Contractivity of a genetic circuit with internal feedback and cell-to-cell communication*

We consider a realistic model of the synthetic gene circuit combining cell-to-cell communication system via quorum sensing, and a synthetic repressible promoter implementing intracellular negative feedback control. The circuit has been shown to increase robustness with respect to both extrinsic and intrinsic noise elsewhere. As a first step towards an analytic analysis, in this paper we use contraction theory to perform a stability analysis. From it, we infer the components of the circuit most affecting the rate of contractivity, using biologically sensible values of the circuit parameters.