In nature, recombinases are site-specific proteins capable of rearranging DNA, and they are expanding the repertoire of gene editing tools used in synthetic biology. The on/off response of recombinases, achieved by inverting the direction of a promoter, makes them suitable for Boolean logic computation; however, recombinase-based logic gate circuits are single-use due to the irreversibility of the DNA rearrangement, and it is still unclear how a dynamical circuit, such as an oscillator, could be engineered using recombinases. Preliminary work has demonstrated that recombinase- based circuits can yield periodic behaviors in a deterministic setting. However, since a few molecules of recombinase are enough to perform the inverting function, it is crucial to assess how the inherent stochasticity at low copy number affects the periodic behavior. Here, we propose six different circuit designs for recombinase-based oscillators. We model them in a stochastic setting, leveraging the Gillespie algorithm for extensive simulations, and we show that they can yield periodic behaviors. To evaluate the incoherence of oscillations, we use a metric based on the statistical properties of auto-correlation functions. The main core of our design consists of two self-inhibitory, recombinase-based modules coupled by a common promoter. Since each recombinase inverts its own promoter, the overall circuit can give rise to switching behavior characterized by a regular period. We introduce different molecular mechanisms (transcriptional regulation, degradation, sequestration) to tighten the control of recombinase levels, which slows down the response timescale of the system and thus improves the coherence of oscillations. Our results support the experimental realization of recombinase-based oscillators and, more generally, the use of recombinases to generate dynamic behaviors in synthetic biology.
Computational characterization of recombinase circuits for periodic behaviors