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.
%0 Journal Article
%1 Xing_2005_1551
%A Xing, Jianhua
%A Wang, Hongyun
%A Oster, George
%D 2005
%J Biophys. J.
%K 't, Adenosine Algorithms; Animals; Biological Biophysics; Chemical; Computer Extramural; Gov't, Gov; Kinetics; Models, Molecular Motors; Myosins; N.I.H., Non-P.H.S.; P.H.S.; Processes; Research Simulation; Statistical; Stochastic Support, Temperature; Theoretical; Thermodynamics Transport; Triphosphate; U.S.
%N 3
%P 1551--1563
%R 10.1529/biophysj.104.055178
%T From continuum Fokker-Planck models to discrete kinetic models.
%U http://dx.doi.org/10.1529/biophysj.104.055178
%V 89
%X 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.
@article{Xing_2005_1551,
abstract = {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.},
added-at = {2009-06-03T11:20:58.000+0200},
author = {Xing, Jianhua and Wang, Hongyun and Oster, George},
biburl = {https://www.bibsonomy.org/bibtex/2753c2e45d82372e4155e022732d4c0d3/hake},
description = {The whole bibliography file I use.},
doi = {10.1529/biophysj.104.055178},
file = {Xing_2005_1551.pdf:Xing_2005_1551.pdf:PDF},
interhash = {d34a7d6cfdf62a7c5ab235ee8041f6f7},
intrahash = {753c2e45d82372e4155e022732d4c0d3},
journal = {Biophys. J.},
keywords = {'t, Adenosine Algorithms; Animals; Biological Biophysics; Chemical; Computer Extramural; Gov't, Gov; Kinetics; Models, Molecular Motors; Myosins; N.I.H., Non-P.H.S.; P.H.S.; Processes; Research Simulation; Statistical; Stochastic Support, Temperature; Theoretical; Thermodynamics Transport; Triphosphate; U.S.},
month = Sep,
number = 3,
pages = {1551--1563},
pii = {biophysj.104.055178},
pmid = {15994886},
timestamp = {2009-06-03T11:21:38.000+0200},
title = {From continuum Fokker-Planck models to discrete kinetic models.},
url = {http://dx.doi.org/10.1529/biophysj.104.055178},
volume = 89,
year = 2005
}