title: Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network.
abstract: It has long been known to control theorists and engineers that integral feedback control leads to, and is necessary for, "perfect" adaptation to step input perturbations in most systems. Consequently, implementation of this robust control strategy in a synthetic gene network is an attractive prospect. However, the nature of genetic regulatory networks (density-dependent kinetics and molecular signals that easily reach saturation) implies that the design and construction of such a device is not straightforward. In this study, we propose a generic two-promoter genetic regulatory network for the purpose of exhibiting perfect adaptation; our treatment highlights the challenges inherent in the implementation of a genetic integral controller. We also present a numerical case study for a specific realization of this two-promoter network, "constructed" using commonly available parts from the bacterium Escherichia coli. We illustrate the possibility of optimizing this network's transient response via analogy to a linear, free-damped harmonic oscillator. Finally, we discuss extensions of this two-promoter network to a proportional-integral controller and to a three-promoter network capable of perfect adaptation under conditions where first-order protein removal effects would otherwise disrupt the adaptation.
authors.affiliation: Department of Chemical and Physical Sciences and Institute for Optical Sciences, University of Toronto Mississauga, Mississauga, Ontario, Canada L5L 1C6.
authors.forename: Jordan
authors.initials: J
authors.lastname: Ang
authors.forename: Sangram
authors.initials: S
authors.lastname: Bagh
authors.forename: Brian P
authors.initials: BP
authors.lastname: Ingalls
authors.forename: David R
authors.initials: DR
authors.lastname: McMillen
mesh_terms: D000222:Adaptation, Physiological / Q000235:genetics*; D003198:Computer Simulation; D004926:Escherichia coli / Q000235:genetics* / Q000254:growth & development; D029968:Escherichia coli Proteins / Q000235:genetics / Q000378:metabolism; D025461:Feedback, Physiological; D015964:Gene Expression Regulation, Bacterial; D053263:Gene Regulatory Networks / Q000235:genetics*; D005813:Genes, Synthetic / Q000235:genetics*; D056968:Lac Repressors / Q000235:genetics / Q000378:metabolism; D011401:Promoter Regions, Genetic / Q000235:genetics; D058615:Synthetic Biology
chemical_list: D029968:Escherichia coli Proteins; D056968:Lac Repressors; C539064:LacI protein, E coli