Dynamic analysis of genetic control and regulation of amino acid synthesis: The tryptophan operon in Escherichia coli

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Abstract
A mathematical model of the tryptophan operon is analyzed to investigate the regulatory effects of feedback repression and the demand for tryptophan in the cell. In this model, feedback repression is considered to be a two‐step process. First, the endproduct tryptophan combines with the inactive repressor produced by the regulatory genes to yield an active complex. This complex subsequently binds to the operator and prevents transcription of the structural genes into mRNA. The demand for tryptophan in the cell is modeled by a hyperbolic saturation function of the Michaelis‐Menten type. Results are obtained for the expression of the tryptophan operon in Escherichia coli and their applicability to tryptophan production by microbial fermentation is discussed. It is shown that, depending on the strain level of the operon and the rate of utilization of tryptophan in the cell, an overproduction of tryptophan can be achieved under stable operating conditions; in other circumstances, the operon may become stable or unstable, and may lead to a periodic synthesis.