Biochemical regulatory networks governing diverse cellular processes such as stress-response,differentiation and cell cycle often contain coupled feedback loops. We aim at understandinghow features of feedback architecture, such as the number of loops, the sign of the loops andthe type of their coupling, affect network dynamical performance. Specifically, we investigatehow bistability range, maximum open-loop gain and switching times of a network withtranscriptional positive feedback are affected by additive or multiplicative coupling withanother positive- or negative-feedback loop. We show that a network's bistability range ispositively correlated with its maximum open-loop gain and that both quantities depend on thesign of the feedback loops and the type of feedback coupling. Moreover, we find that theaddition of positive feedback could decrease the bistability range if we control the basal levelin the signal-response curves of the two systems. Furthermore, the addition of negativefeedback has the capacity to increase the bistability range if its dissociation constant is muchlower than that of the positive feedback. We also find that the addition of a positive feedback toa bistable network increases the robustness of its bistability range, whereas the addition of anegative feedback decreases it. Finally, we show that the switching time for a transition from ahigh to a low steady state increases with the effective fold change in gene regulation. Insummary, we show that the effect of coupled feedback loops on the bistability range andswitching times depends on the underlying mechanistic details.
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