The impact of decoys on a genetic oscillator based on coupled positive-negative feedbacks

Abstract

Within cells, transcription factors (TFs) bind to a wide range of nonspecific genomic sites in addition to their target sites. Binding to such high affinity “decoys” has been shown to qualitatively alter the dynamics of gene regulatory circuits. Analyzing simple gene expression models with decoy binding we derive formulas for the TF response time as a function of the number of decoys, binding affinity, and stability of the decoy-bound TF. Our results show that while on one hand, decoys make the response sluggish whenever decoy binding stabilizes the TF, on the other hand, decoys can accelerate responses by destabilizing the bound TF. We apply these results in the context of a genetic oscillator based on an activator-repressor motif, where sustained oscillations result from a rapid activator-mediated positive feedback working in conjunction with a slow repressor-mediated negative feedback. Consistent with our response time analysis, we find that activator binding to decoy sites can destroy oscillations in the case of a stable decoy-activator complex that functions to slow down the positive feedback. In contrast, an unstable decoy-activator complex can expand the oscillatory parameter regime. In conclusion, our response time analysis provides intuitive insights into the emergence of sustained oscillations.