A comment on neural representations

I noticed by chance that my previous blog post on the metaphor of neural representations has been commented on reddit. It appeared that my argument that the representation metaphor is often misused in neuroscience was not fully understood. I will try to respond to those comments here. Here is one comment:

The brain is a representational system because it takes stimuli from the world, transduces it to a neural signal, and then acts on it.”

What is meant here is that perception is indirect in the sense that it is mediated by the activity of neurons. Certainly, this is obviously true if perception arises from the activity of the nervous system. It is also adequate to call, say, retinal activity a representation, but only in the sense that it is a representation for an external observer. For the brain, that activity is just everything it will ever “see” from the world, so it is not a representation, it is the actual input. The problem is that the case for neural representations is generally made (as in the above quote) from the point of view of the external observer, in which it is a trivial statement (outside world and neural firing are different), but then there is a semantic shift in which neural activity is assumed to form representations for the brain, which is an entirely different claim, and a much more difficult one to back up or even make sense of.

Another comment actually illustrates this point:

Suppose I'm looking at dots on a radar screen for things which are underwater. If I can never actually go underwater to compare the dots with the original stimuli, are the dots merely a "presentation" rather than a "representation? I don't think so...

Well actually: if all you ever had the chance to see in your life were those dots, then indeed they would not be representations for you, they would just be dots on the screen. They become representations once you know they can stand for submarines or whales.

There is another sense of representations that is a bit less trivial, and which was posted as a comment to my post:

Abilities like speech perception would be impossible without representation, as each instantiation of a word is unique (noisy).”

What is meant here is that representations are needed for the formation of perceptual categories. But here the term “representation” is inadequate. A sculpture of a man is not a category of man, it's just a piece of stone that looks like a man. What is meant here is rather abstraction, not representation.

The compartmentalization of spike initiation

A couple of years ago, I proposed a new view on the initiation of spikes, which explains why spike initiation is “sharp” - i.e., spikes seem to rise suddenly rather than gradually. I reviewed that hypothesis recently along with two other hypotheses. I have found it quite difficult to explain it in a simple way, without relying on the equations. After reading the description of spike initiation in a textbook (Purves), I came up with a possibly simpler explanation.

In Purves et al. “Neuroscience”, you find the following description, which is based mostly on the work of Hodgkin and Huxley on squid giant axons:

The threshold is that value of membrane potential, in depolarizing from the resting potential, at which the current carried by Na+ entering the neuron is exactly equal to the K+ current that is flowing out. Once the triggering event depolarizes the membrane beyond this point, the positive feedback loop of Na+ entry on membrane potential closes and the action potential “fires”.

This description corresponds to an isopotential model of neuron. There is an ambiguity in it, which is that initiation actually occurs when the sum of Na+ current and stimulation current (electrode or synaptic) equals the K+ current, so the description is correct only if the current is a short pulse (otherwise for a current step the threshold would be lower).

The active backpropagation hypothesis, put forward by David McCormick to explain the sharpness of spike initiation is as follows: a spike is initiated as described above in the axon, and then it actively backpropagated (that is, with Na channels) to the soma. On its way to the soma, its shape becomes sharper. I discussed in my review why I think this explanation is implausible, but it is not the point of this post.

The compartmentalization hypothesis that I proposed differs in an important way from the textbook explanation above. The site of initiation is very close to the soma, which is big, and the axonal initial segment is very small. This implies that the soma is a “current sink” for the initiation site: this means that when the axon is depolarized at the initiation site, the main outgoing current is not the K+ current (through the axonal membrane) but the resistive current to the soma. So the textbook description is amended as follows:

The threshold is that value of membrane potential, in depolarizing the soma from the resting potential, at which the current carried by Na+ entering the axonal initial segment is exactly equal to the resistive current that is flowing out to the soma. Once the triggering event depolarizes the membrane beyond this point, the positive feedback loop of Na+ entry on membrane potential closes and the action potential “fires”.

The difference is subtle but has at least two important consequences. The first one is that the voltage threshold does not depend on the stimulation current, and so the concept of voltage threshold really does make sense. The second one is that the positive feedback is much faster with compartmentalized initiation. The reason is that in the isopotential case (explanation 1), charging time is the product of membrane resistance and membrane capacitance, which is a few tens of milliseconds, while in the compartmentalized case, it is the product of axial resistance and membrane capacitance. The membrane capacitance of the axon initial segment is small because its surface is small (and the axial resistance is not proportionally larger). This makes the charging time several orders of magnitude smaller in the compartmentalized case.

