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.     

Combining metabolic flux analysis tools and 13C NMR to estimate intracellular fluxes of cultured astrocytes

In this work, brain cell metabolism was investigated by (13)C NMR spectroscopy and metabolic flux analysis (MFA). Monotypic cultures of astrocytes were incubated with labeled glucose for 38 h, and the distribution of the label was analyzed by (13)C NMR spectroscopy. The analysis of the spectra reveals two distinct physiological states characterized by different ratios of pyruvate carboxylase to pyruvate dehydrogenase activities (PC/PDH). Intracellular flux distributions for both metabolic states were estimated by MFA using the isotopic information and extracellular rate measurements as constraints. The model was subsequently checked with the consistency index method. From a biological point of view, the occurrence of the two physiological states appears to be correlated with the presence or absence of extracellular glutamate. Concerning the model, it can be stated that the metabolic network and the set of constraints adopted provide a consistent and robust characterization of the astrocytic metabolism, allowing for the calculation of central intracellular fluxes such as pyruvate recycling, the anaplerotic flux mediated by pyruvate carboxylase, and the glutamine formation through glutamine synthetase.     

13C Nuclear Magnetic Resonance Evidence for γ-Aminobutyric Acid Formation via Pyruvate Carboxylase in Rat Brain: A Metabolic Basis for Compartmentation0

The compartmentation of amino acid metabolism is an active and important area of brain research. 13C labeling and 13C nuclear magnetic resonance (NMR) are powerful tools for studying metabolic pathways, because information about the metabolic histories of metabolites can be determined from the appearance and position of the label in products. We have used 13C labeling and 13C NMR in order to investigate the metabolic history of gamma-aminobutyric acid (GABA) and glutamate in rat brain. [1-13C]Glucose was infused into anesthetized rats and the 13C labeling patterns in GABA and glutamate examined in brain tissue extracts obtained at various times after infusion of the label. Five minutes after infusion, most of the 13C label in glutamate appeared at the C4 position; at later times, label was also present at C2 and C3. This 13C labeling pattern occurs when [1-13C]glucose is metabolized to pyruvate by glycolysis and enters the pool of tricarboxylic acid (TCA) intermediates via pyruvate dehydrogenase. The label exchanges into glutamate from the TCA cycle pool through glutamate transaminases or dehydrogenase. After 30 min of infusion, approximately 10% of the total 13C in brain extracts appeared in GABA, primarily (greater than 80%) at the amino carbon (C4), indicating that the GABA detected is labeled through pyruvate carboxylase. The different labeling patterns observed for glutamate and GABA show that the large detectable glutamate pool does not serve as the precursor to GABA. Our NMR data support previous experiments suggesting compartmentation of metabolism in brain, and further demonstrate that GABA is formed from a pool of TCA cycle intermediates derived from an anaplerotic pathway involving pyruvate carboxylase.     

The mechanism of succinate or fumarate transfer in the tricarboxylic acid cycle allows molecular rotation of the intermediate

Mitochondria were incubated with L[5-13C]glutamic acid and the distribution of the label between the two carboxyl carbon atoms of the L-aspartic acid formed was determined by 13C NMR. The reaction sequence leading from L-glutamic acid to L-aspartic acid spans the tricarboxylic acid cycle reactions involving the two symmetrical intermediates succinate and fumarate. The C2 symmetry of these intermediates in principle permits a discrimination of the mechanism of their transfer between their enzyme sites of production and utilization. A direct transfer of metabolite from site to site by translation alone predicts an unequal distribution of 13C between the C1 and C4 of aspartate, whereas molecular rotation during transfer allows for a scrambling of the original C5 label. Under several conditions of different glutamate concentrations and solvent osmotic pressures, equal labeling in the C1 and C4 carbons of aspartate is observed. This observation is inconsistent with a transfer mechanism restricting molecular rotation for both intermediates but is compatible with both a random diffusion and a direct transfer mechanism provided the latter allows molecular rotation.     

