Journal Article

Stochastic behaviour of ion channels in varying conditions


in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 14, issue 2, pages 125-149
Published in print June 1997 | ISSN: 1477-8599
Published online June 1997 | e-ISSN: 1477-8602 | DOI:
Stochastic behaviour of ion channels in varying conditions

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  • Applied Mathematics
  • Biomathematics and Statistics


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The opening and closing of a single ion channel can be described as the aggregation into two sets of states, open and shut, of an underlying Markov process with a finite number of states. In this paper we consider an inhomogeneous process due to changing physical conditions, in particular a pulse of activity in which the transition rates during the pulse differ from those obtaining both before and after the pulse. Outside the pulse the chain contains an absorbing shut subset, so that no activity is observed before the pulse and, almost surely, at most a finite number of openings are generated by the pulse. We consider, in particular, the probability distribution of first latency (the time to first opening) and the distribution of the total activation time. We take into account the phenomenon of time-interval omission, when short open or shut times fail to be observed.

Keywords: ion channel; time-interval omission; Markov process; semi-Markov process; inhomogeneous process; first latency

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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