A simple genetically structured model of trp repressor-operator interactions

A genetically structured mathematical model of the trp operon based on known molecular interactions of aporepressor, corepressor, and inducer is proposed. The model simulates, both qualitatively and quantitatively, the influence of these regulatory species on the extent of repression and expression of cloned gene products. It shows that at low aporepressor concentration, full repression is not possible even with high tryptophan levels, resulting in leaky expression. Calculations based on the model enabled predictions of optimum levels of aporepressor and tryptophan for effective repression and, concurrently, the beta-indoleacrylic acid concentrations required for induction for both low and high plasmid copy number clones. Using the model we attempted to provide explanations for seemingly anomalous and sometimes contradictory observations by researchers when working with the trp promoter.