Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin—Huxley equations

Abstract

A nerve membrane model with a two-state pore system was investigated by computer simulation in the uniform (space-clamped) case. Both sodium and potassium conducting pores were modelled, each pore having four independent gates which switched randomly between the open and the closed position, governed by the assumed rate constants. Each pore conducted only when all the gates were open. The model was based upon the Hodgkin-Huxley equations for the giant axon in squid, and in the limit of an infinite number of pores it was identical to these. The firing behaviour of this model as a function of the number of pores and the injected current were investigated. The mean firing frequency and the distribution of interspike intervals were mainly used in the presentation of the results. It was found that for pore numbers less than about 20000 the main effects due to a finite number of pores were a lowering of the current threshold for firing and a more linear frequency current relationship relative to that of the original H-H equations. For higher pore numbers an increase in the current threshold and a pronounced burst firing close to the threshold were found.