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.     

Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models.

Complete isotopomer models that simulate distribution of label in 13C tracer experiments are applied to the quantification of metabolic fluxes in the primary carbon metabolism of E. coli under aerobic and anaerobic conditions. The concept of isotopomer mapping matrices (IMMs) is used to simplify the formulation of isotopomer mass balances by expressing all isotopomer mass balances of a metabolite pool in a single matrix equation. A numerically stable method to calculate the steady-state isotopomer distribution in metabolic networks in introduced. Net values of intracellular fluxes and the degree of reversibility of enzymatic steps are estimated by minimization of the deviations between experimental and simulated measurements. The metabolic model applied includes the Embden-Meyerhof-Parnas and the pentose phosphate pathway, the tricarboxylic acid cycle, anaplerotic reaction sequences and pathways involved in amino acid synthesis. The study clearly demonstrates the value of complete isotopomer models for maximizing the information obtainable from 13C tracer experiments. The approach applied here offers a completely general and comprehensive analysis of carbon tracer experiments where any set of experimental data on the labeling state and extracellular fluxes can be used for the quantification of metabolic fluxes in complex metabolic networks.     

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.     

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.     

High-throughput metabolic flux analysis based on gas chromatography-mass spectrometry derived 13C constraints

13C-constrained flux balancing analysis based on gas chromatography-mass spectrometry data is presented here as a simple and robust method for the estimation of intracellular carbon fluxes. In this approach, the underdetermined system of metabolite balances deduced from stoichiometric relations and measured extracellular rates is complemented with 13C constraints from metabolic flux ratio analysis. Fluxes in central carbon metabolism of exponentially growing Escherichia coli were estimated by 13C-constrained flux balancing from three different 13C-labeled glucose experiments. The best resolution of the network was achieved using 13C constraints derived from [U-13C]glucose and [1-13C]glucose experiments. The corresponding flux estimate was in excellent agreement with a solution that was independently obtained with a comprehensive isotopomer model. This new methodology was also demonstrated to faithfully capture the intracellular flux distribution in E. coli shake flasks and 1-ml deep-well microtiter plates. Due to its simplicity, speed, and robustness, 13C-constrained metabolic flux balancing is promising for routine and high-throughput analysis on a miniaturized scale.     

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     

Quantification of intracellular metabolic fluxes from fractional enrichment and 13C-13C coupling constraints on the isotopomer distribution in labeled biomass components

A method for the quantification of intracellular metabolic flux distributions from steady-state mass balance constraints and from the constraints posed by the measured 13C labeling state of biomass components is presented. Two-dimensional NMR spectroscopy is used to analyze the labeling state of cell protein hydrolysate and cell wall components. No separation of the biomass hydrolysate is required to measure the degree of 13C-13C coupling and the fractional 13C enrichment in various carbon atom positions. A mixture of [1-13C]glucose and uniformly labeled [13C6]glucose is applied to make fractional 13C enrichment data and measurements of the degree of 13C-13C coupling informative with respect to the intracellular flux distribution. Simulation models that calculate the complete isotopomer distribution in biomass components on the basis of isotopomer mapping matrices are used for the estimation of intracellular fluxes by least-squares minimization. The statistical quality of the estimated intracellular flux distributions is assessed by Monte Carlo methods. Principal component analysis is performed on the outcome of the Monte Carlo procedure to identify groups of fluxes that contribute major parts to the total variance in the multiple flux estimations. The methods described are applied to a steady-state culture of a glucoamylase-producing recombinant Aspergillus niger strain.     

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.     

Current status of 13C-metabolic flux analysis and future perspectives

Current ¹³C-metabolic flux analysis methods were reviewed as well as the weakness of the conventional metabolic flux analysis without ¹³C-labeled experiments. Although it has been recognized that ¹³C-labeling technique is powerful in estimating the metabolic fluxes, and the program-based flux analysis is necessary, one may not be confident with the result obtained without experiences and exhaustive trial and errors in practice due to its black box nature. In the present article, we call attention to the importance of investigating the relationships between fluxes and isotopomer or mass isotopomer distributions to understand the mechanism of generating specific isotopomers. Then, the experimental design for the preferred mixture of the specific ¹³C-labeled substrate was discussed. The effect of the reversibility in the bidirectional flux on the isotopomer distribution was also mentioned, and it was shown why the reliability of the bidirectional fluxes becomes lower. Moreover, by noting that recent development of measurement techniques enables us to measure the isotopomer patterns of intracellular metabolites instead of proteinogenic amino acids, it is mentioned that this enables us to estimate the flux changes during time-variant batch culture. Some future perspectives are discussed in relation to the integration of different levels of information in the cell.     

