As discussed above, ion channels have a voltage threshold that opens them. We can successfully interpret how the microscopic threshold of the ion channels forms the macroscopic phenomenon that a voltage threshold exists for the membrane. Section 17.3 in [24], introduces further (current and charge) thresholds. After introducing the “slow current” notion, we can understand that the same voltage threshold manifests in apparently different thresholds.
As discussed, introducing a sustained current implies the introduction of a sustained slow current on the membrane’s surface. The sustained current means a sustained presence of ions on the surface, resulting in a continuous increase of potential offset over the resting potential value. As observed, “the somatic membrane potential responds with a slight overshoot”. Given that the charge collection for initiating an AP starts at a voltage above the resting potential, the voltage threshold is reached earlier. The introduced external current is added to the sustained clamping current. The charge delivered by the newly added slow current appears delayed (after the onset). Depending on the point of the membrane the current is added, the delay may be up to 1 msec. (As [50] demonstrated, the propagation speed inside a neuron is in the order of less than 1 cm/s; furthermore, as we discussed, the need to use electrolyte electrodes can prolong the measured delay time considerably.) The current threshold is another manifestation of the voltage threshold.
As we discussed in section 2.2.4, the virtue of a capacitive current is used only to imitate the effect of a slow current: biology has no discrete capacitance. The capacitive current exists only as a virtual notion in the electric circuit comprising discrete elements that are considered parallel with the biology-imitating circuit comprising distributed elements. In the lack of notion of a “slow” current, for “rapid events”, one may attempt to replace the “delayed rectifying current” with an instantaneous current. As formulated in section 17.3.5 in [24]: “Because we are considering rapid events, the steady-state I-V in Eq. 17.4 must be replaced by the instantaneous I-V curve”. However, the rapid events are not rapid enough to make such a replacement in a differential equation. This replacement results in their Eq. (17.7) non-matching values are used. As we explained, Eq. (3.9) formulates Kirchoff’s Law in biology. Using a virtual parameter “capacity ” for biological neurons misleads research: introduces a nonexisting “charge threshold”, which exists only due to mismatching notions of finite-speed biological circuits with notions of the infinite-speed abstract electric circuits, used to imitate a finite-speed current in terms of a virtual infinite-speed current.