Feedback circuits are important building blocks of gene regulatory network. Recent studies with simplified models found the advantage of coupled fast and slow feedback loops in creating bistable switch, and interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory. Based on the same feedback structure and mathematical model, the effect of noise on persistence of memory is investigated. It is found that (1) an intermediate amount of single-parameter noise plays a constructive role in persisting memory through noise-induced changing from monostable to bistable region, while larger single-parameter noise destroys the memory ability of the system through noise-induced transition between two stable states. (2) Different from the single-parameter noise, arbitrary amount of the internal noise destroys the memory ability of the system. (3) For the same feedback structure with less nonlinear feedback which is not enough to render the system bistability, the single-parameter noise can play similar constructive role through rendering the system bistability.

• Received 20 April 2009

DOI:https://doi.org/10.1103/PhysRevE.80.011907