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What is computational neuroscience? (XXVII) The paradox of the efficient code and the neural Tower of Babel

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A pervasive metaphor in neuroscience is the idea that neurons “encode” stuff: some neurons encode pain; others encode the location of a sound; maybe a population of neurons encode some other property of objects. What does this mean? In essence, that there is a correspondence between some objective property and neural activity: when I feel pain, this neuron spikes; or, the image I see is “represented” in the firing of visual cortical neurons. The mapping between the objective properties and neural activity is the “code”. How insightful is this metaphor?

An encoded message is understandable to the extent that the reader knows the code. But the problem with applying this metaphor to the brain is only the encoded message is communicated, not the code, and not the original message. Mathematically, original message = encoded message + code, but only one term is communicated. This could still work if there were a universal code that we could assume all neurons can read, the “language of neurons”, or if somehow some information about the code could be gathered from the encoded messages themselves. Unfortunately, this is in contradiction with the main paradigm in neural coding theory, “efficient coding”.

The efficient coding hypothesis stipulates that neurons encode signals into spike trains in an efficient way, that is, it uses a code such that all redundancy is removed from the original message while preserving information, in the sense that the encoded message can be mapped back to the original message (Barlow, 1961; Simoncelli, 2003). This implies that with a perfectly efficient code, encoded messages are undistinguishable from random. Since the code is determined on the statistics of the inputs and only the encoded messages are communicated, a code is efficient to the extent that it is not understandable by the receiver. This is the paradox of the efficient code.

In the neural coding metaphor, the code is private and specific to each neuron. If we follow this metaphor, this means that all neurons speak a different language, a language that allows expressing concepts very concisely but that no one else can understand. Thus, according to the coding metaphor, the brain is a Tower of Babel.

Can this work?

10 simple rules to format a preprint

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Submitting papers to preprint servers (bioRxiv) is finally getting popular in biology. Unfortunately, many of these papers are formatted in a way that is very inconvenient to read, possibly because authors stick to the format asked by journals. Here are 10 simple rules to format your preprints:

  1. Format your preprint in the way you would like to read it. The next rules simply implement this first rule.
  2. Use single spacing. No one is going to write between the lines.
  3. Insert figures and their captions in the text, at the relevant place. It is really annoying when you have to continuously go back and forth between the text and the last pages. Putting figures at the end of the paper and captions yet at another place should be punished.
  4. Don’t forget the supplementary material.
  5. We don’t really need 10 rules. In fact the first rule is just fine.

Technical draft for chapter 5, Propagation of action potentials

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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?

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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.

What is computational neuroscience (XXV) - Are there biological models in computational neuroscience?

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Computational neuroscience is the science of how the brain “computes”, that is, how the brain performs cognitive functions such as recognizing a face or walking. Here I will argue that most models of cognition developed in the field, especially as regards sensory systems, are actually not biological models but hybrid models consisting of a neural model together with an abstract model.

First of all, many neural models are not meant to be models of cognition. For example, there are models that are developed to explain the irregular spiking of cortical neurons, or oscillations. I will not consider them. According to the definition above, I categorize them in theoretical neuroscience rather than computational neuroscience. Here I consider for example models of perception, memory, motor control.

An example that I know well is the problem of localizing a sound source from timing cues. There are a number of models, including a spiking neuron model that we have developed (Goodman and Brette, 2010). This model takes as input two sound waves, corresponding to the two monaural sounds produced by the sound source, and outputs the estimated direction of the source. But the neural model, of course, does not output a direction. Rather, the output of the neural model is the activity of a layer of neurons. In the model, we consider that direction is encoded by the identity of the maximally active neuron. In another popular model in the field, direction is encoded by the relative total activity of two groups of neurons (see our comparison of models in Goodman et al. 2013). In all models, there is a final step which maps the activity of neurons to estimated sound location, and this step is not a neural model but an abstract model. This causes big epistemological problems when it comes to assessing and comparing the empirical value of models because a crucial part of the models is not physiological. Some argue that neurons are tuned to sound location; others that population activity varies systematically with sound location. Both are right, and thus none of these observations is a decisive argument to discriminate between the models.

The same is seen in other sensory modalities. The output is the identity of a face; or of an odor; etc. The symmetrical situation occurs in motor control models: this time the abstract model is on the side of the input (mapping from spatial position to neural activity or neural input). Memory models face this situation twice, with abstract models both on the input (the thing to be memorized) and the output (the recall).

