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.     

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

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

Metabolic flux analysis in biotechnology processes

Metabolic flux analysis (MFA) has become a fundamental tool of metabolic engineering to elucidate the metabolic state of the cell and has been applied to various biotechnological processes. In recent years, considerable technical advances have been made. Developments of analytical instruments allow us to determine ¹³C labeling distribution of intracellular metabolites with high accuracy and sensitivity. Moreover, kinetic information of intracellular label distribution during isotopic instationary enables us to calculate metabolic fluxes with shortened experimental time and decreased amount of labeled substrate. The ¹³C MFA may be one of the most promising approaches for the target estimation to improve strain performances and production processes.     

13C标记代谢流分析中天然稳定性同位素修正矩阵构建方法及应用

稳定性同位素¹³C标记实验是分析细胞代谢流的一种重要手段,主要通过质谱检测胞内代谢物中¹³C标记的同位素分布,并作为胞内代谢流计算时的约束条件,进而通过代谢流分析算法得到相应代谢网络中的通量分布。然而在自然界中,并非只有C元素存在天然稳定性同位素¹³C,其他元素如O元素也有其天然稳定性同位素¹⁷O、¹⁸O等,这使得质谱方法所测得的同位素分布中会夹杂除¹³C标记之外的其他元素的同位素信息,特别是分子中含有较多其他元素的分子,这将导致很大的实验误差,因此需要在进行代谢流计算前进行质谱数据的矫正。本研究提出了一种基于Python语言的天然同位素修正矩阵的构建方法,用于修正同位素分布测量值中由于天然同位素分布引起的测定误差。文中提出的基本修正矩阵幂方法用于构建各元素修正矩阵,结构简单、易于编码实现,可直接应用于¹³C代谢流分析软件数据前处理。将该修正方法应用于¹³C标记的黑曲霉（Aspergillus niger）胞内代谢流分析,结果表明本研究提出的方法准确有效,为准确获取微生物胞内代谢流分析提供了可靠的数据修正方法。     

Simultaneous tracers and a unified model of positional and mass isotopomers for quantification of metabolic flux in liver

Computational models based on the metabolism of stable isotope tracers can yield valuable insight into the metabolic basis of disease. The complexity of these models is limited by the number of tracers and the ability to characterize tracer labeling in downstream metabolites. NMR spectroscopy is ideal for multiple tracer experiments since it precisely detects the position of tracer nuclei in molecules, but it lacks sensitivity for detecting low-concentration metabolites. GC-MS detects stable isotope mass enrichment in low-concentration metabolites, but lacks nuclei and positional specificity. We performed liver perfusions and in vivo infusions of ²H and ¹³C tracers, yielding complex glucose isotopomers that were assigned by NMR and fit to a newly developed metabolic model. Fluxes regressed from ²H and ¹³C NMR positional isotopomer enrichments served to validate GC-MS-based flux estimates obtained from the same experimental samples. NMR-derived fluxes were largely recapitulated by modeling the mass isotopomer distributions of six glucose fragment ions measured by GC-MS. Modest differences related to limited fragmentation coverage of glucose C1–C3 were identified, but fluxes such as gluconeogenesis, glycogenolysis, cataplerosis and TCA cycle flux were tightly correlated between the methods. Most importantly, modeling of GC-MS data could assign fluxes in primary mouse hepatocytes, an experiment that is impractical by ²H or ¹³C NMR.     

Metabolic Fluxes in an Illuminated Arabidopsis Rosette

Photosynthesis is the basis for life, and its optimization is a key biotechnological aim given the problems of population explosion and environmental deterioration. We describe a method to resolve intracellular fluxes in intact Arabidopsis thaliana rosettes based on time-dependent labeling patterns in the metabolome. Plants photosynthesizing under limiting irradiance and ambient CO₂ in a custom-built chamber were transferred into a ¹³CO₂-enriched environment. The isotope labeling patterns of 40 metabolites were obtained using liquid or gas chromatography coupled to mass spectrometry. Labeling kinetics revealed striking differences between metabolites. At a qualitative level, they matched expectations in terms of pathway topology and stoichiometry, but some unexpected features point to the complexity of subcellular and cellular compartmentation. To achieve quantitative insights, the data set was used for estimating fluxes in the framework of kinetic flux profiling. We benchmarked flux estimates to four classically determined flux signatures of photosynthesis and assessed the robustness of the estimates with respect to different features of the underlying metabolic model and the time-resolved data set.     

