Periodic behaviors in recombinase-based molecular circuits

Abstract: 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 molecular devices for periodic switching between two distinct regimes; the switching rule depends on known concentration thresholds for some circuit components. We consider a deterministic model for this architecture and we analytically characterise the threshold values for which a periodic orbit is guaranteed to exist and attract all trajectories with initial conditions within an invariant set, and provide exact expressions for period and amplitude. We then describe various biological realisations of the recombinase architecture, and show their capacity to exhibit periodic behaviours via extensive computational simulations. We examine the behavior of these circuits also in a stochastic regime, and rank different realisations based on the coherence of the oscillations they produce.

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