Negative and positive transcriptional feedback loops are present in natural and synthetic genetic oscillators. A single gene with negative transcriptional feedback needs a time delay and  nonlinearity in the transmission of the feedback signal in order to produce biochemical rhythms. However, no equivalent requirements have been found for producing oscillations in a single gene with  positive transcriptional feedback . To demonstrate that this single-gene network  can also easily produce rhythms , we examine a model comprised of two well-differentiated parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the dynamics of the oscillator are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. In conclusion , a simple and usual negative interaction, such as degradation, sequestration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. Surprisingly, one gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene  . The model needs neither cooperative binding reactions nor the formation of protein multimers. Therefore, our findings could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators.
Negative and positive transcriptional feedback loops are present in natural and synthetic genetic oscillators. A single gene with negative transcriptional feedback needs a time delay and sufficiently strong nonlinearity in the transmission of the feedback signal in order to produce biochemical rhythms. A single gene with only positive transcriptional feedback does not produce oscillations. Here, we demonstrate that this single-gene network in conjunction with a simple negative interaction can also easily produce rhythms . We examine a model comprised of two well-differentiated parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the dynamics of the oscillator are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. The main conclusion of this paper is that a simple and usual negative interaction, such as degradation, sequestration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. One gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene . This means that at the genetic level an explicit negative feedback loop is not necessary . The model needs neither cooperative binding reactions nor the formation of protein multimers. Therefore, our findings could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators.
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