Genomic decoy sites enhance the oscillatory regime of a biomolecular clock

Rhythms in gene regulatory networks are ubiquitous, from the bacterial circadian clock to the segmentation clock of vertebrates. There are many decoy binding sites in a genome where regulatory proteins bind and control the expression of a gene. The role decoys on oscillatory regulatory networks is not well understood. Here, in the presence of decoy binding sites, we investigate the stability and the precision of the well-known Goodwin oscillator, a minimal model for regulatory oscillators. We derive the stability criterion in the presence of decoys and find that decoy abundance increases the parameter space where oscillating solutions exist. If the Goodwin system does not show any oscillation without decoy binding sites, a sustained oscillation is possible in their presence. Finally, we study precision the oscillation using stochastic simulations and find that the decoy binding makes the oscillation more precise.