Metabolic design based on a coupled gene expression—metabolic network model of tryptophan production in Escherichia coli

The presumably high potential of a holistic design approach for complex biochemical reaction networks is exemplified here for the network of tryptophan biosynthesis from glucose, a system whose components have been investigated thoroughly before. A dynamic model that combines the behavior of the trp operon gene expression with the metabolic network of central carbon metabolism and tryptophan biosynthesis is investigated. This model is analyzed in terms of metabolic fluxes, metabolic control, and nonlinear optimization. We compare two models for a wild-type strain and another model for a tryptophan producer. An integrated optimization of the whole network leads to a significant increase in tryptophan production rate for all systems under study. This enhancement is well above the increase that can be achieved by an optimization of subsystems. A constant ratio of control coefficients on tryptophan synthesis rate has been identified for the models regarding or disregarding trp operon expression. Although we found some examples where flux control coefficients even contradict the trends of enzyme activity changes in an optimized profile, flux control can be used as an indication for enzymes that have to be taken into account in optimization.

Dynamic model of Escherichia coli tryptophan operon shows an optimal structural design

A mathematical model has been developed to study the effect of external tryptophan on the trp operon. The model accounts for the effect of feedback repression by tryptophan through the Hill equation. We demonstrate that the trp operon maintains an intracellular steady-state concentration in a fivefold range irrespective of extracellular conditions. Dynamic behavior of the trp operon corresponding to varying levels of extracellular tryptophan illustrates the adaptive nature of regulation. Depending on the external tryptophan level in the medium, the transient response ranges from a rapid and underdamped to a sluggish and highly overdamped response. To test model fidelity, simulation results are compared with experimental data available in the literature. We further demonstrate the significance of the biological structure of the operon on the overall performance. Our analysis suggests that the tryptophan operon has evolved to a truly optimal design.

Genetic "code": representations and dynamical models of genetic components and networks

Dynamical modeling of biological systems is becoming increasingly widespread as people attempt to grasp biological phenomena in their full complexity and make sense of an accelerating stream of experimental data. We review a number of recent modeling studies that focus on systems specifically involving gene expression and regulation. These systems include bacterial metabolic operons and phase-variable piliation, bacteriophages T7 and lambda, and interacting networks of eukaryotic developmental genes. A wide range of conceptual and mathematical representations of genetic components and phenomena appears in these works. We discuss these representations in depth and give an overview of the tools currently available for creating and exploring dynamical models. We argue that for modeling to realize its full potential as a mainstream biological research technique the tools must become more general and flexible, and formal, standardized representations of biological knowledge and data must be developed.

Modified model for the regulation of the tryptophan operon in Escherichia coli

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.

Computational studies of gene regulatory networks: in numero molecular biology

Remarkable progress in genomic research is leading to a complete map of the building blocks of biology. Knowledge of this map is, in turn, setting the stage for a fundamental description of cellular function at the DNA level. Such a description will entail an understanding of gene regulation, in which proteins often regulate their own production or that of other proteins in a complex web of interactions. The implications of the underlying logic of genetic networks are difficult to deduce through experimental techniques alone, and successful approaches will probably involve the union of new experiments and computational modelling techniques.

Dynamic behavior in mathematical models of the tryptophan operon

This paper surveys the general theory of operon regulation as first formulated by Goodwin and Griffith, and then goes on to consider in detail models of regulation of tryptophan production by Bliss, Sinha, and Santillan and Mackey, and the interrelationships between them. We further give a linear stability analysis of the Santillan and Mackey model for wild type E. coli as well as three different mutant strains that have been previously studied in the literature. This stability analysis indicates that the tryptophan production systems should be stable, which is in accord with our numerical results. (c) 2001 American Institute of Physics.

Genetically structured mathematical modeling of trp attenuator mechanism

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 microM compared with 1 to 100 microM 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.