Polarization kinks and propagation of action potential in axon membranes

A model is proposed for generation and propagation of the action potential in axon membranes based on the concept of a ferroelectric first-order phase transition. The model modifies Leuchtag's hypothesis of the ferroelectric origin of the gating mechanism in sodium ion channels in order to use it for the action potential propagation. The model implies that the membrane conformational change leading to the voltage-gated channel opening is driven by the piezoelectric effect providing the change of membrane polarization by an external electric field. A polarization kink describes the propagation of the action potential as an interphase boundary motion between closed and open gate states associated with different values of polarization. We show that the main dynamic equation of the model is equivalent to the reduced FitzHugh-Nagumo equation provided using Leuchtag's hypothesis on ferroelectric properties of axon membranes. We obtain reasonable dependences of the conduction velocity on temperature, on the diameter, and the resistivity of the axon and its capacitance. The calculated value of the conduction velocity is in agreement with experiment.