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.     

Optimal tracers for parallel labeling experiments and 13C metabolic flux analysis: A new precision and synergy scoring system

¹³C-Metabolic flux analysis (¹³C-MFA) is a widely used approach in metabolic engineering for quantifying intracellular metabolic fluxes. The precision of fluxes determined by ¹³C-MFA depends largely on the choice of isotopic tracers and the specific set of labeling measurements. A recent advance in the field is the use of parallel labeling experiments for improved flux precision and accuracy. However, as of today, no systemic methods exist for identifying optimal tracers for parallel labeling experiments. In this contribution, we have addressed this problem by introducing a new scoring system and evaluating thousands of different isotopic tracer schemes. Based on this extensive analysis we have identified optimal tracers for ¹³C-MFA. The best single tracers were doubly ¹³C-labeled glucose tracers, including [1,6-¹³C]glucose, [5,6-¹³C]glucose and [1,2-¹³C]glucose, which consistently produced the highest flux precision independent of the metabolic flux map (here, 100 random flux maps were evaluated). Moreover, we demonstrate that pure glucose tracers perform better overall than mixtures of glucose tracers. For parallel labeling experiments the optimal isotopic tracers were [1,6-¹³C]glucose and [1,2-¹³C]glucose. Combined analysis of [1,6-¹³C]glucose and [1,2-¹³C]glucose labeling data improved the flux precision score by nearly 20-fold compared to widely use tracer mixture 80% [1-¹³C]glucose +20% [U-¹³C]glucose.     

One-dimensional 13C NMR and HPLC-1H NMR techniques for observing carbon-13 and deuterium labelling in biosynthetic studies

For several decades isotope labelling techniques have been the indispensable tools used to unravel pathways of secondary product biosynthesis. NMR spectroscopy, together with mass spectrometry, is the most effective measuring technique used in the analysis of metabolites enriched with stable isotopes. ²H and ¹³C are the NMR-detectable nuclides which have been most frequently employed in plant secondary metabolite synthesis. Examples from the biosynthesis of phenylpropanoids, phenylphenalenones, and glucosinolates are used when discussing some aspects of one-dimensional NMR analysis of metabolites selectively labelled with ²H and ¹³C. Besides direct NMR detection of ¹³C-enriched metabolites, special emphasis is placed on indirect detection of ¹³C and ²H, especially by HPLC-¹H NMR coupling, to analyse the isotopomer pattern of compounds in low concentration. The examples discussed in this paper were obtained from studies with Anigozanthos preissii (root cultures) (Haemodoraceae) and Eruca sativa (Brassicaceae).     

C isotopomer analysis of glutamate by heteronuclear multiple quantum coherence-total correlation spectroscopy (HMQC-TOCSY)

¹³C has become an important tracer isotope for studies of intermediary metabolism. Information about relative flux through pathways is encoded by the distribution of ¹³C isotopomers in an intermediate pool such as glutamate. This information is commonly decoded either by mass spectrometry or by measuring relative multiplet areas in a ¹³C NMR spectrum. We demonstrate here that groups of glutamate ¹³C isotopomers may be quantified by indirect detection of protons in a 2D HMQC-TOCSY NMR spectrum and that fitting of these data to a metabolic model provides an identical measure of the ¹³C fractional enrichment of acetyl-CoA and relative anaplerotic flux to that given by direct ¹³C NMR analysis. The sensitivity gain provided by HMQC-TOCSY spectroscopy will allow an extension of ¹³C isotopomer analysis to tissue samples not amenable to direct ¹³C detection (∼10 mg soleus muscle) and to tissue metabolites other than glutamate that are typically present at lower concentrations.     

Integrated 13C-metabolic flux analysis of 14 parallel labeling experiments in Escherichia coli

