The Cost of Biological Rhythms: From Dynamical Systems to Thermodynamics

Biological clocks maintain precise rhythmicity despite molecular noise and environmental fluctuations. Using the KaiABC circadian oscillator, we investigate how physical constraints shape the emergence and robustness of biological rhythms. By constructing a dynamical phase diagram based on KaiA and KaiC concentrations, we identify sharply bounded limit-cycle regions. Near the Hopf bifurcation, intrinsic noise induces coherence resonance, enabling oscillations even when deterministic limit cycles are absent. Within the oscillatory regime, increased temporal precision requires higher energetic expenditure, consistent with the thermodynamic uncertainty relation. The cost-minimizing oscillation period (~21 h) lies close to the environmental 24 h cycle, supporting efficient entrainment. Our results reveal a fundamental connection between dynamical systems behavior and thermodynamic constraints, establishing general physical principles that govern the precision, robustness, and efficiency of biological clocks.