimental GCIs (blue) coexisted with a variable load of surrounding neuronal somatic aSyn inclusions (NCIs & NIIs, both in red), which represent the forefront of the somatic aSyn pathology at earlier time points to progressively make way to a growing population of GCIs. The brain sections are the ones shown in Fig. 1f and were stained with DAPI for nuclei, Sox10 to identify the oligodendrocytes, and EP1536Y for pS129Syn. All the inclusions were manually annotated according to these 3 markers. Anatomical quantification regions were as follows: Am: amygdala; ACa: anterior limb of the anterior commissure; ACp: posterior limb of the anterior commissure; BN: bed nucleus of the stria terminalis; CX: cortex; St: caudate putamen (striatum); SN: substantia nigra. In agreement with visual perception, the neuronal inclusions peak at 12 months in the Caudate putamen (St) and the Amygdala (AM) to decrease at 24 months, while the GCIs suddenly increase in the posterior limb of the Anterior Commissure at 12 months, and then in most of the other brain regions. Note that NIIs form especially early (at 6 weeks) in the SN and the AM, then in other regions at 12 months, to eventually disappear but in the AM at 24 months. The mean number of GCIs in all regions at 24 months is significantly increased compared to the 2 other time points (Mean ± SD of the regions shown together with the individual region inclusion number values, * = one-way ANOVA p < 0.05: p = 0.0462 for 6w/24 m, p = 0.0278 for 12 m/24 m).

Source data

Extended Data Fig. 3 Semi-topographic view of a horizontal brain section from a C57BL/6 wild-type mouse injected 17 months earlier at the level of its right substantia nigra (SN) with 1B fibrils.

a. aSyn inclusions are revealed using the anti-phospho aSyn antibody #64 (green), dopaminergic neurons using an anti-tyrosine hydroxylase antibody (TH, red) and nuclei using DAPI (white). Left and right SNs are visible with a loss of immunoreactivity symmetry with depletion of TH-positive neurons and unilateral aSyn inclusions on the right side. The TH-depleted/aSyn inclusion-rich region is enlarged in b, the corresponding left region is enlarged in c. d. Semi-topographic view of the n + 1 horizontal section consecutive to (a). aSyn inclusions in green (anti-phospho aSyn antibody #64), OLs in red (anti-Sox10 antibody), microglial cells in blue (anti-Iba1) and nuclei in white (DAPI). The right SN enlarged in f contains numerous GCIs and sparse microglial cells. e. f. Enlarged view of the corresponding region of the left SN. Scale bars: a, d = 500 µm; b, c = 100 µm; e, f = 20 µm.

Extended Data Fig. 4 Tissue ultrastructure and tomography of 1B-seeded mouse brain.

a-c. High magnification EM images of different types of fibril arrangements, indicated by hand made drawings in the upper row panels, and without indication in the lower row panels. a: “dispersed”, b: “bundled”, and c: “clustered”. d. Tomogram segmentation of aSyn fibril bundles. Tomograms were manually segmented to visualize the fibril bundling (blue), the nuclear membrane (red), the cell membrane (yellow), and other membranous compartments (green). Top: A slice view of the reconstructed tomogram with applied filtering to better visualize the filaments within the inclusion. Bottom: Overlay with 3D-segmented elements. Scale bars: 500 nm.

Extended Data Fig. 5 Immunogold analysis against aSyn in the mouse brain.

a. Immunohistochemistry (IHC) labelling (inset) indicates two regions with aSyn pathology wrapping around the nucleus of an affected cell. The correlated EM image with on-grid immunolabelling against aSyn (left) shows an increase of gold particles in comparison to the background as indicated by the heatmap (right). Higher magnifications are indicated by the labelled boxes. b. Zoomed view on the left side of the nucleus, highlighted are the gold particles in red, laying on top of dispersed fibrils. c. Lower part of the pathology from the right side of the cell. The zoomed area shows four gold particles laying on top of fibril pathology. d. Zoom of right-side pathology, with highest concentration of gold particles, laying on fibril bundles. Scale bars: in a = 5 µm (left) and 1 µm (right); in b-d: 1 µm.

Extended Data Fig. 6 Pathological oligodendrocyte in direct contact with other cells.

Cells with a distinct morphology, previously described as “dark microglia”, can be found in close proximity or in direct contact with pathological cells (white arrowhead). The total cell volume of the dark microglia is indicated by the white dashed line. In this specific case the fibrillar pathology of the oligodendrocyte appears in a dispersed arrangement with two smaller clusters (red arrowheads). Total area of immunopositive IHC is indicated by a red dashed line. Both oligodendrocytes contain aSyn pathology, however, for the upper cell volume, it is not visible in this EM slice (based on IHC positive signal from other EM grids). Scale bar = 3 μm.

Extended Data Fig. 7 Further structure analysis of the 1B conformation.

a. Sequence of aSyn with the resolved density indicated by the coloured line. Secondary beta-sheets are indicated in consecutive order by β1-9. b. The final 1.94 Å map of 1B with the model fitted. The extra densities flanking the starting stretches were not built. c. Surface colour representation by the electrostatic potential. d. 3D class averages from early processing stages indicate a homogeneous sample. e. Fourier Shell Correlation (FSC) curve of 1B with cutoff at 0.143 of the final map at 1.94 Å.

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Extended Data Fig. 8 Cryo-EM analysis of 1B[P] fibrils purified from a tg M83 +/− mouse brain seeded with 1B fibrils.

(a) Negative staining combined with immunolabeling against aSyn-pS129 reveals that, amid aggregated precipitates, individual aSyn fibrils are present. (b-d) Cryo-EM micrographs (left) of intact fibrils observed in the sarkosyl-insoluble fraction, together with their power spectral density (right). A reflection at ~4.8Å (white arrowheads) reveals that these are amyloid fibrils. Presumably, the fibrils in (b), (c) and (d) represent 3 distinct conformations as can be seen from their different morphologies, although the particle counts are too low to verify this with a 3D reconstruction. The crossover distance (X) and largest diameter (ø) are indicated, as well as the number of micrographs (N) displaying at least one crossover of a fibril of the same morphological group as determined by manual inspection. The fibrils in group (d) did eventually yield a 3.8Å structure, while those in groups (b) and (c) did not yield any structure despite many attempts. (e) Reprojection of the 2D inimodel constructed from 2’492 particles selected from group (d). (f) 3D helical reconstruction of 1’913 particles selected from group (d), before (top) and after (bottom) post-processing in Relion. (g) The final 3.8 Å map of 1BP with the model fitted. (h) FSC curve of 1BP. Scalebars: (a) 100 nm, (b-d) 50 nm, (e) 20 nm.

Source data

Extended Data Fig. 9 h-FTAA is a conformation-sensitive probe that enables discrimination between aSyn fibril strains associated with MSA and DLB through FLIM of brain tissue sections.

It was previously reported that FLIM of h-FTAA can be used in histological brain sections to differentiate the aSyn fibrils populating Lewy bodies (LBs) from those populating GCIs in MSA[37]. These findings established h-FTAA as a conformation-sensitive amyloid probe capable of discriminating distinct aSyn fibril strains in human brain sections via FLIM[37]. In agreement with these previous observations, FLIM of h-FTAA allowed us to derive fibril strain-specific phasor plot signatures directly on brain tissue sections. Using this approach, we confirmed that h-FTAA FLIM could indeed discriminate the pS129Syn-positive inclusion pathology of MSA vs. DLB (a: h-FTAA intensity images - pS129Syn not shown) and used the disease-specific hotspots in the respective FLIM phasor plots to define 2D quantification gates (b,c) (α, β: MSA-specific; χ: DLB-specific). The fluorescence lifetime of the gated pixels is shown in d for respectively GCIs (26,6 million inclusion pixels gated) and LBs (3.3 million inclusion pixels gated). In agreement with previously published data[37], the distribution histograms make it clear that the majority of pixels belonging to LBs are characterized by a fluorescence lifetime which is in the nanosecond range, while those populating GCIs show an approximately halved fluorescence lifetime with 2 distinguishable populations. Scale bar = 20 μm.

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Extended Data Fig. 10 In situ h-FTAA FLIM indicates that both the input 1B fibrils and the resulting inclusions seeded in wild-type mice exhibit a high degree of conformational similarity with the MSA strain.

The phasor plot gates discriminating GCIs and LBs described in Extended Data Fig. 9 were applied in the phasor plots of the intracerebral 1B fibril inoculate (positive to the anti-human aSyn antibody LB509, not shown), still observable in the CP of wild-type mice 24 h after injection (a, from left to right: h-FTAA intensity image, corresponding phasor plot with gates and quantifications, distribution of gated pixels in image) or in the plots characterizing the inclusions that formed in neurons and OLs during the 16 months following 1B injection (pS129Syn-positive, not shown) (b). The number of inclusion pixels quantified by FLIM and gated in α, β, and χ was >10^6 in each case, and the distribution of the pixel population in the phasor gates α+β, and χ was eventually used to score the similarity of the different fibril inclusion types (Supplementary Information Table 3). Scale bar = 20 μm.

Source data

Extended Data Fig. 11 The pathology seeded by 1B is Gallyas-positive.

The MSA-specific silver impregnation technique of Gallyas highlights somatic (yellow arrowheads) and neuritic (white arrowheads) inclusions which developed during 16 months in the substantia nigra of WT mice injected with 1B (a); other section in the same region reveals pS129Syn-positive inclusion pathology (b). Scale bar = 100 μm.

Extended Data Fig. 12 Inclusion seeding by 1B is inhibited by E46K which disrupts the pseudo-Greek-key motif stem stabilizer (E46-K80 salt bridge), but not by aSyn mutations in the inter-protofilament interface.

a. 96-well pooled primary cultures of cortical neurons from 8 aSyn-KO mouse embryos were challenged or not at day-in-vitro 7 (DIV7) with 10 nM 1B fibrils (equivalent aSyn monomer concentration), and infected or not with AAV-aSyn or AAV-E46K aSyn at DIV11. The neurons were fixed at DIV30 and the aSyn inclusions revealed using the conformation-dependent antibody SynF1 (red); three immunofluorescence fields of views (FOVs) imaged in a test well for each condition, illustrate: (i) the absence of SynF1and human aSyn signal at DIV30 in the absence of endogenous aSyn (aSyn-/- line, left column), (ii) aSyn inclusion seeding by 1B in conditions of aSyn expression (aSyn -/- + 1B line, middle and right column), and (ii) a minor inclusion seeding when E46K aSyn is expressed instead of wild-type aSyn (aSyn -/- + 1B line, right versus middle column). b. High Content Analysis of the experiment shown in (a) and extended to a series of aSyn mutants based on 18 FOVs from 6 wells for each condition. Mean ± SD as well as individual values are plotted for each condition The AAV-aSyn condition was doubled to document robustness. Kruskal-Wallis test followed by a post-hoc Dunn’s test for multiple comparisons indicates that E46K aSyn is the only mutation reducing inclusion seeding by 1B (p = 0.0001). In the AAV-only conditions, human aSyn deriving from AAV infection was quantified using the human aSyn-specific antibody MJFR1 (no endogenous mouse aSyn is present in these neurons). The results were compared with the same test and post-hoc test combination as before, which indicated the absence of statistically significant differences in terms of levels of expression driven by the different AAVs. In particular, no statistically significant difference existed between AAV wt aSyn and AAV E46K aSyn in terms of expression levels, indicating that the difference seen with SynF1 after seeding with 1B was not due to a lesser expression of E46K aSyn. Scale bar = 100 μm.

Source data

Extended Data Fig. 13 Processing overview (schematic) for 1B reconstruction.

Detailed processing overview representing individual jobs within RELION (white boxes), with the black line indicating subsequent steps. Red boxes indicate estimated resolution at given Refinement steps. Blue dotted line represents the reference volumes used. The background colour represents data preprocessing (grey), binned processing (green), and unbinned processing (yellow). 1. During data acquisition the first 1’334 micrographs (Electron Event Recordings) were processed during the session, to assess the quality of the dataset on the fly. 2. The remaining 19’636 micrographs were processed after the data acquisition had completed and were later introduced to the dataset at step 6 and 11 respectively. 3. For initial analysis manually traced fibril segments were extracted with a box size of 600px, binned to 300px. 4. From the full dataset selections were made based on the estimated CTF resolution to reduce the amount of manual screening of the full dataset. As such two groups were analysed: Add values. Manual picking of particles was done in parallel to the processing of the extracted particles from 3. 5. Initial 3D-Classification was done with a featureless cylinder as a low-pass filtered reference volume. 6. The first set of additional particles from the full data set was introduced to the processing. 7. The full particle batch was cleaned by multiple rounds of 2D classification and was subsequently refined to 2.66Å with a reference volume from the previously obtained 4.95Å structure from the initial screening. 8. With a well-aligned structure, the data was transitioned to unbinned processing, and the respective particles were re-extracted. 9. The second set of additional particles from the full dataset was extracted at the unbinned box size. No further manual selection of the full dataset was made. 10. After transitioning to the unbinned box size the refinement was redone on the 2.66Å structure. 11. All particles are joined together for the final processing. 12. The structure was subjected to Refinement and PostProcessing with intermediate steps of Polish and 13. CTF refinement until the final high-resolution structure was obtained. 14. Processing concluded when no further improvement in the iterative process could be made. The model was built into the final map at 1.94Å resolution.

Supplementary information

Suppementary Tables 1–3

Supplementary Table 1: structural comparison of different aSyn folds with 1B. Structure comparison on the basis of the r.m.s.d. value, as shown in Fig. 3. The fully modelled structures were aligned to the 1B conformation with the matchmaker function in ChimeraX. The best fit subunits were then further compared on three regions on the Cα r.m.s.d. values in respect to the different pocket regions and intermediate sequence based on ChimeraX r.m.s.d. measurements. A r.m.s.d. of less than 1 Å suggests high similarity in the structural conformation. Supplementary Table 2: cryo-EM data collection, refinement and validation statistics. Supplementary Table 3: in situ comparison of 1B inoculate, 1B-seeded inclusions, GCIs in MSA and LBs in DLB using h-FTAA FLIM analysis of human and WT mouse brain tissue sections. Inclusion pixels quantified by FLIM and gated in α, β and χ in Extended data Fig. 10 (>10^6 in each case) were used for comparison of inoculate and inclusions. For each condition, the percentage of the inclusion pixel population situated in the phasor gates α + β (MSA specific) and χ (DLB specific) (Extended data Fig. 9) was used to score the similarity of the different fibril inclusions types using the Jaccard similarity index[52]. Similarity matrix analysis demonstrates that both the input 1B fibrils and the resulting inclusions seeded in WT mice exhibit a high degree of conformational similarity which is shared with the MSA fibrils, and distinct from the DLB ones. Colour code: green, similar; yellow, dissimilar.

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Supplementary Video 1

Section hovering overview corresponding to Fig. 1 panels a-e: DAPI in blue, pS129Syn in white, Sox10 in pink, Iba1 in yellow (only in AC)

Supplementary Video 2

3D animation of NII & NCI co-existing in the dopaminergic neuron shown in Fig. 5 panel b, upper right: DAPI in white, pS129Syn in green, Tyrosine Hydroxylase in red

Supplementary Video 3

3D animation of NII in the dopaminergic neuron shown in Fig. 5 panel b, upper left: DAPI in white, pS129Syn in green, Tyrosine Hydroxylase in red

Supplementary Video 4

3D animation of a Tyrosine Hydroxylase (red) positive neuron from the substantia nigra of the mouse sampled in Fig. 5. pS129Syn is in green. Both NCIs and NIIs can be observed without need for a nuclear marker

Supplementary Video 5

3D animation of Fig. 5 panel b, lower left: The NCI of the cortical neuron (bigger nucleus) seems to protrude within the interior of the lining glial cell (smaller nucleus): DAPI in white, pS129Syn in green, Tyrosine Hydroxylase in red (not expressed in this region)

Supplementary Video 6

“in silico” section of 3D animation of Fig. 5 panel b, lower left: The NCI is in continuity with a glial nuclear inclusion (GNI): DAPI in white, pS129Syn in green, Tyrosine Hydroxylase in red (not expressed in this region)

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Burger, D., Kashyrina, M., van den Heuvel, L. et al. Synthetic α-synuclein fibrils replicate in mice causing MSA-like pathology. Nature 648, 409–417 (2025). https://doi.org/10.1038/s41586-025-09698-1

- Received: 19 May 2024

- Accepted: 01 October 2025

- Published: 05 November 2025

- Version of record: 05 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09698-1

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Nature volume 648, pages 434–442 (2025)

Abstract

Marine picocyanobacteria are abundant photosynthetic organisms of global importance. They coexist in the ocean with cyanophages—viruses that infect cyanobacteria. Cyanophages carry many auxiliary metabolic genes acquired from their hosts that are thought to redirect host metabolism for the phage’s benefit1,2,3,4,5. One such gene is nblA, which is present in multiple cyanophage families2,6,7,8. Under nutrient deprivation cyanobacterial NblA is responsible for inducing proteolytic degradation of the phycobilisome9,10,11, the large cyanobacterial photosynthetic light-harvesting complex. This increases the pool of amino acids available for essential tasks[11], serving as a survival mechanism[12]. Ectopic expression of different cyanophage nblA genes results in host pigment protein degradation6,8,13. However, the benefit of the virus-encoded NblA for cyanophages and the broader impact on the host are unclear. Here, using a recently developed genetic manipulation system for marine cyanophages[14], we reveal that viral NblA significantly accelerates the cyanophage infection cycle, directs degradation of the host phycobilisome and other proteins, and reduces host photosynthetic light-harvesting efficiency. Metagenomic analysis revealed that cyanophages carrying nblA are widespread in the oceans and comprise 35% and 65% of oceanic T7-like cyanophages in surface and deep photic zones, respectively. Our results show a large benefit of NblA to the cyanophage, while it exerts a negative effect on the host photosynthetic apparatus and host photosynthesis. These findings suggest that cyanophage NblA has an adverse global impact on light harvesting by oceanic picocyanobacteria.

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Main

The light-harvesting antennae of most cyanobacteria are composed of phycobilisomes—gigantic membrane-associated soluble supercomplexes—located on the exterior side of the thylakoid membrane9,15. Cyanobacteria capture and funnel solar energy through their phycobilisomes towards the photosynthetic reaction centres[16], where the primary energy-conversion reactions of photosynthesis occur. Typical phycobilisomes of marine Synechococcus are built of multiple subunits that absorb light at different wavelengths, including an allophycocyanin (APC) core and peripheral rods composed of disks of different phycobiliproteins, phycocyanin (PC) and phycoerythrins I and II (PEI, PEII), as well as linker proteins that connect rod subunits to each other and to the core and that attach the phycobilisome to the thylakoid membrane17,18. Each phycobiliprotein is composed of α and β subunits that form heterodimers[10]. These proteins bind to the pigment chromophores phycocyanobilin, phycoerythrobilin (PEB) and phycourobilin (PUB), which absorb light at different wavelengths[19]. Owing to their large size, phycobilisomes can comprise up to half of the soluble protein content of a cell[15]. Prochlorococcus is the most abundant photosynthetic organism on Earth[20]. The vast majority of Prochlorococcus lineages have a chlorophyll-based transmembranal light-harvesting complex rather than the typical phycobilisome21,22,23. However, Prochlorococcus does encode one or two subunits of phycoerythrin (PE)24,25, found at low levels in cells[26]. Notably, some low-light-adapted Prochlorococcus lineages from anoxic marine zones possess both chlorophyll-based and phycobilisome light-harvesting complexes[20].

Viral NblA is beneficial for infection

Evidence collected over the past two decades suggests that cyanophages possess host-like auxiliary metabolic genes that are thought to influence key processes in host metabolism during infection and enhance phage replication1,2,3,4. These include genes that are thought to benefit the phage by maintaining essential cellular metabolic processes as well as those that impair host activities to redirect resources towards phage progeny production3,4. nblA encodes a proteolysis adaptor protein found in multiple cyanophage families2,6,7,8,13,27 and is particularly prevalent in T7-like cyanophages (family Autographiviridae). In nutrient-deprived cyanobacteria, the cyanobacterial NblA is responsible for inducing degradation of the phycobilisome complex, resulting in clear loss of pigmentation9,10,11. Here we use S-TIP37, a typical T7-like cyanophage isolated from the Red Sea that infects the open ocean Synechococcus sp. strain WH8109 (ref. [28]), as our model system to study cyanophage-encoded nblA. We began by examining whether the cyanophage nblA gene is transcribed and translated during the infection process. We found high nblA transcript and protein levels from 2 h after infection onwards (Extended Data Fig. 1). This expression pattern was distinct to that of a host copy of the nblA gene, which displayed fairly consistent transcript and protein levels (Extended Data Fig. 1). The phage nblA expression pattern was similar to that of the phage DNA polymerase gene, and is therefore expressed with phage genes involved in DNA metabolism and replication and before expression of virion morphogenesis genes29,30.

Next, we assessed the influence of the nblA gene on cyanophage infection. For this we constructed nblA cyanophage deletion mutants (∆nblA) using the REEP approach[14] (Methods). Infection of the host with the ∆nblA mutant phage revealed visibly less pigmentation loss compared with when the host cells were infected with the wild-type (WT) phage (Fig. 1a), indicating a clear phenotype for the ∆nblA mutant during infection.

Fig. 1: The influence of nblA on S-TIP37 cyanophage infection dynamics.

a, Culture pigmentation phenotypes in uninfected Synechococcus sp. strain WH8109, and in WH8109 6 h after infection with the WT or the ∆nblA mutant S-TIP37 cyanophage. b, Cyanophage growth curves of the WT and ∆nblA mutant cyanophages. PFU, plaque-forming units. c, Changes in the abundances of different functional groups of phage proteins over time after infection with the WT (left) and ∆nblA (right) cyanophages. LFQ, label-free quantification. d, Cyanophage infection dynamics of the WT and ∆nblA mutant phages when infecting the WT host or the host ectopically expressing the cyanophage NblA. e, The apparent photochemical quantum yield of PSII (QYp) in cells infected with the WT or the ∆nblA cyanophage and in uninfected control cells after excitation of the phycobilisome at 495 nm (absorbance peak of PUB). Infection was performed at a multiplicity of infection (MOI) of 5. For b, linear regression formulas (Supplementary Data 2) are provided for the three near-linear segments of the cyanophage abundance (normalized to the maximum value) with time for WT (in blue) and ∆nblA (in red) cyanophages alongside the significance levels for the factor ‘infection type’ (type II Wald F-test); NS, not significant; ***false-discovery rate (FDR)-adjusted P < 0.001; exact FDR-adjusted P values for each interval: 0.60 (0–3 h), 2.0 × 10−18 (3–10 h), 8.7 × 10−5 (10–12 h). For c, genes were grouped into three clusters reflecting dominant gene functions. Linear models were fit for each cluster and a significant contribution of the factor ‘infection type’ (WT or mutant phage) was found only for the morphogenesis genes (analysis of variance (ANOVA) type II F-test, FDR-adjusted P = 7.1 × 10−8). Further statistical test details are provided in Supplementary Data 2. For b–e, data are mean ± s.d. of n = 3 independent biological experiments.

To investigate the importance of the cyanophage NblA to the infection process, we performed phage growth curve experiments. The ∆nblA mutant demonstrated a substantially longer latent period (the period of infection before the first release of phage progeny from cells) of 8–10 h compared with the 3 h latent period of the WT[31] (Fig. 1b). In addition, synthesis of phage proteins increased with time during infection with the WT phage (Fig. 1c and Supplementary Data 1), whereas most phage protein production ceased 3 h after infection with the ∆nblA mutant, with significantly fewer virion morphogenesis proteins produced (Fig. 1c and Supplementary Data 2). These findings suggest a direct link between phage protein production and NblA expression and indicate that NblA is advantageous to the WT phage. As cyanobacterial NblAs are known to degrade phycobilisomes during nutrient stress9,10,11 and to release amino acids critical for cell survival11,12, we hypothesize that the phage NblA has a similar role during infection but the release of amino acids is used for building new virions.

The gene density in the region of nblA in the phage genome is high; therefore, to verify that the observed phenotype is a result of the lack of the nblA gene and is not due to potential side-effects caused by the deletion (Methods), we performed a rescue experiment. This was achieved by infecting Synechococcus sp. strain WH8109 cells ectopically expressing the cyanophage nblA gene under an inducible expression system32,33 with the ∆nblA mutant phage (Fig. 1d). Indeed, expression of the cyanophage NblA restored the timing of infection to that found for the WT cyanophage (Fig. 1d). The shorter latent period for the WT phage suggests that the nblA gene would improve phage fitness by allowing it to carry out more rounds of infection in a set time period. Our findings confirm that nblA has an important function in cyanophage infection and that it probably enhances phage fitness.

Cyanophage NblA would be expected to impact host photosynthesis if it directs phycobilisome degradation as phycobilisomes transfer energy to the photochemical reaction centres of the photosystems (PSI or PSII)16,34. We assessed the photosynthetic performance of PSII by measuring fluorescence at room temperature after exciting cultures with blue light (495 nm), which preferentially excites the most peripheral disks of the phycobilisome rods consisting of PEII. The apparent photochemical quantum yield of PSII (QYp) was then calculated. While uninfected cells maintained a steady PSII quantum yield, infection with both the WT and ∆nblA mutant phages resulted in a considerable decline (Fig. 1e). Notably, this decline reached low levels by 8 h after infection with the ∆nblA mutant, a delay of 4 h relative to infection with the WT cyanophage. This indicates that the cyanophage NblA negatively impacts the host’s PSII photochemical quantum yield by 50% over the period of infection. This is likely to have a substantial effect on the ability of the host cell to produce the energy and reducing equivalents necessary for many cellular processes. This diminished photosynthetic performance could be attributed to targeted phycobilisome degradation, accelerated cell lysis or a combination of both factors.

Viral NblA directs phycobilisome degradation

Cyanobacterial NblAs are proteolysis adapters that are known to be involved in phycobilisome degradation. To assess whether the cyanophage NblA has a similar effect on host phycobilisome integrity, we monitored whole-cell fluorescence emission spectra as a measure of the energy transfer pathway from phycobilisomes to PSII. Samples collected at different timepoints were excited at the wavelength for PUB, which binds mainly to the peripheral PEII disk of the phycobilisome, and the corresponding fluorescence emission spectra were measured. Infection with the WT cyanophage led to a rapid and substantial decrease in the chlorophyll a (Chl) peak with time (Fig. 2a and Extended Data Fig. 2a). This decline was first obvious at 3 h after infection (Fig. 2a), before the onset of cell lysis (Fig. 1b). By contrast, infection by the ∆nblA-knockout cyanophage led to a more gradual decrease in Chl fluorescence (Fig. 2a and Extended Data Fig. 2a). These findings indicate that energy transfer from PE to Chl was rapidly interrupted during infection with the WT phage, but considerably less so after infection with the ∆nblA-mutant phage.

Fig. 2: The effect of cyanophage NblA on the cyanobacterial photosynthetic antennae.

a–c, Fluorescence emission spectra (a), absorbance spectra (b) and fractionated phycobilisomes on sucrose gradients (c) of uninfected Synechococcus sp. strain WH8109 cells (green), and WH8109 infected by the WT (blue) or ∆nblA mutant (red) S-TIP37 cyanophage at different timepoints after infection. In c, the lower-density (top) bands are disassembled phycobilisome subunits, and the higher-density (bottom) bands are intact phycobilisomes (Extended Data Fig. 3). d,e, Fluorescence (d) and absorbance spectra (e) of WH8109 cells 48 h after induced expression of the cyanophage NblA protein (blue) compared with the non-induced control (green). Fluorescence and absorbance spectra are representatives of five biological replicates. Mean and s.d. values are shown in Extended Data Fig. 2. Measurements were taken at room temperature, and peaks of Chl, PC, PE, PUB and PEB are indicated. Fluorescence measurements were normalized to the PE peak and absorbance measurements were normalized to the Chl peak. For a and d, the PE peak at 560 nm is made up of PEI and PEII, to which the PEB and PUB chromophores bind.

Whole-cell absorbance spectra and proteomic analysis provide a means to assess the levels of host phycobilisome subunits during infection. At 12 h after infection with the WT cyanophage, we observed a flattening of the peaks corresponding to both the PUB and PEB chromophores, which are attached to the PEI and PEII proteins. A less-prominent decrease in these peaks was observed during infection with the ∆nblA mutant (Fig. 2b), suggestive of NblA degradation of the PE proteins by the WT phage. Proteomic analysis during infection with the WT phage revealed significantly lower levels of the α subunits of PEII, PEI and PC rods (CpeA, MpeA and RpcA, respectively), as well as two rod linker proteins (MpeC and MpeE) relative to infection with the ∆nblA mutant at 4 h after infection (Supplementary Data 1). A 10–30% reduction was observed for some of the β subunits, but this was not statistically significant. By contrast, three linker proteins closer to the core[35] that connect PC to APC and both PC and APC to the thylakoid membrane (ApcC, CpcG1, CpcG2) and one rod linker protein (CpeC) had higher protein levels during infection with the WT relative to the ∆nblA mutant (Supplementary Data 1). This may be indicative of attempts by the host to refurbish the phycobilisome core structure in response to the reduction in active phycobilisome rods. Combined, these findings provide further evidence for the role of cyanophage NblA in phycobilisome disassembly and degradation.

Next, we wanted to determine the fate of the antenna complex during infection. To achieve this, we isolated phycobilisomes from host cells 6 h after infection and compared them with those in uninfected cells. Fractionation of phycobilisomes on a sucrose gradient followed by fluorescence spectra analysis (Fig. 2c) enabled us to differentiate between assembled (bottom, high-density, pink bands) and disassembled complexes (top, low-density, orange bands) (Extended Data Fig. 3). While intact and disassembled phycobilisomes were apparent in uninfected host cells, only disassembled phycobilisomes were present in cells infected by the WT cyanophage (Fig. 2c). Cells infected by the ∆nblA mutant cyanophage were composed of both intact and degraded phycobilisomes (Fig. 2c), indicative of only partial phycobilisome disassembly.

The findings above are consistent with a role for NblA in disassembly and degradation of the phycobilisome during infection with the WT cyanophage. However, these findings could also be due, at least in part, to the beginning of cell lysis from 4 h onwards during infection with the WT phage. To more directly assess the impact of phage NblA on host phycobilisomes without the confounding myriad effects of phage infection, we ectopically expressed the viral NblA in host cells without infection. First, we measured whole-cell fluorescence spectra, which showed a decline in the energy transfer from PE to Chl, seen by a reduction in the Chl fluorescence peak after excitation at PUB relative to cells without induction of NblA expression (Fig. 2d). However, this decrease was smaller than that found during infection with the WT phage (Fig. 2a). Second, ectopic expression of the phage NblA resulted in some reduction in the PEB and PUB absorbance peaks (Fig. 2e). Third, we assessed whether the cyanophage NblA could restore phycobilisome disassembly during infection with the ∆nblA cyanophage mutant. Indeed, NblA expression led to a decrease in the Chl fluorescence peak when excited at PUB, declining to levels similar to those during infection with the WT cyanophage by 4 h after infection (Extended Data Fig. 4 (right)). Note that the partial decline in Chl fluorescence at 4 h after infection in the control without induction (Extended Data Fig. 4 (left)) is probably caused by leaky expression in this inducible system[33]. Taken together, our findings suggest a clear effect of the cyanophage NblA on energy transfer from PE to Chl, consistent with a role in phycobilisome disassembly and degradation during infection.

We next assessed the protein targets of the cyanophage NblA protein by following the production of new protein cleavages in host cells ectopically expressing the viral NblA. For this, we analysed proteins with newly produced N termini using mass spectrometry (MS)[36] at 24 and 48 h after induction (at which time maximum protein induction occurs)[33]. Many new cleavages were observed (Supplementary Data 3). Among these, 201 cleavage events in 107 proteins were substantially more abundant (at least twofold) after viral NblA expression, including 81 cleavages in 59 proteins at 24 h and 103 cleavages in 59 proteins at 48 h after induction (Fig. 3 and Supplementary Data 3). These include several cleavages of phycobilisome subunits (Fig. 3a and Extended Data Fig. 5). At 24 h after induction, four phycobiliproteins were cleaved (Fig. 3b,c); the peripheral PEII disk α subunit (MpeA), the phycocyanin β subunit RpcB, the rod linker MpeE and the ApcE linker responsible for energy transfer from the APC core to the chlorophylls of the photosynthetic reaction centres in the thylakoid membranes[9]. At 48 h after induction, many of the new proteolytic cleavages were of phycobilisome subunits (Fig. 3a,b). These included the same three PEII, PEI and PC rod disk α subunits that displayed low levels during infection with the WT phage (MpeA, CpeA and RpcA) (see above) as well as the three PE rod disk β subunits (MpeB, CpeB and RpcB), one core protein (ApcB) and three linker proteins connecting between disks in the rods (CpeC, MpeD and MpeE) (Fig. 3b,c and Supplementary Data 3). These proteolytic cleavages spanned almost all phycobilisome rod proteins, and ApcB of the phycobilisome core (Fig. 3c). These results provide further evidence that the cyanophage NblA protein leads to the degradation and disassembly of the cyanobacterial phycobilisome antenna complex. They also suggest that the cyanophage NblA directs disassembly in a stepwise manner, initially to disconnect the host phycobilisome from the thylakoid membrane and to degrade peripheral PEII disks, followed by cleavage of the more internal PEI and PC disks. This is similar to the process known for cyanobacterial NblA during nutrient stress, in which phycobilisome degradation begins at the peripheral rod disks and moves inwards towards the phycobilisome core[11]. Notably, a previous study[37] reported that infection by a cyanophage lacking a detectable nblA gene leads to the release of PE peptides, suggesting that cyanophages without nblA may have an alternative mechanism for degrading outer PE rods.

Fig. 3: Proteolytic patterns in host cells after ectopic expression of the cyanophage NblA.

Proteomic analysis of newly cleaved proteins after cyanophage NblA expression in Synechococcus sp. strain WH8109 cells for 24 h (left) and 48 h (right), as compared to non-induced cells. n = 2 biologically independent experiments. a, The abundance ratios of neo-N-terminal peptides from phycobilisome proteins plotted against their MS signal intensities (which indicates the overall peptide abundance). The filled triangles indicate neo-N-terminal peptides with absolute log_2-transformed ratios of ≥1 in both replicates. Upward-pointing and downward-pointing triangles represent peptides that are more and less abundant, respectively, after NblA expression relative to the control. b, The numbers of neo-N-terminal peptides and their corresponding proteins in different functional categories that showed consistent abundance changes after NblA expression (log_2-ratio of ≥1 in both replicates; Extended Data Fig. 5). Proteins were categorized according to a modified classification of COG functional groups (Methods), with photosynthesis-related proteins other than phycobilisomes in ‘energy’, translation and DNA and RNA binding proteins in ‘information storage and processing’, cell division and porins in ‘cellular processes and signalling’ and transporters in ‘metabolism’. c, Phycobilisome cartoons showing proteolytic cleavages in phycobilisome subunits. The colours indicate phycobiliprotein cleavages in APC (turquoise), PC (blue), PEI (orange) and PEII (red), and linker proteins with cleavages between the discs, the core and the thylakoid membrane (various colours). Fully coloured discs indicate cleavages in both α and β subunits, semi-coloured discs or quarter-coloured cores represent cleavages only in α or β subunits d, Preferred amino acid cleavage motifs after ectopic expression of the cyanophage NblA. Sequence logos are for neo-N-terminal peptides with abundance ratios that were at least twofold higher in NblA-expressing cells. Residues passing two-sided t-tests are shown (uncorrected P ≤ 0.05), as implemented in IceLogo. Cleavage sites are marked with a dashed line.