Fundamentally, this situation has to do with the fact that most models in computational neuroscience take a representational approach: they describe how neural networks represent in their firing some aspect of the external world. The representational approach requires defining a mapping (called the “decoder”) from neural activity to objective properties of objects, and this mapping cannot be part of the neural model. Indeed, sound location is a property of objects and thus does not belong to the domain of neural activity. So no sound localization model can ever be purely neuronal.

Thus to develop biological models, it is necessary to discard the representational approach. Instead of “encoding” things, neurons control the body; neurons are agents (rather than painters in the representational approach). For example, a model of sound localization should be a model of an orientational response, including the motor command. The model explains not how space is “represented”, but how an animal orients its head (for example) to a sound source. When we try to model an actual behavior, we find that the nature of the problem changes quite significantly. For example, because a particular behavior is an event, neural firing must also be seen as events. In this context, counting spikes and looking at the mutual information between the count and some stimulus property is not very meaningful. What matters is the events that the spikes trigger in the targets (muscles or other neurons). The goal is not to represent the sensory signals but to produce an appropriate behavior. One also realizes that the relation between sensory signals and actions is circular, and therefore cannot be adequately described as “processing”: sensory signals make you turn the head, but if you turn the head, the sensory signals change.

Currently, most models of cognition in computational neuroscience are not biological models. They include neuron models together with abstract models, a necessity stemming from the representational approach. To a make biological model requires including a model of the sensorimotor loop. I believe this is the path that the community should take.

New chapter : Excitability of an isopotential membrane

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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.

Free the journals

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These days, academic journals serve two purposes: to organize peer review, and to make an editorial selection. With internet and in particular “preprint” servers (eg biorxiv), journals are no longer necessary for distributing academic papers. It is also worth reminding that the peer review system has not always been organized in the way it is currently organized, ie with several external reviewers, multiple revision rounds, etc. For example, Nature only introduced formal peer review in 1967. Before that, the selection would be done internally by the editor.

These two missions, organizing peer review and making an editorial selection, are currently coupled. But this is neither necessary, nor a good thing. It is obvious that this coupling is not necessary. One could easily imagine a system where papers are submitted to a mega-journal (e.g. PLoS ONE, PeerJ, F1000 Research), which organizes the peer review, and then journals (e.g. Nature or Cell) make their editorial selection based on perceived “impact”, possibly using the reviews. Instead, authors must submit to each journal separately until their paper is accepted, and reviewers are asked both to check the scientific standards, which is the alleged purpose of peer review, and to judge the perceived importance of papers, which is an editorial task. This results in frustration for the authors, unnecessary delays and tremendous waste of resources. Thus, it is not a good thing.

Once a peer review system is organized (eg by mega-journals), the remaining role of journals is then editorial selection, and this could be done separately. Once we realize that, it becomes clear that very little infrastructure should be needed to run a journal. A journal issue is then just a list of papers selected by an editor, put online with the appropriate links and editorial comments. I propose that every scientist, or lab, or possibly group of interest, starts their own journal, which I will call “free journal” (see my related posts here and there). Free journals are not tied to any commercial interest; they are self-managed academic journals. Crucially, the editor makes a personal selection based on her readings, papers that she personally thinks are interesting. This means in particular that, in contrast with most journals, the editor is highly qualified. The selection is meaningful, not a collection of thumbs up/down made by disparate reviewers based on vague criteria (“impact”). It also implies that it is totally acceptable for the editorial selection to include “preprints”: the editor is a peer and therefore any featured paper is by definition peer reviewed (ie, as in Nature before 1967). I have made my own free journal of theoretical neuroscience in this spirit. I have collected some technical advice on how to make one, and I would be happy to receive any suggestion.

The bottomline is: it is very easy to make a free journal. On the technical side, one essentially needs to use a blogging system, eg WordPress. This automatically generates an RSS feed (eg one post per issue). I also put all the comments associated to the selected papers on PubPeer, with a link to the journal; this way, anyone using their plugin automatically sees that the papers have been selected in the journal when looking at them on pubmed, for example. On the editorial side, it actually represents little work, and I believe that this little amount is actually quite interesting work to do. Every scientist reads and annotates papers. All that is required to run a free journal then, is to set half a day in the month to put your notes together into a post. This helps organizing your bibliographical notes, and it is helpful for your colleagues and your students. One could also imagine coupling this writing with the lab’s journal club.

Please leave me a note if you are making your own free journal and I would be happy to link it from my journal.

My free journal: Brette’s free journal of theoretical neuroscience

Update on the book

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I am writing a book on the theory of action potentials. As I haven't published any new chapter for about 6 months, I will give a brief update on the progress of the book.

