Systematic quantification of complex metabolic flux networks using stable isotopes and mass spectrometry.

Metabolic fluxes provide a detailed metric of the cellular metabolic phenotype. Fluxes are estimated indirectly from available measurements and various methods have been developed for this purpose. Of particular interest are methods making use of stable isotopic tracers as they enable the estimation of fluxes at a high resolution. In this paper, we present data validating the use of mass spectrometry (MS) for the quantification of complex metabolic flux networks. In the context of the lysine biosynthesis flux network of Corynebacterium glutamicum (ATCC 21799) under glucose limitation in continuous culture, operating at 0.1 x h(-1) after the introduction of 50% [1-13C]glucose, we deploy a bioreaction network analysis methodology for flux determination from mass isotopomer measurements of biomass hydrolysates, while thoroughly addressing the issues of measurement accuracy, flux observability and data reconciliation. The analysis enabled the resolution of the involved anaplerotic activity of the microorganism using only one labeled substrate, the determination of the range of most of the exchange fluxes and the validation of the flux estimates through satisfaction of redundancies. Specifically, we determined that phosphoenolpyruvate carboxykinase and synthase do not carry flux at these experimental conditions and identified a high futile cycle between oxaloacetate and pyruvate, indicating a highly active in vivo oxaloacetate decarboxylase. Both results validated previous in vitro activity measurements. The flux estimates obtained passed the chi2 statistical test. This is a very important result considering that prior flux analyses of extensive metabolic networks from isotopic measurements have failed criteria of statistical consistency.     

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.     

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.     

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.     

Identification of optimal measurement sets for complete flux elucidation in metabolic flux analysis experiments

Metabolic flux analysis (MFA) methods use external flux and isotopic measurements to quantify the magnitude of metabolic flows in metabolic networks. A key question in this analysis is choosing a set of measurements that is capable of yielding a unique flux distribution (identifiability). In this article, we introduce an optimization-based framework that uses incidence structure analysis to determine the smallest (or most cost-effective) set of measurements leading to complete flux elucidation. This approach relies on an integer linear programming formulation OptMeas that allows for the measurement of external fluxes and the complete (or partial) enumeration of the isotope forms of metabolites without requiring any of these to be chosen in advance. We subsequently query and refine the measurement sets suggested by OptMeas for identifiability and optimality. OptMeas is first tested on small to medium-size demonstration examples. It is subsequently applied to a large-scale E. coli isotopomer mapping model with more than 17,000 isotopomers. A number of additional measurements are identified leading to maximum flux elucidation in an amorphadiene producing E. coli strain.     

Quantification of intracellular metabolic fluxes from fractional enrichment and 13C-13C coupling constraints on the isotopomer distribution in labeled biomass components

A method for the quantification of intracellular metabolic flux distributions from steady-state mass balance constraints and from the constraints posed by the measured 13C labeling state of biomass components is presented. Two-dimensional NMR spectroscopy is used to analyze the labeling state of cell protein hydrolysate and cell wall components. No separation of the biomass hydrolysate is required to measure the degree of 13C-13C coupling and the fractional 13C enrichment in various carbon atom positions. A mixture of [1-13C]glucose and uniformly labeled [13C6]glucose is applied to make fractional 13C enrichment data and measurements of the degree of 13C-13C coupling informative with respect to the intracellular flux distribution. Simulation models that calculate the complete isotopomer distribution in biomass components on the basis of isotopomer mapping matrices are used for the estimation of intracellular fluxes by least-squares minimization. The statistical quality of the estimated intracellular flux distributions is assessed by Monte Carlo methods. Principal component analysis is performed on the outcome of the Monte Carlo procedure to identify groups of fluxes that contribute major parts to the total variance in the multiple flux estimations. The methods described are applied to a steady-state culture of a glucoamylase-producing recombinant Aspergillus niger strain.     

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.     

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.     

Isotopomer analysis using GC-MS

Knowledge of the complete isotopomer distribution represents the ultimate amount of information on the labeling pattern of a metabolite. One technique for measuring the isotopomer distributions is the analysis of the multiplet intensities arising from the 13C-13C couplings in NMR spectroscopy. While this technique has proven to be very valuable in the elucidation of labeling patterns of C2 and C3 units of various amino acids, fragments larger than C3 are very difficult to measure. Another technique, GC-MS, offers a unique possibility of analyzing fragments larger than C3 and GC-MS is therefore able to give information which is complementary to the information that can be obtained from NMR spectroscopy. In this work we have developed fast, simple, and robust GC-MS methods that can be used to gain information on the labeling patterns of the amino acids in a crude biomass hydrolysate. It is shown that a combination of information obtained from these analyses and information from the NMR spectroscopy is able to yield a much more complete picture of the isotopomer distributions of the amino acids than any of the two techniques alone. The GC-MS method was used for analyzing the labeling patterns of amino acids from a batch cultivation of Penicillium chrysogenum grown on fully labeled glucose. The data from this analysis showed no signs of any significant carbon isotope effects, and the measurements can therefore be used without corrections for metabolic flux analysis.     

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.     

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).     

