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Originally published as Biophys J. BioFAST on July 1, 2005.
doi:10.1529/biophysj.104.055178
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Biophysical Journal 89:1551-1563 (2005)
© 2005 The Biophysical Society

From Continuum Fokker-Planck Models to Discrete Kinetic Models

Jianhua Xing *, Hongyun Wang {dagger} and George Oster *

* Departments of Molecular & Cellular Biology and Environmental Science, Policy, and Management, University of California, Berkeley, California; and {dagger} Department of Applied Mathematics & Statistics, University of California, Santa Cruz, California

Correspondence: Address reprint requests to George Oster, Tel.: 510-642-5277; E-mail: goster{at}nature.berkeley.edu.

Two theoretical formalisms are widely used in modeling mechanochemical systems such as protein motors: continuum Fokker-Planck models and discrete kinetic models. Both have advantages and disadvantages. Here we present a "finite volume" procedure to solve Fokker-Planck equations. The procedure relates the continuum equations to a discrete mechanochemical kinetic model while retaining many of the features of the continuum formulation. The resulting numerical algorithm is a generalization of the algorithm developed previously by Fricks, Wang, and Elston through relaxing the local linearization approximation of the potential functions, and a more accurate treatment of chemical transitions. The new algorithm dramatically reduces the number of numerical cells required for a prescribed accuracy. The kinetic models constructed in this fashion retain some features of the continuum potentials, so that the algorithm provides a systematic and consistent treatment of mechanical-chemical responses such as load-velocity relations, which are difficult to capture with a priori kinetic models. Several numerical examples are given to illustrate the performance of the method.




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