It turns out that writing a book is difficult (!). As I write the book, I get to question some aspects I take for granted and I realize they are actually not that simple. That I have learned a lot about biophysics. In turn, this tends to make the book more complicated, and so it requires some additional digestion work. I also realize that some important questions are just unresolved and require some research work. Finally, it is quite difficult to write a book while continuing the normal course of research. I started with a one hour per day habit, but this may not be optimal; I tend to spend the first half-hour trying to get back to the matter of the book. I am starting a new routine with two mornings twice a week. We will see how it goes!

These last months I have been working on the 4th chapter, on excitability of an isopotential membrane. This will contain in particular some of the material in Platkiewicz & Brette (2010) on the relation between biophysical parameters and threshold. I wanted to use the same theoretical approach to apply it to other aspects of the action potential (speed, peak etc), so that needed some more work. I realized that some approximations we had done could be enhanced, but the math is slightly more complicated. It is a challenge to keep this chapter simple. I also wanted to apply the theory to the original Hodgkin-Huxley model, but unfortunately it works moderately well. One reason is that the model was fitted to the full action potential and not to initiation (as in fact essentially all empirical neuron models). So in particular, H&H experiments show that the Na+ conductance depends exponentially on voltage at low voltage, but their model doesn't (or approximately does with a different factor). Another reason is the K+ channel has less delay than in the actual squid axon (which they acknowledge), so there is some interaction with the initial Na+ current. So I will go with a simpler approach, using a simplified excitability model. Neurons are not isopotential anyway.

I am also planning to reorganize and partly rewrite chapters 2 and 3. I find the current chapter 3 (action potential of an isopotential membrane) a bit too technical. I also want to change chapter 2 (membrane polarization) to talk about alternative theories of the membrane potential (Tasaki, Ling, etc). Then I want to insert a chapter on the ionic channel theory of action potentials, which explains the theory and discusses empirical evidence, before the chapter on the Hodgkin-Huxley model. Generally, I want to simplify the exposition. But given my rather slow progress on the book so far, I will probably postpone this and first write drafts of the following chapters.

Finally, I have worked a bit on energy consumption and pumps, and I found out that the current treatment in the literature is not entirely satisfactory (see for example my comments on a classical paper on the subject). It turns out that it is a pretty complicated problem (especially systems of pumps).

In brief, I am trying to finish a first version of the chapter on excitability of an isopotential membrane, hopefully within one month.

Brette’s micro-journal of theoretical neuroscience - February 2017

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This is the first issue of my journal of theoretical neuroscience.

 

Editorial

This month, I have selected 4 papers on spike initiation (1-4), 1 classical paper on the theory of brain energetics (5), and 1 paper on bibliometrics (6). Three of the papers on spike initiation (1-3) have in common that they are about the relation between geometry (morphology of the neuron and spatial distribution of channels) and excitability. Spikes are initiated in a small region called the axon initial segment (AIS), and this region is very close to the soma. Thus there is a discontinuity in both the geometry (big soma, thin axon) and the spatial distribution of channels (lots in the AIS). It has great impact on excitability, but this has not been very deeply explored theoretically. In fact, as I have discussed in a recent review (Brette, 2015), most theory on excitability (dynamical systems theory) has been developed on isopotential models, and so is largely obsolete. So there is much to do on spike initiation theory that takes into account the soma-AIS system.

 

Articles

1. Evans MD, Tufo C, Dumitrescu AS and MS Grubb. (2017). Myosin II activity is required for structural plasticity at the axon initial segment. (Comment on PubPeer)

A number of studies have shown that the AIS can move over hours or days, with various manipulations such as depolarizing the neuron (as in this study) or stimulating it optogenetically. Two open questions: what are the molecular mechanisms involved in this displacement? Is it actually a displacement or is it just that stuff is removed at one end and inserted at the other end? The same lab previously addressed the first question, showing the involvement of somatic L-type calcium channels and calmodulin. This study shows that myosin (the stuff of muscle, except not the type expressed in muscles) is involved, which strongly suggests that it is an actual displacement; this is in line with previous studies showing that dendrites and axons are contractile structures (e.g. Roland et al. (2014)). This and previous studies start to provide building blocks for a model of activity-dependent structural plasticity of the AIS (working on it!).