The use of parallel labeling experiments for ¹³C metabolic flux analysis (¹³C-MFA) has emerged in recent years as the new gold standard in fluxomics. The methodology has been termed COMPLETE-MFA, short for complementary parallel labeling experiments technique for metabolic flux analysis. In this contribution, we have tested the limits of COMPLETE-MFA by demonstrating integrated analysis of 14 parallel labeling experiments with Escherichia coli. An effort on such a massive scale has never been attempted before. In addition to several widely used isotopic tracers such as [1,2-¹³C]glucose and mixtures of [1-¹³C]glucose and [U-¹³C]glucose, four novel tracers were applied in this study: [2,3-¹³C]glucose, [4,5,6-¹³C]glucose, [2,3,4,5,6-¹³C]glucose and a mixture of [1-¹³C]glucose and [4,5,6-¹³C]glucose. This allowed us for the first time to compare the performance of a large number of isotopic tracers. Overall, there was no single best tracer for the entire E. coli metabolic network model. Tracers that produced well-resolved fluxes in the upper part of metabolism (glycolysis and pentose phosphate pathways) showed poor performance for fluxes in the lower part of metabolism (TCA cycle and anaplerotic reactions), and vice versa. The best tracer for upper metabolism was 80% [1-¹³C]glucose+20% [U-¹³C]glucose, while [4,5,6-¹³C]glucose and [5-¹³C]glucose both produced optimal flux resolution in the lower part of metabolism. COMPLETE-MFA improved both flux precision and flux observability, i.e. more independent fluxes were resolved with smaller confidence intervals, especially exchange fluxes. Overall, this study demonstrates that COMPLETE-MFA is a powerful approach for improving flux measurements and that this methodology should be considered in future studies that require very high flux resolution.     

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.     

NMR-based stable isotope resolved metabolomics in systems biochemistry

An important goal of metabolomics is to characterize the changes in metabolic networks in cells or various tissues of an organism in response to external perturbations or pathologies. The profiling of metabolites and their steady state concentrations does not directly provide information regarding the architecture and fluxes through metabolic networks. This requires tracer approaches. NMR is especially powerful as it can be used not only to identify and quantify metabolites in an unfractionated mixture such as biofluids or crude cell/tissue extracts, but also determine the positional isotopomer distributions of metabolites derived from a precursor enriched in stable isotopes such as (13)C and (15)N via metabolic transformations. In this article we demonstrate the application of a variety of 2-D NMR editing experiments to define the positional isotopomers of compounds present in polar and non-polar extracts of human lung cancer cells grown in either [U-(13)C]-glucose or [U-(13)C,(15)N]-glutamine as source tracers. The information provided by such experiments enabled unambiguous reconstruction of metabolic pathways, which is the foundation for further metabolic flux modeling.     

13C metabolic flux analysis for larger scale cultivation using gas chromatography-combustion-isotope ratio mass spectrometry

¹³C-based metabolic flux analysis (¹³CMFA) is limited to smaller scale experiments due to very high costs of labeled substrates. We measured ¹³C enrichment in proteinogenic amino acid hydrolyzates using gas chromatography-combustion-isotope ratio mass spectrometry (GC-C-IRMS) from a series of parallel batch cultivations of Corynebacterium glutamicum utilizing mixtures of natural glucose and [1-¹³C] glucose, containing 0%, 0.5%, 1%, 2%, and 10% [1-¹³C] glucose. Decreasing the [1-¹³C] glucose content, kinetic isotope effects played an increasing role but could be corrected. From the corrected ¹³C enrichments in vivo fluxes in the central metabolism were determined by numerical optimization. The obtained flux distribution was very similar to those obtained from parallel labeling experiments using conventional high labeling GC-MS method and to published results. The GC-C-IRMS-based method involving low labeling degree of expensive tracer substrate, e.g. 1%, is well suited for larger laboratory and industrial pilot scale fermentations.     

Evidence for transketolase-like TKTL1 flux in CHO cells based on parallel labeling experiments and 13C-metabolic flux analysis

The pentose phosphate pathway (PPP) is a fundamental component of cellular metabolism. It provides precursors for the biosynthesis of nucleotides and contributes to the production of reducing power in the form of NADPH. It has been hypothesized that mammalian cells may contain a hidden reaction in PPP catalyzed by transketolase-like protein 1 (TKTL1) that is closely related to the classical transketolase enzyme; however, until now there has been no direct experimental evidence for this reaction. In this work, we have applied state-of-the-art techniques in ¹³C metabolic flux analysis (¹³C-MFA) based on parallel labeling experiments and integrated flux fitting to estimate the TKTL1 flux in CHO cells. We identified a set of three parallel labeling experiments with [1-¹³C]glucose+[4,5,6-¹³C]glucose, [2-¹³C]glucose+[4,5,6-¹³C]glucose, and [3-¹³C]glucose+[4,5,6-¹³C]glucose and developed a new method to measure ¹³C-labeling of fructose 6-phosphate by GC-MS that allows intuitive interpretation of mass isotopomer distributions to determine key fluxes in the model, including glycolysis, oxidative PPP, non-oxidative PPP, and the TKTL1 flux. Using these tracers we detected a significant TKTL1 flux in CHO cells at the stationary phase. The flux results suggest that the main function of oxidative PPP in CHO cells at the stationary phase is to fuel the TKTL1 reaction. Overall, this study demonstrates for the first time that carbon atoms can be lost in the PPP, by means other than the oxidative PPP, and that this loss of carbon atoms is consistent with the hypothesized TKTL1 reaction in mammalian cells.     

