(Received January 31, 1974)
Excitation phenomena in living membranes are studied theoretically, taking the dissipative 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.
Phenomenological 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 excitation 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.
URL : http://ptp.ipap.jp/link?PTP/52/1094/
DOI : 10.1143/PTP.52.1094