Back from a panel discussion on connectomics

I just came back from a panel discussion on connectomics between Moritz Helmstaedter and myself, in the Donders summer school on neural metrics. I will share my presentation when I figure out how to upload a 50 MB file on this website! (there are a few videos) In my presentation, I essentially point out that connectivity, especially anatomical connectivity (as opposed to functional connectivity), generally tells you very little about function. In particular, it doesn't help you distinguish between general theories of nervous function (say, liquid state machines or attractor networks), because those theories could easily accommodate very different types of connectivity (as long as, say, network connectivity is recurrent).

What came up in reaction to that remark is classical Popperianism. That is, the notion that a scientific theory should aim for critical experiments, experiments that could immediately disqualify that theory. So theories of brain function ought to make falsifiable predictions about connectivity, and if they don't they hardly qualify as scientific theories (the term “laziness” was used).

I have two remarks. First of all, the idea that scientific theories are theories that are falsifiable by critical experiments, and that scientific progress is essentially the performing of those experiments, is an idea that dates back from Popper's 1934 book and a few things have been written since then. Apparently many scientists are philosophically stuck in the 1930s. Thomas Kuhn's historical analysis shows that it is rarely the case that science progresses in this way. Of course it happens sometimes, but it's not the generic case. There are good reasons for that, which have been analyzed by philosophers such as Imre Lakatos. The basic remark is that a scientific theory is one that is falsifiable (the “demarcation criterion”), yes, but in practice it is also one that is falsified. There are always countless observations that do not fit the theoretical framework and those are just ignored or the theory is amended with ad hoc assumptions, which might later be explained in a more satisfactory way (e.g. the feather falls more slowly than the hammer because of some other force, let's call it “friction”). So it is very rare than a single experiment can discard a broad theory, because the outcome can often be accomodated by the theory. This can seem like a flaw in the scientific discovery process, but it's not: it's unavoidable if we are dealing with the complexity of nature; an experimental outcome can be negative because the theory is wrong, or because, say, there might be a new planet that we didn't know about (“let's call it Pluto”). This is why science progresses through the long-term interaction of competing theories (what Lakatos calls “research programs”), and this is why insisting that scientific theories should produce critical experiments is a fundamental epistemological error. Anyone who has spent a little time in research must have noticed that most hypothesis-driven papers actually test positive predictions of theories, the success of which they interpret as support for those theories.

The second remark is that, nonetheless, there is a bit of truth in the claim that theories of neural network function are difficult to confront with experiments. Certainly they are not very mature. I wouldn't say it is out of laziness, though. It is simply a very difficult task to build meaningful theories of the brain! But it is absolutely not true that they are not constrained enough because of the lack of data. Not only are they constrained, but I do not know of any such theory that is not immediately falsified by countless observations. There is not a single model of brain funtion that comes close to accounting for the complexity of animal behavior, let alone of physiological properties. How many theories in systems neuroscience are actually about systems, i.e. about how an organism might interact with an ecological environment, as opposed to describing responses of some neurons to some stimuli, interpreted as “code”? The biggest challenge is not to distinguish between different theories that would all account for current data (none does), but to build at least one that could qualify as a quantitative theory of brain function.

Importantly, if this diagnosis is correct, then our efforts should rather be spent on developing theories (by this I mean broad, ambitious, theories) than on producing yet more data when we have no theoretical framework to make use of them. This will be difficult as long as the field lives in the 1930s when it comes to epistemology, because any step towards an ambitious theory will be a theory that is falsified by current data, especially if we produce much more data. Can you make a scientific career by publishing theories that are empirically wrong (but interesting)? As provocative as it might sound, I believe you should be able to, if we ever want to make progress on the theory of brain function – isn't that the goal of neuroscience?