Catabolism of Branched Chain Amino Acids Contributes Significantly to Synthesis of Odd-Chain and Even-Chain Fatty Acids in 3T3-L1 Adipocytes

The branched chain amino acids (BCAA) valine, leucine and isoleucine have been implicated in a number of diseases including obesity, insulin resistance, and type 2 diabetes mellitus, although the mechanisms are still poorly understood. Adipose tissue plays an important role in BCAA homeostasis by actively metabolizing circulating BCAA. In this work, we have investigated the link between BCAA catabolism and fatty acid synthesis in 3T3-L1 adipocytes using parallel ¹³C-labeling experiments, mass spectrometry and model-based isotopomer data analysis. Specifically, we performed parallel labeling experiments with four fully ¹³C-labeled tracers, [U-¹³C]valine, [U-¹³C]leucine, [U-¹³C]isoleucine and [U-¹³C]glutamine. We measured mass isotopomer distributions of fatty acids and intracellular metabolites by GC-MS and analyzed the data using the isotopomer spectral analysis (ISA) framework. We demonstrate that 3T3-L1 adipocytes accumulate significant amounts of even chain length (C14:0, C16:0 and C18:0) and odd chain length (C15:0 and C17:0) fatty acids under standard cell culture conditions. Using a novel GC-MS method, we demonstrate that propionyl-CoA acts as the primer on fatty acid synthase for the production of odd chain fatty acids. BCAA contributed significantly to the production of all fatty acids. Leucine and isoleucine contributed at least 25% to lipogenic acetyl-CoA pool, and valine and isoleucine contributed 100% to lipogenic propionyl-CoA pool. Our results further suggest that low activity of methylmalonyl-CoA mutase and mass action kinetics of propionyl-CoA on fatty acid synthase result in high rates of odd chain fatty acid synthesis in 3T3-L1 cells. Overall, this work provides important new insights into the connection between BCAA catabolism and fatty acid synthesis in adipocytes and underscores the high capacity of adipocytes for metabolizing BCAA.     

13C-Labeled Gluconate Tracing as a Direct and Accurate Method for Determining the Pentose Phosphate Pathway Split Ratio in Penicillium chrysogenum

In this study we developed a new method for accurately determining the pentose phosphate pathway (PPP) split ratio, an important metabolic parameter in the primary metabolism of a cell. This method is based on simultaneous feeding of unlabeled glucose and trace amounts of [U-¹³C]gluconate, followed by measurement of the mass isotopomers of the intracellular metabolites surrounding the 6-phosphogluconate node. The gluconate tracer method was used with a penicillin G-producing chemostat culture of the filamentous fungus Penicillium chrysogenum. For comparison, a ¹³C-labeling-based metabolic flux analysis (MFA) was performed for glycolysis and the PPP of P. chrysogenum. For the first time mass isotopomer measurements of ¹³C-labeled primary metabolites are reported for P. chrysogenum and used for a ¹³C-based MFA. Estimation of the PPP split ratio of P. chrysogenum at a growth rate of 0.02 h⁻¹ yielded comparable values for the gluconate tracer method and the ¹³C-based MFA method, 51.8% and 51.1%, respectively. A sensitivity analysis of the estimated PPP split ratios showed that the 95% confidence interval was almost threefold smaller for the gluconate tracer method than for the ¹³C-based MFA method (40.0 to 63.5% and 46.0 to 56.5%, respectively). From these results we concluded that the gluconate tracer method permits accurate determination of the PPP split ratio but provides no information about the remaining cellular metabolism, while the ¹³C-based MFA method permits estimation of multiple fluxes but provides a less accurate estimate of the PPP split ratio.     

