Loading As a Design Parameter for Genetic Circuits

A major goal in synthetic biology is to modularly design, build and interconnect biomolecular circuits that perform as originally devised. However, the dynamics of circuits are sensitive to their context, and implementing circuits in vivocould potentially degrade their performance. Retroactivity, a form of context-dependence, affects the dynamics of an upstream system upon interconnection with a downstream system akin to impedance in electrical networks.

We study the effects of retroactivity, modeled as DNA promoter sites, on a genetic oscillator. The DNA promoter sites sequester transcription factors from the upstream system thereby changing the dynamics of the oscillator. The activator-repressor (A-R) oscillator consists of two proteins that transcriptionally activate and repress themselves and one another. Conditions for a stable limit cycle include sufficiently high transcriptional leakiness, relatively strong activation, and weak repression. Our analysis indicates that increasing the load on the repressor protein can activate a quenched clock and give rise to stable oscillations. Conversely, increasing the load on the activator protein dampens oscillations and causes the system trajectories to converge to an equilibrium point. Load, therefore, provides a method to tune the relative strength of the activation and repression branches for stronger or weaker oscillations, without resorting to degradation tags or changing the promoter regions.