Biology – Quantitative Biology – Quantitative Methods
Scientific paper
2011-06-24
Biology
Quantitative Biology
Quantitative Methods
39 pages, 3 figures, accepted for publication in J. Chem. Phys
Scientific paper
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 $\Omega^{-3/2}$ for reaction systems which do not obey detailed balance and at least accurate to order $\Omega^{-2}$ for systems obeying detailed balance, where $\Omega$ 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 $\Omega^{-1/2}$ and variance estimates accurate to order $\Omega^{-3/2}$. 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.
Grima Ramon
Straube Arthur V.
Thomas Philipp
No associations
LandOfFree
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations? will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-393702