  The action potential in a neural membrane is generated by Na+ and K+ channel
ionic currents that may be calculated from a current equation and the rate
equations for activation variables m and n, and the Na+ inactivation variable
h. Assuming that a Na+ channel has three activation sensors, and activation and
inactivation are cooperative processes, a twelve state master equation that
describes channel gating may be reduced to kinetic equations for a five state
system when the occupational probability of the first inactivated state is
small, and the remaining inactivated states contribute to a total inactivated
state. In the case of independent activation sensors, the inactivation rate is,
in general, dependent on the activation variable m(t) as well as the forward
inactivation transition rates. However, when m(t) has a faster time constant
than h(t), the inactivation rate may be approximated by a voltage-dependent
function, and therefore, the solution of the master equation during an action
potential may be approximated by the solution of Hodgkin-Huxley rate equations
for m and h.
