Software for dynamic analysis of tracer-based metabolomic data: estimation of metabolic fluxes and their statistical analysis

MOTIVATION: Metabolic flux analysis of biochemical reaction networks using isotope tracers requires software tools that can analyze the dynamics of isotopic isomer (isotopomer) accumulation in metabolites and reveal the underlying kinetic mechanisms of metabolism regulation. Since existing tools are restricted by the isotopic steady state and remain disconnected from the underlying kinetic mechanisms, we have recently developed a novel approach for the analysis of tracer-based metabolomic data that meets these requirements. The present contribution describes the last step of this development: implementation of (i) the algorithms for the determination of the kinetic parameters and respective metabolic fluxes consistent with the experimental data and (ii) statistical analysis of both fluxes and parameters, thereby lending it a practical application. RESULTS: The C++ applications package for dynamic isotopomer distribution data analysis was supplemented by (i) five distinct methods for resolving a large system of differential equations; (ii) the 'simulated annealing' algorithm adopted to estimate the set of parameters and metabolic fluxes, which corresponds to the global minimum of the difference between the computed and measured isotopomer distributions; and (iii) the algorithms for statistical analysis of the estimated parameters and fluxes, which use the covariance matrix evaluation, as well as Monte Carlo simulations. An example of using this tool for the analysis of (13)C distribution in the metabolites of glucose degradation pathways has demonstrated the evaluation of optimal set of parameters and fluxes consistent with the experimental pattern, their range and statistical significance, and also the advantages of using dynamic rather than the usual steady-state method of analysis. AVAILABILITY: Software is available free from http://www.bq.ub.es/bioqint/selivanov.htm     

Quantification of central metabolic fluxes in the facultative methylotroph methylobacterium extorquens AM1 using 13C-label tracing and mass spectrometry

The metabolic fluxes of central carbon metabolism were measured in chemostat-grown cultures of Methylobacterium extorquens AM1 with methanol as the sole organic carbon and energy source and growth-limiting substrate. Label tracing experiments were carried out using 70% (13)C-methanol in the feed, and the steady-state mass isotopomer distributions of amino acids derived from total cell protein were measured by gas chromatography coupled to mass spectrometry. Fluxes were calculated from the isotopomer distribution data using an isotopomer balance model and evolutionary error minimization algorithm. The combination of labeled methanol with unlabeled CO(2), which enters central metabolism in two different reactions, provided the discriminatory power necessary to allow quantification of the unknown fluxes within a reasonably small confidence interval. In wild-type M. extorquens AM1, no measurable flux was detected through pyruvate dehydrogenase or malic enzyme, and very little flux through alpha-ketoglutarate dehydrogenase (1.4% of total carbon). In contrast, the alpha-ketoglutarate dehydrogenase flux was 25.5% of total carbon in the regulatory mutant strain phaR, while the pyruvate dehydrogenase and malic enzyme fluxes remained insignificant. The success of this technique with growth on C(1) compounds suggests that it can be applied to help characterize the effects of other regulatory mutations, and serve as a diagnostic tool in the metabolic engineering of methylotrophic bacteria.     

Metabolic flux analysis of Escherichia coli K12 grown on 13C-labeled acetate and glucose using GC-MS and powerful flux calculation method

A new algorithm was developed for the estimation of the metabolic flux distribution based on GC-MS data of proteinogenic amino acids. By using a sensitive GC-MS protocol as well as by combining the global search algorithm such as the genetic algorithm with the local search algorithm such as the Levenberg-Marquardt algorithm, not only the distribution of the net fluxes in the entire network, but also certain exchange fluxes which contribute significantly to the isotopomer distribution could be quantified. This mass isotopomer analysis could identify the biochemical changes involved in the regulation where acetate or glucose was used as a main carbon source. The metabolic flux analysis clearly revealed that when the specific growth rate increased, only a slight change in flux distribution was observed for acetate metabolism, indicating that subtle regulation mechanism exists in certain key junctions of this network system. Different from acetate metabolism, when glucose was used as a carbon source, as the growth rate increased, a significant increase in relative pentose phosphate pathway (PPP) flux was observed for Escherichia coli K12 at the expense of the citric acid cycle, suggesting that when growing on glucose, the flux catalyzed by isocitrate dehydrogenase could not fully fulfill the NADPH demand for cell growth, causing the oxidative PPP to be utilized to a larger extent so as to complement the NADPH demand. The GC-MS protocol as well as the new algorithm demonstrated here proved to be a powerful tool for characterizing metabolic regulation and can be utilized for strain improvement and bioprocess optimization.     

