Chen, W. and Erban, R. and Chapman, S. J. (2012) From Brownian dynamics to Markov chain: an ion channel example. SIAM Journal on Applied Mathematics . (Submitted)

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Abstract
A discrete rate theory for general multiion 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 FokkerPlanck 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 the Markovian transition rates can be determined. The theory is illustrated with a twoion onewell channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical FokkerPlanck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1563 
Deposited By:  Peter Hudston 
Deposited On:  20 Jul 2012 06:56 
Last Modified:  29 May 2015 19:15 
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