%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 }