From continuum Fokker-Planck models to discrete kinetic models.
Biophys. J., 89 (3):
1551--1563 (September 2005)DOI: 10.1529/biophysj.104.055178
Zusammenfassung
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.
Beschreibung
The whole bibliography file I use.