Our equations also call attention to a neglected aspect of evoking APs: the rush-in ions increase the local potential in the proximal layer to above the potential of the bulk in the intracellular segment, typically even to slightly above the potential in the bulk of the extracellular segment. Consequently, the concentration must also at least approach or even slightly exceed the level of the extracellular concentration for a short period and in a very thin layer near the membrane (the timing relations were discussed above). The mechanical waves [95] provide indirect evidence for the effect’s existence.
We consider three operating regimes for neuronal membranes. Eq. (2.9) describes the steady state. As we discussed, in the case of the finite membrane width of biological neurons, a gradient of a particular form is created in the electrolyte, also comprising a membrane-width-dependent term. However, otherwise, the state can be described by Eq. (2.9).
In single-shot mode, along the axis of the ion channel, at large distances, the concentration and potential remain essentially unchanged during the process. Using our time derivatives, we can describe the details, including the process’s time course. Given that the slowest interaction defines the propagation speed and the proportion of the layer to the bulk is extremely tiny, no significant change in bulk can be measured. The interaction speed in the bulk is practically the drift speed (and the gradients are zero).
In the case of high-rate, repetitive measurements, the changes occurring in the proximal layers can slowly influence the parameters of the bulk. However, this effect becomes significant only in long-term observations when a large number of single actions take place in quick succession. In a continuous high-rate firing mode, the layers have parameters other than the ones required by Eq.(2.9) for the resting state for a growing fraction of the time. We can estimate the time roughly as how long the ions can diffuse to a distance of 0.1 mm (in the order of ), and how many times that distance is greater that the assumed width of the layer proximal to the membrane’s surface (in the order of , that causes a 100% change). We arrive at that a rate 100 Hz will deliver a charge causing a percentage increase of the bulk concentration is in the order of at least dozens of seconds.