Metabolite and isotopomer balancing in the analysis of metabolic cycles: II. Applications

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

Tracking the metabolic pulse of plant lipid production with isotopic labeling and flux analyses: Past, present and future

Metabolism is comprised of networks of chemical transformations, organized into integrated biochemical pathways that are the basis of cellular operation, and function to sustain life. Metabolism, and thus life, is not static. The rate of metabolites transitioning through biochemical pathways (i.e., flux) determines cellular phenotypes, and is constantly changing in response to genetic or environmental perturbations. Each change evokes a response in metabolic pathway flow, and the quantification of fluxes under varied conditions helps to elucidate major and minor routes, and regulatory aspects of metabolism. To measure fluxes requires experimental methods that assess the movements and transformations of metabolites without creating artifacts. Isotopic labeling fills this role and is a long-standing experimental approach to identify pathways and quantify their metabolic relevance in different tissues or under different conditions. The application of labeling techniques to plant science is however far from reaching it potential. In light of advances in genetics and molecular biology that provide a means to alter metabolism, and given recent improvements in instrumentation, computational tools and available isotopes, the use of isotopic labeling to probe metabolism is becoming more and more powerful. We review the principal analytical methods for isotopic labeling with a focus on seminal studies of pathways and fluxes in lipid metabolism and carbon partitioning through central metabolism. Central carbon metabolic steps are directly linked to lipid production by serving to generate the precursors for fatty acid biosynthesis and lipid assembly. Additionally some of the ideas for labeling techniques that may be most applicable for lipid metabolism in the future were originally developed to investigate other aspects of central metabolism. We conclude by describing recent advances that will play an important future role in quantifying flux and metabolic operation in plant tissues.

Combining genomics, metabolome analysis, and biochemical modelling to understand metabolic networks

Now that complete genome sequences are available for a variety of organisms, the elucidation of gene functions involved in metabolism necessarily includes a better understanding of cellular responses upon mutations on all levels of gene products, mRNA, proteins, and metabolites. Such progress is essential since the observable properties of organisms – the phenotypes – are produced by the genotype in juxtaposition with the environment. Whereas much has been done to make mRNA and protein profiling possible, considerably less effort has been put into profiling the end products of gene expression, metabolites. To date, analytical approaches have been aimed primarily at the accurate quantification of a number of pre-defined target metabolites, or at producing fingerprints of metabolic changes without individually determining metabolite identities. Neither of these approaches allows the formation of an in-depth understanding of the biochemical behaviour within metabolic networks. Yet, by carefully choosing protocols for sample preparation and analytical techniques, a number of chemically different classes of compounds can be quantified simultaneously to enable such understanding. In this review, the terms describing various metabolite-oriented approaches are given, and the differences among these approaches are outlined. Metabolite target analysis, metabolite profiling, metabolomics, and metabolic fingerprinting are considered. For each approach, a number of examples are given, and potential applications are discussed.

Dynamics of Positional Enrichment: Theoretical Development and Application to Carbon Labeling in Zymomonas mobilis

Positional enrichment analysis has become an important technique for assessing detailed flux distributions and the fates of specific atoms in metabolic pathway systems. The typical approach to positional enrichment analysis is performed by supplying specifically labeled substrate to a cell system, letting the system reach steady state, and measuring where label had arrived and accumulated. The data are then evaluated mathematically with the help of a linear stoichiometric flux distribution model. While this procedure has proven to yield new and valuable insights, it does not address the transient dynamics between providing label and its ultimate steady-state distribution, which is often of great interest to the experimentalist (pulse labeling experiments). We show here that an extension of a recent mathematical method for dynamic labeling analysis is able to shed light on these transitions, thereby revealing insights not obtained with traditional positional enrichment analyses. The method traces the dynamics of one or more carbons through fully regulated metabolic pathways, which, in principle, may be arbitrarily complex. After a brief review of the earlier method and description of the theoretical extension, we illustrate the method with an analysis of the pentose phosphate pathway in Zymomonas mobilis, which has been used for traditional positional enrichment analyses in the past. We show how different labeling schemes result in distinctly different transients, which nevertheless eventually lead to a steady-state labeling profile that coincides exactly with the corresponding profile from traditional analysis. Thus, over the domain of commonality, the proposed method leads to results equivalent to those from state-of-the-art existing methods. However, these steady-state results constitute only a small portion of the insights obtainable with the proposed method. Our method can also be used as an "inverse" technique for elucidating the topology and regulation of pathway systems, if appropriate time series data are available. While such dynamic data are still rather rare, they are now being generated with increasing frequency and we believe it is desirable, and indeed necessary, to accompany this trend with an adequate, rigorous method of analysis.

