What does Gödel's theorem mean ?

Gödel's theorem is a result in mathematical logic, which is often stated as showing that « there are true things that cannot proved ». It is sometimes used to comment on the limits of science, or the superiority of human intuition. Here I want to clarify what this theorem means and what the epistemological implications are.

First, this phrasing is rather misleading. It makes the result sound almost mystical. If you phrase the result differently, by avoiding the potentially confusing reference to truth, the result is not that mystical anymore. Here is how I would phrase it : you can always add an independent axiom to a finite system of axioms. This is not an obvious mathematical result, but I wouldn't think it defies intuition.

Why is this equivalent to the first phrasing ? If the additional axiom is independent of the set of axioms, then it cannot be proved from them (by definition). Yet as a logical proposition it has to be either true or not true. So it is true, or its negation is true, but it cannot be proved. What is misleading in the first phrasing is that the statement « there are true things » is contextual. I can start from a set of axioms and add one, and that new one will be true (since it's an axiom). Instead I could add its negation, and then that one will be true. That the proposition is true is not a universal truth, as it would seem with the phrasing « there are true things ». It is true in a particular mathematical world, and you can consider another one where it is not true. Famous examples are Euclidean and non-Euclidean geometries, which are mutually inconsistent sets of axioms.

So, what Gödel's theorem says is simply that no finite system of axioms is complete, in the sense that you can always add one without making the system inconsistent.

What are the epistemological implications ? It does not mean that there are things that science cannot prove. Laws of physics are not proved by deduction anyway. They are hypothesized and empirically tested, and all laws are provisory. Nevertheless, it does raise some deep philosophical questions, which have to do with reductionism. I am generally critical of reductionism, but more specifically of methodological reductionism, the idea that a system can be understood by understanding the elements that compose it. For example : understand neurons and you will understand the brain. I think this view is wrong, because it is the relations between neurons, at the scale of the organism, which make a brain. The right approach is systemic rather than reductionist. Many scientists frown at criticisms of reductionism, but this is only because they confuse methodological and ontological reductionism. Ontological reductionism means that reality can be reduced to a small number of types of things (eg atoms) and laws, and everything can be understood in these terms. For example, the mind can in principle be understood in terms of interactions of atoms that constitute the brain. Most scientists seem to believe in ontological reductionism.

Let us go back now to Gödel's theorem. An interesting remark made by theoretical biologist Robert Rosen is that Gödel's theorem makes ontological reductionism implausible to him. Why ? The theorem says that, whatever system of axioms you choose, it will always be possible to add one which is independent. Let us say we have agreed on a small set of fundamental physical laws, with strong empirical support. To establish each law, we postulate it and test it empirically. At a macroscopic level, scientists postulate and test all sorts of laws. How can we claim that any macroscopic law necessarily derives from the small set of fundamental laws ? Gödel's theorem says that there are laws that you can express but that are independent of the fundamental laws. This means that there are laws that can only be established empirically, not formally, in fact just like the set of fundamental laws. Of course it could be the case that most of what matters to us is captured by a small of set of laws. But maybe not.

Tip for new PIs : always do administrative work at the last minute, or later

This is a tip that has taken me years to really grasp, and I still haven't fully internalized it. I don't like to work at the last minute. If I have something to do and I don't do it, then it stays in the back of my mind until I do it. So, especially if it's some boring task like administrative work, I like to get rid of it as soon as possible. That's a mistake. I'm speaking of my experience in France, so maybe it doesn't apply so much elsewhere. The reason it's a mistake is that what you are required to do changes all the time, so the latest you do it, the least work you will have to do.

Every new politician seems to want to add a new layer of bureaucracy, independently of their political origin, so the amount of administrative work you are required to do as a scientist keeps growing, and it doesn't seem to converge. But setting up new rules and reglementations in a complex bureaucratic monster is not easy, so the monster often outputs nonsensical forms and requirements. One example in France is the evaluation of labs (HCERES), whose role is unclear and changing. The amount of redundancy and the absurdity of some requirements is abysmal. For example, you are required to fill a SWOT diagram, to select and list 20 % of all your « outputs », but also to list each one of them in another form, etc. Because many of the requirements are vague and nonsensical, any organization that deals with them will take some time to converge to a clear set of rules issued to the labs. I have written my evaluation document about 4 times because of the changing instructions.