A metabolic network analysis & NMR experiment design tool with user interface-driven model construction for depth-first search analysis

A Windows program for metabolic engineering analysis and experimental design has been developed. A graphical user interface enables the pictorial, "on-screen" construction of a metabolic network. Once a model is composed, balance equations are automatically generated. Model construction, modification and information exchange between different users is thus considerably simplified. For a given model, the program can then be used to predict all the extreme point flux distributions that optimize an objective function while satisfying balances and constraints by using a depth-first search strategy. One can also find the minimum reaction set that satisfies different conditions. Based on the identified flux distributions or linear combinations, the user can simulate the NMR and GC/MS spectra of selected signal molecules. Alternately, spectra vectorization allows for the automated optimization of labeling experiments that are intended to distinguish between different, yet plausible flux extreme point distributions. The example provided entails predicting the flux distributions associated with deleting pyruvate kinase and designing 13C NMR experiments that can maximally discriminate between the flux distributions.     

TCA cycle kinetics in the rat heart by analysis of (13)C isotopomers using indirect (1)H

This study was designed to test the hypothesis that indirect (1)H[(13)C] detection of tricarboxylic acid (TCA) cycle intermediates using heteronuclear multiple quantum correlation-total correlation spectroscopy (HMQC-TOCSY) nuclear magnetic resonance (NMR) spectroscopy provides additional (13)C isotopomer information that better describes the kinetic exchanges that occur between intracellular compartments than direct (13)C NMR detection. NMR data were collected on extracts of rat hearts perfused at various times with combinations of [2-(13)C]acetate, propionate, the transaminase inhibitor aminooxyacetate, and (13)C multiplet areas derived from spectra of tissue glutamate were fit to a standard kinetic model of the TCA cycle. Although the two NMR methods detect different populations of (13)C isotopomers, similar values were found for TCA cycle and exchange fluxes by analyzing the two data sets. Perfusion of hearts with unlabeled propionate in addition to [2-(13)C]acetate resulted in an increase in the pool size of all four-carbon TCA cycle intermediates. This allowed the addition of isotopomer data from aspartate and malate in addition to the more abundant glutamate. This study illustrates that metabolic inhibitors can provide new insights into metabolic transport processes in intact tissues.     

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.     

In vivo 13C NMR study of the bidirectional reactions of the Wood-Werkman cycle and around the pyruvate node in Propionibacterium freudenreichii subsp. shermanii and Propionibacterium acidipropionici

This study used in vitro 13C NMR spectroscopy to directly examine bidirectional reactions of the Wood-Werkman cycle involved in central carbon metabolic pathways of dairy propionibacteria during pyruvate catabolism. The flow of [2-13C]pyruvate label was monitored on living cell suspensions of Propionibacterium freudenreichii subsp. shermanii and Propionibacterium acidipropionici under acidic conditions. P. shermanii and P. acidipropionici cells consumed pyruvate at apparent initial rates of 161 and 39 micromol min(-1) g(-1) (cell dry weight), respectively. The bidirectionality of reactions in the first part of the Wood-Werkman cycle was evident from the formation of intermediates such as [3-13C]pyruvate and [3-13C]malate and of products like [2-13C]acetate from [2-13C]pyruvate. For the first time alanine labeled on C2 and C3 and aspartate labeled on C2 and C3 were observed during [2-13C]pyruvate metabolism by propionibacteria. The kinetics of aspartate isotopic enrichment was evidence for its production from oxaloacetate via aspartate aminotransferase. Activities of a partial tricarboxylic acid pathway, acetate synthesis, succinate synthesis, gluconeogenesis, aspartate synthesis, and alanine synthesis pathways were evident from the experimental results.     

Channeling of TCA cycle intermediates in Saccharomyces cerevisiae.

Metabolism of 13C labeled substrates viz. glucose and pyruvate in S. cerevisiae has been studied by 13C Nuclear Magnetic Resonance Spectroscopy. C3-Pyruvate, alanine and lactate, and C2-acetate are produced from [1-13C]glucose. The pyruvate, entering TCA cycle, leads to preferential labeling of C2-glutamate. [2-13C]Glucose results in labeling of C2-pyruvate, alanine and lactate. Some C3-pyruvate is also produced, indicating the routing of the label from glucose through pentose phosphate pathway (PPP). In TCA cycle the C2-pyruvate preferentially labels the C3-glutamate. The NMR spectra, obtained with [2-13C]pyruvate as substrate, confirm the above observations. These results suggest that the intermediates of TCA cycle are transferred from one enzyme active site to another in a manner that allows only restricted rotation of the intermediates. That is, the intermediates are partially channeled.     

Innovations in generation and analysis of 2D [(13)C,(1)H] COSY NMR spectra for metabolic flux analysis purposes.