13C isotopomer analysis of glutamate by J-resolved heteronuclear single quantum coherence spectroscopy

13C NMR isotopomer analysis is a powerful method for measuring metabolic fluxes through pathways intersecting in the tricarboxylic acid cycle. However, the inherent insensitivity of 13C NMR spectroscopy makes application of isotopomer analysis to small tissue samples (mouse tissue, human biopsies, or cells grown in tissue culture) problematic. (1)H NMR is intrinsically more sensitive than 13C NMR and can potentially supply the same information via indirect detection of 13C providing that isotopomer information can be preserved. We report here the use of J-resolved HSQC (J-HSQC) for 13C isotopomer analysis of tissue samples. We show that J-HSQC reports isotopomer multiplet patterns identical to those reported by direct 13C detection but with improved sensitivity.     

一种中间代谢途径代谢通量的定量分析方法

以¹³C标记的碳源,用二维核磁共振技术(¹H-¹³C,HMQC)测定代谢中产生的氨基酸标记模式,研究对中间代谢途径胞内代谢通量进行定量分析的方法.通过开发软件包,改进同位素分布的数学模型,提出了反应映射矩阵(RMM)等概念.由简化算法,提高程序的执行效率,建立了定量分析胞内代谢通量的平台.代谢模型涉及了糖酵解途径、磷酸戊糖途径、三羧酸循环、几种回补反应、发酵途径和氨基酸合成途径.     

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.     

Metabolic flux analysis with a comprehensive isotopomer model in Bacillus subtilis

Fluxes in central carbon metabolism of a genetically engineered, riboflavin-producing Bacillus subtilis strain were investigated in glucose-limited chemostat cultures at low (0.11 h(-1)) and high (0.44 h(-1)) dilution rates. Using a mixture of 10% [U-(13)C] and 90% glucose labeled at natural abundance, (13)C-labeling experiments were carried out to provide additional information for metabolic flux balancing. The resulting labeling pattern in the proteinogenic amino acids were analyzed by two-dimensional [(13)C, (1)H] nuclear magnetic resonance (NMR) spectroscopy. To account rigorously for all available data from these experiments, we developed a comprehensive isotopomer model of B. subtilis central metabolism. Using this model, intracellular carbon net and exchange fluxes were estimated on the basis of validated physiological data and biomass composition in combination with 2D NMR data from 45 individual carbon atom spectra in the amino acids. Glucose catabolism proceeded primarily via glycolysis but pentose phosphate pathway fluxes increased with increasing growth rate. Moreover, significant back fluxes from the TCA cycle to the lower part of glycolysis via the gluconeogenic PEP carboxykinase were detected. The malic enzyme reaction, in contrast, was found to be inactive. A thorough statistical analysis was performed to prove the reliability of the isotopomer balance model and the obtained results. Specifically, a chi(2) test was applied to validate the model and the chi-square criterion was used to explore the sensitivity of model predictions to the experimental data.     

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.     

An optimized algorithm for flux estimation from isotopomer distribution in glucose metabolites

MOTIVATION: Analysis of the conversion of (13)C glucose within the metabolic network allows the evaluation of the biochemical fluxes in interconnecting metabolic pathways. Such analyses require solving hundreds of equations with respect to individual isotopomer concentrations, and this assumes applying special software even for constructing the equations. The algorithm, proposed by others could be improved. METHOD: A C-code linked to the program written in Mathematica (Wolfram Research Inc.), constructs and solves differential equations for all isotopomer concentrations, using the general enzyme characteristics (K(m), equilibrium constant, etc.). This code uses innovative algorithm of determination for the isotopomers-products, thus essentially decreasing the computation time. Feasible metabolic fluxes are provided by the parameters of enzyme kinetics found from the data fitting. RESULTS: The software effectively evaluates metabolic fluxes based on the measured isotopomer distribution, as was illustrated by the analysis of glycolysis and pentose phosphate cycle. The mechanism of transketolase and transaldolase catalysis was shown to induce a specific kind of isotopomer re-distribution, which, despite the significance of its effect, usually is not taken into account. AVAILABILITY: The software could be freely downloaded from the site: http://bq.ub.es/bioqint/label_distribution/.     

