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    From Brownian Dynamics to Markov Chain: An Ion Channel Example

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    Type
    Article
    Authors
    Chen, Wan
    Erban, Radek
    Chapman, S. Jonathan
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2014-02-27
    Online Publication Date
    2014-02-27
    Print Publication Date
    2014-01
    Permanent link to this record
    http://hdl.handle.net/10754/598367
    
    Metadata
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    Abstract
    A discrete rate theory for multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model, one can determine the Markovian transition rates. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed. © 2014 Society for Industrial and Applied Mathematics.
    Citation
    Chen W, Erban R, Chapman SJ (2014) From Brownian Dynamics to Markov Chain: An Ion Channel Example. SIAM Journal on Applied Mathematics 74: 208–235. Available: http://dx.doi.org/10.1137/120882780.
    Sponsors
    This work was partially supported by award KUK-C1-013-04 from King Abdullah University of Science and Technology (KAUST) and by funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 239870.The second author's work was partially supported by a Royal Society University Research Fellowship; by a Fulford Junior Research Fellowship of Somerville College, University of Oxford; by a Nicholas Kurti Junior Fellowship of Brasenose College, University of Oxford; and by a Philip Leverhulme Prize awarded by the Leverhulme Trust.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Applied Mathematics
    DOI
    10.1137/120882780
    ae974a485f413a2113503eed53cd6c53
    10.1137/120882780
    Scopus Count
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