2D [(13)C,(1)H] COSY NMR is used by the metabolic engineering community for determining (13)C-(13)C connectivities in intracellular compounds that contain information regarding the steady-state fluxes in cellular metabolism. This paper proposes innovations in the generation and analysis of these specific NMR spectra. These include a computer tool that allows accurate determination of the relative peak areas and their complete covariance matrices even in very complex spectra. Additionally, a method is introduced for correcting the results for isotopic non-steady-state conditions. The proposed methods were applied to measured 2D [(13)C,(1)H] COSY NMR spectra. Peak intensities in a one-dimensional section of the spectrum are frequently not representative for relative peak volumes in the two-dimensional spectrum. It is shown that for some spectra a significant amount of additional information can be gained from long-range (13)C-(13)C scalar couplings in 2D [(13)C,(1)H] COSY NMR spectra. Finally, the NMR resolution enhancement by dissolving amino acid derivatives in a nonpolar solvent is demonstrated.     

Solid-state NMR observation of cysteine and lysine Michael adducts of inactivated estradiol dehydrogenase

The inactivation of estradiol dehydrogenase by enzyme-generated 3-hydroxy-14,15-secoestra-1,3,5(10)-trien-15-yn-17-one is accompanied by the formation of a lysine enaminone. The experiments leading to this conclusion involved degradation of the inactivated enzyme with Pronase and subsequent analysis by solution-state 13C NMR. The present paper reports solid-state 13C NMR experiments on lyophilized intact inactivated enzyme which are free from problems due to Pronase digestion. These experiments combine conventional cross-polarization and magic-angle spinning with selective irradiation of resonances arising from a 13C double label in the steroid. Magnetization transfer between neighboring 13C nuclei is used to simplify the spectra and to identify peaks due to label. The formation of cysteine and lysine Michael adducts of the enzyme is established by comparisons with chemical shifts of solid model adducts.     

13C and 31P NMR study of gluconeogenesis: utilization of 13C-labeled substrates by perfused liver from streptozotocin-diabetic and untreated rats

The metabolism of 13C-labeled substrates was followed by 13C and 31P NMR in perfused liver from the streptozotocin-treated rat model of insulin-dependent diabetes. Comparison was made with perfused liver from untreated littermates, fasted either 24 or 12 h. The major routes of pyruvate metabolism were followed by a 13C NMR approach that provided for the determination of the metabolic fate of several substances simultaneously. The rate of gluconeogenesis was 2-4-fold greater and beta-hydroxybutyrate production was 50% greater in liver from the chronically diabetic rats as compared with the control groups. Large differences in the distribution of 13C label in hepatic alanine were measured between diabetic and control groups. The biosyntheses of 13C-labeled glutathione and N-carbamoylaspartate were monitored in time-resolved 13C NMR spectra of perfused liver. Assignments for the resonances of glutathione and N-carbamoylaspartate were made with the aid of 13C NMR studies of perchloric acid extracts of the freeze-clamped livers. 13C NMR spectroscopy of the perfusates provided a convenient, rapid assay of the rate of oxidation of [2-13C]ethanol, the hepatic output of [2-13C]acetaldehyde, and the accumulation of [2-13C]acetate in the perfusate. By 31P NMR spectroscopy, carbamoyl phosphate was measured in all diabetic livers and an unusual P,P'-diesterified pyrophosphate was observed in one-fourth of the diabetic livers examined. Neither of these phosphorylated metabolites was detected in control liver. Both 13C and 31P NMR were useful in defining changes in hepatic metabolism in experimental diabetes.     

A flux model of glycolysis and the oxidative pentosephosphate pathway in developing Brassica napus embryos

Developing oilseeds synthesize large quantities of triacylglycerol from sucrose and hexose. To understand the fluxes involved in this conversion, a quantitative metabolic flux model was developed and tested for the reaction network of glycolysis and the oxidative pentose phosphate pathway (OPPP). Developing Brassica napus embryos were cultured with [U-13C6]glucose, [1-13C]glucose, [6-13C]glucose, [U-13C12]sucrose, and/or [1,2-13C2]glucose and the labeling patterns in amino acids, lipids, sucrose, and starch were measured by gas chromatography/mass spectrometry and NMR. Data were used to verify a reaction network of central carbon metabolism distributed between the cytosol and plastid. Computer simulation of the steady state distribution of isotopomers in intermediates of the glycolysis/OPPP network was used to fit metabolic flux parameters to the experimental data. The observed distribution of label in cytosolic and plastidic metabolites indicated that key intermediates of glycolysis and OPPP have similar labeling in these two compartments, suggesting rapid exchange of metabolites between these compartments compared with net fluxes into end products. Cycling between hexose phosphate and triose phosphate and reversible transketolase velocity were similar to net glycolytic flux, whereas reversible transaldolase velocity was minimal. Flux parameters were overdetermined by analyzing labeling in different metabolites and by using data from different labeling experiments, which increased the reliability of the findings. Net flux of glucose through the OPPP accounts for close to 10% of the total hexose influx into the embryo. Therefore, the reductant produced by the OPPP accounts for at most 44% of the NADPH and 22% of total reductant needed for fatty acid synthesis.     