Metaphors in neuroscience (IV) - Plasticity

The next metaphor I examine is the brain is plastic. In particular, synapses are plastic: they change with activity. But this is not the same thing as saying that synapses are dynamic. Synapses are plastic means that synapses are objects that can change shape while keeping the same substance. Specifically, they can be manipulated into different shapes. Plasticity is a possibility for change that is 1) limited in that only the shape and not the substance is changed, 2) persistent, 3) reversible, 4) mediated by an external actor. For example, cell death is a change but it is not plasticity; developmental changes are also not considered as plasticity even though they can be activity-dependent. These two examples are irreversible changes and therefore not cases of plasticity. Internal changes entirely mediated by intrinsic events would not normally be called plasticity. Transient changes would also not be called plasticity: for example a change in spike threshold after firing is called adaptation or accommodation, not plasticity.

This is quite clearly a metaphor, which carries a particular view on how neural structures change. For example, part of what we describe as synaptic plasticity actually corresponds to the elimination of synapses or of receptors (synaptic pruning), and therefore might be better described by the sculpting metaphor. The metaphor also hides the fact that the substance that makes all those structures is continually renewed (protein turn-over), and this is quite different from a plastic object. This is in fact quite different from an object. The persistence of shape (e.g. of a synapse) is mediated by active processes (which involve gene expression), as opposed to passive persistence of a plastic object. Changes of shape then involve interaction with those processes, rather than direct manipulation.

Metaphors in neuroscience (III) - Neural representations

A commonplace in neuroscience is to say that the brain represents the world. In particular, sensory systems are thought to represent images or sounds. A representation is an object, for example a picture or a sculpture, that is meant to be recognized as another object. Both the original object and its representation are to be presented to the same perceptual system and recognized by that system as perceptually similar. The idea that the perceptual system itself might represent an external object seems quite peculiar: it seems to entail that there is a second perceptual system that sees both the external object and the representation made by the first perceptual system. The metaphor cannot apply in this way. But then what do people mean when they say that the brain represents the world? A clue might be provided by this quote from David Marr's book “Vision” (1982):

If we are capable of knowing what is where in the world, our brains must somehow be capable of representing this information.”

Here “knowing” cannot simply mean acting as a function of the external world, because it has been well argued that representations are not necessary for that – simple control systems can be sufficient (see e.g. Rodney Brooks and Braitenberg's vehicles). Thus “knowing” must be meant in a stronger sense, the ability of manipulating concepts and relating them to other concepts. If it is assumed that anything mental is produced by the brain, then somehow those concepts must be grounded in the activity of neurons. In what sense does that activity form a “representation” of external objects? For this metaphor to make sense, there must be a system that sees both the original object and its mental representation, where the representation is an object that can be manipulated. The possibility of mental manipulation entails working memory. So for the brain, representing the world means producing persistent neural activity, structured in such a way that it can be compared with the direct sensory flow coming from the external world.

What is surprising is that Marr and many others do not generally use the representational metaphor in this proper way. Instead, the activity of sensory systems, for example the primary visual cortex, is seen as representing the external world, in the same way as a photograph represents the external world. But unless it is meant that the rest of the brain sees and compares retinal activity and cortical activity, cortical activity is a presentation, not a representation. It might be a representation for an external observer (the one that sees both the world and the photographs), but not for the brain. Thus the metaphorical idea that mental/neural representations mediate perception is somewhat self-contradictory, but unfortunately it is one of the dominant metaphors in neuroscience.

P.S.: see this later comment

Metaphors in neuroscience (II) - Neural firing

Neurons communicate by means of short electrical impulses. We say that neurons fire, spike, or discharge. We speak of spikes, impulses, discharges or action potentials. What concepts do these metaphors convey?

“Spike” seems to refer to the shape of the action potential when looked at on a voltage trace, ie, there is an abrupt rise and fall of the potential. The action potential is quite a different notion: it is a particular form of potential that allows some form of action. That is, the terms action potential convey the notion that those potentials, unlike other ones (subthreshold potentials), have an effect on other neurons. This is a notion that is strikingly not representational.

