Fluctuations in gene regulatory networks as Gaussian colored noise.
The study of fluctuations in gene regulatory networks is extended to the case of Gaussian colored noise. First, 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 formulas for the variances and covariance of molecular concentrations for a regulatory network near a stable equilibrium explicitly. Two examples, the gene autoregulatory 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.
Huang
Ming-Chang
MC
Department of Physics and Center for Nonlinear and Complex Systems, Chung-Yuan Christian University, Chungli 32023, Taiwan.
Wu
Jinn-Wen
JW
Luo
Yu-Pin
YP
Petrosyan
Karen G
KG
D008957:Models, Genetic; D013269:Stochastic Processes