A hierarchy of biomolecular proportional-integral-derivative feedback controllers for robust perfect adaptation and dynamic performance

Abstract

Proportional-Integral-Derivative (PID) feedback controllers are the most widely used controllers in industry. Recently, the design of molecular PID-controllers has been identified as an important goal for synthetic biology and the field of cybergenetics. In this paper, we consider the realization of PID-controllers via biomolecular reactions. We propose an array of topologies offering a compromise between simplicity and high performance. We first demonstrate that different biomolecular PI-controllers exhibit different performance-enhancing capabilities. Next, we introduce several derivative controllers based on incoherent feedforward loops acting in a feedback configuration. Alternatively, we show that differentiators can be realized by placing molecular integrators in a negative feedback loop, which can be augmented by PI-components to yield PID-controllers. We demonstrate that PID-controllers can enhance stability and dynamic performance, and can also reduce stochastic noise. Finally, we provide an experimental demonstration using a hybrid setup where in silico PID-controllers regulate a genetic circuit in single yeast cells.

A genetic mammalian proportional–integral feedback control circuit for robust and precise gene regulation

“…In particular, we implement a common control strategy that is extensively applied in various engineering disciplines, referred to as PI control. This control strategy adds to the integral (I) controller proportional (P) feedback action to enhance dynamic performance, such as transient dynamics and variance reduction ( 11 , 36 , 37 ), while maintaining the adaptation property. To implement proportional feedback control that acts faster than the integral feedback, we use a proxy protein, namely, the RNA-binding protein L7Ae, which is produced in parallel with mCitrine-tTA from a single mRNA via the use of a P2A self-cleavage peptide ( Fig.…”

“…Subtracting the differential equations of Z 1 and Z 2 reveals the integral action of the controller that ensures that the steady state of the output converges to a value that is independent of the controlled network parameters. Additionally, through linearization ( 36 ), the individual integral and the proportional control actions of the antithetic PI motif can be expressed separately. ( C ) The elements of PI feedback.…”

Platforms for Optogenetic Stimulation and Feedback Control

“…Furthermore, Kumar et al, 2021 implemented several in silico biomolecular controller motifs in stochastic setting and exhibited transcription regulation in suitably engineered S. cerevisiae via single-cell optogenetics control. With this in vivo (transcription in yeast) - in silico (stochastic controller) hybrid closed-loop set-up, called Cyberloop ( Figure 5B ), they showed characterization and rapid-prototyping of autocatalytic integral ( Briat et al, 2016a ), antithetic integral ( Briat et al, 2016b ), antithetic integral rein ( Gupta and Khammash, 2019 ), and biomolecular PID ( Filo et al, 2022 ) controller motifs. These characterization results provide useful insights for optimal controller performance, which can further guide in vivo implementations of these biomolecular controller motifs.…”

On the Design of a PID Bio-Controller With Set Point Weighting and Filtered Derivative Action

“…Because of the pervasiveness of PID control in technological applications, the biomolecular implementation of PID controllers has seen great interest in Synthetic Biology and several successful research efforts. Notably, the authors in [13] present a hierarchical library of nonlinear PID controllers consisting of up to four biomolecular species with a first-order low-pass filter accompanying some or all the three control terms (P-, Iand D-term). The PID architecture proposed in [14] exploits different variations of Michaelis-Menten functions.…”

“…In this paper, we introduce an alternative biomolecular network functioning as a PID controller around the nominal operation of the resulting closed-loop system. This local approach is also adopted in [13]. The biomolecular interactions involved are defined by general chemical reaction networks (CRNs) based purely on mass action kinetics [19] and without using dual rail encoding.…”