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dc.contributor.authorChen, Wan
dc.contributor.authorErban, Radek
dc.contributor.authorChapman, S. Jonathan
dc.date.accessioned2016-02-25T13:19:30Z
dc.date.available2016-02-25T13:19:30Z
dc.date.issued2014-02-27
dc.identifier.citationChen 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.
dc.identifier.issn0036-1399
dc.identifier.issn1095-712X
dc.identifier.doi10.1137/120882780
dc.identifier.urihttp://hdl.handle.net/10754/598367
dc.description.abstractA 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.
dc.description.sponsorshipThis 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.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectHierarchical Fokker-Planck equations
dc.subjectIon hopping
dc.subjectOptimal flux
dc.subjectTransition rates
dc.titleFrom Brownian Dynamics to Markov Chain: An Ion Channel Example
dc.typeArticle
dc.identifier.journalSIAM Journal on Applied Mathematics
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK-C1-013-04


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