A transient isotopic labeling methodology for 13C metabolic flux analysis of photoautotrophic microorganisms

Metabolic flux analysis is increasingly recognized as an integral component of systems biology. However, techniques for experimental measurement of system-wide metabolic fluxes in purely photoautotrophic systems (growing on CO(2) as the sole carbon source) have not yet been developed due to the unique problems posed by such systems. In this paper, we demonstrate that an approach that balances positional isotopic distributions transiently is the only route to obtaining system-wide metabolic flux maps for purely autotrophic metabolism. The outlined transient (13)C-MFA methodology enables measurement of fluxes at a metabolic steady-state, while following changes in (13)C-labeling patterns of metabolic intermediates as a function of time, in response to a step-change in (13)C-label input. We use mathematical modeling of the transient isotopic labeling patterns of central intermediates to assess various experimental requirements for photoautotrophic MFA. This includes the need for intracellular metabolite concentration measurements and isotopic labeling measurements as a function of time. We also discuss photobioreactor design and operation in order to measure fluxes under precise environmental conditions. The transient MFA technique can be used to measure and compare fluxes under different conditions of light intensity, nitrogen sources or compare strains with various mutations or gene deletions and additions.

Expanding the metabolic engineering toolbox: more options to engineer cells

Metabolic engineering exploits an integrated, systems-level approach for optimizing a desired cellular property or phenotype; and great strides have been made within this scope and context during the past fifteen years. However, due to limitations in the concepts and techniques, these have relied on a focused, pathway-oriented view. Recent advances in 'omics' technologies and computational systems biology have brought the foundational systems approach of metabolic engineering into focus. At the same time, protein engineering and synthetic biology have expanded the breadth and precision of the methods available to metabolic engineers to improve strain properties. Examples are presented that illustrate this broader perspective of tools and concepts, including a recent approach for global transcriptional machinery engineering (gTME), which has demonstrated the ability to elicit multigenic transcriptional changes that have improved phenotypes compared with single-gene perturbations.

Bayesian-based selection of metabolic objective functions

MOTIVATION

A critical component of in silico analysis of underdetermined metabolic systems is the identification of the appropriate objective function. A common assumption is that the objective of the cell is to maximize growth. This objective function has been shown to be consistent in a few limited experimental cases, but may not be universally appropriate. Here a method is presented to quantitatively determine the most probable objective function.

RESULTS

The genome-scale metabolism of Escherichia coli growing on succinate was used as a case-study for analysis. Five different objective functions, including maximization of growth rate, were chosen based on biological plausibility. A combination of flux balance analysis and linear programming was used to simulate cellular metabolism, which was then compared to independent experimental data using a Bayesian objective function discrimination technique. After comparing rates of oxygen uptake and acetate production, minimization of the production rate of redox potential was determined to be the most probable objective function. Given the appropriate reaction network and experimental data, the discrimination technique can be applied to any bacterium to test a variety of different possible objective functions.

SUPPLEMENTARY INFORMATION

Additional files, code and a program for carrying out model discrimination are available at http://www.engr.uconn.edu/~srivasta/modisc.html.

Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements

Metabolic fluxes, estimated from stable isotope studies, provide a key to quantifying physiology in fields ranging from metabolic engineering to the analysis of human metabolic diseases. A serious drawback of the flux estimation method in current use is that it does not produce confidence limits for the estimated fluxes. Without this information it is difficult to interpret flux results and expand the physiological significance of flux studies. To address this shortcoming we derived analytical expressions of flux sensitivities with respect to isotope measurements and measurement errors. These tools allow the determination of local statistical properties of fluxes and relative importance of measurements. Furthermore, we developed an efficient algorithm to determine accurate flux confidence intervals and demonstrated that confidence intervals obtained with this method closely approximate true flux uncertainty. In contrast, confidence intervals approximated from local estimates of standard deviations are inappropriate due to inherent system nonlinearities. We applied these methods to analyze the statistical significance and confidence of estimated gluconeogenesis fluxes from human studies with [U-13C]glucose as tracer and found true limits for flux estimation in specific human isotopic protocols.

