A nine state master equation for Na+ channel gating that describes the coupling between three activation sensors, a two-stage fast inactivation process and a slow inactivated state, may be reduced to a system of kinetic equations for a six state system. Assuming  the activation sensors are independent and the activation variable m has a faster relaxation than the inactivation variable h, the open state probability during the action potential may be expressed as m(t) ^3 h(t) , and the  kinetic equations may be  reduced to rate equations for activation, and  fast and slow inactivation that describe spike frequency adaptation  in the neural membrane, a repetitive bursting oscillation and a cardiac action potential with a plateau oscillation.
A thirteen-state master equation for Na+ channel gating that describes the coupling between three activation sensors, a two-stage fast inactivation process and a slow inactivated state, may be reduced to kinetic equations for a six state system. Assuming that the activation sensors are independent and that activation has a faster relaxation than inactivation, the fast inactivation rate function is, in general, dependent on the activation variable m(t) but may be approximated by a voltage-dependent function , and the rate function for entry into the slow inactivated state is dependent on the fast inactivation variable. The kinetic equations may be further reduced to rate equations for activation, and coupled fast and slow inactivation that describe spike frequency adaptation and a repetitive bursting oscillation in the neural membrane, and a cardiac action potential with a plateau oscillation.
R
nine state
thirteen-state
D
a system of
A
that
R
the activation variable m
that activation
R
the inactivation variable h, the open state probability during the action potential may be expressed as
inactivation, the fast inactivation rate function is, in general, dependent on the activation variable
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^3 h(t)
but may be approximated by a voltage-dependent function
A
rate function for entry into the slow inactivated state is dependent on the fast inactivation variable. The
A
further
A
coupled
A
and a repetitive bursting oscillation
D
a repetitive bursting oscillation