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[WCK+19] Max Whitby, Luca Cardelli, Marta Kwiatkowska, Luca Laurenti, Mirco Tribastone and Max Tschaikowski. PID Control of Biochemical Reaction Networks. In Proc. 58th Conference on Decision and Control - Nice, France - December 11th-13th 2019. 2019. [pdf] [bib] http://arxiv.org/abs/1903.10390
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Abstract. Principles of feedback control have been shown to naturally arise in biological systems and successfully applied to build synthetic circuits. In this work we consider Biochemical Reaction Networks (CRNs) as a paradigm for modelling biochemical systems and provide the first implementation of a derivative component in CRNs. That is, given an input signal represented by the concentration level of some species, we build a CRN that produces as output the concentration of two species whose difference is the derivative of the input signal. By relying on this component, we present a CRN implementation of a feedback control loop with Proportional-Integral-Derivative (PID) controller and apply the resulting control architecture to regulate the protein expression in a microRNA regulated gene expression model.