Planet Neuroscientists

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CCN for social good: 2025 satellite event
We live in times when public trust in science is under threat, misinformation is rife, AI ethics are of increasing concern and climate change is increasingly affecting communities worldwide. How do computational social neuroscientists see ourselves and our role in this world, and can we use our skills for social good? This session will exploreContinue reading "CCN for social good: 2025 satellite event"
in CoCoSys lab on 2025-05-05 07:12:36 UTC.
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Thinking about thinking: AI offers theoretical insights into human memory
We need a new conceptual framework for understanding cognitive functions—particularly how globally distributed brain states are formed and maintained for hours.
in The Transmitter on 2025-05-05 04:00:16 UTC.
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Precision in Practice: Personalised Medicine and the Female Face of Multiple Sclerosis
A girl on ice: tracing shadows to multiple sclerosis In the biting cold of a Dutch winter in 1385, the frozen canals of Schiedam...
in Women in Neuroscience UK on 2025-05-04 17:00:18 UTC.
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Weekend reads: Journal halts submissions, citing NIH cuts; rejected paper published by ‘mistake’; feds cancel grant amid misconduct allegations

Dear RW readers, can you spare $25?

The week at Retraction Watch featured:
- University of Toronto should take action on flawed breast screening study, says longtime critic
- Experiment using AI-generated posts on Reddit draws fire for ethics concerns
- AI-Reddit study leader gets warning as ethics committee moves to ‘stricter review process’
- Why has it taken more than a year to correct a COVID-19 paper?
- A Ph.D. in paper mills?
- Former cancer researcher who sued university for discrimination hits 35 retractions
Our list of retracted or withdrawn COVID-19 papers is up past 500. There are more than 58,000 retractions in The Retraction Watch Database — which is now part of Crossref. The Retraction Watch Hijacked Journal Checker now contains more than 300 titles. And have you seen our leaderboard of authors with the most retractions lately — or our list of top 10 most highly cited retracted papers? What about The Retraction Watch Mass Resignations List — or our list of nearly 100 papers with evidence they were written by ChatGPT?

Here’s what was happening elsewhere (some of these items may be paywalled, metered access, or require free registration to read):
- “Citing N.I.H. Cuts, a Top Science Journal Stops Accepting Submissions.”
- Journal publishes out-of-scope paper by “mistake.”
- “Feds cancel grant, call out U of M amid new case of professor misconduct allegations.”
- Why “misuse of generative AI is worse than plagiarism.”
- “Research Integrity Is A Clown Car.”
- “The politicization of retraction risks harm to science” and could lead to “under-exploration” of issues.
- “Managing Multi-Institutional Jurisdiction in Cases of Research Misconduct.”
- “Recent Drop in Life Science Preprint Posting Due to Capacity Problems at Research Square.”
- “Scientific Integrity Under Threat: The Role of the IDSA, PIDS, and SHEA Journals in an Evolving Political Landscape.”
- “Rethinking the production and publication of machine-readable expressions of research findings.”
- “How to protect research data: Contingency plans are needed to shore up important information.”
- “China’s new journal publishing benchmarks to boost scientific soft power.”
- US NSF director resigns “amid grant terminations, job cuts, and controversy.”
- “Health journals sprint ahead in the race to attract female authors.”
- “As the DOJ questions journals, how can we reasonably promote ‘competing viewpoints’ in science?”
- University “accused of mishandling plagiarism allegations against influential professor.”
- Researchers look at “grammatical constructions used to represent agency and assign responsibility” in over 3,000 retraction notices.
- Case-based learning is more effective at teaching residents about research misconduct than lectures, study finds.
- “The Impact of Inflation on APC Costs.”
- “10 reasons why the science research journal has passed its sell-by date.”
- “Understanding ORCID adoption among academic researchers.”
- Why “using AI in scientific peer review is fraught with danger.”
- “Widespread lack of article accessibility policies among ecology and evolution journals.”
- “I Submitted A Fake Fart Paper.”
Upcoming talks
- Managing editor Kate Travis moderates “Behind the Music: A Candid Conversation with Journal Editors and Publishers,” at the 21st Annual Meeting of the International Society for Medical Publication Professionals (May 13, Washington, D.C. )
Like Retraction Watch? You can make a tax-deductible contribution to support our work, follow us on X or Bluesky, like us on Facebook, follow us on LinkedIn, add us to your RSS reader, or subscribe to our daily digest. If you find a retraction that’s not in our database, you can let us know here. For comments or feedback, email us at team@retractionwatch.com.

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in Retraction watch on 2025-05-03 10:00:00 UTC.
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Self-Driving Cars Have New Rules in the U.S. Here’s Why That Matters

New rules that trim crash reporting requirements and widen testing access for U.S. robotaxis are hailed as an innovation edge and criticized for eroding safety oversight

in Scientific American on 2025-05-02 21:45:00 UTC.
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Former cancer researcher who sued university for discrimination hits 35 retractions

A cancer researcher who was once the subject of a misconduct investigation at an Illinois university more than 10 years ago has made his debut on the Retraction Watch Leaderboard with 35 retractions.

Last month Oncogene, a Springer Nature title, retracted 15 articles by Jasti Rao, formerly of the University of Illinois College of Medicine at Peoria. A 2014 university investigation into his lab’s publications found manipulation and rotation of images that “‘show a disturbing pattern’ indicative that Rao acted intentionally or recklessly,” we previously reported. Rao sued the university for wrongful termination but lost.

More than 100 of Rao’s papers have comments on PubPeer, most originating from a user called Lotus azoricus. We now know that pseudonym belongs to sleuth Elisabeth Bik.

“I had learned from several Retraction Watch articles that Dr. Rao had previously sued the University of Illinois. It seemed wise to file my complaints anonymously at the time, to avoid being sued by him as well,” Bik told us. “I have a couple more years of experience, so I now feel confident on stating publicly that the PubPeer comments by Lotus azoricus were mine.”

Bik had reported the Oncogene papers to the journal in 2019. In February 2024, Bik sought an update and Springer Nature told her the investigation was still ongoing.

A spokesperson for Springer Nature acknowledged that Bik was the first to alert the journal to concerns with the Oncogene papers. Tim Kersjes, head of research integrity, resolutions at Springer Nature, said in a statement:

Whilst we endeavour to complete our investigations as swiftly and efficiently as possible, we do so with care to ensure the integrity of the scientific record. However, we appreciate that substantial delays to investigations can be frustrating, and we apologise for the length of time taken in these cases. We take our responsibility to maintain the scientific record extremely seriously and the retraction of these papers demonstrates our commitment to this.

In a followup statement, a spokesperson added:

[W]e apologise for the length of time taken in these cases. This was in part owing to the age of the articles and the difficulty we had in trying to contact the authors, as stated in the text of the retraction notices.

Rao was once a highly regarded cancer specialist, earning a salary of $700,000 a year. When the university kicked off its investigation in 2013, it focused on concerns about misconduct related to plagiarism and data manipulations — and on allegations of ethics violations related to allegations of kickbacks and fiscal improprieties. Rao had run up tens of thousands of dollars in gambling debts, much of it accrued on university time. Court documents from 2017 alleged that Rao had:

demanded and accepted cash payments from at least one subordinate to pay off alleged gambling debts and concealed the extent of errors in papers published by his lab and then directed subordinates to delete documents evidencing the scope of the errors.

With Rao’s publications, the easily identifiable problems include image duplications and “problems suggestive of photoshopping,” Bik said. But “ it is the sheer number of problematic papers that stand out,” she said. A PubMed search for Rao’s name calls up about 450 papers, and Bik has found issues in over 100 of them. “That means that over one in 5 of his papers have clearly visible problems,” she said. “That is a very high and concerning ratio.”

