Robustness and Nonlinear Dynamic Analysis for Trp Operon and Optimization of Tryptophan Production: An Integrated Model Considering Gene Regulation, Genes Interaction and Product Excretion

The tryptophan operon (trp operon), paradigm for repressible operons, is regulated by three different negative-feedback mechanisms of repression, transcription attenuation and enzyme inhibition. Initiation of transcription is controlled by the interaction of the tryptophan repressor with its target site on the operator. Moreover, the interaction among the regulator genes, the operator genes and the structure genes and excretion of tryptophan play an important factor according to previous works. In this study, an expended mathematical model for the tryptophan operon regulation on the effects of repression, feedback enzyme inhibition, attenuation, interaction among genes and excretion of tryptophan is presented. The new model is first translated into the corresponding S-system version. The robustness of this model is then discussed by using the S-system model and the sensitivity analysis shows that the model is robust enough. The influences of cell growth rate on the biosynthesis of tryptophan, stability and dynamic behavior of the trp operon are also well investigated. The transportation of tryptophan through cytoplasmic membranes, especially the inhibition of tryptophan transport can influence the level of intracellular tryptophan significantly. The theoretical analysis indicates that an increase of inhibition constant of tryptophan transport is favorable for the biosynthesis of tryptophan. Furthermore, a steady-state optimization model is established based on trp operon models. The optimization results indicate that it is possible to attain a stable and robust steady state with a rate of tryptophan production increased more than 4.8 times in which the growth rate is kept as 0.00624h^-1 and some key parameters is modulated.