Abstract
The dynamical theory of ionized media is applied to the semi-electrolyte component of an excitable cell membrane, and the adjacent electrolytes. The equations of conservation of charge and momentum for the ions, and Poisson's equation for the electrostatic potential, are applied first to investigate the steady states of the membrane, and then transient effects in the membrane. A dispersion equation is derived, and the characteristic modes of relaxation within the membrane are determined. Among these are oscillating modes whose frequencies and amplitudes are of the correct order of magnitude to explain the observed excitation phenomena. A pair of coupled non-linear equations in the ionic potentials, with action potential solutions, is derived from the time-dependent electrodiffusion equations, and calculations are presented which model the behaviour of the excitable membrane during the voltage clamp. It is not necessary to postulate large changes in the ionic permeabilities in the course of the action potential and the voltage clamp to account for the large transient membrane conductances. It is suggested that the sodium hypothesis be replaced by one which attributes the action potential to non-linear plasma oscillations.
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