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

Rate equations for a Na+ channel gating master equation during the action potential within a neural membrane