 

2. Hamada M, Goethals S, de Vries S, Brette R, Kole M (2016). Covariation of axon initial segment location and dendritic tree normalizes the somatic action potential. (Comment on PubPeer)

Full disclosure: I am an author of this paper. In the lab, we are currently interested in the relation between neural geometry and excitability. In particular, what is the electrical impact of the location of the axon initial segment (AIS)? Experimentally, this is a difficult question because manipulations of AIS geometry (distance, length) also induce changes in Nav channel and other channel properties, in particular phosphorylation (Evans et al., 2015). So this is typically a good question for theorists. I have previously shown that moving the AIS away from the soma should make the neuron more excitable (lower spike threshold), everything else being equal (Brette, 2013). Here we look at what happens after axonal spike initiation, when the current enters the soma (I try to avoid the term “backpropagate”, see Telenczuk et al., 2016). The basic insight is simple: when the axonal spike is fully developed, the voltage gradient between soma and start of the AIS should be roughly 100 mV, and so the axonal current into the soma should be roughly 100 mV divided by resistance between soma and AIS, which is proportional to AIS distance. Next, to charge a big somatodendritic compartment, you need a bigger current. So we predict that big neurons should have a more proximal AIS. This is what the data obtained by Kole’s lab show in this paper (along with many other things, as our theoretical work is a small part of the paper – as often, most of the theory ends up in the supplementary).

 

3. Michalikova M, Remme MWH and R Kempter. (2017). Spikelets in Pyramidal Neurons: Action Potentials Initiated in the Axon Initial Segment That Do Not Activate the Soma. (Comment on PubPeer)

Using simulations of detailed models, the authors propose to explain the observation of spikelets in vivo (small all-or-none events) by the failed propagation of axonal spikes to the soma. Under certain circumstances, they show that a spike generated at the distal axonal initiation site may fail to reach the somatic threshold for AP generation, so that only the smaller axonal spike is observed at the soma. This paper provides a nice overview of the topic and I found the study convincing. There is in fact a direct relation to our paper discussed above (Hamada et al., 2016): this study shows how the axonal spike can fail to trigger the somatic spike, which explains why the AIS needs to be placed at the right position to prevent this. One can argue (speculatively) that if AIS position is indeed tuned to produce the right amount of somatic depolarization, then sometimes this should fail and result in a spikelet (algorithm: if no spikelet, move AIS distally; if spikelet, move AIS proximally).

 

4. Mensi S, Hagens P, Gerstner W and C Pozzorini (2016). Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons. (Comment on PubPeer)

I had to love this paper, because the authors basically experimentally confirm every theoretical prediction we had made in our paper on spike threshold adaptation (Platkiewicz and Brette, 2011). Essentially, what we had done is derive the dynamics of spike threshold from the dynamics of Nav channel inactivation. There were a number of non-trivial predictions, such as the shortening of the effective integration time constant, sensitivity to input variance, the specific way in which spike threshold depends on membrane potential, and the interaction between spike-triggered and subthreshold adaptation (that we touched upon in the discussion). This study uses a non-parametric model-fitting approach in cortical slices to empirically derive the dynamics of spike threshold (indirectly, based on responses to fluctuating currents), and the results are completely in line with our theoretical predictions.

 

5. Attwell D and SB Laughlin (2001). An energy budget for signaling in the grey matter of the brain (Comment on PubPeer and Pubmed Commons).

This is an old but important paper on energetics of the brain, in particular: how much does it cost to maintain the resting potential? How much does it cost to propagate a spike? The paper explains some theoretical ideas to do these estimations, and is also a good source for relevant empirical numbers. It is important though to look at follow-up studies, which have addressed some issues, for example action potential efficiency is underestimated in this study. One problem in this study is the estimation of the cost of the resting potential, which I think is just wrong (see my detailed comment on Pubmed Commons; I believe the authors will soon respond). Unfortunately, I think it is really hard to estimate this cost by theoretical means; it would require knowing the permeability at rest to various ions, most importantly in the axon.

 

6. Brembs B, Button K and M Munafò (2013). Deep Impact: Unintended consequences of journal rank. (Comment on PubPeer)

The authors look at the relation between journal rank (derived from impact factor) and various indicators, for example effect sizes reported, statistical power, etc. In summary, they found that the only thing journal rank strongly correlates with is the proportion of retractions and frauds. Another interesting finding is about the predictive power of journal rank on future citations. There is obviously a positive correlation since impact factor measures the number of citations. But it is really quite small (see my post on this). What is most interesting is that the predictive power started increasing in the 1960s, when the impact factor was introduced. This strongly suggests that, rather than being a quality indicator, the impact factor biases the citations of papers (increases the visibility of otherwise equally good papers). This paper also shows evidence of manipulation of impact factors by journals (including Current Biology, whose impact factor went from 7 to 12 after its acquisition by Elsevier), and is generally a good source of references on the subject.