Colored noise induced switch in the gene transcriptional regulatory system

Abstract

The colored noise induced switch in the gene transcriptional regulatory system is investigated. The approximate Fokker-Planck equation is obtained based on the Novikov theorem and the Fox approach. The explicit expressions of the steady state probability distribution, the mean value, and the mean first passage time are derived. After the numerical computations, these results show that the TF-A monomer concentration switches from the off position to the on position with the self-correlation time of the multiplicative noise increasing. The TF-A monomer concentration switches from the on position to the off position with the self-correlation time of the additive noise increasing. With the two kinds of the self-correlation time increasing, the mean first passage time becomes large, namely, the TF-A monomer concentration switch becomes difficult. The theoretical predictions are found to be in basic agreement with numerical results.