A genetically structured mathematical model of the trp attenuator in Escherichia coli based on known coupling mechanisms of the transcription of the trp leader region and translation of the trp leader peptide region is proposed. The model simulates, both qualitatively and quantitatively, the effects of tryptophan on the repression of cloned gene products. It shows that repression by attenuation mechanism alone operates over a narrow trp concentration range of 1 to 5 mu M compared with 1 to 100 mu M for trp repressor mechanism. This implies that attenuation by transcription termination is not relaxed until tryptophan starvation is severe. Simulation results show that the attenuator starts to derepress when the repressor is about 40% repressed, and becomes significantly derepressed only when the repressor repression decreased to about 20%. Unlike the case of repressor-operator interaction, the operating range of tryptophan concentration in the attenuator mechanism is not sensitive to plasmid copy number.