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.
Xing
Jianhua
J
Departments of Molecular and Cellular Biology and Environmental Science, University of California, Berkeley, California, USA.
Wang
Hongyun
H
Oster
George
G
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