Firing, impulse and discharge add another aspect: an action potential releases energy. The metaphor is rather accurate as energy is stored in electrochemical gradients across the membrane and the opening of ionic channels releases some of that energy. Firing also conveys a notion of movement: the energy is targeted to some particular place, the axonal terminals. The metaphor is only partially accurate, because when firing a gun, energy is only released at firing time and then the bullet moves to its target. But in neurons, propagation is active and energy is released all along the axon. Thus a better metaphor would be that the neuron ignites, where the axon progressively burns. On the other hand, in myelinated axons, energy is released at discrete locations (Ranvier nodes), so the neuron could be seen as firing in sequence towards the next node: between two nodes, there is a movement that does not use additional energy, as in firing a bullet (dominoes could also be an adequate metaphor). So perhaps a mylienated axon fires (repeatedly), but an unmyelinated axon ignites!

“Discharge” is an interesting term because it relates to a former theory of action potential. The metaphor suggests that the membrane is an electrically charged capacitor, and it gets discharged during the action potential. This seems to correspond to Bernstein's theory (beginning of the twentieth century), according to which the negative resting potential is due to a gradient of potassium concentration across the membrane and the action potential corresponds to a non-selective increase in membrane permeability, resulting in a decrease of the membrane potential (in absolute value). But in 1939, Hodkgin and Huxley made the first intracellar recording of an action potential in an animal and they found out that the membrane potential did not go to 0 mV but actually exceeded it quite substantially. So the discharge metaphor entails a particular model, but one that is now outmoded.

Finally, related to the concept of firing is the notion of threshold. When the membrane potential reaches a threshold, the neuron fires. A threshold is a spatial delimitation between two rooms, or between the outside and the inside of a house. It conveys the notion of a qualitative change. Before threshold, you are outside; after the threshold, you are inside. So the threshold metaphor entails the all-or-none law of neural activity: there is a spike or there is no spike.

In the integration metaphor, inputs and outputs are seen as objects (things that can be manipulated). Specifically, neural output (membrane potential) is a container (inputs are integrated into the membrane potential). In contrast, in the firing metaphor (and related metaphors), neural outputs are seen not as objects but as discrete, timed actions on other neurons (the action potential), which release energy. Thus the integration metaphor and the firing metaphor convey somewhat different views on neural function. Perhaps speculatively, I would suggest that the disonance between these two metaphors is the deep source of the firing rate vs. spike timing debate. In the integration metaphor, the neuron is a container and what matters for a container is what it contains, i.e. the number of inputs. When exactly those inputs come into the container is relatively unimportant. The integration metaphor conveys a representational view of the brain and is consistent with the rate-based view. In the firing metaphor, what is emphasized is the fact that neurons spend energy to act on each other. Actions are events, and therefore time is possibly important. This view is not representational but rather interactional or dynamicist.

An important question is how empirically accurate these metaphors are, especially when some are inconsistent. I have discussed this question indirectly in my series on the firing rate vs. spike timing debate. I will simply point out that the firing metaphor is fairly accurate, as briefly discussed above, possibly if firing is replaced by ignition. There is a release of energy that propagates and acts on other neurons, which occurs discretely when some condition is met. The integration metaphor, on the other hand, is rather loose. It cannot be accurate without substantial qualifications. The main effect of a presynaptic spike is generally short-lived, so an input could be said to be integrated, but only with the qualification that it gets out quickly. The effect of several input spikes on the membrane potential also depends on their relative time of arrival, and this fact does not fit the container metaphor very well.

Metaphors in neuroscience (I) – Neural integration

I have just read Lakoff & Johnson's “Metaphors we live by” (see this summary), which is a classic brilliant book about the use of metaphor in both language and the way we think. The thesis is that we constantly use metaphors when we speak, especially about abstract concepts, and it actually structures the way we think about those concepts, even though we normally don't even notice we speak in metaphors. Typically we tend to speak of abstract concepts by using metaphors that are more concrete. For example, a theory is a building (it has foundations, it requires support and it can fall apart), understanding is seeing (a clear argument; a point of view; an eye opener). Time is an abstract concept that is very difficult to speak of without using metaphors, for example time as space and duration as distance (an hour long, a point in time, etc).

