From Brownian Dynamics to Markov Chain: An Ion Channel Example

Handle URI:
http://hdl.handle.net/10754/598367
Title:
From Brownian Dynamics to Markov Chain: An Ion Channel Example
Authors:
Chen, Wan; Erban, Radek; Chapman, S. Jonathan
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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
27-Feb-2014
DOI:
10.1137/120882780
Type:
Article
ISSN:
0036-1399; 1095-712X
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorChen, Wanen
dc.contributor.authorErban, Radeken
dc.contributor.authorChapman, S. Jonathanen
dc.date.accessioned2016-02-25T13:19:30Zen
dc.date.available2016-02-25T13:19:30Zen
dc.date.issued2014-02-27en
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.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/120882780en
dc.identifier.urihttp://hdl.handle.net/10754/598367en
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.en
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.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectHierarchical Fokker-Planck equationsen
dc.subjectIon hoppingen
dc.subjectOptimal fluxen
dc.subjectTransition ratesen
dc.titleFrom Brownian Dynamics to Markov Chain: An Ion Channel Exampleen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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