Another recent example is the new evaluation system set up by INSERM (national medical research institution). Someone there (external consulting company ?) apparently decided that having an online CV with fields to fill instead of uploading a text would be more convenient. So for example you have to insert, one by one in web forms, the list of all journals for which you have reviewed in your entire career, and how many papers you have reviewed for each of them. You need to insert the list of all students you have supervised in you entire carrier, with names and exact dates, etc, all one by one in separate fields. Imagine that for senior PIs. Guess what : one week before deadline, the requirement of filling that CV was lifted for most scientists because of many complaints (a bit too late for most of them, including me). About a quarter of them still have to, but the message says that the format of the CV will change next year since it was not good, so all the work will basically be for nothing.

So here is my conclusion and tip : bureaucracy is nonsense and don't assume otherwise ; just set yourself some time on the deadline to do the required work, whatever it might become at that time (and it might disappear).

Technical draft for chapter 5, Propagation of action potentials

I have just uploaded a technical draft on chapter 5 of my book on action potentials: Propagation of action potentials. This draft introduces the cable equation, and how conduction velocity depends on axon diameter in unmyelinated and myelinated axons. There is also a short section on the extracellular potential. There are a few topics I want to add, including branching and determinants of conduction velocity (beyond diameter). There is also (almost) no figure at the moment. Finally, it is likely that the chapter is reorganized for clarity. I wanted to upload this chapter nonetheless so as to move on to the next chapter, on spike initiation with an initial segment.

What is computational neuroscience? (XXVI) Is optimization a good metaphor of evolution?

Is the brain the result of optimization, and if so, what is the optimization criterion? The popular argument in favor of the optimization view goes as follows. The brain is the result of Darwinian evolution, and therefore is optimally adapted to its environment, ensuring maximum survival and reproduction rates. In this view, to understand the brain is primarily to understand what “adapted” means for a brain, that is, what is the criterion to be optimized.

Previously, I have pointed out a few difficulties in optimality arguments used in neuroscience, in particular the problem of specification (what is being optimized) and the fact that evolution is a history-dependent process, unlike a global optimization procedure. An example of this history dependence is the fascinating case of mitochondria. Mitochondria are organelles in all eukaryotes cells that produce most of the cellular energy in the form of ATP. At this date, the main view is that these organelles are a case of symbiosis: mitochondria were once prokaryote cells that have been captured and farmed. This symbiosis has been selected and conserved through evolution, but optimization does not seem to be the most appropriate metaphor in this case.

Nonetheless, the optimization metaphor can be useful when applied to circumscribed problems that a biological organism might face, for example the energy consumption of action potential propagation. We can claim for example that, everything else being equal, an efficient axon is better than an inefficient one (with the caveat that in practice, not everything else can be made equal). But when applied at the scale of an entire organism, the optimization metaphor starts facing more serious difficulties, which I will discuss now.

When considering an entire organism, or perhaps an organ like the brain, then what criterion can we possibly choose? Recently, I started reading “Guitar Zero” by Gary Marcus. The author points out that learning music is difficult, and argues that the brain has evolved for language, not music. This statement is deeply problematic. What does it mean that the brain has evolved for language? Language does not preexist to speakers, so it cannot be that language was an evolutionary (“optimization”) criterion for the brain, unless we have a more religious view of evolution. Rather, evolutionary change can create opportunities, which might be beneficial for the survival of the species, but there is no predetermined optimization criterion.

Another example is the color visual system of bees (see for example Ways of coloring by Thompson et al.). A case can be made that the visual system of bees is adapted to the color of flowers they are interested in. But conversely, the color of flowers is adapted to the visual system of bees. This is a case of co-evolution, where the “optimization criterion” changes during the evolutionary process.

Thus, the optimization criterion does not preexist to the optimization process, and this makes the optimization metaphor weak.

