Noise-induced dynamics in the mixed-feedback-loop network motif

In this paper, we present a stochastic model for the mixed-feedback loop (MFL), a motif found in integrated cellular networks of transcription regulation and protein-protein interaction. Previous bifurcation analysis indicates that this motif can serve as a bistable switch or a clock. We investigate how extrinsic and intrinsic noise affects its dynamic behaviors systematically. We find that this motif can exploit noise to enrich its dynamical performance. When the MFL is in the bistable region, under fluctuation of extrinsic noise, the MFL system can switch from one steady state to the other and meanwhile one protein's production is amplified for more than three orders of magnitude. Further, from an engineering perspective, this noise-based switch and amplifier for gene expression is very easy to control. Without extrinsic noise, spontaneous transition between states occurs as the consequence of intrinsic noise. Such a switch is controlled by the parameters and system size. On the other hand, intrinsic noise can induce sustained stochastic oscillation when the corresponding deterministic system does not oscillate. Such stochastic oscillation shows the best performance at an optimal noise level, indicating the occurrence of intrinsic noise stochastic resonance which can contribute to the robustness of this oscillator. When considering the effects of extrinsic noise near bifurcation points, a similar phenomenon of extrinsic noise stochastic resonance is unveiled.