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This paper extends previous work to show that stable non-monotonic steady state response curves in arbitrary systems require either an incoherent feedforward loop (IFFL) or a combination of positive and negative feedback loops, refuting the conjecture that IFFLs are strictly necessary. The authors analyze signaling pathways, gene regulation, and consumer-resource models to identify necessary motifs for non-monotonic responses and offer an alternative proof of the Competitive Exclusion Principle. This work provides a more comprehensive understanding of the network structures that can generate complex dynamic behaviors.
Non-monotonic responses in complex biological systems are not solely dependent on incoherent feedforward loops; a combination of positive and negative feedback is also sufficient.
Non-monotonic steady state response curves can readily arise from an incoherent feedforward loop (IFFL), which has also been conjectured to be a necessary mechanism. In a previous work, we showed this conjecture to be false for systems where the control parameter directly influences only one state variable. Here, we extend this result to arbitrary systems. We show that a stable non-monotonic response requires either an IFFL or a combination of positive and negative feedback loops. Finally, we apply our theoretical findings to three network-structured biological contexts: signaling pathways, gene regulation, and ecological consumer-resource models. For the first two contexts, we identify necessary motifs for non-monotonic responses, while for consumer-resource models, we provide an alternative proof of the Competitive Exclusion Principle.