Mass spectrometry for metabolic flux analysis

Mass spectrometry in combination with tracer experiments based on 13C substrates can serve as a powerful tool for the modeling and analysis of intracellular fluxes and the investigation of biochemical networks. The theoretical background for the application of mass spectrometry to metabolic flux analysis is discussed. Mass spectrometry methods are especially useful to determine mass distribution of metabolites. Additional information gained from fragmentation of metabolites, e.g., by electron impact ionization, allows further localization of labeling positions, up to complete resolution of isotopomer pools. To effectively handle mass distributions in simulation experiments, a matrix based general methodology is formulated. The natural isotope distribution of carbon, oxygen, hydrogen and nitrogen in the target metabolites is considered by introduction of correction matrices. It is shown by simulation results for the central carbon metabolism that neglecting natural isotope distributions causes significant errors in intracellular flux distributions. By varying relative fluxes into pentosephosphate pathway and pyruvate carboxylation reaction, marked changes in the mass distributions of metabolites result, which are illustrated for pyruvate, oxaloacetate, and alpha-ketoglutarate. In addition mass distributions of metabolites are significantly influenced over a broad range by the degree of reversibility of transaldolase and transketolase reactions in the pentosephosphate pathway. The mass distribution of metabolites is very sensitive towards intracellular flux patterns and can be measured with high accuracy by routine mass spectrometry methods. Copyright 1999 John Wiley & Sons, Inc.     

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.     

Parallel labeling experiments with [U-(13)C]glucose validate E. coli metabolic network model for (13)C metabolic flux analysis

(13)C-metabolic flux analysis (MFA) is a widely used method for measuring intracellular metabolic fluxes in living cells. (13)C MFA relies on several key assumptions: (1) the assumed metabolic network model is complete, in that it accounts for all significant enzymatic and transport reactions; (2) (13)C-labeling measurements are accurate and precise; and (3) enzymes and transporters do not discriminate between (12)C- and (13)C-labeled metabolites. In this study, we tested these inherent assumptions of (13)C MFA for wild-type E. coli by parallel labeling experiments with [U-(13)C]glucose as tracer. Cells were grown in six parallel cultures in custom-constructed mini-bioreactors, starting from the same inoculum, on medium containing different mixtures of natural glucose and fully labeled [U-(13)C]glucose, ranging from 0% to 100% [U-(13)C]glucose. Macroscopic growth characteristics of E. coli showed no observable kinetic isotope effect. The cells grew equally well on natural glucose, 100% [U-(13)C]glucose, and mixtures thereof. (13)C MFA was then used to determine intracellular metabolic fluxes for several metabolic network models: an initial network model from literature; and extended network models that accounted for potential dilution effects of isotopic labeling. The initial network model did not give statistically acceptable fits and produced inconsistent flux results for the parallel labeling experiments. In contrast, an extended network model that accounted for dilution of intracellular CO(2) by exchange with extracellular CO(2) produced statistically acceptable fits, and the estimated metabolic fluxes were consistent for the parallel cultures. This study illustrates the importance of model validation for (13)C MFA. We show that an incomplete network model can produce statistically unacceptable fits, as determined by a chi-square test for goodness-of-fit, and return biased metabolic fluxes. The validated metabolic network model for E. coli from this study can be used in future investigations for unbiased metabolic flux measurements.     

Analysis of 13C labeling enrichment in microbial culture applying metabolic tracer experiments using gas chromatography-combustion-isotope ratio mass spectrometry

The applicability of gas chromatography–combustion–isotope ratio mass spectrometry (GC–C–IRMS) for the quantification of ¹³C enrichment of proteinogenic amino acids in metabolic tracer experiments was evaluated. Measurement of the ¹³C enrichment of proteinogenic amino acids from cell hydrolyzates of Corynebacterium glutamicum growing on different mixtures containing between 0.5 and 10% [1-¹³C]glucose shows the significance of kinetic isotope effects in metabolic flux studies at low degree of labeling. We developed a method to calculate the ¹³C enrichment. The approach to correct for these effects in metabolic flux studies using δ¹³C measurement by GC–C–IRMS uses two parallel experiments applying substrate with natural abundance and ¹³C-enriched tracer substrate, respectively. The fractional enrichment obtained in natural substrate is subtracted from that of the enriched one. Tracer studies with C. glutamicum resulted in a statistically identical relative fractional enrichment of ¹³C in proteinogenic amino acids over the whole range of applied concentrations of [1-¹³C]glucose. The current findings indicate a great potential of GC–C–IRMS for labeling quantification in ¹³C metabolic flux analysis with low labeling degree of tracer substrate directly in larger scale bioreactors.     

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.     

