Recently a radically new biophysical theory of action potentials has been proposed, which I will call here the “soliton theory”, according to which action potential propagation is a travelling pulse (soliton) of membrane (lipidic) lateral density, i.e., a sound wave along the axon membrane (Heimburg and Jackson, 2005; Andersen et al., 2009). In this theory, the lipid membrane undergoes a phase transition, from liquid to gel, which propagates along the axon. The electrical spike is then attributed to piezoelectric effects (mechanical changes inducing electrical potential changes). No role is attributed to proteins (ionic channels).

I start with some positive comments. Usually only the electrochemical aspects of neural excitability are considered in the field. But it is known that the electrical phenomenon is accompanied by mechanical, optical and thermal effects, which are the main focus of the soliton theory. The theory also has the merit of bringing attention to non-electrical phenomena in biological membranes, such as structural changes and mechanical effects, which are typically ignored in the field.

The theory appears to be motivated by the observation of reversible heat release during the action potential, i.e., heat is released in the rising phase of the spike and absorbed in the falling phase. Quantitatively, release and absorption have the same magnitude (experimental precision being in the range of 10-20% according to the original papers). This is not explained by HH theory. It does not mean, however, that it is contradictory with HH theory; rather, it would require some additional mechanism that is not part of the theory (there are some speculations in the literature, by Hodgkin, Keynes, Tasaki, and probably others). HH theory does not directly address mechanical changes accompanying the spike, but it does imply mechanical changes by at least two plausible mechanisms: 1) osmotic effects, i.e., water enters the cell along with Na+ influx, and exist with K+ outflux, leading to a diameter variation in phase with the spike (see e.g. (Kim et al., 2007); 2) an electrical field applied on the membrane can change the curvature of the membrane. The appeal of the soliton theory is that a sound wave produces reversible heat and mechanical variations; electrical variation is attributed to piezoelectric effects and therefore all these effects should be in phase. Thus in a way, it has some theoretical elegance. Of course, the actual biophysical mechanisms are not necessary elegant.

Let us now examine the premises and predictions of the theory. First, it is assumed that the lipidic membrane is close to a melting transition, which the authors claim occurs slightly below the body temperature of 37°C. It is rather surprising to read this starting point when the theory is meant to address the shortcomings of the HH model. Let us recall that the HH model is a model of the giant axon of squid, which is a cold-blooded animal living in the ocean. Body temperature is thus much colder and variable. But this is not the most problematic aspect of the theory; let us assume for now that the squid membrane does have the required property.

The main quantitative prediction of the theory is conduction velocity, which follows from membrane properties, and it is calculated to be around 100 m/s. The conclusion is that there is “a minimum velocity of the solitons that is close to the propagation velocity in myelinated nerves”. First, the squid axon is not myelinated (it is anyway not clear why the theory should apply to myelinated nerves rather than unmyelinated ones), and conduction velocity is around 20 m/s. In any case, 100 m/s is not the propagation velocity in myelinated nerves. It is the upper bound of conduction velocity in nerve, which varies over several orders of magnitude and is much smaller for most axons. It actually varies with diameter, quite in line with predictions from HH and cable theory (scaling with square root of diameter for unmyelinated axons; with diameter for myelinated axons). One of the main predictions of the 1952 HH paper where the model is described is conduction velocity, which is accurate within 20% (Hodgkin and Huxley, 1952); to be compared with 500% error in the soliton theory. The prediction was calculated as follows (see chapter 3 of my book in progress): the HH model was built and fitted on a space-clamped (isopotential) squid axon; then it was extended to a model of propagating spike with the cable formalism, ie by adding the axial current term (based on measurement of diameter and intracellular resistivity); then the model was run and a conduction velocity of around 20 m/s was found.

If one of the main predictions of the soliton theory is a minimum conduction velocity of around 100 m/s, then it is definitely wrong. There are of course many other aspects of the theory that are very problematic. HH theory is essentially the ionic hypothesis, ie the idea that changes in membrane potential are due to ionic and capacitive transmembrane currents. There have been numerous quantitative tests of this hypothesis, such as: the peak of the spike is well predicted by the Nernst potential of Na+, the influx of Na+ and outflux of K+ per spike (measured with radioactive tracers) are predicted by the HH model; fluorescence imaging now shows influxes of Na+ in phase with spikes. Early work by HH and colleagues have showed that the squid axon is inexcitable when extracellular Na+ is replaced by choline. All this body of work, which includes many accurate quantitative predictions of HH theory, is contradictory with the soliton theory. The authors seem to deny the existence of ionic channels, which is extremely strange. The detailed molecular and genetic structure of ionic channels is known, as well as their electrophysiological properties (see e.g. (Hille, 2001)); drugs targetting Na+ channels (for which there is huge empirical evidence) block action potentials. There is also the Na/K pump, a major contributor of energy consumption in neurons, which maintains the Na+/K+ concentration gradients necessary in the ionic hypothesis, and which seems totally absurd in the soliton theory.