Bik reported 104 of Rao’s papers to the university in 2019. An official at the University of Illinois College of Medicine told her in 2022 that they were still looking into them. We’ve reached out to the university to ask whether it is still investigating Rao’s published papers, or whether they’ve reported the issues to the journals, but have not heard back.

Like Retraction Watch? You can make a tax-deductible contribution to support our work, follow us on X or Bluesky, like us on Facebook, follow us on LinkedIn, add us to your RSS reader, or subscribe to our daily digest. If you find a retraction that’s not in our database, you can let us know here. For comments or feedback, email us at team@retractionwatch.com.

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in Retraction watch on 2025-05-02 20:21:39 UTC.
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A Life on the Progressive Side: A Review
For MS Awareness Week, Ciara Lee reviews Episode 1 of A Life on the Progressive Side, where Ashleigh Talbot and guest Fiona McMillan share powerful insights into life with primary progressive MS. From delayed diagnoses to disability, music, and mental health - this episode is raw, real, and deeply relatable.
in Women in Neuroscience UK on 2025-05-02 17:00:23 UTC.
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Under Trump, National Science Foundation Cuts Off All Funding to Scientists

National Science Foundation staff were told to freeze outgoing funding days after NSF leadership introduced a new policy that requires that grants be screened for “alignment with agency priorities”

in Scientific American on 2025-05-02 17:00:00 UTC.
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A man let snakes bite him 202 times. His blood helped create a new antivenom
A new antivenom relies on antibodies from the blood of Tim Friede, who immunized himself against snakebites by injecting increasing doses of venom into his body.
in Science News: Health & Medicine on 2025-05-02 15:00:00 UTC.
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Solar Geoengineering Is Possible with Existing Aircraft, Study Finds

Scientists previously thought that solar geoengineering—or releasing particles into the atmosphere to reflect solar rays—would require specialized high-altitude vehicles

in Scientific American on 2025-05-02 14:30:00 UTC.
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Playing this Minecraft game hints at how we learn in real life
A tailor-made version of Minecraft let researchers look at the success of learning individually or taking cues from others while foraging for fruit.
in Science News: Psychology on 2025-05-02 13:00:00 UTC.
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Could the Sun Unleash Dangerous Superflares?

Stars like the sun might erupt with extreme explosions about once per century

in Scientific American on 2025-05-02 10:45:00 UTC.
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The Threatened Fungi on the IUCN Red List Are Important to our Ecology

As conservation targets, fungi aren’t as appealing as giant pandas. But these scientists explain that the health of Earth’s fungal species is critically important.

in Scientific American on 2025-05-02 10:00:00 UTC.
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Schneider Shorts 2.05.2025 – A gross negligence is not detectable
Schneider Shorts 2.05.2025 - German ex-university president once again innocent, US ex-university president heads a big company, a Noble Genius awarded, with talking mice, papermills reaching Science, concerns expressed for male bigwigs, and finally, how to escape heart attack while drunk.
in For Better Science on 2025-05-02 05:00:00 UTC.
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Connectomics 2.0: Simulating the brain
With a complete fly connectome in hand, researchers are taking the next step to model how brain circuits fuel function.
in The Transmitter on 2025-05-02 04:00:43 UTC.
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A Ph.D. in paper mills?

Bank Phrom/Unsplash

A university and a publisher are teaming up to combat paper mills in a unique way: By enlisting a Ph.D. candidate.

In April, the Centre for Science and Technology Studies (CWTS) at Leiden University in the Netherlands announced it would be collaborating with Wiley to establish a four-year research position focused on paper mills.

“Of course one Ph.D. will not fix the problem,” said Cyril Labbé of Grenoble Alpes University in France, whose lab hosted a Ph.D. student in 2014 to detect computer-generated manuscripts. “But going this way is far more constructive than resorting to empty rhetoric and wooden language, as some publishers tend to do.”

The selected candidate will go beyond “diagnosing symptoms” of a paper mill, said Wolfgang Kaltenbrunner, a senior researcher at CWTS and deputy director of the program, and will focus on gaining a more complete conceptual understanding of paper mills. Kaltenbrunner expects this will lead to recommendations for actors in the system, publishers, and policymakers.

“There will certainly be some kind of practical relevance of the research,” he said.

The researcher will focus on how paper mills operate, including the services they offer. These companies produce fake research papers, offer authorship of already-accepted manuscripts, manipulate the peer review process, or some combination.

The candidate will also look into how these business models are enabled by the research culture of different countries, including academic community dynamics. “It’s very much about the embedding of paper mills into different research cultures, which, in turn, has institutional components and community dynamics,” Kaltenbrunner told us.

Mike Streeter, Wiley’s Director of Research Integrity Strategy & Policy, told us Wiley will not be involved in selecting the candidate, supervising the student, or determining the outcome of the project. However, they worked with Kaltenbrunner and other supervising CWTS researchers to “set up the necessary parameters of the project and focus the project.”

Since acquiring Hindawi in 2021, Wiley has shuttered some of its journals and retracted thousands of papers for paper mill activity. Last year, up to one in seven submissions for hundreds of Wiley journals were flagged by the company’s Papermill Detection tool.

Streeter told us the project was “not explicitly” inspired by issues with Hindawi, but part of their larger effort to roll out new screening tools.

The research position in Labbe’s lab, then at Joseph Fourier University in Grenoble, was inspired by a 2014 episode in which 16 fake conference proceedings were discovered in Springer Nature publications. The publisher then funded a Ph.D, student, Tien Nguyen, who looked into detecting SCIgen, a program that generates computer science papers.

Labbé told us the program in his lab differed from CWTS’ in that the solution of automatic detection of SCIgen was “quite clear” even before research started. Nguyen helped to create an open-source software program, SciDetect.

At this stage, the paper mill program coordinators — who, besides Kaltenbrunner, includes Stephen Pinfield at the University of Sheffield and Ludo Waltman, also of Leiden — aren’t sure what methods the researcher will use, and what the expected outputs of the project would be. They are looking for someone with a background in quantitative analysis of publication data and qualitative methods regarding research culture.

Kaltenbrunner emphasized that, at the end of the program, the researcher wouldn’t be releasing a list of “offenders,” whether that be paper mills themselves or individuals involved. “We feel it wouldn’t be particularly effective, since the landscape of paper mills is, of course, constantly in flux,” he said.

The program will have access to confidential publication and submission data behind the scenes at Wiley, Streeter said, but won’t exclusively focus on Wiley publications. The candidate will likely use tools like the Retraction Watch Database and the Problematic Paper Screener as data tools for publications outside of Wiley, he said.

Kaltenbrunner said the publisher’s involvement “raises the possibility that we also touch on issues that will be uncomfortable for Wiley.” Although he said Wiley has the opportunity to comment on drafts coming out of this project, the publisher doesn’t have veto rights, so can’t prevent things from being published that may put them in an unflattering light, Kaltenbrunner said.

Because the program won’t call out particular paper mills or individuals, Kaltenbrunner said he doesn’t expect the Ph.D. candidate to run into any particular legal or safety issues. But in the case the candidate runs into any particularly bad apples, he said the university is prepared to offer them protection.

Updated on May 2, 2025, to correct Labbé’s affiliation.

Like Retraction Watch? You can make a tax-deductible contribution to support our work, follow us on X or Bluesky, like us on Facebook, follow us on LinkedIn, add us to your RSS reader, or subscribe to our daily digest. If you find a retraction that’s not in our database, you can let us know here. For comments or feedback, email us at team@retractionwatch.com.

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in Retraction watch on 2025-05-01 20:31:40 UTC.
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RFK, Jr., Funds Universal Vaccines for Flu and COVID—Here’s What That Means

Trump’s HHS and NIH are planning to invest $500 million in a killed-whole-virus approach to universal vaccines, including such vaccines for flu and COVID. Here’s why that’s challenging

in Scientific American on 2025-05-01 19:00:00 UTC.
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The Scary Implications of U.S. Government Attacks on Medical Journals

A Trump-aligned prosecutor’s attack on medical journals is a threat to your health care—and the medical establishment should not comply

in Scientific American on 2025-05-01 19:00:00 UTC.
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If a Chatbot Tells You It Is Conscious, Should You Believe It?

AI systems could show signs of consciousness. We need to develop better tests to show whether they are actually aware

in Scientific American on 2025-05-01 17:00:00 UTC.
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Trump Quietly Halts Money to States for Preventing Disaster Damage

President Trump is the first president in at least three decades to deny governors’ requests for funding that’s meant to protect people and property

in Scientific American on 2025-05-01 14:45:00 UTC.
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Why ‘Evolving’ Dark Energy Worries Some Physicists

If dark energy is weakening, as suggested by recent results, then the cosmos is far stranger than most physicists had supposed

in Scientific American on 2025-05-01 14:15:00 UTC.
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Chess players rely on familiar moves even when the game changes
In chess as in life, people use memory as a shortcut for decision-making. That strategy can backfire when the present doesn’t resemblance the past.
in Science News: Psychology on 2025-05-01 13:00:00 UTC.
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A new rotation stundent Mr. Breno Calderoni joins our team in May!

Today we welcome a new rotation student, Breno Calderoni to our Unit.

in OIST Japan on 2025-05-01 12:00:00 UTC.
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Kick-off Meeting of Japan/Germany ASPIRE DIAMONDQTECH PROJECT in Germany

The new Japan-Germany ASPIRE project on Diamond Quantum Technology will have a kickoff meeting in Ulm, Germany in June!

in OIST Japan on 2025-05-01 12:00:00 UTC.
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Dr. Shilu Tian gives a talk at FNS2025 at NTT

Dr Shilu Tian from the Quantum Machines Unit will give a talk at FNS2025 at NTT

in OIST Japan on 2025-05-01 12:00:00 UTC.
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Quantum Machines Unit going to Quantum Optics XI Conference in Poland this September.

We will be showcasing the research of our Unit at the prestigious international conference Quantum Optics XI

in OIST Japan on 2025-05-01 12:00:00 UTC.
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Alex visits Chalmers University to work with Prof Witlef Wieczorek

PhD student Alex Hodges visits the optomechanics lab of Prof Witlef Wieczorek in Chalmers University in Sweden

in OIST Japan on 2025-05-01 12:00:00 UTC.
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Two new Postdocs join our team!

We welcome two new researchers to the Quantum Machines Unit: Resmi and Mitchell

in OIST Japan on 2025-05-01 12:00:00 UTC.
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CDC autism prevalence numbers warrant attention—but not in the way RFK Jr. proposes
The head of the U.S. Department of Health and Human Services is ignoring decades of research findings.
in The Transmitter on 2025-05-01 04:00:05 UTC.
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‘These plans are simply not acceptable’: Q&A with Helen Tager-Flusberg
Last week, Tager-Flusberg formed the Coalition of Autism Scientists to push back on the U.S. government’s plans for autism research, as described by Health and Human Services Secretary RFK Jr. The coalition already has 220 members.
in The Transmitter on 2025-05-01 04:00:04 UTC.
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Ozempic and Wegovy ingredient may reverse signs of liver disease
The diabetes and weight loss drug semaglutide reversed liver scarring and inflammation. It’s among several drugs in the works for the condition MASH.
in Science News: Health & Medicine on 2025-04-30 21:00:00 UTC.
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100 Days of Lies

The Number One rule of the Trump administration is to lie. That's it. That's all. Once you understand this mandate, it's easier to realize that yes, the next outrage is false too.
Trump himself stands for nothing and no one (other than his own glory and wealth). He has no principles and no morals. He demands undying loyalty from his unqualified Cabinet and staff, but he'll throw them under a bus when he considers them a liability.

What have been the goals of the first 100 days?
- to dismantle government institutions
- to demoralize federal workers
- to destroy liberal universities
- to demolish federally funded science
- to deport law-abiding foreign students
- to enact a eugenics-based health care system
- to ruin the economy
- to pillage the environment
- to establish an authoritarian state
- to consolidate Executive power
- to neuter Congress and the Courts
- to eliminate conflicts of interest for Oligarchs
- to ensure a dictatorship for billionaires
- to redistribute wealth ever upwards
- to glorify the prejudice of white Christian nationalists
- to starve children in Sudan
- to generate sheer chaos
- to alienate international allies
- to scapegoat immigrants, minorities, and transgender people
- TO CAUSE FEAR AND SUFFERING
These goals have been achieved. The US is no longer a democracy.
Are we winning yet??

100 Days of Failure

Even Fox News — in a rare moment of candor and truthfulness — has a hard time listing Trump's positive accomplishments.

100 Days of Hatred

Everyone deserves human dignity and due process.
But cruelty is the point, the humiliation is deliberate.

The New DEI Is Domination, Exclusion, and Incompetence
There are so many unqualified, white male affirmative action hires in the Trump Administration (Robert F. Kennedy Jr. and Pete Hegseth are among the worst).
I've been trying hard to picture the end game.
I've been trying very hard to understand so many things, especially the unholy alliance between secular billionaire tech bros and the Heritage Foundation (i.e., the Christian theocracy outlined in Project 2025). One proposal: They share a common delusion — an unjustified faith in their own superiority, a self-declared directive to rule the universe and live forever. All other humans are condemned.
Therefore our lives are trivial.

Along with many other Americans, I'm angry and dejected. But we mustn't give up. I'll continue to write, and I'll continue to protest. My voice — and my writing — have been in exile for far too long.

in The Neurocritic on 2025-04-30 20:25:00 UTC.
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Could a Monster Earthquake Actually Sink Parts of the Pacific Northwest?

A new study is fueling speculation and fear about the risks of a major earthquake in the Cascadia subduction zone, including massive flooding in California

in Scientific American on 2025-04-30 19:50:00 UTC.
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Why has it taken more than a year to correct a COVID-19 paper?

A correction to a clinical trial on a potential treatment for COVID-19 has taken more than a year — and counting — to get published. In the meantime, the article remains marked with an expression of concern that appeared in February 2024.

The Lancet Regional Health–Americas published the study, a randomized clinical trial of the effect of metformin on hospitalization rates among COVID-19 patients, in December 2021. It has been cited 36 times, according to Clarivate’s Web of Science, 12 of those since the publication of the expression of concern.

In December 2023, the authors “identified small errors in the statistical analysis primary outcome,” corresponding author Edward Mills, a health research methods professor at McMaster University, in Hamilton, Ontario, told Retraction Watch. “We immediately re-ran the analysis and submitted as an erratum,” he said.

At that point, the journal asked the university to investigate, a spokesperson for The Lancet Group told us by email:

The editors of The Lancet Regional Health – Americas asked McMaster University for an investigation into the analyses from the TOGETHER trial in January 2024. We received the final report from McMaster University on 21st April 2025 which stated the hearing committee concluded the author did not breach the University’s research integrity policy. We are now working with the authors on the best way to correct the record and will keep you updated.

