  Oscillation is an important cellular process that regulates timing of
different vital life cycles. However, in the noisy cellular environment,
oscillations can be highly inaccurate due to phase fluctuations. It remains
poorly understood how biochemical circuits suppress phase fluctuations and what
is the incurred thermodynamic cost. Here, we study four different types of
biochemical oscillations representing three basic oscillation motifs shared by
all known oscillatory systems. We find that the phase diffusion constant
follows the same inverse dependence on the free energy dissipation per period
for all systems studied. This relationship between the phase diffusion and
energy dissipation is shown analytically in a model of noisy oscillation.
Microscopically, we find that the oscillation is driven by multiple
irreversible cycles that hydrolyze the fuel molecules such as ATP; the number
of phase coherent periods is proportional to the free energy consumed per
period. Experimental evidence in support of this universal relationship and
testable predictions are also presented.
