Journal article
A framework model based on the Smoluchowski equation in two reaction coordinates
The Journal of chemical physics, Vol.121(13), pp.6134-6144
10/01/2004
Handle:
https://hdl.handle.net/2376/112948
PMID: 15446907
Abstract
The general form of the Smoluchowski equation in two reaction coordinates is obtained as the diffusion limit of a random walk on an infinite square grid using transition probabilities that satisfy detailed balance at thermodynamic equilibrium. The diffusion limit is then used to construct a generalization of the single-particle model to two reaction coordinates. The state space includes a square on which diffusion takes place and an isolated empty state. Boundary conditions on opposite sides of the square correspond to transitions between the empty state and the square. The two-dimensional (2D) model can be reduced to a 1D single-particle model by adiabatic elimination. A finite element solution of the 2D boundary value problem is described. The method used to construct the 2D model can be adapted to state spaces that have been constructed by other authors to model K+ conduction through gramicidin, proton conduction through dioxolane-linked gramicidin, and chloride conduction through the bacterial H(+)-Cl- antiporter.
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Details
- Title
- A framework model based on the Smoluchowski equation in two reaction coordinates
- Creators
- Mark F Schumaker - Department of Mathematics, Washington State University, Pullman, Washington 99164-3113, USADavid S Watkins
- Publication Details
- The Journal of chemical physics, Vol.121(13), pp.6134-6144
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- United States
- Identifiers
- 99900548078101842
- Language
- English
- Resource Type
- Journal article