A universal biomolecular integral feedback controller for robust perfect adaptation

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. On the 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.A synthetic gene circuit implementing an integral feedback topology is shown to achieve robust perfect adaptation in living cells--mathematical analysis proves this topology is necessary for adaptation in networks with noisy dynamics.

[1]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[2]  R. Miller,et al.  One-step preparation of competent Escherichia coli: transformation and storage of bacterial cells in the same solution. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[3]  S. Leibler,et al.  Robustness in simple biochemical networks , 1997, Nature.

[4]  J. Doyle,et al.  Robust perfect adaptation in bacterial chemotaxis through integral feedback control. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[5]  M. Khammash,et al.  Calcium homeostasis and parturient hypocalcemia: an integral feedback perspective. , 2002, Journal of theoretical biology.

[6]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[7]  Eduardo D. Sontag,et al.  Adaptation and regulation with signal detection implies internal model , 2003, Syst. Control. Lett..

[8]  Paul Miller,et al.  Inhibitory control by an integral feedback signal in prefrontal cortex: a model of discrimination between sequential stimuli. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[9]  T. Terwilliger,et al.  Engineering and characterization of a superfolder green fluorescent protein , 2006, Nature Biotechnology.

[10]  A. Oudenaarden,et al.  A Systems-Level Analysis of Perfect Adaptation in Yeast Osmoregulation , 2009, Cell.

[11]  H. Kwakernaak,et al.  Feedback Systems , 2009, Encyclopedia of Database Systems.

[12]  W. Lim,et al.  Defining Network Topologies that Can Achieve Biochemical Adaptation , 2009, Cell.

[13]  Naama Barkai,et al.  Scaling of morphogen gradients by an expansion-repression integral feedback control , 2010, Proceedings of the National Academy of Sciences.

[14]  Brian Ingalls,et al.  Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network. , 2010, Journal of theoretical biology.

[15]  A. Arkin,et al.  Sequestration-based bistability enables tuning of the switching boundaries and design of a latch , 2012, Molecular systems biology.

[16]  J. Collins,et al.  Tunable protein degradation in bacteria , 2014, Nature Biotechnology.

[17]  Richard M. Murray,et al.  Design and Implementation of a Biomolecular Concentration Tracker , 2014, ACS synthetic biology.

[18]  M. Khammash,et al.  Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth , 2016, Nature Communications.

[19]  Ankit Gupta,et al.  Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks. , 2014, Cell systems.

[20]  Mustafa Khammash,et al.  Design of a synthetic integral feedback circuit: dynamic analysis and DNA implementation , 2016, ACS synthetic biology.

[21]  David R McMillen,et al.  Design principles for the analysis and construction of robustly homeostatic biological networks. , 2016, Journal of theoretical biology.

[22]  J. Helmann Bacillus subtilis extracytoplasmic function (ECF) sigma factors and defense of the cell envelope. , 2016, Current opinion in microbiology.

[23]  Glenn Vinnicombe,et al.  Constraints on Fluctuations in Sparsely Characterized Biological Systems. , 2016, Physical review letters.

[24]  James E Ferrell,et al.  Perfect and Near-Perfect Adaptation in Cell Signaling. , 2016, Cell systems.

[25]  Mustafa Khammash,et al.  A synthetic integral feedback controller for robust tunable regulation in bacteria , 2017, bioRxiv.

[26]  M. di Bernardo,et al.  An Orthogonal Multi-input Integration System to Control Gene Expression in Escherichia coli. , 2017, ACS synthetic biology.

[27]  Y. Benenson,et al.  Synthetic control systems for high performance gene expression in mammalian cells , 2018, Nucleic acids research.

[28]  Domitilla Del Vecchio,et al.  A quasi-integral controller for adaptation of genetic modules to variable ribosome demand , 2018, Nature Communications.

[29]  Ankit Gupta,et al.  Antithetic proportional-integral feedback for reduced variance and improved control performance of stochastic reaction networks , 2018, Journal of The Royal Society Interface.

[30]  G. Stan,et al.  Burden-driven feedback control of gene expression , 2017, Nature Methods.

[31]  Lance A Liotta,et al.  The topological requirements for robust perfect adaptation in networks of any size , 2018, Nature Communications.

[32]  John C. Doyle,et al.  Robust Perfect Adaptation in Biomolecular Reaction Networks , 2018 .

[33]  Andreas W. K. Harris,et al.  Synthetic negative feedback circuits using engineered small RNAs , 2017, bioRxiv.