A possible objection is that there is a preexisting optimization criterion, which is survival or reproduction rate. While this might be correct, it makes the optimization metaphor not very useful. In particular, it applies equally to all living species. The point is, there are species and they are different even though the optimization criterion is the same. Not all have a brain. Thus, optimization does not explain why we have a brain. Species that have a brain have different brains. The nervous system of a nematode is not the same as that of a human, even though they are all equally well adapted, and have evolved for exactly the same amount of time. Therefore, the optimization view does not explain why we speak and nematodes don’t, for example.

The problem is that “fitness” is a completely contextual notion, which depends both on the environment and on the species itself. In a previous post where I discussed an “existentialist” view of evolution, I proposed the following thought experiment. Imagine a very ancient Earth with a bunch of living organisms that do not reproduce but can survive for an indefinite amount of time. By definition, they are adapted since they exist. Then at some point, an accident occurs such that one organism starts multiplying. It multiplies until it occupies the entire Earth and resources become scarce. At this point of saturation, organisms start dying. The probability of dying being the same for both non-reproducing organisms and reproducing ones, at some point there will be only reproducing organisms. Thus in this new environment, reproducing organisms are adapted, whereas non-reproducing ones are not. If we look at the history of evolution, we note that the world of species constantly changes. Species do not appear to converge to some optimal state, because as they evolve, the environment changes and so does the notion of fitness.

In summary, the optimization criterion does not preexist to the optimization process, unless we consider a broad existentialist criterion such as survival, but then the optimization metaphor loses its usefulness.

New chapter : Excitability of an isopotential membrane

I have just uploaded a new chapter of my book on the theory of action potentials: Excitability of an isopotential membrane. In this chapter, I look mostly at the concept of spike threshold: the different ways to define it, its quantitative relation to different biophysical parameters (eg properties of sodium channels), and the conditions for its existence (eg a sufficient number of channels). This is closely related to my previous work on the threshold equation (Platkiewicz and Brette, 2010). It also contains some unpublished work (in particular updates of the threshold equation).

I am planning to extend this chapter with:

  • A few Brian notebooks.
  • A section on excitability types (Hodgkin classification).
  • Some experimental confirmations of the threshold equation that are under way (you will see in section 4.4.2 that current published experimental data do not allow precise testing of the theory).

I am now planning to work on the chapter on action potential propagation.

All comments are welcome.

My appeal to PLoS Computational Biology

I recently reported that one of my papers has been rejected by PLoS Computational Biology after 10 months and 4 revisions, on the ground of general interest. This has generated a little buzz. A colleague mentioned it on his blog. As a result, the editor of my paper contacted him directly to tell his version of the story, which my colleague has now reported on his blog.

Unfortunately, the editor’s story is “misleading”, to be polite. It is a shame that the review process is confidential, as it allows the journal to hide what actually happens behind their closed doors. Nevertheless, I have asked the journal for the authorization to publish the content of my appeal and their response, where I explain what happened in more detail (and more accurately). They have accepted. I have removed names of the persons involved. This illustrates one of the flaws of the current peer-review system (see this post for how it could work better).

(Just one note: the editor has apparently told my colleague that the third reviewer was a collaborator, so they could not take into account his review. Well, that’s a lie. I know because he chose to sign his review. The "collaboration" was the scientist sending me published data.)

So here it is.

Appeal

Re: Manuscript PCOMPBIOL-D-16-00007R4

So after 10 months and 4 revisions, our paper has been rejected, following the recommendation of one reviewer, because it is not considered of broad enough interest. I quote from the final editorial message: “We regret that the specific hypothesis that your manuscript is geared to dispute does not reach that level of general interest.”.

These facts being recalled, it should be obvious enough that the editorial process has gone very wrong. There were no more technical criticisms already after revision 2, on July 8th, 4 months ago, and the paper should have been accepted then. I have repeatedly asked the editors to explain why we were required to justify novelty and significance after having been required to do so much work on technical aspects. But the editors have refused to answer this simple query. Frankly, I was expecting a bit more respect for the authors that make this journal, and I do not think that explaining the journal’s policy and the decisions is so much to ask. All I know is Michael Eisen’s view, founding editor of this journal, who has cared to comment “I agree - a paper going out for review should mean it is of interest”.

