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Multivariate semi-Markov analysis of burst properties of multiconductance single ion channels

Part of: Physiological, cellular and medical topics Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

F. Ball ,
R. K. Milne  and
G. F. Yeo
F. Ball*
Affiliation:
University of Nottingham
R. K. Milne*
Affiliation:
The University of Western Australia
G. F. Yeo*
Affiliation:
Murdoch University
*
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, Nottingham NG7 2RD, UK.
∗∗ Postal address: Department of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia.
∗∗∗ Postal address: Mathematics and Statistics, DSE, Murdoch University, Murdoch, WA 6150, Australia. Email address: yeo@maths.uwa.edu.au
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Abstract

Patch clamp recordings from ion channels often show periods of repetitive activity, known as bursts, which are noticeably separated from each other by periods of inactivity. Depending on the type of channel, such recordings may exhibit (conductance) levels between the closed (zero) level and the fully open level. Properties of bursts are less subject to problems that arise from recording than are properties for individual sojourns at different levels, and study of bursting behaviour provides important information about the finer structure of the underlying channel gating process. For a general finite state space continuous-time Markov chain model allowing one or more nonzero conductance levels, the present paper establishes results about the semi-Markov structure of a single burst and of a sequence of bursts, and uses this in a unified approach to properties of both theoretical and empirical bursts. The distribution and moments of particular burst properties, including the total charge transfer, the total sojourn time and the total number of visits to specified conductance levels during a burst, are derived. Various extensions are also described.

Keywords

Ion channel modellingburstscontinuous-time Markov chainscharge transfersubconductance levelsequilibrium behavioursemi-Markov kernel

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92C05: Biophysics 60K15: Markov renewal processes, semi-Markov processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 179 - 196
Copyright
Copyright © Applied Probability Trust 2002 

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