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.     

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.     

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.     

Evaluation of isotope discrimination in C-based metabolic flux analysis

In a ¹³C experiment for metabolic flux analysis (¹³C MFA), we examined isotope discrimination by measuring the labeling of glucose, amino acids, and hexose monophosphates via mass spectrometry. When Escherichia coli grew in a mix of 20% fully labeled and 80% naturally labeled glucose medium, the cell metabolism favored light isotopes and the measured isotopic ratios (δ¹³C) were in the range of −35 to −92. Glucose transporters might play an important role in such isotopic fractionation. Flux analysis showed that both isotopic discrimination and isotopic impurities in labeled substrates could affect the solution of ¹³C MFA.     

Measuring multiple fluxes through plant metabolic networks

Fluxes through metabolic networks are crucial for cell function, and a knowledge of these fluxes is essential for understanding and manipulating metabolic phenotypes. Labeling provides the key to flux measurement, and in network flux analysis the measurement of multiple fluxes allows a flux map to be superimposed on the metabolic network. The principles and practice of two complementary methods, dynamic and steady-state labeling, are described, emphasizing best practice and illustrating their contribution to network flux analysis with examples taken from the plant and microbial literature. The principal analytical methods for the detection of stable isotopes are also described, as well as the procedures for obtaining flux maps from labeling data. A series of boxes summarizing the key concepts of network flux analysis is provided for convenience.     

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。     

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.     

Efficient Modeling of MS/MS Data for Metabolic Flux Analysis

Metabolic flux analysis (MFA) is a widely used method for quantifying intracellular metabolic fluxes. It works by feeding cells with isotopic labeled nutrients, measuring metabolite isotopic labeling, and computationally interpreting the measured labeling data to estimate flux. Tandem mass-spectrometry (MS/MS) has been shown to be useful for MFA, providing positional isotopic labeling data. Specifically, MS/MS enables the measurement of a metabolite tandem mass-isotopomer distribution, representing the abundance in which certain parent and product fragments of a metabolite have different number of labeled atoms. However, a major limitation in using MFA with MS/MS data is the lack of a computationally efficient method for simulating such isotopic labeling data. Here, we describe the tandemer approach for efficiently computing metabolite tandem mass-isotopomer distributions in a metabolic network, given an estimation of metabolic fluxes. This approach can be used by MFA to find optimal metabolic fluxes, whose induced metabolite labeling patterns match tandem mass-isotopomer distributions measured by MS/MS. The tandemer approach is applied to simulate MS/MS data in a small-scale metabolic network model of mammalian methionine metabolism and in a large-scale metabolic network model of E. coli. It is shown to significantly improve the running time by between two to three orders of magnitude compared to the state-of-the-art, cumomers approach. We expect the tandemer approach to promote broader usage of MS/MS technology in metabolic flux analysis. Implementation is freely available at www.cs.technion.ac.il/~tomersh/methods.html     

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.     

Tandem mass spectrometry: a novel approach for metabolic flux analysis

The goal of metabolic flux analysis (MFA) is the accurate estimation of intracellular fluxes in metabolic networks. Here, we introduce a new method for MFA based on tandem mass spectrometry (MS) and stable-isotope tracer experiments. We demonstrate that tandem MS provides more labeling information than can be obtained from traditional full scan MS analysis and allows estimation of fluxes with better precision. We present a modeling framework that takes full advantage of the additional labeling information obtained from tandem MS for MFA. We show that tandem MS data can be computed for any network model, any compound and any tandem MS fragmentation using linear mapping of isotopomers. The inherent advantages of tandem MS were illustrated in two network models using simulated and literature data. Application of tandem MS increased the observability of the models and improved the precision of estimated fluxes by 2- to 5-fold compared to traditional MS analysis.     

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.     

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 plants using dynamic labeling technique: application to tryptophan biosynthesis in cultured rice cells

The concept and methodology of using dynamic labeling for the MFA of plant metabolic pathways are described, based on a case study to develop a method for the MFA of the tryptophan biosynthetic pathway in cultured rice cells. Dynamic labeling traces the change in the labeling level of a metabolite in a metabolic pathway after the application of a stable isotope-labeled compound. In this study, [1-(13)C] l-serine was fed as a labeling precursor and the labeling level of Trp was determined by using the LC-MS/MS. The value of metabolic flux is determined by fitting a model describing the labeling dynamics of the pathway to the observed labeling data. The biosynthetic flux of Trp in rice suspension cultured cell was determined to be 6.0+/-1.1 nmol (gFWh)(-1). It is also demonstrated that an approximately sixfold increase in the biosynthetic flux of Trp in transgenic rice cells expressing the feedback-insensitive version of anthranilate synthase alpha-subunit gene (OASA1D) resulted in a 45-fold increase in the level of Trp. In this article, the basic workflow for the experiment is introduced and the details of the actual experimental procedures are explained. Future perspectives are also discussed by referring recent advances in the dynamic labeling approach.     

