Oscillator death in coupled biochemical oscillators

Circadian rhythm, cell division and metabolic oscillations are rhythmic cellular behaviors that must be both robust but also to respond to changes in their environment. In this work, we study emergent behavior of coupled biochemical oscillators, modeled as repressilators. While more traditional approaches to oscillators synchronization often use phase oscillators, our approach uses switching systems that may be more appropriate for cellular networks dynamics governed by biochemical switches. We show that while one-directional coupling maintains stable oscillation of individual repressilators, there are well-characterized parameter regimes of mutually coupled repressilators, where oscillations stop. In other parameter regimes, joint oscillations continue. Our results may have implications for the understanding of condition-dependent coupling and un-coupling of regulatory networks.