Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise

Stochastic resonance is investigated to explain the beneficial effect of Lévy noise on gene expression of genetic toggle model with harmonic excitation. The dynamic change of protein concentration of genetic toggle model under combined drives of harmonic excitation and Lévy noise is obtained numerically. Stochastic resonance is presented through the classical measure of signal-to-noise-ratio. Then from two aspects of combined drives on the protein at high or low concentration, the changes of protein concentration and signal-to-noise-ratio are discussed, respectively. When combined drives are within the protein at high concentration, the increasing Lévy noise intensity can promote the transition between the high and low concentrations, and the low protein concentration hardly fluctuates under the small noise intensity. It is also shown that the increase of stability index, skewness parameter of Lévy noise and amplitude of harmonic excitation can suppress the optimum collaboration of stochastic resonance. On the other hand, when combined drives are within the protein at low concentration, the increasing noise intensity can enhance the transition between the high and low concentrations, and the increase of stability index, skewness parameter and amplitude can strengthen the optimum collaboration of stochastic resonance. By the synergic actions of stochastic resonance, it is demonstrated that combined effect of harmonic excitation and Lévy stimuli can be utilized to promote the gene expression of proteins in genetic toggle model.