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### How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

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1106.4891v2.pdf | Accepted version | 350.94 kB | Adobe PDF | View/Open |

Title: | How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations? |

Authors: | Grima, R Thomas, P Straube, AV |

Item Type: | Journal Article |

Abstract: | 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(-3∕2) 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(-1∕2) and variance estimates accurate to order Ω(-3∕2). 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. |

Issue Date: | 28-Aug-2011 |

Date of Acceptance: | 27-Jul-2011 |

URI: | http://hdl.handle.net/10044/1/42208 |

DOI: | https://dx.doi.org/10.1063/1.3625958 |

ISSN: | 1089-7690 |

Publisher: | AIP Publishing |

Journal / Book Title: | Journal of Chemical Physics |

Volume: | 135 |

Issue: | 8 |

Copyright Statement: | © 2011 American Institute of Physics |

Keywords: | Models, Chemical Multivariate Analysis Reproducibility of Results q-bio.QM cond-mat.mes-hall cond-mat.stat-mech Chemical Physics 02 Physical Sciences 03 Chemical Sciences 09 Engineering |

Publication Status: | Published |

Conference Place: | United States |

Article Number: | ARTN 084103 |

Appears in Collections: | Mathematics Applied Mathematics and Mathematical Physics Faculty of Natural Sciences |