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

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

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

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

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

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

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

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

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

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

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.

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.