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

Robin Milne, G.F. Yeo, F.G. Ball

    Research output: Contribution to journalArticle

    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. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60 K15 SECONDARY 60 K20; 92 C05; 92 C30
    Original languageEnglish
    Pages (from-to)529-537
    JournalJournal of Applied Probability
    Issue number30
    DOIs
    Publication statusPublished - 1993

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    Ion Channels
    Channel Model
    Exact Distribution
    Closed
    Semi-Markov Process
    Markov Chain Model
    Continuous-time Markov Chain
    Density Function
    Markov Model
    Aggregation
    State Space
    Model-based
    Class
    Model

    Cite this

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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. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60 K15 SECONDARY 60 K20; 92 C05; 92 C30",
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    On the exact distribution of observed open times in single ion channel models. / Milne, Robin; Yeo, G.F.; Ball, F.G.

    In: Journal of Applied Probability, No. 30, 1993, p. 529-537.

    Research output: Contribution to journalArticle

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    AU - Yeo, G.F.

    AU - Ball, F.G.

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