Topological design principle for the robustness of necroptosis biphasic, emergent, and coexistent (BEC) dynamics

Biphasic dynamics, the variable-dependent ability to enhance or restrain biological function, is prevalent in natural systems. Accompanied by biphasic dynamics, necroptosis signaling dominated by RIP1 also appears emergent and coexistent dynamics. Here, we identify the RIP1-RIP3-C8 incoherent feedforward loop embedded with positive feedback of RIP3 to RIP1 is the core topology, and the scale-free feature of RIP3 peak value dictates necroptosis BEC dynamics. Entropy production is introduced to quantify the uncertainty of coexistent dynamics. RIP3 auto-phosphorylation is further determined as a complementary process for robustly attaining necroptosis BEC dynamics. Through screening all possible two- and three-node circuit topologies, a complete atlas of three-node circuit BEC dynamics is generated and only three minimal circuits emerge as robust solutions, proving incoherent feedforward loop is the core topology. Overall, through highlighting a finite set of circuits, this study yields guiding principles for mapping, modulating, and designing circuits for BEC dynamics in biological systems. ### Competing Interest Statement The authors have declared no competing interest.