Validation-based model selection for 13C metabolic flux analysis with uncertain measurement errors

Accurate measurements of metabolic fluxes in living cells are central to metabolism research and metabolic engineering. The gold standard method is model-based metabolic flux analysis (MFA), where fluxes are estimated indirectly from mass isotopomer data with the use of a mathematical model of the metabolic network. A critical step in MFA is model selection: choosing what compartments, metabolites, and reactions to include in the metabolic network model. Model selection is often done informally during the modelling process, based on the same data that is used for model fitting (estimation data). This can lead to either overly complex models (overfitting) or too simple ones (underfitting), in both cases resulting in poor flux estimates. Here, we propose a method for model selection based on independent validation data. We demonstrate in simulation studies that this method consistently chooses the correct model in a way that is independent on errors in measurement uncertainty. This independence is beneficial, since estimating the true magnitude of these errors can be difficult. In contrast, commonly used model selection methods based on the χ²-test choose different model structures depending on the believed measurement uncertainty; this can lead to errors in flux estimates, especially when the magnitude of the error is substantially off. We present a new approach for quantification of prediction uncertainty of mass isotopomer distributions in other labelling experiments, to check for problems with too much or too little novelty in the validation data. Finally, in an isotope tracing study on human mammary epithelial cells, the validation-based model selection method identified pyruvate carboxylase as a key model component. Our results argue that validation-based model selection should be an integral part of MFA model development.     

A guide to metabolic flux analysis in metabolic engineering: Methods,tools and applications

The field of metabolic engineering is primarily concerned with improving the biological production of value-added chemicals, fuels and pharmaceuticals through the design, construction and optimization of metabolic pathways, redirection of intracellular fluxes, and refinement of cellular properties relevant for industrial bioprocess implementation. Metabolic network models and metabolic fluxes are central concepts in metabolic engineering, as was emphasized in the first paper published in this journal, “Metabolic fluxes and metabolic engineering” (Metabolic Engineering, 1: 1–11, 1999). In the past two decades, a wide range of computational, analytical and experimental approaches have been developed to interrogate the capabilities of biological systems through analysis of metabolic network models using techniques such as flux balance analysis (FBA), and quantify metabolic fluxes using constrained-based modeling approaches such as metabolic flux analysis (MFA) and more advanced experimental techniques based on the use of stable-isotope tracers, i.e. ¹³C-metabolic flux analysis (¹³C-MFA). In this review, we describe the basic principles of metabolic flux analysis, discuss current best practices in flux quantification, highlight potential pitfalls and alternative approaches in the application of these tools, and give a broad overview of pragmatic applications of flux analysis in metabolic engineering practice.     

A Peptide-Based Method for 13C Metabolic Flux Analysis in Microbial Communities

The study of intracellular metabolic fluxes and inter-species metabolite exchange for microbial communities is of crucial importance to understand and predict their behaviour. The most authoritative method of measuring intracellular fluxes, ¹³C Metabolic Flux Analysis (¹³C MFA), uses the labeling pattern obtained from metabolites (typically amino acids) during ¹³C labeling experiments to derive intracellular fluxes. However, these metabolite labeling patterns cannot easily be obtained for each of the members of the community. Here we propose a new type of ¹³C MFA that infers fluxes based on peptide labeling, instead of amino acid labeling. The advantage of this method resides in the fact that the peptide sequence can be used to identify the microbial species it originates from and, simultaneously, the peptide labeling can be used to infer intracellular metabolic fluxes. Peptide identity and labeling patterns can be obtained in a high-throughput manner from modern proteomics techniques. We show that, using this method, it is theoretically possible to recover intracellular metabolic fluxes in the same way as through the standard amino acid based ¹³C MFA, and quantify the amount of information lost as a consequence of using peptides instead of amino acids. We show that by using a relatively small number of peptides we can counter this information loss. We computationally tested this method with a well-characterized simple microbial community consisting of two species.     

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.     

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.     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

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.     

A Method to Constrain Genome-Scale Models with 13C Labeling Data

Current limitations in quantitatively predicting biological behavior hinder our efforts to engineer biological systems to produce biofuels and other desired chemicals. Here, we present a new method for calculating metabolic fluxes, key targets in metabolic engineering, that incorporates data from ¹³C labeling experiments and genome-scale models. The data from ¹³C labeling experiments provide strong flux constraints that eliminate the need to assume an evolutionary optimization principle such as the growth rate optimization assumption used in Flux Balance Analysis (FBA). This effective constraining is achieved by making the simple but biologically relevant assumption that flux flows from core to peripheral metabolism and does not flow back. The new method is significantly more robust than FBA with respect to errors in genome-scale model reconstruction. Furthermore, it can provide a comprehensive picture of metabolite balancing and predictions for unmeasured extracellular fluxes as constrained by ¹³C labeling data. A comparison shows that the results of this new method are similar to those found through ¹³C Metabolic Flux Analysis (¹³C MFA) for central carbon metabolism but, additionally, it provides flux estimates for peripheral metabolism. The extra validation gained by matching 48 relative labeling measurements is used to identify where and why several existing COnstraint Based Reconstruction and Analysis (COBRA) flux prediction algorithms fail. We demonstrate how to use this knowledge to refine these methods and improve their predictive capabilities. This method provides a reliable base upon which to improve the design of biological systems.