The university’s final report came six days after we contacted McMaster about the paper. Jennifer Stranges, communications and media relations manager at McMaster, told us on April 15: “Information about concerns or potential investigative processes are confidential, and anything to be released to the public would be done so at the completion of the process.”

“So a year and 3 months just for them to agree that we weren’t conducting any malfeasance,” Mills said. He said he expects the correction will be published “within the next few weeks.”

Stranges did not reply to our question on why the investigation took so long.

McMaster made headlines a few years ago for its investigation into behavioral ecologist Jonathan Pruitt. Questions about Pruitt’s work garnered public attention in January 2020 and were reported to the university around the same time. The university found Pruitt “engaged in data falsification and fabrication in several papers,” all before joining the faculty, according to a May 2023 statement from the university.

The TOGETHER trial was a multi-arm clinical trial at 13 clinics in Brazil set up to test different drugs in people with COVID-19 at high risk for complications. The metformin arm of the trial started treating patients in January 2021, and the safety committee recommended halting it that April, as the drug was not affecting outcomes.

Other arms of the trial tested ivermectin, hydroxychloroquine and fluvoxamine, among other drugs.

Like Retraction Watch? You can make a tax-deductible contribution to support our work, follow us on X or Bluesky, like us on Facebook, follow us on LinkedIn, add us to your RSS reader, or subscribe to our daily digest. If you find a retraction that’s not in our database, you can let us know here. For comments or feedback, email us at team@retractionwatch.com.

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in Retraction watch on 2025-04-30 19:37:36 UTC.
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Trump’s Energy Secretary Baselessly Blames Spain’s Power Outage on Renewables

In response to a power outage in Spain and Portugal, the U.S. Department of Energy’s secretary Chris Wright tried to blame the use of solar and wind energy, though the cause of the blackout is not yet clear

in Scientific American on 2025-04-30 19:15:00 UTC.
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Mysterious Glowing Structure Discovered Near Solar System

An enormous glowing cloud that contains approximately 3,400 solar masses worth of gas has been discovered near the solar system

in Scientific American on 2025-04-30 17:15:00 UTC.
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Living with MS: Janet Stapleton’s Story
After being diagnosed with MS in 1995 at the age of 37, Janet Stapleton shares her journey through early symptoms, the emotional toll of a progressive illness, and how advances in treatment have transformed her son’s experience of the same condition.
in Women in Neuroscience UK on 2025-04-30 17:00:17 UTC.
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Where Does Consciousness Come From? Two Neuroscience Theories Go Head-to-Head

Two leading theories of consciousness went head-to-head—and the results may change how neuroscientists study one of the oldest questions about existence

in Scientific American on 2025-04-30 15:35:00 UTC.
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Measles Vaccine Denial Is a Massive Brainwashing Campaign

A shameful mass propaganda campaign is unfolding in the U.S., one that will make millions of kids needlessly sick with measles

in Scientific American on 2025-04-30 15:30:00 UTC.
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Why Ozempic and Wegovy Might Change Your Favorite Food

Some users of GLP-1 weight-loss drugs have been reporting strange changes in food preferences, such as a new dislike for meats or fried foods, and scientists are beginning to figure out why

in Scientific American on 2025-04-30 11:00:00 UTC.
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Griefbots Create Digital Immortality and Raise Ethical Concerns around AI Chatbots

AI chatbots called “griefbots” or “deadbots” offer our loved ones a new digital way to grieve but raise ethical and privacy concerns.

in Scientific American on 2025-04-30 10:00:00 UTC.
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Yale Fayle
"An attractive new prospect: Install the Chinese paper mill directly at Yale University, where research oversight is presumably less stringent than at the PRC and NIH funds are more easily accessed to piss up the wall." - Sholto David
in For Better Science on 2025-04-30 05:00:00 UTC.
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Federal funding cuts imperil next generation of autism researchers
As the International Society for Autism Research’s annual meeting begins, its next president reflects on a brewing crisis.
in The Transmitter on 2025-04-30 04:00:24 UTC.
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Null and Noteworthy: Reanalysis contradicts report of immune memory in astrocytes
The analysis, which has not yet been peer reviewed, attributes the finding to misidentified immune cells instead.
in The Transmitter on 2025-04-30 04:00:07 UTC.
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AI-Reddit study leader gets warning as ethics committee moves to ‘stricter review process’

University of Zurich

The university ethics committee that reviewed a controversial study that deployed AI-generated posts on a Reddit forum made recommendations the researchers did not heed, Retraction Watch has learned.

The principal investigator on the study has received a formal warning, and the university’s ethics committees will implement a more rigorous review process for future studies, a university official said.

As we reported yesterday, researchers at the University of Zurich tested whether a large language model, or LLM, can persuade people to change their minds by posting messages on the Reddit subforum r/ChangeMyView (CMV). The moderators of the forum notified the subreddit about the study and their interactions with the researchers in a post published April 26.

The identity of the researchers and the department they work in has not been made public. We reached out via their project’s email address, and they referred us to the University of Zurich media relations office.

Rita Ziegler, head of media relations AI at the University of Zurich, told us by email today that the Ethics Committee of the Faculty of Arts and Social Sciences reviewed the research study in April 2024. It was part of a larger project, and one of four studies, on “investigating the potential of artificial intelligence to reduce polarization in value-based political discourse.”

Ziegler continued:

In its opinion on the project, the Ethics Committee of the Faculty of Arts and Social Sciences advised the researchers that the study in question was considered to be exceptionally challenging and therefore a) the chosen approach should be better justified, b) the participants should be informed as much as possible, and c) the rules of the platform should be fully complied with.

Recommendations from the ethics committees are not legally binding, Ziegler said. “The researchers themselves are responsible for carrying out the project and publishing the results.”

Whether the researchers changed their approach based on that opinion or other factors is unclear, but they did not inform the CMV moderators, nor the CMV commenters, about the study until after the researchers finished their data collection, as we noted in yesterday’s story.

CMV has a rule against undisclosed use of AI, and Reddit itself has a rule that states, “don’t impersonate an individual or an entity in a misleading or deceptive manner.” The study violated both of those policies, CMV moderator u/DuhChappers told us.

“The relevant authorities at the University of Zurich are aware of the incidents and will now investigate them in detail and critically review the relevant assessment processes,” Ziegler said. The principal investigator of the study has been issued a formal warning, Nathalie Huber, a media relations officer, said.

Reddit has issued a response to the study as well. Reddit’s chief legal officer Ben Lee posted on the CMV thread:

What this University of Zurich team did is deeply wrong on both a moral and legal level. It violates academic research and human rights norms, and is prohibited by Reddit’s user agreement and rules, in addition to the subreddit rules. We have banned all accounts associated with the University of Zurich research effort.

Reddit is “in the process of reaching out to the University of Zurich and this particular research team with formal legal demands,” Lee said in the post.

As a result of this study, the University of Zurich’s ethics committee of the Faculty of Arts and Social Sciences “intends to adopt a stricter review process in the future and, in particular, to coordinate with the communities on the platforms prior to experimental studies,” Ziegler said.

The researchers made available a preliminary article on the work, but Ziegler told us the researchers have decided not to publish the findings.

