BPS2026 – From decay to rhythm: Sustained biological oscillators require more than chemistry alone

Many biological systems exhibit rhythmic oscillatory dynamics, yet it is shown that chemical reaction systems governed by Markovian dynamics cannot generate sustained oscillation in the ensemble-average sense. To overcome this limitation, we propose a general mechanism that couples a Markovian system to at least one other degree of freedom, such as a mechanical system, to achieve sustained oscillations with a desired frequency. We introduce two approaches, targeting different dynamical modes in the Markovian system and derive a governing principle for the non-Markovian system by analyzing the eigenvalues of the coupled dynamics. This principle is validated using a trimolecular reaction system, successfully producing sustained oscillations. Our study provides theoretical insights into how any chemical system can be coupled to another non-Markovian system to produce sustained oscillations. We also make a fundamental observation that stability and control of stable limit cycles must arise from the non-Markovian part of the coupled system.