A Hidden Proportional Feedback Mechanism Underlies Enhanced Dynamic Performance and Noise Rejection in Sensor-Based Antithetic Integral Control

Abstract

Efficient regulation of cellular processes is essential for both endogenous and synthetic biological processes. The design of biomolecular feedback controllers that achieve robust and timely regulation is the subject of considerable research at the interface between synthetic biology and control theory. Integral feedback controllers, known for their ability to confer the property of Robust Perfect Adaptation (RPA), are increasingly becoming common features in biological control design. Antithetic integral feedback (AIF) controllers, in particular, have enabled effective chemical reaction realizations of integral controllers that deliver RPA in both deterministic and stochastic settings. This paved the way to experimental implementations of integral controllers in bacterial and mammalian cells. While AIF controllers deliver favorable adaptation properties, they do not necessarily lead to good transient performance or noise reduction properties and may in some cases lead to increased overshoot or cell-to-cell variability. These limitations are commonly circumvented by augmenting new circuitry that realize proportional or derivative feedback mechanisms to enhance dynamic and noise rejection features without affecting the AIF controllers adaptation properties. In this paper, we report that a sensor-based variant of the basic AIF motif exhibits favorable transient dynamic properties and (as reported elsewhere) reduced noise variance. We show that these features are attributed to a "hidden" proportional feedback component that is inherent in the controller structure and that such mechanism is solely responsible for the controllers underlying enhanced dynamic performance and noise rejection properties. This sensor-based AIF controller hence offers a minimal biomolecular realization of Proportional-Integral (PI) control, whereby both integral and proportional feedback mechanisms are achieved through a single actuation reaction.