Cascade PID Control Systems Based on DNA Strand Displacement with Application in Polarization of Tumor-Associated Macrophages

Disturbances are widespread in biochemical systems. Nowadays, prevalent single-loop control strategies only take external disturbances into account. However, internal perturbations that threaten the stability of biochemical systems are invariably ignored. In this paper, a DNA strand displacement (DSD)-based cascade PID control system is designed. In addition to traditionally realizing the tracking of reference input and the attenuation of primary disturbance, the presented control approach also innovatively completes the rejection of secondary disturbance. Specifically, the dynamics of the reference input signal are first governed by a first-order low-pass filter integrated with cascade PID control systems, which efficiently avoids the excessive response of the cascaded primary and secondary controllers to the reference signal. Then, cascade PID controllers and second-order time-delay plants are constructed by utilizing the chemical reaction network (CRN) and the DSD. In terms of secondary perturbation suppression, the obtained control scheme significantly outperforms the single-loop PID control scheme with a smaller overshoot and faster settling time. Finally, the DSD-based cascade PID control method is applied to regulate gene expressions of interferon regulatory factor 4 (IRF4) and interferon regulatory factor 5 (IRF5) that affect the polarization of tumor-associated macrophages (TAMs). Compared with the single-loop PID control strategy, the control strategy exhibits a better inhibitory effect on IRF5 gene overexpression (internal disturbance) and TAMs endogenous gene expression (external disturbance).