A mathematical model based on known molecular interactions has been formulated to describe quantitatively regulation of expression of the lactose (lac) operon in the Escherichia coli chromosome and in multicopy plasmids. This model is genetically structured such that a nucleotide sequence change affecting transcription initiation at the lac promoter–operator influences one or very few directly corresponding model parameters. The model simulates chromosomal lac operon function in good agreement with previous experimental measurements for many lacl and lacO mutant systems as well as for diploid cells which carry F'lac episomes. Simulation results clearly show the loss of cloned lac operator regulation as the plasmid copy number increases, in agreement with experimental trends. The importance of this class of models in designing DNAs, organisms, and reactors for precise regulation of cloned gene expression is discussed.