Modified Hodgkin-Huxley gating kinetics of sodium activation in giant axons of squid (Doryteuthis bleekeri)

The probabilities m of the sodium activation gate being open are shown to fit experimentally-determined running integrals Qg of recordings of the colchicine-sensitive fraction of the asymmetry current, within the Hodgkin-Huxley framework that the gate could have only two conformations, open and closed. Using the Hodgkin-Huxley framework, we are obliged to assume that the transition velocities, alpha m and beta m, between the open and closed gates depend not only on membrane potentials V but also on the time after a potential step was externally applied. We introduce the following functions of alpha m and beta m. (sequence in text) where VH, td and tau p stand for holding potential, constant delay time of 10 microseconds, and transit time of the transition velocity of alpha m (or beta m) from its initial value alpha om (or beta om) to its final steady value alpha infinity m (or beta infinity m), respectively. The transit time tau p was found to be potential-dependent; typically it was 30 microseconds at -20 mV, and 100 microseconds at 20-40 mV. The values of alpha infinity m, alpha om, beta infinity m and beta om were found to be in reasonable agreement with those obtained by others, under the Hodgkin-Huxley assumption that the gate followed first-order kinetics. The requirement of new parameters, tau p and td, in the transition velocities was discussed in a relation to a membrane model where a voltage-receptor and a sodium channel macromolecule are spatially separated but functionally connected through underlying cytoskeletons (Matsumoto, 1984).