Metabolic engineering

Metabolic engineering is a powerful methodology aimed at intelligently designing new biological pathways, systems, and ultimately phenotypes through the use of recombinant DNA technology. Built largely on the theoretical and computational analysis of chemical systems, the field has evolved to incorporate a growing number of genome scale experimental tools. This combination of rigorous analysis and quantitative molecular biology methods has endowed metabolic engineering with an effective synergism that crosses traditional disciplinary bounds. As such, there are a growing number of applications for the effective employment of metabolic engineering, ranging from the initial industrial fermentation applications to more recent medical diagnosis applications. In this review we highlight many of the contributions metabolic engineering has provided through its history, as well as give an overview of new tools and applications that promise to have a large impact on the field's future.

Myocardial phenotyping using isotopomer analysis of metabolic fluxes

Over the past 20 years, stable isotopes combined with isotopomer analysis have proven to be a powerful approach to probe the dynamics of metabolism in various biological systems, including the heart. The aim of this paper is to demonstrate how isotopomer analysis of metabolic fluxes can provide novel insights into the myocardial phenotype. Specifically, building on our past experience using NMR spectroscopy and GC-MS as applied to investigations of cardiac energy metabolism, we highlight specific complex metabolic networks that would not be predicted by classical biochemistry or by static measurements of metabolite, protein and mRNA levels.

Studies of the intermediary metabolism in cultured cells of the insect Spodoptera frugiperda using 13C- or 15N-labelled tracers

Background

Insect cells can serve as host systems for the recombinant expression of eukaryotic proteins. Using this platform, the controlled expression of ¹⁵N/¹³C labelled proteins requires the analysis of incorporation paths and rates of isotope-labelled precursors present in the medium into amino acids. For this purpose, Spodoptera frugiperda cells were grown in a complex medium containing [U-¹³C₆]glucose. In a second experiment, cultures of S. frugiperda were grown in the presence of ¹⁵N-phenylalanine.

Results

Quantitative NMR analysis showed incorporation of the proffered [U-¹³C₆]glucose into the ribose moiety of ribonucleosides (40 – 45%) and into the amino acids, alanine (41%), glutamic acid/glutamine (C-4 and C-5, 30%) and aspartate/asparagine (15%). Other amino acids and the purine ring of nucleosides were not formed from exogenous glucose in significant amounts (> 5%). Prior to the incorporation into protein the proffered ¹⁵N-phenylalanine lost about 70% of its label by transamination and the labelled compound was not converted into tyrosine to a significant extent.

Conclusion

Growth of S. frugiperda cells in the presence of [U-¹³C₆]glucose is conducive to the fractional labelling of ribonucleosides, alanine, glutamic acid/glutamine and aspartic acid/asparagine. The isotopolog compositions of the ribonucleosides and of alanine indicate considerable recycling of carbohydrate intermediates in the reductive branch of the pentose phosphate pathway. The incorporation of ¹⁵N-labelled amino acids may be hampered by loss of the ¹⁵N-label by transamination.

Isotopolog perturbation techniques for metabolic networks: metabolic recycling of nutritional glucose in Drosophila melanogaster

Drosophila melanogaster strain Oregon-R(*) was grown on standard medium supplemented with [U-(13)C(6)]glucose. One to two days after hatching, flies were extracted with water. Glucose was isolated chromatographically from the extract and was analyzed by (13)C NMR spectroscopy. All (13)C signals of the isolated glucose were multiplets arising by (13)C(13)C coupling. Based on a comprehensive analysis of the coupling constants and heavy isotope shifts in glucose, the integrals of individual (13)C signal patterns afforded the concentrations of certain groups of (13)C isotopologs. These data were deconvoluted by a genetic algorithm affording the abundances of all single-labeled and of 15 multiply labeled isotopologs. Among the latter group, seven isotopologs were found at concentrations >0.1 mol % with [1,2-(13)C(2)]glucose as the most prominent species. The multiply (13)C-labeled glucose isotopologs are caused by metabolic remodeling of the proffered glucose via a complex network of catabolic and anabolic processes involving glycolysis and/or passage through the pentose phosphate, the Cori cycle and/or the citrate cycle. The perturbation method described can be adapted to a wide variety of experimental systems and isotope-labeled precursors.

