AMS2005-24: From Continuum Fokker-Planck Models to Discrete Kinetic Models

J. Xing, H. Wang and G. Oster
12/31/2005 09:00 AM
Applied Mathematics & Statistics
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 Ôfinite volumeÕ 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.