Theory of Nerve Excitation in Reference to Energy Dissipation: An Example of Far from Equilibrium System

Excitation phenomena in living membranes are studied theoretically, taking the dissipa-tive interaction caused by local electric current in the membrane into consideration. The steady state solutions are obtained. subject to the variational principle under the assumptions that the statistical ensemble theory and the equal a priori probability distribution are applicable to the dissipative processes in the membrane. It is noted. that the transition between two steady states of the membrane is induced cooperatively by the dissipative interaction of the local eddy current. The characteristic N-shaped current vs. voltage relation derived is favorably compared to the experimental data obtained with squid giant axons. Phenomenologic al equations basic to the dynamic feature of the process of transition of steady states are derived on the basis of continuity of electric current in conjunction with the non-markoffian effect caused by an irreversible ion accumulation at the membrane surface. The time course of an action potential and the abolition threshold potential during excita-tion obtained theoretically are in accord with eXperiments obtained from squid giant axons perfused internally. The probable causes for the discrepancies between theory and experiments are discussed briefly. § 1. Introduction Recent physicochem ical studies carried out with internally perfused squid giant axons have revealed that the process of excitation is interpreted in terms of conformation al change of macromolecu les constituting the membrane rather than a transient variation of membrane p~rmeabilitie s for some. specific ion species such asK+ and Na+. 1 > It is hazardous, however, to conclude that the excitation of. living tissues is accompanied by a phase transition of membrane structure in a classical thermodynam ic sense. In fact, as pointed out byTeorell,2> the excita-tion phenomena similar to those observed in living membranes are reproduced by a sintered glass filter under appropriate external and boundary conditions. In this case, the characteristic behavior of stimulus-resp onse relation is interpreted in terms of dissipative structure or a transition between multiple steady states. 8 > Therefore, a transition of states in a more wide sense may be necessary to ac" count for the process of excitation in living membrane. It has been proved experimental ly that the structure of the membrane is not uniform along the axon surface, and many active patches are coexisting with the