Metaphors are also widespread in science. Because they structure our thought and often go unnoticed, it is quite interesting to identify them: what ways of thinking do scientific metaphors convey, and other ways are possible? For example, neurons code and neurons compute. These are two quite distinct metaphors. In the coding metaphor, the neuron hears about the world and speaks to other neurons, in the language of electrical impulses. In the computing metaphor, the neuron is a sort of factory that processes inputs. But you could also say that neurons push each other, where axonal terminals are hands and spikes are mechanical energy. This is just as true as the metaphor neurons speak to each other (coding metaphor). Each of these metaphors conveys a different way of seeing the activity of neurons (bonus: check the metaphors in this sentence!).

In this series, I want to explore some of the metaphors in neuroscience. I start with two concepts: “integration” (this post) and “firing” (next post). Those two words are found in the integrate-and-fire model, but clearly they appear throughout the neurophysiological literature. Neuron function is generally described as a two-stage process: synaptic integration followed by firing.

The neuron integrates its synaptic inputs: the neuron is a container, and the inputs come into the container. The inputs are objects, they accumulate within the neuron, so after integration they are in the neuron – possibly in a “processed” form (neuron = factory). So in integration there is a concept of summation: inputs add up. Of course there can be qualifications: the integration could be “nonlinear”. But the very fact that “nonlinear” is a qualification means that the basic concept is that of summing up inputs that come in. What is important to realize here is that it is a metaphor, that is, you could imagine other metaphors to think about the propagation of electricity in neurons. For example, you could think of neurotransmitters as pushing dominoes placed all along the neuron; specific things could happen at branch points depending on when the dominoes get pushed on each branch. In both metaphors we are saying that the output depends on the inputs, but each metaphor emphasizes or hides certain aspects of that relation. For example, in the first metaphor, time is deemphasized and is replaced by counting. In the second metaphor, the notion of “summing up” doesn't even make sense because activity is transient.

Importantly, the two metaphors convey very different models of neural function. The integration metaphor entails a model in which the neuron's membrane is gradually charged up and down by synaptic currents. It deemphasizes space by hiding the notion of electrical propagation; it deemphasizes time by seeing inputs as objects (which can be counted) rather than activity (which is transient). In terms of mathematical models, the integration metaphor corresponds to the “perfect integrator” (i.e., a capacitor plus input currents). Of course there are variations around that model, but the prototype is the integrator. The domino model cannot be understood as a variation of an integrator. The domino metaphor views neural activity as intrinsically transient, and there is a clear relation between the timing of inputs and the timing of outputs. A coincidence detection model, in which an output spike is generated when synchronous inputs arrive at the cell, might fit the domino metaphor better than the integration metaphor.

Thus, to talk about synaptic integration or to say that the neuron integrates inputs is not a neutral statement. It entails a particular way of seeing neural activity, specifically a way that deemphasizes the notion of activity and views inputs and outputs as objects. This metaphor is consistent with other dominant metaphors in neuroscience, in particular the notion of representations, which sees neural activity as objects that can be manipulated (specifically, as pictures). Thus, the integration metaphor refers to the more general metaphor neural activity = object. A weakness of this dominant metaphor is that there is a strong disonance between the notion of activity, which is transient, and the notion of object, which is persistent. This disonance appears with the next metaphor: neurons fire.

Connectomics bashing (III) - Connectomics vs genomics

In my first post, I argued that 1) to understand a complex organized system, one needs to understand the organization rather than have a detailed description of the structure, 2) an incomplete or imprecise measurement of structure, as is necessarily the case with any physical measurement, does not in general convey the functionality of the system. In his reply, Bernhard Englitz rightly argued that the knowledge of the connectome is nonetheless useful. I do not disagree with that claim, and I do believe that connectomics is certainly a great neuroanatomical tool. So the question is: what can and what cannot offer the knowledge of the connectome?

