A universal biomolecular integral feedback controller for robust perfect adaptation.

Mustafa Khammash,Armin Baumschlager,Ankit Gupta,David Schweingruber,Gabriele Lillacci,Stephanie K. Aoki

doi:10.1038/s41586-019-1321-1

Abstract

Homeostasis is a recurring theme in biology that ensures that regulated variables robustly-and in some systems, completely-adapt to environmental perturbations. This robust perfect adaptation feature is achieved in natural circuits by using integral control, a negative feedback strategy that performs mathematical integration to achieve structurally robust regulation1,2. Despite its benefits, the synthetic realization of integral feedback in living cells has remained elusive owing to the complexity of the required biological computations. Here we prove mathematically that there is a single fundamental biomolecular controller topology3 that realizes integral feedback and achieves robust perfect adaptation in arbitrary intracellular networks with noisy dynamics. This adaptation property is guaranteed both for the population-average and for the time-average of single cells. Onthe basis of this concept, we genetically engineer a synthetic integral feedback controller in living cells4 and demonstrate its tunability and adaptation properties. A growth-rate control application in Escherichia coli shows the intrinsic capacity of our integral controller to deliver robustness and highlights its potential use as a versatile controller for regulation of biological variables in uncertain networks. Our results provide conceptual and practical tools in the area of cybergenetics3,5, for engineering synthetic controllers that steer the dynamics of living systems3-9.

Highlights

Homeostasis is a recurring theme in biology
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 works by measuring the deviation of a variable of interest from the desired target value, computing the mathematical integral of that deviation over time, and using it in a negative feedback configuration to drive processes that counteract the deviation and drive it to zero (Fig. 1a, b). This can be achieved despite considerable uncertainty in process dynamics and constant or slowly varying perturbations. This fundamental network property is known as robust perfect adaptation (RPA), and the importance of integral feedback as a regulation strategy derives from its capacity to realize it

Summary

Introduction

Homeostasis is a recurring theme in biology. Homeostatic mechanisms commonly ensure that regulated variables robustly and completely adapt to environmental perturbations. 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.

Results

Conclusion