From continuum Fokker-Planck models to discrete kinetic models.
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.
Departments of Molecular and Cellular Biology and Environmental Science, University of California, Berkeley, California, USA.
Jianhua
J
Xing
Hongyun
H
Wang
George
G
Oster
D000255:Adenosine Triphosphate / Q000737:chemistry; D000465:Algorithms; D000818:Animals; D001692:Biological Transport; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D007700:Kinetics; D008956:Models, Chemical; D015233:Models, Statistical; D008962:Models, Theoretical; D020409:Molecular Motor Proteins; D009218:Myosins / Q000737:chemistry; D013269:Stochastic Processes; D013696:Temperature; D013816:Thermodynamics
D020409:Molecular Motor Proteins; D000255:Adenosine Triphosphate; D009218:Myosins