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On the exact distribution of observed open times in single ion channel models

Part of: Special processes Physiological, cellular and medical topics

Published online by Cambridge University Press:  14 July 2016

Frank Ball ,
Robin K. Milne  and
Geoffrey F. Yeo
Frank Ball*
Affiliation:
The University of Nottingham
Robin K. Milne*
Affiliation:
The University of Western Australia
Geoffrey F. Yeo*
Affiliation:
Murdoch University
*
∗ Postal address: Department of Mathematics, The University of Nottingham, Nottingham, NG7 2RD, UK.
∗∗ Postal address: Department of Mathematics, The University of Western Australia, Nedlands, WA 6009, Australia.
∗∗∗ Postal address: School of Mathematical and Physical Sciences, Murdoch University, Murdoch, WA 6150, Australia.
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Abstract

Continuous-time Markov chain models have been widely considered for the gating behaviour of a single ion channel. In such models the state space is usually partitioned into two classes, designated ‘open' and ‘closed', and there is ‘aggregation' in that it is possible to observe only which class the process is in at any given time. Hawkes et al. (1990) have derived an expression for the density function of the exact distribution of an observed open time in such an aggregated Markov model, where brief sojourns in either the open or the closed class are unobservable. This paper extends their result to single ion channel models based on aggregated semi-Markov processes, giving a more direct derivation which is probabilistic and exhibits clearly the combinatorial content.

Keywords

MARKOV RENEWAL PROCESSCONTINUOUS-TIME MARKOV CHAINEQUILIBRIUM BEHAVIOURTIME INTERVAL OMISSION

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 92C05: Biophysics 92C30: Physiology (general)
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 529 - 537
Copyright
Copyright © Applied Probability Trust 1993 

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References

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