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.     

Metabolic isotopomer labeling systems. Part II: structural flux identifiability analysis

Metabolic flux analysis using carbon labeling experiments (CLEs) is an important tool in metabolic engineering where the intracellular fluxes have to be computed from the measured extracellular fluxes and the partially measured distribution of 13C labeling within the intracellular metabolite pools. The relation between unknown fluxes and measurements is described by an isotopomer labeling system (ILS) (see Part I [Math. Biosci. 169 (2001) 173]). Part II deals with the structural flux identifiability of measured ILSs in the steady state. The central question is whether the measured data contains sufficient information to determine the unknown intracellular fluxes. This question has to be decided a priori, i.e. before the CLE is carried out. In structural identifiability analysis the measurements are assumed to be noise-free. A general theory of structural flux identifiability for measured ILSs is presented and several algorithms are developed to solve the identifiability problem. In the particular case of maximal measurement information, a symbolical algorithm is presented that decides the identifiability question by means of linear methods. Several upper bounds of the number of identifiable fluxes are derived, and the influence of the chosen inputs is evaluated. By introducing integer arithmetic this algorithm can even be applied to large networks. For the general case of arbitrary measurement information, identifiability is decided by a local criterion. A new algorithm based on integer arithmetic enables an a priori local identifiability analysis to be performed for networks of arbitrary size. All algorithms have been implemented and flux identifiability is investigated for the network of the central metabolic pathways of a microorganism. Moreover, several small examples are worked out to illustrate the influence of input metabolite labeling and the paradox of information loss due to network simplification.     

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.     

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.     

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.     

The metabolic architecture of plant cells. Stability of central metabolism and flexibility of anabolic pathways during the growth cycle of tomato cells

The changes in the intermediary metabolism of plant cells were quantified according to growth conditions at three different stages of the growth cycle of tomato cell suspension. Eighteen fluxes of central metabolism were calculated from (13)C enrichments after near steady-state labeling by a metabolic model similar to that described in Dieuaide-Noubhani et al. (Dieuaide-Noubhani, M., Raffard, G., Canioni, P., Pradet, A., and Raymond, P. (1995) J. Biol. Chem. 270, 13147-13159), and 10 net fluxes were obtained directly from end-product accumulation rates. The absolute flux values of central metabolic pathways gradually slowed down with the decrease of glucose influx into the cells. However, the relative fluxes of glycolysis, the pentose-P pathway, and the tricarboxylic acid cycle remained unchanged during the culture cycle at 70, 28, and 40% of glucose influx, respectively, and the futile cycle of sucrose remained high at about 6-fold the glucose influx, independently from carbon nutritional conditions. This natural resistance to flux alterations is referred to as metabolic stability. The numerous anabolic pathways, including starch synthesis, hexose accumulation, biosynthesis of wall polysaccharides, and amino and organic acid biosynthesis were comparatively low and variable. The phosphoenolpyruvate carboxylase flux decreased 5-fold in absolute terms and 2-fold in relation to the glucose influx rate during the culture cycle. We conclude that anabolic fluxes constitute the flexible part of plant cell metabolism that can fluctuate in relation to cell demands for growth.     

Nuclear magnetic resonance and plant metabolic engineering.

Nuclear magnetic resonance (NMR) can be used to measure metabolite levels and metabolic fluxes, to probe the intracellular environment, and to follow transport and energetics nondestructively. NMR methods are therefore powerful aids to understanding plant metabolism and physiology. Both spectroscopy and imaging can help overcome the unique challenges that plants present to the metabolic engineer by detecting, identifying, quantifying, and localizing novel metabolites in vivo and in extracts; revealing the composition and physical state of cell wall and other polymers; allowing the identification of active pathways; providing quantitative measures of metabolic flux; and testing hypotheses about the effects of engineered traits on plant physiological function. The aim of this review is to highlight recent studies in which NMR has contributed to metabolic engineering of plants and to illustrate the unique characteristics of NMR measurements that give it the potential to make greater contributions in the future.     