Ectopic expression of the cyanophage NblA led to proteolytic processing of additional photosynthesis-related proteins beyond phycobilisome proteins (Fig. 3b, Extended Data Fig. 5 and Supplementary Data 3). These include those related to PSI (PsaC, PsaK), the PSII oxygen evolution complex (PsbO, PbsU) and carbon fixation (CcmK2, CsoS2). This suggests that the cyanophage NblA negatively impacts host photosynthesis through proteolytic degradation not only of phycobilisome components but also of photosystem proteins and proteins that are needed for carbon fixation. Moreover, a set of proteins with functions other than those related to photosynthesis was also cleaved as a result of expression of the cyanophage NblA (Fig. 3b and Extended Data Fig. 5). This includes proteins involved in translation, such as ribosomal proteins as well as RNA- or DNA-binding proteins at 24 h after induction (Fig. 3b and Supplementary Data 3). Translation initiation and elongation factors were also cleaved 48 h after induction (Fig. 3b and Supplementary Data 3). Other key cellular proteins cleaved include proteins involved in carbon metabolism, a subunit of the cellular RNA polymerase (RpoC2), the cell division protein FtsZ, as well as porin and transporter proteins (Fig. 3b and Supplementary Data 3). It is unclear whether host NblA proteins also direct the degradation of these proteins. Cleavage of these proteins would therefore disrupt multiple cellular processes during infection, in addition to photosynthesis.

In freshwater cyanobacteria, NblA proteins function by binding to phycobilisome subunits as well as to the ClpC chaperone responsible for recruiting the protease that induces proteolytic degradation of the phycobilisome11,38. As proteolytic enzymes often have preferred cleavage sites, we investigated cleavage sites after ectopic expression of the cyanophage NblA in the Synechococcus host (Fig. 3d). At 24 h after induction, we detected cleavages primarily between medium-sized, polar or partially polar residues (Met, Gln, Thr) and small, polar or nucleophilic residues (Ser, Thr, His), while, at 48 h after induction, an additional cleavage site was detected between Lys and Arg residues (Fig. 3d), providing an explanation for the additional cleaved proteins at 48 h after induction. This could be a result of NblA recruiting different proteases or the different substrates being cleaved by the same proteolytic system (presumably the Clp protease complex) with broad cleavage specificity.

Viral nblA is common in the oceans

T7-like cyanophages are very abundant in the oceans31,39. However, the prevalence of the nblA gene in this group is unclear. Thus, to understand the environmental importance of our findings, we first assessed the distribution of nblA genes in assembled genomes of both isolated and environmental T7-like cyanophages. Our search revealed that 46.4% of the complete non-redundant T7-like cyanophage genomes encode nblA genes (Extended Data Fig. 6). nblA-encoding cyanophages have been isolated on picocyanobacterial hosts from the three main lineages: marine Synechococcus subcluster 5.1 (Parasynechococcus[40] in the broad sense), Synechococcus subcluster 5.2 (Cyanobium and related genera) and Prochlorococcus (the Prochlorococcus collective) (Fig. 4), even though the vast majority of the latter do not have phycobilisomes as their light-harvesting antennae21,23. We also found that the gene is present in a rare prophage residing in a Synechococcus subcluster 5.1 genome (AG-670-B23)[41]. Thus, cyanophage nblA is quite common in the genomes of T7-like cyanophages, infecting both Synechococcus and Prochlorococcus.

Fig. 4: The distribution of nblA genes among isolated T7-like cyanophages and selected environmental phage genomes.

The maximum-likelihood phylogenetic tree is based on concatenation of trimmed amino acid alignments of nine core genes (Methods), is outgroup-rooted and was pruned to include the chosen genomes (the complete phylogeny of the cyanophages and the associated metadata are provided in Extended Data Fig. 5 and Supplementary Data 4 and 5). The genomes were subdivided into previously delineated clades A, B and C, as well as the newly defined minor clades: R (P-RSP2-like phages), S (S-SRP02-like phages) and T (no isolated representatives). For each representative, the genomic region containing the exonuclease gene and downstream of it is shown. Frequently appearing orthologous genes are indicated with colour. The colour of the phage names indicates the host lineage that they were isolated on, where known. Environmental genomes are indicated by asterisks. The solid circles mark branches with ultrafast bootstrap support values of ≥95.

A close examination showed two types of nblA genes with differential distribution among the phylogenetic clades of T7-like cyanophages (Fig. 4 and Extended Data Figs. 6 and 7). nblA genes of one type are dominant and are present in clade B cyanophages (to which S-TIP37 belongs) and, to a lesser extent, in clade A. These nblA genes are consistently located downstream of the exonuclease gene and frequently have up to a 110-nucleotide overlap with it. nblA genes of another type are restricted to some P-RSP2-like cyanophages (designated here as clade R) and are located downstream of an HNH endonuclease gene. Neither nblA gene type was found in the genomes of cyanophages from the newly discovered clade C (Fig. 4).

To assess the relationships between NblA proteins from the T7-like cyanophages and those of their hosts, we performed a targeted search for NblA homologues among marine picocyanobacteria. Notably, we found nblA genes not only in marine Synechococcus, but also in many Prochlorococcus low-light-adapted ecotypes (Extended Data Figs. 7 and 8). While marine Synechococcus typically possesses several nblA genes, with, for example, Synechococcus sp. strain WH8109 having five intact genes and a pseudogene, Prochlorococcus strains have a single nblA gene. These findings indicate that nblA genes are also found in cyanobacteria that do not possess phycobilisomes as well as in the cyanophages that infect them.

NblAs from the marine picocyanobacteria are substantially divergent from the well-characterized freshwater cyanobacterial NblAs (as exemplified by the chromosomally encoded NblA from Nostoc sp. strain PCC 7120) with respect to sequence, yet their predicted structures preserve the classical dimeric NblA architecture (Extended Data Fig. 8). However, NblA from the T7-like cyanophages demonstrate higher overall sequence similarity to the well-characterized cyanobacterial NblAs rather than to those of their hosts (Extended Data Fig. 8). The T7-like cyanophage NblAs cluster together in a phylogenetic network, suggesting that they represent a monophyletic group (Extended Data Fig. 7). Together these findings suggest that the acquisition of nblA by T7-like cyanophages occurred in the distant evolutionary past. This is in contrast to nblA genes from freshwater cyanophages infecting Microcystis and Planktothrix that have high similarity to nblA genes from the corresponding cyanobacterial groups6,8,27.

We next assessed the relative abundance of T7-like cyanophages carrying the nblA gene in the oceans. We used the consistent genomic association of the dominant nblA type with the exonuclease gene, a core gene found in all T7-like cyanophages sequenced so far42,43 to examine the read data from the Global Ocean Viromes (GOV) metagenomic dataset. This enabled us to determine both the presence or absence of the nblA gene and the relative abundance of the different clades from the exonuclease gene. Our quantification strategy yielded general distribution patterns of T7-like cyanophages similar to previously reported studies. Cyanophages belonging to clades B and C dominated the global oceans31,42, while clade A and R phages were relatively rare (Fig. 5). The vast majority of cyanophages from clade B possess the nblA gene (Fig. 5), with around 72% of those at the surface and 89% of those deeper in the photic zone at the deep chlorophyll maximum (DCM) carrying the gene. The proportion of nblA-encoding cyanophages among the less abundant clade A group was much lower, averaging about 24% at the surface and 10% at the DCM. In accordance with the distribution of the nblA genes in complete genomes, none of the clade C and R cyanophages had nblA genes downstream of the exonuclease gene. As the nblA gene is located in a different genomic position in clade R, our quantification method could not be applied to them. Overall around 35% and 65% of the T7-like cyanophages (from clades A, B and C) encoded nblA in the surface and at the DCM, respectively. These findings indicate that nblA is widespread among the abundant clade B cyanophages both at the surface and deeper in the photic zone.

Fig. 5: The global distribution of T7-like cyanophages with and without nblA genes.

a,b, The relative abundance of T7-like cyanophages in surface waters (a) and at the DCM (b). Quantifications are based on fragments per kilobase per million total reads (FPKM) abundances for exonuclease genes with and without downstream nblA genes and assigned to one of the five clades of T7-like cyanophages. Raw data and exonuclease-containing contigs for read recruitment were retrieved from the Global Ocean Viromes 2.0 dataset (GOV 2.0). The insets show the relative abundances of the different clades of cyanophages across the data (based on the FPKM values added together) and serve as the legend for the colours on the maps. Map data are from Natural Earth.

Among the T7-like cyanophage isolates that encode nblA, half infect marine Synechococcus strains while the rest infect phycobilisome-less Prochlorococcus strains (Fig. 4). Both groups of cyanobacteria are prevalent in surface waters, whereas Prochlorococcus is considerably more abundant than marine Synechococcus at the DCM21,44. Thus, we anticipate that many of the clade B phages at the DCM infect Prochlorococcus. As the vast majority of Prochlorococcus lineages have a different type of light-harvesting antenna to the phycobilisomes of most cyanobacteria21,22,23, we expect that NblA of the phages infecting Prochlorococcus direct the degradation of other proteins. This possibility is supported by the finding that multiple low-light-adapted Prochlorococcus ecotypes encode an nblA gene (Extended Data Fig. 7), even though they do not have phycobilisomes. Furthermore, our proteomics data indicate that NblA-directed degradation is not restricted to phycobilisome proteins, even for a clade B phage that infects Synechococcus (Fig. 3a,b and Extended Data Fig. 5). Thus, other photosynthesis-related proteins and proteins involved in other cellular processes are probably targeted by many nblA-encoding cyanophages deep in the photic zone of the oceans.

Cyanobacteria acclimatize to low light to maximize their ability to harvest light. This is achieved through increasing the number and size of their antenna complexes45,46,47 as well as the number of their photosystems[48]. As such, more cyanobacterial resources are bound up in the photosynthetic apparatus at depth. Thus, we propose that the ability of cyanophages to degrade the photosynthetic apparatus deep in the photic zone would provide a considerable advantage through the release of amino acids for use in cyanophage progeny production and may explain why relatively more cyanophages at depth carry the nblA gene.

The general distribution of the dominant nblA type in T7-like cyanophages parallels that for the psbA gene (encoding the PSII reaction centre protein D1). Both genes are present in the majority of clade B cyanophages, sporadically in clade A and are absent from clade C. However, they do not always co-occur[28] (Fig. 4 and Extended Data Fig. 6). nblA is more common in T7-like cyanophages than psbA, with 36% of the complete genomes (including environmentally assembled genomes) across all clades encoding psbA compared with 46% for nblA (see above). As psbA is considered to be one of the most common auxiliary metabolic genes in cyanophage genomes2,3,28,42,43, our results suggest that the cyanophage-encoded nblA is very common in oceanic environments as well.

An interesting aspect of T7-like cyanophages that carry both psbA and nblA is that psbA is thought to enable continued photosynthetic energy production during infection3,49,50 while nblA degrades the complex that harvests the light funnelled to the photosystems (this study). This raises the question of how these potentially conflicting functions for two different auxiliary metabolic genes in the same cyanophage can be reconciled. We propose that the two genes are most beneficial to the phage under different conditions. The psbA gene has been hypothesized to be more important under conditions of high light51,52 in which more photodamage to the D1 protein is expected. By contrast, nblA is probably more important to the phage under low-light conditions in which more of the cell’s resources are invested in building the photosynthetic apparatus (see above). Moreover, under high-light conditions, degradation of the phycobilisome by cyanophage NblA could serve to reduce photodamage to D1[7], such that photosynthesis can continue at some level despite less light being harvested by the phycobilisome. Thus, a balance between the activities of these two proteins is probably needed under high light.

The vast abundance of clade B T7-like cyanophages in the oceans encoding nblA raises the possibility that they have a global impact on cyanobacterial photosynthesis. This group of cyanophages is considerably more abundant deep in the photic zone than at the surface31,53, where a very large percentage of them encode nblA (Fig. 5). While it is difficult to quantify the global impact of a single gene, we have performed some rough calculations to estimate the potential effect of viral nblA on picocyanobacterial light harvesting. We base our calculation on the findings that the cyanophage gene caused a 50% reduction in PSII photosynthetic performance (Fig. 1e), that 1–15% of marine cyanobacterial cells are infected by T7-like cyanophages at a given time39,54,55 and that 35–65% of marine T7-like cyanophages encode nblA in different layers of the photic zone (Fig. 5 and Methods). We estimate that 0.2–1.1% and 1.6–4.9% of cyanobacterial photosynthesis in the surface and DCM layers, respectively, could be impacted by nblA. These estimations suggest that, collectively, T7-like cyanophages carrying the nblA gene have a global impact, reducing picocyanobacterial photosynthetic light harvesting by 0.2–5% in the upper oceans.

Concluding remarks

Auxiliary metabolic genes in viruses56,57 are a widespread phenomenon, especially in marine cyanophages1,2,3,4. Previous studies have investigated the putative function of several such genes using in vitro biochemical approaches58,59 or ectopic expression6,13,59,60. Here we combined a recently developed cyanophage genetic engineering system[14], together with inducible ectopic expression[33] and state-of-the-art N-terminal proteomics[36] to directly examine the role of nblA, a gene encoding a small proteolysis adaptor, in cyanophage infection and its impact on the host photosynthetic apparatus. While NblA in cyanobacteria serves as a stress-response mechanism under nutrient deprivation and mediate the controlled degradation of the phycobilisome photosynthetic antenna9,10,11, we propose that its cyanophage counterpart is important not for cell survival, but for virion synthesis. Our results further reveal that the viral NblA directs degradation not only of host phycobilisomes, but also of a suite of other proteins, including important core photosynthesis and house-keeping proteins. Thus, this small auxiliary metabolic gene is likely to have a large impact on both the host’s light-harvesting efficiency, energy production and other essential cellular processes.

The implications of the nblA gene for the cyanophage are considerable, with an approximately threefold shorter infection cycle, suggestive of considerably improved fitness. These findings, together with genomic and metagenomic results of high abundance and widespread distribution of cyanophages carrying the nblA gene in the oceans (this study) and in freshwater ecosystems7,8,13 suggest that these cyanophages have a negative global effect of up to 5% on the amount of light harvested by oceanic cyanobacteria.

Methods

Cyanobacterial growth

Synechococcus sp. strain WH8109 was grown in artificial seawater (ASW) medium[61], with modifications as described previously[62]. Cultures were grown at 21 °C under a light intensity of 20 µmol photons per m^2 per s, under a 14 h–10 h light–dark cycle. Pour-plates were obtained using ASW medium with low-melting-point agarose at a final concentration of 0.28% with an additional 1 mM of sodium sulfite. A heterotrophic helper strain, Alteromonas sp. EZ55, was added to the pour-plate mixture for isolating Synechococcus colonies[63].

qPCR with reverse transcription

For RNA extraction, a 1 ml culture sample was collected by centrifugation at 4 °C, 15,000g for 15 min, and the pellets were flash-frozen in liquid nitrogen. Cell pellets were thawed and incubated with lysozyme L6876-5G (Sigma-Aldrich) at a final concentration of 30 mM and 200 U of RNase inhibitor (Murine BioLabs) for 60 min at 37 °C. An equal volume of lysis buffer was added and cell debris was centrifuged at 4 °C, 16,000g for 1 min. Nucleic acids in the supernatant were precipitated with an equal volume of 95% ethanol and centrifuged as described above. RNA wash buffer (500 µl) from Monarch Total RNA Miniprep Kit (NEB, T2010) was added, and the sample was centrifuged again for 30 s. The supernatant was discarded and the step was repeated. DNase I reaction buffer (5 µl) and 4 U of DNase I from the TURBO DNA-free kit were added to the 45-µl sample and incubated for 10 min at 4 °C. The samples were incubated with 0.5 µl of 0.5 M of EDTA, pH 8.0, for 10 min at 75 °C.

Total RNA was reverse transcribed into cDNA using the LunaScript RT SuperMix Kit (New England Biolabs, E3010). The reaction mixture was prepared in a total volume of 20 µl, 4 µl of LunaScript RT SuperMix containing random hexamers and 16 µl of nuclease-free water, with the RNA sample added to reach the final volume. As a control, a similar mixture was prepared, but without addition of the reverse transcriptase enzyme. The reaction was incubated at 25 °C for 2 min, 55 °C for 10 min and 95 °C for 1 min.

Quantitative PCR (qPCR) reactions were prepared using LightCycler 480 SYBR Green I Master mix from Roche, combined with 0.2 µM of each primer and the nblA/rnpB DNA template. The reactions were run on the LightCycler 480 Real-Time PCR System. Cycle threshold fluorescence values for each reaction were determined using LightCycler 480 software. To quantify DNA copy numbers, a standard curve was generated by running tenfold serial dilutions of the template and correlating cycle threshold values to known DNA concentrations (Supplementary Data 6).

The genes of which the expression levels were analysed using qPCR were as follows: host nblA2 (Syncc8109_1607, see explanation below; primers: 5′-GCGATCAAGCGGTCAATCAAC-3′ and 5′-CTCTCTGCCGCACGTAGAGG-3′), host rnpB (Syncc8109_0157; primers: 5′-CATCGGCGGTGTGTTTCT-3′ and 5′-CAGGCTTGCTGGGT-3′), S-TIP37 nblA (primers: 5′-TTCCCGAGGCAGACAAGAG-3′ and 5′-TAATGGGATGGTGACTCGGC-3′), S-TIP37 DNA polymerase (STIP37_17B; primers: 5′-TGAGCTACTACGCAACAGGC-3′ and 5′-AGCGCGATCATTCAGGGAAG-3′). The Synechococcus sp. strain WH8109 nblA gene chosen for qPCR is the one that we reported previously[6], although a more refined remote homology search with hhsearch[64] using a custom NblA profile reveals that the genome carries four additional nblA-like genes and an nblA pseudogene. To clarify which homologue has the highest structural similarity to previously characterized proteins and is therefore most likely to have a function similar to that of freshwater cyanobacterial NblAs, we obtained the structures for the corresponding monomers with ColabFold[65] and searched them against the Protein Data Bank (PDB) using Foldseek[66]. The best match was indeed obtained for NblA2 (Syncc8109_1607), with the highest similarity to the NblA protein from Nostoc sp. strain PCC 7120 (ref. [10]; PDB: 1OJH chain E; probability, 0.94; TM-score, 0.6621).

Cyanophage-infection experiments

Before infection, Synechococcus sp. strain WH8109 was grown in liquid medium to mid-log growth of around 1 × 10^8 cells per ml. Infection experiments were initiated by adding the S-TIP37 cyanophage strains at an MOI of 5. Infection dynamics were determined by collecting samples at hourly time intervals during the initial 6 h, followed by sampling every 2 h thereafter. The samples were filtered through a 0.22 µm syringe filter and the filtrate containing free cyanophages was plated to determine the number of infective cyanophages using the plaque assay[67] in semi-solid pour-plates (see above). Statistical analysis of the infection course was performed using segmented linear regression by selecting near-linear ranges in the infection curves and obtaining linear fits for the relative cyanophage abundance (obtained by dividing the abundance in the extracellular medium by its maximum across all experiments) with the factors time after inoculation, cyanophage type (WT or mutant) and their interaction, and replicate as random effects using lme4 (v.1.1-31)[68]. The significance of the model terms was tested using the Anova function from the car package (v.3.1-1)[69]. The distributions of the residuals were checked using QQ plots.

Spectral measurements

Absorbance spectra were measured at room temperature using a double-beam Shimadzu spectrophotometer equipped with deuterium and halogen lamps. Spectral data were obtained at a constant bandpass with a resolution of 1 nm. Absorbance spectra were normalized to chlorophyll (680 nm). Fluorescence emission spectra were collected using the Jobin-Yvon Horiba spectrofluorometer. The samples were placed into 1 ml micro quartz cuvettes and excited at 495 nm, and fluorescence emission was measured from 500 nm to 750 nm and normalized to the fluorescence intensity at the emission maximum of PEI (562–564 nm).

The apparent photochemical quantum yield of PSII (QYp), or efficiency of light use by PSII, was determined by measuring fluorescence emission after dark adaptation for 15 min, with and without the addition of (3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU) to a final concentration of 10 µM. DCMU blocks electron transfer between the primary quinone electron acceptor (QA) and the secondary quinone electron acceptor (QB) on the acceptor side of PSII, causing the reaction centres to remain in a closed state[70] The samples were excited at 495 nm and fluorescence emission was measured from 500 nm to 750 nm. The apparent PSII quantum yield was calculated as described previously[71], from the onset of infection up to 10 h after infection, at which point all values fell below zero. QYP was calculated as QYP = (QYF+DCMU − QYF–DCMU)/QYF+DCMU. Absorbance-corrected fluorescence quantum yield (QYF) was calculated as QYF = F/f_495, where F is the integrated area under the fluorescence emission spectrum and f_495 is the fraction of incident light actually absorbed at 495 nm (\({f}_{495}=1-1{0}^{{A}_{495}};{A}_{495}\) is the measured absorbance at 495 nm).

Quantification of the absorption of the different pigments was performed by subtracting the background with the package baseline (v.1.3-4)[72] using the modpolyfit method, identifying the peaks of PUB and PEB and chlorophyll and scaling the intensities to the intensity of the chlorophyll peak. The differences between the uninfected cells and cells infected with the WT and mutant cyanophages 12 h after infection were analysed with linear models and Tukey’s post hoc tests. Fluorescence emission spectra were scaled to the maximum intensity (intensity of the PE peak) to obtain the relative emission intensity of the chlorophyll peak. As the fluorescence measurements were performed repeatedly for the same batches, a mixed model was built to analyse the relative fluorescence of chlorophyll as a function of infection (uninfected cells and two types of cyanophages), time after infection and their interaction, taking into account the random effect of batch with lmer4. The distributions of the residuals were checked with QQ plots. The Anova function from the car package was used to obtain an analysis of deviance tables and P values for the model terms; Tukey’s test was performed as a post hoc test in both cases.

Phycobilisome extraction

Synechococcus sp. strain WH8109 cells were collected by centrifugation at 6,000g for 10 min at 4 °C, 6 h after infection, and kept at −80 °C. The pellets were thawed at room temperature, resuspended with 7.5 M potassium phosphate, pH 7.5, and homogenized. Cells were disrupted with a microfluidizer (Microfluidics, HC-2000) at 80 p.s.i. The supernatant was collected after centrifugation at 20,000g for 30 min at 4 °C and loaded onto a 0.25–1.25 M linear sucrose gradient in 7.5 M potassium phosphate buffer, pH 7.5. The samples were centrifuged in an ultracentrifuge at 170,000g for 18 h at 4 °C. The fractions were collected with a syringe and analysed by fluorometry at 77 K and spectrophotometry as described above.

Construction of S-TIP37 nblA-deletion mutant

The open reading frame (ORF) encoding nblA is 237 bp long (NCBI: MH540083.1, located at nucleotides 12467–12706) and was previously identified by us in the genome of S-TIP37 based on a match to our custom NblA protein profile[6]. Profile–profile searches with hhsearch using the HHpred server[73] for this protein yield high-scoring matches to cyanobacterial NblA sequences and Pfam NblA profile (PF04485). Analogously, folding the protein with ColabFold[65] produces a typical dimeric structure of NblA with the two monomers composed of two helices each and unstructured terminal regions (Extended Data Fig. 7).

The nblA mutant was produced as described previously[14]. As phages gain random mutations readily, we constructed two independent S-TIP37 ∆nblA mutant cyanophages to ensure that the observed phenotype was directly related to the lack of the nblA gene. In brief, the nblA ORF was used to prepare a construct containing a recombination template for viral homologous recombination. We replaced 137 bp of the nblA gene from position 12,572 to 12,707 with a tag of 23 bp. As the nblA gene has an overlap of 94 nucleotides with the upstream exonuclease ORF exo, the region chosen for the deletion covered the part of nblA not overlapping this gene. However, this region covered the part of nblA overlapping a downstream ORF coding for a protein homologous to gp1.7, a nucleotide kinase, of the T7 Escherichia coli phage, resulting in deletion of 41 nucleotides at the 5′ end of the gene (this short gene is underannotated in T7-like cyanophage genomes and was not originally annotated in S-TIP37). The construct was cloned into the replicative pRL-proCAT[14] plasmid and conjugated into Synechococcus sp. strain WH8109 (refs. 14,74). The strain expressing the recombination template was infected with WT S-TIP37. The lysate was filtered through a 0.22-µm syringe filter to remove cell debris. The presence of recombinant phages was verified by PCR with one primer for the inserted TAG sequence and one in the phage genome: 5′-TGGTGATCAGACCGATGGG-3′ (forward) and 5′-GAGCTCATAGCAAAGAAGACGTC-3′ (reverse).

Enrichment and PCR screening for recombinant cyanophages was performed in 96-well plates containing the Synechococcus host[14]. Wells containing recombinant cyanophages were filtered and plated on semi-solid medium. Single phages were plaque-purified twice and the whole genome of each purified mutant phage clone was sequenced alongside the corresponding WT. Illumina MiSeq trimmed read pairs were received and the genomes were assembled de novo with Spades (v.3.14.1)[75]. Both ∆nblA mutants had additional mutations in their genomes compared with their corresponding WT genomes (Supplementary Data 7 for the genome sequences). Non-synonymous mutations in the first mutant relative to the first WT had a T > C substitution at position 11142 (position according to reference genome MH540083.1) leading to a V208A mutation in the gene for the DNA polymerase nucleotidyl transferase subunit (NCBI: AXF42115.1) and an A > C substitution at position 37714 in gene 42, encoding a putative 2OG-Fe(ii) oxygenase (NCBI: AXF42102.1), leading to a K34T change. The second ∆nblA mutant had two non-synonymous differences compared with its WT in gene 40, encoding a putative tail fibre protein (NCBI: AXF42100.1): an A > C substitution at position 36856 in the WT genome leading to a D454A change (relative to the reference genome) and an A > G substitution at 36888 in the ∆nblA genome, leading to a N465D change. As both ∆nblA mutants had additional mutations compared with the WT, infection and spectral experiments were performed with both mutants and gave the same results. Results with the second mutant are shown. Rescue and proteomics experiments were performed with the second mutant. The mutant does not express the putative nucleotide kinase. The relevance of this gene to the phenotype was addressed in the rescue experiments through ectopic expression of nblA but not the putative kinase (see below section).

Ectopic expression of the cyanophage nblA

A theophylline translational induction system was used for expression of the cyanophage NblA protein in Synechococcus sp. strain WH8109 (refs. 32,33). A riboswitch sequence that theophylline binds to and the full-length S-TIP37 nblA gene were cloned into the pRL-proCAT replicative plasmid downstream of the rnpB promoter as described previously[33] and were conjugated into Synechococcus sp. strain WH8109(refs. 14,74). The construct consists of the regions from nucleotides 12467 to 12703 relative to the reference S-TIP37 genome (GenBank: MH540083.1) and six additional amino acids that were added at the NblA C-terminus (Gly, Ser, Tyr, Ser, Val, Thr) during the cloning process. As nblA overlaps two neighbouring genes, the insert contains the last 95 nucleotides of the 3′ region of the putative exonuclease gene and the first 37 nucleotides of the 5′ region of the putative nucleotide kinase gene. The latter corresponds to 12 out of 94 amino acids of the protein, and proteomic analysis verified that this protein was not present in the induction experiments. As such, rescue experiments reinstated expression of NblA but not the putative nucleotide kinase.

Expression experiments were carried out with the exponentially growing WH8109 conjugant. Theophylline (0.3 mM), dissolved in ASW, was added to induce translation of the NblA protein. Expression of proteins under this theophylline-inducible system is leaky, with differences between induced and non-induced expression detected from 7.5 h after addition of theophylline that increased until 48 h after induction[33]. For rescue experiments, theophylline was added 8 h before infection with cyanophages. For assessing the effect of NblA on Synechococcus sp. strain WH8109 protein cleavage, samples were collected 24 and 48 h after induction. Induced samples were compared to non-induced samples. Each expression experiment was accompanied by a control construct carrying the pRL-proCAT plasmid containing the riboswitch but lacking a downstream gene.

Proteomic analyses

Protein extraction

Cyanobacteria were collected and washed three times using 50 mM HEPES, pH 7.5. After the final centrifugation, the cyanobacterial pellet was resuspended with 8 M guanidine hydrochloride (GuHCl), 100 mM HEPES, pH 7.5, and was heated at 95 °C for 10 min. The samples were then sonicated using the VialTweeter (Hielscher) system at maximum amplitude, 70% cycle time for 5 min, then heated for another 5 min at 95 °C to ensure maximal extraction and denaturation. Cellular debris was pelleted at 18,000g for 10 min, and the clear supernatant containing proteins was transferred to a new tube. Protein concentrations of each sample were measured with the BCA assay, before splitting each sample; 10 µg was taken for total proteome analysis and 50 µg was taken for N-terminome analysis.

Total proteomics sample preparation

Proteins were reduced with 5 mM dl-dithiothreitol (DTT) at 65 °C for 30 min then cooled to room temperature and alkylated with 12.5 mM chloroacetamide (CAA) for 30 min in the dark. The guanidinium concentration was diluted to 1 M using 100 mM HEPES, pH 8, and trypsin (Promega, V115A) was added at 1:100 (w/w) ratio overnight at 37 °C. Next, trypsin was quenched with 1% formic acid and the samples were desalted using C18 stage tips (Empore 66883-U) before subjecting them to MS analysis.

N-terminal proteomics sample preparation

N-terminal enrichment was performed using an optimized hydrophobic tagging-assisted N-termini enrichment (HYTANE) procedure as described previously[36]. Proteins were reduced and alkylated with DTT and CAA as described above. Different isotopes (heavy and light) of formaldehyde were then used to label primary amines in each pair of comparative samples. The labelling was done with 40 mM formaldehyde and 20 mM of sodium cyanoborohydride at 37 °C overnight. Leftover formaldehyde was quenched using 100 mM glycine for 1 h at 37 °C before mixing the heavy and light labelled samples together. The samples were diluted to reduce GuHCl concentration to 1 M using 100 mM HEPES, pH 8, before adding trypsin at 1:100 (w/w) and incubating overnight at 37 °C. The trypsin was then quenched with 1% (final) formic acid, and the samples were desalted using OASIS-HLB columns (Waters). The elution was done using 60% acetonitrile, 0.1% formic acid and the samples were dried using a speed-vac. The peptides were resuspended using 100 µl of 100 mM HEPES pH 7 and had undecanal solution (20 mg ml−1 prepared in ethanol) added to them at a w/w ratio of 1:50 (protein:undecanal), followed by the addition of sodium cyanoborohydride at a final concentration of 20 mM. Undecanal tagging was done for 2 h at 50 °C, renewing the sodium cyanoborohydride after 1 h. The samples were then centrifuged at 16,000g for 5 min and the supernatant was transferred to a new tube before drying in a Speed-Vac. The dried samples were resuspended in 500 µl of 2% acetonitrile, 0.1% formic acid and subjected again to the OASIS-HLB column. Elution was done using 60% acetonitrile, 0.1% formic acid, and the samples were dried in a Speed-Vac before being resuspended again and analysed using MS.

LC–MS analysis

Desalted samples were subjected to liquid chromatography (LC)–MS analysis using an Orbitrap Exploris 480 coupled with an EvoSep One HPLC. The samples were introduced onto the EvoTip, which was then washed twice with 20 μl of 0.1% formic acid. The washed peptides were kept wet by applying 150 μl of 0.1% formic acid atop the EvoTip until MS analysis. The samples loaded onto the EvoTips underwent chromatography separation on a 15 cm × 150 μm analytical column, filled with 1.9 μm C18 beads (EV1106). Peptides were separated over an 88-min gradient according to the manufacturer’s standard method. Full MS scans acquired in positive-ion mode, scanning from 300 to 1,800 m/z, were recorded at a resolution of 120,000 by a data-dependent mode, selecting the top 20 ions with high-energy collisional dissociation (HCD) fragmentation ion at a resolution of 17,500 and with dynamic exclusion enabled.

MS data analysis

For total proteomics, data analysis was conducted using FragPipe v.22.0 (https://fragpipe.nesvilab.org/) using DDA+ mode[76] with the default label-free quantification–match between runs (LFQ-MBR) settings. The search enzyme was set to trypsin, allowing up to two missed cleavages. Variable modifications included methionine oxidation and protein N-terminal acetylation, while carbamidomethylation of cysteine was set as a fixed modification. For N-terminomics data, raw files were first converted to MzML format and then analysed using the Trans-Proteomic Pipeline (v.6.3)[77] with the Comet search engine v.2023_01 rev2. The search enzyme was set to Semi-ArgC, allowing for up to two missed cleavages. Variable modifications included methionine oxidation and the mass difference between heavy and light dimethylation at lysine residues or the N termini of peptides. Fixed modifications included carbamidomethylation of cysteine and light dimethylation at lysine residues or peptide N termini.

Relative peptide quantifications were performed using XPRESS, with parameters set to mass tolerance of 20 ppm, a minimum of three chromatogram points for quantitation and the number of isotopic peaks to sum set to zero. Post-analysis table creation, cleavage motif extraction and ratio normalization were performed using an in-house script[78]. The search database included all Synechococcus sp. strain WH8109 proteins in UniProt (taxon ID: 166314, both reviewed and unreviewed) in addition to the vector added genes and standard contaminant proteins. For viral infection samples, this database was expanded to also include all Synechococcus T7-like phage S-TIP37 (taxon ID: 1332145) protein sequences from UniProt and the NblA sequence. In the analysis of the N-terminomics data, we considered three classes of blocked N-terminal peptides: ORF N termini, neo-N termini generated by internal proteolysis (SemiN1), and proteolysis-adjacent peptides truncated before the first arginine (SemiN2). Only NblA-induced cleavage events that were identified in both biological replicates and showed greater than twofold abundance increases in NblA-expressing cells compared with the control in each replicate were considered for downstream analysis. To bin host proteins into functional groups, we used the COG functional category assignments for Synechococcus sp. strain WH8109 proteins in the eggNOG database (v.5.0)[79]. The proteins were assigned to one of the broad functions based on a modified classification of COG functional groups as follows: phycobilisome components—phycobilisome; other photosynthesis-related genes and other proteins assigned to COG functional category C (energy production and conversion)—energy; COG functional categories J, A, K, L and B—information storage and processing; COG functional categories D, Y, V, T, M, N, Z, W, U and O—cellular processes and signalling; COG functional categories G, E, F, H, I, P and Q—metabolism; COG functional categories R, S and proteins assigned to multiple categories—other.

Phage proteins were classified into functional categories based on the functions of the majority of genes in three genomic and expression clusters29,43. Statistical analysis of the dynamics of abundance of the different functional groups of phage proteins in the total proteomics data as a function of time after infection onset was performed as follows. Genes were grouped into three clusters, with the cluster names reflecting functions of the majority of the corresponding genes: takeover (genes STIP37_1-12 in GenBank MH540083.1), DNA replication and metabolism (genes STIP37_13-23 (including nblA) and STIP37_55) and morphogenesis (genes STIP37_24-54). For each gene cluster, cumulative MS label-free quantification intensities were used as a response variable in a linear model with time after infection, infection type (by WT or ∆nblA mutant), and their interaction as predictor terms. The distributions of the residuals were checked with QQ plots. Detailed results of the statistical analysis are provided in Supplementary Data 2.

