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.     

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.     

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.     

Determination of metabolic flux changes during fed-batch cultivation from measurements of intracellular amino acids by LC-MS/MS

Metabolic flux analysis using (13)C-labeled substrates is a well-developed method for investigating cellular behavior in steady-state culture condition. To extend its application, in particular to typical industrial conditions, such as batch and fed-batch cultivations, a novel method of (13)C metabolic flux analysis is proposed. An isotopomer balancing model was developed to elucidate flux distributions in the central metabolism and all amino acids synthetic pathways. A lysine-producing strain of Escherichia coli was cultivated by fed-batch mode in a growth medium containing yeast extract. Mass distribution data was derived from both intracellular free amino acids and proteinogenic amino acids measured by LC-MS/MS, and a correction parameter for the protein turnover effect on the mass distributions of intracellular amino acids was introduced. Metabolic flux distributions were determined in both exponential and stationary phases. Using this new approach, a culture phase-dependent metabolic shift was detected in the fed-batch culture. The approach presented here has great potential for investigating cellular behavior in industrial processes, independent of cultivation modes, metabolic phase and growth medium.     

Isotopic non-stationary 13C gluconate tracer method for accurate determination of the pentose phosphate pathway split-ratio in Penicillium chrysogenum

Current (13)C labeling experiments for metabolic flux analysis (MFA) are mostly limited by either the requirement of isotopic steady state or the extremely high computational effort due to the size and complexity of large metabolic networks. The presented novel approach circumvents these limitations by applying the isotopic non-stationary approach to a local metabolic network. The procedure is demonstrated in a study of the pentose phosphate pathway (PPP) split-ratio of Penicillium chrysogenum in a penicillin-G producing chemostat-culture grown aerobically at a dilution rate of 0.06h(-1) on glucose, using a tracer amount of uniformly labeled [U-(13)C(6)] gluconate. The rate of labeling inflow can be controlled by using different cell densities and/or different fractions of the labeled tracer in the feed. Due to the simplicity of the local metabolic network structure around the 6-phosphogluconate (6pg) node, only three metabolites need to be measured for the pool size and isotopomer distribution. Furthermore, the mathematical modeling of isotopomer distributions for the flux estimation has been reduced from large scale differential equations to algebraic equations. Under the studied cultivation condition, the estimated split-ratio (41.2+/-0.6%) using the novel approach, shows statistically no difference with the split-ratio obtained from the originally proposed isotopic stationary gluconate tracing method.     

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.     

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.     

Application of MALDI-TOF MS to lysine-producing Corynebacterium glutamicum: a novel approach for metabolic flux analysis.

In the present work, a novel comprehensive approach of (13)C-tracer studies with labeling measurements by MALDI-TOF MS, and metabolite balancing was developed to elucidate key fluxes in the central metabolism of lysine producing Corynebacterium glutamicum during batch culture. MALDI-TOF MS methods established allow the direct quantification of labeling patterns of low molecular mass Corynebacterium products from 1 microL of diluted culture supernatant. A mathematical model of the central Corynebacterium metabolism was developed, that describes the carbon transfer through the network via matrix calculations in a generally applicable way and calculates steady state mass isotopomer distributions of the involved metabolites. The model was applied for both experimental planning of tracer experiments and parameter estimation. Metabolic fluxes were calculated from stoichiometric data and from selected mass intensity ratios of lysine, alanine, and trehalose measured by MALDI-TOF MS in tracer experiments either with 1-(13)C glucose or with mixtures of (13)C6/(12)C6 glucose. During the phase of maximum lysine production C. glutamicum ATCC 21253 exhibited high relative fluxes into the pentose phosphate pathway of 71%, a highly reversible glucose-6-phosphate isomerase, significant backfluxes from the tricarboxylic acid cycle to the pyruvate node consuming the lysine precursor oxaloacetate, 36% net flux of anaplerotic carboxylation and 63% contribution of the dehydrogenase branch in the lysine biosynthetic pathway. Due to the straightforward and simple measurements of selected labeling patterns by MALDI-TOF MS sensitively reflecting the flux parameters of interest, the presented approach has an excellent potential to extend metabolic flux analysis from single experiments with enormous experimental effort to a broadly applied technique.     

