Improved Hodgkin-Huxley type model for neural action potentials.

Abstract

The simple Goldman-Hodgkin-Katz model for resting-state membrane potentials has been generalized to provide a new nonlinear theoretical model for action potentials in perfused axons. Our minimalistic model appeals naturally to physically based electrodiffusion principles to describe electric-current densities inside sodium and potassium-ion channels whereas the 1952 Hodgkin-Huxley model describes such current densities in an ad hoc way. Although the two models share similar schemes for the kinetics of ion-channel gating, our relaxation times for channel gating are simpler, being independent of membrane potential. Like the theoretical model of Hodgkin and Huxley, based primarily on experimental data at [Formula: see text], our dynamical system behaves as a 4-dimensional resonator exhibiting subthreshold oscillations. Although our present analysis refers to experiments at [Formula: see text], re-parameterizations of this model should permit consideration of action potentials at alternative temperatures. The predicted speed of propagating action potentials in giant axons of squid at [Formula: see text] is in excellent agreement with the Hodgkin-Huxley experimental value at [Formula: see text]. In cases where our model predictions differ from those of the Hodgkin-Huxley model, new experiments will be required to determine which model is more accurate.