Mathematical description of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations

Abstract

Modifications based on experimental results reported in the literature are made to the Hodgkin-Huxley equations to describe the electrophysiological behavior of the Aplysia abdominal ganglion R15 cell. The system is then further modified to describe the effects with the application of tetrodotoxin to the cell bathing medium. Methods of the qualitative theory of differential equations are used to determine the conditions necessary for such a system of equations to have an oscillatory solution. A model satisfying these conditions predicts many experimental observations of R15 cell behavior. Numerical solutions are obtained for differential equations satisfying the conditions of the model. These solutions have a form similar to that of the bursting characteristic of this cell, and predicts many results of experiments conducted on this cell. The physiological implications of the model are discussed.