Bioinformatic analyses

Analysis of T7-like cyanophage genomes

Genomes of cultured T7-like cyanophages and outgroup phages (coliphage T7 and pelagiphages HTVC011P and HTVC019P) were collected from GenBank. Complete genomes and genomic fragments of environmental T7-like cyanophages and cyanoprophages were obtained from the JGI IMG/VR (v.4.1)[80] and Global Ocean Virome (v.2.0) assemblies[81]. To collect genomic fragments containing exonuclease genes with sufficiently long downstream regions, a conserved region in the C-terminal part of the exonuclease (corresponding to residues 86–221 in the exonuclease protein from S-TIP37; RefSeq accession YP_009807515.1) was chosen and homologous regions from a reference set of cyanophages were used as queries for tblastn from NCBI blast (v.2.15.0)[82]. Fragments were retained when they had matches at least 400 bp long, identity of ≥40%, bit score of ≥400 and at least 500 bp of downstream sequence available. To collect genomes for phylogenetic analysis, out of the contigs with the exonuclease gene, we extracted sequences ≥30 kb long and dereplicated them with dRep (v.3.4.5)[83] at the ANImf identity level of 0.95. Genes were predicted with Prodigal (v.2.6.3)[84] and maximum-likelihood phylogeny was reconstructed with Phylophlan (v.3.0.2)[85], Diamond (v.2.1.8)[86], MAFFT (v.7.475)[87], trimAl (v.1.4.1)[88] and IQ-TREE (v.2.1.2)[89]) based on concatenated alignments of protein sequences of nine core genes: primase-helicase, exonuclease, portal protein (head-to-tail adaptor), head assembly protein, major capsid protein, tail tubular proteins A and B, and small and large terminase subunits. The genes were extracted by searching with Diamond blastp using representative protein sequences as queries from two distantly related cyanophages, P60 and S-SRP02: P60_gp14 (primase-helicase is missing from S-SRP02), P60_gp18 and SSRP02_p034, P60_gp26 and SSRP02_p038, P60_gp27 and SSRP02_p039, P60_gp28 and SSRP02_p040, P60_gp29 and SSRP02_p041, P60_gp30 and SSRP02_p042, P60_gp40 and SSRP02_p011, and P60_gp49 and SSRP02_p012, respectively. IQ-TREE was run with ‘-m LG --alrt 1000 -pers 0.2 -nstop 500’ with 1,000 ultrafast bootstrap replicates[90], and the resulting tree was outgroup-rooted with the ingroup defined as the branch encompassing the known cyanophages. We also assessed the incidence and type of DNA polymerase in the genomes by searching the ORFs with blastp using the sequences of the exonuclease (YP_009807513.1) and polymerase (YP_009807514.1) subunits of the split polymerase of S-TIP37 with an E-value threshold of 10−10. Different T7-like cyanophage lineages were found to diverge in the presence and type of the DNA polymerase gene (Extended Data Fig. 6), and this gene was therefore not used as a phylogenetic marker. The cyanophage genomes were classified on the basis of the phylogeny into six clades: the previously recognized clades A (with a single-ORF DNA polymerase), B (a split DNA polymerase) and C (no DNA polymerase) and the newly defined clades R (for P-RSP2-like phages, single-ORF DNA polymerase), S (S-SRP02-like phages, no DNA polymerase) and T (represented by GOV contig Station52_DCM_ALL_NODE_78, no DNA polymerase) (Extended Data Fig. 6). Metadata of the genomes chosen to represent each of the clades are provided in Supplementary Data 4. Two outlier genomes were found to cause spurious clustering and were excluded from the phylogenetic analysis: IMGVR_UViG 3300032116_000204 and IMGVR_UViG 3300029337_000223. The incidence of nblA and psbA genes in the genomes was assessed by searching ORFs (between stop codons) with hmmsearch from HMMER (v.3.4)[91] using a custom NblA profile (see below) and the PsbA profile TIGR01151.1 from NCBI Protein Family Models. A version of the tree focusing on representative genomes as shown in the main text was obtained by trimming the full tree. The trees were visualized with ggtree (v.3.2.0)[92]. The full phylogenetic tree without the outgroups is available in Supplementary Data 5.

Picocyanobacterial genomes

Metadata and genome sequences for picocyanobacteria were downloaded from Cyanorak (v.2)[93] and additional Prochlorococcus genomes20,25 were downloaded from Integrated Microbial Genomes & Microbiomes[94]. Genes were predicted with prodigal and GeneMarkS-2 (v.1.14_1.25)[95], with the predictions merged using gffcompare (v.0.12.6)[96].

Analysis of NblAs

The NblA HMM profile used to search for nblA genes in T7-like cyanophage genomes was obtained from an alignment of the previously released NblA sequences[6] and manually curated NblA sequences from representative T7-like cyanophages. The searches for the NblA hits were performed without heuristic filters and the results were filtered using an empirically determined full score threshold of 20. The same NblA profile was also initially used to search for nblA genes in the protein sequences from picocyanobacteria. After finding that many of their NblAs yield sub-significant hits, we built a separate NblA profile specifically targeting picocyanobacterial NblAs based on the sequences collected in the first round of the search. Note that, due to the high divergence of the NblAs from picocyanobacteria, many of them avoided detection in our previous screen of cyanobacterial genomes using a general NblA protein profile[6]. The two NblA protein profiles are available in Supplementary Data 10.

A NeighborNet network was constructed to visualize similarity relationships between NblA proteins of different origins. NblAs from T7-like cyanophages and picocyanobacteria were combined with cyanobacterial sequences assigned in UniProt r.2025_2[97] to Pfam profile PF04485, as well as selected NblA sequences from non-T7-like cyanophages. To reduce redundancy, the sequences were clustered at 90% identity level with CD-HIT (v.4.8.1)[98]. The cluster representatives were aligned with MAFFT in automated mode, and trimAl was used to trim the alignment (strict mode, minimum column block size of 15). The resulting trimmed alignment was used as input to SplitsTree (v.4.17.0)[99], which generated a NeighborNet network based on uncorrected distances. The network was visualized with tanggle (v.1.8.0)[100].

Sequence logos were generated for different groups of NblAs using DiffLogo (v.2.26.0)[101]. The original MAFFT alignment was trimmed in a similar way to that above, but only regions outside of the core NblA domain were trimmed. The fasta file was converted to A3M format (matching columns with <50% gaps) and secondary structure predictions were added with tools from HH-suite (v.3.3.0)[64]. For the sequence logos, the remaining gaps were coded as the separate state X.

Representative structures of NblA dimers were predicted with ColabFold v.1.5.5 (based on AlphaFold2)[65].

Analysis of the global distribution of the cyanophage nblAs

For the analysis of the distribution of nblA downstream of the exonuclease gene, we took all of the initially collected environmental contigs with T7-cyanophage type exonucleases and extracted regions containing the 3′ end of the exonuclease gene with up to 100 bp upstream and up to 1,000 bp downstream. These fragments were searched against exonuclease sequences from the genomes used for phylogeny using blastx and clades were assigned to fragments with best hits to cyanophages at identity level of ≥60%. The fragments coming from the GOV2.0 assemblies were used for recruitment of GOV raw data with bwa (v.0.7.17)[102]. Quantification was performed with featureCounts from subread (v.2.0.6)[103]. As the exonuclease and nblA genes frequently overlap, we selected strictly defined windows for read quantification instead of ORF boundaries: the exonuclease was represented by the above-mentioned conservative region at the 3′ end of the gene. For nblA, we chose the location corresponding to the core NblA region based on the hmmsearch matches. Genes assigned to the same cyanophage clade were grouped into metafeatures for quantification and the resulting per-station mapped read pair counts were converted to FPKM values by dividing them by the median feature length (in kb) and the total number of the reads per sample (in millions). The sequences used for recruitment and quantification results in tabular format are provided in Supplementary Data 9.

The bioinformatic workflow was implemented in snakemake[104], Python and R.

Calculations of the ocean-wide impact of viral nblA genes on light harvesting by picocyanobacteria

To estimate the ocean-wide impact of viral nblA genes on light harvesting by picocyanobacteria, we used the following data: a 100% reduction in photosynthetic performance for 50% of the time attributable to the cyanophage nblA (Fig. 1e); 1–15% of marine cyanobacterial cells infected by T7-like cyanophages at a given time39,54,55; and 35% (surface waters) to 65% (DCM zone) of marine T7-like cyanophages encoding nblA (Fig. 5). The impact of viral NblA proteins on marine cyanobacterial photosynthesis in surface water was calculated as follows: 50% reduction in photosynthetic light-harvesting performance, with 1–6% of cells infected and 35% of T7-like cyanophages carrying nblA genes, giving an estimated impact of 0.175–1.05% on the photosynthetic performance of the picocyanobacteria. The impact on marine cyanobacterial photosynthesis at the DCM was estimated as follows: 50% reduction in photosynthetic light-harvesting performance, with 5–15% of cells infected and 65% of T7-like cyanophages carrying nblA genes, giving an estimated impact of 1.625–4.875% on the photosynthetic performance of picocyanobacteria.

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 in the Article and its Supplementary Information. The MS proteomics data have been deposited to the ProteomeXchange Consortium via the PRIDE partner repository under the following dataset identifiers: PXD057452 (whole proteome data) and PXD057454 (N-terminomics data).

Code availability

The code used for the bioinformatic analyses is available from the GitHub repository (https://github.com/BejaLab/T7_nblA).

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Acknowledgements

We thank F. Salama for biophysical guidance; M. Suissa-Szlejf for help in setting up the phycobilisome isolation gradients; R. Edrei for help with spectroscopy measurements; G. Sabehi for discussions on infection experiments; S. Goldin for help with qPCR calculations; S. Larom for technical support; N. Keren and C. Kranzler for discussions on photosynthesis experiments; N. Keren for help in performing spectroscopy; and N. Frankenberg-Dinkel for comments on the manuscript. This work was funded by the European Research Council (ERC Advanced Grant 321647 to O.B. and ERC Consolidator Grant 646868 to D.L.), the Nancy and Stephen Grand Technion Energy Program (GTEP), Israel Science Foundation grants to O.B. (143/18) and O.K. (1515/23), and the Simons Foundation Life Science Award 735081 to D.L.; O.B. holds the Louis and Lyra Richmond Chair in Life Sciences and D.L. holds the Dresner Chair in Life Sciences and Medicine.

Author information

Authors and Affiliations

1. Faculty of Biology, Technion—Israel Institute of Technology, Haifa, Israel

Omer Nadel, Rawad Hanna, Andrey Rozenberg, Dror Shitrit, Ran Tahan, Irena Pekarsky, Oded Béjà, Oded Kleifeld & Debbie Lindell

2. The Nancy and Stephen Grand Technion Energy Program (GTEP), Technion—Israel Institute of Technology, Haifa, Israel

Oded Béjà

Contributions

O.N. conceived the project, performed viral work, phycobilisome isolation and experimentation and, together with O.B., O.K. and D.L., designed the experiments. I.P. performed phage growth curve experiments. A.R. performed bioinformatic and statistical analyses. R.H. and O.K. performed proteomic analyses. D.S., R.T. and D.L. developed the methods for constructing the mutant phage and the cyanobacterial NblA expression strain. O.B. coordinated the project. O.N., A.R., O.B., O.K. and D.L. wrote the paper, which was revised and approved by all authors.

Corresponding authors

Correspondence to Oded Béjà, Oded Kleifeld or Debbie Lindell.

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Competing interests

The authors declare no competing interests.

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

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Extended data figures and tables

Extended Data Fig. 1 Expression of the cyanophage nblA gene during S-TIP37 infection of Synechococcus sp. strain WH8109.

a, Transcript levels of S-TIP37 cyanophage nblA and DNA polymerase genes and one of the host nblA genes during infection with WT cyanophage determined by qRT-PCR. Transcript levels are normalized to the rnpB gene. Among the host nblA genes, nblA2 was chosen as the gene coding for the NblA protein with the highest structural similarity to previously characterized NblAs (see Methods). b, Protein mass spectrometry intensity levels of the S-TIP37 cyanophage NblA, DNA polymerase, and host NblA6 proteins during infection with WT (left) or ∆nblA mutant (right) cyanophages, determined by LC-MS/MS analysis. NblA6 was the only host NblA protein detected. Data are presented as mean ± standard deviation of three independent biological replicates, n = 3.

Extended Data Fig. 2 Spectroscopic characteristics of cells infected with wild-type and ∆nblA mutant S-TIP37 cyanophages.

a, Relative absorbance of PUB and PEB at 12 h post-infection. Relative absorbance was determined as follows (see the panel to the left): the absorbance spectra were background-subtracted (red line) and the intensities were scaled to the height of the Chl peak. UI, uninfected, KO, infection with the ∆nblA mutant, and WT, infection with the wild-type phage. b, Relative chlorophyll fluorescence at different time points during infection. The samples were excited at 495 nm (excitation maximum of PUB), emission spectra were obtained and the height of the chlorophyll peak relative to the PE peak was calculated (see the panel to the left). The PE peak at 560 nm is made up of PEI and PEII, to which the PEB and PUB chromophores bind. In both panels, values in the pairwise comparisons indicate p-values from the Tukey’s (two-sided) post-hoc tests and asterisks denote significant pairs of differences: *** — p-value < 0.001 (after FDR adjustment in panel b). See Suppl. Data File 2 for further statistical details and exact p-values. Boxplots reflect minimum-maximum range (vertical line), interquartile range (rectangle) and median (horizontal line). The results are based on five biological replicates of each condition: uninfected cells and cells infected either with the ∆nblA (KO) or wild-type (WT) phage, sampled repeatedly at different time points for measurement. For further results of the statistical analyses refer to Suppl. Data File 2. Representative spectra are shown in Fig. 2a,b.

Extended Data Fig. 3 Fluorescence spectral analysis of fractionated phycobilisomes.

Fluorescence emission spectra at 77 K of fractionated phycobilisomes from uninfected Synechococcus sp. strain WH8109. The lower density, top band (see Fig. 2c), contains disassembled phycobilisome complexes as seen by the single fluorescence peak corresponding to the excited PE protein. In comparison, the higher density, bottom band (see Fig. 2c), contains assembled phycobilisome complexes characterized by the presence of three phycobiliprotein peaks which indicates intact energy transfer from PE to PC and APC.

Extended Data Fig. 4 Fluorescence emission spectra upon ectopic expression of cyanophage NblA in Synechococcus sp. strain WH8109 during infection.

Fluorescence emission spectra of uninfected cells (green), cyanobacteria infected by the WT cyanophage (blue) and by the ∆nblA mutant cyanophage (red) at different time points post-infection. The host strain carries a plasmid for inducible expression of the cyanophage nblA gene. Ectopic expression was induced in the host 8 h prior to addition of the phages (NblA induction, the panels to the right). Control experiments (the panels to the left) were performed with the same host strain but without the addition of the inducer. Measurements were taken at room temperature and normalized using the PE peak.

Extended Data Fig. 5 Cleavage and proteome changes upon ectopic expression of cyanophage NblA in Synechococcus sp. strain WH8109.

Proteomic analysis of cleavage events (a and b) and total protein abundance changes (c and d) following ectopic expression of the cyanophage NblA in Synechococcus sp. strain WH8109 cells for 24 h (a and c) and 48 h (b and d), compared to non-induced controls. In both analyses, n = 2 biologically independent experiments. The top panels show the abundance ratios of neo-N-terminal peptides identified by N-terminomics, calculated as the ratio of signal intensities between induced and non-induced samples, reflecting changes in peptide abundance. The bottom panels show the abundance ratios for proteins in the total proteomic analysis based on the intensities of tryptic peptides. i.e. Each data point represents an individual peptide or protein. The values represent averages of two biological replicates. Proteins are categorized according to a modified classification of COG functional groups (see Methods). Filled triangles indicate neo-N-terminal peptides and proteins with absolute log_2-ratios ≥1 in both replicates. Upward-pointing and downward-pointing triangles represent peptides more and less abundant, respectively, upon NblA ectopic expression relative to the control. Red asterisks indicate significant deviations of the category-wise mean ratios from zero (two-sided one-sample t-test) after FDR adjustment across all comparisons: *** — adjusted p-value ≤ 0.001, ** — adjusted p-value ≤ 0.01, see Suppl. Data File 2 for details of the statistics and the exact p-values.

Extended Data Fig. 6 Phylogeny and distribution of nblA genes among T7-like cyanophages.

Maximum likelihood phylogenetic tree was built based on concatenation of protein alignments of nine core genes coding for: primase-helicase, exonuclease, portal protein (head-tail adaptor), head assembly, major capsid protein, tail tubular proteins A and B, and small and large terminase subunits. Phage genomes used in the phylogeny were recruited from among cultured T7-like cyanophages and from environmental sources: Global Ocean Virome v. 2 assemblies and JGI IMG/VR v. 4.1 (see Suppl. Data File 4). The environmental genomes were recruited by searching for the exonuclease gene, selecting genomes at least 30 kb long, dereplicating them at 0.95 ANImf identity level and requiring the presence of at least eight core genes. The tree was outgroup-rooted by inclusion of coliphage T7, pelagiphage HTVC011P, pelagiphage HTVC019P and environmental phages falling outside of the cyanophage cluster. The pie chart summarizes the numbers of non-redundant phage genomes with and without nblA in each clade (notice that no clade C, S or T genomes were found to code for nblA). Phages were categorized into previously recognized clades A (P60-like), B (S-TIP37-like) and C (P-SCSP1a/2-like) and newly-delineated clades R (P-RSP2-like), S (S-SRP02-like) and T (Ga0063588_100037_PP-like, no cultured representatives). Presence and type of DNA polymerase genes is indicated with the clades dominated by phages falling in one of the following categories: no DNA polymerase gene (clades C, S, T), DNA polymerase coded in a single ORF (clades A and R) and a split DNA polymerase gene[105] with the exonuclease domain coded in a separate ORF (clade B). Clade representatives are coloured with labels according to the host’s phylogenetic affiliation when known. Environmental genomes are indicated by asterisks. Note that each of the three picocyanobacterial lineages represents an assemblage of several genus-level taxa. The incidence of nblA (circles) and psbA (squares) genes is indicated with symbols at the tips of the corresponding branches and the nblA genes of two categories are differentiated: those located downstream of the exonuclease gene (as in S-TIP37) and the nblA gene downstream of an HNH endonuclease gene (in a subclade of clade R). Solid circles mark branches with ultrafast bootstrap support of ≥95. See Suppl. Data File 7 for the source data.

Extended Data Fig. 7 Phylogenetic network of NblA proteins from the T7-like cyanophages, marine picocyanobacteria and other cyanophages and cyanobacteria.

The NblA protein sequences were aligned, trimmed and a NeighborNet network was obtained based on uncorrected distances. The proteins are categorized by the corresponding cyanophage or cyanobacterial group. NblA was found in the low-light adapted Prochlorococcus ecotypes LLII/LLIII, LLIV, LLVII, LVIII, AMZIA, AMZIB, and AMZII but not in LLI and AMZIII nor any of the high-light-adapted ecotypes. NblAs from selected cyanophages and model cyanobacteria with the NblAs from S-TIP37, Synechococcus sp. strain WH8109 and Prochlorococcus sp. strain SS120, are highlighted in bold. The network and trimmed sequences of cluster representatives in NEXUS format are available in Suppl. Data File 8 and metadata and untrimmed sequences and aligned sequences of the core NblA region are available in Suppl. Data File 11.

Extended Data Fig. 8 Structures and protein profiles of NblA proteins from T7-like cyanophages and cyanobacteria.

Left: Dimeric structures of selected representatives of the NblA proteins. All of the structures, except that of the NblA from Nostoc sp. strain PCC 7120 [PDB:1OJH[10]] were obtained with ColabFold (AlphaFold2)[65]. Right: Sequence logos generated based on a trimmed alignment of clustered NblA sequences. Numbers of cluster representatives per group are provided in parentheses. Secondary structure predictions based on the whole alignment of all NblA types are shown at the bottom (H: helix, C: coil) with the height proportional to the prediction score. Positions known to mediate phycobiliprotein binding[38] are highlighted with red-framed boxes: protein profile positions 47 (residues L51 in Nostoc sp. strain PCC 7120 and L64 in cyanophage S-TIP37) and 49 (residues K53 in PCC 7120 and T66 in S-TIP37).

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Nadel, O., Hanna, R., Rozenberg, A. et al. Viral NblA proteins negatively affect oceanic cyanobacterial photosynthesis. Nature 648, 434–442 (2025). https://doi.org/10.1038/s41586-025-09656-x

- Received: 04 November 2024

- Accepted: 19 September 2025

- Published: 12 November 2025

- Version of record: 12 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09656-x

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Mapping Plasmodium transitions and interactions in the Anopheles female

Yan Yan,

Lisa H. Verzier,

Elaine Cheung,

Federico Appetecchia,

Sandra March,

Ailsa R. Craven,

Esrah Du,

Alexandra S. Probst,

Tasneem A. Rinvee,

Laura E. de Vries,

Jamie Kauffman,

Sangeeta N. Bhatia,

Elisabeth Nelson,

Naresh Singh,

Duo Peng,

W. Robert Shaw &

…

Flaminia Catteruccia

Nature volume 648, pages 451–458 (2025)

Abstract

The human malaria parasite, Plasmodium falciparum, relies exclusively on Anopheles mosquitoes for transmission. Once ingested during blood feeding, most parasites die in the mosquito midgut lumen or during epithelium traversal[1]. How surviving ookinetes interact with midgut cells and form oocysts remains poorly understood, yet these steps are essential to initiate a remarkable growth process culminating in the production of thousands of infectious sporozoites[2]. Here, using single-cell RNA sequencing of both parasites and mosquito cells across different developmental stages and metabolic conditions, we unveil key transitions and mosquito–parasite interactions that occur in the midgut. Functional analyses uncover processes that regulate oocyst growth and identify the Plasmodium transcription factor PfSIP2 as essential for sporozoite infection of human hepatocytes. Combining shared mosquito–parasite barcode analysis with confocal microscopy, we reveal that parasites preferentially interact with midgut progenitor cells during epithelial crossing, potentially using their basal location as an exit landmark. Additionally, we show tight connections between extracellular late oocysts and surrounding muscle cells that may ensure parasite adherence to the midgut. We confirm our major findings in several mosquito–parasite combinations, including field-derived parasites. Our study provides fundamental insight into the molecular events that characterize previously inaccessible biological transitions and mosquito–parasite interactions, and identifies candidates for transmission-blocking strategies.

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Main

The apicomplexan parasite P. falciparum is responsible for 90% of cases of malaria, a disease that in 2023 alone caused the death of close to 600,000 people, mostly young children in sub-Saharan Africa[3]. Like all malaria parasites, P. falciparum requires a blood-feeding vector for transmission between humans, and over the course of a long co-evolutionary history it has adapted to be exclusively transmitted by mosquitoes of the Anopheles genus. The parasite journey in the Anopheles female starts when male and female gametocytes are ingested during a blood meal and rapidly mature into gametes, leading to fertilization and formation of a zygote which transforms into a motile ookinete in the blood bolus. Between 24 h and 36 h after ingestion, ookinetes must cross the midgut epithelium to avoid being killed during blood digestion. These initial steps result in substantial parasite loss, and represent one of the most severe bottlenecks in the parasite life cycle[1]. After reaching the basal side of the midgut, ookinetes round up via an intermediate ‘took’ (transforming ookinete) stage[4] to transform into extracellular oocysts, which over the next 7–10 days will extensively grow in size just beneath the basal lamina surrounding the midgut epithelial layer while undergoing DNA replication. This remarkable growth process culminates in the formation of thousands of infectious sporozoites, an intricate process in which individual parasites must be segmented precisely over a relatively short period of time[2] (Fig. 1a). When mature, sporozoites egress from oocysts and invade the mosquito salivary glands, from where they can be transmitted to the next person when the mosquito bites again.

Fig. 1: scRNA-seq provides a complete map of P. falciparum midgut stages.

a, Schematic of dual scRNA-seq, displaying expected parasite forms and mosquito midgut cell types. Single P. falciparum parasites and A. gambiae midgut cells were collected from 80 GFP-depleted (control) and 80 EcR-depleted mosquitoes at the time points indicated by the shaded area: 36 hpi, 2 dpi, 4 dpi and 7 dpi and across four biological replicates. b, PCA plots of the 3,495 parasites collected across the 4 time points (top) and the 2 treatments (bottom). c,d, UMAP plots integrating our scRNA-seq data with midgut stage data from two other studies21,22 (c) and showing 11 distinct parasite clusters (d). BB, blood bolus. e, Dot plot of the top marker genes for each of the parasite clusters, showing their normalized average expression (colour) and the proportion of parasites expressing each gene (size). f, Pseudotime analysis of the integrated scRNA-seq data with trajectory (grey line). g, Gene cluster analysis of our expression data (coloured by Z-scores) identifies four main branches of co-expressed genes across the different clusters (cl., gene cluster; n represents the number of genes in the cluster). Selected GO terms and Kyoto Encyclopedia of Genes and Genomes (KEGG) annotations enriched in each gene cluster are indicated where present. Mosquito schematics in a are adapted from ref. [36], CC BY 4.0 and parasite drawings were adapted with permission from ref. [24], Elsevier.

The mosquito stages of P. falciparum development are relatively poorly characterized compared with asexual blood stages, despite their essential role in transmission, and current knowledge is largely extrapolated from work on more tractable rodent malaria models5,6,7,8,9,10. Although several studies have visualized the route by which ookinetes invade the midgut epithelium11,12,13,14,15, whether they interact with specific midgut cell types and the mechanisms that govern their transition into oocysts remain largely unknown. The processes that fuel oocyst development and promote sporozoite formation are also not fully understood. Tackling these questions has been challenging, as mosquito stages of P. falciparum are restricted to in vivo study and have limited genetic tools relative to asexual blood stage parasites[16]. Moreover, the low ookinete and oocyst load in a midgut limits genome-wide multi-omics approaches of those stages, which have therefore been mostly confined to non-human Plasmodium species, where parasite densities are substantially higher17,18,19,20. For similar reasons, single-cell RNA-sequencing (scRNA-seq) studies of P. falciparum in the mosquito have focused on stages during which parasites are numerous and readily isolated (that is, blood bolus stages and sporozoites)21,22, leaving significant gaps in the parasite life cycle.

Here we reconstruct critical bottleneck stages of parasite growth in the midgut and identify mosquito–parasite interactions by performing dual scRNA-seq of parasites and midgut cells over time, capturing key processes that mediate midgut crossing, oocyst growth and the initial stages of sporozoite formation.

scRNA-seq of midgut and parasite cells

We infected Anopheles gambiae—the major malaria vector in sub-Saharan Africa—with P. falciparum and isolated both parasites and midgut cells at 4 different time points: invading ookinetes (36 hours post-infection (hpi)); newly formed oocysts (2 days post-infection (dpi)); growing oocysts (4 dpi); and late oocysts that may have begun sporozoite segmentation (7 dpi) (Fig. 1a and Extended Data Fig. 1a). We did not attempt to isolate oocysts at later time points given their large size (more than 50 µm), which exceeds the limits of 10x technology. Owing to low parasite numbers relative to the overwhelming number of mosquito cells[23], we enriched for parasites by optimizing the single-cell isolation protocol (Methods) and applied deeper sequencing. In brief, infected midguts were partially digested with collagenase IV and elastase, then filtered through a series of cell strainers to remove large clumps of mosquito cells. The resulting single-cell suspensions contained both midgut cells and parasites, with a cell viability of over 93% as determined by trypan blue staining. We compared parasites developing in mosquitoes under two metabolic conditions: control mosquitoes (injected with double-stranded RNA targeting eGFP (dsGFP)) and mosquitoes depleted of the ecdysone receptor (dsEcR), the nuclear co-receptor of the steroid hormone 20-hydroxyecdysone[24] (Extended Data Fig. 1b–e). Impairing 20-hydroxyecdysone signalling reliably accelerated oocyst growth, which we reasoned would provide more granular resolution at the later stages, and did not affect parasites numbers as previously observed at low parasite densities24,25 (Extended Data Fig. 1b,c). After removing low-quality parasites with low transcript and gene counts and high mitochondrial percentage, we successfully profiled 3,495 parasites, detecting a median of 242–1,773 genes at the various time points and treatments (Extended Data Fig. 1f and Supplementary Table 1).

Principal component analysis (PCA) revealed a large separation along the first component, with parasites at 2, 4 and 7 dpi clustering away from 36 hpi parasites (Fig. 1b). The ookinete–oocyst transition (2 dpi versus 36 hpi) was characterized by a downregulation of RNA metabolism paralleled by an upregulation of translation, and oocyst growth was marked by increased aerobic respiration (4 dpi versus 2 dpi) (Extended Data Fig. 2 and Supplementary Table 2). PCA at early time points showed no clear separation between parasites developing in dsGFP and dsEcR mosquitoes, and consistently, there was no difference in gene expression between these groups. At 7 dpi, however, we detected the upregulation of several genes in parasites from dsEcR female mosquitoes (Extended Data Fig. 2 and Supplementary Table 2), probably reflecting the more advanced oocyst stage in this group (Extended Data Fig. 1b). Among the upregulated genes were the gene encoding circumsporozoite protein (CSP; the most abundant sporozoite surface protein) and genes from the rhoptries, secretory organelles that are essential for invasion of host cells[26], suggesting that we successfully captured the start of sporozoite segmentation.

Parasite atlas across all midgut stages

Next, we generated a uniform manifold approximation and projection (UMAP) of parasites in the mosquito midgut by integrating our datasets with parasites from previous scRNA-seq studies21,22, including gametes and blood bolus ookinetes as well as sporozoites isolated from oocysts (Fig. 1c). This complete midgut atlas uncovered 11 parasite clusters, which we annotated on the basis of marker genes and data source as follows: gametes/zygotes, blood bolus ookinetes, invading ookinetes (Ookinete 1 and 2), Took, newly formed oocysts (day 2 oocyst), growing oocysts (Oocyst 1–4) and oocysts that are segmenting into sporozoites (Oocyst spz) (Fig. 1d,e and Extended Data Fig. 3a, Supplementary Table 3). In agreement with our observation of early segmentation signals at 7 dpi, a few cells bridged the gap between oocysts in an advanced growth phase and sporozoites isolated from oocysts (Fig. 1c,d and Extended Data Fig. 3b). Pseudotime analysis revealed a single trajectory aligning with the expected clusters (Fig. 1f).

Gene clusters unveil key transitions

We clustered genes with similar expression patterns over pseudotime, using only our data owing to differences in gene detection rates among scRNA-seq techniques. The 15 gene clusters identified in this analysis separated into 4 major branches (Fig. 1g and Supplementary Table 4). The first branch (gene clusters 6 and 9) captured expected differences between blood bolus ookinetes and ookinetes that are crossing the epithelium. Cluster 6, highly expressed in blood bolus parasites, was associated with ookinete maturation and characterized by genes involved in cytoskeleton and myosin complex[27]. Cluster 9, expressed across all ookinete clusters, comprised micronemal proteins that are critical for motility and midgut traversal, such as circumsporozoite-and TRAP-related protein (CTRP), chitinase and glycosylphosphatidylinositol-anchored micronemal antigen (GAMA)28,29.

The second branch was largely characterized by processes related to transcription, surface remodelling and adhesion—notable, given that this branch encompasses a transition (ookinete–oocyst) during which parasites undergo profound morphological changes. At the onset of this transition (clusters 13 and 2) we detected strong signals of genes encoding proteins involved in helicase activity and RNA processing, including splicing. Clusters 2 and 5 instead comprised membrane and vesicle trafficking genes, which may facilitate protein transport and surface remodelling. Additionally, two clusters in this branch (13 and 11) contained several var genes encoding variants of PfEMP1 proteins, which are well characterized for their adhesion properties in the asexual blood stage[30]. We speculate that young oocysts may use PfEMP1 to anchor themselves between midgut cells and basal lamina, similar to the manner in which asexual parasites adhere to the lining of blood vessels[30].

The largest branch, spanning from day 2 oocyst to Oocyst spz, captured the processes fuelling the growth phase, including genes regulating translation, proteasome activity and ribonucleoprotein complex (clusters 12, 8 and 7) as well as genes involved in aerobic respiration, lipid biosynthesis and apicoplast functions (clusters 8, 1 and 4). Gene cluster 4, highest in oocyst 4, included functions related to the cell cycle, such as DNA replication (Fig. 1g and Supplementary Table 4).

The final branch, highly expressed in Oocyst spz, was characterized by clear signatures of sporozoite segmentation. Clusters 3, 10, 14 and 15 included genes involved in nuclear migration, components of the inner membrane complex (a scaffolding compartment essential for daughter cell formation) and the cytoskeleton network supporting it, and genes from the invasive organelles rhoptries and micronemes—probably preparing sporozoites for salivary gland and hepatocyte invasion26,31,32 (Fig. 1g and Supplementary Table 4).

Although poly-A capture is not designed to target ribosomal RNAs (rRNAs), these molecules are ubiquitously present in Plasmodium bulk and single-cell RNA-sequencing data[33]. We detected limited expression of different rRNAs via random binding, organized in distinct gene expression patterns (Extended Data Fig. 3c). Expression of the A1/A2 forms that are dominant in asexual parasites[34] appeared highest in ookinete clusters, then gradually decreased—although not entirely to zero—in later stages. The two mosquito-stage rRNAs, S1 and S2 (ref. [34]), were expressed throughout oocyst growth, with S1 starting in Took and S2 in day 2 oocyst.

Combined, these gene expression networks provide significant information on the key developmental transitions that parasites undergo in the mosquito midgut, shedding light into the biology of these understudied stages.

PfATP4 and PfLRS regulate oocyst growth

To assess the functional role of factors emerging from the gene network analysis, we prioritized candidates from different gene clusters that have known potent inhibitors. We selected PfATP4, an Na+-ATPase that is essential for sodium ion efflux (gene cluster 2), which is inhibited by the drug cipargamin (CIP (original name NITD609)), and the leucine-tRNA ligase (PfLRS, gene cluster 1), which is inhibited by the compound MMV670325 (original name AN6426) (Figs. 1g and 2a). We provided these drugs to infected female mosquitoes via sugar solution, from the onset of oocyst formation (2 dpi) until 10 dpi (Fig. 2b). Although neither drug reduced oocyst intensity or prevalence (Extended Data Fig. 4a), both CIP and MMV670325 considerably impaired oocyst growth. As a result, we detected no sporozoites in the salivary glands of CIP-treated mosquitoes at 14 dpi and observed a 54% reduction in sporozoite prevalence after MMV670325 ingestion relative to controls (Fig. 2b). Shorter exposure times of CIP (2–4 dpi and 2–7 dpi) gave similar results, suggesting that regulation of sodium efflux is essential during the early phases of oocyst growth, and the effects were dose-dependent (Fig. 2c,d and Extended Data Fig. 4b–d).

Fig. 2: Functional analysis of candidate genes.

a, Expression profile of PfATP4, target of CIP, and PfLRS, target of MMV670325. b, Left, A. gambiae infected with NF54 parasites were exposed to CIP and MMV670325 via sugar solution at 100 µM delivered from 2 dpi to 10 dpi. Drug ingestion reduced oocyst size at 7 dpi (middle; P < 0.0001), subsequently leading to reduced sporozoite prevalence (right; P < 0.0001 and P = 0.008) in salivary glands at 14 dpi. c, Shortening CIP exposure to 2–7 dpi and 2-4 dpi (left) also reduced oocyst size at 7 dpi (middle; P < 0.0001), subsequently leading to no sporozoites in the salivary glands by 14 dpi (right; P < 0.0001). d, Reducing CIP dosage from 100 µM to 10 and 1 µM in A. gambiae infected with NF54 parasites led to a dose-dependent reduction in sporozoite prevalence (10 μM versus DMSO: P = 0.0108; 100 μM CIP versus DMSO: P < 0.0001) and intensity (10 μM CIP versus DMSO: P < 0.0001). e, Exposure to CIP and MMV670325 in A. stephensi mosquitoes infected with ART29 field isolate (left) resulted in comparable reduction in oocyst size at 7 dpi (middle; P < 0.0001) and no sporozoites in the salivary glands at 14 dpi (right; P < 0.0001). Number of mosquitoes dissected (n) and prevalence of infection (%) are indicated for each sample. Oocyst size (cross-sectional area, μm^2), averaged per midgut, is represented as mean ± s.e.m., sporozoite intensity is represented as median and both are compared using Kruskal–Wallis test and Dunn’s correction (b–d) or Mann–Whitney two-tailed test (e). Infection prevalences represented by pie charts are compared with Fisher’s exact test, two-tailed. Data are pooled from two independent infections. *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001. Schematics in b–e are adapted from ref. [36], CC BY 4.0.

Source data

Similar results were obtained with both drugs in a different mosquito–parasite combination (Anopheles stephensi infected with P. falciparum ART29, an artemisinin-resistant field isolate from Cambodia), and also when exposing female A. gambiae to CIP after infection with P. falciparum P5, a polyclonal field isolate from Burkina Faso[25] (Fig. 2e and Extended Data Fig. 4e,f). These results validate PfATP4 and PfLRS as essential for oocyst development in P. falciparum.

Two additional targets—elongation factor 2 PfeEF2 (cluster 12) and the lactate/H+ transporter PfFNT (cluster 7)—showed smaller effects when mosquitoes were exposed to sugar solutions of their respective inhibitors, MMV643121 and MMV007839 (Fig. 1g and Extended Data Fig. 4g,h). MMV643121 slightly decreased oocyst size at 7 dpi but did not affect sporozoite intensity or prevalence, whereas MMV007839 had no effect on oocyst size but significantly reduced sporozoite intensity, indicating a possible role for this transporter in sporozoite segmentation or salivary gland invasion (Extended Data Fig. 4g,h).

These results highlight how our scRNA-seq data can be systematically mined to uncover essential targets for parasite development. The genes validated here could be targeted in novel mosquito-based malaria control strategies, as previously demonstrated using cytochrome b inhibitors35,36.

PfSIP2 ensures hepatocyte invasion

In the final branch, along with rhoptry and cytoskeletal genes, we also detected the ApiAP2 transcription factor PfSIP2 (gene cluster 10) (Figs. 1g and 3a). In asexual blood stages, PfSIP2 has an essential role probably in daughter merozoite formation[37], yet its role during mosquito stages remains unknown. To test its function, we generated a conditional PfSIP2-knockdown (PfSIP2-cKD) line integrating the TetR-DOZI aptamer system at the C terminus (Extended Data Fig. 5a,b). Removal of anhydrotetracycline (ATC) in asexual blood stage cultures led to parasite death, confirming the essentiality of PfSIP2 (ref. [37]) (Extended Data Fig. 5c). We adapted this system to mosquito stages by providing ATC throughout gametocyte cultures and in the mosquito daily sugar solutions, and induced gene knockdown by withdrawing the compound immediately before mosquito infection (Fig. 3b). PfSIP2-cKD parasites were less infectious to mosquitoes than wild-type (WT) co-cultured ones, but this is often observed in mosquito infections with transgenic parasites that have undergone bottlenecks during the selection process. When we compared PfSIP2-cKD +ATC and −ATC groups, we found no differences in terms of oocyst intensity, prevalence and size at 7 dpi, nor in sporozoite intensity and prevalence at 14 dpi (Extended Data Fig. 5d–f). ATC withdrawal, however, severely impaired the ability of PfSIP2-cKD sporozoites to invade primary human hepatocytes, inducing a remarkable decrease in both invasion efficiency (67% reduction) and the formation of exoerythrocytic forms (96% reduction) (Fig. 3c,d).

Fig. 3: PfSIP2 knockdown impairs hepatocyte infection.

a, Expression of PfSIP2 (PF3D7_0604100) is highest in segmenting sporozoites within late oocysts (circled in the UMAP). b, Schematic representation of primary human hepatocyte infections with WT or PfSIP2-cKD parasites. c,d, Knockdown by ATC (500 nM) withdrawal impaired sporozoite invasion of primary hepatocytes at 3 hpi (c; PfSIP2-cKD, no ATC versus WT, no ATC: P = 0.0147; PfSIP2-cKD, +ATC versus no ATC: P = 0.0009) and reduced formation of exoerythrocytic forms (EEFs) at 2 dpi (d; PfSIP2-cKD, no ATC versus WT, +ATC: P = 0.0048; PfSIP2-cKD, no ATC versus WT, no ATC: P = 0.0004; PfSIP2-cKD, +ATC versus no ATC: P < 0.0001). Kruskal–Wallis test, Dunn’s correction. Data are represented as median. n indicates the number of independent wells across three biological replicates. Schematics in b are adapted from ref. [36], CC BY 4.0.

Source data

PfSIP2 expression is not detected in salivary gland sporozoites5,21,38 (although we cannot rule out expression below detection limits), suggesting that hepatocyte infection is a function of its expression in oocysts. Regardless, our data reveal that the downstream targets of PfSIP2 could provide new candidates for transmission-blocking strategies.

Parasites interact with progenitor cells

Sequencing of both parasites and mosquito cells gave us the opportunity to identify possible interactions between the two organisms. We first analysed the mosquito datasets from all four time points and the two treatments (dsGFP and dsEcR). After quality control using read and gene counts, mitochondrial read percentages, and complexity score (Extended Data Fig. 6a and Supplementary Table 1), we successfully profiled 55,789 high-quality midgut cells. Cells from each sample were then integrated using reciprocal PCA (RPCA) to correct for treatment and batch effects, followed by dimensionality reduction and clustering based on transcriptional profiles. We annotated the 16 resulting clusters on the basis of marker gene expression and gene ontology (GO) terms (Fig. 4a, Extended Data Fig. 6b,c and Supplementary Table 5; a detailed description is provided in the Supplementary Note). The major clusters included progenitor cells (intestinal stem cells/enteroblast (ISC/EB, headcase-positive)); posterior enterocytes (pEC, nubbin-positive); anterior enterocytes (aEC, sugar transporter-positive); enteroendocrine cells (EE, prospero-positive); visceral muscles (VM, myosin-positive); and proventriculus cells (PV, eupolytin-positive (also called cardia)). A group of prospero-positive cells with mixed markers were annotated as EE-like. Of note, comparing dsGFP samples with dsEcR samples revealed limited effect on mosquito transcriptomes, with fewer than ten genes being differentially expressed at each time point (Extended Data Fig. 6d and Supplementary Table 6). By contrast, time post blood meal strongly affected gene expression across all major cell types (Extended Data Fig. 6e and Supplementary Table 7).

Fig. 4: Parasite interactions with progenitor cells during midgut traversal.

a, UMAP of A. gambiae midgut cells across all 4 time points forms 16 cell clusters, representing different cell types: aECs, EE, haemocyte and fat body cell (HC/FB), ISC/EB, pEC, PV, VM and a cluster with mixed markers that we annotate as EE-like. b, UMAP plots of A. gambiae coloured by cell type and overlaid with dual-read cells (cells with the same mosquito and parasite barcodes, indicated by grey circles) at 36 hpi (left) and 2 dpi (right). c, UMAP plot of P. falciparum from this study overlaid with dual-read parasites (grey circles) at 36 hpi. d, Distribution of 107 dual-read parasites over 8 independent samples in mosquito cell types at 36 hpi with the observed versus expected numbers under the random distribution (left x axis) and the resulting odds ratio ± 95% confidence interval (right x axis). Two-sided Fisher’s exact test with Benjamini–Hochberg multiple comparison correction. **FDR = 0.003. e, Confocal imaging shows that some parasites are inside of, or interact with, progenitor cells at 36 hpi. Left, maximum intensity projection of a 2.31 µm z-stack (0.21 µm between each plane) showing interactions between parasites (Pfs25, green) and progenitor cells (centrin, magenta). Two orthogonal slices (yellow boxes) show parasites possibly inside (1) and adjacent (2) to progenitor cells on the basal side (B, top) of the midgut. L marks the luminal brush border. Similar interactions were observed across three independent infections. Nuclei were stained with DAPI (cyan) and muscle actin was stained with phalloidin (Phal, white). LSM Plus processing was used. Scale bars, 5 µm.

Source data

To identify mosquito–parasite interactions, we focused on the 36 hpi time point when parasites are crossing the epithelial layer. As dsGFP and dsEcR samples presented very similar mosquito and parasite transcriptomes, we pooled cells from these two groups (Extended Data Fig. 2a and 6d and Supplementary Table 6). We reasoned that a parasite captured inside or in strong association with a midgut cell would have the same cellular barcode as the mosquito cell. Despite the fleeting nature of crossing11,12,13, we detected 107 parasites that shared a barcode with a mosquito cell (defined here as dual-read cells) out of the 1,017 sequenced at this time point (10.5%) (Fig. 4b and Extended Data Fig. 7a). This percentage is significantly higher than the 3.9% observed at 2 dpi (21 dual-read parasites out of 533 total, Fisher’s exact test, P value < 0.001), when parasites have mostly transformed into extracellular oocysts.

Of note, dual-read parasites appeared to interact preferentially with the ISC/EB midgut cluster (Fig. 4b–d). Indeed, 32.7% of dual-read cells (3.3% of total parasites) included a progenitor cell, although this cluster represents only 12.1% of all mosquito cells at this time point (Fig. 4d, odds ratio 3.3, false discovery rate (FDR) = 0.003). This enrichment was not due to lower mRNA content in ISC/EB cells, which might artificially increase parasite mRNA detection rates, and was not observed at 2 dpi (Extended Data Fig. 7b,c). Parasites were also less likely to be associated with pECs than expected by chance (Fig. 4d, odds ratio 0.37, FDR = 0.003). In differential expression analyses, no protein coding genes of midgut progenitor cells were affected by the presence of an interacting parasite (FDR = 1), and similarly, parasites interacting with a progenitor cell showed no difference in their transcriptomes relative to those of non-interacting parasites (FDR = 1), although these results may be due to the limited number of dual-read cells.

To confirm these findings, we performed confocal microscopy using a centrin antibody that labels progenitor cells, as determined by their basal location, smaller triangular shape and colocalization with the known progenitor marker armadillo[39] (Extended Data Fig. 7d). We observed close interactions between parasites and progenitor cells, with 10.1% of parasites (35 out of 347) appearing to be inside or in close contact with an ISC/EB (Fig. 4e, regions 1 and 2), or oriented towards one (Extended Data Fig. 7e,f). This number exceeds the 3.3% observed by scRNA-seq, suggesting that the single-cell isolation process preferentially preserved the strongest interactions. Consistent with previous studies12,15,40, we also observed parasites near pECs that were either extruded or positive for the parasite surface protein Pfs25 (Extended Data Fig. 7e,f and Supplementary Video 1), potentially accounting for the reduced number of dual-read pECs associated with parasites.

We confirmed these findings by confocal microscopy in different mosquito–parasite combinations, observing close interactions between parasites and progenitor cells in 10.9% (56 out of 512) of parasites of the field isolate P. falciparum P5 in A. gambiae and in 8.71% (31 out of 356) of a different NF54 clone (referred to here as NF54_H) in a recently colonized Anopheles coluzzii strain[41] (Extended Data Fig. 7g,h).

Combined, these data reveal a preferential interaction, conserved across Anopheles species and P. falciparum isolates, between parasites and mosquito progenitor cells during traversal of the midgut epithelium, as ookinetes transform into oocysts.

Late oocysts are associated with muscles

Notably, midgut progenitor cells were not observed to interact with ookinetes in the rodent-infecting Plasmodium berghei model, but were instead associated with late oocysts, where their expansion eventually led to parasite death[42]. However, we did not find evidence of accumulation of centrin-positive cells near oocysts at 7 dpi (Fig. 5a), and conversely detected a decrease in the proportion of progenitors over time (Supplementary Table 5).

Fig. 5: Late oocysts interact with visceral muscles.

a, Maximum intensity projection of confocal images showing the absence of progenitor cell accumulation (centrin, magenta) around 7 dpi oocysts (dashed circle; Supplementary Video 2). b,c, Two representative images showing muscle fibres (phalloidin, grey) forcefully stretched (arrowhead) around a large oocyst (dashed circle) (b) or encasing an oocyst (c) (Supplementary Video 3). Infections were performed in triplicate. Projections of 6.72 µm (a) and 2.94 µm z-stacks (b,c) are presented. Scale bars, 5 µm.

In our confocal microscopy analyses, however, we identified phalloidin-stained visceral muscles closely wrapped around late oocysts, with muscle fibres extending beyond their usual width (Fig. 5b,c and Supplementary Videos 2 and 3). This interaction was conserved in several other mosquito–parasite combinations: A. gambiae–P. falciparum P5; A. coluzzii–NF54_H; and A. stephensi–ART29 (Extended Data Fig. 8a–c). Physical interactions with muscle cells may potentially tether oocysts to the midgut while minimizing disruption of the epithelial layer, as discussed below.

Discussion

By focusing on developmental stages that had previously escaped large-scale analysis, our study provides a comprehensive reconstruction of the events that characterize the P. falciparum transmission cycle. This rich volume of information expands the repertoire of potential targets for preventing parasite transmission in strategies based on transmission-blocking drugs and vaccines[43] or mosquito-targeted antimalarials35,36. Indeed, our functional analyses validate parasite factors (PfATP4, PfLRS and PfSIP2) as essential for parasite growth and the acquisition of infectivity to human hepatocytes. We also reveal pathways that are potentially involved in the ookinete–oocyst transition, a possible role of PfEMP1 in adherence of newly formed oocysts to the midgut, and processes that fuel oocyst development, although these findings will require validation in future studies. Of note, our results demonstrate that much of the core machinery necessary for daughter cell formation (inner membrane complex, basal complex and other components) is conserved between blood stage parasites and oocysts, despite the marked difference in scale of this process between these stages (tens of merozoites versus thousands of sporozoites).

The parallel sequencing of both parasites and mosquito cells enabled the identification of a previously unappreciated interaction between parasites and midgut progenitor cells. Ookinete traversal of the midgut epithelium is an asynchronous process that occurs between 24 hpi and 36 hpi. The best supported model for midgut crossing to date suggests that ookinetes initially invade an epithelial cell, then move laterally to adjacent cells before reaching the basal side, often leading to the extrusion of the invaded cells14,44. The observation that dual-read parasites contain not only ookinetes but also transforming tooks suggests that this interaction with progenitor cells occurs as parasites reach the basal side, where they transition into oocysts. Although our findings only begin to uncover the mechanisms that govern ookinete exit and transformation into an oocyst, it is plausible that P. falciparum uses progenitor cells as landmarks for the basal side of the midgut. Here, parasite exit may be facilitated by the remodelling of tight junctions during division of ISCs45,46, although several alternative hypotheses are possible. It is likely that these interactions occur after ookinetes have rapidly escaped extruding pECs, as observed both in this study and in several others14,15,40, and in alignment with our observation of a slightly reduced number of parasite-associated pECs.

In our analysis, P. falciparum oocysts were found to interact tightly with muscle cells. This interaction may be the result of the specific co-evolutionary trajectories of human malaria parasites with human-biting mosquitoes. Indeed, P. falciparum possesses mechanisms to minimize the damage inflicted to its Anopheles vectors24,47, including a low number of ookinetes crossing the midgut epithelium. By contrast, rodent malaria parasites have high parasite loads that induce substantial epithelial damage and overall fitness costs48,49, and their oocysts are deeply embedded in the epithelium[50], probably causing damage and consequent proliferation of ISCs[42]. A close association with muscle cells might enable P. falciparum oocysts, which on the contrary jut farther out of the midgut[50], to limit epithelial damage by tethering growing parasites in a less invasive way. Further research will clarify the biological relevance of these mosquito–parasite interactions.

Methods

Rearing of Anopheles mosquitoes

A. gambiae (G3 strain), A. stephensi (SDA-500), and recently colonized A. coluzzi[41] mosquitoes were reared in an insectary maintained at 27 °C, 70–80% relative humidity, on a 12 h:12 h light:dark cycle. Larvae were fed on fish food and adults were provided with 10% w/v glucose solution ad libitum. Adult mosquitoes were fed with purchased human blood (Research Blood Components) to induce egg laying.

dsRNA production and microinjection

PCR fragments of eGFP control (495 bp) and EcR (AGAP029539; 435 bp) were amplified from the plasmids pCR2.1-eGFP and pCR2.1-EcR as previously described[51]. PCR product was used to transcribe dsRNA using the Megascript T7 transcription kit (Thermo Fisher Scientific), per the manufacturer’s protocol. The resulting dsRNA was purified via phenol-chloroform and diluted to a concentration of 10 µg µl−1. Microinjections were performed as detailed previously[24], with adult mosquitoes, randomly assigned to each group, being injected one day post-eclosion and given an infectious blood meal 3 days post-injection.

EcR knockdown confirmation

Resulting knockdown confirmation post-injection was performed as previously described[24]. Pools of 6–8 infected female mosquitoes were aspirated at 24 hpi and transferred to TRI reagent (Thermo Fisher Scientific). RNA was extracted, DNase treated, quantified and reverse transcribed. cDNA from four biological replicates was diluted tenfold and run in duplicate for quantitative PCR with reverse transcription. Gene-specific primers were used, and relative quantification was performed with the ribosomal gene Rpl19 as the reference[52] (Supplementary Table 8). RNA extraction from one replicate of the single-cell experiments failed and were thus repeated with samples collected at 2 dpi. For phenotypic EcR knockdown confirmation, individual mosquito ovaries were also collected 7 dpi in 80% ethanol for later manual egg counts.

Culturing of P. falciparum parasites

P. falciparum strains used in this study include: (1) NF54 originally provided by C. Barillas-Mury from BEI Resources (MRA-1000); (2) NF54_H, highly infectious to mosquitoes, from the laboratory of M. Delves; (3) an artemisinin-resistant, Cambodian field isolate ART29 (ref. [53]); and (4) a Burkina Faso polyclonal isolate P5 (refs. 25,35). All strains were identified as P. falciparum parasites by nested PCR or whole genome sequencing, and confirmed mycoplasma free. Asexual stages of parasites were cultured at 37 °C between 0.2 and 2% parasitaemia in human erythrocytes at 5% haematocrit (Interstate Blood Bank) using RPMI medium 1640 supplemented with 25 mM HEPES, 10 mg l−1 hypoxanthine, 0.2% sodium bicarbonate, and 10% heat-inactivated human serum (Interstate Blood Bank) under a gas mixture of 5% O_2, 5% CO_2, balanced N_2. Stage V female and male gametocytes were induced by raising parasitaemia over 4% and incubating cultures for 14–20 days with daily medium change.

P. falciparum infections of Anopheles mosquitoes

Female mosquitoes were blood-fed on a mix of P. falciparum gametocyte culture, human red blood cells and human serum (ratio 1:3:6) via heated membrane feeders 3–5 days post-eclosion, and introduced into a custom-built glove box (Inert Technology) as previously described[24]. Unfed mosquitoes were removed, and remaining mosquitoes were kept on 10% glucose solution ad libitum, with added ATC or compound (see below). At dissection time points, mosquitoes were aspirated into 80% ethanol, frozen for 10 min and transferred to phosphate-buffered saline (PBS) on ice.

Generation of single-cell suspension

Eighty midguts from P. falciparum-infected mosquitoes injected with dsGFP or dsEcR were dissected at 36 hpi, 2 dpi, 4 dpi and 7 dpi across 4 biological replicates in ice-cold PBS. Any remaining blood meal was removed before storing the dissected midguts in ice-cold PBS. Dissections were completed within 1 h to preserve the viability of parasite and mosquito cells. Midguts were pooled into 200 µl of PBS with 1 mg ml−1 elastase (Sigma-Aldrich E7885) and 1 mg ml−1 collagenase IV (Thermo Fisher Scientific 17104019), and incubated at 30 °C, 300 rpm for 30 min in a shaking heat block. To facilitate the isolation of single cells, samples were disrupted every 10 min by pipetting with low protein-binding tips.

Samples were assessed using trypan blue staining to quantify live, single midgut cells during protocol optimization. This included systematically testing variables such as digestion time, temperature, tissue preparation (intact or minced gut) and types of pipette tip. On average, approximately 400 live, single cells were consistently recovered per mosquito midgut, while many cells remained in clumps. Given the low number of parasites (~20–30) relative to mosquito cells (~5,000) in a midgut, rather than further optimizing for complete dissociation of the midgut, we chose to enrich the parasite-to-mosquito cell ratio by removing cell clumps as they were composed mostly of midgut cells. Therefore, the cell suspension was sequentially filtered through 70 µm, 40 µm and 20 µm cell strainers (pluriSelect), with each strainer being immediately washed with 200 µl of 1× PBS to collect any adherent cells. The 20 µm cell strainers were not used for the 7 dpi samples, as oocysts at this time point are, on average, over 25 µm in diameter[24]. Based on the final dataset, this approach yielded an approximate 1:16 parasite-to-mosquito cell ratio. Given an estimated 5,000 midgut cells and 30 oocysts per gut—an expected ratio of about 166:1—our protocol represents a tenfold enrichment of parasites.

We chose not to collect samples beyond 7 dpi, as oocysts larger than 30 µm may clog the 10x Chromium chip. We chose not to use fluorescence-activated or magnetic-activated cell sorting as they both lengthen the isolation protocol and cause stress, reducing cell viability. The final single-cell suspension was pelleted, resuspended in 20 µl of PBS, and cell concentration and viability were determined by haemocytometer count with trypan blue staining.

Single-cell library preparation and sequencing

Single-cell libraries were prepared following the Chromium Next GEM Single Cell 3′ Reagents Kit v.3.1 (Dual Index) User Guide (RevC). In brief, single-cell suspensions were diluted to target a recovery of 4,000 cells per sample, then mixed with reverse transcription reagents and barcoded gel beads. The mixtures were loaded into wells containing partitioning oil on a 10x Chromium chip to generate single-cell emulsions. Samples from dsGFP and dsEcR mosquitoes collected at the same time point were loaded into two separate wells on the same chip. In total, 16 chips were used across 4 time points and 4 biological replicates. Within each emulsion droplet, individual cells were lysed, mRNA molecules were captured, and cDNAs were generated with cell-specific barcodes. Barcoded cDNAs were pooled, then amplified, fragmented and purified using SPRIselect, followed by ligation with Illumina adaptors and sample-specific barcodes. Each sample was assessed using an Agilent Bioanalyzer to ensure library integrity and quantified by qPCR using i7 and i5 Illumina primers, following the protocol from Universal Kapa Library Quantification Kit (Roche). The cDNA libraries from each sample were then mixed in equal proportions, spiked with 1% phage cDNA (PhiX, Illumina). The proportion of parasite reads relative to mosquito reads was estimated using an initial Illumina iSeq 100 run, which showed that around 0.05%, 0.1%, 0.6% and 1.3% reads mapped to parasites at 36 hpi, 2 dpi, 4 dpi and 7 dpi, respectively. To obtain sufficient coverage of parasite transcripts, final sequencing was performed across all lanes of two NovaSeq S4 flow cells (Broad Institute), with an expectation of 1,974–51,316 reads per parasite ranging from 36 h to 7 dpi (see Supplementary Note for detailed calculation).

scRNA-seq data processing and analysis of P. falciparum

FASTQ files from each sample originating from different flow cells were concatenated and mapped to the genomes of P. falciparum 3D7 (PlasmoDB.org, v.58)[54] using 10x Cell Ranger software v.7.0.1 (ref. [55]). The resulting count matrix for each sample was processed and filtered using Scanpy (v.1.9.1) in Python (v.3.10)[56]. Based on the individual sample profile, low-quality cells, dead cells and empty droplets were removed according to the number of reads (unique molecular identifier (UMI) count), number of genes (gene count) and proportion of mitochondrial reads per cell (Supplementary Table 1). The count matrix from each sample was merged into a single AnnData object by Scanpy, and doublets were removed running Scrublet software in Python before conversion to Seurat using SeuratDisk’s function Convert[57]. After quality control, the average number of reads per cell ranged from 649 at 36 hpi to 9,043 at 7 dpi. Pseudobulk differential expression analyses were initially conducted treating the samples as independent observations for comparison. The pseudobulk count matrix was generated for each sample by summing raw gene counts across all cells in Python with Pegasus. Several comparisons were conducted—between each time point in parasites from dsGFP-injected mosquitoes as well as between parasites from dsEcR- and dsGFP-injected mosquitoes of the same time point—using a Python wrapper for the DESeq2 package in R[58]. Significance was set as log_2 fold change greater than 1 or less than −1, and an adjusted P value below 0.05. Functional enrichment analysis of upregulated or downregulated gene lists was performed using GoProfiler[59].

A standard single-cell analysis pipeline was then performed with Seurat and dependent packages in R 4.3.2 in RStudio 2023.9.1.494 (ref. [60]). Highly variable genes were identified with the FindVariableFeatures function before data were scaled (ScaleData, default settings) and a PCA plot was generated based on these features only. Next, high-quality parasite cells were integrated with existing datasets, including blood bolus ookinetes at 24 hpi and 48 hpi, gametes, zygotes and ookinetes from 2–20 hpi, and sporozoites released from oocysts21,22 at 12 dpi. In brief, Seurat objects (v.5) were created for external datasets and reads were normalized to 10,000 transcripts, before the three Seurat objects were merged. Variable features were identified with default parameters of the FindVariableFeatures function, the data were scaled (ScaleData), and PCA was performed on the first 50 dimensions (RunPCA, default settings). Integration to correct for batch effect and differences in single-cell methodology was conducted using RPCA, which is the preferred approach when minimal overlap between datasets is expected. Subsequently, a UMAP was generated including the top 12 principal components through the RunUMAP function, with parameters set to min.dist = 0.4, and repulsion.strength = 2. Cell clusters were defined by the Louvain algorithm at a resolution of 0.5. Cluster markers were identified using the FindAllMarkers function, focusing only on positive markers with a log_2 fold change above 1. Genes with FDR values below 0.01 were utilized to label each cluster.

The Seurat object was converted into a cds object in Monocle3 (ref. [61]), and the trajectory analysis was performed using the learn_graph function (close_loop = F, ncenter=500). Pseudotime analysis was conducted by setting the node in the gamete–zygote cluster as the start point. Gene network analysis focused on our data and was performed using the graph_test function (neighbor_graph = “principal_graph”), to identify co-expressed genes that change as a function of pseudotime (FDR < 0.05). Co-expressed genes were further clustered by the find_gene_modules function with a resolution of 0.0023. The expression of all genes within each gene cluster was aggregated using the aggregate_gene_expression function. Enriched GO terms were determined by analysing all the genes within a gene cluster in GoProfiler[59]. Differential expression of protein coding genes was compared between dual-read parasites at 36 hpi and parasites that do not share a barcode with a mosquito cell, binning for parasite cluster, using logistic regression. A subsequent analysis focused on dual-read parasites only at 36 hpi, and compared those interacting with an ISC/EB to the remainder.

Mosquito scRNA-seq data processing and analysis

All FASTQ files from the different sequencing runs were concatenated and mapped to the A. gambiae PEST genome (VectorBase.org, v.58)[54], using the 10x Cell Ranger software v.7.0.1 (ref. [55]). Quality control was initially performed in Python using Scanpy based on the number of reads (UMI count), number of genes (gene count), percentage of reads mapping to the mitochondrial genome and cell complexity (Supplementary Table 1). Cells with a complexity score (ratio of number of transcripts by genes logged) below 0.7 or more than 30% reads mapping to the mitochondrial genome were removed62,63,64,65,66,67. The mitochondrial threshold was chosen on the basis of published scRNA-seq studies of Anopheles haemocytes[62] and Aedes midguts[63], noting that a similar threshold (25%) was used by two scRNA-seq studies on the midgut of Drosophila melanogaster[64] and Culex tarsalis[65], whereas snRNA studies used lower cutoffs due to inherent differences in the technology66,67. The resulting count matrix from each sample was merged into a single AnnData object by Scanpy, before conversion to Seurat using SeuratDisk’s function Convert. Doublet removal was performed in R using scDblFinder[68]. Quality metrics indicate that mitochondrial percentage is lower in 36 h and 2 dpi samples compared to the 4 dpi and 7 dpi ones, probably owing to a combination of biological factors, including time after blood feeding, age and infectious stages (ookinetes or young oocysts versus large oocysts).

After quality control, mosquito cells from each time point were processed using a similar workflow as for parasite analysis. The top 25% variable genes were identified, the data were scaled, and PCA was performed computing the first 100 PCs. Integration was conducted using RPCA with the highest k.weight (64) to correct batch effect while avoiding overcorrecting for biological variation between time points and treatments. The UMAP was calculated using the first 56 PCs, and cluster identification was based on the Louvain algorithm with a resolution of 0.3. Positive markers were identified using the FindAllMarkers function with a log_2 fold change greater than 1. Proventriculus, anterior and posterior midgut scores were calculated based on A. gambiae midgut bulk RNA-seq results[69]. Clusters were then annotated by identifying the functional enrichment of each cluster’s marker genes as well as cross-referencing cluster markers from four references: the Fly Cell Atlas, the D. melanogaster gut single-cell study, the Aedes aegypti gut single-cell study, and the haemocyte single-cell study from A. gambiae62,64,66,67. A. gambiae orthologues were identified using VectorBase[54], and all significant cluster markers with an orthologue specific to a cell type were used for cluster annotation.

Pseudobulk analyses were performed to assess the effect of either EcR knockdown or time post-infectious blood meal on the midgut transcriptome using AggregateExpression from the Seurat package. To assess the effect of EcR knockdown on transcription, differential expression analyses were performed using DESeq2 (ref. [58]) by pooling cells from each cell type at each time point. To evaluate the effect of time on transcription, only cells from dsGFP mosquitoes were used to compare between consecutive time points. Functional enrichment analyses were performed using GoProfiler[59] when more than 20 genes were significant. Dual-read differential expression analyses of protein coding genes were performed using logistic regression framework comparing dual-read cells at 36 hpi with cells not interacting with a parasite at the same time point, binning for dsRNA treatment and annotation. The analysis was repeated by comparing protein coding gene expression between dual-read ISC/EB cells at 36 hpi and ISC/EBs not interacting with a parasite.

Post-infection exposure assays via sugar feeding

Candidate target selection for drug exposure was based on two criteria: (1) belonging to a distinct gene cluster in our gene model; and (2) having known potent activity against the candidate target in the P. falciparum blood stage. Four drugs were selected: cipargamin (ChemPartner), MMV670325, MMV643121 and MMV007839 (refs. 70,71,72,73) (Medicine for Malaria Venture). Stock solutions were made in DMSO at 100 mM, stored at −20 °C and diluted 1:1,000 in 10% glucose solution shortly before sugar change. As the bioavailability of these compounds in mosquitoes is unknown, a single high concentration of 100 µM was chosen initially as it is close to the solubility limit while keeping DMSO content to 0.1%. Mosquito compound exposure through sugar feeding was performed similarly to previously described[53]. In brief, sugar solutions containing compounds or corresponding controls (0.1% DMSO) were randomly assigned to a mosquito group and replaced every day from 2 dpi to 10 dpi (unless specified). For oocyst counts, midguts were collected at 7 dpi and stained in 0.2% (w/v) mercurochrome (Sigma-Aldrich). Midguts were imaged using an Olympus Inverted CKX41 microscope, and oocyst number and mean size were calculated using OocystMeter[74]. For salivary gland sporozoite quantification, salivary glands of individual female mosquitoes were dissected at 14 dpi in PBS and counted on a haemocytometer.

Plasmid construction

The PfSIP2 homology-directed repair (HDR) plasmid was assembled by Golden Gate cloning (New England Biolabs) using purified PCR products of (1) a C-terminal homology region (Cterm-HR) that was codon-altered to avoid repeated CRISPR cuts; (2) a cassette containing haemagglutinin (HA) tags, tet-aptamers[75], a TetR-DOZI fusion protein75,76, and a human dihydrofolate reductase (hDHFR) selection marker; (3) a 3′ homology region; and (4) a bacterial backbone. Primers used to amplify fragments are listed in Supplementary Table 8 and assembly was confirmed by whole plasmid sequencing (Plasmidsaurus). Two CRISPR–Cas9 guide plasmids were constructed to cut the C terminus of the endogenous PfSIP2. Guide oligonucleotides were annealed and ligated into BpiI-digested pRR216 (ref. [77]), which contains SpCas9, a U6 guide cassette, and a yeast dihydroorotate dehydrogenase (DHODH) selection marker. Sequences were confirmed by Sanger sequencing (Psomagen).

Generation of PfSIP2-cKD parasite line

The HDR and guide plasmids of PfSIP2 were extracted using a Qiagen Maxi kit, and 100 μg of the HDR plasmid was linearized with XhoI, NotI, and ApaL1 at 37 °C overnight. The linearized HDR plasmid and a mixture of the 2 guide plasmids (60 μg each) were sterilized by ethanol precipitation and resuspend in TE buffer. The plasmids were then mixed with 270 µl of Cytomix (120 mM KCl, 0.15 mM CaCl_2, 2 mM EGTA, 5 mM MgCl_2, 10 mM K_2HPO_4, 10 mM KH_2PO_4, 25 mM HEPES, pH 7.6) and transfection by red blood cell loading was performed as described[78]. The parasite line was maintained at 5% haematocrit with 500 nM ATC (Sigma) from the onset of transfection. Drug pressure for the guide plasmid was applied from 6 h to 5 days post-transfection using 1.5 μM DSM1 (Sigma), whereas drug pressure for the HDR plasmid was maintained with 2.5 nM WR99210 hydrochloride (Sigma) starting 6 h post-transfection until integration was confirmed. To do so, genomic DNA was extracted from WT and PfSIP2-cKD lines using the Qiagen Blood & Tissue kit. Each integration site of the double crossover was amplified as well as the whole locus and PCR products were analysed by gel electrophoresis.

Asexual stage growth assay

ATC was washed out from PfSIP2-cKD parasites three times with RPMI 1640. The resulting parasites were diluted to 0.5% starting parasitaemia at 2.5% haematocrit and treated with either 500 nM ATC, 1.5 nM ATC or 0.025% of DMSO. Parasitaemia was calculated daily by counting Giemsa-stained smears of each technical replicate. The experiment was repeated twice, with four technical replicates for each biological replicate. Data were analysed by two-way ANOVA with Dunn’s correction.

Mosquito infection with transgenic parasites

Transgenic parasites were cultured in the asexual blood and gametocyte stages and fed to mosquitoes as described above, with the following specifications for ATC usage. Both asexual and gametocyte cultures were maintained in 500 nM ATC (dissolved in DMSO). One hour prior to mosquito infection, ATC was washed out from the gametocyte cultures by replacing the media three times, and either 500 nM ATC or 0.025% DMSO was added to the blood meal. Mosquitoes were maintained on a 10% glucose solution supplemented with 100 µM ATC, which was dissolved directly in the solution.

Culturing of primary human hepatocytes and infection with transgenic parasites

Cryopreserved human primary hepatocytes (BioIVT) were thawed, seeded on collagen-coated micropatterned islands in 96 well plates, and infected with WT or PfSIP2-cKD sporozoites as previously described[79]. In short, WT or PfSIP2-cKD-infected mosquito salivary glands were dissected in Schneider’s medium (Gibco) containing 200 U ml−1 of penicillin, 200 µg ml−1 of streptomycin (2×, Gibco) for less than 1 h. Sporozoites were released from glands, filtered through a 35 µm cell strainer and counted on a haemocytometer. Parasites were spun at 10,000g for 3 min, resuspended in hepatocyte media containing 2.5 μg ml−1 Fungizone (Cytiva) and 2× penicillin/streptomycin as well as either 500 nM ATC or 0.025% of DMSO and seeded onto hepatocytes. For invasion assays, 7,000 sporozoites were seeded per well, wells were fixed in 4% paraformaldehyde 3 hpi and in and out PfCSP staining was performed[79]. For infection assays, 70,000–100,000 sporozoites were used, and subsequently washed off 3 hpi before supporting cells from the male mouse fibroblast cell line 3T3-J2 (ref. [80]) were added. Cells were washed daily and wells were fixed at 2 dpi in 100% methanol and stained with rabbit PfHSP70 monoclonal primary antibody (antibodies-online, ABIN361730) and goat anti-rabbit IgG 546.

Immunofluorescent microscopy

Midguts were dissected from female mosquitoes at specified time points. Any remaining blood bolus was removed in ice-cold PBS when present and clean midguts were incubated at room temperature in 4% paraformaldehyde for 45 min, followed by 3 washes in PBS for 10 min each. Midguts were permeabilized and blocked in 0.1% Triton X-100, 3% bovine serum albumin (BSA) in PBS for 1 h at room temperature or overnight at 4 °C before incubation in primary antibody at room temperature for 2 h, shaking. The following primary antibodies were used: 1:200 anti-Toxoplasma gondii centrin-1 rabbit polyclonal (Kerafast EBC004); 1:5 anti-Drosophila armadillo mouse monoclonal supernatant N2 7A1 (ref. [81]) (deposited to the DSHB by E. Weischaus), 1:200 anti-Pfs25 mouse monoclonal 4B7 (ref. [82]) (deposited to BEI resources by L. H. Miller and A. Saul). Another 3 washes in PBS were performed before incubating the samples in secondary antibodies and phalloidin for 1 h at room temperature rocking (goat anti-rabbit IgG AlexaFluor 488, goat anti-mouse IgG AlexaFluor 488, goat anti-mouse AlexaFluor 568 from Invitrogen used at 1:400, Ebioscience Phalloidin eFluor 660 used at 1:300). Midguts were then stained in PBS containing 5 µg ml−1 DAPI before the remaining 3 washes in PBS only. Midguts were mounted using Vectashield HardSet Antifade Mounting Medium and imaged on a Zeiss Inverted Observer Z1 with Apotome3 or a Zeiss LSM 980 confocal microscope. Using ZEN 3.10 software, confocal images were processed with LSM Plus whereas Airyscan images were processed with default parameters, followed by brightness and contrast adjustments in Fiji (v.2.14.0). Gamma was not adjusted unless specified.

Statistical analysis

Specific statistical tests are detailed in the corresponding figure legend. Confirmation of EcR knockdown and analysis of parasite prevalence, intensity and infection rates were conducted using GraphPad Prism 10.1.1. Odds ratios of dual-read parasites in mosquito cell types were calculated in R using Fisher’s exact tests followed by correction for multiple comparisons with Benjamini–Hochberg multiple comparison correction.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

Reference genomes from P. falciparum and A. gambiae were obtained from PlasmoDB (https://plasmodb.org/plasmo/app) and VectorBase (https://vectorbase.org/vectorbase/app), respectively (release v.58)[54]. The published datasets were obtained from the Malaria Cell Atlas website (www.malariacellatlas.org) and from the Gene Expression Omnibus (GEO) repository, accession number GSE222586 (refs. 21,22). The source data for the single-cell analysis are accessible from the GEO repository, accession number GSE284537. Additional source data, including mosquito infection data, are deposited into Harvard Dataverse repository (https://doi.org/10.7910/DVN/DCNUFV). Source data are provided with this paper. Datasets generated in this study are archived on Zenodo (https://doi.org/10.5281/zenodo.16876946 (ref. [83])).

Code availability

The scripts used for data processing and analysis are hosted on GitHub at https://github.com/lverzier/Pfalciparum_midgut_singlecell. Scripts generated in this study are archived on Zenodo (https://doi.org/10.5281/zenodo.16876946 (ref. [83])).

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Acknowledgements

The authors thank R. Dinglasan and M.-J. Gubbels for insights on the centrin antibody; J. D. Dvorin for the TetR-DOZI and guide plasmids; M. Delves for the NF54_H parasites; S. E. Lindner for valuable discussions on rRNA; K. W. Deitsch for insights into PfEMP1; members of the Catteruccia laboratory for comments; L. Ricci for help with graphics; and N. Damaraju for assistance with hepatocyte infections. The armadillo monoclonal antibody N2 7A1 developed by E. Wieschaus was obtained from the Developmental Studies Hybridoma Bank, created by the NICHD and maintained at The University of Iowa. We are deeply grateful to VEuPathDB for aiding the analysis of the datasets. F.C. is funded by the Howard Hughes Medical Institute (HHMI) as an Investigator and by the National Institutes of Health (NIH) grants R01AI148646 and R01AI153404. L.E.d.V. was funded by a Rubicon grant (452021309) from the Dutch Research Council (NWO).

Author information

Author notes

1. These authors contributed equally: Yan Yan, Lisa H. Verzier, Elaine Cheung

Authors and Affiliations

1. Department of Immunology and Infectious Disease, Harvard T. H. Chan School of Public Health, Boston, MA, USA

Yan Yan, Lisa H. Verzier, Elaine Cheung, Federico Appetecchia, Ailsa R. Craven, Esrah Du, Alexandra S. Probst, Tasneem A. Rinvee, Laura E. de Vries, Jamie Kauffman, Elisabeth Nelson, Naresh Singh, Duo Peng, W. Robert Shaw & Flaminia Catteruccia

2. Howard Hughes Medical Institute, Cambridge, MA, USA

Sandra March & Sangeeta N. Bhatia

3. Institute for Medical Engineering and Science, Massachusetts Institute of Technology (MIT), Cambridge, MA, USA

Sandra March & Sangeeta N. Bhatia

4. David H. Koch Institute for Integrative Cancer Research, MIT, Cambridge, MA, USA

Sandra March & Sangeeta N. Bhatia

5. Broad Institute of MIT and Harvard, Cambridge, MA, USA

Sandra March & Sangeeta N. Bhatia

6. Wyss Institute at Harvard University, Boston, MA, USA

Sangeeta N. Bhatia

7. The Chan Zuckerberg Biohub, San Francisco, CA, USA

Duo Peng

8. Howard Hughes Medical Institute, Boston, MA, USA

W. Robert Shaw & Flaminia Catteruccia

Contributions

Y.Y., E.C., W.R.S., D.P. and F.C. conceived the study. Y.Y., E.C., E.D. and A.S.P. performed the dissections for the scRNA experiments, and Y.Y. and E.C. performed the single-cell isolation and scRNA library generation. Y.Y., L.H.V., and D.P. performed the scRNA analysis. Y.Y., L.H.V., E.C., F.A. and T.A.R. performed and analysed drug infection experiments. Y.Y., E.D. and L.E.d.V. generated transgenic parasites. Y.Y. performed PfSIP2-cKD experiments and Y.Y., L.H.V., S.M. and J.K. performed the primary human hepatocytes infections. E.N. reared mosquitoes used in the study. N.S. generated gametocyte culture and infected mosquitoes. L.H.V., E.C. and A.R.C. performed immunofluorescence imaging and analysis. S.N.B., D.P., W.R.S. and F.C. provided supervision and oversaw experiments and analyses. Y.Y., L.H.V., E.C. and F.C. wrote the original draft. Y.Y., L.H.V., W.R.S. and F.C. reviewed and edited the manuscript. All authors approved the final manuscript.

Corresponding author

Correspondence to Flaminia Catteruccia.

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Competing interests

The authors declare no competing interests.

Peer review

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

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Extended data figures and tables

Extended Data Fig. 1 Quality control (QC) of scRNA-seq in two metabolic conditions.

a, Representative images of the parasite forms collected during the four experimental time points. Ookinetes (ook) and tooks found at 36 hpi, and oocysts (ooc) identified at 2 dpi, 4 dpi, and 7 dpi. Parasites were stained with Pfs25 (green) and nuclei with DAPI (cyan). Scale bar: 5 µm. b-c, EcR knockdown across four replicates (b) did not affect oocyst prevalence (pie charts, Fisher’s exact test, two-tailed) or intensity (Mann Whitney test, two-tailed), but (c) increased oocyst size at 7 dpi (Mann Whitney test, two-tailed). d-e, Knockdown of EcR was confirmed by (d) detecting the expected reduction in egg numbers in the ovaries (unpaired t-test, two-tailed) and (e) RT-qPCR (unpaired t-test, two-tailed). f, Violin plots displaying key metrics of the P. falciparum scRNA-seq data after QC. n indicates the number of mosquitoes, % the prevalence of infected mosquitoes. Data are represented as mean ± SEM in panels c, d and e, and as median in panels b.

Source data

Extended Data Fig. 2 Pseudobulk differential expression analysis of P. falciparum across time and treatment.

a, Table summarizing the number of upregulated and downregulated genes identified in the comparisons of time points and/or treatments by pseudobulk (significance defined as FDR < 0.05 and absolute value of log_2 fold change >1). b, Volcano plots representing the differentially regulated genes in the four comparisons that yield significant changes. c, Corresponding GO terms that are significantly enriched in upregulated and downregulated genes (Fisher’s one-tailed test, g:SCS algorithm for multiple test correction).

Extended Data Fig. 3 Integrated P. falciparum UMAPs across data origin and time.

a-b, UMAP plots representing the integrated data of P. falciparum (a) split by their study of origin and (b) coloured by time points of single cell collection. c, Heatmap showing the Z scores of expression patterns of ribosomal RNA (rRNA). Each row represents a cumulative expression of 18S (when present), 5.8S and 28S for each rRNA type (A1, A2, S1, S2). The gene ID given is of the corresponding 28S.

Extended Data Fig. 4 Functional validation of candidate genes in oocyst growth and sporozoite infection.

a, CIP and MMV670325 delivered in sugar from 2–10 dpi to An. gambiae infected with NF54 had no effect on oocyst prevalence, while MMV670325 treatment slightly increased oocyst intensity (p = 0.041). b-d, CIP exposure for three different (b) durations or (c-d) concentrations had no effect on (b-c) oocyst prevalence or intensity but (d) significantly reduced oocyst size in a dose dependent manner (p = 0.0033, p = 0.0002, p < 0.0001; representative images of DMSO and 100 µM CIP treatment in right panel, Scale bar: 20 µm). e, The same treatments to An. stephensi infected with the ART29 isolate resulted in no prevalence difference, but a slight decrease in oocyst intensity (p = 0.002) after CIP treatment. f, CIP treatment in An. gambiae infected with the P5 isolate slightly decreased oocyst numbers (p = 0.016), but significantly reduced oocyst size (p < 0.0001) at 7 dpi, resulting in no sporozoites in the salivary glands at 14 dpi. g, Expression profile of PfeEF2 and PfFNT, targets of MMV643121 and MMV007839, respectively. h, Exposure to either drug did not affect oocyst prevalence or intensity. MMV643121 treatment led to a decrease in oocyst size (p = 0.0005), while MMV007839 did not affect oocyst size but resulted in reduced sporozoite intensity (p = 0.0009). Oocyst size data are represented as mean ± SEM, oocyst and sporozoite intensity data as medians. All are compared using either a Mann Whitney two-tailed test (panels e and f) or a Kruskal-Wallis test and Dunn’s correction (all other panels). n indicates the number of mosquitoes from at least two independent infections. Pie charts indicate infection prevalences, compared with two-tailed Fisher’s exact test. *p < 0.05, **p < 0.01, ***p < 0.001, ****p < 0.0001. Schematics in f are adapted from ref. [36], CC BY 4.0.

Source data

Extended Data Fig. 5 Conditional knockdown of PfSIP2 does not affect sporozoite intensity.

a, Scheme (not to scale) of the PfSIP2 conditional knockdown (cKD) construct. Positions of primer pairs for integration validation are indicated. b, PCR amplifications of the 5′ and 3′ integrated regions (5′INT and 3′INT) and locus in WT NF54 and PfSIP2-cKD parasites, demonstrating the absence of WT parasites in the cKD line. For gel source data, see Supplementary Fig. 1. c, PfSIP2 knockdown by ATC withdrawal in the asexual blood stage led to parasite death (Mixed-effects model, Dunn’s correction, p < 0.0001). d-f, PfSIP2 knockdown by ATC withdrawal had no effect on (d) oocyst prevalence (Fisher’s exact test, two-tailed), intensity (Kruskal-Wallis test, Dunn’s correction, p = 0.0004, p = 0.0007, and p < 0.0001), and (e) size (Kruskal-Wallis test, Dunn’s correction, p = 0.0152, p = 0.0082, and p = 0.0258) at 7 dpi, and had no effect on (f) prevalence (p = 0.0211, p = 0.0076, and p < 0.0001) and intensity (p = 0.0024, p = 0.0213, and p < 0.0001) of salivary gland sporozoites at 14 dpi (two-tailed Fisher’s exact tests and Kruskal-Wallis test with Dunn’s correction, respectively). Data are represented as mean ± SEM in panels c, and e, and as median in d, and f. n indicates the number of mosquitoes and pie charts and % infection prevalence. *p < 0.05, **p < 0.01, ***p < 0.001, ****p < 0.001.

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Extended Data Fig. 6 Quality control and clustering of the An. gambiae scRNA-seq data.

a, Violin plots displaying key quality metrics for the mosquito scRNA-seq datasets (left to right: total number of reads, of genes, and percentage of mitochondrial reads) after QC. b, Dot plot displays cell type-specific markers, showing their average expression (colour) and the proportion of expressing each marker (size). Cell types shown are anterior enterocytes (aEC), enteroendocrine (EE), EE-like cluster, haemocytes and fat body cell (HC/FB), intestinal stem cells/enteroblasts, (ISC/EB), posterior enterocytes (pEC), proventriculus or cardia (PV) and visceral muscles (VM). c, Expression of markers characteristic to the proventriculus, and anterior or posterior part of the midgut based on the study by Hixson et al.[69]. d, Number of genes differentially expressed by pseudobulk analysis between dsGFP- and dsEcR-treated mosquitoes per time point and cell type (Wald test, significance defined as adjusted p-value < 0.05 and absolute value of log_2 fold change > 0.5). e, UMAPs of An. gambiae cells split by time point, showing the dynamic changes of the midgut cell population shortly after blood digestion (36 hpi and 2 dpi) and when subsequently maintained on sugar-only diet (4 dpi and 7 dpi). Pseudobulk differential expression analysis was performed in dsGFP-treated mosquitoes by pooling each cell type and comparing consecutive time points. Changes to significant GO term enrichment are represented by up and down arrows, coloured by cell type.

Extended Data Fig. 7 Dual-read parasites at 36 hpi show an association with intestinal progenitor cells.

a, An. gambiae UMAPs at 36 hpi and 2 dpi coloured by cell type and overlaid with dual-read cells (gray circles) and contour lines (light gray lines) displaying the density of dual-read cells. b, Violin plot showing similar read counts in mosquito cells regardless of whether they are dual-read cells. c, twenty-one dual-read parasites over eight independent samples at 2 dpi were randomly distributed across mosquito cell types, with no differences in (left x-axis) the observed vs. expected numbers and (right x-axis) resulting odds ratio (point) ± 95% confidence interval (error bar). Fisher’s exact test, two-tailed, with BH multiple comparison correction. d, Maximum intensity projection from confocal imaging (9.66 µm Z-stack) showing colocalization of the centrin (magenta) signal with the well-characterized ISC marker, armadillo (Arm, yellow), located on the basal side of the midgut (B, top). e-f, Confocal imaging of NF54 parasites (Pfs25, green) traversing the An. gambiae midgut epithelium at 36 hpi. (e) Parasites were found to point towards a progenitor cell (centrin, magenta) directly above an extruding cell (asterisk, nucleus of the extruded cell), located between two actin brushes (ab, yellow dashed lines) delimiting each epithelium (phalloidin, gray, gamma 0.5). (f) Ookinete left a Pfs25 trail into a large cell reminiscent of an enterocyte (see Supplementary Video 1). g-h, The interaction was also observed in (g) An. gambiae midguts infected with P5 parasites and (h) An. coluzzii midguts infected with NF54_H parasites (max intensity projection of 1.69 and 1.68 µm Z-stacks, respectively). Imaging was performed on at least two independent infections. Phalloidin (phal, gray) was used to define the basal side (B, top) and the luminal brush border (L, bottom), and nuclei were stained with DAPI (cyan). Scale bar: 5 µm.

Source data

Extended Data Fig. 8 Visceral muscle wraps around late-stage oocysts.

a-b, Visceral muscle (Phal, gray) wrapped closely around late oocysts (arrowheads), with no apparent increase in progenitor cell (centrin, magenta) populations near oocysts in (a) An. gambiae midguts infected with P5 parasites and (b) An. coluzzii midguts infected with NF54_H parasites by confocal imaging (max intensity projection of 4.60 µm and 2.60 µm Z-stacks, respectively). c, Similar muscle deformation was observed in An. stephensi midguts infected with ART29 parasites (max intensity projection of 3.60 µm Z-stack), though inconsistent centrin staining prevented analysis of progenitor cell distribution. At least two independent infections were used for imaging. Scale bar: 5 µm.

Supplementary information

Supplementary Information

Supplementary Note, Supplementary Figures, legends for Supplementary Tables 1–8, legends for Supplementary Videos 1–3 and Supplementary References.

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Supplementary Tables

Supplementary Tables 1–8

Supplementary Video 1

3D rendering of Extended Data Fig. 7f illustrating an ookinete that has left a Pfs25 trail into a large cell reminiscent of an enterocyte. DNA was labelled with DAPI (cyan), VM with phalloidin (grey), ISC with centrin (magenta) and parasite with Pfs25 (green).

Supplementary Video 2

Basal-to-lumen video of successive slices from the Fig. 5a z-stack illustrating the muscle stretch around an oocyst. DNA was labelled with DAPI (cyan), VM with phalloidin (grey) and ISC with centrin (magenta). Scale bar: 10 μm.

Supplementary Video 3

Lumen-to-basal video of successive slices from the Fig. 5c z-stack illustrating the muscle lattice encasing an oocyst. DNA was labelled with DAPI (cyan) and VM with phalloidin (grey).

Source data

Source Data Fig. 2

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Source Data Extended Data Fig. 1

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Yan, Y., Verzier, L.H., Cheung, E. et al. Mapping Plasmodium transitions and interactions in the Anopheles female. Nature 648, 451–458 (2025). https://doi.org/10.1038/s41586-025-09653-0

- Received: 08 November 2024

- Accepted: 18 September 2025

- Published: 22 October 2025

- Version of record: 22 October 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09653-0

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Article Open access Published: 19 November 2025

A skin-permeable polymer for non-invasive transdermal insulin delivery

Qiuyu Wei,

Zhi He,

Zifan Li,

Zhuxian Zhou,

Ying Piao,

Jianxiang Huang,

Yu Geng,

Runnan Zhang,

Yaqi Fu,

Jiayi Ye,

Yue Yuan,

Haoru Zhu,

Jiaheng Zeng,

Yan Zhang,

Quan Zhou,

Mingyu Xu,

Shiqun Shao,

Jianbin Tang,

Jiajia Xiang,

Rongjun Chen,

Ruhong Zhou &

…

Youqing Shen

Nature volume 648, pages 459–467 (2025)

Abstract

Non-invasive skin permeation is widely used for convenient transdermal delivery of small-molecule therapeutics (less than 500 Da) with appropriate hydrophobicities[1]. However, it has long been deemed infeasible for large molecules—particularly polymers, proteins and peptides2,3—due to the formidable barrier posed by the skin structure. Here we show that the fast skin-permeable polyzwitterion poly[2-(N-oxide-N,N-dimethylamino)ethyl methacrylate] (OP) can efficiently penetrate the stratum corneum, viable epidermis and dermis into circulation. OP is protonated to be cationic and is therefore enriched in the acidic sebum and paracellular stratum corneum lipids containing fatty acids, and subsequently diffuses through the intercorneocyte lipid lamella. Beneath the stratum corneum, at the normal physiological pH, OP becomes a neutral polyzwitterion, ‘hopping’ on cell membranes, enabling its efficient migration through the epidermis and dermis and ultimately entering dermal lymphatic vessels and systemic circulation. As a result, OP-conjugated insulin efficiently permeates through the skin into the blood circulation; transdermal administration of OP-conjugated insulin at a dose of 116 U kg−1 into mice with type 1 diabetes quickly lowers their blood glucose levels to the normal range, and a transdermal dose of 29 U kg−1 normalizes the blood glucose levels of diabetic minipigs. Thus, the skin-permeable polymer may enable non-invasive transdermal delivery of insulin, relieving patients with diabetes from subcutaneous injections and potentially facilitating patient-friendly use of other protein- and peptide-based therapeutics through transdermal delivery.

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Main

Transdermal delivery of biomacromolecules, such as proteins and peptides[4], through topical application is advantageous in terms of convenience, patient compliance, avoiding denaturation and minimal first-pass effects5,6. However, it has been considered to not be feasible owing to the impermeable barriers presented by the unique skin structure2,3, consisting of hydrophobic stratum corneum (SC) layers, a 10–15-μm-thick matrix with dehydrated and dead corneocytes embedded in highly ordered lipid layers, as well as the tight junctions in the viable epidermis and dermis[7]. Subdermal insulin injection is still the standard treatment for type 1 and advanced type 2 diabetes and is associated with pain, needle phobia, skin complications and poor patient compliance[8]. Non-invasive insulin administration has been extensively explored but has not yet been successful[9].

Various strategies have been explored to enhance the skin permeability of biomacromolecules[10], including chemical penetration enhancers that fluidize the SC lipid bilayers, electrical devices that force penetration, ultrasound and jet injection that create transient channels on the skin surface11,12,13, and microneedles that pierce the SC into dermal tissues14,15. These invasive techniques compromise skin integrity, raising inconvenience, infection and safety concerns.

One may imagine that a skin-permeable material is required to concentrate on the skin surface and then efficiently diffuse through the hydrophobic intercorneocyte lipid matrix of the SC into the hydrophilic viable epidermis[16]. Cationic peptides, which can electrostatically bind to the negatively charged alkyl carboxylic acids in the sebum and SC, have been tested for transdermal delivery, and some have been reported to be skin permeable17,18. However, such skin permeation does not act by diffusion through the intercorneocyte lipid matrix because the strong binding immobilizes them in the SC without diffusion, and instead acts through the appendageal paths[19], including hair follicles and sweat glands, and is therefore inefficient in humans because the appendageal areas occupy less than 0.1% of the human skin area20,21.

Thus, we propose that a polymer capable of transitioning from a polycation that binds to the skin SC surface to a polyzwitterion in the deeper SC layers for free diffusion would be skin permeable. Inspired by the skin’s characteristic acidic (pH ≈ 5)-to-neutral pH gradient from the sebum layer and SC surface to the deeper layers of the SC and viable epidermis[22], we further propose that the highly water-soluble polyzwitterion OP[23] is skin permeable. OP was protonated and positively charged at pH 5 or lower and deprotonated to a polyzwitterion at neutral pH (Supplementary Fig. 1). This alignment of OP’s pH-dependent charge transition with the skin pH gradient can render it able to bind to the skin surface and efficiently diffuse through the intercorneocyte lipid matrix; it therefore has high skin permeability (Extended Data Fig. 1).

The molecular mass of OP was controlled by living radical polymerization to approximately 4.5 kDa (Supplementary Fig. 2), and a terminal amine was introduced to label the polymer chain with a fluorescent dye (Supplementary Fig. 3), giving OPCy5. The skin permeability of OP was first assessed through a topical application on the dorsal skin of male C57BL/6J mice. Four hours after application of OPCy5, Cy5 fluorescence was observed throughout all skin layers in histological sections imaged using confocal laser-scanning microscopy (CLSM) (Fig. 1a,b). By contrast, control PEGCy5 remained confined to the skin surface. The SC penetration of OP was further validated by high-resolution imaging of 5 nm gold nanoparticles tethered to OP chains (OP–AuNPs) (Supplementary Fig. 4a) applied onto the mouse dorsal skin. High-angle annular dark-field imaging—scanning transmission electron microscopy (HAADFI–STEM), energy-dispersive X-ray spectroscopy (EDS) elemental mapping (Fig. 1c and Supplementary Fig. 4b) and EDS analysis (Fig. 1d) revealed the distribution of OP–AuNPs within the intercorneocyte lipid lamella of the SC. These findings confirm that OP does penetrate the SC layers and exhibited exceptional skin permeability. As a result, the topical OPCy5 percutaneously entered the bloodstream within 0.5 h and reached a maximum concentration at about 2 h after topical application (Fig. 1e). In circulation, OP predominantly accumulated in the liver, followed by the kidneys and lungs (Fig. 1f,g).

Fig. 1: Skin permeability of OP.

a, CLSM images of the section slices of the C57BL/6J mouse dorsal skin after 4 h of post-topical application with OPCy5 or PEGCy5 (Cy5-equivalent dose, 0.2 ml of 10 μg ml−1) through a diffusion cell (1.13 cm^2); the nuclei were stained with DAPI (blue). The images are representative of n = 3 independent experiments. b, Cy5 fluorescence intensities plotted from the skin surface to the subcutis along randomly selected lines (yellow arrows in a). c,d, Transmission electron microscopy characterization of cryosections of the SC layer of the dorsal skin after 4 h of topical application with OP–AuNPs (OP-equivalent dose, 0.2 ml of 0.5 mg ml−1; application area, 1.13 cm^2). HAADFI–STEM and EDS elemental mapping (c) and EDS analysis (d) are shown. A large view of the SC region is shown in Supplementary Fig. 4b. The images are representative of n = 3 independent experiments. e–g, Cy5 fluorescence intensity in the blood as a function of the time of topical application with OPCy5 on the mouse dorsal skin (e), and ex vivo fluorescence imaging (f) and fluorescence intensity quantification (g) of the major organs of the mice after 2 h of topical application of OPCy5 (Cy5-equivalent dose, 0.2 ml of 10 μg ml−1; application area, 1.13 cm^2). Data are mean ± s.d. n = 3 mice. Scale bars, 50 μm (a) and 50 nm (c).

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The transdermal ability of OPCy5 was further corroborated using porcine skin, which closely resembles human skin in structure, thickness, hair sparseness, and collagen and lipid composition[24]. OPCy5 topically applied onto a minipig abdominal skin distributed across all of the skin layers (Supplementary Fig. 5).

The skin permeability of OP was gauged by the hypoglycaemic effect of its percutaneously delivered insulin. Insulin was conjugated to OP (OP–I) using the strain-promoted alkyne-azide cycloaddition reaction[25] of recombinant human insulin with an azide group at the lysine residual amine and OP with a terminal DBCO group (molecular mass of 4.5 kDa; Supplementary Fig. 6). A PEGylated insulin (PEG–I, PEG molecular mass of 5 kDa) was synthesized similarly and was used as a control[26]. Both conjugates were characterized by reversed-phase high-performance liquid chromatography (RP-HPLC), matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS) and gel-permeation chromatography (Extended Data Fig. 2a–c). The conjugation did not alter the secondary structure of insulin as analysed by circular dichroism (Extended Data Fig. 2d) or its hypoglycaemic efficacy through blood glucose level (BGL) analysis (Extended Data Fig. 2e). For BGL analysis, 5 U kg−1 subcutaneous insulin was used, as it produced a faster and more-sustained glucose-lowering effect compared with lower doses (Supplementary Fig. 7). Fluorescently labelled conjugates were also prepared using a similar method and were stable (Supplementary Fig. 8).

Surface plasmon resonance (SPR) analysis on a sensor chip immobilized with the insulin receptor extracellular domains (ECD-IR) or the extracellular domain of IGF1R (ECD-IGF1R) was used to measure the receptor binding kinetics of insulin and OP–I (Extended Data Fig. 3a,b). No substantial difference was observed in their dissociation constants (Kd) (26.06 nM for OP–I versus 14.03 nM for insulin). OP–I and insulin also had comparable association rate constants (kon), dissociation rate constants (koff) and half-lives (t1/2) to the immobilized ECD-IR, demonstrating similar binding kinetics (Extended Data Fig. 3c). Similar to insulin, OP–I also showed minimal binding to the extracellular domain of IGF1R—a membrane receptor that is closely related to IR (Extended Data Fig. 3d). The results together indicate that the OP conjugation does not change the affinity and specificity of insulin to its receptor.

All-atom molecular dynamics (MD) simulations illustrated that OP–I stably adsorbed at two major binding sites of its receptor (Extended Data Fig. 3e and Supplementary Video 1). Potential of mean force (PMF) analyses estimated the binding affinities of OP–I with the receptor site 1 and site 2 to be −14.0 and −22.9 kcal mol−1, respectively, comparable to those of insulin (−16.7 and −22.0 kcal mol−1) (Extended Data Fig. 3f). The simulations confirm that the OP conjugation preserves the binding affinity of insulin to the ECD-IR. Collectively, these findings suggest that OP–I preserves the binding affinity of the insulin receptor and activation of downstream signalling pathways, and therefore its hypoglycaemic effects.

The blood-clearance kinetics of insulin and OP–I were compared after intravenous administration. The blood-clearance curves revealed that the half-life of OP–I (around 15–20 min) was marginally longer than that of native insulin (around 5–10 min) (Supplementary Fig. 9). This extended circulation time is attributed to the zwitterionic nature of the conjugated OP, which reduces interactions with plasma proteins and limits uptake by the reticuloendothelial system[23]. The protein resistance of OP made it unable to hitchhike on plasma proteins[27].

The time-dependent skin permeation of the conjugates was first visualized using CLSM in the three-dimensional (3D) skin-equivalent EpiKutis model, which mimics the reconstructed human epidermis[28]. The fluorescence of OP–IFITC spread throughout the entire epidermal layer within 30 min, whereas PEG–IFITC and insulinFITC gave only weak fluorescence confined to the EpiKutis surface (Fig. 2a). The steady-state flux (Jss) of OP–I in EpiKutis was measured to be 0.50 ± 0.12 μg cm−2 h−1, significantly higher than that of PEG–I (0.10 ± 0.01 μg cm−2 h−1) and insulin (0.05 ± 0.01 μg cm−2 h−1). The permeability coefficient (Kp) of OP–I was 4.50× and 9.17× higher than that of PEG–I and insulin, respectively (Fig. 2b and Supplementary Table 1).

Fig. 2: Skin permeability of OP–I.

a, CLSM images of the distribution of OP–IFITC, PEG–IFITC or insulinFITC across the in vitro 3D skin equivalent EpiKutis model at 4 h after treatment (FITC-equivalent dose, 0.2 ml of 10 μg ml−1; application area, 0.081 cm^2; width, 1,272 μm; height, 1,272 μm; depth, 170 μm). b, Time-dependent permeation curves of OP–I, PEG–I and insulin across the EpiKutis model (insulin-equivalent dose, 0.2 ml of 0.5 mg ml−1; application area, 0.081 cm^2). Data are mean ± s.d. n = 3 independent experiments. c, CLSM images of the mouse dorsal skin after 4 h of topical application of OP–IFITC (FITC-equivalent dose, 0.2 ml of 10 μg ml−1; application area, 1.13 cm^2). E, epidermis; H, hair follicle; S, subcutis; D, dermis. The images are representative of n = 3 independent experiments. d, CLSM images of immunofluorescence staining of LYVE-1AF488 (lymphatic vessel endothelial hyaluronan receptor-1, green) in the subcutaneous tissue of Sprague–Dawley rats after 4 h topical application of OP–ICy5 (red) (Cy5-equivalent dose, 0.2 ml of 10 μg ml−1; application area, 1.13 cm^2). The nuclei were labelled with DAPI (blue). The images are representative of n = 3 independent experiments. e, CLSM images of the slices of the minipig abdominal skin after 4 h of topical application of OP–ICy5-containing cream (Cy5-equivalent dose, 10 ml of 10 μg ml−1; application area, 100 cm^2). The images are representative of n = 3 independent experiments. f, Cy5-fluorescence intensity profile from the skin surface to the subcutis plotted along a randomly selected line (yellow arrow in e). Scale bars, 100 μm (c,d) and 50 μm (e).

Source Data

Sequential z-stack imaging of the inner layers of mouse skin using intravital two-photon microscopy demonstrated that OP–IFITC penetrated deeply into the skin tissues and even reached the subcutis after topical application on C57BL/6J mice (Supplementary Fig. 10). By contrast, PEG–IFITC and free insulinFITC gave only sparse and scattered fluorescence within the skin. The skin permeation of OP–I was fast and time dependent. Cy5 fluorescence was already substantial in the subcutaneous adipose tissue labelled with BODIPY after 10 min of topical application of OP–ICy5 on the dorsal skin, and accumulated more over time (Extended Data Fig. 4a,b and Supplementary Fig. 11). By contrast, little PEG–IFITC and insulinFITC were found in the skin (Extended Data Fig. 4c,d).

OP–IFITC was found to localize in all mouse skin compartments, including the epidermis (SC and viable epidermis), dermis, hair follicles and subcutis (Fig. 2c). Extensive OP–ICy5 was around or inside rat lymphatic capillaries (Fig. 2d), suggesting that OP–I enters leaky lymphatic capillaries and subsequently the bloodstream, consistent with the reports that subcutaneously administered large molecules enter systemic circulation through lymphatic uptake29,30. Moreover, OP–ICy5 effectively permeated minipig skin after 4 h of topical application, further demonstrating its transdermal delivery potency (Fig. 2e,f).

After topical application of OP–I, the mouse plasma insulin concentration increased rapidly, peaking at around 230 μU ml−1 at 1 h after treatment, and then gradually decreased to around 30 μU ml−1 after 12 h (Fig. 3a), similar to the blood concentration profile of topical OP (Fig. 1e). Notably, while topical OP–I exhibited a comparable plasma profile to subcutaneously injected insulin within the initial 2 h, its plasma levels remained consistently higher thereafter by 1.6–6 fold. Topically applied insulin or PEG–I did not affect the blood insulin levels (Fig. 3a). Moreover, repeated topical applications of OP–I gave very similar plasma insulin profiles, demonstrating high reproducibility and reliability (Fig. 3b).

Fig. 3: Hypoglycaemic effect of topical OP–I in STZ-induced diabetic mice and minipigs.

a, Plasma insulin concentrations in diabetic mice after topical application of PBS, insulin, PEG–I or OP–I (insulin-equivalent dose, 116 U kg−1; 0.2 ml of 0.5 mg ml−1, 1.13 cm^2 dorsal skin). n = 5 mice. Mice injected subcutaneously with insulin (5 U kg−1) were used as a control. b, The plasma insulin concentrations in diabetic mice after three consecutive days of topical application of OP–I as in a. n = 5 mice. c, BGLs of diabetic mice after treatments as in a. n = 8 mice. d, BGLs of the diabetic mice after topical application with lower doses of OP–I (insulin-equivalent dose, 58 or 29 U kg−1; 0.1 ml or 0.05 ml of 0.5 mg ml−1, 1.13 cm^2 dorsal skin). n = 8 mice. e,f, The plasma insulin concentrations (e; n = 5 mice) and BGLs (f; n = 8 mice) of diabetic mice after topical application of OP–I on the dorsal or abdominal skin as in a. The two experiments were performed using separate groups. g, IPGTTs in diabetic mice. n = 5 mice. Mice received treatments as in a and, 1 h later, were injected intraperitoneally with glucose (1.5 g per kg); their BGLs were then measured. Healthy mice were used as controls. h, The AUC (0–120 min) in the IPGTT experiment in g. n = 5 mice. i, BGLs in the diabetic minipigs after topical application on the abdominal skin with insulin, PEG–I or OP–I dispersed in water-in-oil cream (insulin-equivalent dose, 29 U kg−1, 1 mg ml−1, 40 ml, 400 cm^2; low-dose group (L), 7.25 U kg−1, 1 mg ml−1, 10 ml, 100 cm^2); n = 3 minipigs. Data are mean ± s.d. For c, d, f, g and i, the shaded areas outline the normal blood glucose range (50–200 mg dl−1). The diagram in i was created using BioRender.

