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A fifteen state kinetic model for Na+ channel gating that describes thecoupling between three activation sensors, a two-stage fast inactivationprocess and slow inactivated states, may be reduced to equations for a sixstate system by application of the method of multiple scales. By expressing theoccupation probabilities for closed states and the open state in terms ofactivation and fast inactivation variables, and assuming that activation has afaster relaxation than inactivation and that the activation sensors aremutually independent, the kinetic equations may be further reduced to rateequations for activation, and coupled fast and slow inactivation that describespike frequency adaptation, a repetitive bursting oscillation in the neuralmembrane, and a cardiac action potential with a plateau oscillation. The fastinactivation rate function is, in general, dependent on the activation variablem(t) but may be approximated by a voltage-dependent function, and the ratefunction for entry into the slow inactivated state is dependent on the fastinactivation variable.

Reduction of a kinetic model for Na+ channel activation, and fast and slow inactivation within a neural or cardiac membrane