  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.
