Firing behaviour in nerve cell models with a two-state pore system.

Abstract

The firing behaviour of simple nerve cell models with a two-state pore system was investigated by computer simulation. The pores were assumed to open and close randomly, with the probabilities for opening an closing calculated from the equations found by Hodgkin and Huxley for the squid giant axon. The cell models had a cell body and an axon with an initial segment with a smaller diameter. Both the case of a uniform membrane with constant pore densities all over the cell, and the case of a cell body membrane with only a leakage conductance (a "passive" membrane) were investigated. The results indicate that the firing behaviour of a small nerve cell may be significantly influenced by the finite number of pores in the initial segment. In contrast to the original Hodgkin-Huxley equations which give a very non-linear frequency-current relationship in such nerve cell models, a fairly linear relationship over a large current range was found in many cases. It was estimated that the diameter of the initial segment must be less than approximately 1 micron and the length larger than half a space constant, in order to obtain a current frequency relationship significantly different from that predicted by the original Hodgkin-Huxley equations.