Temperature effects on the properties of the Hodgkin-Huxley propagated action potential model determined by computed solutions and phase-plane analysis

ABSTRACT

The equation for membrane potential (V) of the squid giant axon or some muscle cells, which is the heart of the Hodgkin-Huxley model for the action potential, can be written in three ways first, as a partial differential equation in time and space; second, as an ordinary differential equation in time, assuming uniform wave propagation for the action potential, and third, as an even simpler ordinary differential equation for the potential at a point, so-called [quot ]space clamp[quot ] conditions. Solutions were computed for the first two of these equations, at three different temperatures, and the results compared. Temperature dependence of the appropriate parameters was calculated from a simple exponential relationship. Significant changes in the quantitative predictions of the model were found as the temperature was changed from 6.3 C to 18.5 C. Phase-plane (V v V, I v V) analysis has been used to examine the nature of these differences.