Stochastic resonance in the gene transcriptional regulatory system subjected to noises

We have investigated in the adiabatic limit the phenomenon of stochastic resonance in the gene transcriptional regulatory system subjected to an additive noise, a multiplicative noise, and a weakly periodic signal. Using the general two-state approach for the asymmetry system, the analytic expression of signal-to-noise ratio is obtained. The effects of the additive noise intensity alpha, the multiplicative noise intensity D and the amplitude of input periodic signal A on the signal-to-noise ratio are analysed by numerical calculation. It is found that the existence of a maximum in the R(SNR-alpha) and R(SNR)-D plots is the identifying characteristic of the stochastic resonance phenomenon in the weakened noise intensity region. The stochastic resonance phenomena are restrained with increasing alpha and D, and enhanced with increasing A.