Analysis of flux estimates based on (13)C-labelling experiments.

Modelling of the fluxes in central metabolism can be performed by combining labelling experiments with metabolite balancing. Using this approach, multiple samples from a cultivation of Saccharomyces cerevisiae in metabolic and isotopic steady state were analysed, and the metabolic fluxes in central metabolism were estimated. In the various samples, the estimates of the central metabolic pathways, the tricarboxylic acid cycle, the oxidative pentose phosphate pathway and the anaplerotic pathway, showed an unprecedented reproducibility. The high reproducibility was obtained with fractional labellings of individual carbon atoms as the calculational base, illustrating that the more complex modelling using isotopomers is not necessarily superior with respect to reproducibility of the flux estimates. Based on these results some general difficulties in flux estimation are discussed.     

Quantification of hepatic carbohydrate metabolism in conscious mice using serial blood and urine spots

In vivo studies of hepatic carbohydrate metabolism in (genetically modified) conscious mice are hampered by limitations of blood and urine sample sizes. We developed and validated methods to quantify stable isotope dilution and incorporation in small blood and urine samples spotted onto filter paper. Blood glucose and urinary paracetamol-glucuronic acid were extracted from filter paper spots reproducibly and with high yield. Fractional isotopomer distributions of glucose and paracetamol-glucuronic acid when extracted from filter paper spots were almost identical to those isolated from the original body fluids. Rates of infusion of labeled compounds could be adjusted without perturbing hepatic glucose metabolism. This approach was used in mice to find the optimal metabolic condition for the study of hepatic carbohydrate metabolism. In fed mice, no isotopic steady state was observed during a 6-h label-infusion experiment. In 9-h-fasted mice, isotopic steady state was reached after 3 h of label infusion and important parameters in hepatic glucose metabolism could be calculated. The rate of de novo glucose-6-phosphate synthesis was 143 +/- 17 micromol kg(-1) min(-1) and partitioning to plasma glucose was 79.0 +/- 5.2%. In 24-h-fasted mice, abrupt changes were noticed in whole body and in hepatic glucose metabolism at the end of the experiment.     

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 network fluxes in heterotrophic Arabidopsis cells: stability of the flux distribution under different oxygenation conditions

Steady-state labeling experiments with [1-¹³C]Glc were used to measure multiple metabolic fluxes through the pathways of central metabolism in a heterotrophic cell suspension culture of Arabidopsis (Arabidopsis thaliana). The protocol was based on in silico modeling to establish the optimal labeled precursor, validation of the isotopic and metabolic steady state, extensive nuclear magnetic resonance analysis of the redistribution of label into soluble metabolites, starch, and protein, and a comprehensive set of biomass measurements. Following a simple modification of the cell culture procedure, cells were grown at two oxygen concentrations, and flux maps of central metabolism were constructed on the basis of replicated experiments and rigorous statistical analysis. Increased growth rate at the higher O₂ concentration was associated with an increase in fluxes throughout the network, and this was achieved without any significant change in relative fluxes despite differences in the metabolite profile of organic acids, amino acids, and carbohydrates. The balance between biosynthesis and respiration within the tricarboxylic acid cycle was unchanged, with 38% ± 5% of carbon entering used for biosynthesis under standard O₂ conditions and 33% ± 2% under elevated O₂. These results add to the emerging picture of the stability of the central metabolic network and its capacity to respond to physiological perturbations with the minimum of rearrangement. The lack of correlation between the change in metabolite profile, which implied significant disruption of the metabolic network following the alteration in the oxygen supply, and the unchanging flux distribution highlights a potential difficulty in the interpretation of metabolomic data.     

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.     

Insights into plant metabolic networks from steady-state metabolic flux analysis

Steady-state metabolic flux analysis (MFA) is an experimental approach that allows the measurement of multiple fluxes in the core network of primary carbon metabolism. It is based on isotopic labelling experiments, and although well established in the analysis of micro-organisms, and some mammalian systems, the extension of the method to plant cells has been challenging because of the extensive subcellular compartmentation of the metabolic network. Despite this difficulty there has been substantial progress in developing robust protocols for the analysis of heterotrophic plant metabolism by steady-state MFA, and flux maps have now been published that reflect the metabolic phenotypes of excised root tips, developing embryos and cotyledons, hairy root cultures, and cell suspensions under a variety of physiological conditions. There has been a steady improvement in the quality, extent and statistical reliability of these analyses, and new information is emerging on the performance of the plant metabolic network and the contributions of specific pathways.     