Sharpness of spike initiation explained with photos of moutain roads

In a previous post, I tried to explain the idea that spike initiation is “sharp” using a few drawings. The drawings represent a ball on a hilly landscape. The position of the ball represents the state of the system (neuron), and the altitude represents its energy. The ball tends to reside in positions of local minima of the energy. Spiking occurs when some energy is added to the system (stimulation with electrode or synaptic input) so that the ball is moved past a hill and then falls down:

Sharp-initiation-2

What is not seen in this drawing is what happens next. The membrane potential is reset and the neuron can fire again, in principle, but in the drawing the ball ends up on a lower valley than at the start. Biophysically, that corresponds to the fact part of the energy that was stored in electrochemical gradients of ion concentration across the membrane has been released by the spike, and so indeed the energy is now lower. Spiking again would mean falling down to an even lower valley. But since energy is finite, this has to stop at some point. In reality it doesn't stop because the neuron slowly rebuilds its electrochemical energy by moving ions against their concentration gradients with the sodium/potassium pump, which requires some external energy (provided by ATP). In the drawing, this would correspond to slowly moving up from the low valley to the high valley. Unfortunately you can't represent that in two dimensions, you need to represent a road spiraling up around a hill. This is the best photographic illustration I have found:

Tianmen-road

This is a road in China (Tianmen mountain). The neuron starts on top (red ball). With some external energy, the ball can be moved up past the barrier and then it falls. It lands on the road, but on a lower level. It can be made to spike again. Slowly, continuously, some energy is added to the neuron to rebuild its electrochemical gradients: the ball moves up the road. As long as spikes are rare enough, the neuron can continue to spike at any time (ideally, the road should spiral around the hill but it's close enough!).

Smooth spike initiation would correspond to something like that (a road in the Alps):

Alps-road

Are there alternatives to animal research?

Recently, Nikos Logothetis announced that he quit primate research because of lack of support against animal activism. Logethetis is a highly respected scientist; one of his contributions is the understanding of the relation between fMRI, a non-invasive brain imaging technique, and neural electrical activity, as recorded with electrodes. In other words, his work allows scientists to use non-invasive recording techniques in experiments instead of implanting electrodes into animal brains; in particular, it allows scientists to use humans instead of animals in some experiments. Quite paradoxically, animal activists chose him as a target in September 2014, when an animal rights activist infiltrated his lab to shoot a movie that was broadcasted on German television. The movie showed a rare emergency situation following surgery as if it were the typical situation in the lab, and it showed stress behaviors deliberately provoked by the activist (yes: the activist intentionally induced stress himself in the animal and then blamed the lab!).

This case raises at least three different types of questions: political, moral and epistemological. Here I mainly want to address the epistemological question, which is the role of animal experiments in knowledge, but let me first very briefly address the two other questions.

First, the political question: it's anybody's right to think that animals should not be used for research, but it's an entirely different thing to use manipulation, slander and terrorism rather than collective social debate for that end. There is ongoing debate about the conditions of animal experiments in research and there are strict regulations enforced by governmental bodies. As far as I know, Logothetis followed those regulations. Maybe regulations should be stricter (the moral question), but in any case I don't think it's right to let minority groups impose their own rules by fear.

Second, the moral question: is it right to use animals (either kill or inflict pain or suffering) for the good of our own species? As all moral questions (see Michael Sandel's excellent online lectures), this is a very difficult question and I'm not going to answer it here. But it's useful to put it in context. About 10 billion land animals (mostly chicken) are killed every year in the US for food. We are all aware that the living conditions of animals in industrial farms is not great, to say the least. According to official data, there are about 1 million warm-blooded animals used for research every year in the US (of which a fraction are killed), excluding mice and rats, which might account for about 10 times more. Animal use is much tightly regulated in research than in industrial farming (for example, any research project needs to be approved by an ethical committee). So animals used in research represent no more than 0.1% of all animals that are killed by humans. In other words, the effect of banning animal research would be equally obtained by having Americans eating 66.3 grams of chicken every day instead of their 67 gram daily consumption. This does not answer the general moral question, but it certainly puts the specific question of animal experimentation in perspective.

Finally, the epistemological question: what kind of science can we do without animal experiments? A number of animal rights activists seem to think that there are alternatives to animal experiments. On the other hand, many (if not most) scientists claim that virtually every major discovery, especially in medicine, has relied on animal experimentation. Since I'm a theoretical neuroscientist, I certainly think that a lot of science can be done without experiments. But it is definitely true that our civilization would be entirely different if we had not done animal experiments. And I'm not just talking about medicine or even biology. To give just one example, the invention of the electrical battery by Volta was triggered by experiments on frogs done by Galvani in the 18th century.