This editorial process has gone beyond anything I have ever witnessed in my career in terms of absurdity and waste. Why scientists (“peers”) would voluntarily make each other’s life so unnecessarily hard instead of cooperating and debating is beyond my understanding. In the end it appears that the ego of one (important?) reviewer matters more than science, and that is very sad. This being said, I have been notified that appeals are only considered when “a) a reviewer or editor is thought to have made a significant factual error” or “b) his/her objectivity is compromised by a documented competing interest”, and since bureaucracy apparently beats reason and ethics, I will now explain how this applies.

I have already explained at length the factual errors of the first reviewer, who is apparently the only one that is trusted by the editors. This editorial message repeats some of them (no, we are not criticizing simulation results of a particular model, but the biophysical interpretation (what goes on physically), and we did so in several state-of-the-art biophysical models, not one). I will therefore focus on case (b), and attach my previous letter to the editors for reference; please also read the responses to reviewers as regards case (a), in particular to reviewer-editor Dr. YYY who has unfortunately not cared to reply to our point-by-point response that he had required from us. The editorial decisions that have led to rejecting the paper on the basis of general interest after 10 months are so bizarre that I am compelled to question senior editor Dr. YYY’s objectivity – I presume that Dr. XXX, who sent the paper for review in the first place, does consider the paper of interest. The sequence of facts speaks for itself:

- On June 6th (revision #2), the editorial message reads “We understand that Reviewer 2 was very enthusiastic, and Reviewer 3 had relatively minor comments, but we both stress that addressing Reviewer 1's reservations are essential. Indeed, it is only fair to say that it seems to us that it will be challenging to address these comments in the context of the presented results.”. The exclusive reliance on one reviewer and the presumption that we could not address the comments is rather surprising. Nonetheless, the editorial message that followed was exclusively about the match with experimental data, not about interest (“the reviewer's point about (apparently) unrealistic voltage dependencies of the currents […]”). We did successfully address these comments, pointing out that the reviewer had made factual errors (such as misreading the figure he was commenting, and discussing the results of an experimental paper he had not opened).

- On July 8th (revision #3), the editorial message was now asking to explain the novelty compared to what we had done in the past (and published in the same journal), blindly following the 3-sentence report of reviewer #1, and making no mention whatsoever to the fact that we had just answered the major (and flawed) criticisms on experimental observations, which constituted the previous editorial message. At this point we complained that we were asked to justify the novelty of our study 7 months after submission, especially when it was explicit in the introduction; nonetheless, we complied and explained again.

- On August 25th (revision #4), we were appalled to read that, instead of finally accepting the paper, senior editor Dr. YYY decided to nominate himself as a reviewer, admitting that “the latest revision is first one he has had the chance to read”. The report was not an assessment of the novelty of the paper, as would have been logical since this was what the previous editorial message was about. Instead, it was a 6 pages long report full of technical queries, making negative criticisms that, for most of them, had already been addressed in previous reports, and asking for substantial modifications of the paper.

- At this point, I replied to the editorial message and obtained no response; as the message stated “If you would like to discuss anything, please don't hesitate to contact either of us directly”, I emailed Dr. YYY, and he started his response as follows: “To answer your email, allow me to be brief, because this sort of exchange should really be going through the journal, and indeed that will be the case from now on.”. Nonetheless, we exchanged a few emails, in which he offered no explanation; in the end we agreed that I would write a point-by-point response to his six-page review, but not modify the paper. I submitted it, together with a response to the first reviewer, and a letter to the editors, on September 22nd.

- Three weeks later, on October 10th, I received a message where I was asked to edit the letter so that it could be passed on to the reviewers. Apparently the editors had not noticed the response to reviewers. It still took them three weeks to read a letter, which, considering the history of this paper, does not strike me as very respectful. I complained to Dr. YYY, who replied “We believe that you have been adequately notified by the PLoS administrative team concerning the status of your revision.”. I had to exchange several emails with Dr. XXX who realized the error. I received no apology from Dr. YYY.

- On November 11th, I received the reject decision, together with the response of reviewer #1 and, oddly enough, of reviewer #3 to which I had not replied (since there was no remaining comment). He also was surprised, since he wrote “I don’t have the expertise, authority or, honestly, the time to judge whether the new comments from Reviewers 1 & 4 are fair, or whether the authors’ responses have fully addressed them – this is clearly a job for the Editors (although hopefully not for the Editor who just became a Reviewer)”. But, editor-reviewer #4 Dr. YYY did not bother replying to my point-by-point response, which he had explicitly required.

