A study of the accuracy of moment-closure approximations for stochastic chemical kinetics
A study of the accuracy of moment-closure approximations for stochastic chemical kinetics
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DOI：
10.1063/1.3702848
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发表时间：
2012-04-21
影响因子：
4.4
通讯作者：
Grima, Ramon
中科院分区：
文献类型：
--
作者：
Grima, Ramon
近些年来，矩闭合近似已成为一种流行的方法来估计随机化学反应中涉及的物种的平均浓度以及浓度波动的方差和协方差，例如细胞内的那些。这些方法背后的典型假设是，化学主方程的概率分布函数解的所有高于某一阶的累积量都可以忽略不计地很小，因此可以设为零。这些近似是临时的，因此这类方法的预测的可靠性目前尚不清楚。本文研究了由单分子和双分子反应组成的单稳态化学体系的两矩近似(2MA)(三阶和高阶累积量为零)和三矩近似(3MA)(四阶和高阶累积量为零)的精度。我们利用系统规模展开这一求解单稳态反应体系化学主方程的系统方法，在大反应体积的限制下，计算了速率方程平均浓度预测的一阶和二阶修正，以及线性噪声近似的方差和协方差预测的一阶修正。我们还使用2MA和3MA计算了这些修正。将后者的结果与系统规模展开式的结果进行了比较，结果表明：(1)2MA准确地捕捉到了速率方程的一阶修正，但它对线性噪声近似的一阶修正显示了对速率常数的错误依赖。(Ii)3MA准确地捕获了速率方程预测的一阶和二阶修正以及线性噪声近似的一阶修正。因此，虽然2MA和3MA都比速率方程更准确，但只有3MA比所有参数空间的线性噪声近似更准确。分析结果在二聚化和酶催化反应中得到了数值验证。(C)2012年美国物理研究所。[http://dx.doi.org/10.1063/1.3702848]
Moment-closure approximations have in recent years become a popular means to estimate the mean concentrations and the variances and covariances of the concentration fluctuations of species involved in stochastic chemical reactions, such as those inside cells. The typical assumption behind these methods is that all cumulants of the probability distribution function solution of the chemical master equation which are higher than a certain order are negligibly small and hence can be set to zero. These approximations are ad hoc and hence the reliability of the predictions of these class of methods is presently unclear. In this article, we study the accuracy of the two moment approximation (2MA) (third and higher order cumulants are zero) and of the three moment approximation (3MA) (fourth and higher order cumulants are zero) for chemical systems which are monostable and composed of unimolecular and bimolecular reactions. We use the system-size expansion, a systematic method of solving the chemical master equation for monostable reaction systems, to calculate in the limit of large reaction volumes, the first-and second-order corrections to the mean concentration prediction of the rate equations and the first-order correction to the variance and covariance predictions of the linear-noise approximation. We also compute these corrections using the 2MA and the 3MA. Comparison of the latter results with those of the system-size expansion shows that: (i) the 2MA accurately captures the first-order correction to the rate equations but its first-order correction to the linear-noise approximation exhibits the wrong dependence on the rate constants. (ii) the 3MA accurately captures the first-and second-order corrections to the rate equation predictions and the first-order correction to the linear-noise approximation. Hence while both the 2MA and the 3MA are more accurate than the rate equations, only the 3MA is more accurate than the linear-noise approximation across all of parameter space. The analytical results are numerically validated for dimerization and enzyme-catalyzed reactions. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/ 1.3702848]