title: Determining the bistability parameter ranges of artificially induced lac operon using the root locus method.
abstract: This paper employs the root locus method to conduct a detailed investigation of the parameter regions that ensure bistability in a well-studied gene regulatory network namely, lac operon of Escherichia coli (E. coli). In contrast to previous works, the parametric bistability conditions observed in this study constitute a complete set of necessary and sufficient conditions. These conditions were derived by applying the root locus method to the polynomial equilibrium equation of the lac operon model to determine the parameter values yielding the multiple real roots necessary for bistability. The lac operon model used was defined as an ordinary differential equation system in a state equation form with a rational right hand side, and it was compatible with the Hill and Michaelis-Menten approaches of enzyme kinetics used to describe biochemical reactions that govern lactose metabolism. The developed root locus method can be used to study the steady-state behavior of any type of convergent biological system model based on mass action kinetics. This method provides a solution to the problem of analyzing gene regulatory networks under parameter uncertainties because the root locus method considers the model parameters as variable, rather than fixed. The obtained bistability ranges for the lac operon model parameters have the potential to elucidate the appearance of bistability for E. coli cells in in vivo experiments, and they could also be used to design robust hysteretic switches in synthetic biology.
authors: Department of Electrical and Electronics Engineering, Faculty of Engineering, Dokuz Eylül University, D1-041 Buca Izmir, 35390 Izmir, Turkey. Electronic address: neslihan.avcu@deu.edu.tr.
authors: N
authors: N
authors: Avcu
authors: Institute of Marine Sciences and Technology, Dokuz Eylül University, 35340 Izmir, Turkey. Electronic address: hakan.alyuruk@deu.edu.tr.
authors: H
authors: H
authors: Alyürük
authors: Department of Electrical and Electronics Engineering, Faculty of Engineering, Dokuz Eylül University, D1-041 Buca Izmir, 35390 Izmir, Turkey. Electronic address: guleser.demir@deu.edu.tr.
authors: G K
authors: GK
authors: Demir
authors: Université Paris 13, Sorbonne Paris Cité, LIPN, CNRS, Paris, France. Electronic address: ferhan.pekergin@lipn.univ-paris13.fr.
authors: F
authors: F
authors: Pekergin
authors: Department of Chemistry, Faculty of Science, Dokuz Eylül University, 35390 Izmir, Turkey. Electronic address: lcavas@deu.edu.tr.
authors: L
authors: L
authors: Cavas
authors: Department of Electrical and Electronics Engineering, Faculty of Engineering and Computer Sciences, Izmir University of Economics, 35330 Izmir, Turkey. Electronic address: cuneyt.guzelis@ieu.edu.tr.
authors: C
authors: C
authors: Güzeliş
mesh_terms: D004926:Escherichia coli / Q000235:genetics*; D053263:Gene Regulatory Networks / Q000502:physiology*; D005798:Genes, Bacterial / Q000502:physiology*; D007763:Lac Operon / Q000502:physiology*; D008957:Models, Genetic
keywords: Bistability; IPTG; Lac operon; Root locus; TMG