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Semi-Markov Models for Brownian Dynamics Permeation in Biological Ion Channels
January-February 2011 (vol. 8 no. 1)
pp. 273-281
Vikram Krishnamurthy, University of British Columbia, Vancouver
Kai Yiu Luk, University of British Columbia, Vancouver
Constructing accurate computational models that explain how ions permeate through a biological ion channel is an important problem in biophysics and drug design. Brownian dynamics simulations are large-scale interacting particle computer simulations for modeling ion channel permeation but can be computationally prohibitive. In this paper, we show the somewhat surprising result that a small-dimensional semi-Markov model can generate events (such as conduction events and dwell times at binding sites in the protein) that are statistically indistinguishable from Brownian dynamics computer simulation. This approach enables the use of extrapolation techniques to predict channel conduction when performing the actual Brownian dynamics simulation that is computationally intractable. Numerical studies on the simulation of gramicidin A ion channels are presented.

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Index Terms:
Ion channel permeation, semi-Markov model, Brownian dynamics, binding sites, gramicidin.
Vikram Krishnamurthy, Kai Yiu Luk, "Semi-Markov Models for Brownian Dynamics Permeation in Biological Ion Channels," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 1, pp. 273-281, Jan.-Feb. 2011, doi:10.1109/TCBB.2008.136
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