Graphs, random sums, and sojourn time distributions, with application to ion-channel modeling (Q811439)

For modelling of ion-channel kinetics and drug-receptor interactions the distribution of a sojourn time in a subset of the state space of a stochastic process is derived in which sojourn times in an individual state are independent and identically distributed. Transitions between states follow a Markov chain. The state space and possible transitions of the stochastic process are represented by a graph identified with an underlying chemical kinetic scheme. A sojourn time in a composition state is expressed as a random sum. The random sum structure of the required sojourn time can be derived algorithmically on the basis of graph operations. This random sum method is legitimate if there are no correlations between sojourn times in adjacent composition states. But also for cases where correlation is weak the random-sum approach may provide useful approximations. A standard five-state model of a single ion channel is used to illustrate the ideas and to discuss results.