Determination of full 13C isotopomer distributions for metabolic flux analysis using heteronuclear spin echo difference NMR spectroscopy

13C-isotopomer labeling experiments play an increasingly important role in the analysis of intracellular metabolic fluxes for genetic engineering purposes. 13C NMR spectroscopy is a key technique in the experimental determination of isotopomer distributions. However, only subsets of isotopomers can be quantitated using this technique due to redundancies in the scalar coupling patterns and due to invisibility of the 12C isotope in NMR. Therefore, we developed and describe in this paper a 1H NMR spectroscopy method that allows to determine the complete isotopomer distribution in metabolites having a backbone consisting of up to at least four carbons. The proposed pulse sequences employ up to three alternately applied frequency-selective inversion pulses in the 13C channel. In a first application study, the complete isotopomer distribution of aspartate isolated from [1-13C]ethanol-grown Ashbya gossypii was determined. A tentative model of the central metabolism of this organism was constructed and used for metabolic flux analysis. The aspartate isotopomer NMR data played a key role in the successful determination of the flux through the peroxisomal glyoxylate pathway. The new NMR method can be highly instrumental in generating the data upon which isotopomer labeling experiments for flux analysis, that are becoming increasingly important, are based.     

Validation-based model selection for 13C metabolic flux analysis with uncertain measurement errors

Accurate measurements of metabolic fluxes in living cells are central to metabolism research and metabolic engineering. The gold standard method is model-based metabolic flux analysis (MFA), where fluxes are estimated indirectly from mass isotopomer data with the use of a mathematical model of the metabolic network. A critical step in MFA is model selection: choosing what compartments, metabolites, and reactions to include in the metabolic network model. Model selection is often done informally during the modelling process, based on the same data that is used for model fitting (estimation data). This can lead to either overly complex models (overfitting) or too simple ones (underfitting), in both cases resulting in poor flux estimates. Here, we propose a method for model selection based on independent validation data. We demonstrate in simulation studies that this method consistently chooses the correct model in a way that is independent on errors in measurement uncertainty. This independence is beneficial, since estimating the true magnitude of these errors can be difficult. In contrast, commonly used model selection methods based on the χ²-test choose different model structures depending on the believed measurement uncertainty; this can lead to errors in flux estimates, especially when the magnitude of the error is substantially off. We present a new approach for quantification of prediction uncertainty of mass isotopomer distributions in other labelling experiments, to check for problems with too much or too little novelty in the validation data. Finally, in an isotope tracing study on human mammary epithelial cells, the validation-based model selection method identified pyruvate carboxylase as a key model component. Our results argue that validation-based model selection should be an integral part of MFA model development.     

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.     

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     

Metabolomic and mass isotopomer analysis of liver gluconeogenesis and citric acid cycle: II. Heterogeneity of metabolite labeling pattern

In this second of two companion articles, we compare the mass isotopomer distribution of metabolites of liver gluconeogenesis and citric acid cycle labeled from NaH(13)CO(3) or dimethyl [1,4-(13)C(2)]succinate. The mass isotopomer distribution of intermediates reveals the reversibility of the isocitrate dehydrogenase + aconitase reactions, even in the absence of a source of alpha-ketoglutarate. In addition, in many cases, a number of labeling incompatibilities were found as follows: (i) glucose versus triose phosphates and phosphoenolpyruvate; (ii) differences in the labeling ratios C-4/C-3 of glucose versus (glyceraldehyde 3-phosphate)/(dihydroxyacetone phosphate); and (iii) labeling of citric acid cycle intermediates in tissue versus effluent perfusate. Overall, our data show that gluconeogenic and citric acid cycle intermediates cannot be considered as sets of homogeneously labeled pools. This probably results from the zonation of hepatic metabolism and, in some cases, from differences in the labeling pattern of mitochondrial versus extramitochondrial metabolites. Our data have implications for the use of labeling patterns for the calculation of metabolic rates or fractional syntheses in liver, as well as for modeling liver intermediary metabolism.     

