Model analysis concerning the effects of growth rate and intracellular tryptophan level on the stability and dynamics of tryptophan biosynthesis in bacteria

A Molecular Dynamic Model of Tryptophan Overproduction in Escherichia coli

Several deterministic models simulate the main molecular biology interactions among the numerous mechanisms controlling the dynamics of the tryptophan operon in native strains. However, no models exist to investigate bacterial tryptophan production from a biotechnological point of view. Here, we modified tryptophan models for native production to propose a biotechnological working model that incorporates the activity of tryptophan secretion systems and genetic modifications made in two reported E. coli strains. The resultant deterministic model could emulate the production of tryptophan in the same order of magnitude as those quantified experimentally by the genetically engineered E. coli strains GPT1001 and GPT1002 in shake flasks. We hope this work may contribute to the rational development of biological models that define and include the main parameters and molecular components for designing and engineering efficient biotechnological chassis to produce valuable chemicals.

Tryptophan Production Maximization in a Fed-Batch Bioreactor with Modified E. coli Cells, by Optimizing Its Operating Policy Based on an Extended Structured Cell Kinetic Model

Hybrid kinetic models, linking structured cell metabolic processes to the dynamics of macroscopic variables of the bioreactor, are more and more used in engineering evaluations to derive more precise predictions of the process dynamics under variable operating conditions. Depending on the cell model complexity, such a math tool can be used to evaluate the metabolic fluxes in relation to the bioreactor operating conditions, thus suggesting ways to genetically modify the microorganism for certain purposes. Even if development of such an extended dynamic model requires more experimental and computational efforts, its use is advantageous. The approached probative example refers to a model simulating the dynamics of nanoscale variables from several pathways of the central carbon metabolism (CCM) of Escherichia coli cells, linked to the macroscopic state variables of a fed-batch bioreactor (FBR) used for the tryptophan (TRP) production. The used E. coli strain was modified to replace the PTS system for glucose (GLC) uptake with a more efficient one. The study presents multiple elements of novelty: (i) the experimentally validated modular model itself, and (ii) its efficiency in computationally deriving an optimal operation policy of the FBR.

Repeated fed-batch strategy and metabolomic analysis to achieve high docosahexaenoic acid productivity in Crypthecodinium cohnii

Background

Docosahexaenoic acid (DHA) is essential for human diet. However, high production cost of DHA using C. cohnii makes it currently less competitive commercially, which is mainly caused by low DHA productivity. In recent years, repeated fed-batch strategies have been evaluated for increasing the production of many fermentation products. The reduction in terms of stability of culture system was one of the major challenges for repeated fed-batch fermentation. However, the possible mechanisms responsible for the decreased stability of the culture system in the repeated fed-batch fermentation are so far less investigated, restricting the efforts to further improve the productivity. In this study, a repeated fed-batch strategy for DHA production using C. cohnii M-1-2 was evaluated to improve DHA productivity and reduce production cost, and then the underlying mechanisms related to the gradually decreased stability of the culture system in repeated fed-batch culture were explored through LC– and GC–MS metabolomic analyses.

Results

It was discovered that glucose concentration at 15–27 g/L and 80% medium replacement ratio were suitable for the growth of C. cohnii M-1-2 during the repeated fed-batch culture. A four-cycle repeated fed-batch culture was successfully developed and assessed at the optimum cultivation parameters, resulting in increasing the total DHA productivity by 26.28% compared with the highest DHA productivity of 57.08 mg/L/h reported using C. cohnii, including the time required for preparing seed culture and fermentor. In addition, LC– and GC–MS metabolomics analyses showed that the gradually decreased nitrogen utilization capacity, and down-regulated glycolysis and TCA cycle were correlated with the decreased stability of the culture system during the long-time repeated fed-batch culture. At last, some biomarkers, such as Pyr, Cit, OXA, FUM, l-tryptophan, l-threonine, l-leucine, serotonin, and 4-guanidinobutyric acid, correlated with the stability of culture system of C. cohnii M-1-2 were identified.

Conclusions

The study proved that repeated fed-batch cultivation was an efficient and energy-saving strategy for industrial production of DHA using C. cohnii, which could also be useful for cultivation of other microbes to improve productivity and reduce production cost. In addition, the mechanisms study at metabolite level can also be useful to further optimize production processes for C. cohnii and other microbes.

Nanotube-mediated cross-feeding couples the metabolism of interacting bacterial cells

Bacteria frequently engage in cross-feeding interactions that involve an exchange of metabolites with other micro- or macroorganisms. The often obligate nature of these associations, however, hampers manipulative experiments, thus limiting our mechanistic understanding of the ecophysiological consequences that result for the organisms involved. Here we address this issue by taking advantage of a well-characterized experimental model system, in which auxotrophic genotypes of E. coli derive essential amino acids from prototrophic donor cells using intercellular nanotubes. Surprisingly, donor-recipient cocultures revealed that the mere presence of auxotrophic genotypes was sufficient to increase amino acid production levels of several prototrophic donor genotypes. Our work is consistent with a scenario, in which interconnected auxotrophs withdraw amino acids from the cytoplasm of donor cells, which delays feedback inhibition of the corresponding amino acid biosynthetic pathway and, in this way, increases amino acid production levels. Our findings indicate that in newly established mutualistic associations, an intercellular regulation of exchanged metabolites can simply emerge from the architecture of the underlying biosynthetic pathways, rather than requiring the evolution of new regulatory mechanisms.

A newton cooperative genetic algorithm method for in silico optimization of metabolic pathway production

This paper presents an in silico optimization method of metabolic pathway production. The metabolic pathway can be represented by a mathematical model known as the generalized mass action model, which leads to a complex nonlinear equations system. The optimization process becomes difficult when steady state and the constraints of the components in the metabolic pathway are involved. To deal with this situation, this paper presents an in silico optimization method, namely the Newton Cooperative Genetic Algorithm (NCGA). The NCGA used Newton method in dealing with the metabolic pathway, and then integrated genetic algorithm and cooperative co-evolutionary algorithm. The proposed method was experimentally applied on the benchmark metabolic pathways, and the results showed that the NCGA achieved better results compared to the existing methods.

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.

Modeling operon dynamics: the tryptophan and lactose operons as paradigms

Understanding the regulation of gene control networks and their ensuing dynamics will be a critical component in the understanding of the mountain of genomic data being currently collected. This paper reviews recent mathematical modeling work on the tryptophan and lactose operons which are, respectively, the classical paradigms for repressible and inducible operons.

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.

Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data

A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics.

Modeling and simulation of genetic regulatory systems: a literature review

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.

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.

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

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.