Effect of multiplicative and additive noise on genetic transcriptional regulatory mechanism

A multiplicative noise and an additive noise are introduced in the kinetic model of Smolen–Baxter–Byrne [P. Smolen, D.A. Baxter, J.H. Byrne, Amer. J. Physiol. Cell. Physiol. 274 (1998) 531], in which the expression of gene is controlled by protein concentration of transcriptional activator. The Fokker–Planck equation is solved and the steady-state probability distribution is obtained numerically. It is found that the multiplicative noise converts the bistability to monostability that can be regarded as a noise-induced transition. The additive noise reduces the transcription efficiency. The correlation between the multiplicative noise and the additive noise works as a genetic switch and regulates the gene transcription effectively.