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Biophys. J. BioFAST: First Published July 1, 2005. doi:10.1529/biophysj.104.055178
© 2005 by the Biophysical Society.

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Jianhua Xing
Hongyun Wang
George Oster
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BIOPHYSICAL THEORY AND MODELING

From continuum Fokker-Planck models to discrete kinetic models

Jianhua Xing 1, Hongyun Wang 1 and George Oster 1*

1 University of California

* To whom correspondence should be addressed. E-mail: goster{at}nature.berkeley.edu.

Submitted on October 27, 2004
Revised on January 11, 2005
Accepted on 7 June 2005


  Abstract
Two theoretical formalisms are widely used in modeling mechanochemical systems such as protein motors: continuum Fokker-Planck (FP) models and discrete kinetic (DK) 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 by Wang, Peskin and Elston, (J. Theo. Biol. 221:491-511, 2003) 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. MatlabTM codes are provided in the Supplementary materials.

Key Words: Fokker-Planck, Molecular motor, kinetics, mathematical model




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Copyright © 2005 by the Biophysical Society.