Rapid simulation and analysis of isotopomer distributions using constraints based on enzyme mechanisms: an example from HT29 cancer cells

MOTIVATION: Addition of labeled substrates and the measurement of the subsequent distribution of the labels in isotopomers in reaction networks provide a unique method for assessing metabolic fluxes in whole cells. However, owing to insufficiency of information, attempts to quantify the fluxes often yield multiple possible sets of solutions that are consistent with a given experimental pattern of isotopomers. In the study of the pentose phosphate pathways, the need to consider isotope exchange reactions of transketolase (TK) and transaldolase (TA) (which in past analyses have often been ignored) magnifies this problem; but accounting for the interrelation between the fluxes known from biochemical studies and kinetic modeling solves it. The mathematical relationships between kinetic and equilibrium constants restrict the domain of estimated fluxes to the ones compatible not only with a given set of experimental data, but also with other biochemical information. METHOD: We present software that integrates kinetic modeling with isotopomer distribution analysis. It solves the ordinary differential equations for total concentrations (accounting for the kinetic mechanisms) as well as for all isotopomers in glycolysis and the pentose phosphate pathway (PPP). In the PPP the fluxes created in the TK and TA reactions are expressed through unitary rate constants. The algorithms that account for all the kinetic and equilbrium constant constraints are integrated with the previously developed algorithms, which have been further optimized. The most time-consuming calculations were programmed directly in assembly language; this gave an order of magnitude decrease in the computation time, thus allowing analysis of more complex systems. The software was developed as C-code linked to a program written in Mathematica (Wolfram Research, Champaign, IL), and also as a C++ program independent from Mathematica. RESULTS: Implementing constraints imposed by kinetic and equilibrium constants in the isotopomer distribution analysis in the data from the cancer cells eliminated estimates of fluxes that were inconsistent with the kinetic mechanisms of TK and TA. Fluxes measured experimentally in cells can be used to estimate better the kinetics of TK and TA as they operate in situ. Thus, our approach of integrating various methods for in situ flux analysis opens up the possibility of designing new types of experiments to probe metabolic interrelationships, including the incorporation of additional biochemical information. AVAILABILITY: Software is available freely at: http://www.bq.ub.es/bioqint/selivanov.htm CONTACT: martacascante@ub.edu     

Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models.

Complete isotopomer models that simulate distribution of label in 13C tracer experiments are applied to the quantification of metabolic fluxes in the primary carbon metabolism of E. coli under aerobic and anaerobic conditions. The concept of isotopomer mapping matrices (IMMs) is used to simplify the formulation of isotopomer mass balances by expressing all isotopomer mass balances of a metabolite pool in a single matrix equation. A numerically stable method to calculate the steady-state isotopomer distribution in metabolic networks in introduced. Net values of intracellular fluxes and the degree of reversibility of enzymatic steps are estimated by minimization of the deviations between experimental and simulated measurements. The metabolic model applied includes the Embden-Meyerhof-Parnas and the pentose phosphate pathway, the tricarboxylic acid cycle, anaplerotic reaction sequences and pathways involved in amino acid synthesis. The study clearly demonstrates the value of complete isotopomer models for maximizing the information obtainable from 13C tracer experiments. The approach applied here offers a completely general and comprehensive analysis of carbon tracer experiments where any set of experimental data on the labeling state and extracellular fluxes can be used for the quantification of metabolic fluxes in complex metabolic networks.     