Modeling of yeast metabolism and process dynamics in batch fermentation

Much is known about yeast metabolism and the kinetics of industrial batch fermentation processes. In this study, however, we provide the first tool to evaluate the dynamic interaction that exists between them. A stoichiometric model, using wine fermentation as a case study, was constructed to simulate batch cultures of Saccharomyces cerevisiae. Five differential equations describe the evolution of the main metabolites and biomass in the fermentation tank, while a set of underdetermined linear algebraic equations models the pseudo-steady-state microbial metabolism. Specific links between process variables and the reaction rates of metabolic pathways represent microorganism adaptation to environmental changes in the culture. Adaptation requirements to changes in the environment, optimal growth, and homeostasis were set as the physiological objectives. A linear programming routine was used to define optimal metabolic mass flux distribution at each instant throughout the process. The kinetics of the process arise from the dynamic interaction between the environment and metabolic flux distribution. The model assessed the effect of nitrogen starvation and ethanol toxicity in wine fermentation and it was able to simulate fermentation profiles qualitatively, while experimental fermentation yields were reproduced successfully as well.

Starch biosynthesis and intermediary metabolism in maize kernels. Quantitative analysis of metabolite flux by nuclear magnetic resonance

The seeds of cereals represent an important sink for metabolites during the accumulation of storage products, and seeds are an essential component of human and animal nutrition. Understanding the metabolic interconversions (networks) underpinning storage product formation could provide the foundation for effective metabolic engineering of these primary nutritional sources. In this paper, we describe the use of retrobiosynthetic nuclear magnetic resonance analysis to establish the metabolic history of the glucose (Glc) units of starch in maize (Zea mays) kernels. Maize kernel cultures were grown with [U-(13)C(6)]Glc, [U-(13)C(12)]sucrose, or [1,2-(13)C(2)]acetate as supplements. After 19 d, starch was hydrolyzed, and the isotopomer composition of the resulting Glc was determined by quantitative nuclear magnetic resonance analysis. [1,2-(13)C(2)]Acetate was not incorporated into starch. [U-(13)C(6)]Glc or [U-(13)C(12)]sucrose gave similar labeling patterns of polysaccharide Glc units, which were dominated by [1,2,3-(13)C(3)]- and [4,5,6-(13)C(3)]-isotopomers, whereas the [U-(13)C(6)]-, [3,4,5,6-(13)C(4)]-, [1,2-(13)C(2)]-, [5,6-(13)C(2)], [3-(13)C(1)], and [4-(13)C(1)]-isotopomers were present at lower levels. These isotopomer compositions indicate that there is extensive recycling of Glc before its incorporation into starch, via the enzymes of glycolytic, glucogenic, and pentose phosphate pathways. The relatively high abundance of the [5,6-(13)C(2)]-isotopomer can be explained by the joint operation of glycolysis/glucogenesis and the pentose phosphate pathway.

Computing positional isotopomer distributions from tandem mass spectrometric data

The isotopomer distributions of metabolites are invaluable pieces of information in the computation of the flux distribution in a metabolic network. We describe the use of tandem mass spectrometry with the daughter ion scanning technique in the discovery of positional isotopomer distributions (PID). This technique increases the possibilities of mass spectrometry since given the same fragment ions, it uncovers more information than the full scanning mode. The mathematics of the new technique is slightly more complicated than the techniques needed by full scanning mode methods. Our experiments, however, show that in practice the inadequacy of the fragmentation of amino acids in the tandem mass spectrometer does not allow uncovering the PID exactly even if the daughter ion scanning is used. The computational techniques have been implemented in a MATLAB application called PIDC (Positional Isotopomer Distribution Calculator).

Metabolic engineering of Lactococcus lactis: the impact of genomics and metabolic modelling

Lactic acid bacteria display a relatively simple and well described metabolism where the sugar source is converted mainly to lactic acid. Here we will shortly describe metabolic engineering strategies that led to the efficient re-routing of the lactococcal pyruvate metabolism to end-products other than lactic acid, including diacetyl and alanine. Moreover, we will review current metabolic engineering approaches that aim at increasing the flux through complex biosynthetic pathways, leading to exopolysaccharides and folic acid. Finally, the (future) impact of the developments in the area of genomics and corresponding high-throughput technologies will be discussed.

