A Functional Approach to Approximations for the Observed Open Times in Single Ion Channel Models

The openings and closures of a single ion channel in a biological membrane are often modelled by a finite statespace continuous time Markov chain, whose states are aggregated into two classes, of open and closed states, respectively. Time interval omission occurs when short sojourns in either class of states are not observed. Many approximations for the distributions of the resulting apparent open and closed times have appeared in the literature. In this paper, a functional approach is used to derive new approximation formulae for these quantities, and to obtain first order correction terms for some existing approximations.