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Biomolecular feedback systems are now a central application area of interestwithin control theory. While classical control techniques provide invaluableinsight into the function and design of both natural and synthetic biomolecularsystems, there are certain aspects of biological control that have provendifficult to analyze with traditional methods. To this end, we describe herehow the recently developed tools of dominance analysis can be used to gaininsight into the nonlinear behavior of the antithetic integral feedbackcircuit, a recently discovered control architecture which implements integralcontrol of arbitrary biomolecular processes using a simple feedback mechanism.We show that dominance theory can predict both monostability and periodicoscillations in the circuit, depending on the corresponding parameters andarchitecture. We then use the theory to characterize the robustness of theasymptotic behavior of the circuit in a nonlinear setting.

Antithetic integral feedback for the robust control of monostable and oscillatory biomolecular circuits