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in Retraction watch on 2025-04-29 14:36:16 UTC.
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Trump Dismisses Scientists Writing the National Climate Assessment

President Trump has dismissed hundreds of scientists working on the congressionally mandated National Climate Assessment, raising concerns about whether the void will be filled with pseudoscience

in Scientific American on 2025-04-29 14:20:00 UTC.
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Building a virtual neuron – part 2

Image credit: Ionut Stefan

It’s been a tad longer than I intended since our intro on differential equations came out, but hopefully that means you had some extra time for memory consolidation. Otherwise, you can refresh your memory here. Today it’s finally time to tackle the long-awaited virtual neuron. But before we jump in, we need to have a quick housekeeping chat. As you can already glimpse from the list below, we mean business this time, so I strongly recommend that you read this article in chunks. Then again, I’m just a disembodied voice on the Internet and I can’t tell you what to do.
Defining the goal

First, we need to understand what we want to do. “Building a virtual neuron” sounds cool (well, about as cool as math can ever sound), but it tells us surprisingly little about the task. We need to define the level at which we build this neuron. Do we want to simulate every protein and ion, and all their interactions? I mean, maybe. I admit that does sound pretty cool, but would we be able to interpret the results? My computational neuroscience professor used to say: “If you build a simulation as complex as the system you’re studying, you now have two systems you don’t understand.” And leaving that aside, could we even construct such a simulation right now? Well, no, not really. So instead we need to define three things:
1. what we want to do;
2. what we can and want to get out of it;
3. what we can realistically accomplish.
For today, we want to build a model capable of producing action potentials, just like real neurons (1). We want to use this model to understand how neurons produce these potentials and how they are affected by both external stimuli and ion channel properties (2). And we can realistically accomplish this with a run-of-the-mill laptop and our own brains (3).

The plurality of virtual neurons

There isn’t just one single way to simulate a neuron. In fact, there are a lot of options. If you don’t believe me, have a look here. Choosing a computational model is an act of balance between complexity and efficiency. On the one hand, we want something complex enough to capture what we’re interested in: for example, if we want to know what happens to a neuron when we mess with its calcium channels, we need a model that includes them. On the other hand, this model needs to run on the available hardware and we should be able to make some sense of its results. So if we only care about calcium channels, it’s not such a good idea to include 300 other types of ion channels.

The foundation model

For today, I’ve chosen the Hodgkin-Huxley (HH) model. As some of you might already know, this is kind of the bedrock of modern computational modeling, and often the first boss you will encounter if you ever attend such a course.

While arguably not the first computational model, the HH was pioneering as a quantitative, dynamic, biologically grounded one, and it remains remarkably elegant to this day. Of course, now it’s quite easy to look at it and think “well, big whoop, we already know how action potentials work”. But given the limited amount of information Hodgkin and Huxley had available at the time, it’s nothing short of fascinating how well the model reproduced empirical data and what predictions they were able to derive from it.

At the same time, coming from the biology side, I always had a bunch of questions about action potentials that remained largely unanswered until I made my way through the math jungle. For example, why do sodium (Na+) channels open slowly at first, then all at once? Why does the threshold for spike generation have that value and not another one? Why do potassium (K+) channels take so long to open? And why is it that we don’t always get one spike after another?

As we work our way through the model, we will be answering these questions and more. But similar to the previous article, we’ll start with a series of small, made-up examples (the code to follow along is here) and work our way up to the main beast. I hope that these examples bring clarity, but if they have the opposite effect, please let me know in the comments. That way, I can improve this guide (and future ones).

Throughout, I’ll try to highlight the underlying biology, as well as what Hodgkin and Huxley actually knew at the time. If you’d like a refresher on neuron structure and function, we do have this older post covering the basics, but I’ll try to weave those concepts in as we go.

From cats to neurons

Abstracting the movements of a cat to math is somewhat straightforward. If we get stuck in the equation, we have something tangible to go back to. So before we start with the math, let’s try to build the same kind of concreteness for neurons and action potentials.

We can begin from the same information Hodgkin and Huxley had available at the time. Neurons are enclosed by membranes, which usually block the movement of ions. Since the membrane is typically sealed, we can have different concentrations of ions on both sides: more Na+ outside, more K+ inside. While they didn’t yet know how these concentration gradients were maintained, HH recognized their importance.

They also observed that, if one were to place an electrode outside of the neuron and stick another one inside, a potential difference in voltage of about -65 mV could be measured (by the way, these days it’s also known the exact voltage difference varies by neuron type). In other words, the inside of the cell is more negative compared to the outside. Importantly, the value and its sign don’t matter that much, at least not for understanding the general principles. What matters is that there is a measurable difference and that sometimes there is a change in this difference.

If the membrane were forever sealed to the passage of any and all ions, then that would be the end of the story. We’d have no action potential to talk about (and we couldn’t anyway, because no intelligence, language, movement, nothing). But sometimes, the membrane allows ions to flow through it. You can imagine the ion concentrations we mentioned above as water stored in a tank. There’s much more Na+ outside the neuron than inside, so when the Na+ “tap” (i.e., ion channels) opens, Na+ rushes into the neuron, like water gushing into an empty chamber. This happens very fast and leads to a temporary reversal of the voltage difference sign: the inside becomes more positive than the outside. Then the Na⁺ tap closes and the K+ tap opens, allowing K+ to flow out and bring things back to normal.

This information is pretty much all we need for the HH model, although I’m sure you still have some questions.

Small detour # 1: hypothesized, but not modeled

We mentioned above that Hodgkin and Huxley didn’t know how the Na+ and K+ gradients were maintained. However, they hypothesized there must be some active mechanism that pushes Na+ out and brings K+ into the neuron, thus working to maintain the concentration gradients. Otherwise, each neuron would only have a few action potentials to fire before the ion concentration on both sides of the membrane equalizes.

And they were right. Years later, we found out that there are proteins embedded in the membrane, called ion pumps, that are open only on one side of the neuron at a time. They act kind of like a shuttle bus that only allows Na+ to board from the inside going out and K+ from the outside going in.

Small detour # 2: positive, yet negative?

I’m sure it’s not lost on any of you that: 1) both Na+ and K+ are positive ions, and 2) cells, including neurons, aren’t electrically charged. So how can we talk about a voltage difference?

There are a few key points here:
1. overall, the amount of positive and negative charges is equal both inside and outside the membrane, but it’s the distribution of these charges close to the membrane that makes a difference;
2. inside the neuron, there are also large negatively charged proteins which can’t leave the cell and tend to cluster close to the membrane;
3. even though both Na+ and K+ each carry a +1 charge, the concentration of Na+ outside the cell is larger than that of K+ inside the cell (around 150 mM for Na+ vs 100 mM for K+, depending on neuron type). Additionally, the pump we mentioned earlier throws out 3 Na+ ions for every 2 K+ brought in, thus maintaining the imbalance;
4. there are also some K+ channels that remain open at rest. Due to the K+ concentration gradient, some of it flows out of the neuron, which means that some positive charge trickles outward, leaving the inside slightly more negative relative to the outside.
The combination of these factors generates the voltage difference measured by Hodgkin and Huxley.

From neurons to circuits

Coming back to our neuron model, now that we have the biology basics, we can begin to abstract. But instead of inventing an entirely new mathematical framework to describe how neurons behave, Hodgkin and Huxley realized that it was easier to repurpose what was already in the physics of electric circuits.

All the elements we described above have an equivalent in a circuit:
- since the membrane stores charge, it behaves like something called a capacitor, i.e. a device which stores charge by accumulating it on two closely spaced surfaces insulated from each other;
- the only way for ions to passively go through the membrane is through ion channels, which are typically closed. In other words, the channels provide resistance to the flow of ions, so we can represent them through resistors;
- we also explained that there are differences in the concentration of ions between the inside and the outside of the neuron and that these differences drive the ion flow, so the ion concentration differences are our voltage sources or batteries;
- and finally, although not explicitly included in the HH model, the ion pumps which restore the concentration gradients represent the current sources in our circuit, pushing ions in a specific direction to keep the system going.
As I said, even at the time, there was already a lot of math for how to work with electrical circuits. And that’s the key for cracking our simulations.

