Proportional-integral degradation (PI-Deg) control allows accurate tracking of biomolecular concentrations with fewer chemical reactions

We show how an embedded reference tracking biomolecular controller for enzymatic reactions can be designed within the framework of chemical reaction network theory, and implemented using DNA strand displacement-based chemistry. To achieve reference tracking, embedded biomolecular controllers require a ‘subtractor’ that is able to compute the error between the process output and the reference signal. However, biomolecular subtractors designed using standard chemical reaction network theory can only realise a one-sided subtraction, i.e. the subtractor cannot produce negative error signals. To date, the only known framework that is able to realise two-sided subtraction leads to a doubling in the total number of chemical reactions required in the circuit, thereby significantly increasing the difficulty of experimental implementation. We propose an alternative approach based on the use of an inversion-based feedforward controller that compensates for the limitations of a one-sided subtractor, while requiring significantly fewer chemical reactions to implement