A current-based model for time interval omission in Markov single ion channel gating mechanisms

A new model for time interval omission in single ion channel analysis is presented. The gating mechanism of a single ion channel is assumed to be modelled by an underlying continuous time Markov chain with a finite state space, partitioned into two classes termed ‘open’ and ‘closed’. The recorded current flowing across the channel is assumed to be piecewise linear in time, with it increasing (decreasing) at rate −1 if the channel is in an open (closed) state, subject to the constraint that it remains within the interval [0, 1]. The observed process, i.e., the observed sequence of open and closed sojourns of the channel, is derived from the recorded current process via a double-threshold algorithm. It is shown that complete information concerning the observed process is contained in an embedded semi-Markov sequence, and an explicit expression is derived for the Laplace–Stieltjes transform of its associated semi-Markov kernel. The equilibrium behaviours of both the joint underlying and current process and the observed process are determined. Moments of observed open and closed sojourns are obtained.