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Explicit asymptotic results for open times in ion channel models

Part of: Physiological, cellular and medical topics Special processes Distribution theory

Published online by Cambridge University Press:  01 July 2016

Valeri T. Stefanov  and
Geoffrey F. Yeo
Valeri T. Stefanov*
Affiliation:
The University of Western Australia
Geoffrey F. Yeo*
Affiliation:
Murdoch University
*
*Postal address: Department of Mathematics, The University of Western Australia, Nedlands, WA 6907, Australia.
**Postal address: Department of Mathematics and Statistics, Murdoch University, Murdoch, WA 6150, Australia.
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Abstract

The dynamical aspects of single channel gating can be modelled by a Markov renewal process, with states aggregated into two classes corresponding to the receptor channel being open or closed, and with brief sojourns in either class not detected. This paper is concerned with the relation between the amount of time, for a given record, in which the channel appears to be open compared to the amount in which it is actually open and the difference in their proportions; this may be used to obtain information on the unobserved actual process from the observed one. Results, with extensions, on exponential families have been applied to obtain relevant generating functions and asymptotic normal distributions, including explicit forms for the parameters. Numerical results are given as illustration in special cases.

Keywords

ASYMPTOTICSEXPONENTIAL FAMILYION CHANNELMARKOV RENEWAL PROCESS

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 62E20: Asymptotic distribution theory 92C05: Biophysics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 4 , December 1997 , pp. 947 - 964
Copyright
Copyright © Probability Trust 1997 

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Footnotes

The research of the first author was supported by a grant from the Faculty of Engineering and Mathematical Sciences of UWA.

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