ON THE EXACT DISTRIBUTION OF OBSERVED OPEN TIMES IN SINGLE-ION CHANNEL MODELS

Continuous-time Markov chain models have been widely considered for th e gating behaviour of a single ion channel. In such models the state s pace is usually partitioned into two classes, designated 'open' and 'c losed', and there is 'aggregation' in that it is possible to observe o nly which class the process is in at any given time. Hawkes et al. (19 90) have derived an expression for the density function of the exact d istribution of an observed open time in such an aggregated Markov mode l, where brief sojourns in either the open or the closed class are uno bservable. This paper extends their result to single ion channel model s based on aggregated semi-Markov processes, giving a more direct deri vation which is probabilistic and exhibits clearly the combinatorial c ontent. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60 K15 SECONDARY 60 K 20; 92 C05; 92 C30