First of all, a quick comment. Bernhard complained that connectomics is often portrayed as an extreme claim. I was only referring to published texts by supporters of connectomics. One is Seung's book, Connectome. Arguably, this is a popular science book so I agree that the claims in the book may be overstated for the sake of communication. But there are also articles in peer-reviewed journals, which I think make quite similar claims, for example “Structural neurobiology: missing link to a mechanistic understanding of neural computation”, Nature Rev Neuro (2012), by Denk, Briggman and Helmstaedter. The basic claim in that text and in Seung's book is that there is a strong relationship between structure (specifically, connectome) and function, and implicitly that connectionism provides an adequate account of neural function. For example, both the paper above and Seung's book envisage the reading of memories from the connectome as a distinct possibility (I wouldn't say that they make a strong claim, but they certainly consider it as a reasonable possibility). I wouldn't necessarily qualify this view as extreme, but I simply do not think that the structure-function relationship is so strong in this case.

In this post, I want to address a particular comparison that is often used to emphasize the potential of connectomics: the comparison between connectomics and genomics, in particular the human genome project. This comparison is also used by other large initiatives, for example the Human Brain Project. There is no doubt that the human genome project was useful, and that sequencing entire genomes is a very useful tool in genomics. But what about the relationship between structure and function? How do you know, for example, the function of a particular gene that you have sequenced? You would know by manipulating the gene (e.g. knock-out) and looking at functional changes in the organism; or you would examine a large database of genomes and look for correlates between that gene and function (for example pathologies). In both cases, function is observed in the organism, it is not derived from the knowledge of the genome. As far as I know, we don't know how to predict the function of a gene from its DNA sequence. So even if there were a one-to-one relationship between structure (DNA) and function, the knowledge of the structure would not tell us what that relationship is and so it would not tell us the function. In addition to this, we know that the relationship between structure and function is not one-to-one in the case of the genome: this is what epigenetics is all about (and so the example of genomics is completely in line with the arguments of my first post).

So, if the structure-function relationship is similarly strong in connectomics as in genomics, then 1) the connectome itself will provide little direct insight into brain function, 2) insight might come from correlating connectomes and the function of brains (in a yet to be specified way), 3) the connectome will not determine brain function. In particular, point (3) makes it quite unlikely that memories can be inferred from the connectome. I would also like to point out that a complete comparison with genomics regarding point (2) requires the possibility not only to measure the connectome but also to finely manipulate the connectome and observe functional changes in living organisms. I do not see how current connectomics technologies (electron microscopy) could make it possible. There is a critical limitation, at least for the foreseeable future, which is that the connectome can only be measured on dead organisms, in contrast with DNA sequencing, which greatly limits the possibilities of connectome manipulation or diagnosis based on (detailed) connectome.

Finally I want to point out that the structure-function relationship is likely to be weaker in connectomics than in genomics. First, there is a fundamental difference: the DNA is a discrete structure (4 bases), the connectome is not, if you consider synapse strength. So it should be possible to exactly measure the graph of connectivity in the same way as you can sequence DNA, but measuring the extended connectome (with synaptic strength or delays) can only be measured with limited precision. A second, probably more serious difference, is that while there is a concept of gene that has some functional unity and correspond to a well-identified portion of the genome, there is no equivalent concept in the connectome. In genomics, one can knock-out a gene or look for structure-function correlates for different versions of the same gene. In connectomics, there is in general no similarly well-defined portion of the connectome that can be identified across individuals. This might be partially possible when considering connections made onto well-identified sensors and effectors (say, in the retina), but comparing cortical connectomes across individuals is another story.

So connectomics suffers from the same problems about structure-function relationship as genomics, but quite a bit worse. Again I am not saying that it is not a useful set of tools. But it is just this: additional measurement tools in the hands of neuroscientists, not fundamental data that would specify or in general even suggest brain function. One example where it might be quite useful is in finding new markers of neurological disorders. It has been hypothesized that some neurological diseases are “connectopathies”, ie are due to abnormal connections. Here as in genomics, one could compare the connectomes of subjects that have suffered from those diseases and of control subjects and perhaps identify systematic differences. Whether those differences are correlates of the disease or have a more causal role in the disease, such an identification could certainly help understand the origins and mechanisms of the pathologies. This is a completely different claim than saying that brain function can be understood from the connectome: in this case brain function is observed at the functional level, and simply correlated with some particular element of structure, it is not the structure itself that informs us of function.

In summary: 1) the structure-function relationship is not that strong in genomics and is certainly weaker in connectomics, and more importantly the structure-function relationship is unknown, 2) connectomics is more limited as a set of tools than genomics, 3) what we should expect from connectomics is not so much the possibility to infer brain function from connectome as to correlate some aspects of brain function or dysfunction with connectomes.

