From Decay to Rhythm: Coherent Biological Oscillators Require More Than Chemistry Alone

Many biological systems exhibit sustained, coherent oscillations despite substantial noise. In contrast, chemical reaction systems governed by Markovian dynamics cannot sustain coherent ensemble oscillations, as the stochastic nature of state transitions inevitably causes the oscillation period to drift. 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 noiseresistant coherent 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 and coherent oscillations. Our study provides theoretical insights into how any chemical system can be coupled to another non-Markovian system to produce sustained and coherent oscillations with a precise period. 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.