A Simple Negative Interaction in the Positive Transcriptional Feedback of a Single Gene Is Sufficient to Produce Reliable Oscillations

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.

天然与人工合成的遗传振荡器中，均存在正负转录反馈环。单基因负转录反馈系统若要产生生化节律，需具备时间延迟与足够强的反馈信号传递非线性特性。仅含正转录反馈的单基因系统则无法产生振荡。本研究表明，此类单基因网络与简单负相互作用结合后，亦可轻易产生节律性振荡。我们构建了由两个高度分化模块组成的模型：其一为正反馈模块，即某蛋白质结合自身基因的启动子并激活转录，由此形成正反馈回路；其二为负相互作用模块，即阻遏蛋白分子可阻止该蛋白质结合自身启动子。随机模拟研究表明，该系统对噪声具有鲁棒性。确定性分析则揭示，振荡器的动力学主要由两类生物分子驱动：目标蛋白质，以及阻遏蛋白与该蛋白质形成的复合物。本研究的核心结论为：作用于单基因正转录反馈的常见简单负相互作用（如降解、隔离或抑制），即可作为产生可靠振荡的充分条件。仅需单个基因即可实现，且正转录反馈信号无需激活第二个阻遏基因。这意味着在遗传层面，无需构建显性负反馈环。该模型既无需协同结合反应，也无需蛋白质多聚体的形成。因此，本研究成果有助于阐明细胞生物钟的设计原理，并为人工合成遗传振荡器的工程化构建提供全新高效的工具。