Stochastic behavior of ion channels in varying conditions

The opening and closing of a single ion channel can be described as the aggregation into two sets of states, open and shut, of an underlying Markov process with a finite number of states. In this paper we consider an inhomogeneous process due to changing physical conditions, in particular a pulse of activity in which the transition rates during the pulse differ from those obtaining both before and after the pulse. Outside the pulse the chain contains an absorbing shut subset, so that no activity is observed before the pulse and almost surely, at most a finite number of openings are generated by the pulse. We consider, in particular, the probability distribution of first latency (the time to first opening) and the distribution of the total activation time. We take into account the phenomenon of time-interval omission, when short open or shut times fail to be observed.