Response of the central metabolism in Corynebacterium glutamicum to the use of an NADH-dependent glutamate dehydrogenase

The extensive use of 13C enrichments in precursor metabolites for flux quantification does not rely on NADPH stoichiometries and can therefore be used to quantify reducing power fluxes. As an application of this concept, the NADPH fluxes were quantified in an L-lysine producer of Corynebacterium glutamicum grown into metabolic and isotopic steady state with [1-13C]glucose. In this case, where the organism's NADPH-dependent glutamate dehydrogenase consumes reducing power, the NADPH flux generated is 210% (molar flux relative to glucose uptake rate) with its major part (72% of the total) generated via the pentose phosphate pathway activity. An isogenic strain in which the glutamate dehydrogenase of C. glutamicum was replaced by the NADH-dependent glutamate dehydrogenase of Peptostreptococcus asaccharolyticus was made and the metabolite fluxes were again estimated. The major response to this local perturbation is a drastically reduced NADPH generation of only 139%. Most of the NADPH (62% of the total) is now generated via the tricarboxylic acid cycle activity. This shows the extraordinary flexibility of the central metabolism and provides a picture of the global regulatory properties of the central metabolism. Furthermore, a detailed analysis of the fluxes and exchange fluxes within the anaplerotic reactions is given. It is hypothesized that these reactions might also serve to balance the total reducing power budget as well as the energy budget within the cell.     

Determination of the fluxes in the central metabolism of Corynebacterium glutamicum by nuclear magnetic resonance spectroscopy combined with metabolite balancing

To determine the in vivo fluxes of the central metabolism we have developed a comprehensive approach exclusively based on the fundamental enzyme reactions known to be present, the fate of the carbon atoms of individual reactions, and the metabolite balance of the culture. No information on the energy balance is required, nor information on enzyme activities, or the directionalities of reactions. Our approach combines the power of (1)H-detected (13)C nuclear magnetic resonance spectroscopy to follow individual carbons with the simplicity of establishing carbon balances of bacterial cultures. We grew a lysine-producing strain of Corynebacterium glutamicum to the metabolic and isotopic steady state with [1-(13)C]glucose and determined the fractional enrichments in 27 carbon atoms of 11 amino acids isolated from the cell. Since precursor metabolites of the central metabolism are incorporated in an exactly defined manner in the carbon skeleton of amino acids, the fractional enrichments in carbons of precursor metabolites (oxaloacetate, glyceraldehyde 3-phosphate, erythrose 4-phosphate, etc.) became directly accessible. A concise and generally applicable mathematical model was established using matrix calculus to express all metabolite mass and carbon labeling balances. An appropriate all-purpose software for the iterative solution of the equations is supplied. Applying this comprehensive methodology to C. glutamicum, all major fluxes within the central metabolism were determined. The result is that the flux through the pentose phosphate pathway is 66.4% (relative to the glucose input flux of 1.49 mmol/g dry weight h), that of entry into the tricarboxylic acid cycle 62.2%, and the contribution of the succinylase pathway of lysine synthesis 13.7%. Due to the large amount and high quality of measured data in vivo exchange reactions could also be quantitated with particularly high exchange rates within the pentose phosphate pathway for the ribose 5-phosphate transketolase reaction. Moreover, the total net flux of the anaplerotic reactions was quantitated as 38.0%. Most importantly, we found that in vivo one component within these anaplerotic reactions is a back flux from the carbon 4 units of the tricarboxylic acid cycle to the carbon 3 units of glycolysis of 30.6%. (c) 1996 John Wiley & Sons, Inc.     

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.     

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.     

Response of the central metabolism of Corynebacterium glutamicum to different flux burdens

To evaluate the importance of reactions within the central metabolism under different flux burdens the fluxes within the pentose phosphate pathway (PPP), as well as the other reactions of the central metabolism, were intensively analyzed and quantitated. For this purpose, Corynebacterium glutamicum was grown with [1-(13)C]glucose to metabolic and isotopic steady state and the fractional enrichments in precursor metabolites (e.g., pentose 5-phosphate) were quantified. Matrix calculus was used to express these data together with metabolite mass data. The detailed analysis of the dependence of (13)C enrichments on exchange fluxes enabled the transketolase-catalyzed exchange rate (2 pentose 5-phosphate <--> sedoheptulose 7-phosphate + glyceraldehyde 3-phosphate) to be quantified as 74.3% (molar metabolite flux) at a net flux of 10.3% and the exchange rate (pentose 5-phosphate + erythrose 4-phosphate <--> fructose 6-phosphate + glyceraldehyde 3-phosphate) to be quantified as 5.6% at a net flux of 8.1%. The flux entering the tricarboxylic acid cycle was 93.3%. The same comprehensive flux analysis as performed for the nonexcreting condition was done with the identical strain that had been forced to excrete L-glutamate. Because we had already quantified the fluxes for L-lysine excretion with an isogenic strain, three directly comparable flux situations are thus available. Consequently, this comparison permits a direct cause-and-effect relationship to be specified. In response to the different flux burdens of the cell, the PPP flux decreased from a maximum of 67% to 26%, with the glycolytic flux increasing accordingly. The carbon flux through isocitrate dehydrogenase increased from 20% to 36%. The bidirectional carbon flux between pyruvate and oxaloacetate decreased from 36% to 9%. Since the cause of the three different flux states was the allelic exchange in the final L-lysine assembling pathway or the glutamate export activity, respectively, the flexible response is the effect. This shows conclusively the enormous flexibility within the central metabolism of C. glutamicum to supply precursors upon their withdrawal for the synthesis of amino acids. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 168-180, 1997.     