- The final decision comes with excuses that are frankly hard to swallow. One is that the editors had failed to see the word “models” in the title. In 10 months and 4 revisions! Who can seriously believe that? And yes, the paper is about models – it is a computational biology journal (note that we have also successfully related the models to experimental observations, on request of the editors). The other excuse is that an anonymous reviewer (reviewer #2) had a conflict of interest and his reviews had to be dismissed. I am of course fine with that decision (let me simply state for the record that none of reviewers I have suggested are in such a position). But this happened in April, more than 6 months ago. Quite appropriately, the editor Dr. XXX asked for another reviewer who identified himself (Dr. ZZZ). Dr. ZZZ wrote a positive review, and in addition he read our responses to the other reviewers and wrote “the revisions of the manuscript in response to the other reviewers' comments seem entirely appropriate.”. At this point, given that no objection had been raised by any reviewer or editor on methods, results or clarity, the paper should have been accepted. Instead, the editors decided to follow a nonsensical comment from reviewer #1 alone: “unlikely to be of broad interest to the computational biology field, but could be of interest to computational neuroscientists”, which was not even consistent with his/her own first positive assessment (“this is an interesting paper”). Given that Dr. XXX sent the paper for review in the first place, this decision must originate from Dr. YYY (who at this point had not read the paper, by his own admission). I am compelled to conclude that Dr. YYY has not been objective, and in fact has been actively blocking our paper. Unfortunately, this is not the first time I witness the questionable attitude of Dr. YYY, as he has recently been a reviewer for an essay I wrote. The review process was extremely long, went over multiple rounds with massive lists of requests, where Dr. YYY basically wanted to rewrite the text to follow his own views and style. During the review process, Dr. YYY contacted me directly by email to discuss the paper, going so far as asking for co-authorship (“Indeed, the level of suggestions are approaching collaboration on this paper- something I would be happy with but I assume is not what you have in mind.”). In the same email, and while the review process was not over, he asked me for an experimental collaboration – which of course I have not followed up. I had to ask the editor to intervene to stop the madness – which he did: “Indeed your paper has been unduly delayed and I have asked the reviewer to answer me within 24 hours.”. I apologize for disclosing these email excerpts, but I have no other choice since I am asked to provide documentation. It is clear that, had I imagined that Dr. YYY could be chosen as a reviewer (which seemed unlikely given his recent track record), I would have opposed him. But I did not anticipate that he would nominate himself, or overthrow the editor’s decision without even reading my paper (by his own admission).

Therefore, I am asking that Dr. YYY is replaced by a new senior editor with a more reasonable attitude.

As far as I can see: 1) the three reviewers were initially positive on the interest of the paper; 2) the editor Dr. XXX, who as far as I can tell is the only scientist involved in this process who is a member of the computational biology community, supported our paper since he sent it for review; 3) one reviewer, who seems to be an experimental electrophysiologist (unfortunately he or she has decided to remain anonymous), reverted his subjective opinion on the paper’s interest after we have pointed out the errors in his/her report, and even then, still judged the paper interesting for the computational neuroscience community. I have failed to see to how the decision is “not trivial to reach”.

Best regards,

Romain Brette

Attached: Letter to the editors from September 16th

 

Letter to the editors, September 16th

Dear Editors,

In the previous revision, I raised serious objections regarding the abusive attitude of reviewer #1. These objections have apparently been completely dismissed, but what I have been most disappointed about is the total lack of response to these objections. I am writing this letter in the hope that this time it will be given some consideration.

This manuscript has been submitted 8 months ago. This is the fourth major revision that we have been asked to make. The responses are now totaling more than 25 pages, much longer than the article itself. We have now entered a phase where a large part of the responses consist in citing previous revisions where the issues have already been addressed. This revision reaches a new level, where a fourth reviewer is added and repeats mostly questions that we have already answered in previous revisions. Why a fourth reviewer is considered necessary after 8 months of revision is not clear, when none of the three reviewers has raised any serious concern.