From measurements to interventions

In the circuit above, we could measure the voltage difference of the inside compared to the outside of the membrane. In fact, that’s what Hodgkin and Huxley did at first. They used giant axons from squids and silver electrodes to measure the so-called membrane or resting potential, which we said sits at around -65 mV.

But measurements alone aren’t enough. And by itself, the neuron and its membrane potential at rest aren’t that exciting. We want action…potentials. Those happen when neurons receive stimuli or input. One could try to do these measurements in vivo, that is when the one neuron we measure receives input naturally, either from other neurons or from the environment. But in this particular situation, Hodgkin and Huxley wanted to have precise control over the neuron’s input and they wanted to use the circuit framework from above. So instead, they used another set of electrodes to directly inject current into the axon of an isolated neuron.

Now, looking at the circuit diagram, physics tells us that if we inject some external current (we’ll call it $I_{ext}$ ) into this system before the point where the individual elements (capacitor and resistors) are branching out, this current will split to flow through each available path. So we’ll have a capacitive current $I_c$ and, for each type of channel, ionic currents, which for now we’ll lump under a generic $I_{ion}$ . As nothing is lost in this idealized circuit, our original $I_{ext}$ will be the sum of the currents flowing through the individual elements, so: $I_{ext} = I_c + I_{ion}$ .

Cool, but we actually care about voltage, right? That’s what the action potential is, a change in voltage difference between the inside and the outside of the neuron over time. Yes, and here’s how physics helps us again: it tells us that $I_c$ – our capacitive or membrane current, can be expressed in terms of the rate of change of the voltage, i.e. our old friend $\frac{dx}{dt}$ . Since we’re talking about membrane voltage, we’ll just rename x to $V_m$ . And the full formula is $I_c = C_m \cdot \frac{dV_m}{dt}$ , where $C_m$ represents something called the membrane capacitance, and it’s just a constant, a number that we normally determine experimentally or read from a paper that already measured it. In this case, Hodgkin and Huxley measured $C_m$ and found it equal to 1 ( $\mu F/cm^2$ , but don’t stress about the units yet; by the way, what you’ve just heard is the collective shudder of all the world’s physicists at the idea of not stressing about units).

With that, we can rewrite $I_{ext} = C_m \cdot \frac{dV_m}{dt} + I_{ion}$ , and shifting the terms, we get $C_m \cdot \frac{dV_m}{dt} = -I_{ion} + I_{ext}$ . Since $C_m$ is a constant, you will often see it written on the same side as $\frac{dV_m}{dt}$ (basically, constant = we don’t care much about it), but to make it clearer, we can also isolate $\frac{dV_m}{dt} = \frac{1}{C_m} \cdot (-I_{ion} + I_{ext})$ . This will be our stepping stone for the full model. The lefthand side of the equation won’t change anymore. That’s the potential we’ve been wanting to simulate for a while now. The righthand side will gradually expand in complexity until it allows us to get something looking like the image below:

Virtual neuron 1 – linear, boring, and instructive

In the equation $\frac{dV_m}{dt} = \frac{1}{C_m} \cdot (-I_{ion} + I_{ext})$ , we already know that $C_m$ is a constant equal to 1 $\mu F/cm^2$ . $I_{ext}$ is what we pump into the system and we have full control over it. For now, we will try out three values: 0, 1, and 2 mA/ $cm^2$ . $I_{ion}$ tells us about how ions, like Na+ and K+, behave, but for now, we will completely ignore it by setting it to zero. So our equation reduces to $\frac{dV_m}{dt} = \frac{1}{C_m} \cdot I_{ext}$ or $\frac{dV_m}{dt} =$ 0, 1 or 2 (mV), depending on which $I_{ext}$ we pick. This is very similar to the first cat example from last time, except that our starting point, $V_m(t=0)$ , is -65 mV.

But just because this example is so simple, it doesn’t mean we can’t extract any information from it. We observe that the higher the input current $I_{ext}$ is, the faster our membrane voltage $V_m$ increases. And of course, if there is no input whatsoever, nothing happens.

We can also check what happens if we start from different $V_m$ values at $t = 0$ (in this case, -100 mV, -65 mV, and 10 mV). And we’ll look at just one external input value, $I_{ext}$ = 1 mA/ $cm^2$ . As you see below, not much. The line looks exactly the same, except that it starts from different values of $V_m$ . We’ll check this again in the more complex model and see if it holds.

Virtual neuron 2 – to the moon and beyond

Now it’s time to tackle $I_{ion}$ . Instead of zero, we could give it another random value, like 3. But no matter what fixed value we give it, the only thing that would change in our equation $\frac{dV_m}{dt} = \frac{1}{C_m} \cdot (-I_{ion} + I_{ext})$ would be how fast the membrane voltage increases. More importantly, we know this is unrealistic in neurons because when Na+ and K+ channels open and the ions travel from one side of the membrane to the other, the ionic currents also change.

That means $I_{ion}$ needs to be not a constant, but a function. More specifically, a function which changes over time (and later, over voltage too). One such example would be $I_{ion}(t) = -t$ – at every time step, our ionic current would be equal to the negative value of that time step. Our base equation would then transform into $\frac{dV_m}{dt} = \frac{1}{C_m} \cdot (t + I_{ext})$ . For $I_{ext} = 1$ mA/ $cm^2$ , we would get the following:

We see that the membrane voltage now rises much faster, up to very unrealistic values (in practice, if we actually injected the current necessary for reaching such voltages, we’d fry the neuron long before getting there). And if we were to slightly vary either $I_{ext}$ or $V_m(t=0)$ as we did above, there would be barely any noticeable difference in the result.

But remember how we represented our ion channels through resistors? Similar to capacitors, there is also a formula that relates current and voltage for these elements: $I_{ion} = g_{ion} \cdot (V_m - V_{ion})$ . $V_m$ is our membrane voltage, the one we’ve been plotting so far. So our base equation now expands into $C_m\frac{dV_m}{dt} = -g_{ion} \cdot (V_m - V_{ion}) + I_{ext}$ (I’ve moved $C_m$ to the lefthand side to avoid using too many brackets). $g_{ion}$ is the conductance for that ion. Conductance is a measure of how easily electric current flows through a material. In our case, this means how easily the ions pass through their respective channels. For now, we will pretend that $g_{ion}$ is a constant, like 0.1 (mS/ $cm^2$ ).

And $V_{ion}$ is our battery from the circuit above. It represents the equilibrium potential of each ion, what they aspire to, and the voltage at which the membrane would settle if there were no other ions around and if the membrane were permeable all the time. In this case, we don’t need to pretend: $V_{ion}$ is always constant for a given ion type. For example, for Na+, $V_{Na}$ is about +45 mV. If the membrane potential, $V_m$ , were equal to +45 mV, we would say that Na+ is at equilibrium and there would be no movement of Na+ ions across the membrane. In real neurons, this is never reached, since other ions have different equilibrium potentials (for example, K+ sits at around -82 mV), but we’ll learn more about that later.

Small detour # 3: that Nernst guy

But hold up: what does ion concentration have to do with voltage? And where do ion equilibrium potentials actually come from? Well, in practice, from neat little tables.

