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Temporal clustering of ion channel openings incorporating time interval omission. (English) Zbl 0642.92001

Markov chains have been used in the past fifty years for modelling a variety of phenomena in a vast spectrum ranging from physical sciences and engineering on one end to biological, ecological and economic and social sciences at the other. The paper under review is yet another one but a new application to a situation in membrane science.
The authors investigate the gating mechanism of the behaviour of individual channel molecules in the membranes of excitable cells. The temporal pattern of the pulses of electrical current (due to opening and closing of pores in the membrane) is essentially determined by the opening and closing mechanism of the channel. The characteristics are apparently described by the number of channel openings in successive intervals of duration t.
The authors present a brief review of Markov chain theory with special reference to sojourn time distributions and then proceed to model the channel openings. In the concluding section the authors attempt to discuss the model from the inferential point of view.
Reviewer: S.K.Srinivasan

MSC:

92C05 Biophysics
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
60J27 Continuous-time Markov processes on discrete state spaces
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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