Topology protects the emergence of coherent oscillations in the circadian rhythm

Stable collective dynamics are often observed in complex biochemical networks, such as in emergent oscillations or attractors, and are crucial for system regulation and navigation. How these robust dynamics arise remains unclear, given the large reaction space and stochasticity demonstrated by underlying components. Here, we introduce a topological model that demonstrates emergent oscillations at the network edge, reducing the reaction space to an effectively lower-dimensional current without imposing this simplification by hand. We demonstrate that the entropy production reduces to contributions from the edge current, resulting in a high oscillation coherence for a given thermodynamic drive as compared to other typical oscillator models. We further introduce a new predictor of coherence from the analysis of spectral gaps that is inspired by topological band theory and show that our spectrum saturates a thermodynamic bound. We discuss the model’s relevance to the KaiC system that regulates the circadian rhythm and propose experimental predictions. Our work points to a new mechanism for emergent robust dynamics in complex biological networks and fresh insights into why biological function remains stable despite widespread stochasticity and heterogeneity.