Different effects of redundant feedback loops on a bistable switch

Bistable switches have important roles in cellular decision-making processes. Bistability can be the consequence of positive or double-negative feedback loops. Although necessary, such feedback is not sufficient for bistability, which also requires nonlinearity. Nonlinearity can be provided by synergy of multiple feedback loops or by an ultrasensitive response within a single feedback loop. However, these two possibilities are not mutually exclusive; a combination of them is also possible. Here we analyze a biochemical regulatory network that controls a crucial cell cycle transition in all eukaryotic cells and contains multiple redundant feedback loops and nonlinearity. We show in this realistic biological example that two redundant feedback loops have different effects on the position of one of the saddle-node bifurcations of the system, which determines where the system switches. This illustrates that even though the roles of positive and double-negative feedbacks have been regarded as equivalent, the difference in their architectures can lead to differences in their effects on the system. We speculate that this conclusion could be general for other bistable systems with redundant feedback loops.