Glucose isotope, carbon recycling, and gluconeogenesis using [U-13C]glucose and mass isotopomer analysis

Experimental determinations of glucose carbon recycling using 14C or 13C glucose tracer often underestimate true Cori cycle activity because of dilution and exchange of isotope tracer through the tricarboxylic acid (TCA) cycle. The term glucose isotope recycling therefore is used to distinguish recycling of isotope from recycling of glucose carbon, the actual quantity of circulating glucose recycled. Recently, per-labeled glucose ([U-13C6]glucose) has been used to estimate glucose appearance rate and glucose isotope recycling. Chemical structural information determined by mass isotopomer analysis has been used to correct for dilution of isotope through the TCA cycle. In this report, we present experiments in the study of glucose turnover and recycling using [U-13C6]glucose. Methods of single injection and continuous infusion of [U-13C6]glucose are compared. A formula for the calculation of a dilution factor using TCA cycle parameters is derived. In this study of six rabbits, glucose turnover rate ranged from 3.4 to 8.8 mg/kg/min, and glucose m + 3 mass isotopomer recycling from 7 to 12%. The rate of pyruvate carboxylation (Y) was comparable to that of citrate synthetase, having an average relative flux of 0.89. Applying the correction factor for tracer dilution to the observed mass isotopomer recycling, we determined glucose carbon recycling (or Cori cycle activity) to be 22-35% of hepatic glucose output.     

Simultaneous Steady-state and Dynamic 13C NMR Can Differentiate Alternative Routes of Pyruvate Metabolism in Living Cancer Cells

Metabolic reprogramming facilitates cancer cell growth, so quantitative metabolic flux measurements could produce useful biomarkers. However, current methods to analyze flux in vivo provide either a steady-state overview of relative activities (infusion of ¹³C and analysis of extracted metabolites) or a dynamic view of a few reactions (hyperpolarized ¹³C spectroscopy). Moreover, although hyperpolarization has successfully quantified pyruvate-lactate exchanges, its ability to assess mitochondrial pyruvate metabolism is unproven in cancer. Here, we combined ¹³C hyperpolarization and isotopomer analysis to quantify multiple fates of pyruvate simultaneously. Two cancer cell lines with divergent pyruvate metabolism were incubated with thermally polarized [3-¹³C]pyruvate for several hours, then briefly exposed to hyperpolarized [1-¹³C]pyruvate during acquisition of NMR spectra using selective excitation to maximize detection of H[¹³C]O₃⁻ and [1-¹³C]lactate. Metabolites were then extracted and subjected to isotopomer analysis to determine relative rates of pathways involving [3-¹³C]pyruvate. Quantitation of hyperpolarized H[¹³C]O₃⁻ provided a single definitive metabolic rate, which was then used to convert relative rates derived from isotopomer analysis into quantitative fluxes. This revealed that H[¹³C]O₃⁻ appearance reflects activity of pyruvate dehydrogenase rather than pyruvate carboxylation followed by subsequent decarboxylation reactions. Glucose substantially altered [1-¹³C]pyruvate metabolism, enhancing exchanges with [1-¹³C]lactate and suppressing H[¹³C]O₃⁻ formation. Furthermore, inhibiting Akt, an oncogenic kinase that stimulates glycolysis, reversed these effects, indicating that metabolism of pyruvate by both LDH and pyruvate dehydrogenase is subject to the acute effects of oncogenic signaling on glycolysis. The data suggest that combining ¹³C isotopomer analyses and dynamic hyperpolarized ¹³C spectroscopy may enable quantitative flux measurements in living tumors.     

Software for dynamic analysis of tracer-based metabolomic data: estimation of metabolic fluxes and their statistical analysis

