Mathematical Description of the Lac Operon Regulation in Diauxic and Non-Diauxic Growth on Glucose and Lactose

Two mathematical models for the regulation of the lac operon are presented to study diauxic growth and non- diauxic growth on glucose and lactose. The two models take into account all of the known regulatory mechanisms including catabolite repression, inducer exclusion, lactose hydrolysis to glucose, as well as the time delays inherent to transcription and translation. A new mechanism for catabolite repression is tested: cyclic AMP synthesis is correlated not only with the external glucose concentration but also with the internal glucose concentration. We have paid particular attention to the intracellular cAMP and the beta-galactosidase in the models. Numerical studies have been tested to show that agreement in manners between the experiments and the models predictions. Changes in the extracellular glucose concentration that inhibited lactose transport could not extend or contract the diauxic growth period during growth in the presence of glucose and lactose.