Levent CavasNeslihan AvcuHakan AlyurukGüleser Kalaycı DemirCüneyt GÜZELİŞFerhan PEKERGİNPekergin, FerhanDemir, Güleser KalayciGuzelis, CuneytKalayci Demir, GuleserCavas, LeventAvcu, NeslihanAlyuruk, Hakan2025-10-222016[1] Jacob F Perrin D Sanchez C Monod J. L operon: groupe de gene a expression par un operatour. C R Acad Sci 1960, 250: 1727 1729 (in French).[2] Novick A Wiener M. Enzyme induction as an all-or-none phenomenon. P Natl Acad Sci USA 1957, 43: 553 566.[3] Ozbudak M Thattai M Lim HN Shraiman BI Van Oudenaarden A. Multistability in the lactose utilization ¨ network of Escherichia coli. Nature 2004, 42: 737 740.[4] Yıldırım N Santillan M Horike D Mackey MC. Dynamics and bistability in a reduced model of the lac operon. Chaos 2004, 4: 279 292.[5] Danchin A. Cells need safety valves. BioEssays 2009, 31: 769 773.[6] Wong P Gladney S Keasling JD. Mathematical model of the lac operon: inducer exclusion catabolite repression and diauxic growth on glucose and lactose. Biotechnol Prog 1997, 13: 132 143.[7] Avcu N. Analysis of bistability behaviour of lac operon by using systems theory. PhD Dokuz Eyl¨ul University ˙Izmir Turkey 2013.[8] Van Hoek MJ Hogeweg P. In silico evolved lac operons exhibit bistability for artificial inducers but not for lactose. Biophys J 2006, 91: 2833 2843.[9] Julius A Halasz A Sakar S Harvey R Pappas GJ. Stochastic modeling and control of biological systems: the lactose regulation system of E. coli. IEEE T Automat Contr 2008, 53: 51 65.[10] Yagil G Yagil E. On the relation between effector concentration and the rate of induced enzyme synthesis. Biophys J 1971, 11: 11 27.[11] Santillan M Mackey MC. Influence of catabolite repression and inducer exclusion on the bistable behavior of the lac operon. Biophys J 2004, 86: 1282 1292.[12] Vidyasagar M. Nonlinear System Analysis. Upper Saddle River NJ USA: Prentice Hall 1972.[13] Avcu N Demir GK Pekergin F Aly¨ur¨uk H C¸ ava¸s L G¨uzeli¸s C. Boundedness and local stability analysis for a TMG induced lac operon model. In: ELECO2012 Elektrik-Elektronik ve Bilgisayar M¨uhendisli˘gi Sempozyumu, 29 November 1 December 2012, Bursa Turkey. pp. 420 425 (in Turkish with abstract in English).1300-06321303-620310.3906/elk-1305-2642-s2.0-84963819002https://gcris.yasar.edu.tr/handle/123456789/11047https://search.trdizin.gov.tr/en/yayin/detay/244679https://doi.org/10.3906/elk-1305-264This paper presents the results of a theoretical and numerical study on the analysis of bistable behavior of the most studied gene regulatory network the lac operon in terms of the model parameters. The boundedness of the state variables for the considered model are demonstrated the parameter values providing the existence of the multiple equilibria and thus the bistable behavior are determined and a local stability analysis of the equilibria is performed. The parameter region yielding the existence of multiple equilibria is determined in an algebraic way based on discriminants. The model given in the state equation form is defined by the ordinary differential equations with the rational right-hand sides constituted within Hill and Michaelis Menten approaches based on enzyme kinetics. The presented method can also be used in the parametric studies of other gene regulatory and metabolic networks given by state equations with rational right hand sides.İngilizceinfo:eu-repo/semantics/closedAccessMühendislik- Elektrik ve Elektronik-Biyokimya ve Moleküler BiyolojiBistabilityGene Regulatory NetworksMühendislik, Elektrik Ve ElektronikLac OperonDiscriminantBiyokimya Ve Moleküler BiyolojiTMGArticle