Gómez-Uribe Carlos A, Verghese George C
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
J Chem Phys. 2007 Jan 14;126(2):024109. doi: 10.1063/1.2408422.
The intrinsic stochastic effects in chemical reactions, and particularly in biochemical networks, may result in behaviors significantly different from those predicted by deterministic mass action kinetics (MAK). Analyzing stochastic effects, however, is often computationally taxing and complex. The authors describe here the derivation and application of what they term the mass fluctuation kinetics (MFK), a set of deterministic equations to track the means, variances, and covariances of the concentrations of the chemical species in the system. These equations are obtained by approximating the dynamics of the first and second moments of the chemical master equation. Apart from needing knowledge of the system volume, the MFK description requires only the same information used to specify the MAK model, and is not significantly harder to write down or apply. When the effects of fluctuations are negligible, the MFK description typically reduces to MAK. The MFK equations are capable of describing the average behavior of the network substantially better than MAK, because they incorporate the effects of fluctuations on the evolution of the means. They also account for the effects of the means on the evolution of the variances and covariances, to produce quite accurate uncertainty bands around the average behavior. The MFK computations, although approximate, are significantly faster than Monte Carlo methods for computing first and second moments in systems of chemical reactions. They may therefore be used, perhaps along with a few Monte Carlo simulations of sample state trajectories, to efficiently provide a detailed picture of the behavior of a chemical system.
化学反应中的内在随机效应，尤其是在生化网络中，可能导致行为与确定性质量作用动力学（MAK）预测的行为显著不同。然而，分析随机效应通常在计算上既费力又复杂。作者在此描述了他们所称的质量涨落动力学（MFK）的推导和应用，这是一组确定性方程，用于跟踪系统中化学物质浓度的均值、方差和协方差。这些方程是通过对化学主方程的一阶和二阶矩的动力学进行近似得到的。除了需要知道系统体积外，MFK描述只需要用于指定MAK模型的相同信息，并且写下来或应用起来并没有显著更难。当涨落的影响可以忽略不计时，MFK描述通常简化为MAK。MFK方程能够比MAK更好地描述网络的平均行为，因为它们纳入了涨落对均值演化的影响。它们还考虑了均值对方差和协方差演化的影响，以在平均行为周围产生相当准确的不确定带。MFK计算虽然是近似的，但比用于计算化学反应系统中一阶和二阶矩的蒙特卡罗方法要快得多。因此，它们也许可以与一些样本状态轨迹的蒙特卡罗模拟一起使用，以有效地提供化学系统行为的详细图景。