Metabolic flux analysis at ultra short time scale: isotopically non-stationary 13C labeling experiments

A novel approach to (13)C metabolic flux analysis (MFA) is presented using cytosolic metabolite pool sizes and their (13)C labeling data from an isotopically non-stationary (13)C labeling experiment (INST-CLE). The procedure is demonstrated with an E. coli wild type strain grown at fed batch conditions. The intra cellular labeling dynamics are excited by a sudden step increase of the (13)C portion in the substrate feed. Due to unchanged saturation of the substrate uptake system, the metabolic fluxes remain constant during the following sampling time period of only 16s, in which 20 samples are taken by an automated rapid sampling device immediately stopping metabolism by methanol quenching. Subsequent cell disruptive sample preparation and LC-MS/MS enabled simultaneous determination of pool sizes and mass isotopomers of intra cellular metabolites requiring detection limits in the nM range. Based on this data the new computational flux analysis tool 13CFLUX/INST is used to determine the intra cellular fluxes based on a complex carbon labeling network model. The measured data is in good agreement with the model predictions, thus proving the applicability of the new isotopically non-stationary (13)C metabolic flux analysis (INST-(13)C-MFA) concept. Moreover, it is shown that significant new information with respect to flux identifiability, non-measurable pool sizes, data consistency, or large storage pools can be taken from the novel kind of experimental data. This offers new insight into the biological operation of the metabolic network in vivo.     

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.     

Systematic quantification of complex metabolic flux networks using stable isotopes and mass spectrometry.

Metabolic fluxes provide a detailed metric of the cellular metabolic phenotype. Fluxes are estimated indirectly from available measurements and various methods have been developed for this purpose. Of particular interest are methods making use of stable isotopic tracers as they enable the estimation of fluxes at a high resolution. In this paper, we present data validating the use of mass spectrometry (MS) for the quantification of complex metabolic flux networks. In the context of the lysine biosynthesis flux network of Corynebacterium glutamicum (ATCC 21799) under glucose limitation in continuous culture, operating at 0.1 x h(-1) after the introduction of 50% [1-13C]glucose, we deploy a bioreaction network analysis methodology for flux determination from mass isotopomer measurements of biomass hydrolysates, while thoroughly addressing the issues of measurement accuracy, flux observability and data reconciliation. The analysis enabled the resolution of the involved anaplerotic activity of the microorganism using only one labeled substrate, the determination of the range of most of the exchange fluxes and the validation of the flux estimates through satisfaction of redundancies. Specifically, we determined that phosphoenolpyruvate carboxykinase and synthase do not carry flux at these experimental conditions and identified a high futile cycle between oxaloacetate and pyruvate, indicating a highly active in vivo oxaloacetate decarboxylase. Both results validated previous in vitro activity measurements. The flux estimates obtained passed the chi2 statistical test. This is a very important result considering that prior flux analyses of extensive metabolic networks from isotopic measurements have failed criteria of statistical consistency.     

Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions

(13)C metabolic flux analysis (MFA) has become an important and powerful tool for the quantitative analysis of metabolic networks in the framework of metabolic engineering. Isotopically instationary (13)C MFA under metabolic stationary conditions is a promising refinement of classical stationary MFA. It accounts for the experimental requirements of non-steady-state cultures as well as for the shortening of the experimental duration. This contribution extends all computational methods developed for classical stationary (13)C MFA to the instationary situation by using high-performance computing methods. The developed tools allow for the simulation of instationary carbon labeling experiments (CLEs), sensitivity calculation with respect to unknown parameters, fitting of the model to the measured data, statistical identifiability analysis and an optimal experimental design facility. To explore the potential of the new approach all these tools are applied to the central metabolism of Escherichia coli. The achieved results are compared to the outcome of the stationary counterpart, especially focusing on statistical properties. This demonstrates the specific strengths of the instationary method. A new ranking method is proposed making both an a priori and an a posteriori design of the sampling times available. It will be shown that although still not all fluxes are identifiable, the quality of flux estimates can be strongly improved in the instationary case. Moreover, statements about the size of some immeasurable pool sizes can be made.     

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.     

Respirometric 13C flux analysis, Part I: design, construction and validation of a novel multiple reactor system using on-line membrane inlet mass spectrometry

A novel method for (13)C flux analysis based on on-line CO(2) labeling measurements is presented. This so-called respirometric (13)C flux analysis requires multiple parallel (13)C labeling experiments using differently labeled tracer substrates. In Part I of the work, a membrane-inlet mass spectrometry-based measurement system with 6 parallel reactors with each 12 ml liquid volume and associated experimental and computational methods for the respirometric (13)C data acquisition and evaluation are described. Signal dynamics after switching between membrane probes follow exactly first-order allowing extrapolation to steady state. Each measurement cycle involving 3 reactors takes about 2 min. After development of a dynamic calibration method, the suitability and reliability of the analysis was examined with a lysine-producing mutant of Corynebacterium glutamicum using [1-(13)C(1)], [6-(13)C(1)], [1,6-(13)C(2)] glucose. Specific rates of oxygen uptake and CO(2) production were estimated with an error less than +/-0.3 mmol g(-1) h(-1) and had +/-3% to +/-10% deviations between parallel reactors which is primarily caused by inaccuracies in initial biomass concentration. The respiratory quotient could be determined with an uncertainty less than +/-0.02 and varied only +/-3% between reactors. Fractional labeling of CO(2) was estimated with much higher precision of about +/-0.001 to +/-0.005. The detailed statistical analysis suggested that these data should be of sufficient quality to allow physiological interpretation and metabolic flux estimation. The obtained data were applied for the respirometric (13)C metabolic flux analysis in Part II.