Source Data

Topically applied OP–ICy5 accumulated in key glucose-regulating tissues, including the liver, adipose tissues and skeletal muscles (Supplementary Figs. 12–14). It was taken up by their cells (Supplementary Figs. 15–17) and effectively activated the insulin receptor signalling pathway, as shown by the phosphorylation levels of both the receptor and its downstream protein kinase B (also known as AKT) protein, comparable to those induced by subcutaneous-injected native insulin31,32 (Supplementary Figs. 18 and 19). Thus, OP–I exerted the functions of insulin in these tissues, including enhancing glucose uptake, promoting glycogenesis and inhibiting gluconeogenesis[33]. As a result, the interplay of skin permeation, tissue distribution and metabolism of OP–I gave its plasma concentration profile (Fig. 3a). By contrast, subcutaneous-injected insulin was rapidly cleared from the bloodstream, with minimal accumulation in adipose and muscle tissues, limiting its ability to sustain hypoglycaemic effects over time.

The ability of topical OP–I to regulate glycaemic levels was evaluated using streptozotocin (STZ)-induced type 1 diabetic mice (Fig. 3c and Supplementary Fig. 20). OP–I, PEG–I or native insulin solution (insulin-equivalent dose, 116 U kg−1; 0.2 ml of 0.5 mg ml−1) was applied to the dorsal skin (1.13 cm^2) of randomly grouped diabetic mice using diffusion cells, with subcutaneous insulin (5 U kg−1) injection as a positive control. Subcutaneous-injected insulin rapidly reduced BGLs from around 400 to 100 mg dl−1 within 1 h, followed by a rebound to hyperglycaemic levels (around 400 mg dl−1) within 4 h. Topically applied insulin and PEG–I had a negligible effect on BGLs. By contrast, topical OP–I demonstrated efficient, dose-dependent hypoglycaemic effects. At a dose of 116 U kg−1, OP–I rapidly lowered BGLs to below 200 mg dl−1 within 1 h, comparable to the subcutaneous insulin, but maintained normoglycaemic levels (50–200 mg dl−1) for 12 h. Lower doses of topical OP–I (58 or 29 U kg−1) reduced the BGLs more slowly but still effectively restored BGLs to the normal range (Fig. 3d), highlighting the potential for dose optimization for individual patients. The hypoglycaemic efficacy of OP–I was further validated in healthy mice (Supplementary Fig. 21). Notably, after removal of the diffusion cell, OP–ICy5 was cleared from the skin within 8 h (Supplementary Fig. 22). Importantly, topical application sites did not affect the transdermal delivery efficiency or hypoglycaemic activity of OP–I (Fig. 3e,f).

Intraperitoneal glucose tolerance tests (IPGTTs) further confirmed the glycaemic regulation ability of topical OP–I. Diabetic mice were first treated with topical OP–I for 1 h and then injected intraperitoneally with glucose solution (1.5 g per kg). The mouse BGLs peaked at 330 mg dl−1 within 30 min after glucose administration and gradually declined to around 100 mg dl−1 within 1 h, maintaining normoglycaemia thereafter. As a reference, healthy mice subjected to the same glucose administration exhibited a similar BGL profile, but their BGLs were above 200 mg dl−1 even after 2 h. The BGLs of the diabetic mice topically applied with insulin or PEG–I increased to around 600 mg dl−1 and maintained a hyperglycaemic state after the intraperitoneal glucose administration (Fig. 3g). The area under the curve (AUC) from 0 to 2 h demonstrated that transdermal OP–I provided superior BGL regulation compared with other treatments (Fig. 3h).

OP–I, PEG–I or native insulin was incorporated into a water-in-oil cream and smeared onto the abdominal skin of STZ-induced diabetic minipigs to evaluate their in vivo hypoglycaemic performance (Fig. 3i and Supplementary Fig. 23). The OP–I cream reduced BGLs to normoglycaemic levels within 2 h, reaching a minimum of 100 mg dl−1 at 6 h and maintaining normoglycaemia for 12 h. The hypoglycaemic effect of OP–I in minipigs was also dose dependent; lower doses produced a similar hypoglycaemic trend but a reduced BGL-regulating efficiency. Again, topical PEG–I or insulin treatment caused almost no obvious changes in minipig BGLs. These results demonstrate that topical OP–I effectively exerts hypoglycaemic effects in both diabetic mice and minipigs, highlighting its potential as a non-invasive alternative to subcutaneous insulin injections.

Topical application of OP–I caused no irritation or damage to the mouse skin (Extended Data Fig. 5a). The skin treated with OP–I showed no micromorphological differences, negligible neutrophil infiltration, no changes in thickness (Extended Data Fig. 5b) and no increased cell apoptosis (Extended Data Fig. 5c) compared with the PBS-treated group. Similar observations were found in porcine skin (Extended Data Fig. 5d,e). Furthermore, no adverse effects were observed on blood cell counts, biochemical parameters, or liver and kidney function (Supplementary Table 2).

Next, the mechanism of OP–I penetration through the skin SC layer was investigated. The outer SC layers on tape were peeled from the mouse skin after 4 h of topical application of OP–ICy5 using a previously reported method[34]; NBD-C6-HPC was used to stain SC lipids. CLSM revealed a pronounced overlap of Cy5 fluorescence (red) with NBD-C6-HPC staining (green), indicating that OP–I localizes within the SC lipids surrounding corneocytes (Fig. 4a and Extended Data Fig. 6a). Intravital two-photon microscopy further confirmed the presence of OP–IFITC around corneocytes (Fig. 4b and Supplementary Fig. 24). Similar results were observed in the minipig skin, of which the thicker SC layers allowed for easier observation, showing that OP–ICy5 coincided with SC lipids around corneocytes (Extended Data Fig. 6b–d). These findings demonstrate that OP–I accumulates and diffuses through the intercorneocyte lipid matrix, effectively penetrating the SC layers. Moreover, Fourier transform infrared (FTIR) spectroscopy studies revealed that neither OP nor OP–I enhanced the lipid fluidity within the SC (Supplementary Fig. 25). Consistently, mixing OP with Cy5 or insulinCy5 did not enhance their transdermal penetration, and topical application of OP and insulin mixture did not exhibit hypoglycaemic efficacy. By contrast, conjugation with OP (OPCy5, OP–ICy5 or OP–I) granted them efficient skin permeability (Supplementary Figs. 26–28). These results indicate that OP or OP–I permeates the SC without altering its lipid order or fluidization.

Fig. 4: Mechanism study of the SC penetration of OP and OP–I.

a, CLSM images of SC samples from the mouse dorsal skin after 4 h of topical application with OP–ICy5 (red; Cy5-equivalent dose, 0.2 ml of 10 μg ml−1, 1.13 cm^2). The SC samples were obtained by peeling the skin using adhesive tape, and the SC intercellular lipids were stained with NBD-C6-HPC (green). Additional images are provided in Extended Data Fig. 6a. The images are representative of n = 3 independent experiments. b, 3D reconstructed view from sequential z-stack intravital two-photon microscopy imaging of the mouse skin after 4 h of topical application with OP–IFITC (FITC-equivalent dose, 0.2 ml of 10 μg ml−1, 1.13 cm^2). Separate images are provided in Supplementary Fig. 24. The images are representative of n = 3 independent experiments. c, Representative binding modes from MD simulations of insulin, OP and OP–I on SC lipids at pH 5.5. The SC lipid membrane, composed of equimolar ceramide, cholesterol and free fatty acids, was generated using the membrane builder of CHARMM-GUI. See also Supplementary Video 2. d, PMF results perpendicular to the SC surface, showing the binding free energies of insulin, OP and OP–I to SC lipids at pH 5.5. z represents the distance between the centre of mass of insulin, OP or OP–I, and the SC lipid surface. Umbrella sampling distance, 9 nm; window resolution, 0.1 nm; sampling time, 35 ns per window; restraint force constant, 1,000 kJ mol−1 nm−2. e, MSD results parallel to the SC surface, comparing the diffusivities of insulin, OP or OP–I on SC lipids at pH 5.5. f, Representative interaction modes of OP–I with SC lipids at pH 5.5 and pH 7.0. See also Supplementary Video 4. g, MSD results comparing the diffusivities of OP–I on SC lipids under weak acidic (pH 5.5) and neutral (pH 7.0) conditions. Data are from n = 3 independent experiments. Scale bar, 50 μm (a).

Source Data

MD simulations were conducted to examine the interaction between OP–I and SC lipids; the model SC lipids were composed of an equimolar mixture of ceramide, cholesterol and fatty acids. The binding process of OP and OP–I to SC lipids under mildly acidic conditions (pH 5.5) is illustrated in Supplementary Video 2, demonstrating that both OP and OP–I adsorbed onto the SC lipids more rapidly than insulin. Figure 4c illustrates the corresponding binding configurations. PMF analyses (Fig. 4d) estimated a binding free energy to SC lipids of −8.5 kcal mol−1 for OP, −11.7 kcal mol−1 for OP–I and −6.0 kcal mol−1 for insulin, indicating stronger binding to the lipid membrane of OP and OP–I at the acidic pH. PMF analyses along the surface of SC lipids (in the x direction) estimated diffusion energy barriers to be 0.9 ± 0.1 kcal mol−1 for OP, 1.7 ± 0.2 kcal mol−1 for OP–I and 2.2 ± 0.3 kcal mol−1 for insulin (Extended Data Fig. 7a). Accordingly, the friction coefficient (γ) derived from the Stokes–Einstein relation was 2.07 × 10−10 Ns m−1 for OP, 4.31 × 10−10 Ns m−1 for OP–I and 8.49 × 10−10 Ns m−1 for insulin. The lower friction coefficients of OP and OP–I with SC lipids suggest that they have reduced ‘local trapping’ by SC lipids and faster diffusion compared with insulin (Extended Data Fig. 7b). This observation was further supported by Supplementary Video 3 and Extended Data Fig. 7c, as well as the mean squared displacement (MSD) calculations shown in Fig. 4e. MD simulations also compared the OP–I interactions with SC lipids at weakly acidic (pH 5.5) and neutral (pH 7.0) conditions (Fig. 4f and Supplementary Video 4). At pH 7.0, OP transitioned to a zwitterionic state (Supplementary Fig. 1), substantially reducing its electrostatic interactions with SC lipids and allowing OP and OP–I to diffuse freely (Fig. 4g). Notably, insulin was negatively charged while OP was slightly positively charged at pH 5.3–7.4. MD simulations demonstrated that, at pH 6.0, insulin and OP did not bind to form aggregates owing to the low charge density of insulin and the strong hydrophilicity of OP (Supplementary Fig. 29 and Supplementary Video 5).

As a result, once OP or OP–I was applied to the skin, the acidic surface protonated OP, enabling both OP and OP–I to bind to SC lipids and become enriched within the SC layers. The reduced acidity beneath the upper SC layers freed this binding, enabling OP and OP–I to diffuse through the intercorneocyte lipids and penetrate deeper into the viable epidermis (Extended Data Fig. 1).

After entering the viable epidermis of the skin from the SC, OP–I was transported either through transcytosis pathways[23] or through intercellular spaces. This process was first investigated using 3D-cultured spheroids of the human immortal keratinocyte line (HaCat)[35]. The spheroids treated with OP–IFITC for 12 h exhibited intense fluorescence, whereas those incubated with PEG–IFITC or insulinFITC had only weak fluorescence (Fig. 5a,b). Pretreatment with endocytosis or exocytosis inhibitors did not suppress OP–IFITC infiltration in the HaCat spheroids (Supplementary Fig. 30). Notably, even after 24 h of incubation, OP–ICy5 still exclusively localized on cell membranes, with no detectable fluorescence in the cytoplasm (Fig. 5c and Extended Data Fig. 8a). Similarly, CLSM imaging of porcine skin slices topically treated with OP–ICy5 revealed that OP–ICy5 was predominantly distributed on cell membranes rather than inside cells (Extended Data Fig. 8b,c).

Fig. 5: The mechanism of OP–I penetration in the viable epidermis.

a,b, Penetration of OP–IFITC in HaCat spheroids observed by CLSM (a) and line-scan analysis of fluorescence intensity along the yellow arrows in a (b). Spheroids were incubated with each formulation (FITC-equivalent dose, 1 μg ml−1) for 12 h, and the middle layers of the spheroids were imaged. The images are representative of n = 3 independent experiments. c, Fluorescence intensities of NBD-C6-HPC (green) and OP–ICy5 (red) along the yellow arrows in CLSM images of HaCat cells after 6, 12 or 24 h of incubation with OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1). See also the CLSM images in Extended Data Fig. 8a. The images are representative of n = 3 independent experiments. d, CLSM images of OP–ICy5 hopping on HaCat cell membranes. The images show the fixed views from a time-lapse acquisition mode in Supplementary Video 7 (Cy5-equivalent dose, 1 μg ml−1). The images are representative of n = 3 independent experiments. e,f, Cell-contact-dependent transfer of OP–ICy5 from OP–ICy5-pretreated HaCat cells to untreated HaCatGFP cells. e, Representative CLSM images of n = 3 independent experiments. f, Flow cytometry analysis of transfer efficiency at different timepoints. n = 3 independent experiments. Cy5-equivalent dose, 1 μg ml−1. g, Cell-contact-dependent transfer of OP–ICy5 between HaCat cells on two apposed coverslips. HaCat cells on coverslip 1 were treated with OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1) for 12 h, washed and imaged using CLSM. Coverslip 1 was then pressed face-to-face with coverslip 2 seeded with untreated HaCat cells. The paired coverslips were incubated in fresh medium for 0.5 or 1 h at 37 °C, washed and analysed using CLSM imaging (left) and ImageJ fluorescence quantification (right). Data are mean ± s.d. n = 3 independent experiments. Significance was determined using one-way analysis of variance for multiple comparisons. Scale bars, 500 μm (g), 100 μm (a), 50 μm (d (left), e (left)), 25 μm (c) and 20 μm (d (right) and e (right)).

Source Data

Total internal reflection fluorescence microscopy (TIRFM) was used to study the movement patterns of OP–I on cell membranes using membrane-labelled (NBD-C6-HPC) cells (green) cultured with OP–ICy3 (Supplementary Video 6). The active movement of red fluorescent dots on cell membranes indicated that OP–ICy5 hopped between adjacent cells (Fig. 5d and Supplementary Video 7). An experiment observing the direct cell-to-cell transfer of OP–ICy5 was performed by mixing the OP–ICy5-pretreated HaCat cells (donor cells) with fresh HaCat cells stably expressing green fluorescent protein (HaCatGFP, acceptor cells) (Supplementary Fig. 31). CLSM imaging and flow cytometry analysis showed that HaCatGFP cells gradually acquired Cy5 fluorescence from the donor cells (Fig. 5e,f). The transfer efficiency was enhanced by prolonging the contact time between donor and acceptor cells (Fig. 5f) or by increasing the densities of both cell populations (Extended Data Fig. 8d). Placing coverslip 1 (OP–ICy5-treated HaCat cells) and coverslip 2 (untreated HaCat cells) in face-to-face contact also facilitated the transfer of OP–ICy5 (Fig. 5g). On the other hand, the transfer of OP–ICy5 was completely inhibited when the two cell populations were separated even in the same culture medium (Supplementary Fig. 32). Together, these observations confirm the cell-contact-dependent transfer of OP–I.

Thus, OP–I transport in the epidermis or dermis did not involve intracellular processes[36], and instead occurred through an intercellular process using membrane-mediated diffusion.

The synergy between the characteristic acidic-to-neutral pH gradient of the skin and the pH-dependent binding of OP with SC lipids underpins the fast skin penetration of OP and OP–I. OP was zwitterionic at pH > 7 but gradually protonated to be positively charged as the pH decreased (Supplementary Fig. 1). At the acidic surface of the skin (pH of around 5), cationic OP bound strongly to and thus was enriched in the SC and intercorneocyte lipids, which contain about 15% fatty acids[37]. As the pH gradually increased to around 7 in deeper SC layers, OP transitioned to a neutral state, losing its affinity for SC lipids and diffusing freely through the para-corneocyte spaces into the viable epidermis (Extended Data Fig. 1). In the viable epidermis and dermis, OP and OP–I did not enter cells but hopped on the cell membranes, which avoided intracellular degradation and facilitated efficient skin permeation. OP and OP–I in the dermis were then drained into leaky lymphatic capillaries and subsequently entered systemic circulation, similar to other large molecules29,30.

The efficient skin permeation of OP–I enabled sufficient plasma insulin delivery (Fig. 3) and accumulation in key glucose-regulating tissues, particularly the liver, adipose and muscles, producing immediate, robust and prolonged hypoglycaemic effects, as well as IPGTT outcomes comparable to, or even superior to, subcutaneous-injected insulin in diabetic mice and minipigs.

The skin permeation of OP and OP–I was entirely non-invasive and non-irritative. Repeated topical application caused no structural changes to SC microstructures, no corneocyte shedding, no widening of intercellular gaps and no signs of inflammation or cell death (Extended Data Fig. 5). Thus, OP represents a promising non-invasive transdermal insulin delivery system, offering an ideal alternative to hypodermic injections for diabetes management[38].

In summary, we present a non-invasive transdermal insulin delivery system that achieves in vivo hypoglycaemic efficacy comparable to subcutaneous injections for diabetes treatment, resulting from the efficient skin permeation of OP. The OP conjugation is versatile for transdermal delivery of biomacromolecules such as peptides, proteins and nucleic acids, with broad therapeutic applications, warranting further investigation in future studies.

Methods

Cell lines and animals

The HaCat, mouse hepatoma (AML-12), mouse embryonic fibroblast (3T3-L1) and mouse skeletal muscle (MSMC) cell lines were obtained from the Cell Bank of the Chinese Academy of Sciences. The cells expressing green fluorescent protein (HaCatGFP cells) were established by lentivirus transfection of GFP plasmids into HaCat cells according to the manufacturer’s protocol (Shanghai Genechem). All of the cell lines were incubated in a nutritious DMEM medium containing 10% FBS and 1% (v/v) penicillin–streptomycin at 37 °C with 5% CO_2.

Male C57BL/6J mice (aged 6–8 weeks, 25 g) and female Sprague–Dawley (SD) rats (aged 8–12 weeks, 200 g) were purchased from Shanghai SLAC Laboratory Animal. The mice and rats were housed in the Laboratory Animal Center of Zhejiang University under specific-pathogen-free conditions. Guangxi Bama-minipigs (male, aged 6 months, 35–40 kg) were purchased from Shanghai Jiagan Laboratory Animal and housed in the Laboratory Animal Center of Zhejiang University. The animals were fed with a standard diet and maintained under a 12 h–12 h light–dark cycle, with free access to water throughout the experiment unless otherwise specified. The ambient environment was controlled at 20–26 °C and 50–70% relative humidity. All of the animal experiments were carried out according to the protocols approved by the Institutional Animal Care and Use Committee of Zhejiang University (ZJU20250230).

Experimental materials

Unless otherwise indicated, all materials were purchased from Sinopharm Chemical Reagent. Dichloromethane (CH_2Cl_2) and tetrahydrofuran (THF) were distilled over calcium hydride (CaH_2) or treated with a 4 Å molecular sieve. Trifluoroacetic acid (TFA), 2,2′-azobis(2-methylpropionitrile) (AIBN), 2-(dimethylamino) ethyl methacrylate (DMA), N-Boc-ethylenediamine, N,N-diisopropylethylamine (DIPEA), 1-(3-dimethylaminopropyl)-3-ethylcarbodiimide hydrochloride (EDC·HCl) and 1-hydroxybenzotriazole (HOBT) were purchased from Energy Chemical. Fluorescein isothiocyanate (FITC), sulfo-cyanine3 succinimidyl ester (Sulfo-Cy3-NHS) and sulfo-cyanine5 succinimidyl ester (Sulfo-Cy5-NHS) were purchased from Lumiprobe. Human recombinant insulin (29 U mg−1, I8830) was purchased from Solarbio Science & Technology. NBD-C6-HPC was purchased from J&K Scientific. 4-Cyano-4-[[(dodecylthio) carbonothioyl] thio]pentanoic acid (CTA) was purchased from Aladdin. 2-Iminothiolane hydrochloride and STZ were purchased from Macklin. Gold nanoparticles (AuNPs, 5 nm) were purchased from Feynman Biotechnology. N-Succinimidyl 15-azido-4,7,10,13-tetraoxapentadecanoate (NHS-PEG_4-N_3) was purchased from Aikon. N-succinimidyl 4-[(5-aza-3,4:7,8-dibenzocyclooct-1-yne)-5-yl]-4-oxobutyrate (DBCO-NHS) was purchased from New Research Biosciences.

Synthesis of N-[2-(N-tert-butoxycarbonylamino)]ethyl-4-(dodecyltrithio-carbonate)-4-cyanopenteramide (N-Boc-CTA)

CTA (2 mmol), EDC·HCl (2.5 mmol) and HOBT (2.5 mmol) were dissolved in 20 ml dry CH_2Cl_2 and stirred at room temperature for 4 h. N-Boc-ethylenediamine (2.5 mmol) and DIPEA (2.5 mmol) were dissolved in CH_2Cl_2 (10 ml) and added dropwise to the above solution to continue the reaction overnight at room temperature. The mixture was successively washed twice with a saturated solution of Na_2CO_3, a 0.1 M HCl solution and a saturated brine solution, and then dried over MgSO_4. The crude product was passed through a column packed with silica gel using a mobile phase of n-hexane and ethyl acetate mixture (1:1). A yellow solid was obtained.

Synthesis of Boc-amino-terminated poly[2-(N,N-dimethylamino)ethyl methacrylate] (N-Boc-PDMA)

DMA (30 mmol), N-Boc-CTA (0.35 mmol) and AIBN (0.07 mmol) were dissolved in THF (30 ml) in a Schlenk flask and bubbled with dry N_2 for 20 min. The reaction was carried out at 65 °C for 12 h. After terminating the polymerization by opening the flask, the solution was concentrated and poured into cold n-hexane. The precipitated N-Boc-PDMA was isolated and then dried under a vacuum.

Synthesis of Boc-amino-terminated poly[2-(N-oxide-N,N-dimethylamino)ethyl methacrylate) (N-Boc-OP)

N-Boc-PDMA (0.5 g) was dissolved in 5 ml of 30% hydrogen peroxide (H_2O_2) solution. The mixture was stirred at room temperature for 4 h and then dialysed against deionized water to remove the unreacted H_2O_2 completely. N-Boc-OP was obtained after lyophilization.

Synthesis of OP-NH_2

N-Boc-OP (500 mg) dissolved in 5 ml CH_2Cl_2 and 5 ml TFA was added dropwise under ice cooling. This solution was stirred for 2 h at room temperature. The reaction solution was evaporated to remove TFA, vacuum-dried and then dissolved in deionized water. The pH of the solution was adjusted to 7.4 with sodium hydroxide solution (1 M) and then dialysed against deionized water. OP-NH_2 was obtained after lyophilization.

Synthesis of OP-DBCO

OP-NH_2 (30 mg) was dissolved in 3 ml of PBS (pH 7.4), and DBCO-NHS (3 mg) in 2 ml of DMF was added. The mixture was stirred at room temperature for 4 h and then dialysed sequentially against a water-DMF mixture (3:2 (v/v)) and water. The product, OP-DBCO, was obtained by lyophilization. PEG-DBCO was prepared according to the same procedure.

Synthesis of OP–I

The lysine residue on insulin was introduced with an azide group using N_3-PEG_4-NHS. Insulin (21.6 mg) was dissolved in 5 ml of 0.1 M Na_2CO_3 (adjusted to pH 10), and N_3-PEG_4-NHS (1.44 mg, 10 mg ml−1 in DMSO) was added at an azido-to-amine ratio of 1:3. The mixture was stirred at room temperature for 4 h, and the azide-modified insulin (insulin-N_3) was purified using preparative HPLC (prep-HPLC). For OP–I synthesis, insulin-N_3 (2 mg, 0.29 μmol) and OP-DBCO (3.9 mg, 0.88 μmol) were dissolved in PBS (pH 7.4) and stirred at room temperature for 4 h. The product, OP–I, was purified using prep-HPLC. PEG–I was synthesized similarly.

Labelling OP, OP–I, PEG–I and insulin with FITC, Cy3 or Cy5

FITC, Sulfo-Cy3-NHS or Sulfo-Cy5-NHS solutions in DMSO (5 mg ml−1) were added dropwise with gentle stirring to OP-NH_2, PEG-NH_2, insulin or their conjugates (OP–I or PEG–I) dissolved in PBS (10 mg ml−1, pH 7.4) at a dye-to-insulin molar ratio of 1:1. The reaction was carried out overnight at room temperature in the dark. The labelled polymers, insulin and conjugates were purified using Sephadex G-25 resin to remove the unreacted dye and then lyophilized. The products were stored in the dark at 4 °C for further use.

RP-HPLC analysis

The RP-HPLC analysis was performed using a 1260 binary HPLC pump equipped with a ZORBAX SB-C18 column (5 μm, 4.6 × 250 mm) and a 1260 infinity II variable wavelength detector set at 280 nm. The mobile phase consisted of water with 0.1% TFA (phase A) and acetonitrile with 0.1% TFA (phase B). The flow rate was set at 1 ml min−1. The elution gradient was set as follows: 30% to 40% B, 0–5 min; constant 40% B, 5–10 min; 40% to 100% B, 10–11 min; constant 100% B, 11–16 min; 100% to 30% B, 16–17 min; constant 30% B, 17–22 min.

Stability of OP–ICy5

OP–ICy5 (0.4 mg) was incubated in 200 μl of DMEM culture medium with 10% FBS at 37 °C. The solution was sampled at 0 h, 6 h and 12 h for RP-HPLC detection (n = 3 per timepoint), as described above, except that an Agilent 1260 Infinity II fluorescence detector (640 nm excitation, 660 nm emission) was used. The mobile phase remained the same, but the elution gradient was as follows: 0%–100% B, 0–15 min; isocratic at 100% B, 15–20 min; 100%–0% B, 20–21 min; and isocratic at 0% B, 21–26 min. OP–ICy5 had a retention time of 8.8 min. The target peak integral area was quantified, confirming its structural stability even after 12 h.

Prep-HPLC for purification

Prep-HPLC was performed using the Waters Prep 150 LC system equipped with a Pursuit 5 C18 column (250 × 21.2 mm) and a Waters 2489 UV/VIS detector set at 214 nm and 280 nm. The mobile phases included water with 0.1% TFA (phase A) and acetonitrile with 0.1% TFA (phase B). The elution gradient and flow rates were set as follows: 20% to 40% B with flow rates increasing from 10 to 15 ml min−1, 0–10 min; constant 40% B with a constant flow rate of 15 ml min−1, 10–20 min. The retention times were 11.8 min for insulin-N3, 10.1 min for OP–I and 12.8 min for PEG–I.

Gel-permeation chromatography

The Shimadzu Prominence Plus LC-20AD LC system was equipped with two columns connected in series (PL aquagel-OH MIXED-H and PL aquagel-OH 30), a refractive index detector and a UV/VIS detector. The mobile phase was prepared by mixing acetic acid (100 ml), acetonitrile (150 ml) and deionized water (200 ml). The pH was then adjusted to 2.3 using a concentrated ammonia solution, and the final volume was brought to 500 ml with deionized water. The flow rate was 0.5 ml min−1, and the column temperature was 40 °C.

Circular dichroism spectroscopy

Far UV circular dichroism spectra were recorded at 37 °C on the JASCO J-815 spectropolarimeter. Quartz cuvettes with a path length of 1 mm were used. Each spectrum was an average of four scans recorded from 260 to 200 nm at 1 nm steps.

MALDI-TOF MS analysis

All MALDI-TOF MS analyses were performed on a Bruker Autoflex maX TOF/TOF mass spectrometer (Bruker), equipped with a modified Nd:YAG laser in positive-ion mode; data acquisition was conducted using the Bruker flexControl 3.4 software. α-Cyano-4-hydroxycinnamic acid was used as the matrix. As OP did not generate detectable signals in mass spectra owing to its zwitterionic N-oxide structure, the OP–I was then reduced to PDMA-I by bis(pinacolato)diboron[39] for analysis. Ions were extracted into the mass spectrometer in reflection mode using an extraction potential of 20 kV using a high-mass detection method.

Zeta potential measurements

The solutions were prepared by dissolving OP (0.1 mg ml−1) or OP–I (0.04 mg ml−1) in HEPES buffers at varied pH values (10 mM). A Nano ZS Zetasizer (Malvern Instruments) was used to measure the zeta potentials using a 4 mW 633 nm He-Ne laser at 25 °C.

Synthesis of OP–AuNPs

OP-NH_2 (60 mg) was dissolved in 6 ml of PBS (pH 8.0), and 2-iminothiolane hydrochloride (Traut’s reagent, 10 mg ml−1) was added. The mixture was stirred at room temperature for 4 h and dialysed against water (MWCO 1 kDa) to remove the unreacted components. The product was lyophilized to obtain OP-SH. OP-SH (1 mg) was added to a solution of AuNPs (50 μg ml−1) and stirred at 4 °C for 12 h. The resulting OP–AuNPs were purified by centrifugation at 19,000g for 10 min at 4 °C and then resuspended in water.

In vivo skin permeation of OPCy5, OP–IFITC, OP–ICy5 and their mixtures

The dorsal skin of male C57BL/6J mice was exposed using depilatory cream and cleaned using PBS. A diffusing cell of 1.13 cm^2 was attached onto the dorsal skin. OPCy5, OP–IFITC, PEG–IFITC, insulinFITC, OP–ICy5 (FITC or Cy5-equivalent dose, 10 μg ml−1; 0.2 ml per mouse) or their physical mixture was injected into the cell. After timed topical administration, the mice were euthanized. The treated skin sites were washed and dissected. The entire skin samples were carefully washed three times with PBS, fixed with 4% paraformaldehyde (PFA) solution and sectioned into 10-μm-thick slices using a cryostat (UV800, Leica Microsystems). 4′,6-Diamidino-2′-phenylindole (DAPI) was used to stain and label the nuclei of skin tissues, and BODIPY was used to stain and localize subcutaneous fat deposits. Fluorescence images were taken using CLSM with excitation at 405 nm for DAPI, 488 nm for BODIPY or FITC, and 640 nm for OP–ICy5. The CLSM images were analysed using ImageJ.

OPCy5 solution (0.2 ml, Cy5-equivalent dose, 10 μg ml−1) was applied to the mice as described above. Blood samples (200 μl) were collected from the orbit venous plexus at timed intervals, and their Cy5 fluorescence intensities were measured using a microplate spectrophotometer with excitation at 640 nm. The main organs of the mice, including the heart, liver, spleen, lung and kidneys, were also collected at timed topical administration of OPCy5, and their fluorescence intensities were measured using the IVIS Spectrum imaging system (IVIS Lumina XRMS Series III, PerkinElmer).

OPCy5 was dispersed in a cream (water-in-oil, Aquaphor; Cy5-equivalent dose, 10 μg ml−1). The OPCy5 cream was topically applied on the minipig abdominal skin (cream volume, 10 ml; application area, 100 cm^2) for 4 h. The minipigs were euthanized, and the treated skin sites were dissected and sectioned into slices, as mentioned above. Fluorescence images were taken using CLSM with excitation at 405 nm for DAPI and 640 nm for OP–ICy5. The CLSM images were analysed using ImageJ.

Biological half-life of OP–I

Male C57BL/6J mice were randomly assigned to groups (n = 3 for each group). The solution (0.1 ml; Cy5-equivalent dose, 0.1 mg per kg) of insulinCy5 or OP–ICy5 was injected through the tail vein. Blood samples were collected from the orbital venous plexus at timed intervals. The fluorescence intensity was quantified using the IVIS Spectrum system. The insulin concentration was also measured using human insulin ELISA kits (Elabscience). The half-lives of insulin and OP–I were calculated using DAS2 software based on the plasma concentration data.

HAADFI–STEM-EDS analysis of OP–AuNP-treated skin cryosections

C57BL/6J male mice were topically administered with 0.2 ml OP–AuNPs (OP-equivalent dose, 0.5 mg ml−1). After 4 h, the mice were anaesthetized. The skin at the treated site was dissected and fixed overnight at 4 °C. The samples were trimmed into small sections and then treated with 1% osmium tetroxide (diluted in 100 mM cacodylate buffer) for 2 h, dehydrated with ethanol and acetone, and embedded in Spurr resin. Then, 10-μm-thick slices were sectioned (LKB 11800 Pyramitome) and stained with toluidine blue to select the desired regions. The ultrathin sections (50–100 nm) were prepared using an ultramicrotome (UC7, Leica).

HAADFI STEM-EDS analysis of the skin cryosections was performed on a field emission transmission electron microscope (JEOL JEM F200) at an accelerating voltage of 200 keV equipped with an EDS detector.

Cellular uptake

AML-12 cells, 3T3-L1 differentiated adipocytes and MSMC cells were seeded into confocal dishes at a density of 1 × 10^5 cells per ml and incubated for 24 h. The cells were treated with OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1) for 4 h. After incubation, the nuclei were stained with Hoechst 33342 (2 μM) for 20 min. The cells were washed twice with PBS and imaged using CLSM at an excitation wavelength of 405 nm for Hoechst 33342 and 640 nm for Cy5.

SPR analysis of binding affinity

SPR experiments were performed on a Biacore X100 instrument (Cytiva) with data acquisition using Biacore X100 system control software (v.2.0.1.201). The CM5 chip sensor (GE Healthcare) was used in this study. Anti-His antibodies were immobilized on the surface of the CM5 chip sensor according to the manufacturer’s instructions. His-tag-ECD-IR/IGF1R protein (Sino Biological) was then injected over the anti-His antibody-coated surface of the CM5 chip sensor at a specific concentration and flow rate. The binding affinities of insulin and OP–I were evaluated by injecting various concentrations of insulin (9.75, 19.5, 39.0, 78.0 and 156 nM) or OP–I (4.06, 8.13, 16.3, 32.5 and 65.0 nM) in HEPES running buffer (pH 7.4) over the His-tag-ECD-IR/IGF1R-coated surface under a single-cycle kinetics mode. Each cycle included a 180 s binding phase and a 300 s dissociation phase. The dissociation equilibrium constant (Kd), association rate constant (kon) and dissociation rate constant (koff) were determined using the BIA evaluation software (v.2.0.1.201). The t1/2 values, which define the residence time, were determined using the formula ln2/koff.

Western blotting for insulin signalling analysis

Mice were injected subcutaneously with PBS or insulin (insulin-equivalent dose, 5 U kg−1), or topical administration with OP–I (insulin-equivalent dose, 116 U kg−1; concentration, 0.5 mg ml−1; volume, 0.2 ml; diffusing area, 1.13 cm^2). The mice were euthanized, and their skeletal muscle tissues were collected at 1 h after subcutaneous injection or 4 h after topical administration. Muscle samples were weighed and lysed in radioimmunoprecipitation buffer (Sigma-Aldrich) containing protease and phosphatase inhibitors (Thermo Fisher Scientific) and incubated on ice for 30 min. The lysates were centrifuged at 20,000g for 20 min at 4 °C and quantified using the BCA protein assay. The proteins were resuspended in Laemmli sample buffer with 2.5% 2-mercaptoethanol, denatured at 95 °C for 5 min, separated by SDS–PAGE and transferred to polyvinylidene fluoride membranes. The membranes were blocked in Tris-buffered saline with 0.5% Tween-20 (TBST) and 5% BSA for 1 h, followed by overnight incubation at 4 °C with primary antibodies against phosphorylated IRβ/IGF1Rβ (1:1,000), phosphorylated AKT-Thr308 (1:1,000) or GAPDH (1:5,000). After washing three times with TBST, the membranes were incubated with horseradish-peroxidase-conjugated secondary antibodies (HRP-labelled goat anti-rabbit IgG (H+L) or HRP-labelled Goat Anti-Mouse IgG (H+L)) at a dilution of 1:1,000 at room temperature for 1 h. Signal detection was performed using Immobilon Forte chemiluminescence substrate on the ChemiScope 3600 Mini Imaging System (Clinx Science Instruments). The membranes were next incubated in stripping buffer (BL526, Biosharp) at room temperature with gentle agitation for 15 min, followed by extensive washing with TBST, and then overnight incubation at 4 °C with primary antibodies against IRβ and AKT. The membranes were processed as previously described, including incubation with HRP-conjugated secondary antibodies and signal detection through chemiluminescence.