Metabolic flux analysis in Escherichia coli by integrating isotopic dynamic and isotopic stationary 13C labeling data

The novel concept of isotopic dynamic 13C metabolic flux analysis (ID-13C MFA) enables integrated analysis of isotopomer data from isotopic transient and/or isotopic stationary phase of a 13C labeling experiment, short-time experiments, and an extended range of applications of 13C MFA. In the presented work, an experimental and computational framework consisting of short-time 13C labeling, an integrated rapid sampling procedure, a LC-MS analytical method, numerical integration of the system of isotopomer differential equations, and estimation of metabolic fluxes was developed and applied to determine intracellular fluxes in glycolysis, pentose phosphate pathway (PPP), and citric acid cycle (TCA) in Escherichia coli grown in aerobic, glucose-limited chemostat culture at a dilution rate of D = 0.10 h(-1). Intracellular steady state concentrations were quantified for 12 metabolic intermediates. A total of 90 LC-MS mass isotopomers were quantified at sampling times t = 0, 91, 226, 346, 589 s and at isotopic stationary conditions. Isotopic stationarity was reached within 10 min in glycolytic and PPP metabolites. Consistent flux solutions were obtained by ID-13C MFA using isotopic dynamic and isotopic stationary 13C labeling data and by isotopic stationary 13C MFA (IS-13C MFA) using solely isotopic stationary data. It is demonstrated that integration of dynamic 13C labeling data increases the sensitivity of flux estimation, particularly at the glucose-6-phosphate branch point. The identified split ratio between glycolysis and PPP was 55%:44%. These results were confirmed by IS-13C MFA additionally using labeling data in proteinogenic amino acids (GC-MS) obtained after 5 h from sampled biomass.     

Determination of metabolic fluxes in a non-steady-state system

Estimation of fluxes through metabolic networks from redistribution patterns of (13)C has become a well developed technique in recent years. However, the approach is currently limited to systems at metabolic steady-state; dynamic changes in metabolic fluxes cannot be assessed. This is a major impediment to understanding the behaviour of metabolic networks, because steady-state is not always experimentally achievable and a great deal of information about the control hierarchy of the network can be derived from the analysis of flux dynamics. To address this issue, we have developed a method for estimating non-steady-state fluxes based on the mass-balance of mass isotopomers. This approach allows multiple mass-balance equations to be written for the change in labelling of a given metabolite pool and thereby permits over-determination of fluxes. We demonstrate how linear regression methods can be used to estimate non-steady-state fluxes from these mass balance equations. The approach can be used to calculate fluxes from both mass isotopomer and positional isotopomer labelling information and thus has general applicability to data generated from common spectrometry- or NMR-based analytical platforms. The approach is applied to a GC-MS time-series dataset of (13)C-labelling of metabolites in a heterotrophic Arabidopsis cell suspension culture. Threonine biosynthesis is used to demonstrate that non-steady-state fluxes can be successfully estimated from such data while organic acid metabolism is used to highlight some common issues that can complicate flux estimation. These include multiple pools of the same metabolite that label at different rates and carbon skeleton rearrangements.     

Theory of metabolism regulation: a complete system of equations for regulation coefficients

Basic quantitative parameters of control in a metabolic system are considered: control coefficients of enzymes with respect to metabolic fluxes and concentrations, and in the case when there are conservation laws, the response coefficients of metabolic fluxes and concentrations to changes in the conserved sums of metabolite concentrations (e. g. conserved moieties). Relationships are obtained which generalize the well known connectivity relations for the case of metabolites binding by conservation laws. Additional relationships are obtained which complement the set of connectivity relations up to the complete system of equations for determining all the control coefficients. The control coefficients are expressed through the enzyme elasticity coefficients, steady state metabolic fluxes and concentrations. Formulas are derived which express response coefficients of flux and concentrations through the enzyme control and elasticity coefficients and metabolite concentrations.     

Automated Bayesian model development for frequency detection in biological time series

Background

The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results

This article addresses the mathematical and computational formulation of ¹³C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions

Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.     

Numerical bias estimation for mass spectrometric mass isotopomer analysis

Mass spectrometric (MS) isotopomer analysis has become a standard tool for investigating biological systems using stable isotopes. In particular, metabolic flux analysis uses mass isotopomers of metabolic products typically formed from ¹³C-labeled substrates to quantitate intracellular pathway fluxes. In the current work, we describe a model-driven method of numerical bias estimation regarding MS isotopomer analysis. Correct bias estimation is crucial for measuring statistical qualities of measurements and obtaining reliable fluxes. The model we developed for bias estimation corrects a priori unknown systematic errors unique for each individual mass isotopomer peak. For validation, we carried out both computational simulations and experimental measurements. From stochastic simulations, it was observed that carbon mass isotopomer distributions and measurement noise can be determined much more precisely only if signals are corrected for possible systematic errors. By removing the estimated background signals, the residuals resulting from experimental measurement and model expectation became consistent with normality, experimental variability was reduced, and data consistency was improved. The method is useful for obtaining systematic error-free data from ¹³C tracer experiments and can also be extended to other stable isotopes. As a result, the reliability of metabolic fluxes that are typically computed from mass isotopomer measurements is increased.     