I have officially asked a detailed explanation for this peculiar decision. The only response I have obtained so far is that there was “a tie” between “conflicting reviews”. So apparently the editorial decision has been based on a vote between reviewers. This is yet what I read on the journal’s website:

If reviewers appear to disagree fundamentally, the editors may choose to share all the reviews with each of the reviewers and by this means elicit additional comment that may help the editors to make a decision. That said, decisions are not necessarily made according to majority rule. Instead, the editors evaluate the recommendations and comments of the reviewers alongside comments by the authors and material that may not have been made available to those reviewers.

If one followed this process, then one would realize that:

- None of the three reviewers has any remaining objection about results, methods, or clarity of the text.

- Reviewer #2 and #3 have an overall very positive assessment of the paper and in particular of its interest. Rev #2: “This is a great revision. The authors have clarified and addressed all my previous concerns. […] I strongly believe the study is publishable as it stands”; Rev# 3: “This is a very clear and logically presented manuscript dealing with a key question in fundamental cellular neuroscience”.

- On his/her first report, reviewer #1 also made a positive assessment of the paper and of its interest: “This is a clearly written manuscript that addresses an interesting question regarding the nature of spike initiation. Specifically, the authors propose a plausible explanation […] This is an interesting paper.”.

- After two rounds of technical revisions, in which we pointed out the reviewer’s errors and to which no objection has been made, reviewer #1 changed his mood and now concludes, without any argument: “unlikely to be of broad interest to the computational biology field, but could be of interest to computational neuroscientists” (sic).

- Reviewer #3 has read our responses to the two other reviewers and concluded: “the revisions of the manuscript in response to the other reviewers' comments seem entirely appropriate.” From these facts, it appears clearly that there are in fact 3 convergent reviews. All 3 reviewers have concluded that results and methods are rigorous and the text is well written. All 3 reviewers have found the paper interesting. It might be that reviewer #1 has “voted” negatively; however I would expect the editorial decision to be based on the content of reviews and responses, which in this case is convergent, and not on the mood of one reviewer, which in this case is inconsistent between the reports. It is my understanding that an editorial decision should be based on arguments and facts, not on the reviewer’s emotions.

Nonetheless, we have replied in detail, again, to all criticisms. We have pointed out in particular the factual errors of reviewer #1. To help the editors, we have underlined the important points. We would appreciate if the editors checked for themselves whether reviewer #1 is right or not. We have also replied to reviewer/senior editor Dr YYY, although I deeply regret that this fourth version is “the first one he has had the chance to read”.

Finally, I would like to call your attention on the conclusion of reviewer #1, on which his/her recommendation is based, which requires in my opinion a clarification from the journal: “Finally, now in their third revision, the authors acknowledge that this work strongly builds on the previous resistive-coupling hypothesis, and tests whether this hypothesis is compatible with sharp spike onset (a view they have already proposed), vs the alternative proposed by Yu, of back propagation. This very specific theoretical result I feel is unlikely to be of broad interest to the computational biology field, but could be of interest to computational neuroscientists” (Please see also our response, pointing out that the said acknowledgement was clear already in the very first version.)

This recommendation makes some important presumptions about this journal’s editorial views. Therefore I would very much like to know if this journal:

- also considers that proposing a hypothesis is more important than testing one, and that only the former should be published;

- considers that interesting computational neuroscience studies do not belong to this journal. I would also very much like to know if this journal considers that it is ok for a reviewer to ask for substantial technical revisions when he/she has already decided that the paper should not be published anyway. This has been indeed a lot of work for a decision ultimately based on the mood of one reviewer.

As I have argued in this letter, it is very clear that, given the content of the reports of the 3 reviewers and of our responses, this manuscript should have been accepted already. After 8 months and 4 revisions, and no serious objection on the manuscript, I can only hope very much that this journal does not confuse rigorous peer review with author harassment.

Again, I am hoping that this letter will be seriously taken into consideration, and even perhaps responded to.

Best regards,

Romain Brette

 

Response of the editors-in-chief

Dear Dr. Brette,

Thank you for your response to the recent decision on your paper “The Basis of Sharp Spike Onset in Standard Biophysical Models”. The manuscript and your appeal letter have been carefully evaluated by Dr. XXX and the journal’s Editors-in-Chief.

