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Genetic oscillators, such as circadian clocks, are constantly perturbed bymolecular noise arising from the small number of molecules involved in generegulation. One of the strongest sources of stochasticity is the binary noisethat arises from the binding of a regulatory protein to a promoter in thechromosomal DNA. In this study, we focus on two minimal oscillators based onactivator titration and repressor titration to understand the key parametersthat are important for oscillations and for overcoming binary noise. We showthat the rate of unbinding from the DNA, despite traditionally being considereda fast parameter, needs to be slow to broaden the space of oscillatorysolutions. The addition of multiple, independent DNA binding sites furtherexpands the oscillatory parameter space for the repressor-titration oscillatorand lengthens the period of both oscillators. This effect is a combination ofincreased effective delay of the unbinding kinetics due to multiple bindingsites and increased promoter ultrasensitivity that is specific for repression.We then use stochastic simulation to show that multiple binding sites increasethe coherence of the oscillations by mitigating the binary noise. Slow valuesof DNA unbinding rate are also effective in alleviating molecular noise due tothe increased distance from the bifurcation point. Our work demonstrates howDNA binding sites and slow unbinding kinetics, which are often omitted inbiophysical models of gene circuits, can have a significant impact on thetemporal and stochastic dynamics of genetic oscillators.

Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators