Linking fast and slow positive feedback loops creates an optimal bistable switch in cell signaling

Interlinked positive feedback loops are frequently found in biological signaling pathways. It is intriguing to study the dynamics, functions, and robustness of these motifs. Using numerical simulations and theoretical analysis, here we explore the sensitiveness and robustness of positive feedback loops with various time scales. Both single and dual loops can behave as a bistable switch. We study the responses of five types of bistable switches to noisy stimuli. The noise-induced transitions between two states are discussed in detail by using energy landscape. The dual-time switch, consisting of interconnected fast and slow loops, is both sensitive to stimuli and resistant to fluctuations in stimulus. This provides a novel mechanism for creating optimal bistable switches and memory modules. Our results also suggest that the dual-time switch can act as a ubiquitous motif with sensitive robustness in biological systems.