We understand your frustration regarding the length and complexity of the review process, and we would like to apologize for the time taken to reach a final decision.

We would like to provide some further clarification on how the editorial decision was reached. The manuscript addresses the issue - how do cortical neuronal action potentials rise so sharply? – and after an initial evaluation, Dr. XXX found it interesting enough to merit sending out for review, so that the reviewers could assess the technical solidity of the work and the conceptual advance proposed. The paper received mixed reviews, and hence merited a revision. After several rounds of revision, Reviewer 1 remained unconvinced. In order to aid the review process, Dr. YYY volunteered to evaluate the paper in depth, and his opinion concurred with that of Reviewer 1. Dr. XXX also re-read the paper and came to the conclusion that this manuscript is critically close conceptually to the previous PLOS publications - in fact the idea was laid out clearly and beautifully in the 2013 and 2015 PLOS papers. The present manuscript is an implementation of this idea, showing that other biophysically realistic models used to examine the spike sharpness issue show the mechanism that was suggested in the 2013 and 2015 PLOS papers.

We regret that this did not become fully clear before the third revision, and we understand your disappointment with the final outcome.

However, we agree that the findings of the paper are not significant enough for PLOS Computational Biology, and we will not be reconsidering the paper. We are sorry not to be more encouraging, but we hope that you can understand the reasons for this decision.

This week's paper selection (10 November 2016)

This week I got interested in automatic patch clamp. I would like to write an open source Python package to do that: contact me if you have relevant material or expertise! (eg controlling acquisition boards; video analysis; pressure control)

 

This week's paper selection (6 October 2016)

 

Comments on the soliton model of action potential

Recently a radically new biophysical theory of action potentials has been proposed, which I will call here the “soliton theory”, according to which action potential propagation is a travelling pulse (soliton) of membrane (lipidic) lateral density, i.e., a sound wave along the axon membrane (Heimburg and Jackson, 2005; Andersen et al., 2009). In this theory, the lipid membrane undergoes a phase transition, from liquid to gel, which propagates along the axon. The electrical spike is then attributed to piezoelectric effects (mechanical changes inducing electrical potential changes). No role is attributed to proteins (ionic channels).

I start with some positive comments. Usually only the electrochemical aspects of neural excitability are considered in the field. But it is known that the electrical phenomenon is accompanied by mechanical, optical and thermal effects, which are the main focus of the soliton theory. The theory also has the merit of bringing attention to non-electrical phenomena in biological membranes, such as structural changes and mechanical effects, which are typically ignored in the field.

The theory appears to be motivated by the observation of reversible heat release during the action potential, i.e., heat is released in the rising phase of the spike and absorbed in the falling phase. Quantitatively, release and absorption have the same magnitude (experimental precision being in the range of 10-20% according to the original papers). This is not explained by HH theory. It does not mean, however, that it is contradictory with HH theory; rather, it would require some additional mechanism that is not part of the theory (there are some speculations in the literature, by Hodgkin, Keynes, Tasaki, and probably others). HH theory does not directly address mechanical changes accompanying the spike, but it does imply mechanical changes by at least two plausible mechanisms: 1) osmotic effects, i.e., water enters the cell along with Na+ influx, and exist with K+ outflux, leading to a diameter variation in phase with the spike (see e.g. (Kim et al., 2007); 2) an electrical field applied on the membrane can change the curvature of the membrane. The appeal of the soliton theory is that a sound wave produces reversible heat and mechanical variations; electrical variation is attributed to piezoelectric effects and therefore all these effects should be in phase. Thus in a way, it has some theoretical elegance. Of course, the actual biophysical mechanisms are not necessary elegant.

Let us now examine the premises and predictions of the theory. First, it is assumed that the lipidic membrane is close to a melting transition, which the authors claim occurs slightly below the body temperature of 37°C. It is rather surprising to read this starting point when the theory is meant to address the shortcomings of the HH model. Let us recall that the HH model is a model of the giant axon of squid, which is a cold-blooded animal living in the ocean. Body temperature is thus much colder and variable. But this is not the most problematic aspect of the theory; let us assume for now that the squid membrane does have the required property.

