Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise

Details Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise

2009-10-23

arxiv.org/abs/0910.4468v2

Biology

Quantitative Biology

Molecular Networks

10 pages, 4 figures

Scientific paper

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.

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