1.5.2 Robustness of the control circle

An exciting thought experiment is discussed in [73]. ”First, we consider a hypothetical membrane that is permeable only to $N{a}^{+}$ ions. Suppose that ${[N{a}^{+}]}_o$, the outside or extracellular sodium concentration, is $145mM$, and ${[N{a}^{+}]}_i$ is 12 mM. And suppose that initially, there is no membrane potential. The diffusion gradient for $N{a}^{+}$ favors $N{a}^{+}$ entry into the cell, and the initial $N{a}^{+}$ influx carries a charge that builds up on the inside of the cell. This produces a potential (recall that separation of charge produces a potential) across the membrane that impedes further $N{a}^{+}$ ion movement because the positive charges repel the positively charged $N{a}^{+}$ ion.”

The paper correctly explains that in the case of $N{a}^{+}$ only, the potential sets up to $66.6mV$. (We quietly add that plus a layer of the corresponding $C{l}^{-}$ ions on the other segment, in a similar concentration ratio, builds up; so also, the attraction between positive and negative charges contributes to the effect.) In lack of our argumentation, it cannot explain why that potential builds up; only why that concentration ratio establishes: the Nernst law, alone, does not explain the effect. Furthermore, the statement is valid only for a well-defined semipermeable membrane. We can add that the same concentrations develop if initially identical concentrations are present on both sides. The finite width of the membrane creates its electric potential, which is a consequence of charge separation, as stated. If there are no ions initially inside, then no charge separation occurs, and therefore, no ion transport begins due to the membrane’s electric potential. However, the thermal driving force exists, and the started ion transport quickly builds the electric layer, which effectively helps to establish the resting potential.

This robustness also explains why, during replication (cell division), cells also inherit their operating ability and resting potential; the existing membrane cell continues to grow in the same way. Its voltage remains the same, and the voltage defined in this way adjusts the concentrations appropriately. Moreover, it explains why, during evolution, cells first formed: a couple of lipids came together to form a membrane, establishing cellular electricity. As Fig. 1.5 depicts, the concentrations may adapt to the living conditions (whether living in see-water), but the general operating principles remained the same. The see-water environment enables using thinner membrane and lower membrane voltage; however, the same electric field is is used in all cases.

Given that neurons share the external (global) concentrations (defined by the vast amount of ions in bulk), they provide a firmly fixed offset value to the always-the-same electric potential. This way, the operations of the individual neurons do not interfere. Furthermore, the internal (local) concentrations can adjust themselves even following a very rough charge perturbation while issuing an AP; moreover, when the living organism is growing.