Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise

摘要

The study of fluctuations in gene regulatory networks is extended to the caseof Gaussian colored noise. Firstly, the solution of the corresponding Langevinequation with colored noise is expressed in terms of an Ito integral. Then, twoimportant lemmas concerning the variance of an Ito integral and the covarianceof two Ito integrals are shown. Based on the lemmas, we give the generalformulae for the variances and covariance of molecular concentrations for aregulatory network near a stable equilibrium explicitly. Two examples, the geneauto-regulatory network and the toggle switch, are presented in details. Ingeneral, it is found that the finite correlation time of noise reduces thefluctuations and enhances the correlation between the fluctuations of themolecular components.