The two electric fields show essentially different dependencies on the neuron’s parameters. Recall that although the parameters we used are biologically plausible, they are only estimations from non-dedicated measurements. The qualitative conclusions, however, remain valid. As Figure 2.8 shows, in the function of the membrane’s thickness, the electric field across the membrane due to electric charges (it does not depend on the thickness of the membrane), for different physically plausible assumptions; furthermore, the thermal electric field.
The balanced state is set to where the thermodynamic and electric ”electric field” diagram lines cross each other; around ; the value we assumed in evaluating our equations. On the other hand, we can check the electric field’s dependence on the summed-up concentration of the ions in the segment (see Fig. 2.16). Here, the thermodynamic electrical field is constant but different at different width parameters. The classic condenser does not provide a reasonably balanced state (a matching line). The dielectric diagram line seems to provide a realistic estimation when using biologically reasonable parameters. One can describe the neuron as a balanced system at the intersection of the sloping and the horizontal lines. In the resting state, only minor deviations from this state exist in both the electric field and the chemical concentration.
In the transient state, if we assume that a charge transfer causes a significant potential change around in the layer of width , it means a jump in the electric field that corresponds to a jump in the concentration (for only a short time and only in that mentioned layer not in bulk; see also Fig. 1.8). During issuing an AP, the system finds its way back to the crossing point (the path is not simple: both concentrations on both sides of the membrane and the electric field in the mentioned layer change; the process is relaxation, as it is seen in the shape of an AP).
Even we can imagine how the electric process happens in this controlled system (for visibility, the positions of the marks are not proportional to the mentioned numbers). The system is in a balanced state at a crossing point. The two circles connected by bent arrows represent that when an excitation begins at the point with lower concentration and higher potential (the cytoplasm side and negative resting potential), ions rush into the surface layer, so the ion concentration increases, that increases the electric field; which is seen that the membrane potential suddenly increases. The increased potential starts a current, but the current is slow, and the intensity of the current through the channels in the membrane’s wall is higher than the current of the drain (AIS) so the system issues an AP while returning to its starting point. The system will move along the line, with the restriction that it is a movement in the phase space (the change in concentration is not proportional with the time), and the different points on the membrane’s surface may have the potential at different times (the spatiotemporal behavior). Due to the capacitive current, the local potential may temporarily drop below the set-point (as observed in physiology, this is known as hyperpolarization). The time course of the processes are described by the laws of motion of biology [22] (the time derivatives of the Nernst-Planck equation), and the simplified model works as described in section 4 of [11] and its computational details in [23].