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The Na+ current in nerve and muscle membranes may be described in terms ofthe activation variable m(t) and the inactivation variable h(t), which aredependent on the transitions of S4 sensors of each of the Na+ channel domainsDI to DIV. The time-dependence of the Na+ current and the rate equationssatisfied by m(t) and h(t) may be derived from the solution to a masterequation which describes the coupling between two or three activation sensorsregulating the Na+ channel conductance and a two stage inactivation process. Ifthe inactivation rate from the closed or open states increases as the S4sensors activate, a more general form for the Hodgkin-Huxley expression for theopen state probability may be derived where m(t) is dependent on bothactivation and inactivation processes. The voltage dependence of the ratefunctions for inactivation and recovery from inactivation are consistent withthe empirically determined expressions, and exhibit saturation for bothdepolarized and hyperpolarized clamp potentials.

Derivation of Hodgkin-Huxley equations for a Na+ channel from a master equation for coupled activation and inactivation