A dual role of extrinsic noise in coupled synthetic clock cells due to a two-steps synchronization mechanism

Based on the model describing two coupled synthetic clock cells, the synchronization dynamics under stochastic noise are explored. As extrinsic noise from signal is the predominant form of noise for all gene promoters, we investigate the effects of extrinsic noise original from signal molecule by evaluating the order parameters. It is found that strong noise is beneficial for the synchronization of loose-coupling system, while it destroys the synchronization of tight-coupling system. The underlying mechanisms of these two opposite effects are clarified numerically and theoretically. Our research illustrates that (i) when the coupling strength is small, the noise mainly adjusts the period difference of two cells and the system becomes regular. Theoretical study reveals that the mean effect of noise is like to be influx while signal flow is efflux under such a situation. (ii) With the increment of coupling strength, the cells have the same frequency. It is obvious that the noise mainly changes the phase difference between the two cells and destroys the synchronization of the system. (iii) We also demonstrate that, under certain moderate noise intensities, the noise can induce the synchronization order to be the worst. This nonlinear behavior only can be observed in a very narrow region of coupling strength.