  Living systems regulate many aspects of their behavior through periodic
oscillations of molecular concentrations, which function as `biochemical
clocks.' These clocks are intrinsically subject to thermal fluctuations, so
that the duration of a full oscillation cycle is random. Their success in
carrying out their biological function is thought to depend on the degree to
which these fluctuations in the cycle period can be suppressed. Biochemical
oscillators also require a constant supply of free energy in order to break
detailed balance and maintain their cyclic dynamics. For a given free energy
budget, the recently discovered `thermodynamic uncertainty relation' yields the
magnitude of period fluctuations in the most precise conceivable free-running
clock. In this paper, we show that computational models of real biochemical
clocks severely underperform this optimum, with fluctuations several orders of
magnitude larger than the theoretical minimum. We argue that this suboptimal
performance is due to the small number of internal states per molecule in these
models, combined with the high level of thermodynamic force required to
maintain the system in the oscillatory phase. We introduce a new model with a
tunable number of internal states per molecule, and confirm that it approaches
the optimal precision as this number increases.