MOTIVATION: Metabolic flux analysis of biochemical reaction networks using isotope tracers requires software tools that can analyze the dynamics of isotopic isomer (isotopomer) accumulation in metabolites and reveal the underlying kinetic mechanisms of metabolism regulation. Since existing tools are restricted by the isotopic steady state and remain disconnected from the underlying kinetic mechanisms, we have recently developed a novel approach for the analysis of tracer-based metabolomic data that meets these requirements. The present contribution describes the last step of this development: implementation of (i) the algorithms for the determination of the kinetic parameters and respective metabolic fluxes consistent with the experimental data and (ii) statistical analysis of both fluxes and parameters, thereby lending it a practical application. RESULTS: The C++ applications package for dynamic isotopomer distribution data analysis was supplemented by (i) five distinct methods for resolving a large system of differential equations; (ii) the 'simulated annealing' algorithm adopted to estimate the set of parameters and metabolic fluxes, which corresponds to the global minimum of the difference between the computed and measured isotopomer distributions; and (iii) the algorithms for statistical analysis of the estimated parameters and fluxes, which use the covariance matrix evaluation, as well as Monte Carlo simulations. An example of using this tool for the analysis of (13)C distribution in the metabolites of glucose degradation pathways has demonstrated the evaluation of optimal set of parameters and fluxes consistent with the experimental pattern, their range and statistical significance, and also the advantages of using dynamic rather than the usual steady-state method of analysis. AVAILABILITY: Software is available free from http://www.bq.ub.es/bioqint/selivanov.htm     

Metabolic flux analysis of CHO cells at growth and non-growth phases using isotopic tracers and mass spectrometry

Chinese hamster ovary (CHO) cells are the main platform for production of biotherapeutics in the biopharmaceutical industry. However, relatively little is known about the metabolism of CHO cells in cell culture. In this work, metabolism of CHO cells was studied at the growth phase and early stationary phase using isotopic tracers and mass spectrometry. CHO cells were grown in fed-batch culture over a period of six days. On days 2 and 4, [1,2-¹³C] glucose was introduced and the labeling of intracellular metabolites was measured by gas chromatography-mass spectrometry (GC–MS) at 6, 12 and 24 h following the introduction of tracer. Intracellular metabolic fluxes were quantified from measured extracellular rates and ¹³C-labeling dynamics of intracellular metabolites using non-stationary ¹³C-metabolic flux analysis (¹³C-MFA). The flux results revealed significant rewiring of intracellular metabolic fluxes in the transition from growth to non-growth, including changes in energy metabolism, redox metabolism, oxidative pentose phosphate pathway and anaplerosis. At the exponential phase, CHO cell metabolism was characterized by a high flux of glycolysis from glucose to lactate, anaplerosis from pyruvate to oxaloacetate and from glutamate to α-ketoglutarate, and cataplerosis though malic enzyme. At the stationary phase, the flux map was characterized by a reduced flux of glycolysis, net lactate uptake, oxidative pentose phosphate pathway flux, and reduced rate of anaplerosis. The fluxes of pyruvate dehydrogenase and TCA cycle were similar at the exponential and stationary phase. The results presented here provide a solid foundation for future studies of CHO cell metabolism for applications such as cell line development and medium optimization for high-titer production of recombinant proteins.     

Automated Bayesian model development for frequency detection in biological time series

Background

The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results

This article addresses the mathematical and computational formulation of ¹³C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions

Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.     

Isotopomer analysis of myocardial substrate metabolism: a systems biology approach

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

The relationships between the metabolic fluxes and 13C-labeled isotopomer distribution for the flux analysis of the main metabolic pathways

It has been known that ¹³C-labeling technique is quite useful in estimating the metabolic fluxes. Although the program-based flux analysis is powerful, it is not easy to be confident with the result obtained without experiences and exhaustive trial and errors based on statistical analysis for the confidence intervals in practice. It is, therefore, quite important to grasp the relationship between the fluxes and the ¹³C-labeled isotopomer distribution to get deeper insight into the metabolic flux analysis. In the present research, it was shown explicitly how the isotopomer distribution changes with respect to the fluxes in relation to the labeling patterns of the substrate, where either labeled glucose, acetate, or pyruvate was used as a carbon source. Some of the analytical expressions were derived based on the matrix representation, and they were utilized for analysis. It was shown that the isotopomer pattern does not necessarily change uniformly with respect to fluxes, but changes in a complicated way in particular for the case of using pyruvate as a carbon source where some isotopomers do not necessarily change monotonically. It was shown to be quite important to grasp how the isotopomer pattern changes with respect to fluxes and the labeling pattern of the substrate for flux determination and the experimental design. It was also shown that the mixture of [1-¹³C] acetate and [2-¹³C] acetate should not be used from the information index point of view. Some of the experimental data were evaluated from the present approach. It was also shown that the isotopomer distribution is less sensitive to the bidirectional fluxes in the reversible pathway.