Identification of metabolic fluxes in hepatic cells from transient 13C-labeling experiments: Part I. Experimental observations

An experimental set-up for acquiring metabolite and transient (13)C-labeling data in mammalian cells is presented. An efficient sampling procedure was established for hepatic cells cultured in six-well plates as a monolayer attached to collagen, which allowed simultaneous quenching of metabolism and extraction of the intracellular intermediates of interest. Extracellular concentrations of glucose, amino acids, lactate, pyruvate, and urea were determined by GC-MS procedures and were used for estimation of metabolic uptake and excretion rates. Sensitive LC-MS and GC-MS methods were used to quantify the intracellular intermediates of tricarboxylic acid cycle, glycolysis, and pentose phosphate pathway and for the determination of isotopomer fractions of the respective metabolites. Mass isotopomer fractions were determined in a transient (13)C-labeling experiment using (13)C-labeled glucose as substrate. The absolute amounts of intracellular metabolites were obtained from a non-labeled experiment carried out in exactly the same way as the (13)C-labeling experiment, except that the media contained naturally labeled glucose only. Estimation of intracellular metabolic fluxes from the presented data is addressed in part II of this contribution.     

Revisiting the 13C-label distribution of the non-oxidative branch of the pentose phosphate pathway based upon kinetic and genetic evidence

The currently applied reaction structure in stoichiometric flux balance models for the nonoxidative branch of the pentose phosphate pathway is not in accordance with the established ping-pong kinetic mechanism of the enzymes transketolase (EC 2.2.1.1) and transaldolase (EC 2.2.1.2). Based upon the ping-pong mechanism, the traditional reactions of the nonoxidative branch of the pentose phosphate pathway are replaced by metabolite specific, reversible, glycolaldehyde moiety (C(2)) and dihydroxyacetone moiety (C(3)) fragments producing and consuming half-reactions. It is shown that a stoichiometric model based upon these half-reactions is fundamentally different from the currently applied stoichiometric models with respect to the number of independent C(2) and C(3) fragment pools in the pentose phosphate pathway and can lead to different label distributions for (13)C-tracer experiments. To investigate the actual impact of the new reaction structure on the estimated flux patterns within a cell, mass isotopomer measurements from a previously published (13)C-based metabolic flux analysis of Saccharomyces cerevisiae were used. Different flux patterns were found. From a genetic point of view, it is well known that several micro-organisms, including Escherichia coli and S. cerevisiae, contain multiple genes encoding isoenzymes of transketolase and transaldolase. However, the extent to which these gene products are also actively expressed remains unknown. It is shown that the newly proposed stoichiometric model allows study of the effect of isoenzymes on the (13)C-label distribution in the nonoxidative branch of the pentose phosphate pathway by extending the half-reaction based stoichiometric model with two distinct transketolase enzymes instead of one. Results show that the inclusion of isoenzymes affects the ensuing flux estimates.     

