  The Na+ current in nerve and muscle membranes may be described in terms of
the activation variable m(t) and the inactivation variable h(t), which are
dependent on the transitions of S4 sensors of each of the Na+ channel domains
DI to DIV. The time-dependence of the Na+ current and the rate equations
satisfied by m(t) and h(t) may be derived from the solution to a master
equation which describes the coupling between two or three activation sensors
regulating the Na+ channel conductance and a two stage inactivation process. If
the inactivation rate from the closed or open states increases as the S4
sensors activate, a more general form for the Hodgkin-Huxley expression for the
open state probability may be derived where m(t) is dependent on both
activation and inactivation processes. The voltage dependence of the rate
functions for inactivation and recovery from inactivation are consistent with
the empirically determined expressions, and exhibit saturation for both
depolarized and hyperpolarized clamp potentials.