Probably the failure to recognize this fact comes a general misconception that the public has about the nature of research, the idea that discoveries come from specific projects aimed at making those discoveries, as if research projects were engineering projects. According to that misconception, there is medical or applied research, which is useful, and there is basic research, which does not seem to pursue any useful goal, apart from satisfying the curiosity of scientists. But the fact is: it is inaccurate to speak of “applied research”, the right terms should be applications of research. How can you invent a light bulb if you have never heard about electricity? Similarly, a lot of what we know about cancer comes from basic research on cells.

So it's clear that a large part of our knowledge and consequently our current welfare is linked to previous animal experimentation. Now there is a different question, which is: what can we do now without animal experimentation? First of all, there can be no new pharmaceutical drugs without animal experimentation. Any drug put on the market must pass a series of tests: first test the drug on an animal model, then test on humans for safety, then test on humans for efficacy. Most drugs do not pass those tests. If we ban animal tests, then we have to accept that an equivalent number of humans will face secondary effects or die. I don't think society will ever value animal life more than human life, so that means no more drugs would ever be tested.

This does not mean that all aspects of medicine rely on animal experimentation. For example, it would certainly be quite useful to develop prevention, and this could be done with epidemiological studies (although they are certainly quite limited), or with intervention studies in humans (e.g. experimenting with the diet of human volunteers). So prevention could progress without animal experimentation (although animal experiments would certainly help), but progress of cures, probably not. By pointing this out, I am not making a moral or political statement: you could well argue that, after all, better prevention might save more lives than better cures and so perhaps we should focus on the development of prevention anyway and get rid of animal experimentation. But one has to keep in mind that it means essentially giving up on curing diseases, including new infectious diseases (and those happen: in 1918, Spanish flu killed 50-100 million people).

How about basic research, which, as I pointed out above, is the basis of any kind of application? There is of course a lot of interesting research that does not rely on animal experimentation. But if you want to understand biology, you need at some point to look at and interact with biological organisms. What kind of alternative can there be to animal experiments in biology? First of all, let me make a very elementary observation: to demonstrate that something can be used as an alternative to animal experiments, you first need to compare that thing with animal experiments and so you need to do animal experiments at least initially. This is basically what Logothetis did when comparing fMRI signals with electrophysiological signals in monkeys.

I can think of only two possible alternatives: human experiments and computer models. Let's start with human experiments. I have read somewhere that we could use human stem cells for biological experiments. This may well apply to a number of studies in cellular biology. But a cell is not an organism (except for unicellular organisms), so you can't understand human biology by just studying stem cells. Human stem cells won't help you understand how the brain recovers after a stroke (or at least not without other types of experiments), or how epileptic seizures develop. You need at some point to use living organisms, and so to do experiments on living humans, not just human cells. But the kind of experiments you can do on living humans is rather limited. For example in neuroscience, which is my field, you cannot directly record the activity of single neurons, except during surgery on epileptic patients. These days a lot of human experiments are done using fMRI, which is an imaging technique that measures metabolic activity (basically oxygen in the blood vessels of the brain) at a gross spatial and temporal scale. Then to interact with a human brain, there are not many ways. Essentially, you can present something through normal sensory stimulation, for example images or sounds. The kind of information we get with that is: that brain area is involved in language. Useful maybe, but that won't tell us much about how we speak, and certainly not very much about Alzheimer and Parkinson diseases. A lot of modern biology uses mice with altered genomes to understand to the function of genes (e.g. you suppress a gene and see what difference it makes to the organism, or to the development of pathologies). Obviously this can't be done in humans. In fact, even if it were ethically right, it would not even be practical because human development is too long. So, in most cases, animal experiments cannot be replaced by human experiments. Again this is not a political or moral statement: it's anybody's right to think that animal experiments should be banned, but I'm simply pointing out that human experiments are not an alternative.