13C NMR evidence for pyruvate kinase flux attenuation underlying suppressed acid formation in Bacillus subtilis

When batch and continuous Bacillus subtilis cultures are provided with a small amount of citrate, acid production ceases, carbon yield increases by more than 2-fold, and the productivity of recombinant protein increases. It has been hypothesized that pyruvate kinase activity is attenuated, which in turn lowers glucose flux and minimizes the acid overflow prompted by low Krebs cycle capacity. To complement existing enzyme activity, linear programming, and metabolite pool studies, (13)C NMR studies were performed. Atom mapping and isotopomer mapping matrix methods were used to select the best glucose label. "Best" was defined such that the NMR spectra of glutamate associated with metabolizing labeled glucose via the different candidate metabolic trafficking scenarios would differ considerably in fine structure (e.g., relative singlet intensities). When experiments were performed with 1-(13)C glucose, the observed NMR spectra corresponded well to the one predicted to arise when the metabolic trafficking occurs according to a pyruvate kinase attenuation scenario. This evidence further fortifies the prospects for successfully basing a metabolic engineering strategy on reducing pyruvate kinase activity to better match glycolytic and Krebs cycle capacities.     

Use of 31P and 13C NMR to study enzyme mechanisms

A number of complex biochemical problems have been solved recently by application of new techniques in which 31P and 13C NMR spectroscopy is used. Oxygen isotope exchange phenomena were studied by these NMR methods and used to analyze individual mechanistic events in enzymatic reactions. The existence of intermediates in the reactions catalyzed by glutamine synthetase (EC 6.3.1.2) and carbamyl-phosphate synthetase (EC 2.7.2.9) has been established as well as the kinetic competence of these intermediates for each enzyme. The NMR theory and kinetic experiments required to conduct such studies are discussed.     

13C-NMR study of glycerol metabolism in rabbit renal cells of proximal convoluted tubules

Perchloric acid extracts of rabbit renal proximal convoluted tubular cells (PCT) incubated with [2-13C]glycerol and [1,3-13C]glycerol were investigated by 13C-NMR spectroscopy. These 13C-NMR spectra enabled us to determine cell metabolic pathways of glycerol in PCT cells. The main percentage of 13C-label, arising from 13C-enriched glycerol, was found in glucose, lactate, glutamine and glutamate. So far it can be concluded that glycerol is a suitable substrate for PCT cells and is involved in gluconeogenesis and glycolysis as well in the Krebs cycle intermediates. Label exchange and label enrichment in 13C-labelled glucose, arising from [2-13C]glycerol and [1,3-13C]glycerol, is explained by label scrambling through the pentose shunt and a label exchange in the triose phosphate pool. From relative enrichments it is estimated that the ratio of the pyruvate kinase flux to the gluconeogenetic flux is 0.97:1 and that the ratio of pyruvate carboxylase activity relative to pyruvate dehydrogenase activity is 2.0:1. Our results show that 13C-NMR spectroscopy, using 13C-labelled substrates, is a powerful tool for the examination of renal metabolism.     

13C-NMR, 1H-NMR and gas-chromatography mass-spectrometry studies of the biosynthesis of 13C-enriched L-lysine by Brevibacterium flavum