一种中间代谢途径代谢通量的定量分析方法

以¹³C标记的碳源,用二维核磁共振技术(¹H-¹³C,HMQC)测定代谢中产生的氨基酸标记模式,研究对中间代谢途径胞内代谢通量进行定量分析的方法.通过开发软件包,改进同位素分布的数学模型,提出了反应映射矩阵(RMM)等概念.由简化算法,提高程序的执行效率,建立了定量分析胞内代谢通量的平台.代谢模型涉及了糖酵解途径、磷酸戊糖途径、三羧酸循环、几种回补反应、发酵途径和氨基酸合成途径.     

The relationships between the metabolic fluxes and 13C-labeled isotopomer distribution for the flux analysis of the main metabolic pathways

It has been known that ¹³C-labeling technique is quite useful in estimating the metabolic fluxes. Although the program-based flux analysis is powerful, it is not easy to be confident with the result obtained without experiences and exhaustive trial and errors based on statistical analysis for the confidence intervals in practice. It is, therefore, quite important to grasp the relationship between the fluxes and the ¹³C-labeled isotopomer distribution to get deeper insight into the metabolic flux analysis. In the present research, it was shown explicitly how the isotopomer distribution changes with respect to the fluxes in relation to the labeling patterns of the substrate, where either labeled glucose, acetate, or pyruvate was used as a carbon source. Some of the analytical expressions were derived based on the matrix representation, and they were utilized for analysis. It was shown that the isotopomer pattern does not necessarily change uniformly with respect to fluxes, but changes in a complicated way in particular for the case of using pyruvate as a carbon source where some isotopomers do not necessarily change monotonically. It was shown to be quite important to grasp how the isotopomer pattern changes with respect to fluxes and the labeling pattern of the substrate for flux determination and the experimental design. It was also shown that the mixture of [1-¹³C] acetate and [2-¹³C] acetate should not be used from the information index point of view. Some of the experimental data were evaluated from the present approach. It was also shown that the isotopomer distribution is less sensitive to the bidirectional fluxes in the reversible pathway.     

Using isotopomer path tracing to quantify metabolic fluxes in pathway models containing reversible reactions

As a more complete picture of the genetic and enzymatic composition of cells becomes available, there is a growing need to describe how cellular regulatory elements interact with the cellular environment to affect cell physiology. One means for describing intracellular regulatory mechanisms is concurrent measurement of multiple metabolic pathways and their interactions by metabolic flux analysis. Flux of carbon through a metabolic pathway responds to all cellular regulatory systems, including changes in enzyme and substrate concentrations, enzyme activation or inhibition, and ultimately genetic control. The extent to which metabolic flux analysis can describe cellular physiology depends on the number of pathways in the model and the quality of the data. Intracellular information is obtainable from isotopic tracer experiments, the most extensive being the determination of the isotopomer distribution, or specific labeling pattern, of intracellular metabolites. We present a rapid and novel solution method that determines the flux of carbon through complex pathway models using isotopomer data. This time-consuming problem was solved with the introduction of isotopomer path tracing, which drastically reduces the number of isotopomer variables to the number of isotopomers observed experimentally. We propose a partitioned solution method that takes advantage of the nearly linear relationship between fluxes and isotopomers. Whereas the stoichiometric matrix and the isotopomer matrix are invertible, simulated annealing and the Newton-Raphson method are used for the nonlinear components. Reversible reactions are described by a new parameter, the association factor, which scales hyperbolically with the rate of metabolite exchange. Automating the solution method permits a variety of models to be compared, thus enhancing the accuracy of results. A simplified example that contains all of the complexities of a comprehensive pathway model is presented. Copyright John Wiley & Sons, Inc.     