Modeling and simulation: tools for metabolic engineering

Mathematical modeling is one of the key methodologies of metabolic engineering. Based on a given metabolic model different computational tools for the simulation, data evaluation, systems analysis, prediction, design and optimization of metabolic systems have been developed. The currently used metabolic modeling approaches can be subdivided into structural models, stoichiometric models, carbon flux models, stationary and nonstationary mechanistic models and models with gene regulation. However, the power of a model strongly depends on its basic modeling assumptions, the simplifications made and the data sources used. Model validation turns out to be particularly difficult for metabolic systems. The different modeling approaches are critically reviewed with respect to their potential and benefits for the metabolic engineering cycle. Several tools that have emerged from the different modeling approaches including structural pathway synthesis, stoichiometric pathway analysis, metabolic flux analysis, metabolic control analysis, optimization of regulatory architectures and the evaluation of rapid sampling experiments are discussed.

Mathematical modeling of plant metabolic pathways

The understanding of the control of metabolic flux in plants requires integrated mathematical formulations of gene and protein expression, enzyme kinetics, and developmental biology. Plants have a large number of metabolically active compartments, and non-steady-state conditions are frequently encountered. Consequently steady-state metabolic flux balance and isotopic flux balance modeling approaches have limited utility in probing plant metabolic systems. Transient isotopic flux analysis and kinetic modeling are powerful proven techniques for the quantification of metabolic fluxes in compartmentalized, dynamic metabolic systems. These tools are now widely used to address metabolic flux responses to environmental and genetic perturbations in plant metabolism. Continued developments in isotopic and kinetic modeling, quantifying metabolite exchange between compartments, and transcriptional and posttranscriptional regulatory mechanisms governing enzyme level and activity will enable simulation of large sections of plant metabolism under non-steady-state conditions. Metabolic control analysis will continue to make substantial contributions to the understanding of quantitative distribution of control of flux. From the synergy between mathematical models and experiments, creative methods for controlling the distribution of flux by genetic or environmental means will be discovered and rationally implemented.

Metabolomics--the link between genotypes and phenotypes

Metabolites are the end products of cellular regulatory processes, and their levels can be regarded as the ultimate response of biological systems to genetic or environmental changes. In parallel to the terms 'transcriptome' and proteome', the set of metabolites synthesized by a biological system constitute its 'metabolome'. Yet, unlike other functional genomics approaches, the unbiased simultaneous identification and quantification of plant metabolomes has been largely neglected. Until recently, most analyses were restricted to profiling selected classes of compounds, or to fingerprinting metabolic changes without sufficient analytical resolution to determine metabolite levels and identities individually. As a prerequisite for metabolomic analysis, careful consideration of the methods employed for tissue extraction, sample preparation, data acquisition, and data mining must be taken. In this review, the differences among metabolite target analysis, metabolite profiling, and metabolic fingerprinting are clarified, and terms are defined. Current approaches are examined, and potential applications are summarized with a special emphasis on data mining and mathematical modelling of metabolism.

Application of radiolabeled tracers to biocatalytic flux analysis

Radiolabeled tracers can provide valuable information about the structure of and flux distributions in biocatalytic reaction networks. This method derives from prior studies of glucose metabolism in mammalian systems and is implemented by pulsing a culture with a radiolabeled metabolite that can be transported into the cells and subsequently measuring the radioactivity of all network metabolites following separation by liquid chromatography. Intracellular fluxes can be directly determined from the transient radioactivity count data by tracking the depletion of the radiolabeled metabolite and/or the accompanying accumulation of any products formed. This technique differs from previous methods in that it is applied within a systems approach to the problem of flux determination. It has been used for the investigation of the indene bioconversion network expressed in Rhodococcus sp. KY1. Flux estimates obtained by radioactive tracers were confirmed by macroscopic metabolite balancing and showed that indene oxidation in steady state chemostat cultures proceeds primarily through a monooxygenase activity forming (1S,2R)-indan oxide, with no dehydrogenation of trans-(1R,2R)-indandiol. These results confirmed the significance of indan oxide formation and identified the hydrolysis of indan oxide as a key step in maximizing the production of (2R)-indandiol, a chiral precursor of the HIV protease inhibitor, Crixivan.

