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Abstract
Feedback control is widely used in chemical engineering to improve the performance and robustness of chemical processes. Feedback controllers require a 'subtractor' that is able to compute the error between the process output and the reference signal. In the case of embedded biomolecular control circuits, subtractors designed using standard chemical reaction network theory can only realise one-sided subtraction, rendering standard controller design approaches inadequate. Here, we show how a biomolecular controller that allows tracking of required changes in the outputs of enzymatic reaction processes can be designed and implemented within the framework of chemical reaction network theory. The controller architecture employs an inversion-based feedforward controller that compensates for the limitations of the one-sided subtractor that generates the error signals for a feedback controller. The proposed approach requires significantly fewer chemical reactions to implement than alternative designs, and should have wide applicability throughout the fields of synthetic biology and biological engineering.
Highlights
A major challenge in synthetic biology is to develop practically implementable design methods for the synthesis of feedback controllers that achieve reference tracking, i.e. force the output of a biomolecular process of interest to track desired changes in its concentration over time (Hsiao et al, 2015)
According to standard chemical reaction network (CRN) theory a CRN with n species and m reactions can be represented by an ordinary differential equation (ODE) following generalised mass-action kinetic in the form of dx dt where x ∈ Rn≥0 is the species concentration, f (x) ∈ Rm is a function describing the reaction rates of the CRN, P ∈ Rn×m is the stoichiometric matrix that describe the dynamics of the species concentrations following their associated reaction rates, R≥0 is the non-negative real number set, R is the real number set, and n and m are positive integers
We have shown for the first time how a controller architecture for implementing reference tracking, based on the use of an inverse-feedforward controller, can be adapted to the specific context of embedded biomolecular feedback systems
Summary
A major challenge in synthetic biology is to develop practically implementable design methods for the synthesis of feedback controllers that achieve reference tracking, i.e. force the output of a biomolecular process of interest to track desired changes in its concentration over time (Hsiao et al, 2015). Henson, 2003; Baldea et al, 2013), and the construction of synthetic control circuits has become a major focus of research in the new field of synthetic biology. Such circuits should be made up of well-defined modules consisting only of molecular reactions, in order to allow the realisation of embedded biomolecular control systems (Cosentino et al, 2016). A CRN is a collection of chemical reactions written in the form. According to standard CRN theory (see e.g. Feinberg, 1986, 1988) a CRN with n species and m reactions can be represented by an ordinary differential equation (ODE) following generalised mass-action kinetic in the form of dx dt
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