Colored noise induced bistable switch in the genetic toggle switch systems

Noise can induce various dynamical behaviors in nonlinear systems. White noise perturbed systems have been extensively investigated during the last decades. In gene networks, experimentally observed extrinsic noise is colored. As an attempt, we investigate the genetic toggle switch systems perturbed by colored extrinsic noise and with kinetic parameters. Compared with white noise perturbed systems, we show there also exists optimal colored noise strength to induce the best stochastic switch behaviors in the single toggle switch, and the best synchronized switching in the networked systems, which demonstrate that noise-induced optimal switch behaviors are widely in existence. Moreover, under a wide range of system parameter regions, we find there exist wider ranges of white and colored noises strengths to induce good switch and synchronization behaviors, respectively; therefore, white noise is beneficial for switch and colored noise is beneficial for population synchronization. Our observations are very robust to extrinsic stimulus strength, cell density, and diffusion rate. Finally, based on the Waddington's epigenetic landscape and the Wiener-Khintchine theorem, physical mechanisms underlying the observations are interpreted. Our investigations can provide guidelines for experimental design, and have potential clinical implications in gene therapy and synthetic biology.