  Temperature compensation is a notable property of circadian oscillators that
indicates the insensitivity of the oscillator system's period to temperature
changes; the underlying mechanism, however, is still unclear. We investigated
the influence of protein dimerization and cooperative stability in protein
degradation on the temperature compensation ability of two oscillators. Here,
cooperative stability means that high-order oligomers are more stable than
their monomeric counterparts. The period of an oscillator is affected by the
parameters of the dynamic system, which in turn are influenced by temperature.
We adopted the Repressilator and the Atkinson oscillator to analyze the
temperature sensitivity of their periods. Phase sensitivity analysis was
employed to evaluate the period variations of different models induced by
perturbations to the parameters. Furthermore, we used experimental data
provided by other studies to determine the reasonable range of parameter
temperature sensitivity. We then applied the linear programming method to the
oscillatory systems to analyze the effects of protein dimerization and
cooperative stability on the temperature sensitivity of their periods, which
reflects the ability of temperature compensation in circadian rhythms. Our
study explains the temperature compensation mechanism for circadian clocks.
Compared with the no-dimer mathematical model and linear model for protein
degradation, our theoretical results show that the nonlinear protein
degradation caused by cooperative stability is more beneficial for realizing
temperature compensation of the circadian clock.
