Superposition of Spatially Interacting Aggregated Continuous Time Markov Chains

Frank Ball and Geoffrey Yeo ()
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Geoffrey Yeo: Murdoch University

Methodology and Computing in Applied Probability, 2000, vol. 2, issue 1, 93-115

Abstract: Abstract A system s{ X(t)} = {X 1(t),X 2(t),..., X N(t)} of N interacting time reversible continuous time Markov chains is considered. The state space of each of the processes {X i(t)} (i = 1, 2,...,N) is partitioned into two aggregates. Interaction between the processes {X i(t)},{X 2(t)},...,{X N(t)} is introduced by allowing the transition rates of an individual process at time t to depend on the configuration of aggregates occupied by the other N - 1 processes at that time. The motivation for this work comes from ion channel modeling, where {(X}(t)} describes the gating mechanisms of N channels and the partitioning of the state space of {X i(t)} correspond to whether the channel is conducting or not. Let S(t) denote the number of conducting channels at time t. For a time-reversible class of such processes, expressions are derived for the mean and probability density function of the sojourns of {S(t)} at its different levels when {X(t)} is in equilibrium. Particular attention is paid to the situation when the N channels are located on a circle with nearest neighbor interaction. Necessary and sufficient conditions for a general co-operative multiple channel system to be time reversible are derived.

Keywords: ion channel modeling; spatial process; time reversibility; equilibrium behavior; sojourn time distributions (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1010011418887

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