The theoretical basis for non-exponential time-course of the recovery from inactivation of Hodgkin-Huxley-type ionic currents.

In this paper, we have carried out a theoretical analysis of the recovery process of inactivating currents whose voltage-dependent conductances obey the Hodgkin-Huxley equations. We demonstrate that the recovery process is complex, and, in particular, is non-exponential. Consequently, it cannot be characterized by a single-time constant. Nevertheless, its time-course is completely determined by the properties of the activation and inactivation kinetics at the membrane potential at which the deinactivation of the current takes place. Moreover, we show that the recovery asymptotically approaches an exponential time-course whose time-constant, in turn, is found to be identical to that of the inactivation at the membrane potential of deinactivation. The method commonly used to reconstruct the recovery process can, therefore, provide a way of estimating the inactivation time-constant at membrane potentials where a measurement with the usual voltage-clamp protocol would not be possible. The conclusions of our analysis are discussed with regard to recent theoretical and experimental results.