But conceptually, we need to make something clear, using Na+ as an example: we said that there are more Na+ ions outside than inside the neuron, so there is a higher concentration of Na+ on the outside of the membrane. If we open the tap, this concentration difference will push Na+ inside. But when does the pushing stop? Is it when the Na+ concentration is exactly equal on both sides of the membrane? It would be, if only Na+ were the only one around and there were no voltage difference between the two sides of the membrane.

But let’s imagine that we also have those negatively charged proteins from earlier. This changes the game, because even though the concentration of Na+ ions might equalize at some point, there would be another force pulling it in: the negative charge of the proteins, or the electrical gradient. Because these two forces compete, the actual voltage at which no Na+ moves around anymore is the one given above.

We can calculate this number from yet another equation that some guy named Nernst came up with: $V_{ion} = \frac{RT}{zF} \cdot ln(\frac{[ion]_{out}}{[ion]_{in}})$ . R, T, z, and F are constants, so we again ignore them. What matters is that this formula allows us to relate the ion concentrations $[ion]_{out}$ (outside) and $[ion]_{in}$ (inside) the neuron to voltage, thus giving us the equilibrium potential of each ion.

Bonus: this nifty formula tells us why sudden influxes of K+ can kill you. When the concentration of K+ outside the neuron increases a lot, the equilibrium potential of K+ ends up being much higher than -82 mV. In turn, this messes with the generation of action potentials, thus impairing communication between neurons. Once we have the full HH model, we’ll be able to check exactly how this happens.

Back to virtual neuron 2

For now, we see that if we were to model just Na+ currents and assume a constant conductance (in this example, $g_{Na} = 0.1$ mS/ $cm^2$ ), the membrane potential would eventually settle to the equilibrium potential of Na+.

This time, if we change our starting point $V_m(t = 0)$ , we observe a different behavior compared to the first virtual neuron: here, the membrane potential always settles at the Na+ equilibrium, regardless of whether we start from a value above or below that.

But what happens if we keep the resting state voltage the same and change the conductance $g_{Na}$ ? A higher conductance means that Na+ ions barrel through channels quicker (because more channels are open, not because the ions move any faster). That translates into the equilibrium potential being reached sooner.

I want to stress here that conductance isn’t just an abstract thing that makes the graph sharper. In real life, alterations in Na+ channel conductance can have devastating effects. For example, tetrodotoxin, a powerful toxin derived from pufferfish, effectively decreases Na+ conductance to zero by blocking Na+ channels and preventing its influx into the cell. This is deadly. And in different types of epilepsy, Na+ conductance is again affected: either too high or too low, depending on the type of epilepsy. As we’ll see later, changes in conductance affect the properties of action potentials, such as shape and timing. At the level of the whole brain, this results in abnormal communication between neurons and can lead to the symptoms observed in epilepsy.

Moving on to varying the external input current $I_{ext}$ , we see that the membrane potential no longer settles at the ion’s equilibrium potential, but at another value that changes with the strength of the external input $I_{ext}$ . Looking again at our equation $C_m\frac{dV_m}{dt} = -g_{ion} \cdot (V_m - V_{ion}) + I_{ext}$ , we see that when $I_{ext}$ is zero, the membrane voltage is only governed by $V_{ion}$ . But once we inject a steady flow of current into this system, the balance point shifts higher or lower, depending on the sign of $I_{ext}$ . This will be important for action potential generation later on.

Virtual neuron 3 – other ions have joined the party

Alright, but we know Na+ doesn’t act alone. There is at least a K+ current. There are other ions as well, but Hodgkin and Huxley lumped everything else that might act in a neuron under a so-called “leak” current that is modeled as an additional resistor.

Once we add the K+ and leak currents in our model ( $I_K = g_K \cdot (V_m - V_K)$ and $I_l = g_l \cdot (V_m - V_l)$ ), we now have a slightly longer differential equation for the membrane voltage:

$C_m\frac{dV_m}{dt} = -g_{Na} \cdot (V_m - V_{Na}) - g_K \cdot (V_m - V_K) - g_l \cdot (V_m - V_l) + I_{ext}$ .

Simulating this allows us to see that, like before, the membrane voltage settles at an equilibrium point. But this point is no longer equal to the equilibrium voltage of any single ion. Instead, it sits somewhere in-between. This in-between value is nothing more than the weighted average of the contributions of all ions to the membrane potential. The contribution of an ion is given by the product between its equilibrium potential and its conductance, so the full equation reads like this: $V_{eq} = \frac{g_{Na} \cdot V_{Na} + g_K \cdot V_K + g_l \cdot V_l}{g_{Na} + g_K + g_l}$ .

We saw above that changing the Na+ conductance when only Na+ is present allows us to manipulate how fast we reach the equilibrium potential. But the equilibrium potential itself remains unchanged. But now we have more than one ion, each with their own conductance, and we see in the equation above that the membrane equilibrium potential takes into account conductances as well. So what happens if we change each ionic conductance individually?

We should be able to deduce this from the equation, but we’ll check it against the simulation results below. The blue line represents our original case from above. Since the K+ equilibrium potential is more negative than our original resting state potential $V_m$ , increasing the K+ conductance $g_K$ while keeping the Na+ conductance $g_{Na}$ the same means that the membrane will settle at a new, more negative potential (orange line). In contrast, since the Na+ equilibrium potential is positive, increasing the ionic conductance $g_{Na}$ while keeping the same $g_K$ means that our neuron’s equilibrium potential goes up and we also reach it faster (green line). Now, if we increase $g_K$ while maintaining this higher $g_{Na}$ , our membrane resting potential comes down, closer to that of K+. But we still get there fast, since the Na+ conductance is so high (red line).

In principle, we could also play around with the leak conductance $g_l$ . However, as we will see later, in the HH model, the leak conductance is always assumed to be static, whereas $g_{Na}$ and $g_K$ do change under certain conditions.

The full model – everybody gets a function

We’ve already added quite a few details to our model, but there’s still a bit to go on. So far, we have a simulation of the membrane potential which includes multiple ion channels. This model is capable of settling at an equilibrium point, the resting state potential, but it still doesn’t produce spikes yet. So let’s fix that. Fair warning, this next part is the trickiest (I know! As if the novel before was soooo easy!), so go slowly, pause often, and don’t worry if things take a few reads to click.

Key takeaway # 1: conductances are voltage-dependent
Let’s bridge biology and math now: we said that when the Na+ conductance increases (i.e. Na+ channels open), the membrane voltage also increases. But we also know from experiments that when the membrane voltage increases, K+ channels open. In other words, the K+ conductance increases. In math terms, that suggests conductance (for both Na+ and K+) is voltage-dependent.

Key takeaway # 2: there is a maximum conductance
Imagine all Na+ channels are open. Even then, there is still a limit to how much Na+ can pass through the membrane at every time step, because the ions need to wait for their turn to go through the channels, just like cars have to wait to pass through a crowded tunnel. That means conductance has a maximum value, which we can call $g_{Na}^{max}$ . When all channels are open, $g_{Na} = g_{Na}^{max}$ for Na+ and similarly, $g_K = g_K^{max}$ for K+.

Key takeaway # 3: we can work directly with proportions of open channels
But what if only 50% of the channels were open? Well, the limit would be half of the maximum: $g_{Na} = 0.5 \cdot g_{Na}^{max}$ . Why is it this relevant? Because instead of directly relating conductance to voltage, we can relate proportion of open (or closed) channels to voltage. The math is easier and it’s a bit more intuitive.

Putting it all together
First of all, since conductances are voltage-dependent and the membrane voltage changes over time, we actually have voltage- and time-dependent conductances. Important to note, only for Na+ and K+; we assume the leak conductance to be fixed.

