Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules

The capability to engineer de novo feedback control with biological molecules is ushering in an era of robust functionality for many applications in biotechnology and medicine. To fulfill their potential, these control strategies need to be generalizable, modular, and operationally predictable. Proportional-integral-derivative (PID) control fulfills this role for technological systems. Integral feedback control allows a system to return to an invariant steady-state value after step disturbances. Proportional and derivative feedback control used with integral control modulate the dynamics of the return to steady state following perturbation. Recently, a biomolecular implementation of integral control was proposed based on an antithetic motif in which two molecules interact stoichiometrically to annihilate each other's function. In this work, we report how proportional and derivative implementations can be layered on top of this integral architecture to achieve a biochemical PID control design. We investigate computationally and analytically their properties and ability to improve performance.