  Genetic oscillators, such as circadian clocks, are constantly perturbed by
molecular noise arising from the small number of molecules involved in gene
regulation. One of the strongest sources of stochasticity is the binary noise
that arises from the binding of a regulatory protein to a promoter in the
chromosomal DNA. In this study, we focus on two minimal oscillators based on
activator titration and repressor titration to understand the key parameters
that are important for oscillations and for overcoming binary noise. We show
that the rate of unbinding from the DNA, despite traditionally being considered
a fast parameter, needs to be slow to broaden the space of oscillatory
solutions. The addition of multiple, independent DNA binding sites further
expands the oscillatory parameter space for the repressor-titration oscillator
and lengthens the period of both oscillators. This effect is a combination of
increased effective delay of the unbinding kinetics due to multiple binding
sites and increased promoter ultrasensitivity that is specific for repression.
We then use stochastic simulation to show that multiple binding sites increase
the coherence of the oscillations by mitigating the binary noise. Slow values
of DNA unbinding rate are also effective in alleviating molecular noise due to
the increased distance from the bifurcation point. Our work demonstrates how
DNA binding sites and slow unbinding kinetics, which are often omitted in
biophysical models of gene circuits, can have a significant impact on the
temporal and stochastic dynamics of genetic oscillators.
