Abstract

Abstract The opening and closing mechanism of Na+ channels in excitable membranes has been discussed by applying our chemical self-organized theory to the ferroelectric diffused electrical bilayer model modified from Leuchtag's ferroelectric hypothesis for the channel gating. A state equation for membrane potential η is described by η3 + Aη + B = 0, where A and B are the control variables related to dipole-dipole and dipole-ion interactions, respectively. By a stimulus above the threshold, A and B move along the equilibrium space of the above equation and membrane excitation occurs with a cusp catastrophe at a point on the bifurcation sets when A < 0; T < T c. The Na± current or -conductance in the voltage clamp method is analyzed by use of the functions for Ȧ and [Bdot] modified from Zeeman's formulas and the experimental results have been explained successfully by this model.

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