DNA Strand Displacement Reactions to Accomplish a Two-Degree-of-Freedom PID Controller and Its Application in Subtraction Gate

Synthesis control circuits can be used to effectively control biochemical molecule processes. In the controller design based on chemical reaction networks (CRNs), generally only the tracking set-point is considered. However, the influence of disturbances, which are frequently encountered in biochemical systems, is often neglected, thus weakening the control effect of the system. In this article, tracking set-point input and suppressing disturbance input are considered in the control effect. Firstly, CRNs are adopted to construct a two-degree-of-freedom PID controller by combining a one-degree-of-freedom PID controller with a feedforward controller for the first time. Then, CRN expressions of the two input functions (step function and ramp function) used as input signals are defined. Furthermore, the two-degree-of-freedom PID controller is founded by DNA strand displacement (DSD) reaction networks, because DNA is an ideal engineering material to constitute molecular devices based on CRNs. The overshoot of the two-degree-of-freedom PID control system is significantly reduced compared to the one-degree-of-freedom PID control system. Finally, a leak reaction is treated as an extraneous disturbance input to a subtraction gate. The influence of external disturbance is solved by the two-degree-of-freedom PID controller. It is worth noting that the two-degree-of-freedom subtraction gate control system better restrains the impact of a disturbance input (leak reaction).