Theoretical characterization of ion channel blockade: ligand binding to periodically accessible receptors

With repetitive stimulation, the time course of use-dependent blockade as assessed by peak membrane ion currents can be described by a sequence of blocking relationships that have the form of recurrence equations. The equations of the sequence describe blockade acquired during each interval of a stimulus where the possibly different binding and unbinding rates are assumed constant during each interval. The solution predicts that use-dependent uptake follows an exponential time course. Furthermore, the exponential uptake rate is a linear function of uptake rates associated with the stimulus time intervals. Similarly, the fraction of blocked channels at steady state is a linear function of the interval dependent blockade equilibria. Several novel tests of consistency between the model and observations are derived from these theoretical results. It is also shown that as the stimulus interval increases to infinity, steady state dissociation constants measured by peak membrane currents are theoretically equivalent to those measured with true equilibrium methods such as radioligand binding studies.