Principles of feedback control have been shown to naturally arise in biological systems and applied with success build synthetic circuits. Here, we present an implementation a proportional–integral–derivative (PID) controller as chemical reaction network mass-action kinetics. This makes the synthesizable in vitro using DNA strand displacement technology, owing its demonstra...

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoi...