A universal biomolecular integral feedback controller for robust perfect adaptation

Abstract

Homeostasis is a recurring theme in biology. Homeostatic mechanisms commonly ensure that regulated variables robustly and completely adapt to environmental perturbations. This robust perfect adaptation (RPA) feature is achieved by incorporating mathematical integration in a negative feedback strategy. 1, 2 Despite its benefits in natural circuits, the synthetic realization of integral feedback has remained elusive due to the complexity of the required biological computations. Here we first mathematically prove that there is fundamentally a single biomolecular controller topology 3 that realizes integral feedback for arbitrary intracellular networks with noisy dynamics. Such a topology guarantees RPA for both the cell populationaverage and for the time-average of single cells. We then develop the first synthetic gene network implementation of such an integral controller in a living cell, 4 and demonstrate its tunability and adaptation properties. A growth control application shows the inherent capacity of our integral feedback controller to deliver robustness, and highlights its potential use as a versatile controller for regulation of biological variables in uncertain networks. Our results provide new conceptual and practical tools in the area of Cybergenetics 3,5 where control theory and synthetic biology come together to enable the engineering of novel synthetic controllers that steer the dynamics of living systems. [3][4][5][6][7][8][9] Integral feedback control is arguably one the most fundamental regulation strategies in engineering practice. From modern jetliners to industrial plants, integral feedback loops reliably drive physical variables to their desired values with great robustness and precision. 10 It is becoming increasingly appreciated that

Cell volume homeostatically controls the rDNA repeat copy number and rRNA synthesis rate in yeast

“…Intriguingly, our mathematical model corresponds to an integral feedback mechanism to control the concentration of rDNA repeats at a prescribed set point. Such integral feedbacks have recently been shown to be essential for robust perfect adaptation when faced with environmental perturbations [41]. We refer readers to the Supplementary Information for details on the mathematical modelling.…”

Layered Feedback Control Improves Robust Functionality across Heterogeneous Cell Populations

“…Integral negative feedback is an appealing controller since it effectively drives the regulated protein level to a constant set-point without error [9]. Using a strong sequestration pair of a σ -factor and a anti-σ -factor, an antithetic integral feedback controller has been recently implemented for robust perfect adaptation [10].…”

Antithetic integral feedback for the robust control of monostable and oscillatory biomolecular circuits

“…In the past few years, a great deal of progress has been made towards this goal of designing universal feedback controllers that can easily be used in a wide variety of contexts (Aoki et al (2019); Samaniego and Franco (2017); Chevalier et al (2019); Becskei and Serrano (2000); Huang et al (2018)). Among these, a particularly promising architecture relies on what has been named the Antithetic Integral Feedback (AIF) circuit, which has been shown to implement integral feedback using a simple irreversible bimolecular interaction as the primary feedback mechanism (Briat et al (2016)).…”

“…Among these, a particularly promising architecture relies on what has been named the Antithetic Integral Feedback (AIF) circuit, which has been shown to implement integral feedback using a simple irreversible bimolecular interaction as the primary feedback mechanism (Briat et al (2016)). This architecture has several appealing properties: it relies on a single molecular interaction that appears in a variety of natural contexts (e.g., the nearly irreversible sequestration of sigma factor/antisigma This work is supported in part by factor pairs), and the model of its dynamics is simple enough that it is possible to prove general results about stability and optimality (Aoki et al (2019); Olsman et al (2019a)). Recent theoretical work has focused both on global results for arbitrary plant-controller systems and local results focused on applying classic tools from control theory to simplified models of closed-loop dynamics ; ; Olsman et al (2019a,b); Briat et al (2016Briat et al ( , 2018).…”