Computational Re-Design of Synthetic Genetic Oscillators for Independent Amplitude and Frequency Modulation

Engineering robust and tuneable genetic clocks is a topic of current interest in Systems and Synthetic Biology with wide applications in biotechnology. Synthetic genetic oscillators share a common structure based on a negative feedback loop with a time delay, and generally display only limited tuneability. Recently, the dual-feedback oscillator was demonstrated to be robust and tuneable, to some extent, by the use of chemical inducers. Yet no engineered genetic oscillator currently allows for the independent modulation of amplitude and period. In this work, we demonstrate computationally how recent advances in tuneable synthetic degradation can be used to decouple the frequency and amplitude modulation in synthetic genetic oscillators. We show how the range of tuneability can be increased by connecting additional input dials, e.g. orthogonal transcription factors that respond to chemical, temperature or even light signals. Modelling and numerical simulations predict that our proposed re-designs enable amplitude tuning without period modulation, coupled modulation of both period and amplitude, or period adjustment with near-constant amplitude. We illustrate our work through computational re-designs of both the dual-feedback oscillator and the repressilator, and show that the repressilator is more flexible and can allow for independent amplitude and near-independent period modulation.