Mass spectrometry for metabolic flux analysis

Mass spectrometry in combination with tracer experiments based on 13C substrates can serve as a powerful tool for the modeling and analysis of intracellular fluxes and the investigation of biochemical networks. The theoretical background for the application of mass spectrometry to metabolic flux analysis is discussed. Mass spectrometry methods are especially useful to determine mass distribution of metabolites. Additional information gained from fragmentation of metabolites, e.g., by electron impact ionization, allows further localization of labeling positions, up to complete resolution of isotopomer pools. To effectively handle mass distributions in simulation experiments, a matrix based general methodology is formulated. The natural isotope distribution of carbon, oxygen, hydrogen and nitrogen in the target metabolites is considered by introduction of correction matrices. It is shown by simulation results for the central carbon metabolism that neglecting natural isotope distributions causes significant errors in intracellular flux distributions. By varying relative fluxes into pentosephosphate pathway and pyruvate carboxylation reaction, marked changes in the mass distributions of metabolites result, which are illustrated for pyruvate, oxaloacetate, and alpha-ketoglutarate. In addition mass distributions of metabolites are significantly influenced over a broad range by the degree of reversibility of transaldolase and transketolase reactions in the pentosephosphate pathway. The mass distribution of metabolites is very sensitive towards intracellular flux patterns and can be measured with high accuracy by routine mass spectrometry methods. Copyright 1999 John Wiley & Sons, Inc.     

Isotopomer analysis of myocardial substrate metabolism: a systems biology approach

The increasing accessibility of mass isotopomer data via GC-MS and NMR technology has necessitated the use of a systematic and reliable method to take advantage of such data for flux analysis. Here we applied a nonlinear, optimization-based method to study substrate metabolism in cardiomyocytes using (13)C data from perfused mouse hearts. The myocardial metabolic network used in this study accounts for 257 reactions and 240 metabolites, which are further compartmentalized into extracellular space, cytosol, and mitochondrial matrix. Analysis of the perfused mouse heart showed that the steady-state ATP production rate was 16.6 +/- 2.3 micromol/min . gww, with 30% of the ATP coming from glycolysis. Of the four substrates available in the perfusate (glucose, pyruvate, lactate, and oleate), exogenous glucose forms the majority of cytosolic pyruvate. Pyruvate decaboxylation is significantly higher than carboxylation, suggesting that anaplerosis is low in the perfused heart. Exchange fluxes were predicted to be high for reversible enzymes in the citric acid cycle (CAC), but low in the glycolytic pathway. Pseudoketogenesis amounted to approximately 50% of the net ketone body uptake. Sensitivity analysis showed that the estimated flux distributions were relatively insensitive to experimental errors. The application of isotopomer data drastically improved the estimation of reaction fluxes compared to results computed with respect to reaction stoichiometry alone. Further study of 12 commonly used (13)C glucose mixtures showed that the mixtures of 20% [U-(13)C(6)] glucose, 80% [3 (13)C] glucose and 20% [U-(13)C(6)] glucose, 80% [4 (13)C] were best for resolving fluxes in the current network.     

Simultaneous tracers and a unified model of positional and mass isotopomers for quantification of metabolic flux in liver

Computational models based on the metabolism of stable isotope tracers can yield valuable insight into the metabolic basis of disease. The complexity of these models is limited by the number of tracers and the ability to characterize tracer labeling in downstream metabolites. NMR spectroscopy is ideal for multiple tracer experiments since it precisely detects the position of tracer nuclei in molecules, but it lacks sensitivity for detecting low-concentration metabolites. GC-MS detects stable isotope mass enrichment in low-concentration metabolites, but lacks nuclei and positional specificity. We performed liver perfusions and in vivo infusions of ²H and ¹³C tracers, yielding complex glucose isotopomers that were assigned by NMR and fit to a newly developed metabolic model. Fluxes regressed from ²H and ¹³C NMR positional isotopomer enrichments served to validate GC-MS-based flux estimates obtained from the same experimental samples. NMR-derived fluxes were largely recapitulated by modeling the mass isotopomer distributions of six glucose fragment ions measured by GC-MS. Modest differences related to limited fragmentation coverage of glucose C1–C3 were identified, but fluxes such as gluconeogenesis, glycogenolysis, cataplerosis and TCA cycle flux were tightly correlated between the methods. Most importantly, modeling of GC-MS data could assign fluxes in primary mouse hepatocytes, an experiment that is impractical by ²H or ¹³C NMR.     

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.     

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.