Pathway confirmation and flux analysis of central metabolic pathways in Desulfovibrio vulgaris hildenborough using gas chromatography-mass spectrometry and Fourier transform-ion cyclotron resonance mass spectrometry

Flux distribution in central metabolic pathways of Desulfovibrio vulgaris Hildenborough was examined using 13C tracer experiments. Consistent with the current genome annotation and independent evidence from enzyme activity assays, the isotopomer results from both gas chromatography-mass spectrometry (GC-MS) and Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR MS) indicate the lack of an oxidatively functional tricarboxylic acid (TCA) cycle and an incomplete pentose phosphate pathway. Results from this study suggest that fluxes through both pathways are limited to biosynthesis. The data also indicate that >80% of the lactate was converted to acetate and that the reactions involved are the primary route of energy production [NAD(P)H and ATP production]. Independently of the TCA cycle, direct cleavage of acetyl coenzyme A to CO and 5,10-methyl tetrahydrofuran also leads to production of NADH and ATP. Although the genome annotation implicates a ferredoxin-dependent oxoglutarate synthase, isotopic evidence does not support flux through this reaction in either the oxidative or the reductive mode; therefore, the TCA cycle is incomplete. FT-ICR MS was used to locate the labeled carbon distribution in aspartate and glutamate and confirmed the presence of an atypical enzyme for citrate formation suggested in previous reports [the citrate synthesized by this enzyme is the isotopic antipode of the citrate synthesized by the (S)-citrate synthase]. These findings enable a better understanding of the relation between genome annotation and actual metabolic pathways in D. vulgaris and also demonstrate that FT-ICR MS is a powerful tool for isotopomer analysis, overcoming the problems with both GC-MS and nuclear magnetic resonance spectroscopy.     

Current status of 13C-metabolic flux analysis and future perspectives

Current ¹³C-metabolic flux analysis methods were reviewed as well as the weakness of the conventional metabolic flux analysis without ¹³C-labeled experiments. Although it has been recognized that ¹³C-labeling technique is powerful in estimating the metabolic fluxes, and the program-based flux analysis is necessary, one may not be confident with the result obtained without experiences and exhaustive trial and errors in practice due to its black box nature. In the present article, we call attention to the importance of investigating the relationships between fluxes and isotopomer or mass isotopomer distributions to understand the mechanism of generating specific isotopomers. Then, the experimental design for the preferred mixture of the specific ¹³C-labeled substrate was discussed. The effect of the reversibility in the bidirectional flux on the isotopomer distribution was also mentioned, and it was shown why the reliability of the bidirectional fluxes becomes lower. Moreover, by noting that recent development of measurement techniques enables us to measure the isotopomer patterns of intracellular metabolites instead of proteinogenic amino acids, it is mentioned that this enables us to estimate the flux changes during time-variant batch culture. Some future perspectives are discussed in relation to the integration of different levels of information in the cell.     

Metabolic flux analysis using 13C peptide label measurements

¹³C metabolic flux analysis (MFA) has become the experimental method of choice to investigate the cellular metabolism of microbes, cell cultures and plant seeds. Conventional steady‐state MFA utilizes isotopic labeling measurements of amino acids obtained from protein hydrolysates. To retain spatial information in conventional steady‐state MFA, tissues or subcellular fractions must be dissected or biochemically purified. In contrast, peptides retain their identity in complex protein extracts, and may therefore be associated with a specific time of expression, tissue type and subcellular compartment. To enable ‘single‐sample’ spatially and temporally resolved steady‐state flux analysis, we investigated the suitability of peptide mass distributions (PMDs) as an alternative to amino acid label measurements. PMDs are the discrete convolution of the mass distributions of the constituent amino acids of a peptide. We investigated the requirements for the unique deconvolution of PMDs into amino acid mass distributions (AAMDs), the influence of peptide sequence length on parameter sensitivity, and how AAMD and flux estimates that are determined through deconvolution compare to estimates from a conventional GC–MS measurement‐based approach. Deconvolution of PMDs of the storage protein β–conglycinin of soybean (Glycine max) resulted in good AAMD and flux estimates if fluxes were directly fitted to PMDs. Unconstrained deconvolution resulted in inferior AAMD and flux estimates. PMD measurements do not include amino acid backbone fragments, which increase the information content in GC–MS‐derived analyses. Nonetheless, the resulting flux maps were of comparable quality due to the precision of Orbitrap quantification and the larger number of peptide measurements.     