Improvements in metabolic flux analysis using carbon bond labeling experiments: bondomer balancing and Boolean function mapping

The biosynthetically directed fractional (13)C labeling method for metabolic flux evaluation relies on performing a 2-D [(13)C, (1)H] NMR experiment on extracts from organisms cultured on a uniformly labeled carbon substrate. This article focuses on improvements in the interpretation of data obtained from such an experiment by employing the concept of bondomers. Bondomers take into account the natural abundance of (13)C; therefore many bondomers in a real network are zero, and can be precluded a priori--thus resulting in fewer balances. Using this method, we obtained a set of linear equations which can be solved to obtain analytical formulas for NMR-measurable quantities in terms of fluxes in glycolysis and the pentose phosphate pathways. For a specific case of this network with four degrees of freedom, a priori identifiability of the fluxes was shown possible for any set of fluxes. For a more general case with five degrees of freedom, the fluxes were shown identifiable for a representative set of fluxes. Minimal sets of measurements which best identify the fluxes are listed. Furthermore, we have delineated Boolean function mapping, a new method to iteratively simulate bondomer abundances or efficiently convert carbon skeleton rearrangement information to mapping matrices. The efficiency of this method is expected to be valuable while analyzing metabolic networks which are not completely known (such as in plant metabolism) or while implementing iterative bondomer balancing methods.     

A metabolic flux analysis to study the role of sucrose synthase in the regulation of the carbon partitioning in central metabolism in maize root tips

In order to understand the role of sucrose synthase (SuSy) in carbon partitioning, metabolic fluxes were analyzed in maize root tips of a double mutant of SuSy genes, sh1 sus1 and the corresponding wild type, W22. [U-¹⁴C]-glucose pulse labeling experiments permitted the quantification of unidirectional fluxes into sucrose, starch and cell wall polysaccharides. Isotopic steady-state labeling with [1-¹³C]-, [2-¹³C]- or [U-¹³C]-glucose followed by the quantification by ¹H-NMR and ¹³C-NMR of enrichments in carbohydrates and amino acids was also performed to determine 29 fluxes through central metabolism using computer-aided modeling. As a consequence of the suppression of SUS1 and SH1 isozymes, maize root tips diameter was significantly decreased and respiratory metabolism reduced by 30%. Our result clearly established that, in maize root tips, starch is produced from ADP-Glc synthesized in the plastid and not in the cytosol by sucrose synthase. Unexpectedly, the flux of cell wall synthesis was increased in the double mutant. This observation indicates that, in maize root tips, SH1 and SUS1 are not specific providers for cellulose biosynthesis.     

Design of substrate label for steady state flux measurements in plant systems using the metabolic network of Brassica napus embryos

Steady state metabolic flux analysis using (13)C labeled substrates is of growing importance in plant physiology and metabolic engineering. The quality of the flux estimates in (13)C metabolic flux analysis depend on the: (i) network structure; (ii) flux values; (iii) design of the labeling substrate; and (iv) label measurements performed. Whereas the first two parameters are facts of nature, the latter two are to some extent controlled by the experimenter, yet they have received little attention in most plant studies. Using the metabolic flux map of developing Brassica napus (Rapeseed) embryos, this study explores the value of optimal substrate label designs obtained with different statistical criteria and addresses the applicability of different optimal designs to biological questions. The results demonstrate the value of optimizing the choice of labeled substrates and show that substrate combinations commonly used in bacterial studies can be far from optimal for mapping fluxes in plant systems. The value of performing additional experiments and the inclusion of measurements is also evaluated.     

Metabolic flux analysis at ultra short time scale: isotopically non-stationary 13C labeling experiments

A novel approach to (13)C metabolic flux analysis (MFA) is presented using cytosolic metabolite pool sizes and their (13)C labeling data from an isotopically non-stationary (13)C labeling experiment (INST-CLE). The procedure is demonstrated with an E. coli wild type strain grown at fed batch conditions. The intra cellular labeling dynamics are excited by a sudden step increase of the (13)C portion in the substrate feed. Due to unchanged saturation of the substrate uptake system, the metabolic fluxes remain constant during the following sampling time period of only 16s, in which 20 samples are taken by an automated rapid sampling device immediately stopping metabolism by methanol quenching. Subsequent cell disruptive sample preparation and LC-MS/MS enabled simultaneous determination of pool sizes and mass isotopomers of intra cellular metabolites requiring detection limits in the nM range. Based on this data the new computational flux analysis tool 13CFLUX/INST is used to determine the intra cellular fluxes based on a complex carbon labeling network model. The measured data is in good agreement with the model predictions, thus proving the applicability of the new isotopically non-stationary (13)C metabolic flux analysis (INST-(13)C-MFA) concept. Moreover, it is shown that significant new information with respect to flux identifiability, non-measurable pool sizes, data consistency, or large storage pools can be taken from the novel kind of experimental data. This offers new insight into the biological operation of the metabolic network in vivo.     