The other potential alternative is to use computer models instead of animals to do “virtual experiments”. As I am a computational neuroscientist, I can tell you with very high confidence that there is no way that a computer model might be useful for that purpose either now or in the foreseeable future. It is unfortunate that some scientists have occasionally claimed otherwise, perhaps exaggerating their claims to get large funding. We still have no idea how a genome is mapped to an organism. In fact, even when we have the complete sequence of a gene, and therefore the complete specification of the composition of the protein it encodes, we don't know how the protein will look like in a real cell, how it will fold - let alone the way it interacts with other constitutents of cell. And so we are far, very very far, from having something that remotely looks like a functional computer model of a cell, let alone of an organism. Today the only way to know the function of a gene is to express it in a living organism. The same is obviously true of the brain. No one has ever reported that a simulated neural network was conscious, so something quite important must be missing. We have some good (but still incomplete) knowledge of the electrophysiology of neurons, but little knowledge of how they wire, adapt and coordinate to produce behavior and mind. Computer models are not used to simulate actual organisms – not one computer model has ever been reported to live or think. They are used to support scientific theories, which are built through theoretical work combined with empirical (experimental) work (you can have a look at this series of posts on the epistemology of computational neuroscience, starting with this one).

So no, animal experiments cannot (for most of them) be replaced by human experiments or computer simulations. A lot of research can be done without animal experimentation, but it is a distinct type of research and it cannot answer the same questions. Of course, one can consider that those questions are not worth answering, but this is a moral and political debate, which I have just scratched in this post. But as far as epistemological questions are concerned, it is pretty clear that there cannot be much research in biology without animal experiments.

We may agree that research in biology is important enough (say, at least as important as 0.1% of the chicken we eat) and still care about the welfare of animals, try to reduce the number of animals used in research, and reduce their suffering. This is of course partly the job of ethical committees. Personally, I think one relatively simple way in which we could make animal experiments either less frequent or more useful is to impose that labs make all the experimental data they acquire publicly available, so that other scientists can use them (possibly after some embargo period). Today, for a number of reasons, the only data that come out from a lab are in the publications, generally in the form of plots, while tons of potentially useful data remain on hard drives, hidden from other scientists (see my previous post on this question). I think there is increasing recognition of that issue and potential, as seen in the emergence of data sharing infrastructures (e.g. CRCNS or the Allen Institute Brain Atlas) and in the new data sharing policies of some journals (e.g. Neuron or PLoS).

Sharpness of spike initiation explained with a few drawings

In cortical neurons, and probably in most vertebrate neurons, spikes recorded at the soma look “sharp”, ie, the voltage suddenly rises, unlike the more gradual increase seen in standard biophysical models (eg the Hodgkin-Huxley model of the squid giant axon). Recently I reviewed that phenomenon and current explanations. My own explanation, which I called the “compartmentalization of spike initiation”, is related to the fact that the main outward current at spike initiation (where “outward” is relative to the initiation site) is not the transmembrane K+ current but the axial current flowing between the axonal initiation site and the soma (see the original paper where I explain it). An important consequence is that the proportion of open Na+ channels is a discontinuous function of somatic voltage. In other words, spikes are initiated as in an integrate-and-fire model.

I came up with a few simple illustrations to explain what “sharp” initiation means. Imagine that the somatic membrane potential is represented by a ball moving on a landscape:

Spike-initiation-1
Synaptic inputs can make the ball move to right (red, excitation) or to the left (blue, inhibition). If the input moves the ball past the top of the hill, then the ball will continue going down the hill without any additional excitation: it's a spike.

Spike-initiation-2
This is more or less the standard account of spike initiation. Note that if the ball is just past the hill, then it is possible to make it move back with an appropriate amount of inhibition. Sharpness here is represented by the steepness of the slope: a steeper slope will give faster spikes, and will also make it more difficult to go back once the hill has been passed.

What I proposed is that the correct drawing is rather this:

Sharp-initiation-1
When the ball goes past the hill, the ball falls:

Sharp-initiation-2
This occurs quickly, and importantly, there is a point after which there is no possible coming back. So the situation is qualitatively different from the standard account of spike initiation: it's not just that the slope is more or less steep, but rather there is a ravine.

You will note that there is a short distance between the top of the hill and the ravine, where the ball is pushed towards the ravine but not irreversibly. This corresponds to the persistent sodium current near spike initiation, which comes from the axon.

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.