Convection-Diffusion as a Model of the Early Current in the Giant Axon

Abstract

Convection and diffusion in a membrane with a low density of fixed positive charges have been theoretically analysed as a model of the early current in the giant axon. The model can be regarded as a part of Teorell's excitability analogue. The non-linear transient behaviour of the model conductance has been numerically compared with the conductance associated with sodium activation, using Hodgkin & Huxley's equations. The two models show considerable similarities. The sigmoidal increase of the conductance under depolarization and the exponential decay under repolarization is well reproduced by the convection-diffusion model. The time constant of the model conductance is approximately a function of the instantaneous potential, as in the Hodgkin-Huxley theory. The voltage dependence of the time constant is also in agreement with Hodgkin & Huxley. A quantitative comparison has been made, giving the approximate values of the model parameters necessary for compatibility with squidaxon data.