  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.
