Improved Hodgkin–Huxley type model for neural action potentials

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 6.3ºC, our dynamical system behaves as a 4-dimensional resonator exhibiting subthreshold oscillations. Although our present analysis refers to experiments at 20°C, 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 20ºC is in excellent agreement with the Hodgkin–Huxley experimental value at 18.5ºC. 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.