标题： 基因调控网络中的波动作为高斯色噪声 显示英文标题

标题： Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise

摘要： 研究基因调控网络中的波动扩展到了高斯色噪声的情况。 首先，用伊藤积分表达了带有色噪声的相应朗之万方程的解。 然后，展示了两个关于伊藤积分方差和两个伊藤积分协方差的重要引理。 基于这些引理，我们明确给出了接近稳定平衡点的调控网络中分子浓度的方差和协方差的一般公式。 详细介绍了两个例子，即基因自调控网络和切换开关。 一般来说，发现噪声的有限相关时间会减少波动，并增强分子组分波动之间的相关性。 显示英文摘要

摘要： The study of fluctuations in gene regulatory networks is extended to the case of Gaussian colored noise. Firstly, the solution of the corresponding Langevin equation with colored noise is expressed in terms of an Ito integral. Then, two important lemmas concerning the variance of an Ito integral and the covariance of two Ito integrals are shown. Based on the lemmas, we give the general formulae for the variances and covariance of molecular concentrations for a regulatory network near a stable equilibrium explicitly. Two examples, the gene auto-regulatory network and the toggle switch, are presented in details. In general, it is found that the finite correlation time of noise reduces the fluctuations and enhances the correlation between the fluctuations of the molecular components.