期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 74, 期 1, 页码 208-235出版社
SIAM PUBLICATIONS
DOI: 10.1137/120882780
关键词
ion hopping; hierarchical Fokker-Planck equations; transition rates; optimal flux
资金
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- European Research Council under the European Community [239870]
- Royal Society University Research Fellowship
- Fulford Junior Research Fellowship of Somerville College, University of Oxford
- Nicholas Kurti Junior Fellowship of Brasenose College, University of Oxford
- Philip Leverhulme Prize
- Leverhulme Trust
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.
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