Secondly, we work with the proportion of open channels, not with conductances directly. Let’s pause for a moment and think about what we want to model. We basically want a sort of push-pull mechanism, such that when the voltage goes up, the proportion of open Na+ channels goes up, and when the voltage decreases, the proportion of closed channels increases. And the same way for K+.

Let’s start with K+. We can denote the proportion of open K+ channels with n. The proportion of closed channels will be simply 1 – n (total minus how many are open). Since we’re interested in how this evolves over time, we need to bring back our differential equation friend, in this case $\frac{dn}{dt}$ . The push-pull mechanism we want can be written in the following form: $\frac{dn}{dt} = functionA_{voltage} \cdot (1-n) - functionB_{voltage} \cdot n$ or following the Hodgkin-Huxley convention: $\frac{dn}{dt} = \alpha_n(V_m) \cdot (1-n) - \beta_n(V_m) \cdot n$ . There are two parts that matter here:
1. the two functions A and B act like weights for the proportion of closed, respectively open, channels. A controls how fast closed channels open and B controls how fast open channels close;
2. the above is not enough. A and B are voltage-dependent functions themselves and they need to be chosen in such a way that, when the voltage goes up, A goes up and B goes down, and vice-versa when the voltage goes down.
But how to choose them? Well, the equation above is called a first-order differential equation and has a known solution. Without going further into mathematical detail, Hodgkin and Huxley used that solution together with experimental measurements of K+ currents to derive specific formulas for $\alpha_n$ and $\beta_n$ . I am including them here for completeness and because you will see them in the code, but there is no reason to stress over them. In practice, unless you use them on a daily basis, you’re just going to look them up when needed (and by the way, depending on the neuron type, the actual numerical values in these formulas will change): $\alpha_n(V_m) = \frac{0.01(10 - V)}{exp(\frac{10 - V}{10}) - 1}$ and $\beta_n(V_m) = 0.125 \cdot exp(-\frac{V}{80})$ .

(Side note: the sign convention. One thing to notice above is that we use both $V_m$ and V. That’s not a typo. Normally, we define the membrane voltage $V_m = V_{inside} - V_{outside}$ , so the membrane voltage is negative at rest. In the HH model, however, V is defined as $V= V_{rest} - V_m$ . That means the voltage is shifted such that at rest, $V = 0$ mV. And because all $\alpha$ s and $\beta$ s were fitted to these shifted values, we need to take that into account when working with the original HH model.)

For Na+, they modeled the Na+ channel activation in a similar manner, except they called the proportion of activated channels m. Again, for completeness, the respective equations were $\alpha_m(V_m) = \frac{0.1(25 - V)}{exp(\frac{25 - V}{10}) - 1}$ and $\beta_m(V_m) = 4 \cdot exp(-\frac{V}{18})$ .

Now we almost have the full functioning HH model, but there are just a couple of minor tweaks left. Because Hodgkin and Huxley fitted their model to experimental data, they observed two interesting tidbits:
1. the model fit better when the variable n was raised to the power of 4 and when m was raised to the power of 3. At the time, they didn’t know why that was the case, but in the meantime, we’ve found out that the K+ ion channel is made up of 4 subunits, each of which needs to be activated for the channel to allow the passage of K+. In that case, you can think of n as the proportion of channels where subunit 1 is activated (or the probability for this subunit to be activated). The proportion of channels where 2 subunits are activated is $n \cdot n$ , and so on. Similarly, Na+ channels have 3 activation domains that need to be opened for Na+ to pass through the channel;
2. when the membrane voltage was held constant at a high value, K+ kept flowing out of the cell until the voltage was allowed to return to normal. But for Na+, Hodgkin and Huxley observed a different behavior: Na+ flowed into the cell at first, then it stopped. The Na+ current sharply decreased and regardless of how long the voltage was kept high, the Na+ current didn’t increase anymore. To model this behavior, they introduced a second variable for Na+, called h, which they used to model the proportion of inactivated Na+ channels. This needed the same $\alpha_h$ and $\beta_h$ functions, with $\alpha_h(V_m) = 0.07 \cdot exp(-\frac{V}{20})$ and $\beta_h(V_m) = \frac{1}{exp(\frac{30 - V}{10}) + 1}$ . Again, nowadays, we know that Na+ has an inactivation domain that rapidly blocks Na+ channels at high voltages and only unlocks them when the voltage goes down again. That’s also why action potentials cannot spread backwards from where they came from.
And that’s it, we now have a full HH model. Put all together, it looks like this:
$C_m\frac{dV_m}{dt} = -g_{Na}^{max} \cdot m^3 \cdot h \cdot (V_m - V_{Na}) - g_K^{max} \cdot n^4 \cdot (V_m - V_K) - g_l \cdot (V_m - V_l) + I_{ext}$ ,
$\frac{dn}{dt} = \alpha_n(V_m) \cdot (1-n) - \beta_n(V_m) \cdot n$ ,
$\frac{dm}{dt} = \alpha_m(V_m) \cdot (1-m) - \beta_m(V_m) \cdot m$ ,
$\frac{dh}{dt} = \alpha_h(V_m) \cdot (1-h) - \beta_h(V_m) \cdot n$ .

Importantly, by itself, the model doesn’t really do anything. If the external input is zero and we start the model from an initial membrane voltage below a certain threshold (in this case, $V_m(t = 0) =$ -60 mV), it quickly decays back to the resting state potential (which you can calculate yourself using the formula given above and the maximum conductances and ionic equilibrium potentials given in the code here.)

If we start the model above a certain threshold (for example, $V_m(t = 0) =$ -50 mV), it will fire a single spike before going silent forever.

To get more than one spike, we need to drive it with external input current. So far, we’ve used constant current, and we’ll stick with that for today (in the next part, we’ll also try out time-varying currents). For a high enough current, we see that the model fires one action potential after the next. You can try it out for yourself to see what happens for different values of $I_{ext}$ , and next time we’ll try a more systematic analysis as well.

Finally, we can inspect our gating variables m, h, and n, to see how they evolve over time. In the plot below, you see that the Na+ channel activation variable m (in blue), goes up really quickly – Na+ channels open fast; but it goes down just as quickly – they also close fast. The Na+ inactivation variable, h, quickly decreases during the spike – Na+ channels are blocked and cannot open again for some time. In the meantime, the K+ activation variable n goes up, lagging a bit behind m – K+ channels open more slowly and the membrane voltage goes back down.

Still alive?

I don’t know about you, but I’m tired. The good news is that now we have a functional HH model. Also good news is that we can do a lot of things with it, but unfortunately, that requires additional explanations, and I think we could all use a break. So I’ll see you for the next part. Until then, feel free to toy with the model parameters.

P.S.: If someone knows a better solution for displaying LaTeX equations in WordPress, do let me know. The current method is hurting my soul.

What did you think about this post? Let us know in the comments below. And if you’d like to support our work, feel free to share it with your friends, buy us a coffee here, or even both.

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References
Goaillard, J.-M., & Marder, E. (2021). Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience. Annual Review of Neuroscience, 44(1), 335–357. https://doi.org/10.1146/annurev-neuro-092920-121538

Hodgkin, A. L., Huxley, A. F., & Katz, B. (1952). Measurement of current‐voltage relations in the membrane of the giant axon of Loligo. The Journal of Physiology, 116(4), 424–448. Portico. https://doi.org/10.1113/jphysiol.1952.sp004716

Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500–544. Portico. https://doi.org/10.1113/jphysiol.1952.sp004764

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