Physical Constraints on the Rhythmicity of the Biological Clock

Abstract: Circadian rhythms in living organisms are temporal orders emerging from biochemical circuits driven out of equilibrium. Here, we study how the rhythmicity of a biochemical clock is shaped using the KaiABC system. A phase diagram constructed as a function of KaiC and KaiA concentrations reveals a sharply bounded limit-cycle region, which naturally explains arrhythmia upon protein over-expression. Beyond the Hopf bifurcation, intrinsic noise enables regular oscillation via coherence resonance. Within the limit-cycle region, greater rhythmic precision incurs a higher energetic cost, following the thermodynamic uncertainty relation. The cost-minimizing period of the KaiABC clock ($\sim$21-hr) is close enough to entrain to 24-hr cycle of environment. Our study substantiates universal physical constraints on the robustness, precision, and efficiency of noisy biological clocks.