Metabolic flux analysis in a nonstationary system: fed-batch fermentation of a high yielding strain of E. coli producing 1,3-propanediol

Metabolic fluxes estimated from stable-isotope studies provide a key to understanding cell physiology and regulation of metabolism. A limitation of the classical method for metabolic flux analysis (MFA) is the requirement for isotopic steady state. To extend the scope of flux determination from stationary to nonstationary systems, we present a novel modeling strategy that combines key ideas from isotopomer spectral analysis (ISA) and stationary MFA. Isotopic transients of the precursor pool and the sampled products are described by two parameters, D and G parameters, respectively, which are incorporated into the flux model. The G value is the fraction of labeled product in the sample, and the D value is the fractional contribution of the feed for the production of labeled products. We illustrate the novel modeling strategy with a nonstationary system that closely resembles industrial production conditions, i.e. fed-batch fermentation of Escherichia coli that produces 1,3-propanediol (PDO). Metabolic fluxes and the D and G parameters were estimated by fitting labeling distributions of biomass amino acids measured by GC/MS to a model of E. coli metabolism. We obtained highly consistent fits from the data with 82 redundant measurements. Metabolic fluxes were estimated for 20 time points during course of the fermentation. As such we established, for the first time, detailed time profiles of in vivo fluxes. We found that intracellular fluxes changed significantly during the fed-batch. The intracellular flux associated with PDO pathway increased by 10%. Concurrently, we observed a decrease in the split ratio between glycolysis and pentose phosphate pathway from 70/30 to 50/50 as a function of time. The TCA cycle flux, on the other hand, remained constant throughout the fermentation. Furthermore, our flux results provided additional insight in support of the assumed genotype of the organism.     

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.     

Elementary metabolite units (EMU): a novel framework for modeling isotopic distributions

Metabolic flux analysis (MFA) has emerged as a tool of great significance for metabolic engineering and mammalian physiology. An important limitation of MFA, as carried out via stable isotope labeling and GC/MS and nuclear magnetic resonance (NMR) measurements, is the large number of isotopomer or cumomer equations that need to be solved, especially when multiple isotopic tracers are used for the labeling of the system. This restriction reduces the ability of MFA to fully utilize the power of multiple isotopic tracers in elucidating the physiology of realistic situations comprising complex bioreaction networks. Here, we present a novel framework for the modeling of isotopic labeling systems that significantly reduces the number of system variables without any loss of information. The elementary metabolite unit (EMU) framework is based on a highly efficient decomposition method that identifies the minimum amount of information needed to simulate isotopic labeling within a reaction network using the knowledge of atomic transitions occurring in the network reactions. The functional units generated by the decomposition algorithm, called EMUs, form the new basis for generating system equations that describe the relationship between fluxes and stable isotope measurements. Isotopomer abundances simulated using the EMU framework are identical to those obtained using the isotopomer and cumomer methods, however, require significantly less computation time. For a typical (13)C-labeling system the total number of equations that needs to be solved is reduced by one order-of-magnitude (100s EMUs vs. 1000s isotopomers). As such, the EMU framework is most efficient for the analysis of labeling by multiple isotopic tracers. For example, analysis of the gluconeogenesis pathway with (2)H, (13)C, and (18)O tracers requires only 354 EMUs, compared to more than two million isotopomers.     

COMPLETE-MFA: Complementary parallel labeling experiments technique for metabolic flux analysis

We have developed a novel approach for measuring highly accurate and precise metabolic fluxes in living cells, termed COMPLETE-MFA, short for complementary parallel labeling experiments technique for metabolic flux analysis. The COMPLETE-MFA method is based on combined analysis of multiple isotopic labeling experiments, where the synergy of using complementary tracers greatly improves the precision of estimated fluxes. In this work, we demonstrate the COMPLETE-MFA approach using all singly labeled glucose tracers, [1-¹³C], [2-¹³C], [3-¹³C], [4-¹³C], [5-¹³C], and [6-¹³C]glucose to determine precise metabolic fluxes for wild-type Escherichia coli. Cells were grown in six parallel cultures on defined medium with glucose as the only carbon source. Mass isotopomers of biomass amino acids were measured by gas chromatography–mass spectrometry (GC–MS). The data from all six experiments were then fitted simultaneously to a single flux model to determine accurate intracellular fluxes. We obtained a statistically acceptable fit with more than 300 redundant measurements. The estimated flux map is the most precise flux result obtained thus far for E. coli cells. To our knowledge, this is the first time that six isotopic labeling experiments have been successfully integrated for high-resolution ¹³C-flux analysis.     

Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems

The last few years have brought tremendous progress in experimental methods for metabolic flux determination by carbon-labeling experiments. A significant enlargement of the available measurement data set has been achieved, especially when isotopomer fractions within intracellular metabolite pools are quantitated. This information can be used to improve the statistical quality of flux estimates. Furthermore, several assumptions on bidirectional intracellular reaction steps that were hitherto indispensable may now become obsolete. To make full use of the complete measurement information a general mathematical model for isotopomer systems is established in this contribution. Then, by introducing the important new concept of cumomers and cumomer fractions, it is shown that the arising nonlinear isotopomer balance equations can be solved analytically in all cases. In particular, the solution of the metabolite flux balances and the positional carbon-labeling balances presented in part I of this series turn out to be just the first two steps of the general solution procedure for isotopomer balances. A detailed analysis of the isotopomer network structure then opens up new insights into the intrinsic structure of isotopomer systems. In particular, it turns out that isotopomer systems are not as complex as they appear at first glance. This enables some far-reaching conclusions to be drawn on the information potential of isotopomer experiments with respect to flux identification. Finally, some illustrative examples are examined to show that an information increase is not guaranteed when isotopomer measurements are used in addition to positional enrichment data.