13C metabolic flux analysis

Metabolic flux analysis using 13C-labeled substrates has become an important tool in metabolic engineering. It allows the detailed quantification of all intracellular fluxes in the central metabolism of a microorganism. The method has strongly evolved in recent years by the introduction of new experimental procedures, measurement techniques, and mathematical data evaluation methods. Many of these improvements require advanced skills in the application of nuclear magnetic resonance and mass spectrometry techniques on the one hand and computational and statistical experience on the other hand. This minireview summarizes these recent developments and sketches the major practical problems. An outlook to possible future developments concludes the text.

Microbial pathway engineering for industrial processes: evolution, combinatorial biosynthesis and rational design

Microbial pathway engineering has made significant progress in multiple areas. Many examples of successful pathway engineering for specialty and fine chemicals have been reported in the past two years. Novel carotenoids and polyketides have been synthesized using molecular evolution and combinatorial strategies. In addition, rational design approaches based on metabolic control have been reported to increase metabolic flux to specific products. Experimental and computational tools have been developed to aid in design, reconstruction and analysis of non-native pathways. It is expected that a hybrid of evolutionary, combinatorial and rational design approaches will yield significant advances in the near future.

Large-scale prediction of phenotype: concept

The capability to gather organism wide data has far outstripped the ability to understand it. Transforming large-scale data into a "better" cell requires tools that integrate physiology with its environment. One such tool is large-scale mathematical models that marry stoichiometry and kinetics with metabolic regulation and control. It is straightforward to determine stoichiometry (at least for central pathways), and kinetics can be roughly approximated where need be. However, the molecular details of the "metabolic wiring" managing the cell are often missing. Presented here is a surrogate for these missing details based on a simple premise; over evolutionary time, biological systems have developed objective-based programs that frugally manage gene expression and enzyme activity. Mathematically, this notion can be represented as sets of nonlinear control or "management" problems which, when solved in parallel with the model balances, offer a prediction of how gene expression and enzyme activity are modulated, in the absence of specific mechanistic details. We present a model of Escherichia coli central carbon metabolism, describing batch aerobic growth on glucose, in which transcription, translation, and activity of the gene products of 45 genes is "managed" using this approach. The model consists of 122 species (metabolites, enzymes, mRNA pools, and biomass) and describes 46 reactions (17 reversible). The model is identified (kinetic parameters as well as management structure) from metabolic flux ratio (METAFoR) analysis and physiological measurements. Simulations of a pyruvate kinase knockout strain are compared with experiments and it is shown the model is capable of accurately capturing the metabolic reprogramming resulting from the deletion. Analysis of the mRNA expression pattern, translational pattern and enzyme activity pattern of the wild-type versus mutant indicates a combination of expression and specific activity shifts are responsible for observed differences. While being only a first step toward large-scale physiological modeling, this work is important in two ways. First, it strengthens the hypothesis that unknown mechanism can be reasonably approximated using objective-based management criteria. Second, it provides a dynamic means to couple large-scale analysis technologies with physiology at the single-gene, single-protein level.

Environmental biotechnology informatics

Environmental biotechnology informatics is in its infancy and is growing fast. Computer and information science can assist environmental biotechnology by developing biological databases and building mathematical models of biological systems. Funding and training limitations in this field may, however, hinder its future growth.

Metabolite and isotopomer balancing in the analysis of metabolic cycles: I. Theory

Proper analysis of label distribution in metabolic pathway intermediates is critical for correct interpretation of experimental data and strategic experimental design. While, for example, 13C nuclear magnetic resonance (NMR) spectroscopy is usually limited to the measurement of degrees of 13C enrichment, more information about metabolic fluxes can be extracted from the fine structure of NMR spectra, or molecular weight distributions of isotopomers of metabolic intermediates (measured by gas chromatography-mass spectrometry). For this purpose, rigorous accounting for the contribution of all pathways to label distribution is required, especially contributions resulting from multiple turns of metabolic cycles. In this paper we present a mathematical model developed to analyze isotopomer distributions of tricarboxylic acid cycle (TCA) intermediates following the administration of 13C (or 14C) labeled substrates. The theory presented provides the basis to analyze 13C NMR spectra and molecular weight distributions of metabolites. In a companion paper (Park et al., 1999), the theory is applied to the analysis of several cases of biological significance. Copyright 1999 John Wiley & Sons, Inc.