OP–I permeation in 3D skin equivalent EpiKutis

The 3D skin model (EpiKutis) was fabricated according to a previously reported method[40]. In brief, keratinocytes (5 × 10^5) were seeded onto the permeable membrane of a Transwell chamber, cultured at 37 °C in a 5% CO_2 atmosphere for 2 days and then cultured at the air–liquid interface for 8 days with daily medium replacement. The complete EpiKutis 3D model was obtained and used as a skin model for investigating OP–I skin permeability. OP–I, PEG–I or insulin solution (insulin-equivalent dose, 0.5 mg ml−1; 0.2 ml) was added to the donor compartment, and 0.4 ml fresh medium was added to the receiving compartment. The temperature was maintained at 37 °C. At timed intervals, 50 μl solution was withdrawn from the receiving compartment and an equal volume of fresh medium was added. The insulin concentration was quantified by ELISA kits. The unit conversion was calculated according to the following formula, and the cumulative amount of insulin permeating per unit area of the model skin (Qn) was calculated:

$${Q}_{n}=\frac{{C}_{n}{V}_{{\rm{r}}}+{\sum }_{i=1}^{n-1}{C}_{{\rm{i}}}{V}_{{\rm{s}}}}{A}$$

Where, Qn is the cumulative amount of insulin permeating per unit area (μg cm−2); Cn is the insulin concentration in the receiver cell at sampling timepoint t (μg ml−1); Ci is the insulin concentration of the receiving liquid at the intermediate point (μg ml−1); Vr is the volume of the receiving pool (0.4 ml); Vs is the volume of the sampled receiving solution (50 μl); and A is the effective transmission area of the EpiKutis (0.081 cm^2).

The steady-state flow rate (Jss) was obtained as the slope of the curve of Qn as a function of time. The apparent permeability coefficient (Kp) was calculated by the following formula:

$${K}_{{\rm{p}}}=\frac{{J}_{\mathrm{ss}}}{{C}_{0}}$$

Where C_0 is the initial concentration of insulin or its conjugate in the donor cell.

EpiKutis (0.081 cm^2) was incubated with 0.2 ml OP–IFITC, PEG–IFITC or insulinFITC (FITC-equivalent concentration, 1 μg ml−1) for 4 h, then washed three times with PBS, stained with DAPI and finally imaged using CLSM with the z-stack tomoscan model at a 10-μm interval from the bottom to top of the 3D skin model with excitation at 405 nm for DAPI and 488 nm for FITC.

Skin penetration analysis by intravital two-photon microscopy

The mice were topically treated with OP–ICy5, as described above. The skin was mounted between a coverslip and a sliding glass for two-photon imaging analysis. The laser wavelength for two-photon excitation was 480 nm, and the laser power delivered to the skin sample was 90 mW. Sequential z-stack images were captured at 3-μm intervals from the skin surface until the fluorescence signal became undetectable. The xz-axis orthogonal view of the SC layers was reconstructed using volume viewer plugins in ImageJ.

Subcutaneous lymphatic vessel co-localization

OP–ICy5 (Cy5-equivalent dose, 0.2 ml of 10 μg ml−1) was topically applied on the dorsal skin of SD rats. After 4 h, the tissue at the application site was excised and frozen-sectioned. The lymphatic vessels were immunostained using LYVE-1AF488 (1:1,000), and the nuclei were counterstained with DAPI. Subsequently, the distribution of OP–ICy5 within the lymphatic vessels was examined using CLSM.

Skin retention of OP–ICy5

After 4 h of topical application with OP–ICy5 on the dorsal skin of C57BL/6J mice (Cy5-equivalent dose, 10 μg ml−1; 0.2 ml per mouse), the OP–ICy5 solution was removed and the treated skin site was gently washed three times with PBS. Subsequently, the mice were euthanized at 4 or 8 h after removal of the OP–ICy5 solution. The fluorescence intensity in the skin was imaged using the IVIS Spectrum imaging system and CLSM.

In vivo skin permeation of OP–ICy5 in minipigs

The OP–ICy5 cream (Cy5-equivalent dose, 10 μg ml−1) was topically applied onto the minipigs’ abdominal skin (cream volume, 10 ml; application area, 100 cm^2). After 4 h, the minipigs were euthanized, and the treated site skins were washed three times with PBS, dissected, fixed with 4% PFA and sectioned into slices, as described above. The slices were stained with DAPI to label the cell nuclei and with NBD-C6-HPC to label the SC lipids and the cell membranes in the viable epidermis. Fluorescence images were taken using CLSM with excitation at 405 nm for DAPI, 488 nm for NBD-C6-HPC and 640 nm for OP–ICy5. The CLSM images were analysed using ImageJ.

OP–ICy5 biodistribution in mice

Male C57BL/6J mice were randomly grouped (n = 3 mice). Each mouse was topically applied with 0.2 ml OP–ICy5, PEG–ICy5 or insulinCy5 solution (Cy5-equivalent dose, 10 μg ml−1) on the mouse dorsal skin for 4 h, and then the solution was removed. InsulinCy5 was administered subcutaneous to the mice in the control group (Cy5-equivalent dose, 25 μg per kg). The mice were euthanized at timed intervals. The main organs and tissues, including the heart, liver, spleen, lung, kidneys, adipose tissues (including brown adipose tissue,subcutaneous white adipose tissue and visceral white adipose tissue), and skeletal muscles were collected, and their fluorescence intensities were measured using the IVIS Spectrum imaging system.

In vivo studies using STZ-induced diabetic mice

Type 1 diabetic mice were established through intraperitoneal delivery of STZ (150 mg per kg in 10 mg ml−1 disodium citrate buffer, pH 4.5) into healthy male C57BL/6J mice (aged 6–8 weeks, ~25 g). BGLs were monitored, and the mice with BGLs exceeding 300 mg dl−1 were considered diabetic. Diabetic mice with fasting BGLs within the 300 to 600 mg dl−1 range were selected for the experiments. BGLs were measured from tail-vein blood (around 3 μl) using a calibrated Sinocare glucose meter.

A diffusion cell (diffusing area: 1.13 cm^2) containing insulin, OP–I or PEG–I (insulin-equivalent dose, 116, 58 or 29 U kg−1; concentration, 0.5 mg ml−1; volume, 0.2, 0.1 or 0.05 ml per mouse) or the mixture of OP and insulin (OP + insulin; insulin-equivalent dose, 116 U kg−1, 0.5 mg ml−1; 0.2 ml per mouse) was applied on the dorsal or abdominal skin of STZ-induced diabetic mice. For the positive control group, mice were administered insulin subcutaneously at a dose of 5 U kg−1. BGLs were measured at timed intervals. The skin insulin concentrations and plasma insulin concentrations in the blood samples (25 μl) collected from the tail vein were quantified using ELISA kits according to the manufacturer’s protocol. The diabetic mice were subjected to a fasting period of 12 h during the experimental procedures.

The repeatability of OP–I’s hypoglycaemic effect was assessed by applying OP–I (insulin-equivalent dose, 116 U kg−1, 0.5 mg ml−1; 0.2 ml per mouse) topically onto the same diabetic mice over three consecutive days. Plasma insulin concentrations were measured at timed intervals using ELISA.

For the IPGTT experiment, diabetic mice were topically applied with OP–I (insulin-equivalent dose, 116 U kg−1, 0.5 mg ml−1; 0.2 ml per mouse); then, 1 h later, they were intraperitoneally injected with 0.2 ml of glucose solution (1.5 g per kg). BGLs were monitored over time. The diabetic mice were subjected to a fasting period of 3 h during the experimental procedures.

In vivo studies using STZ-induced diabetic minipigs

Guangxi Bama minipigs (aged 6 months; weight, 35–40 kg) were infused with STZ in freshly prepared disodium citrate buffer (75 mg ml−1, pH 4.5) at a 150 mg per kg dose within 10 min and then maintained for recovery. The glucose levels were monitored using CGMS[15] (Dexcom G4 Platinum Continuous Glucose Monitor System, Dexcom). A BGL that is constantly higher than 250 mg dl−1 indicates the successful establishment of the insulin-deficient diabetic minipig model.

OP–I, PEG–I or native insulin was dispersed in the cream (water-in-oil) at an insulin-equivalent concentration of 1 mg ml−1, as described above. The cream was topically applied onto the minipig abdominal skin at an insulin-equivalent dose of 40 mg or 10 mg (n = 3 for each group). The area with the cream was wrapped with plastic film. The BGLs of minipigs were continuously monitored using the CGMS. The diabetic minipigs were subjected to a fasting period of 12 h during the experimental procedures.

The skin samples were excised from the administration skin site at the end of the experiment. The samples were processed for sectioning and stained with haematoxylin and eosin and terminal deoxynucleotidyl transferase dUTP nick end labelling (TUNEL). Moreover, control skin samples were collected from healthy minipigs in the same anatomical region without treatment.

SC sample collection and observation

The procedure was performed according to a previously reported method[34]. At 4 h after topical application of OP–ICy5, PEG–ICy5 or insulinCy5 (Cy5-equivalent dose, 10 μg ml−1; 0.2 ml per mouse), the treated sites were carefully washed three times with PBS and dried. Double-sided adhesive tape (Scotch 3M) was pressed onto the skin surface for 2 s and then peeled off in the longitudinal direction. The middle part of the tape was fixed on a microscopy slide, stained with NBD-C6-HPC and then observed under CLSM at 488 nm excitation for NBD-C6-HPC and 640 nm excitation for Cy5.

FTIR spectrometry

PBS (1 ml), OP (0.5 mg ml−1 in 1 ml PBS), OP–I (0.5 mg ml−1 in 1 ml PBS) or oleic acid (50 mg ml−1 in 1 ml propylene glycol) was evaluated using RYJ-12B Franz diffusion cells with male C57BL/6J mouse skin. Mouse skin samples (3 cm × 3 cm) were fixed in glass holders with a 2.2 cm^2 circular permeation area, mounted in Franz cells with the epidermal side up, and the acceptor compartment (8 ± 0.5 ml) was filled with pH 7.4 PBS. The setup was maintained on a magnetic stirrer in a water bath at 37 ± 0.5 °C. After incubating for 24 h with the test compounds, skin samples were gently washed with PBS and analysed using a Thermo Fisher Scientific Nicolet iS50 FTIR spectrometer. Spectra were acquired by co-adding 128 scans at 4 cm−1 resolution over the frequency range of 4,000–650 cm−1.

MD simulations

The insulin (PDB: 1AI0 (ref. [41]), chain I) and its receptor (IR, PDB: 6SOF (ref. [42])) structures were obtained from the Protein Data Bank (PDB). The structures of OP and OP–I were constructed using Avogadro software[43]. OP was set to have 32 repeating units. The force-field parameters of OP and OP–I were obtained from the Paramchem webserver[44] and CGenFF[45]. The SC lipid membrane, composed of an equimolar mixture of ceramide, cholesterol and free fatty acids, was generated by the membrane builder CHARMM-GUI46,47. The CHARMM36[48] force field was used to model the insulin and SC lipids. At pH 5.5, 20% of the N-oxide groups of OP were assumed to be protonated, whereas 50% of the fatty acids were considered to be deprotonated. At pH 7.0, OP was zwitterionic, while all fatty acids were deprotonated. Each system was solvated in an 11.4 × 11.4 × 16.1 nm^3 water box with around 219,000 atoms. To study the binding interactions of insulin or OP–I with IR, the respective system was solvated in a 23.0 × 23.0 × 23.0 nm^3 water box containing around 1,225,000 atoms. To study the interactions of multiple insulin, OP or OP–I molecules, the respective system was solvated in a 14.7 × 14.7 × 14.7 nm^3 water box containing around 325,000 atoms. Water molecules were modelled by the TIP3P water model[49]. Na+ and Cl− ions were added to neutralize each system and bring its total ionic strength to 0 at the physiological concentration of 150 mM.

All MD simulations were carried out using the program GROMACS 2020.650,51. VMD[52] was used for trajectory visualization. The covalent bonds with hydrogen atoms were constrained by the LINCS algorithm[53], which allowed a time step of 2 fs. The long-range electrostatic interactions were calculated using the particle-mesh Ewald method[54], whereas the van der Waals interactions were calculated with a smooth cut-off of 1.2 nm. Periodic boundary conditions were applied in all directions. The NPT ensemble with semi-isotropic pressure coupling was applied with the pressure (1 bar) controlled by the Parrinello–Rahman barostat[55] and the temperature (310 K) by the v-rescale thermostat[56]. Before production runs, the lipid system was equilibrated for 100 ns; then, 200-ns runs were conducted to monitor insulin, OP or OP–I adsorption on the SC lipids. After adsorptions, three independent 100-ns runs were further performed for insulin, OP or OP–I to monitor their diffusions on SC lipids. To analyse the binding interactions of insulin or OP–I with IR, 200-ns MD simulations were conducted for each system. To investigate the interactions of multiple insulin, OP or OP–I molecules at pH 6.0, 400-ns MD simulations were conducted for each system. In production simulations, all atoms were free to move.

The friction coefficient γ of insulin/OP/OP–I on SC lipids was derived from the Stokes–Einstein relation:

$$\gamma =\frac{{k}_{{\rm{B}}}T}{D}$$

where kB is the Boltzmann constant, T is the temperature and the diffusion coefficient D follows

$$D=\frac{\langle {r}^{2}(t)\rangle }{{k}{\rm{t}}}$$

Where k = 4 on a 2D surface, the time t and the displacement r(t) were obtained from three independent 100-ns MD runs after adsorption.

PMF analyses

The PMF results were calculated using the umbrella sampling protocol[57]. The PMF setups were similar to the aforementioned MD setups to estimate the energy barriers for the diffusion of insulin, OP or OP–I on the SC lipids. The total transverse distance along each representative path was 2 nm, which was divided into 20 windows with a resolution of 0.1 nm. Position restraints were applied to the SC lipids when the energy barriers were scanned. For monitoring the adsorption of insulin, OP, or OP–I on SC lipids, the simulation boxes were extended to 11.4 × 11.4 × 22.1 nm^3 by adding 0.15 mM NaCl solution in the boxes. After a further 30-ns equilibration, the sampling path of each system was obtained by pulling insulin, OP or OP–I in the perpendicular (z) direction to the SC lipid membrane with a constant velocity of 0.2 nm ns−1. The total sampling distance in the z direction was 9 nm for each system, which was divided into 90 windows with a resolution of 0.1 nm. At each window, the system was first equilibrated for 5 ns, followed by a 35-ns productive umbrella sampling with a restraint force constant of 1,000 kJ mol−1 nm−2. To evaluate the binding affinity of insulin or OP–I with IR, the sampling path of each system was determined by pulling insulin or OP–I perpendicular to the IR surface at a constant velocity of 0.2 nm ns−1. The total sampling distance of 5 nm was divided into 50 windows with a resolution of 0.1 nm. At each window, the system underwent a 2-ns equilibration phase followed by a 20-ns productive umbrella sampling simulation, applying a restraint force constant of 1,000 kJ mol−1 nm−2.

VE penetration study using 3D-cultured multilayer HaCat spheroids

Multilayer cell spheroids were prepared using the hanging-drop method. HaCat cells were suspended in fresh DMEM medium (containing 0.12% (w/v) methylcellulose) at a density of 4 × 10^5 cells per ml. The cell suspensions (25 μl) were dropped onto the lids of the cell culture plate to form uniform droplets, and 20 ml PBS was added to the plate to keep the droplets moist. The cells were incubated for 72 h and formed dense spheroids, which were transferred to an agarose-coated (1% (w/v) in PBS) 96-well plate with one spheroid per well and incubated for another 72 h to mature. The spheroids were incubated with OP–IFITC, PEG–IFITC or insulinFITC at an FITC-equivalent dose of 1 μg ml−1 for timed intervals. The spheroids were washed with PBS and imaged using CLSM by z-stack tomoscan at 20 μm intervals from the bottom to the middle of the spheroids. The integration of FITC fluorescence density and linescan analysis were performed using Image J.

For the effects of the endocytosis and exocytosis inhibitors on the penetration of OP–IFITC, the HaCat spheroids were separately treated with PBS, wortmannin (2 μM), cytochalasin D (20 μM), monensin (20 μM), nocodazole (10 μM) or brefeldin A (10 μM) for 2 h, and then incubated with OP–IFITC (FITC-equivalent dose, 1 μg ml−1) for 4 h. The HaCat spheroids were imaged and analysed as described above.

Localization of OP–ICy5 at HaCat cell membranes

HaCat cells were plated onto glass-bottom dishes at a density of 1 × 10^5 cells per dish and incubated for 24 h. The HaCat cells were incubated with OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1) for 6 h, 12 h or 24 h. The cell membrane was stained with NBD-C6-HPC (1 μM) for 5 min, and then the cells were washed three times with PBS and observed under CLSM. Fluorescence images were taken using CLSM with excitation at 488 nm for NBD-C6-HPC and 640 nm for Cy5.

The cells were imaged immediately at maximum projection after adding OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1) for time-lapse videos.

Observation of contact-dependent direct transfer of OP–I among HaCat cells

HaCat cells were seeded into six-well plates at 1.25 × 10^5 or 2.5 × 10^5 cells per well and allowed to adhere overnight. The cells were then incubated with OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1) for 12 h and then extensively rinsed with sterilized PBS and isolated. The OP–ICy5-treated HaCat cells were mixed with untreated HaCatGFP cells at the same cell density. The mixed cells were co-cultured in DMEM medium for 12 h and imaged with CLSM with excitation at 488 nm for GFP and 640 nm for Cy5. The mixed cells co-cultured in DMEM medium for 3 h, 6 h or 12 h were further isolated and analysed by flow cytometry. First, an FSC-A versus SSC-A gate was applied to exclude debris and select live cells based on forward scatter (FSC) and side scatter (SSC) characteristics. Next, a GFP gate (FL1-H) was set to include cells with fluorescence in the GFP channel, followed by establishing a Cy5 gate (FL4-H) to isolate Cy5-positive cells. Finally, an intersection gate between the GFP and Cy5 gates was used to identify dual-positive cells. Every 10,000 cells were counted to determine GFP-positive cells at the FL1 channel and Cy5-positive cells at the FL4 channel. The experiment was repeated three times independently; FlowJo (v.10.0) software was used for analysis. The transfer efficiency of OP–ICy5 to HaCatGFP cells was calculated according to the formula.

$$\mathrm{Transfer}\,\mathrm{efficiency}( \% )=\frac{{\mathrm{Number\; of\; HaCat}}^{\mathrm{GFP}+\mathrm{Cy}5}\,\mathrm{cells}}{\mathrm{Total\; counted\; number\; of}\,{\mathrm{HaCat}}^{\mathrm{GFP}}\,\mathrm{cells}}\times 100$$

Non-contact inhibition of intercellular transfer of OP–ICy5

HaCat cells were seeded onto two coverslips (1 and 2) and incubated overnight. The cells on a coverslip 1 were first cultured with OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1) for 4 h, rinsed with PBS three times and then co-incubated with the coverslip 2 with untreated cells in a fresh medium for 12 h. The cells on the coverslips were washed with PBS, and the cell membrane was stained with NBD-C6-HPC (1 μM) for 5 min. The cells were imaged with CLSM at 488 nm excitation for NBD-C6-HPC and 640 nm for Cy5.

Intercellular transfer between cells on separate coverslips

Two coverslips were seeded with HaCat cells (10^5 each) and cultured overnight to ensure full adherence. The cells on one coverslip were incubated with OP–ICy5 (Cy5-equivalent dose, 1 μg ml−1) for 12 h and then washed three times with PBS, noted as coverslip 1. Coverslip 1 was placed on top of the other coverslip with untreated HaCat cells (coverslip 2) and pressed slightly. The coverslips were cultured together in DMEM medium for 0.5 or 1 h and then observed using CLSM for the transfer of OP–ICy5.

TIRFM imaging

HaCat cells were seeded onto a confocal dish at a density of 1 × 10^5 cells per well and incubated for 24 h. Subsequently, OP–ICy3 (Cy3-equivalent dose, 1 μg ml−1) was added. After 4 h, NBD-C6-HPC was added to stain the cell membrane for 5 min, and the cells were then washed three times with PBS. Time-lapse imaging of the cell membrane was conducted using the TIRF function of an Olympus IX83 microscope. ImageJ was used for image analysis.

Statistical analyses

Statistical tests were performed using Prism (GraphPad software, v.10.4.0). One-way analysis of variance was used for multiple comparisons. Unpaired Student’s t-tests were used to analyse the difference between two groups.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

Data supporting the findings of this study are provided in the Article and its Supplementary Information. The input files (.tpr files) for the key simulations in this study are available at Zenodo[58] (https://doi.org/10.5281/zenodo.17078485). Source data are provided with this paper.

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Acknowledgements

This work was supported by the National Key Research and Development Program (2021YFA1201200), the National Natural Science Foundation (52495010, 51833008, 52203193, U1967217) of China, the National Center of Technology Innovation for Biopharmaceuticals (NCTIB2022HS02010), Shanghai Artificial Intelligence Lab (P22KN00272) and the Starry Night Science Fund (SN-ZJU-SIAS-003). We thank Q. Lin for her technical assistance on TEM (JEOL JEM F200) characterization; J. Li for her technical assistance on FTIR and MALDI-TOF MS characterization; S. Fang and S. Liu for their technical support on CLSM and TIRFM; D. Xu for help with minipig experiments. Cartoons in Fig. 3i and Extended Data Fig. 3a were created using BioRender with granted publication licences.

Author information

Author notes

1. These authors contributed equally: Qiuyu Wei, Zhi He, Zifan Li, Zhuxian Zhou

Authors and Affiliations

1. Zhejiang Key Laboratory of Smart Biomaterials and Center for Bionanoengineering, Key Laboratory of Biomass Chemical Engineering of Ministry of Education, State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou, China

Qiuyu Wei, Zifan Li, Zhuxian Zhou, Ying Piao, Yu Geng, Runnan Zhang, Jiayi Ye, Yue Yuan, Haoru Zhu, Jiaheng Zeng, Yan Zhang, Quan Zhou, Shiqun Shao, Jianbin Tang, Jiajia Xiang & Youqing Shen

2. Institute of Quantitative Biology, Zhejiang Key Laboratory of Cell and Molecular Intelligent Design and Development, College of Life Science, Zhejiang University, Hangzhou, China

Zhi He, Jianxiang Huang, Yaqi Fu, Mingyu Xu & Ruhong Zhou

3. Department of Chemical Engineering, Imperial College London, London, UK

Rongjun Chen

Contributions

Y.S. conceived and supervised the project. R. Zhou, J.X., Z.Z. and R.C. co-supervised the project. Q.W., Y.P., R. Zhang, Y.F., J.Y. and Y.Y. performed the biological experiments and analysed the data. Z.L., Y.G. and H.Z. carried out the synthesis. Z.H., J.H. and M.X. carried out the MD simulations supervised by R. Zhou. J.Z. and Y.Z. established type 1 diabetic models. Q.Z., S.S. and J.T. helped with the discussion of the synthesis and mechanism. All of the authors discussed the results and contributed to the writing of the manuscript.

Corresponding authors

Correspondence to Jiajia Xiang, Rongjun Chen, Ruhong Zhou or Youqing Shen.

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Competing interests

The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1

Schematic of the skin penetration mechanism of OP and its conjugate with insulin (OP-I).

Extended Data Fig. 2 Characterization of insulin conjugates OP-I and PEG-I.

a, RP-HPLC traces at an absorbance of 280 nm. b, MALDI-TOF MS spectra (OP-I was reduced to PDMA-I). c, GPC traces in H_2O. d, CD spectra in H_2O. e, BGLs of diabetic mice after subcutaneous (s.c.) injection of OP-I, PEG-I, or native insulin; insulin-equivalent dose, 5 U kg−1. Data are mean ± s.d.; n = 5 mice.

Source Data

Extended Data Fig. 3 SPR characterization of insulin receptor (IR) binding and activation of insulin and OP-I.

a, Schematic illustration of the experimental setup, where anti-His antibody was immobilized on the CM5 chip sensor surface, followed by the addition of Histag-ECD-IR/IGF1R, and then insulin/OP-I was introduced to study their interactions. Created in BioRender.com. b, SPR traces showing the binding of insulin and OP-I to ECD-IR; RU, resonance unit. c, Dissociation constant (KD), association rate constant (kon), dissociation rate constant (koff), and half-life (t1/2) of insulin or OP-I binding to ECD-IR, calculated from SPR binding curves in Extended Data Fig. 3b. d, SPR traces showing minimal binding of insulin and OP-I to ECD-IGF1R; RU, resonance unit. e, Representative binding modes from all-atom MD simulations of insulin and OP-I on the ECD-IR. f, PMF analysis of the binding affinities with two major ECD-IR binding sites. Umbrella sampling distance: 5 nm; window resolution: 0.1 nm; sampling time: 20 ns per window; restraint force constant: 1000 kJ mol−1 nm−2.

Source Data

Extended Data Fig. 4 Characterization of OP-I permeability in mouse skin.

a, Fluorescence distribution in the skin (left) and its s.c. fat (right, enlarged view) of the C57BL/6J mouse dorsal skin after topical application with OP-ICy5 for timed intervals (Cy5-equivalent dose, 0.2 ml of 10 μg ml−1 applied on 1.13 cm^2). BODIPY (green) was used to label the s.c. adipose tissue, and DAPI (blue) was used to label the nuclei. b, CLSM images of the slices of the C57BL/6J mouse dorsal skin after topical application with OP-ICy5 (Cy5-equivalent dose, 0.2 ml of 10 μg ml−1 applied on 1.13 cm^2) for 2 or 4 h. c,d, CLSM images (c) and line-scan analysis of FITC fluorescence intensity from the skin surface to the subcutis along randomly drawn lines (yellow arrows in c) (d) of vertically sectioned slices of treated mouse dorsal skin after 4 h topical administration of OP-IFITC. The images are representative of n = 3 independent experiments.

Source Data

Extended Data Fig. 5 Biological safety evaluation of OP-I for transdermal application.

a-c, Representative images of SEM (a), H&E staining (b), and immunohistological staining with TUNEL assay (green) and Hoechst (blue) (c) of the mouse dorsal skin after 4 h of topical treatment with OP-I, PEG-I, native insulin, or PBS (insulin-equivalent dose, 116 U kg−1; 0.2 ml of 0.5 mg ml−1; application area, 1.13 cm^2). d,e, Representative images of H&E staining (d) and immunohistological staining with TUNEL assay (green) and Hoechst (blue) (e) of the treated sites of the minipig abdominal skin after 4 h of topical treatment with OP-I, PEG-I, native insulin, or PBS (insulin-equivalent dose, 40 ml of 1 mg ml−1, 29 U kg−1; application area, 400 cm^2). The untreated skin was designated as the Control group. The images are representative of n = 3 independent experiments.

Extended Data Fig. 6 Co-localization of OP-I with SC lipids.

a, CLSM images of the adhesive tape peeled from the mouse dorsal skin after 4 h of topical application with OP-ICy5, PEG-ICy5, or insulinCy5 (Cy5-equivalent dose, 0.2 ml of 10 μg ml−1; application area, 1.13 cm^2). The images are representative of n = 3 independent experiments. b, CLSM images of the vertically sectioned slices of minipig abdominal skin after 4 h of topical application with OP-ICy5 (Cy5-equivalent dose, 10 ml of 10 μg ml−1; application area, 100 cm^2). The images are representative of n = 3 independent experiments. c, Enlarged view of the selected area in (b) outlining a corneocyte. d, Line-scan analysis of NBD-C6-HPC and Cy5 fluorescence along the yellow arrow in (c). Cy5 fluorescence is shown in red, and SC intercellular lipids stained with NBD-C6-HPC are in green.

Source Data

Extended Data Fig. 7 Modelling of the interactions of OP-I with SC lipids.

a, PMF analyses along the surface of the model SC lipids in different paths to estimate the energy barriers for diffusion. The energy barriers were 2.2 ± 0.3 kcal mol−1 for insulin, 0.9 ± 0.1 kcal mol−1 for OP, and 1.7 ± 0.2 kcal mol−1 for OP-I. Umbrella sampling distance: 2 nm; window resolution: 0.1 nm; sampling time: 35 ns per window; restraint force constant: 1000 kJ mol−1 nm−2. b, Representative local binding modes of insulin and OP on the rough model SC lipid surface at pH 5.5. c, Traces of insulin, OP, and OP-I on the model SC lipids at pH 5.5 in three 100-ns independent MD trajectories for each. See also Supplementary Video 3. Data are mean ± sem; n = 3 independent experiments.

Source Data

Extended Data Fig. 8 Cell-contact-mediated transfer of OP-I between HaCat cells.

a, CLSM imaging of the OP-ICy5 retention in cell membranes of HaCat cells cultured with OP-ICy5 for 6, 12, or 24 h (Cy5-equivalent dose, 1 μg ml−1); the cell membrane was stained with NBD-C6-HPC in green. The images are representative of n = 3 independent experiments. b, Enlarged view of the viable epidermis layer in Extended Data Fig. 6b. Minipig abdominal skin was treated with OP-ICy5 (Cy5-equivalent dose, 10 ml of 10 μg ml−1; application area, 100 cm^2) via topical application for 4 h. Cy5 fluorescence is shown in red, DAPI in blue, and NBD-C6-HPC fluorescence in green. The images are representative of n = 3 independent experiments. c, Line-scan analysis of NBD-C6-HPC and Cy5 fluorescence along the yellow arrow in (b). d, Flow cytometry analysis of the effect of cell density on OP-ICy5 transfer efficiency (Cy5-equivalent dose, 1 μg ml−1). The cell densities were 1.25 × 10^5 per well or 2.5 × 10^5 per well for both cell types (OP-ICy5-pretreated HaCat cells and untreated HaCatGFP cells), with untreated HaCat cells and HaCatGFP cells as controls. Data are mean ± s.d.; n = 3 independent experiments. Significance was determined using a two-tailed unpaired Student’s t-test.

Source Data

Supplementary information

Supplementary Information

Supplementary Figs 1–32 and Supplementary Tables 1 and 2.

Reporting Summary

Supplementary Video 1

MD trajectories comparing the binding of insulin and OP-I on the IR.

Supplementary Video 2

Binding processes of insulin, OP, or OP-I onto the SC lipids under the weakly acidic condition (pH 5.5). OP and OP-I adsorbed more rapidly onto the SC lipids than insulin.

Supplementary Video 3

MD trajectories demonstrating the stronger diffusivity of OP and OP-I on the SC lipids than insulin.

Supplementary Video 4

MD trajectories comparing the diffusion of OP-I on the SC membrane under weakly acidic (pH 5.5) and neutral conditions (pH 7.0).

Supplementary Video 5

Molecular dynamics trajectories involving multiple insulin, OP, and OP-I molecules at pH 6.0.

Supplementary Video 6

TIRFM imaging of OP-ICy3 movement on HaCat cell membranes. The cells were cultured with OP-ICy3 at a Cy3-equivalent dose of 1 μg ml−1 for 12 h, washed, and then imaged.

Supplementary Video 7

Direct transfer of OP-ICy5 (shown in red) between HaCat cells observed by CLSM. The cells were imaged in time-lapse-acquisition mode right after adding OP-ICy5. The green colour represented cell membranes stained with NBD-C6-HPC.

Peer Review File

Source Data Supplementary Figs 1–32

Source data

Source Data Fig. 1

Source Data Fig. 2

Source Data Fig. 3

Source Data Fig. 4

Source Data Fig. 5

Source Data Extended Data Fig. 2

Source Data Extended Data Fig. 3

Source Data Extended Data Fig. 4

Source Data Extended Data Fig. 6

Source Data Extended Data Fig. 7

Source Data Extended Data Fig. 8

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Wei, Q., He, Z., Li, Z. et al. A skin-permeable polymer for non-invasive transdermal insulin delivery. Nature 648, 459–467 (2025). https://doi.org/10.1038/s41586-025-09729-x

- Received: 29 May 2024

- Accepted: 09 October 2025

- Published: 19 November 2025

- Version of record: 19 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09729-x

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Amendments & Corrections

- Author Correction: A pangenome and pantranscriptome of hexaploid oat

- Author Correction: An asymmetric fission island driven by shell effects in light fragments

- Author Correction: Spatial fibroblast niches define Crohn’s fistulae

- Author Correction: Photocatalytic low-temperature defluorination of PFASs

- Author Correction: Matrix viscoelasticity promotes liver cancer progression in the pre-cirrhotic liver

- Author Correction: Nasal delivery of an IgM offers broad protection from SARS-CoV-2 variants

- Author Correction: Inhibiting membrane rupture with NINJ1 antibodies limits tissue injury

Author Correction Open access Published: 20 November 2025

Author Correction: A pangenome and pantranscriptome of hexaploid oat

Raz Avni,

Nadia Kamal,

Lidija Bitz,

Eric N. Jellen,

Wubishet A. Bekele,

Tefera T. Angessa,

Petri Auvinen,

Oliver Bitz,

Brian Boyle,

Francisco J. Canales,

Craig H. Carlson,

Brett Chapman,

Harmeet Singh Chawla,

Yutang Chen,

Dario Copetti,

Samara Correia de Lemos,

Viet Dang,

Steven R. Eichten,

Kathy Esvelt Klos,

Amit M. Fenn,

Anne Fiebig,

Yong-Bi Fu,

Heidrun Gundlach,

Rajeev Gupta,

Georg Haberer,

Tianhua He,

Matthias H. Herrmann,

Axel Himmelbach,

Catherine J. Howarth,

Haifei Hu,

Julio Isidro y Sánchez,

Asuka Itaya,

Jean-Luc Jannink,

Yong Jia,

Rajvinder Kaur,

Manuela Knauft,

Tim Langdon,

Thomas Lux,

Sofia Marmon,

Vanda Marosi,

Klaus F. X. Mayer,

Steve Michel,

Raja Sekhar Nandety,

Kirby T. Nilsen,

Edyta Paczos-Grzęda,

Asher Pasha,

Elena Prats,

Nicholas J. Provart,

Adriana Ravagnani,

Robert W. Reid,

Jessica A. Schlueter,

Alan H. Schulman,

Taner Z. Sen,

Jaswinder Singh,

Mehtab Singh,

Nick Sirijovski,

Nils Stein,

Bruno Studer,

Sirja Viitala,

Shauna Vronces,

Sean Walkowiak,

Penghao Wang,

Amanda J. Waters,

Charlene P. Wight,

Weikai Yan,

Eric Yao,

Xiao-Qi Zhang,

Gaofeng Zhou,

Zhou Zhou,

Nicholas A. Tinker,

Jason D. Fiedler,

Chengdao Li,

Peter J. Maughan,

Manuel Spannagl &

…

Martin Mascher

Nature volume 648, page E5 (2025)

The Original Article was published on 29 October 2025

Correction to: Nature https://doi.org/10.1038/s41586-025-09676-7 Published online 29 October 2025

In the version of the article initially published, the wrong caption was included for Extended Data Fig. 10. The correct caption is now available in the HTML and PDF versions of the article, and the original, incorrect caption is available for comparison in the Supplementary information accompanying this notice.

