Improved Hodgkin & Huxley-type model for action potentials in squid

Abstract: By extending the crude Goldman-Hodgkin-Katz electrodiffusion model for resting-state membrane potentials in perfused giant axons of squid, we reformulate the Hodgkin-Huxley (HH) phenomenological quantitative model to create a new model which is simpler and based more fundamentally on electrodiffusion principles. Our dynamical system, like that of HH, behaves as a 4-dimensional resonator exhibiting subthreshold oscillations. The predicted speed of propagating action potentials at 20 degrees Celsius is in good agreement with the HH experimental value at 18.5 degrees Celsius. After the external concentration of calcium ions is reduced, the generation of repetitive rebound action potentials is predicted by our model, in agreement with experiment, when the membrane is stimulated by a brief (0.1 ms) depolarizing current. Unlike the HH model, our model predicts, in agreement with experiment, that prolonged constant-current stimulation does not generate spike trains in perfused axons. Our resonator model predicts rebound spiking following prolonged hyperpolarizing stimulation, observed at 18.5 degrees Celsius by HH but not predicted at this temperature by their quantitative model. Spiking promoted by brief hyperpolarization is also predicted, at room temperature, by our electrodiffusion model, but only at much lower temperatures (ca. 6 degrees Celsius) by the HH model. We discuss qualitatively, more completely than do HH, temperature dependences of the various physical effects which determine resting and action potentials.