Numerical bias estimation for mass spectrometric mass isotopomer analysis

Mass spectrometric (MS) isotopomer analysis has become a standard tool for investigating biological systems using stable isotopes. In particular, metabolic flux analysis uses mass isotopomers of metabolic products typically formed from ¹³C-labeled substrates to quantitate intracellular pathway fluxes. In the current work, we describe a model-driven method of numerical bias estimation regarding MS isotopomer analysis. Correct bias estimation is crucial for measuring statistical qualities of measurements and obtaining reliable fluxes. The model we developed for bias estimation corrects a priori unknown systematic errors unique for each individual mass isotopomer peak. For validation, we carried out both computational simulations and experimental measurements. From stochastic simulations, it was observed that carbon mass isotopomer distributions and measurement noise can be determined much more precisely only if signals are corrected for possible systematic errors. By removing the estimated background signals, the residuals resulting from experimental measurement and model expectation became consistent with normality, experimental variability was reduced, and data consistency was improved. The method is useful for obtaining systematic error-free data from ¹³C tracer experiments and can also be extended to other stable isotopes. As a result, the reliability of metabolic fluxes that are typically computed from mass isotopomer measurements is increased.     

Cumulative bondomers: a new concept in flux analysis from 2D [13C,1H] COSY NMR data

A well-established way of determining metabolic fluxes is to measure 2D [(13)C,(1)H] COSY NMR spectra of components of biomass grown on uniformly (13)C-labeled carbon sources. When using the entire set of measured data to simultaneously determine all fluxes in a proposed metabolic network model, the (13)C-labeling distribution in all measured compounds has to be simulated. This requires very large sets of isotopomer or cumomer balances. This article introduces the new concept of bondomers; entities that only vary in the numbers and positions of C-C bonds that have remained intact since the medium substrate molecule entered the metabolism. Bondomers are shown to have many analogies to isotopomers. One of these is that bondomers can be transformed to cumulative bondomers, just like isotopomers can be transformed to cumomers. Similarly to cumomers, cumulative bondomers allow an analytical solution of the entire set of balances describing a metabolic network. The main difference is that cumulative bondomer models are considerably smaller than corresponding cumomer models. This saves computational time, allows easier identifiability analysis, and yields new insights in the information content of 2D [(13)C,(1)H] COSY NMR data. We illustrate the theoretical concepts by means of a realistic example of the glycolytic and pentose phosphate pathways. The combinations of 2D [(13)C,(1)H] COSY NMR data that allow identification of all metabolic fluxes in these pathways are analyzed, and it is found that the NMR data contain less information than was previously expected.     

Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements

Metabolic fluxes, estimated from stable isotope studies, provide a key to quantifying physiology in fields ranging from metabolic engineering to the analysis of human metabolic diseases. A serious drawback of the flux estimation method in current use is that it does not produce confidence limits for the estimated fluxes. Without this information it is difficult to interpret flux results and expand the physiological significance of flux studies. To address this shortcoming we derived analytical expressions of flux sensitivities with respect to isotope measurements and measurement errors. These tools allow the determination of local statistical properties of fluxes and relative importance of measurements. Furthermore, we developed an efficient algorithm to determine accurate flux confidence intervals and demonstrated that confidence intervals obtained with this method closely approximate true flux uncertainty. In contrast, confidence intervals approximated from local estimates of standard deviations are inappropriate due to inherent system nonlinearities. We applied these methods to analyze the statistical significance and confidence of estimated gluconeogenesis fluxes from human studies with [U-13C]glucose as tracer and found true limits for flux estimation in specific human isotopic protocols.     

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.     

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.