  A fifteen state kinetic model for Na+ channel gating that describes the
coupling between three activation sensors, a two-stage fast inactivation
process and slow inactivated states, may be reduced to equations for a six
state system by application of the method of multiple scales. By expressing the
occupation probabilities for closed states and the open state in terms of
activation and fast inactivation variables, and assuming that activation has a
faster relaxation than inactivation and that the activation sensors are
mutually independent, the kinetic equations may be further reduced to rate
equations for activation, and coupled fast and slow inactivation that describe
spike frequency adaptation, a repetitive bursting oscillation in the neural
membrane, and a cardiac action potential with a plateau oscillation. 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.
