A synthetic proportional-integral controller for chemical reaction networks

Chemical Reaction Network Theory (CRNT) is an effective framework to model the behaviour of biochemical systems. A currently open question, in the context of CRNT, is the design of networks with a prescribed input-output behaviour; indeed, at present, there is no general methodology to design control systems for CRNs. The main novel contribution of this work is a modular approach to the design of a Proportional- Integral (PI) controller for CRNs, based on the interconnection of simple CRN modules. Three basic modules (amplification, subtraction and integration) are devised, which can be easily composed to form the classical PI-control scheme. The proposed approach is tested in silico, showing that it can effectively control the output flux of an example reaction network. Although the treatment is maintained at a theoretical level, the minimality of the proposed modules, which are composed of few simple reactions, suggests that a real biological counterpart for each of them may be found in metabolic, signaling and gene regulatory networks, thus paving the way to the realization of synthetic embedded biological controllers.