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Negative and positive transcriptional feedback loops are present in naturaland synthetic genetic oscillators. A single gene with negative transcriptionalfeedback needs a time delay and sufficiently strong nonlinearity in thetransmission of the feedback signal in order to produce biochemical rhythms. Asingle gene with only positive transcriptional feedback does not produceoscillations. Here, we demonstrate that this single-gene network in conjunctionwith a simple negative interaction can also easily produce rhythms. We examinea model comprised of two well-differentiated parts. The first is a positivefeedback created by a protein that binds to the promoter of its own gene andactivates the transcription. The second is a negative interaction in which arepressor molecule prevents this protein from binding to its promoter. Astochastic study shows that the system is robust to noise. A deterministicstudy identifies that the dynamics of the oscillator are mainly driven by twotypes of biomolecules: the protein, and the complex formed by the repressor andthis protein. The main conclusion of this paper is that a simple and usualnegative interaction, such as degradation, sequestration or inhibition, actingon the positive transcriptional feedback of a single gene is a sufficientcondition to produce reliable oscillations. One gene is enough and the positivetranscriptional feedback signal does not need to activate a second repressorgene. This means that at the genetic level an explicit negative feedback loopis not necessary. The model needs neither cooperative binding reactions nor theformation of protein multimers. Therefore, our findings could help to clarifythe design principles of cellular clocks and constitute a new efficient toolfor engineering synthetic genetic oscillators.

A simple negative interaction in the positive transcriptional feedback of a single gene is sufficient to produce reliable oscillations