  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.