The main quantitative prediction of the theory is conduction velocity, which follows from membrane properties, and it is calculated to be around 100 m/s. The conclusion is that there is “a minimum velocity of the solitons that is close to the propagation velocity in myelinated nerves”. First, the squid axon is not myelinated (it is anyway not clear why the theory should apply to myelinated nerves rather than unmyelinated ones), and conduction velocity is around 20 m/s. In any case, 100 m/s is not the propagation velocity in myelinated nerves. It is the upper bound of conduction velocity in nerve, which varies over several orders of magnitude and is much smaller for most axons. It actually varies with diameter, quite in line with predictions from HH and cable theory (scaling with square root of diameter for unmyelinated axons; with diameter for myelinated axons). One of the main predictions of the 1952 HH paper where the model is described is conduction velocity, which is accurate within 20% (Hodgkin and Huxley, 1952); to be compared with 500% error in the soliton theory. The prediction was calculated as follows (see chapter 3 of my book in progress): the HH model was built and fitted on a space-clamped (isopotential) squid axon; then it was extended to a model of propagating spike with the cable formalism, ie by adding the axial current term (based on measurement of diameter and intracellular resistivity); then the model was run and a conduction velocity of around 20 m/s was found.

If one of the main predictions of the soliton theory is a minimum conduction velocity of around 100 m/s, then it is definitely wrong. There are of course many other aspects of the theory that are very problematic. HH theory is essentially the ionic hypothesis, ie the idea that changes in membrane potential are due to ionic and capacitive transmembrane currents. There have been numerous quantitative tests of this hypothesis, such as: the peak of the spike is well predicted by the Nernst potential of Na+, the influx of Na+ and outflux of K+ per spike (measured with radioactive tracers) are predicted by the HH model; fluorescence imaging now shows influxes of Na+ in phase with spikes. Early work by HH and colleagues have showed that the squid axon is inexcitable when extracellular Na+ is replaced by choline. All this body of work, which includes many accurate quantitative predictions of HH theory, is contradictory with the soliton theory. The authors seem to deny the existence of ionic channels, which is extremely strange. The detailed molecular and genetic structure of ionic channels is known, as well as their electrophysiological properties (see e.g. (Hille, 2001)); drugs targetting Na+ channels (for which there is huge empirical evidence) block action potentials. There is also the Na/K pump, a major contributor of energy consumption in neurons, which maintains the Na+/K+ concentration gradients necessary in the ionic hypothesis, and which seems totally absurd in the soliton theory.

As it stands, the soliton theory of spikes is contradictory with an extremely large body of experimental evidence, which is explained by HH theory (ie the ionic hypothesis) (note that there have been a number of alternative theories, eg by Ling and Tasaki).

 

Update (21.7.2016): A great resource about the evidence in favor of the ionic hypothesis is (Hodgkin, 1951). There is in fact a section dealing with heat production, where it is by the way noted that overall nerve activity does produce heat, but a quite small amount. It is also clear in the text that heat production in the ionic hypothesis is not that of the equivalent electrical circuit that is used to present the HH model – which is only equivalent in terms of the mathematical equations describing the currents, not physically. That is, the axial current does follow the expectation from the electrical circuit, since in the theory it is due to the electrical field in an electrolyte, but not the transmembrane current, which corresponds to mixing of extra- and intra-cellular solutions in addition to field effects (plus the at the time unknown mechanisms of permeability changes).

 

Andersen SSL, Jackson AD, Heimburg T (2009) Towards a thermodynamic theory of nerve pulse propagation. Prog Neurobiol 88:104–113.

Heimburg T, Jackson AD (2005) On soliton propagation in biomembranes and nerves. Proc Natl Acad Sci U S A 102:9790–9795.

Hille B (2001) Ion Channels of Excitable Membranes. Sinauer Associates.

Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol Lond 117:500.

Hodgkin AL (1951) The Ionic Basis of Electrical Activity in Nerve and Muscle. Biol Rev 26:339–409.

Kim GH, Kosterin P, Obaid AL, Salzberg BM (2007) A mechanical spike accompanies the action potential in Mammalian nerve terminals. Biophys J 92:3122–3129.