As it stands, the soliton theory of spikes is contradictory with an extremely large body of experimental evidence, which is explained by HH theory (ie the ionic hypothesis) (note that there have been a number of alternative theories, eg by Ling and Tasaki).

Update (21.7.2016): A great resource about the evidence in favor of the ionic hypothesis is (Hodgkin, 1951). There is in fact a section dealing with heat production, where it is by the way noted that overall nerve activity does produce heat, but a quite small amount. It is also clear in the text that heat production in the ionic hypothesis is not that of the equivalent electrical circuit that is used to present the HH model – which is only equivalent in terms of the mathematical equations describing the currents, not physically. That is, the axial current does follow the expectation from the electrical circuit, since in the theory it is due to the electrical field in an electrolyte, but not the transmembrane current, which corresponds to mixing of extra- and intra-cellular solutions in addition to field effects (plus the at the time unknown mechanisms of permeability changes).

In previous posts, I have tried to explain why spike initiation is “sharp” or abrupt, basically as in an integrate-and-fire model. The explanation relies on the fact that spikes are initiated in the axon, next to the soma. What may not be so obvious is how this differs from the textbook account of spike initiation. That textbook account would go as follows: first, the spike is initiated at a distal site in the axon, through the interplay between transmembrane currents, then the spike is propagated to the soma. On the course of its propagation, its shape changes and becomes sharper (see the explanation in this paper for example).

This account is wrong on several levels. But fundamentally, it has to do with the inadequacy of the transportation metaphor. Let us take a step back. What do we mean when we say that a spike propagates along an axon? In fact, not much actually moves physically along the axon. There is very little ion movement in the longitudinal direction. Ions move mostly through the membrane, in the radial direction. It produces a spatiotemporal pattern of electrical activity, and the reason we say a spike propagates is that in certain conditions that pattern is a solitary wave for which we can define a velocity. This is actually how Hodgkin and Huxley predicted spike velocity in the squid giant axon, by postulating that the potential V(x,t) can be written as U(x-v.t), and then looking for the velocity v that was consistent with their equations. This velocity has actually nothing to do with the velocity of the ions that carry the electrical charges. So basically we often describe electrical activity in axons in terms of transportation of spikes, but one should keep in mind that this is just a metaphor.

Now when we say that there is a spike that moves and gets transformed on its way, we should realize that the metaphor has reached its limits. As nothing actually gets transported, we are not saying anything else than there is an irregular spatiotemporal pattern of activity. That is, we are not saying anything at all. That is all the more true when we are talking of time scales shorter than the duration of a spike (as in the backprogation from initiation site to soma).

The transportation metaphor, unfortunately, is highly misleading. It leads to incorrect reasoning in this case. Here is the reasoning in question. The onset of a spike at the axonal initiation site is smooth. The onset of a spike at the soma is sharp. Therefore, the spike onset gets sharper through the propagation from initiation site to soma. On the surface, the reasoning seems flawless. But now here is a disturbing fact: from the spike shape at the axonal initiation site, I can make a quantitative prediction of onset rapidness at the soma, without knowing anything of what's in between (that's in a paper being submitted). Therefore, onset rapidness at the soma is determined by properties of spike initiation, not of propagation. How can that be?

The flaw is this: in the transportation metaphor, somatic and axonal spikes are implicitly seen as local events both in space and time, which can then be related by the transportation metaphor (object at place A and time t1 travels to place B at time t2). As mentioned above, the relevance of the transportation metaphor is questionable at this spatial and temporal scale, all the more when what is being transported changes. What I showed in my previous paper and review is precisely that spike initiation is not local. It is determined both by the properties of local Na channels and by resistive properties of the coupling between soma and axonal initiation site, which are not local. For example, if you moved the Na channels away from the soma, the neuron would become more excitable, even though local properties at the initiation site would be identical. Spike initiation is not a local phenomenon because of the proximity of the axonal initial segment to the big somatodendritic compartment.

Thus the sharpness of somatic spikes is actually determined not by propagation properties, contrary to what was claimed before, but by spike initiation properties. The catch is that those properties are not local but rather encompass the whole soma-initial segment system.

I had previously called this biophysical explanation the “compartmentalization hypothesis”. I realize now that this can be very misleading because physiologists tend to think in terms of initiation in one compartment and transportation from one compartment to the other. I will now use a different terminology: “critical resistive coupling”, which emphasizes that spike initiation relies on a system of coupled compartments.

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:

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:

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):