This aim of this paper is mainly to investigate the performance of two typical moment closure schemes in gene regulatory master equations of rational rate laws. When the reaction rate is polynomial, the error bounds between the authentic and approximate moments obtained by schemes of Gaussian moment closure and log-normal moment closure are explicitly given. When the reaction rate is not polynomial, it is shown that the two schemes both behave well in the absence of active-inactive state switch, but in the presence of active-inactive state switch the log-normal closure scheme is far superior to the Gaussian closure scheme in capturing the asymptotic ensemble statistics. Moreover, the accuracy of the log-normal closure method is further confirmed by steady-state analytic results and the conditional Gaussian closure method. It is also disclosed that optimal negative feedback exists in suppressing protein noise in the presence of the on-off switch control.

中文翻译：

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利用合理速率定律进行基因调控的矩动力学

本文的主要目的是研究两种典型的矩闭合方案在有理速率定律的基因调节主方程中的性能。当反应速率为多项式时，明确给出了由高斯矩闭合和对数正态矩闭合方案获得的真实和近似矩之间的误差范围。当反应速率不是多项式时，表明这两种方案在没有活动-非活动状态切换的情况下都表现良好，但是在存在活动-非活动状态切换的情况下，对数正态闭合方案远优于高斯型捕获渐近集合统计中的闭合方案。此外，通过稳态分析结果和条件高斯封闭法进一步证实了对数正态封闭法的准确性。