Implementing nonlinear feedback controllers using DNA strand displacement reactions

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions that can be implemented via DNA strand dis-placement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize ultrasensitive input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, entropy-driven DNA reactions using DNA strand displacement via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs