PID and State Feedback Controllers Using DNA Strand Displacement Reactions

Nucleic acid-based chemistry is a strong candidate framework for the construction of future synthetic biomolecular control circuits. Previous work has demonstrated the capacity of circuits based on DNA strand displacement (DSD) reactions to implement digital and analogue signal processing in vivo, including in mammalian cells. To date, however, feedback control system designs attempted within this framework have been restricted to extremely simple proportional or proportional-integral controller architectures. In this letter, we significantly extend the potential complexity of such controllers by showing how time-delays, numerical differentiation (to allow PID control), and state feedback may be implemented via chemical reaction network-based designs. Our controllers are implemented and tested using VisualDSD, a rapid-prototyping tool that allows precise analysis of computational devices implemented using nucleic acids, via both deterministic and stochastic simulations of the DSD reactions.