Periodic Switching in a Recombinase-Based Molecular Circuit

An important challenge in synthetic biology is the construction of periodic circuits with tunable and predictable period. We propose a general architecture, based on the use of recombinase proteins and negative feedback, to build a molecular device for periodic switching between two distinct regimes; the switching rule depends on known concentration thresholds for some circuit components. We analytically characterize the threshold values for which a periodic orbit is guaranteed to exist and attract all trajectories with initial conditions within an invariant set, and we provide expressions for period and amplitude. We describe two distinct biological realizations of the recombinase architecture, and show their capacity to exhibit periodic behaviors via extensive numerical simulations.