Modeling isotopomer distributions in biochemical networks using isotopomer mapping matrices

Within the last decades NMR spectroscopy has undergone tremendous development and has become a powerful analytical tool for the investigation of intracellular flux distributions in biochemical networks using (13)C-labeled substrates. Not only are the experiments much easier to conduct than experiments employing radioactive tracer elements, but NMR spectroscopy also provides additional information on the labeling pattern of the metabolites. Whereas the maximum amount of information obtainable with (14)C-labeled substrates is the fractional enrichment in the individual carbon atom positions, NMR spectroscopy can also provide information on the degree of labeling at neighboring carbon atom positions by analyzing multiplet patterns in NMR spectra or using 2-dimensional NMR spectra. It is possible to quantify the mole fractions of molecules that show a specific labeling pattern, i.e., information of the isotopomer distribution in metabolite pools can be obtained. The isotopomer distribution is the maximum amount of information that in theory can be obtained from (13)C-tracer studies. The wealth of information contained in NMR spectra frequently leads to overdetermined algebraic systems. Consequently, fluxes must be estimated by nonlinear least squares analysis, in which experimental labeling data is compared with simulated steady state isotopomer distributions. Hence, mathematical models are required to compute the steady state isotopomer distribution as a function of a given set of steady state fluxes. Because 2(n) possible labeling patterns exist in a molecule of n carbon atoms, and each pattern corresponds to a separate state in the isotopomer model, these models are inherently complex. Model complexity, so far, has restricted usage of isotopomer information to relatively small metabolic networks. A general methodology for the formulation of isotopomer models is described. The model complexity of isotopomer models is reduced to that of classical metabolic models by expressing the 2(n) isotopomer mass balances of a metabolite pool in a single matrix equation. Using this approach an isotopomer model has been implemented that describes label distribution in primary carbon metabolism, i.e., in a metabolic network including the Embden-Meyerhof-Parnas and pentose phosphate pathway, the tricarboxylic acid cycle, and selected anaplerotic reaction sequences. The model calculates the steady state label distribution in all metabolite pools as a function of the steady state fluxes and is applied to demonstrate the effect of selected anaplerotic fluxes on the labeling pattern of the pathway intermediates. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55:831-840, 1997.     

GC-MS analysis of amino acids rapidly provides rich information for isotopomer balancing

Gas chromatography-mass spectrometry (GC-MS) is a rapid method that provides rich information on isotopomer distributions for metabolic flux analysis. First, we established a fast and reliable experimental protocol for GC-MS analysis of amino acids from total biomass hydrolyzates, and common experimental pitfalls are discussed. Second, a suitable interface for the use of mass isotopomer data is presented. For this purpose, a general, matrix-based correction procedure that accounts for naturally occurring isotopes is introduced. Simulated and experimentally determined mass distributions of unlabeled amino acids showed a deviation of less than 3% for 89% of the analyzed fragments. Third, to investigate general properties of GC-MS-based isotopomer balancing, altered flux ratios through glycolysis and pentose phosphate pathway and/or exchange fluxes were simulated. Different fluxes were found to exert specific and significant influence on the mass isotopomer distributions, thus indicating that GC-MS data contain valuable information for metabolic flux analysis. Fourth, comparison of different methods revealed that GC-MS analysis provides the largest number of independent constraints on amino acid isotopomer abundance, followed by correlation spectroscopy and fractional enrichment analysis by nuclear magnetic resonance.     

Carbon-fate maps for metabolic reactions

MOTIVATION: Stable isotope labeling of small-molecule metabolites (e.g. (13)C-labeling of glucose) is a powerful tool for characterizing pathways and reaction fluxes in a metabolic network. Analysis of isotope labeling patterns requires knowledge of the fates of individual atoms and moieties in reactions, which can be difficult to collect in a useful form when considering a large number of enzymatic reactions. RESULTS: We report carbon-fate maps for 4605 enzyme-catalyzed reactions documented in the KEGG database. Every fate map has been manually checked for consistency with known reaction mechanisms. A map includes a standardized structure-based identifier for each reactant (namely, an InChI string); indices for carbon atoms that are uniquely derived from the metabolite identifiers; structural data, including an identification of homotopic and prochiral carbon atoms; and a bijective map relating the corresponding carbon atoms in substrates and products. Fate maps are defined using the BioNetGen language (BNGL), a formal model-specification language, which allows a set of maps to be automatically translated into isotopomer mass-balance equations. AVAILABILITY: The carbon-fate maps and software for visualizing the maps are freely available (http://cellsignaling.lanl.gov/FateMaps/).     

