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@article{Grima:2011:10.1063/1.3625958,
author = {Grima, R and Thomas, P and Straube, AV},
doi = {10.1063/1.3625958},
journal = {Journal of Chemical Physics},
title = {How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?},
url = {http://dx.doi.org/10.1063/1.3625958},
volume = {135},
year = {2011}
}
TY - JOUR
AB - The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order Ω(-32) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order Ω(-12) and variance estimates accurate to order Ω(-32). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.
AU - Grima,R
AU - Thomas,P
AU - Straube,AV
DO - 10.1063/1.3625958
PY - 2011///
SN - 1089-7690
TI - How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?
T2 - Journal of Chemical Physics
UR - http://dx.doi.org/10.1063/1.3625958
UR - http://www.ncbi.nlm.nih.gov/pubmed/21895155
UR - http://hdl.handle.net/10044/1/42208
VL - 135
ER -