Incoherent feedforward loop dominates the robustness and tunability of necroptosis biphasic, emergent, and coexistent dynamics.

Biphasic dynamics, the variable-dependent ability to enhance or restrain biological function, is prevalent in natural systems. Accompanied by biphasic dynamics, necroptosis signaling also appears emergent and coexistent dynamics. However, it remains elusive how the properties of these dynamics are characterized by specific circuit structures and components. Starting with necroptosis circuit modeling, we systematically analyzed the network topology for achieving RIP1-dependent biphasic, emergent, and coexistent (BEC) dynamics. RIP1-RIP3-Caspase-8 (C8) incoherent feedforward loop embedded with positive feedback of RIP3 to RIP1 is identified as the core topology. The peak value of RIP3 phosphorylation is determined to present a scale-invariant feature, dictating BEC dynamics and the bell-shaped regulation of necroptosis biphasic dynamics. To quantitatively determine the uncertainty of necroptosis coexistent dynamics, potential landscape and Shannon entropy that measure entropy production during cell death are introduced for the first time. Further random necroptosis circuit analysis identifies the bell-shaped regulation of necroptosis biphasic dynamics by RIP3 auto-phosphorylation, which acts as a complementary process for robustly attaining BEC dynamics. Finally, we searched all possible two- and three-node circuit topologies to screen those that could perform BEC dynamics. A complete atlas of three-node circuit BEC dynamics is generated and only three minimal circuits emerge as robust solutions, confirming incoherent feedforward loop is the core topology. Analysis of the association between the minimal circuit structure and robustness proves that the identified optimal functional achievement structure is highly consistent with the experimental observed RIP1-RIP3-C8 topology. Overall, through highlighting a finite set of circuits, this study yields guiding principles that enable the mapping, modulation, and design of circuits for BEC dynamics in diverse synthetic biology applications.