Towards a metabolic and isotopic steady state in CHO batch cultures for reliable isotope-based metabolic profiling

Attaining metabolic and isotopic balanced growth is one critical condition for physiological studies using isotope-labeled tracers, but is very difficult to obtain in batch culture due to the extensive metabolite exchange with the surrounding medium and related physiological changes. In the present study, we investigated metabolic and isotopic behavior of CHO cells in differently designed media. We observed that the assumption of balanced cell growth cannot be justified in batch culture of CHO cells directly using conventional, commercially available media. By systematically redesigning media composition and characterizing metabolic steady state based on mass balances and measurement of labeling dynamics, we achieved balanced cell growth for the main cellular substrates in CHO cells. This was done in a step-by-step analysis of growth and primary metabolism of CHO cells with the use of [U-¹³C]glucose feeding and adjusting concentrations of amino acids in the growth medium. The optimized media obtained at the end of the study provide balanced growth and isotopic steady state or at least asymptotic steady state. As a result, we established a platform to conduct isotope-based physiological studies of mammalian systems more reliably and therefore well suited for later use in metabolic profiling of mammalian systems such as ¹³C-labeled metabolic flux analysis.     

Contribution of exogenous substrates to acetyl coenzyme A: measurement by 13C NMR under non-steady-state conditions

A method is presented for the rapid determination of substrate selection in a manner that is not restricted to conditions of metabolic and isotopic steady state. Competition between several substrates can be assessed directly and continuously in a single experiment, allowing the effect of interventions to be studied. It is shown that a single proton-decoupled 13C NMR spectrum of glutamate provides a direct measure of the contribution of exogenous 13C-labeled substrates to acetyl-CoA without measurement of oxygen consumption and that steady-state conditions need not apply. Two sets of experiments were performed: one in which a metabolic steady state but a non-steady-state 13C distribution was achieved and another in which both metabolism and labeling were not at steady state. In the first group, isolated rat hearts were supplied with [1,2-13C]acetate, [3-13C]lactate, and unlabeled glucose. 13C NMR spectra of extracts from hearts perfused under identical conditions for 5 or 30 min were compared. In spite of significant differences in the spectra, the measured contributions of acetate, lactate, and unlabeled sources to acetyl-CoA were the same. In the second set of experiments, the same group of labeled substrates was used in a regional ischemia model in isolated rabbit hearts to show regional differences in substrate utilization under both metabolic and isotopic non steady state. This sensitive probe of substrate selection was also demonstrated in intact hearts where excellent time resolution (3 min) of substrate selection was feasible.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Fitness, Flux and Phantoms in Temporally Variable Environments

The evolutionary problem of selection in temporally variable environments is addressed by investigating a metabolic model describing the approach to steady state of a flux emanating from a simple linear pathway of unsaturated enzymes catalyzing reversible monomolecular reactions. Analysis confirms previous claims that steps having no influence on the steady state flux may influence transient behavior, and that enzymes immune to natural selection at steady state may become subject to selection when fitness is a function of individual transient metabolic events. Indeed, calculations show that the β-galactosidase of Escherichia coli, which exerts a negligible effect on the steady state lactose flux, controls the approach to steady state. However, after 6 sec the lactose flux is within 0.1% of steady state, and so an ever changing environment must be invoked to continually expose β-galactosidase to selection. Analysis of the metabolic model undergoing multiple transient events reveals that fitness differences remain unaffected if enzyme activities remain constant and become minimized if enzyme activities differ among environments. Until suitable data become available, claims that metabolic behavior away from steady state necessarily exposes a far greater proportion of allozymes to natural selection should be treated with great skepticism.     

Network identification and flux quantification in the central metabolism of Saccharomyces cerevisiae under different conditions of glucose repression

The network structure and the metabolic fluxes in central carbon metabolism were characterized in aerobically grown cells of Saccharomyces cerevisiae. The cells were grown under both high and low glucose concentrations, i.e., either in a chemostat at steady state with a specific growth rate of 0.1 h(-1) or in a batch culture with a specific growth rate of 0.37 h(-1). Experiments were carried out using [1-(13)C]glucose as the limiting substrate, and the resulting summed fractional labelings of intracellular metabolites were measured by gas chromatography coupled to mass spectrometry. The data were used as inputs to a flux estimation routine that involved appropriate mathematical modelling of the central carbon metabolism of S. cerevisiae. The results showed that the analysis is very robust, and it was possible to quantify the fluxes in the central carbon metabolism under both growth conditions. In the batch culture, 16.2 of every 100 molecules of glucose consumed by the cells entered the pentose-phosphate pathway, whereas the same relative flux was 44.2 per 100 molecules in the chemostat. The tricarboxylic acid cycle does not operate as a cycle in batch-growing cells, in contrast to the chemostat condition. Quantitative evidence was also found for threonine aldolase and malic enzyme activities, in accordance with published data. Disruption of the MIG1 gene did not cause changes in the metabolic network structure or in the flux pattern.