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.

Perceiving and knowing

Perceiving space is knowing where things are in the world. Or is it?

I am sitting in my living room, and there are big windows on a courtyard. The windows are sound-proof and so if I open just one, acoustical waves mostly enter the room through that window. Now someone enters the courtyard on the right, walks across it and arrives at the door on the left. If I close my eyes, I know that the person is walking from right to left. However, what I hear is the sound of someone walking, always coming from the same direction, that of the window. If someone asks me where the person is at a given moment time, I could point to the more or less correct direction, by inference. But this is not what I perceive. I always perceive the sound coming from the same direction. There is a difference between perceiving (phenomenological) and knowing (conceptual). And there is a difference between phenomenology and behavior.

Another striking example is referred pain. Referred pain is a pain that one feels at a location away from the cause of the injury. For example, in a heart attack, one may feel pain in the arm rather than in the chest. This is a known phenomenon and if you know it, you may correctly identify the location of injury in the heart when you feel pain in the arm. But it doesn't change the fact that you feel pain in the arm. You may entirely convince yourself that the injury is in the heart, and all your behavior might be consistent with that belief, but still you will feel the pain in the arm.

There are several interesting conclusions we can draw from these remarks. First, perception is not entirely reducible to behavior. Here we are touching the hard problem of consciousness (qualia): you could observe a cat turning its head to a sound source and you would think that the cat perceives that the sound came from the source, but in reality you don't know. Maybe the cat perceives it somewhere else but it corrects its movement because it knows its perception tends to be biased. With humans, you could perhaps distinguish between these possibilities because humans speak. But without this option, a purely functionalist approach to perception (in terms of relationships between sensory stimuli and behavior) misses part of the phenomenon.

Second, inference is not the same as perception. Spatial perception is not just the process of inferring where something is from sensory inputs. There is also the experience of perception, which is not captured by the objectivist view.

Spatial perception of pain (III) How can we feel pain inside the body?

I will first start with a summary of the different propositions I made in the previous post about where it hurts.

- Proposition A (independent channels): there are two independent channels, one that provides pain information (intensity or quality of pain, through pain receptors) and another one that provides spatial information (through tactile receptors or vision). The two channels are bound by co-occurrence.
- Proposition B (sensorimotor): you feel pain at a particular location because specific movements that you make produce that pain.
- Proposition B2 (sensorimotor): you feel pain at a particular location because whenever this particular activation pattern of pain receptors is present, you can manipulate this pattern or the intensity of pain by specific movements or actions.
- Proposition C (learned association): the localization of pain is inferred from the activation pattern of pain receptors (which must be spatially selective), by association with another channel that carries spatial information (e.g. tactile receptors).

Note that in A and C, I have moved the problem of spatial information to another modality, either touch or vision. We may consider that spatial information in touch and vision is constituted by sensorimotor contingencies, but it is not an important assumption here. The puzzle is the following: we can only touch our skin, the surface of our body, and we cannot see inside our body. If touch is central to the spatial perception of pain, then how is it possible that we can feel pain inside the body (say, in the stomach or in the head)?

I have discussed a similar example in spatial perception: when one hears music or speech through headphones, it usually feels like the sound comes from “inside the head”. First of all, there is a simple argument why sounds should feel as coming from your body in this case: when you move the head, the sound is unaffected, which means the source is part of your head – either on the surface (skin) or inside the head. The same argument applies to pain felt inside the body: rigid displacements of the body do not change the pain or any information associated with it. Therefore the pain is in you, not in the external world. However, this remark does not explain why pain feels inside the body and not on the skin.

I mentioned another possibility for sounds, inside as a default hypothesis: if you cannot identify the source as coming from somewhere outside, then the sound feels located inside. The default hypothesis raises a question: why does it feel located inside rather than not located at all? There is also another problem here: pain does not simply feel inside, it feels at a particular place inside the body (e.g. the stomach).

A first answer is proposition B2. Perhaps you feel a headache in the head and not in the stomach because the pain is only affected by movements of the head. In the same way, touching your stomach may alter the intensity of pain but not touching other parts. This explanation is a combination of default hypothesis (it's not on the skin so it's inside) and sensorimotor theory (B2). It is appealing but let's see how it applies to the perception of sounds inside the head. Here again, sounds do not simply feel inside the head, but at a particular place inside the head (say on the left or on the right). But no movement that you make has any impact on the sound, and so proposition B2 only explains why the sound is inside the head, but not where in the head it is.

Let us formalize the problem more precisely. Your stomach hurts. There is a pattern of activation of receptors that is characteristic of this condition, but no movement that you can make generates this pattern. In addition, in the case of auditory perception inside the head, no movement may alter this pattern. The default hypothesis is logical inference: since it is a new pattern, it must be located where I cannot produce it: in my body. But as we saw, this not sufficiently precise. To make some progress, I will start with an experiment of thought.

Imagine that in your life, you have touched only two points on your skin, points A and B. When something touches point A, you feel it located at A because you recognize the activation pattern of the tactile receptors. But what if something touches a point between A and B? One possibility would be that you don't feel it located at all, you just feel that something touches you. But it contradicts the fact that you feel sounds inside the head or pain inside the body. Another possibility is the default hypothesis: since you have never encountered the activation pattern, then you know it is neither A nor B, so you feel the touch somewhere outside of A and B. But this logical inference does not produce anything more precise. It seems to contradict the fact that we can hear sounds in our head on the left or on the right. To feel the touch somewhere between A and B requires some form of interpolation: if the new activation pattern resembles the pattern that is characteristic of A, then the touch was probably located somewhere near A; if it resembles both A and B, then it was probably located between A and B.

More generally, we can only have a finite number of experiences, and so t is unlikely that the exact activation pattern of receptors is encountered twice. Even if physical stimuli were identical, the body changes over time. Thus, it appears that we could not have any perceptual experience at all unless there is some form of interpolation. A natural proposition is then that detailed perception inside our body results from perceptual interpolation. This is not the same as logical inference, as in the case of the default hypothesis, because it necessary involves some arbitrariness: there is no way you can logically know where exactly between A and B your skin was touched if you have never encountered the activation pattern before, so the perceived location is a guess.

Now let us go back to our specific problem. How can pain be located inside our body? The idea of interpolation seems to imply that the pattern of receptor activation induced by such pains should resemble that of pains induced on the skin at opposite locations on the body. For example, pain in a joint, say the knee, should produce activation patterns resembling those of pains induced at the skin all around the knee.

There are two interesting points to note about the interpolation idea:
1) Sounds and pains located inside the body tend be less precisely localized, the location is “vague”. This means that the concept of interpolation as in picking a particular point between two points is incorrect: somehow the process of perceptual interpolation also affects the uncertainty of the location, or perhaps the perceived size.
2) How specifically are perceptual locations interpolated? In other words, what is the topology of spatial perception?