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This 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 dened 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.

Discriminant-based bistability analysis of a TMG-induced lac operon model supported with boundedness and local stability results