Dynamic regulation of the tryptophan operon: a modeling study and comparison with experimental data

Abstract

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Figure 1

Schematic representation of the tryptophan operon regulatory system. See text for details.

Figure 2

Enzyme activity vs. time after a nutritional shift (minimal + tryptophan medium to minimal medium), with wild-strain cultures of E. coli. Two different sets of experimental results (crosses and pluses) as well as the model simulation (solid line), with the parameters of Table 3, are presented. The simulation was calculated by numerically solving the differential equations. The selection of initial conditions is described in the text. The normal enzyme activity is that of the steady state in a medium without tryptophan.

Figure 3

Enzyme activity vs. time after a nutritional shift (minimal + tryptophan medium to minimal medium), with wild-strain (crosses and pluses) and trpL29-mutated (circles) cultures of E. coli. The numerical simulations for each strain (solid lines), are also shown. The simulation for the trpL29-mutated strain was calculated by solving numerically the differential equations with the parameters estimated in Table 3 except for the parameter k_p, which was decreased to 0.04 times the normal value to simulate mutation. The selection of initial conditions is described in the text. The normal enzyme activity is that of the wild-strain steady state in a medium with no tryptophan.

Figure 4

Enzyme activity vs. time after a nutritional shift (minimal + tryptophan medium to minimal medium), with wild-strain (crosses and pluses) and trpL75-mutated (asterisks) cultures of E. coli. The numerical simulations for each strain (solid line) are also shown. The simulation for the trpL75-mutated strain was calculated by solving numerically the differential equations with the parameters of Table 3, except parameter b, which was increased to 0.9996 to simulate the mutation. The selection of initial conditions is described in the text. The normal enzyme activity is that of the wild-strain steady state, in a medium with no tryptophan.