Quantification of compartmented metabolic fluxes in developing soybean embryos by employing biosynthetically directed fractional (13)C labeling, two-dimensional [(13)C, (1)H] nuclear magnetic resonance, and comprehensive isotopomer balancing

Metabolic flux quantification in plants is instrumental in the detailed understanding of metabolism but is difficult to perform on a systemic level. Toward this aim, we report the development and application of a computer-aided metabolic flux analysis tool that enables the concurrent evaluation of fluxes in several primary metabolic pathways. Labeling experiments were performed by feeding a mixture of U-(13)C Suc, naturally abundant Suc, and Gln to developing soybean (Glycine max) embryos. Two-dimensional [(13)C, (1)H] NMR spectra of seed storage protein and starch hydrolysates were acquired and yielded a labeling data set consisting of 155 (13)C isotopomer abundances. We developed a computer program to automatically calculate fluxes from this data. This program accepts a user-defined metabolic network model and incorporates recent mathematical advances toward accurate and efficient flux evaluation. Fluxes were calculated and statistical analysis was performed to obtain sds. A high flux was found through the oxidative pentose phosphate pathway (19.99 +/- 4.39 micromol d(-1) cotyledon(-1), or 104.2 carbon mol +/- 23.0 carbon mol per 100 carbon mol of Suc uptake). Separate transketolase and transaldolase fluxes could be distinguished in the plastid and the cytosol, and those in the plastid were found to be at least 6-fold higher. The backflux from triose to hexose phosphate was also found to be substantial in the plastid (21.72 +/- 5.00 micromol d(-1) cotyledon(-1), or 113.2 carbon mol +/-26.0 carbon mol per 100 carbon mol of Suc uptake). Forward and backward directions of anaplerotic fluxes could be distinguished. The glyoxylate shunt flux was found to be negligible. Such a generic flux analysis tool can serve as a quantitative tool for metabolic studies and phenotype comparisons and can be extended to other plant systems.     

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.     

13C metabolic flux analysis of microbial and mammalian systems is enhanced with GC-MS measurements of glycogen and RNA labeling

¹³C metabolic flux analysis (¹³C-MFA) is a widely used tool for quantitative analysis of microbial and mammalian metabolism. Until now, ¹³C-MFA was based mainly on measurements of isotopic labeling of amino acids derived from hydrolyzed biomass proteins and isotopic labeling of extracted intracellular metabolites. Here, we demonstrate that isotopic labeling of glycogen and RNA, measured with gas chromatography-mass spectrometry (GC-MS), provides valuable additional information for ¹³C-MFA. Specifically, we demonstrate that isotopic labeling of glucose moiety of glycogen and ribose moiety of RNA greatly enhances resolution of metabolic fluxes in the upper part of metabolism; importantly, these measurements allow precise quantification of net and exchange fluxes in the pentose phosphate pathway. To demonstrate the practical importance of these measurements for ¹³C-MFA, we have used Escherichia coli as a model microbial system and CHO cells as a model mammalian system. Additionally, we have applied this approach to determine metabolic fluxes of glucose and xylose co-utilization in the E. coli ΔptsG mutant. The convenience of measuring glycogen and RNA, which are stable and abundant in microbial and mammalian cells, offers the following key advantages: reduced sample size, no quenching required, no extractions required, and GC-MS can be used instead of more costly LC-MS/MS techniques. Overall, the presented approach for ¹³C-MFA will have widespread applicability in metabolic engineering and biomedical research.     

Mitochondrial metabolism in developing embryos of Brassica napus

The metabolism of developing plant seeds is directed toward transforming primary assimilatory products (sugars and amino acids) into seed storage compounds. To understand the role of mitochondria in this metabolism, metabolic fluxes were determined in developing embryos of Brassica napus. After labeling with [1,2-(13)C2]glucose + [U-(13)C6]glucose, [U-(13)C3]alanine, [U-(13)C5]glutamine, [(15)N]alanine, (amino)-[(15)N]glutamine, or (amide)-[(15)N]glutamine, the resulting labeling patterns in protein amino acids and in fatty acids were analyzed by gas chromatography-mass spectrometry. Fluxes through mitochondrial metabolism were quantified using a steady state flux model. Labeling information from experiments using different labeled substrates was essential for model validation and reliable flux estimation. The resulting flux map shows that mitochondrial metabolism in these developing seeds is very different from that in either heterotrophic or autotrophic plant tissues or in most other organisms: (i) flux around the tricarboxylic acid cycle is absent and the small fluxes through oxidative reactions in the mitochondrion can generate (via oxidative phosphorylation) at most 22% of the ATP needed for biosynthesis; (ii) isocitrate dehydrogenase is reversible in vivo; (iii) about 40% of mitochondrial pyruvate is produced by malic enzyme rather than being imported from the cytosol; (iv) mitochondrial flux is largely devoted to providing precursors for cytosolic fatty acid elongation; and (v) the uptake of amino acids rather than anaplerosis via PEP carboxylase determines carbon flow into storage proteins.     