Supplementary information is available in the online version of this amendment.

Author information

Author notes

1. Nick Sirijovski

Present address: Global Oatly Science and Innovation Centre, Lund, Sweden

2. These authors contributed equally: Raz Avni, Nadia Kamal, Lidija Bitz, Eric N. Jellen, Wubishet A. Bekele

Authors and Affiliations

1. Leibniz Institute of Plant Genetics and Crop Plant Research (IPK) Gatersleben, Seeland, Germany

Raz Avni, Anne Fiebig, Axel Himmelbach, Manuela Knauft, Nils Stein & Martin Mascher

2. School of Life Sciences, Technical University of Munich, Freising, Germany

Nadia Kamal, Samara Correia de Lemos, Vanda Marosi & Klaus F. X. Mayer

3. Plant Genome and Systems Biology (PGSB), Helmholtz Center Munich–German Research Center for Environmental Health, Neuherberg, Germany

Nadia Kamal, Amit M. Fenn, Heidrun Gundlach, Georg Haberer, Thomas Lux, Vanda Marosi, Klaus F. X. Mayer & Manuel Spannagl

4. Natural Resources Institute Finland (LUKE), Helsinki, Finland

Lidija Bitz, Oliver Bitz, Alan H. Schulman & Sirja Viitala

5. Plant and Wildlife Sciences, Brigham Young University, Provo, UT, USA

Eric N. Jellen & Peter J. Maughan

6. Ottawa Research and Development Centre, Agriculture and Agri-Food Canada, Ottawa, Ontario, Canada

Wubishet A. Bekele, Asuka Itaya, Charlene P. Wight, Weikai Yan & Nicholas A. Tinker

7. Western Crop Genetics Alliance, Food Futures Institute and School of Agriculture, Murdoch University, Perth, Western Australia, Australia

Tefera T. Angessa, Brett Chapman, Viet Dang, Tianhua He, Haifei Hu, Yong Jia, Xiao-Qi Zhang, Gaofeng Zhou & Chengdao Li

8. Institute of Biotechnology, University of Helsinki, Helsinki, Finland

Petri Auvinen & Alan H. Schulman

9. Institut de Biologie Intégrative et des Systèmes, Université Laval, Québec City, Quebec, Canada

Brian Boyle

10. Institute for Sustainable Agriculture, CSIC, Córdoba, Spain

Francisco J. Canales & Elena Prats

11. Cereal Crops Improvement Research Unit, USDA-ARS, Edward T. Schafer Agricultural Research Center, Fargo, ND, USA

Craig H. Carlson, Rajeev Gupta, Raja Sekhar Nandety & Jason D. Fiedler

12. Department of Plant Science, University of Manitoba, Winnipeg, Manitoba, Canada

Harmeet Singh Chawla & Kirby T. Nilsen

13. Molecular Plant Breeding, Institute of Agricultural Sciences, ETH Zurich, Zurich, Switzerland

Yutang Chen & Bruno Studer

14. Arizona Genomics Institute, University of Arizona, Tucson, AZ, USA

Dario Copetti

15. Agriculture and Food Solutions, General Mills, Minneapolis, MN, USA

Steven R. Eichten

16. Small Grains and Potato Germplasm Research Unit, USDA-ARS, Aberdeen, ID, USA

Kathy Esvelt Klos

17. Plant Gene Resources of Canada, Saskatoon Research and Development Centre, Agriculture and Agri-Food Canada, Saskatoon, Saskatchewan, Canada

Yong-Bi Fu

18. Julius Kuehn Institute (JKI), Federal Research Centre for Cultivated Plants, Institute for Breeding Research on Agricultural Crops, Sanitz, Germany

Matthias H. Herrmann

19. IBERS Gogerddan, Aberystwyth University, Aberystwyth, UK

Catherine J. Howarth, Tim Langdon & Adriana Ravagnani

20. Centro de Biotecnología y Genómica de Plantas (CBGP), Universidad Politécnica de Madrid (UPM) & Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Madrid, Spain

Julio Isidro y Sánchez

21. R. W. Holley Center for Agriculture and Health, USDA-ARS, Ithaca, NY, USA

Jean-Luc Jannink

22. School of Integrative Plant Science, Cornell University, Ithaca, NY, USA

Jean-Luc Jannink

23. Department of Plant Science, McGill University, Sainte-Anne-de-Bellevue, Quebec, Canada

Rajvinder Kaur, Jaswinder Singh, Mehtab Singh & Zhou Zhou

24. ScanOats Industrial Research Center, Department of Chemistry, Division of Pure and Applied Biochemistry, Lund University, Lund, Sweden

Sofia Marmon & Nick Sirijovski

25. Crop Improvement and Genetics Research Unit, USDA-ARS, Albany, CA, USA

Steve Michel, Taner Z. Sen & Eric Yao

26. Agriculture and Agri-Food Canada, Brandon, Manitoba, Canada

Kirby T. Nilsen

27. Institute of Plant Genetics, Breeding and Biotechnology, University of Life Sciences in Lublin, Lublin, Poland

Edyta Paczos-Grzęda

28. Department of Cell and Systems Biology and Centre for the Analysis of Genome Evolution and Function, University of Toronto, Toronto, Ontario, Canada

Asher Pasha, Nicholas J. Provart & Shauna Vronces

29. Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, NC, USA

Robert W. Reid & Jessica A. Schlueter

30. Viikki Plant Science Centre, Helsinki, Finland

Alan H. Schulman

31. Department of Bioengineering, University of California, Berkeley, Berkeley, CA, USA

Taner Z. Sen

32. Institute of Agricultural and Nutritional Sciences, Martin Luther University Halle-Wittenberg, Halle, Germany

Nils Stein

33. Canadian Grain Commission, Winnipeg, Manitoba, Canada

Sean Walkowiak

34. School of Medical, Molecular and Forensic Sciences, Murdoch University, Perth, Western Australia, Australia

Penghao Wang

35. Research and Development Division, PepsiCo, Valhalla, NY, USA

Amanda J. Waters

36. Centre for Crop and Food Innovation, Food Futures Institute, Murdoch University, Perth, Western Australia, Australia

Chengdao Li, Manuel Spannagl & Martin Mascher

37. Department of Primary Industry and Regional Development, Government of Western Australia, Perth, Western Australia, Australia

Chengdao Li

38. College of Agronomy, Shandong Agricultural University, Tai’An, China

Chengdao Li

39. German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Leipzig, Germany

Martin Mascher

Corresponding authors

Correspondence to Nicholas A. Tinker, Jason D. Fiedler, Chengdao Li, Peter J. Maughan, Manuel Spannagl or Martin Mascher.

Supplementary information

Original, uncorrected Extended Data Fig. 10 caption

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Avni, R., Kamal, N., Bitz, L. et al. Author Correction: A pangenome and pantranscriptome of hexaploid oat. Nature 648, E5 (2025). https://doi.org/10.1038/s41586-025-09919-7

- Published: 20 November 2025

- Version of record: 20 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09919-7

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Author Correction Open access Published: 25 November 2025

Author Correction: An asymmetric fission island driven by shell effects in light fragments

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L. M. Fonseca,

D. Galaviz,

G. García-Jiménez,

I. Gasparic,

E. I. Geraci,

R. Gernhäuser,

B. Gnoffo,

K. Göbel,

A. Graña-González,

E. Haettner,

A.-L. Hartig,

M. Heil,

A. Heinz,

T. Hensel,

M. Holl,

C. Hornung,

A. Horvat,

A. Jedele,

D. Jelavic Malenica,

T. Jenegger,

L. Ji,

H. T. Johansson,

B. Jonson,

B. Jurado,

N. Kalantar-Nayestanaki,

E. Kazantseva,

A. Kelic-Heil,

O. A. Kiselev,

P. Klenze,

R. Knöbel,

D. Körper,

D. Kostyleva,

T. Kröll,

N. Kuzminchuk,

B. Laurent,

I. Lihtar,

Yu. A. Litvinov,

B. Löher,

N. S. Martorana,

B. Mauss,

S. Murillo Morales,

D. Mücher,

I. Mukha,

E. Nacher,

A. Obertelli,

E. V. Pagano,

V. Panin,

J. Park,

S. Paschalis,

M. Petri,

S. Pietri,

S. Pirrone,

G. Politi,

L. Ponnath,

A. Revel,

H.-B. Rhee,

J. L. Rodríguez-Sánchez,

L. Rose,

D. Rossi,

P. Roy,

P. Russotto,

C. Scheidenberger,

H. Scheit,

H. Simon,

S. Storck-Dutine,

A. Stott,

Y. L. Sun,

C. Sürder,

Y. K. Tanaka,

R. Taniuchi,

O. Tengblad,

I. Tisma,

H. T. Törnqvist,

M. Trimarchi,

S. Velardita,

J. Vesic,

B. Voss,

F. Wamers,

H. Weick,

F. Wienholtz,

J. Zhao &

…

M. Zhukov

Nature volume 648, page E6 (2025)

The Original Article was published on 30 April 2025

Correction to: Nature https://doi.org/10.1038/s41586-025-08882-7 Published online 30 April 2025

This article was originally published under standard Springer Nature license (© The Author(s), under exclusive licence to Springer Nature Limited). It is now available as an open-access paper under a Creative Commons Attribution 4.0 International license, © The Author(s). The error has been corrected in the HTML and PDF versions of the article.

Author information

Authors and Affiliations

1. CEA, DAM, DIF, Arpajon, France

P. Morfouace, J. Taieb, A. Chatillon, G. Blanchon, N. Dubray, N. Pillet, D. Regnier, P. Carpentier, B. Laurent & B. Mauss

2. Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, Bruyères-le-Châtel, France

P. Morfouace, J. Taieb, A. Chatillon, G. Blanchon, N. Dubray, N. Pillet, D. Regnier, B. Laurent & B. Mauss

3. Université Paris-Saclay, CNRS, IJC Lab, Orsay, France

L. Audouin

4. CEA, DES, IRESNE, DER, SPRC, Cadarache, Saint-Paul-Lès-Durance, France

R. N. Bernard

5. IGFAE, University of Santiago de Compostela, Santiago de Compostela, Spain

H. Alvarez-Pol, M. Feijoo, G. García-Jiménez, A. Graña-González & J. L. Rodríguez-Sánchez

6. GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany

F. Amjad, T. Aumann, K. Boretzky, C. Caesar, T. Dickel, L. M. Fonseca, E. Haettner, M. Heil, C. Hornung, A. Jedele, E. Kazantseva, A. Kelic-Heil, O. A. Kiselev, R. Knöbel, D. Körper, D. Kostyleva, N. Kuzminchuk, Yu. A. Litvinov, B. Löher, I. Mukha, V. Panin, S. Pietri, D. Rossi, P. Roy, C. Scheidenberger, H. Simon, Y. K. Tanaka, H. T. Törnqvist, B. Voss, F. Wamers, H. Weick & J. Zhao

7. CEA Saclay, IRFU/DPhN, Centre de Saclay, Gif-sur-Yvette, France

P. André, G. Authelet, A. Corsi & A. Revel

8. Technische Universität Darmstadt, Fachbereich Physik, Institut für Kernphysik, Darmstadt, Germany

L. Atar, T. Aumann, L. M. Fonseca, A.-L. Hartig, A. Horvat, A. Jedele, L. Ji, T. Kröll, A. Obertelli, L. Ponnath, H.-B. Rhee, D. Rossi, H. Scheit, S. Storck-Dutine, Y. L. Sun, C. Sürder, H. T. Törnqvist, S. Velardita & F. Wienholtz

9. Helmholtz Research Academy Hesse for FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany

T. Aumann, L. M. Fonseca, L. Ji, T. Kröll, Yu. A. Litvinov, A. Obertelli, L. Ponnath, C. Scheidenberger & C. Sürder

10. Instituto de Física Corpuscular, CSIC - Univ. of Valencia, Valencia, Spain

J. Benlliure, D. Cortina-Gil & E. Nacher

11. Goethe-Universität Frankfurt, Frankfurt am Main, Germany

L. Bott & K. Göbel

12. Jozef Stefan Institute, Ljubljana, Slovenia

T. Brecelj, A. Cvetinović, I. Tisma & J. Vesic

13. CINTECX, Universidade de Vigo, DSN, Department of Mechanical Engineering, Vigo, Spain

E. Casarejos

14. Department of Physics, Lund University, Lund, Sweden

J. Cederkäll

15. INFN Sezione di Catania, Catania, Italy

E. De Filippo, E. I. Geraci, B. Gnoffo, N. S. Martorana, S. Pirrone, G. Politi & M. Trimarchi

16. II. Physikalisches Institut, Justus-Liebig-Universität, Giessen, Germany

T. Dickel & C. Scheidenberger

17. Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil

L. M. Fonseca

18. Laboratório de Instrumentação e Física Experimental de Partículas, LIP, Lisbon, Portugal

D. Galaviz

19. Physics Department, Faculty of Sciences, University of Lisbon, Lisbon, Portugal

D. Galaviz

20. RBI Zagreb, Zagreb, Croatia

I. Gasparic, D. Jelavic Malenica & I. Lihtar

21. Dipartimento di Fisica e Astronomia ‘Ettore Majorana’, Università degli Studi di Catania, Catania, Italy

E. I. Geraci, B. Gnoffo & G. Politi

22. Technische Universität München, Garching, Germany

R. Gernhäuser, T. Jenegger & P. Klenze

23. Institutionen för Fysik, Chalmers Tekniska Högskola, Gothenburg, Sweden

A. Heinz, M. Holl, H. T. Johansson, B. Jonson & M. Zhukov

24. Helmholtz-Zentrum Dresden-Rossendorf, Institute of Radiation Physics, Dresden, Germany

T. Hensel

25. Université de Bordeaux, CNRS, LP2IB, Gradignan, France

B. Jurado

26. ESRIG, University of Groningen, Groningen, The Netherlands

N. Kalantar-Nayestanaki

27. School of Physics, Engineering and Technology, University of York, York, UK

S. Murillo Morales, S. Paschalis, M. Petri, L. Rose, A. Stott & R. Taniuchi

28. University of Guelph, Guelph, Ontario, Canada

D. Mücher

29. Institut für Kernphysik der Universität zu Köln, Cologne, Germany

D. Mücher

30. INFN Laboratori Nazionali del Sud, Catania, Italy

E. V. Pagano & P. Russotto

31. Institute for Basic Science, Center for Exotic Nuclear Studies, Daejeon, Republic of Korea

J. Park

32. CITENI, Campus Industrial de Ferrol, Universidade de Coruña, Ferrol, Spain

J. L. Rodríguez-Sánchez

33. Instituto de Estructura de la Materia, CSIC, Madrid, Spain

O. Tengblad

34. Università degli Studi di Messina, Messina, Italy

M. Trimarchi

Corresponding author

Correspondence to P. Morfouace.

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Morfouace, P., Taieb, J., Chatillon, A. et al. Author Correction: An asymmetric fission island driven by shell effects in light fragments. Nature 648, E6 (2025). https://doi.org/10.1038/s41586-025-09936-6

- Published: 25 November 2025

- Version of record: 25 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09936-6

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Author Correction Open access Published: 25 November 2025

Author Correction: Spatial fibroblast niches define Crohn’s fistulae

Colleen McGregor,

Xiao Qin,

Marta Jagielowicz,

Tarun Gupta,

Zinan Yin,

Verena Lentsch,

David Fawkner-Corbett,

Vy Wien Lai,

Paula Gomez Castro,

Esther Bridges,

Chloe Hyun-Jung Lee,

Huei-Wen Chuang,

Lei Deng,

Anna Aulicino,

Renuka Teague,

Sorayya Moradi,

Jun Sung Park,

Jeongmin Woo,

Kexin Xu,

Ruchi Tandon,

Nicole Cianci,

Jan Bornschein,

Ling-Pei Ho,

Paulina Siejka-Zielinska,

Zoe Christoforidou,

Sarah Hill,

Johannes Lehmann,

Rhea Kujawa,

Paola Vargas Gutierrez,

Carol Cheng,

Maria Greco,

Katherine Baker,

Mark Bignell,

Bruce George,

Eve Fryer,

Michael Vieth,

Agne Antanaviciute &

…

Alison Simmons

Nature volume 648, page E7 (2025)

The Original Article was published on 12 November 2025

Correction to: Nature https://doi.org/10.1038/s41586-025-09744-y Published online 12 November 2025

In the version of the article initially published, the “TWIST1” and “OSR2” labels in Fig. 2c were switched and have now been amended so that the columns labels (from left to right) read “Control, ORS2, TWIST1” in the HTML and PDF versions of the article.

Author information

Author notes

1. These authors contributed equally: Colleen McGregor, Xiao Qin

Authors and Affiliations

1. Medical Research Council Translational Immune Discovery Unit (MRC TIDU), Weatherall Institute of Molecular Medicine (WIMM), University of Oxford, Oxford, UK

Colleen McGregor, Xiao Qin, Marta Jagielowicz, Tarun Gupta, Zinan Yin, Verena Lentsch, David Fawkner-Corbett, Vy Wien Lai, Paula Gomez Castro, Esther Bridges, Chloe Hyun-Jung Lee, Huei-Wen Chuang, Lei Deng, Anna Aulicino, Jun Sung Park, Jeongmin Woo, Kexin Xu, Jan Bornschein, Ling-Pei Ho, Paulina Siejka-Zielinska, Zoe Christoforidou, Agne Antanaviciute & Alison Simmons

2. Translational Gastroenterology and Liver Unit, John Radcliffe Hospital, Oxford, UK

Colleen McGregor, Tarun Gupta, Jan Bornschein & Alison Simmons

3. Academic Paediatric Surgery Unit, Nuffield Department of Surgical Sciences, University of Oxford, Oxford, UK

David Fawkner-Corbett

4. MRC WIMM Centre for Computational Biology, WIMM, Oxford, UK

Vy Wien Lai, Chloe Hyun-Jung Lee, Jun Sung Park, Jeongmin Woo, Kexin Xu & Agne Antanaviciute

5. Oxford Centre for Histopathological Research, Oxford University Hospitals NHS Trust, Oxford, UK

Renuka Teague & Sorayya Moradi

6. Department of Cellular Pathology, Oxford University Hospitals NHS Trust, Oxford, UK

Ruchi Tandon & Eve Fryer

7. Center for Human Genetics, Nuffield Department of Medicine, University of Oxford, Oxford, UK

Nicole Cianci

8. Kennedy Institute of Rheumatology, University of Oxford, Oxford, UK

Sarah Hill & Johannes Lehmann

9. MRC WIMM Advanced Single Cell OMICS Facility, WIMM, Oxford, UK

Rhea Kujawa, Paola Vargas Gutierrez, Carol Cheng & Maria Greco

10. Department of Colorectal Surgery, Oxford University Hospitals NHS Trust, Oxford, UK

Katherine Baker, Mark Bignell & Bruce George

11. Institute of Pathology, Friedrich-Alexander University Erlangen-Nuremberg, Klinikum Bayreuth, Bayreuth, Germany

Michael Vieth

Corresponding authors

Correspondence to Agne Antanaviciute or Alison Simmons.

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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/.

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McGregor, C., Qin, X., Jagielowicz, M. et al. Author Correction: Spatial fibroblast niches define Crohn’s fistulae. Nature 648, E7 (2025). https://doi.org/10.1038/s41586-025-09956-2

- Published: 25 November 2025

- Version of record: 25 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09956-2

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Author Correction Published: 26 November 2025

Author Correction: Photocatalytic low-temperature defluorination of PFASs

Hao Zhang,

Jin-Xiang Chen,

Jian-Ping Qu &

…

Yan-Biao Kang

Nature volume 648, page E8 (2025)

The Original Article was published on 20 November 2024

Correction to: Nature https://doi.org/10.1038/s41586-024-08179-1 Published online 20 November 2024

The original article contained several errors and inconsistencies which were spotted by a reader. The article and its Supplementary Information have now been amended to correct these errors and to improve the reproducibility of the work. In Fig. 1a and the associated text, “*Eox” should have read “excited-state oxidation potential”. The redox potentials for Cz, CBZ4, CBZ5, KQGZ anions were incorrect due to insufficient deprotonation during the original photophysical measurements. These measurements have been repeated, and the correct redox potentials are as follows: Cz anion (−2.83 V vs. SCE), CBZ4 anion (−2.54 V vs. SCE), CBZ5 anion (−2.69 V vs. SCE), and KQGZ anion (−2.45 V vs. SCE). Statements referring to CBZ4 and its anion as being super-photoreductants in the “Defluorination of PTFE” section have been removed to reflect this change. In Fig. 2a, “Cs_2CO_3 (2.0 equiv.)” has been removed for consistency with the figure legend. The text and figure have now been amended in the HTML and PDF versions of the article. Updates to the Supporting Information include corrected characterizations of the photocatalysts, as well as an elaboration of the key factors essential for reproducibility of the reaction.

The figures, text and Supplementary Information have been amended in the HTML and PDF versions of the article. These corrections do not affect the reported reactivity of the photocatalysts or the overall conclusions of the article. We thank the reader for bringing these errors to our attention.

Author information

Authors and Affiliations

1. Hefei National Research Center for Physical Sciences at the Microscale, Department of Chemistry, University of Science and Technology of China, Hefei, China

Hao Zhang, Jin-Xiang Chen & Yan-Biao Kang

2. Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Nanjing Tech University, Nanjing, China

Jian-Ping Qu

Corresponding authors

Correspondence to Jian-Ping Qu or Yan-Biao Kang.

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Zhang, H., Chen, JX., Qu, JP. et al. Author Correction: Photocatalytic low-temperature defluorination of PFASs. Nature 648, E8 (2025). https://doi.org/10.1038/s41586-025-09871-6

- Published: 26 November 2025

- Version of record: 26 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09871-6

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Author Correction Open access Published: 27 November 2025

Author Correction: Matrix viscoelasticity promotes liver cancer progression in the pre-cirrhotic liver

Weiguo Fan,

Kolade Adebowale,

Lóránd Váncza,

Yuan Li,

Md Foysal Rabbi,

Koshi Kunimoto,

Dongning Chen,

Gergely Mozes,

David Kung-Chun Chiu,

Yisi Li,

Junyan Tao,

Yi Wei,

Nia Adeniji,

Ryan L. Brunsing,

Renumathy Dhanasekaran,

Aatur Singhi,

David Geller,

Su Hao Lo,

Louis Hodgson,

Edgar G. Engleman,

Gregory W. Charville,

Vivek Charu,

Satdarshan P. Monga,

Taeyoon Kim,

Rebecca G. Wells,

Ovijit Chaudhuri &

…

Natalie J. Török

Nature volume 648, page E9 (2025)

The Original Article was published on 31 January 2024

Correction to: Nature https://doi.org/10.1038/s41586-023-06991-9 Published online 31 January 2024

In the version of this article initially published, due to mistakes when outputting final source data, the plot shown in Fig. 1n and Fig. 1n source data were incorrect. The conclusions are unaffected by the change. The source data and figure panel are updated in the HTML and PDF versions of the article.

Author information

Author notes

1. These authors contributed equally: Kolade Adebowale, Lóránd Váncza

Authors and Affiliations

1. Gastroenterology and Hepatology, Stanford University, Stanford, CA, USA

Weiguo Fan, Lóránd Váncza, Yuan Li, Koshi Kunimoto, Dongning Chen, Gergely Mozes, Yi Wei, Nia Adeniji, Renumathy Dhanasekaran & Natalie J. Török

2. VA, Palo Alto, CA, USA

Weiguo Fan, Lóránd Váncza, Yuan Li, Koshi Kunimoto, Dongning Chen, Gergely Mozes, Yi Wei, Nia Adeniji, Renumathy Dhanasekaran & Natalie J. Török

3. Department of Chemical Engineering, Stanford University, Stanford, CA, USA

Kolade Adebowale

4. Chemistry, Engineering and Medicine for Human Health (ChEM-H), Stanford University, Stanford, CA, USA

Kolade Adebowale & Ovijit Chaudhuri

5. Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA

Md Foysal Rabbi & Taeyoon Kim

6. Department of Pathology, Stanford University, Stanford, CA, USA

David Kung-Chun Chiu, Edgar G. Engleman, Gregory W. Charville & Vivek Charu

7. Division of Immunology, Stanford University, Stanford, CA, USA

David Kung-Chun Chiu & Edgar G. Engleman

8. Department of Automation, Tsinghua University, Beijing, China

Yisi Li

9. Pittsburgh Liver Research Center, University of Pittsburgh and University of Pittsburgh Medical Center, Pittsburgh, PA, USA

Junyan Tao, Aatur Singhi, David Geller & Satdarshan P. Monga

10. Department of Radiology, Stanford University, Stanford, CA, USA

Ryan L. Brunsing

11. Department of Biochemistry and Molecular Medicine, University of California at Davis, Sacramento, CA, USA

Su Hao Lo

12. Department of Molecular Pharmacology, Albert Einstein College of Medicine, New York, NY, USA

Louis Hodgson

13. Quantitative Sciences Unit, Department of Medicine, Stanford University School of Medicine, Stanford, CA, USA

Vivek Charu

14. Faculty of Science and Technology, Keio University, Yokohama, Japan

Taeyoon Kim

15. Departments of Medicine and Bioengineering, University of Pennsylvania, Philadelphia, PA, USA

Rebecca G. Wells

16. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

Ovijit Chaudhuri

Corresponding author

Correspondence to Natalie J. Török.

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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/.

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Fan, W., Adebowale, K., Váncza, L. et al. Author Correction: Matrix viscoelasticity promotes liver cancer progression in the pre-cirrhotic liver. Nature 648, E9 (2025). https://doi.org/10.1038/s41586-025-09947-3

- Published: 27 November 2025

- Version of record: 27 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09947-3

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Author Correction Published: 27 November 2025

Author Correction: Nasal delivery of an IgM offers broad protection from SARS-CoV-2 variants

Zhiqiang Ku,

Xuping Xie,

Paul R. Hinton,

Xinli Liu,

Xiaohua Ye,

Antonio E. Muruato,

Dean C. Ng,

Sujit Biswas,

Jing Zou,

Yang Liu,

Deepal Pandya,

Vineet D. Menachery,

Sachi Rahman,

Yu-An Cao,

Hui Deng,

Wei Xiong,

Kevin B. Carlin,

Junquan Liu,

Hang Su,

Elizabeth J. Haanes,

Bruce A. Keyt,

Ningyan Zhang,

Stephen F. Carroll,

Pei-Yong Shi &

…

Zhiqiang An

Nature volume 648, page E10 (2025)

The Original Article was published on 03 June 2021

Correction to: Nature https://doi.org/10.1038/s41586-021-03673-2 Published online 3 June 2021

In the version of the article initially published, in Extended Data Fig. 5b, the “K444R” image was a duplicate of the “K444R+E484A” image due to an error in figure assembly. Extended Data Fig. 5 has now been updated with the correct “K444R” image in the HTML and PDF versions of the article.

Author information

Author notes

1. These authors contributed equally: Zhiqiang Ku, Xuping Xie, Paul R. Hinton, Xinli Liu

Authors and Affiliations

1. Texas Therapeutics Institute, Brown Foundation Institute of Molecular Medicine, The University of Texas Health Science Center at Houston, Houston, TX, USA

Zhiqiang Ku, Xiaohua Ye, Hui Deng, Wei Xiong, Junquan Liu, Hang Su, Ningyan Zhang & Zhiqiang An

2. Department of Biochemistry and Molecular Biology, University of Texas Medical Branch, Galveston, TX, USA

Xuping Xie, Jing Zou, Yang Liu & Pei-Yong Shi

3. IGM Biosciences, Mountain View, CA, USA

Paul R. Hinton, Dean C. Ng, Deepal Pandya, Sachi Rahman, Yu-An Cao, Kevin B. Carlin, Elizabeth J. Haanes, Bruce A. Keyt & Stephen F. Carroll

4. Department of Pharmacological and Pharmaceutical Sciences, College of Pharmacy, University of Houston, Houston, TX, USA

Xinli Liu & Sujit Biswas

5. Institute for Human Infection and Immunity, University of Texas Medical Branch, Galveston, TX, USA

Antonio E. Muruato & Pei-Yong Shi

6. Department of Microbiology and Immunology, University of Texas Medical Branch, Galveston, TX, USA

Antonio E. Muruato & Vineet D. Menachery

7. Sealy Institute for Vaccine Sciences, University of Texas Medical Branch, Galveston, TX, USA

Pei-Yong Shi

8. Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, TX, USA

Pei-Yong Shi

9. Department of Pharmacology and Toxicology, University of Texas Medical Branch, Galveston, TX, USA

Pei-Yong Shi

Corresponding authors

Correspondence to Bruce A. Keyt, Ningyan Zhang, Stephen F. Carroll, Pei-Yong Shi or Zhiqiang An.

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Ku, Z., Xie, X., Hinton, P.R. et al. Author Correction: Nasal delivery of an IgM offers broad protection from SARS-CoV-2 variants. Nature 648, E10 (2025). https://doi.org/10.1038/s41586-025-09953-5

- Published: 27 November 2025

- Version of record: 27 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09953-5

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Author Correction Open access Published: 27 November 2025

Author Correction: Inhibiting membrane rupture with NINJ1 antibodies limits tissue injury

Nobuhiko Kayagaki,

Irma B. Stowe,

Kamela Alegre,

Ishan Deshpande,

Shuang Wu,

Zhonghua Lin,

Opher S. Kornfeld,

Bettina L. Lee,

Juan Zhang,

John Liu,

Eric Suto,

Wyne P. Lee,

Kellen Schneider,

WeiYu Lin,

Dhaya Seshasayee,

Tushar Bhangale,

Cecile Chalouni,

Matthew C. Johnson,

Prajakta Joshi,

Jan Mossemann,

Sarah Zhao,

Danish Ali,

Neil M. Goldenberg,

Blayne A. Sayed,

Benjamin E. Steinberg,

Kim Newton,

Joshua D. Webster,

Ryan L. Kelly &

…

Vishva M. Dixit

Nature volume 648, page E11 (2025)

The Original Article was published on 17 May 2023

Correction to: Nature https://doi.org/10.1038/s41586-023-06191-5 Published online 17 May 2023

In the version of this article initially published, due to a figure preparation error, in Fig. 3a, bottom row, the fourth image on the right was an inadvertent duplicate of the second image from left in the bottom row. The figure has been amended in the HTML and PDF versions of the article.

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Author notes

1. These authors contributed equally: Nobuhiko Kayagaki, Irma B. Stowe

Authors and Affiliations

1. Department of Physiological Chemistry, Genentech, South San Francisco, CA, USA

Nobuhiko Kayagaki, Irma B. Stowe, Kamela Alegre, Ishan Deshpande, Opher S. Kornfeld, Bettina L. Lee, Kim Newton & Vishva M. Dixit

2. Department of Structural Biology, Genentech, South San Francisco, CA, USA

Ishan Deshpande & Matthew C. Johnson

3. Department of Antibody Engineering, Genentech, South San Francisco, CA, USA

Shuang Wu, Zhonghua Lin, Kellen Schneider, WeiYu Lin, Dhaya Seshasayee & Ryan L. Kelly

4. Department of Translational Immunology, Genentech, South San Francisco, CA, USA

Juan Zhang, John Liu, Eric Suto & Wyne P. Lee

5. Department of Human Genetics, Genentech, South San Francisco, CA, USA

Tushar Bhangale

6. Department of Pathology, Genentech, South San Francisco, CA, USA

Cecile Chalouni & Joshua D. Webster

7. Department of Biomolecular Resources, Genentech, South San Francisco, CA, USA

Prajakta Joshi

8. Program in Cell Biology, Hospital for Sick Children, Toronto, Ontario, Canada

Jan Mossemann, Danish Ali, Neil M. Goldenberg & Blayne A. Sayed

9. Program in Neuroscience and Mental Health, Hospital for Sick Children, Toronto, Ontario, Canada

Sarah Zhao & Benjamin E. Steinberg

10. Department of Anesthesia and Pain Medicine, Hospital for Sick Children, Toronto, Ontario, Canada

Neil M. Goldenberg & Benjamin E. Steinberg

11. Division of General Surgery, Hospital for Sick Children, Toronto, Ontario, Canada

Blayne A. Sayed

Corresponding authors

Correspondence to Nobuhiko Kayagaki or Vishva M. Dixit.

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Kayagaki, N., Stowe, I.B., Alegre, K. et al. Author Correction: Inhibiting membrane rupture with NINJ1 antibodies limits tissue injury. Nature 648, E11 (2025). https://doi.org/10.1038/s41586-025-09955-3

- Published: 27 November 2025

- Version of record: 27 November 2025

- Issue date: 11 December 2025

- DOI: https://doi.org/10.1038/s41586-025-09955-3

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Pancreatic cancer

Research offers glimmers of hope for a deadly disease.

Published 10 December 2025

Illustration: Daniel Stolle

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This Nature Outlook is editorially independent, produced with financial support from Ipsen and Champalimaud Foundation. About this content.

For decades, pancreatic cancer has been synonymous with a bleak outlook. It is the third-leading cause of cancer-related deaths, despite being only the tenth most commonly diagnosed cancer in the United States. The more advanced the disease is at the point of diagnosis, the more grim are the statistics.

The five-year-survival rate for all stages and types of pancreatic cancer is 13%, up from 7% a decade ago. Although that increase might seem small, any progress against this challenging disease should be celebrated.

Researchers are engaged in myriad efforts to tackle pancreatic cancer and further positive change could be on the horizon.

Some of these efforts are focused on detecting the cancer before it has spread, when it might be easier to treat. These include simple blood tests that can spot proteins that are characteristic of the disease, as well as non-invasive breath tests. Other teams are trying to expand the pool of available therapies to include personalized vaccines that unleash the immune system on the proteins that drive a person’s cancer.

Scientists are also working to uncover hidden truths about how pancreatic cancer stakes a claim on the body. In the past decade or so, for instance, researchers have begun to learn how pancreatic tumours harness the nervous system to thrive in low-oxygen conditions and suppress the immune system. As researchers’ understanding improves, these survival strategies could be leveraged to design therapies.

Underlying all these endeavours are improved ways to model the disease. Pancreatic organoids — miniature versions of the organ that are cultured in a dish — are being used to explore what makes pancreatic cancer so deadly. These models can also be engineered to develop tumours that precisely match those found in individuals and that can then be used to test treatments.

We are pleased to acknowledge the financial support of Ipsen Pharma US and Botton-Champalimaud Pancreatic Cancer Centre in producing this Outlook. As always, Nature retains sole responsibility for all editorial content.

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The Champalimaud Foundation (CF), created in 2005, is a private, non-profit institution internationally recognized for its pioneering work in science and medicine. Its mission is to bridge the gap between basic research and clinical practice, with a strong focus on neuroscience and cancer. By applying a translational approach, CF transforms cutting-edge scientific discoveries into real-world solutions, aiming to improve health outcomes and quality of life worldwide.

At the heart of its activities is the Champalimaud Centre for the Unknown (CCU), a unique campus that integrates research, innovation, and clinical care. Within the CCU, the Foundation hosts the Champalimaud Clinical Centre (CCC), the Botton-Champalimaud Pancreatic Cancer Centre (BCPCC), Champalimaud Research (CR), and the Centre for Restorative Neurotechnology (CRN). This structure fosters collaboration between scientists, physicians, and technologists to accelerate discoveries and deliver advanced care.

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Amendments & Corrections

Author Correction: A pangenome and pantranscriptome of hexaploid oat

Author Correction: An asymmetric fission island driven by shell effects in light fragments

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Author Correction: Photocatalytic low-temperature defluorination of PFASs

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