Metabolic network simulation using logical loop algorithm and Jacobian matrix

A novel method to accomplish efficient numerical simulation of metabolic networks for flux analysis was developed. The only inputs required are the set of stoichiometric balances and the atom mapping matrices of all components of the reaction network. The latter are used to automatically calculate isotopomer mapping matrices. Using the symbolic toolbox of MATLAB the analytical solution of the stoichiometric balance equation system, isotopomer balances and the analytical Jacobian matrix of the total set of stoichiometric and isotopomer balances are created automatically. The number of variables in the isotopomer distribution equation system is significantly reduced applying modified isotopomer mapping matrices. These allow lumping of several consecutive isotopomer reactions into a single one. The solution of the complete system of equations is improved by implementing an iterative logical loop algorithm and using the analytical Jacobian matrix. This new method provided quick and robust convergence to the root of such equation systems in all cases tested. The method was applied to a network of lysine producing Corynebacterium glutamicum. The resulting equation system with the dimension of 546 x 546 was directly derived from 12 isotopomer balance equations. The results obtained yielded identical labeling patterns for metabolites as compared to the relaxation method.     

INCA 2.0: A tool for integrated,dynamic modeling of NMR- and MS-based isotopomer measurements and rigorous metabolic flux analysis

Metabolic flux analysis (MFA) combines experimental measurements and computational modeling to determine biochemical reaction rates in live biological systems. Advancements in analytical instrumentation, such as nuclear magnetic resonance (NMR) spectroscopy and mass spectrometry (MS), have facilitated chemical separation and quantification of isotopically enriched metabolites. However, no software packages have been previously described that can integrate isotopomer measurements from both MS and NMR analytical platforms and have the flexibility to estimate metabolic fluxes from either isotopic steady-state or dynamic labeling experiments. By applying physiologically relevant cardiac and hepatic metabolic models to assess NMR isotopomer measurements, we herein test and validate new modeling capabilities of our enhanced flux analysis software tool, INCA 2.0. We demonstrate that INCA 2.0 can simulate and regress steady-state ¹³C NMR datasets from perfused hearts with an accuracy comparable to other established flux assessment tools. Furthermore, by simulating the infusion of three different ¹³C acetate tracers, we show that MFA based on dynamic ¹³C NMR measurements can more precisely resolve cardiac fluxes compared to isotopically steady-state flux analysis. Finally, we show that estimation of hepatic fluxes using combined ¹³C NMR and MS datasets improves the precision of estimated fluxes by up to 50%. Overall, our results illustrate how the recently added NMR data modeling capabilities of INCA 2.0 can enable entirely new experimental designs that lead to improved flux resolution and can be applied to a wide range of biological systems and measurement time courses.     

Profiling of central metabolism in human cancer cells by two-dimensional NMR, GC-MS analysis, and isotopomer modeling

Tracking metabolic profiles has the potential to reveal crucial enzymatic steps that could be targeted in the drug discovery process. It is of special importance for various types of cancer known to be associated with substantial rewiring of metabolic networks. Here we introduce an integrated approach for the analysis of metabolome that allows us to simultaneously assess pathway activities (fluxes) and concentrations of a large number of the key components involved in central metabolism of human cells. This is accomplished by in vivo labeling with [U-¹³C]glucose followed by two-dimensional nuclear magnetic resonance (NMR) spectroscopy and gas chromatography-mass spectrometry (GC-MS) analysis. A comprehensive isotopomer model was developed, which enabled us to compare fluxes through the key central metabolic pathways including glycolysis, pentose phosphate pathway, tricarboxylic acid cycle, anaplerotic reactions, and biosynthetic pathways of fatty acids and amino acids. The validity and strength of this approach is illustrated by its application to a number of perturbations to breast cancer cells, including exposure to hypoxia, drug treatment, and tumor progression. We observed significant differences in the activities of specific metabolic pathways resulting from these perturbations and providing new mechanistic insights. Based on these findings we conclude that the developed metabolomic approach constitutes a promising analytical tool for revealing specific metabolic phenotypes in a variety of cell types and pathological conditions. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Chen Yang and Adam D. Richardson contributed equally to this work.     

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 101-117, 1997.