Framework models of ion permeation through membrane channels and the generalized King-Altman method

A modern approach to studying the detailed dynamics of biomolecules is to simulate them on computers. Framework models have been developed to incorporate information from these simulations in order to calculate properties of the biomolecules on much longer time scales than can be achieved by the sim...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2006-10, Vol.68 (7), p.1429-1460
Main Authors: Mapes, Eric J, Schumaker, Mark F
Format: Article
Language:English
Subjects:
Algorithms
Bacterial Proteins - chemistry
Diffusion
Enzyme kinetics
Gramicidin - chemistry
Ion Channels - chemistry
Ions - chemistry
Markov Chains
Models, Chemical
Potassium - chemistry
Potassium Channels - chemistry
Protons
Sodium - chemistry
Stochastic Processes
Studies
Water - chemistry
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Summary:A modern approach to studying the detailed dynamics of biomolecules is to simulate them on computers. Framework models have been developed to incorporate information from these simulations in order to calculate properties of the biomolecules on much longer time scales than can be achieved by the simulations. They also provide a simple way to think about the simulated dynamics. This article develops a method for the solution of framework models, which generalizes the King-Altman method of enzyme kinetics. The generalized method is used to construct solutions of two framework models which have been introduced previously, the single-particle and Grotthuss (proton conduction) models. The solution of the Grotthuss model is greatly simplified in comparison with direct integration. In addition, a new framework model is introduced, generalizing the shaking stack model of ion conduction through the potassium channel.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-005-9016-1