Phase Separation Induces Oscillations in Negative Feedback Loops

Oscillations constitute a defining feature of nonequilibrium processes of life. We analyze a minimal degradation-mediated negative feedback loop, in which the final species in a linear cascade enzymatically degrades the first component. By coupling mean-field ordinary differential equations with a phase-separated component, we reveal novel inhibition scalings that expand the parameter regime supporting oscillations. Extending to arbitrary sublinear exponents and network sizes, we derive general bifurcation criteria and identify universal relations for oscillation onset in a reduced time-delay model. Our results show that phase separation promotes oscillations, uncovering a nonequilibrium mechanism for dynamic regulation in cellular systems.