Regulating oscillation dynamics of a synthetic genetic circuit through positive feedback

In cellular systems, sustained oscillations of mRNAs and proteins can be generated by negative feedback mechanism. However, the negative feedback is often accompanied by the positive feedback, raising the intriguing question of what the extra function the positive feedback imparts. In this work, we investigate how the positive feedback affect the systems-level oscillation dynamics (e.g., frequency, amplitude and robustness) of a synthetic repressilator circuit. We show numerically that the original repressilator can produce oscillations with a tunable frequency and near-constant amplitude. But adding a self-positive feedback loop to the repressilator is found to simultaneously weaken its frequency's tunability and amplitude. Moreover, this positive feedback reduces robustness of the repressilator to environmental perturbations. Combining with previous results on the negative-plus-positive feedback design principle, our findings indicate that the positive feedback may play different functions in different network structures of the cellular circuits.