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.