Analysis of bistability behaviour of lac operon by using systems theory

This thesis presents the original results of theoretical and numerical studies on the analysis of bistable behavior of the most studied gene regulatory network ?lac operon? in terms of the model parameters. In the study, two different lac operon models, one that ignores the transacetylase effect while the other takes it into account, are analyzed. The lac operon models assume methyl-1-thio-ß-D-galactoside as the artificial inducer. The bistability regions in the parameter space for both of the models are thoroughly determined by newly introduced discriminant and root locus based methods. The developed methods not only identify the ranges of the physical parameters ensuring the bistable behavior of the lac operon models, but also provide a way of tackling the problem of model analysis for this gene regulatory network under parameter uncertainties.For the lac operon model with no transacetylase effect, the boundedness of the state variables are demonstrated, the parameter values providing the existence of the multiple equilibria, thus the bistable behavior, are determined by the discriminant and root locus based analyses and a local stability analysis of the equilibria is performed. All these studies for the lac operon model with no transacetylase effect are performed in algebraic, graphical and numerical ways all supporting to each other. It is observed along the studies that, as in the lac operon model considering the transacetylase effect, the algebraic and graphical methods may get stuck for models yielding greater than third order polynomial equilibrium equations, and that the developed root locus based method provides an efficient numerical tool for any kind of gene regulatory and metabolic networks model given in a state equation form with rational right-hand side, derived based on enzyme kinetics employing Hill and Michaelis-Menten approaches.