13C tracer experiments and metabolite balancing for metabolic flux analysis: comparing two approaches

Conventional metabolic flux analysis uses the information gained from determination of measurable fluxes and a steady-state assumption for intracellular metabolites to calculate the metabolic fluxes in a given metabolic network. The determination of intracellular fluxes depends heavily on the correctness of the assumed stoichiometry including the presence of all reactions with a noticeable impact on the model metabolite balances. Determination of fluxes in complex metabolic networks often requires the inclusion of NADH and NADPH balances, which are subject to controversial debate. Transhydrogenation reactions that transfer reduction equivalents from NADH to NADPH or vice versa can usually not be included in the stoichiometric model, because they result in singularities in the stoichiometric matrix. However, it is the NADPH balance that, to a large extent, determines the calculated flux through the pentose phosphate pathway. Hence, wrong assumptions on the presence or activity of transhydrogenation reactions will result in wrong estimations of the intracellular flux distribution. Using 13C tracer experiments and NMR analysis, flux analysis can be performed on the basis of only well established stoichiometric equations and measurements of the labeling state of intracellular metabolites. Neither NADH/NADPH balancing nor assumptions on energy yields need to be included to determine the intracellular fluxes. Because metabolite balancing methods and the use of 13C labeling measurements are two different approaches to the determination of intracellular fluxes, both methods can be used to verify each other or to discuss the origin and significance of deviations in the results. Flux analysis based entirely on metabolite balancing and flux analysis, including labeling information, have been performed independently for a wild-type strain of Aspergillus oryzae producing alpha-amylase. Two different nitrogen sources, NH4+ and NO3-, have been used to investigate the influence of the NADPH requirements on the intracellular flux distribution. The two different approaches to the calculation of fluxes are compared and deviations in the results are discussed. Copyright 1998 John Wiley & Sons, Inc.     

Metabolic cartography: experimental quantification of metabolic fluxes from isotopic labelling studies

For the past decade, flux maps have provided researchers with an in-depth perspective on plant metabolism. As a rapidly developing field, significant headway has been made recently in computation, experimentation, and overall understanding of metabolic flux analysis. These advances are particularly applicable to the study of plant metabolism. New dynamic computational methods such as non-stationary metabolic flux analysis are finding their place in the toolbox of metabolic engineering, allowing more organisms to be studied and decreasing the time necessary for experimentation, thereby opening new avenues by which to explore the vast diversity of plant metabolism. Also, improved methods of metabolite detection and measurement have been developed, enabling increasingly greater resolution of flux measurements and the analysis of a greater number of the multitude of plant metabolic pathways. Methods to deconvolute organelle-specific metabolism are employed with increasing effectiveness, elucidating the compartmental specificity inherent in plant metabolism. Advances in metabolite measurements have also enabled new types of experiments, such as the calculation of metabolic fluxes based on (13)CO(2) dynamic labelling data, and will continue to direct plant metabolic engineering. Newly calculated metabolic flux maps reveal surprising and useful information about plant metabolism, guiding future genetic engineering of crops to higher yields. Due to the significant level of complexity in plants, these methods in combination with other systems biology measurements are necessary to guide plant metabolic engineering in the future.     

Gas chromatography-mass spectrometry analysis of 13C labeling in sugars for metabolic flux analysis

Metabolic flux analysis, using 13C labeled substrates, has become a powerful methodology for quantifying intracellular fluxes. Most often, analysis is restricted to nuclear magnetic resonance or mass spectrometry measurement of 13C label incorporation into protein amino acids. However, amino acid isotopomer distribution insufficiently covers the entire network of central metabolism, especially in plant cells with highly compartmented metabolism, and analysis of other metabolites is required. Analysis of label in saccharides provides complementary data to better define fluxes around hexose, pentose, and triose phosphate pools. Here, we propose a gas chromatography-mass spectrometry (GC-MS) method to analyze 13C labeling in glucose and fructose moieties of sucrose, free glucose, fructose, maltose, inositol, and starch. Our results show that saccharide labeling for isotopomer quantification is better analyzed by chemical ionization than by electron ionization. The structure of the generated fragments was simulated and validated using labeled standards. The method is illustrated by analysis of saccharides extracted from developing rapeseed (Brassica napus L.) embryos. It is shown that glucose 6-phosphate isomerase and plastidial glucose 6-phosphate transport reactions are not at equilibrium, and light is shed on the pathways leading to fructose, maltose, and inositol synthesis.