Connectomics bashing (II) - Invited post by Bernhard Englitz

My friend and colleague Bernhard Englitz reacted to my previous post on connectomics. What follows is his defense of connectomics:

The connectomics viewpoint is often portrayed as an extreme claim, namely that knowing the connectome (with or without weights) is the sole key to understanding the brain. Certainly, some of its proponents are guilty of generating this viewpoint, however, from a plain funding level, it can be understood why claims are exaggerated (the Human Brain Project being a good example where extreme claims can lead to extreme payoffs). I contend however, that even the strongest proponents of connectomics are far from believing their claims. Much rather I claim that the value of the connectome would not lie in a final explanation, but a solid basis for further exploration.

Across all domains of life, availability of data/resources enables new studies, the genome probably being the best example in this respect. The availability of the genome did not solve many fundamental questions that existed before, but it opened the space for new question, such as systematic interorganism comparison, genome wide searches for homology etc. The value of the availability of one or multiple genomes in these particular questions was that one could suddenly make certain statements with safety, rather than with a large amount of speculation.

Also, proponents of connectomics do not emphasize the value of the structural connectome, because they think that functional data/neural activity are unimportant, but they are simply not as available with the current technology. Science has always been opportunistic and profited from new techniques to address or open certain questions from a new perspective (which does not exclude profiting from ideas equally). Blockface imaging is available and can be applied today, whereas a lot of functional methods are on the verge of scaling to large systems, but not achieving a similar resolution or range as methods in connectomics.

However, new methods always come at a cost, which was again demonstrated well by the human genome projects, whose cost must seem like a gigantuan waste of money in retrospect, given the steep decline in sequencing costs. From my perspective, drastic shifts in the funding landscape are maybe the biggest dangers to fear, in the light of the potential of a much lower price tag just a few years from now. On the other hand, methods development and scientific discovery often go hand in hand, and some of the saving are only realized by public investment, thus creating a market for new techonologies. Hence, hardly anyone doubts that the availability of connectomical data would be useful for a range of questions, the main question is ‘now’ or ‘tomorrow’ (although this decision is clearly complex).

But what are the domains in which the availability of a connectome could really make a difference in neuroscience? Before addressing this question I would like to caution against the use of analogies, since the differences are subtle and may not transfer. Taking Romain’s example of the membrane, it is clear that the question posed about the membrane’s basic nature does not profit from the knowledge of all lipids and proteins that form the membrane, but many essential questions relating to compartmentalization of a cell, trafficking, expression of proteins, would profit. Undoubtedly we would have a much harder time thinking about the space of possibilities in a cell without precise knowledge of the cell’s structure. I interpret Romain’s example to illustrate that ‘certain questions’ will not profite from overly detailed knowledge, and in some cases too much data can even inhibit conceptual development.

However, I contend that many questions in neuroscience are of a different kind and will profit strongly from the availability of a connectome. These questions reach from subcellular structure to network structure. For example, current modeling approaches of cortical neurons are usually based on detailed reconstructed cells, or simplified estimates of individual cells. Both approaches - the first to mimick reality , the second to make it minimal and thus tractable - suffer from the lack of the RIGHT reductions and the RIGHT level of detail. Connectomics can provide a tool to arrive at this middle ground, by offering the possibility to quantify typical structures, their relative occurrence and variability. Such a family of model neurons, will be free from the particularities of the single precise neuron, and will be less dependent on the creative reduction previously performed, based on small data-sets (clearly this has been realized before, and pre-connectomics attempts have tried to close this gap, but a publicly available connectome would open the possibilities to put a wide range of modelling efforts on safer ground, rather than single labs, making insular, small, guarded advances). Similar arguments hold for the statistics of connectivity in neural networks, where we are currently witnessing a wide range of ‘random-connected’ network studies, which may ultimately be of little use, depending on how well their assumptions are matched. Again, to emphasize, the goal has to be finding the right statistics, not replicating the exact structure.

In a nutshell, I think increased accountability and the arbitrariness of assumptions could be widely reduced in this case, thus opening a new era of midlevel modelling, i.e. quite the opposite of what the Human Brain Project is trying to achieve, and Romain is criticizing.