The basic metabolic pathways of lysine biosynthesis in Brevibacterium flavum, a strain which excretes excessive amounts of L-lysine, have been followed by using two 13C-labeled precursors. 13C- and 1H-NMR spectroscopies in conjunction with gas chromatography mass spectrometry (GC-MS) have revealed the various metabolic pathways leading to L-[13C]lysine. Discrete metabolic pathways give rise to distinct labeling patterns. L-Lysine resulting from [1-13C]glucose fermentation is relatively specifically labeled: L-[3,5-13C]lysine is the main product. Experimental and theoretical approaches based on the 13C-enrichment values of intracellular glutamate, a major intermediate metabolite, allowed us to assess the relative contribution of the major metabolic pathways forming lysine. The labeling pattern of glutamate reflects the isotope distribution in 2-oxoglutarate. When [2-13C]acetate is used as the sole carbon source in the culture, the energy-producing steps of the Krebs cycle are essential. The higher activity of the Krebs cycle, when endogenous carbohydrates are exhausted from the culture, is indicated by the increased 13C enrichment in C-1 of lysine and reveal a high content of isotopomers of four, five and six 13C atoms in the lysine molecule, pointing out that the four-carbon intermediates of the cycle are being derived from the glyoxylate shunt pathway. Such a phenomenon does not occur in glucose fermentation. GC-MS analyses of 13C enrichments and isotopomer distributions in metabolites and end products are in good agreement with the predicted contribution of each metabolic pathway. This new methodological approach of combined NMR and GC-MS has been demonstrated to be applicable to various other metabolic studies.     

Simultaneous monitoring of peptide aggregate distributions, structure, and kinetics using amide hydrogen exchange: application to Abeta(1-40) fibrillogenesis

Increasing evidence indicates that soluble aggregates of amyloid beta protein (Abeta) are neurotoxic. However, difficulty in isolating these unstable, dynamic species impedes studies of Abeta and other aggregating peptides and proteins. In this study, hydrogen-deuterium exchange (HX) detected by mass spectrometry (MS) was used to measure Abeta(1-40) aggregate distributions without purification or modification that might alter the aggregate structure or distribution. Different peaks in the mass spectra were assigned to monomer, low molecular weight oligomer, intermediate, and fibril based on HX labeling behavior and complementary assays. After 1 h labeling, the intermediates incorporated approximately ten more deuterons relative to fibrils, indicating a more solvent exposed structure of such intermediates. HX-MS also showed that the intermediate species dissociated much more slowly to monomer than did the very low molecular weight oligomers that were formed at very early times in Abeta aggregation. Atomic force microscopy (AFM) measurements revealed the intermediates were roughly spherical with relatively homogenous diameters of 30-50 nm. Quantitative analysis of the HX mass spectra showed that the amount of intermediate species was correlated with Abeta toxicity patterns reported in a previous study under the same conditions. This study also demonstrates the potential of the HX-MS approach to characterizing complex, multi-component oligomer distributions of aggregating peptides and proteins.     

In vivo 31P and multilabel 13C NMR measurements for evaluation of plant metabolic pathways

Reliable measurements of intracellular metabolites are useful for effective plant metabolic engineering. This study explored the application of in situ 31P and 13C NMR spectroscopy for long-term measurements of intracellular pH and concentrations of several metabolites in glycolysis, glucan synthesis, and central carbon metabolic pathways in plant tissues. An NMR perfusion reactor system was designed to allow Catharanthus roseus hairy root cultures to grow for 3-6 weeks, during which time NMR spectroscopy was performed. Constant cytoplasmic pH (7.40+/-0.06), observed during the entire experiment, indicated adequate oxygenation. 13C NMR spectroscopy was performed on hairy root cultures grown in solutions containing 1-13C-, 2-13C-, and 3-13C-labeled glucose in separate experiments and the flow of label was monitored. Activities of pentose phosphate pathways, nonphotosynthetic CO2 fixation, and glucan synthesis pathways were evident from the experimental results. Scrambling of label in glucans also indicated recycling of triose phosphate and their subsequent conversion to hexose phosphates.     

NMR studies of melanins: characterization of a soluble melanin free acid from Sepia ink.

This paper deals with the nuclear magnetic resonance characterization of a soluble derivative (melanin free acid) of Sepia melanin obtained by a peroxidative treatment of the parent (insoluble) species. High resolution 13C and 15N solid state NMR spectroscopies allow the assessment of the chemical changes occurring in the macromolecule upon solubilization. 1H and 13C NMR solution spectra are discussed in light of the results obtained from the solid state spectra. Furthermore, the coordination properties of melanin have been investigated through 27Al NMR spectroscopy and proton relaxation enhancement studies of the paramagnetic gadolinium complex of melanin free acid. Through these experiments it has been possible to evaluate the molecular reorientational time tau R (and from it an estimated molecular weight close to 20 KDa) and the strength of the metal-macromolecule interaction.