This article proposes a modification of the model developed by Sinha (1988) and Sen and Liu (1990) for the regulation dynamics of the tryptophan operon in E. coli based on a consistent overall balance of the agent repressing the mRNA transcription. The dynamics of the model are analyzed by means of continuation techniques and the influence of periodic fluctuations in the intracellular demand for tryptophan is addressed. The analysis provides deeper insight into the dynamics of this operon system and the results obtained may be a useful starting point for the optimization of tryptophan yield in bacterial cultures.