Feedback loops interlocked at competitive binding sites amplify and facilitate genetic oscillations.

Positive and negative feedback loops are often present in regulatory networks for genetic oscillations. Relative time scales and integration of these feedback loops are key to robust oscillations in expression levels. Using examples from the circadian clock and synthetic genetic oscillators, we study positive and negative feedback loops interlocked at competitive binding sites. In the mammalian circadian clock, a key clock gene Bmal1 is regulated by the activator ROR and the repressor REV-ERB. Conversely, Bmal1 activates both of them, forming interlocked feedback loops. Previous experiments indicate that the activator and repressor compete for the same binding sites in the Bmal1 promoter. Transcription patterns predict that ROR peaks later than REV-ERB and, moreover, the peak phase difference between them is small. Using mathematical modeling we reveal an optimal ratio of dissociation constants of an activator and a repressor for the competitive binding sites to enhance the amplitude of Bmal1 oscillations. This optimal ratio arises only when the amplitude of the repressor is larger than that of the activator. Secondly, we reveal that the preference of binding sites for an activator and a repressor depends on their relative time scales. A previous study demonstrated that noncompetitive binding sites are preferable for synthetic genetic oscillators that comprise a fast activator and a slow repressor with a large time scale separation. Here we show that when their time scales are similar, competitive binding sites are more likely to generate oscillation than noncompetitive sites. In contrast, for a slow activator and a fast repressor with a small phase difference as in Bmal1 regulation, noncompetitive binding sites are advantageous for amplifying oscillations. Our results, therefore, predict that additional mechanisms are necessary to compensate the disadvantage of the Bmal1 promoter and further facilitate amplification under the regulation by ROR and REV-ERB.