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.     

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.     

A review on metabolic pathway analysis with emphasis on isotope labeling approach

The recent progress on metabolic systems engineering was reviewed based on our recent research results in terms of (1) metabolic signal flow diagram approach, (2) metabolic flux analysis (MFA) in particular with intracellular isotopomer distribution using NMR and/or GC-MS, (3) synthesis and optimization of metabolic flux distribution (MFD), (4) modification of MFD by gene manipulation and by controlling culture environment, (5) metabolic control analysis (MCA), (6) design of metabolic regulation structure, and (7) identification of unknown pathways with isotope tracing by NMR. The main characteristics of metabolic engineering is to treat metabolism as a network or entirety instead of individual reactions. The applications were made for poly-3-hydroxybutyrate (PHB) production usingRalstonia eutropha and recombinantEscherichia coli, lactate production by recombinantSaccharomyces cerevisiae, pyruvate production by vitamin auxotrophic yeastToluropsis glabrata, lysine production usingCorynebacterium glutamicum, and energetic analysis of photosynthesic microorganisms such as Cyanobateria. The characteristics of each approach were reviewed with their applications. The approach based on isotope labeling experiments gives reliable and quantitative results for metabolic flux analysis. It should be recognized that the next stage should be toward the investigation of metabolic flux analysis with gene and protein expressions to uncover the metabolic regulation in relation to genetic modification and/or the change in the culture condition.     

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.     

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.     

Improving lycopene production in Escherichia coli by engineering metabolic control

Metabolic engineering has achieved encouraging success in producing foreign metabolites in a variety of hosts. However, common strategies for engineering metabolic pathways focus on amplifying the desired enzymes and deregulating cellular controls. As a result, uncontrolled or deregulated metabolic pathways lead to metabolic imbalance and suboptimal productivity. Here we have demonstrated the second stage of metabolic engineering effort by designing and engineering a regulatory circuit to control gene expression in response to intracellular metabolic states. Specifically, we recruited and altered one of the global regulatory systems in Escherichia coli, the Ntr regulon, to control the engineered lycopene biosynthesis pathway. The artificially engineered regulon, stimulated by excess glycolytic flux through sensing of an intracellular metabolite, acetyl phosphate, controls the expression of two key enzymes in lycopene synthesis in response to flux dynamics. This intracellular control loop significantly enhanced lycopene production while reducing the negative impact caused by metabolic imbalance. Although we demonstrated this strategy for metabolite production, it can be extended into other fields where gene expression must be closely controlled by intracellular physiology, such as gene therapy.     

Evaluation of regression models in metabolic physiology: predicting fluxes from isotopic data without knowledge of the pathway

This study explores the ability of regression models, with no knowledge of the underlying physiology, to estimate physiological parameters relevant for metabolism and endocrinology. Four regression models were compared: multiple linear regression (MLR), principal component regression (PCR), partial least-squares regression (PLS) and regression using artificial neural networks (ANN). The pathway of mammalian gluconeogenesis was analyzed using [U−¹³C]glucose as tracer. A set of data was simulated by randomly selecting physiologically appropriate metabolic fluxes for the 9 steps of this pathway as independent variables. The isotope labeling patterns of key intermediates in the pathway were then calculated for each set of fluxes, yielding 29 dependent variables. Two thousand sets were created, allowing independent training and test data. Regression models were asked to predict the nine fluxes, given only the 29 isotopomers. For large training sets (>50) the artificial neural network model was superior, capturing 95% of the variability in the gluconeogenic flux, whereas the three linear models captured only 75%. This reflects the ability of neural networks to capture the inherent non-linearities of the metabolic system. The effect of error in the variables and the addition of random variables to the data set was considered. Model sensitivities were used to find the isotopomers that most influenced the predicted flux values. These studies provide the first test of multivariate regression models for the analysis of isotopomer flux data. They provide insight for metabolomics and the future of isotopic tracers in metabolic research where the underlying physiology is complex or unknown.We acknowledge the support of NIH Grant DK58533 and the DuPont-MIT Alliance.     

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.     

Elementary metabolite units (EMU): a novel framework for modeling isotopic distributions

Metabolic flux analysis (MFA) has emerged as a tool of great significance for metabolic engineering and mammalian physiology. An important limitation of MFA, as carried out via stable isotope labeling and GC/MS and nuclear magnetic resonance (NMR) measurements, is the large number of isotopomer or cumomer equations that need to be solved, especially when multiple isotopic tracers are used for the labeling of the system. This restriction reduces the ability of MFA to fully utilize the power of multiple isotopic tracers in elucidating the physiology of realistic situations comprising complex bioreaction networks. Here, we present a novel framework for the modeling of isotopic labeling systems that significantly reduces the number of system variables without any loss of information. The elementary metabolite unit (EMU) framework is based on a highly efficient decomposition method that identifies the minimum amount of information needed to simulate isotopic labeling within a reaction network using the knowledge of atomic transitions occurring in the network reactions. The functional units generated by the decomposition algorithm, called EMUs, form the new basis for generating system equations that describe the relationship between fluxes and stable isotope measurements. Isotopomer abundances simulated using the EMU framework are identical to those obtained using the isotopomer and cumomer methods, however, require significantly less computation time. For a typical (13)C-labeling system the total number of equations that needs to be solved is reduced by one order-of-magnitude (100s EMUs vs. 1000s isotopomers). As such, the EMU framework is most efficient for the analysis of labeling by multiple isotopic tracers. For example, analysis of the gluconeogenesis pathway with (2)H, (13)C, and (18)O tracers requires only 354 EMUs, compared to more than two million isotopomers.     

Metabolic profiling by 13C-NMR spectroscopy: [1,2-13C2]glucose reveals a heterogeneous metabolism in human leukemia T cells

Metabolic profiling is defined as the simultaneous assessment of substrate fluxes within and among the different pathways of metabolite synthesis and energy production under various physiological conditions. The use of stable-isotope tracers and the analysis of the distribution of labeled carbons in various intermediates, by both mass spectrometry and NMR spectroscopy, allow the role of several metabolic processes in cell growth and death to be defined. In the present paper we describe the metabolic profiling of Jurkat cells by isotopomer analysis using (13)C-NMR spectroscopy and [1,2-(13)C(2)]glucose as the stable-isotope tracer. The isotopomer analysis of the lactate, alanine, glutamate, proline, serine, glycine, malate and ribose-5-phosphate moiety of nucleotides has allowed original integrated information regarding the pentose phosphate pathway, TCA cycle, and amino acid metabolism in proliferating human leukemia T cells to be obtained. In particular, the contribution of the glucose-6-phosphate dehydrogenase and transketolase activities to phosphoribosyl-pyrophosphate synthesis was evaluated directly by the determination of isotopomers of the [1'-(13)C], [4',5'-(13)C(2)]ribosyl moiety of nucleotides. Furthermore, the relative contribution of the glycolysis and pentose cycle to lactate production was estimated via analysis of lactate isotopomers. Interestingly, pyruvate carboxylase and pyruvate dehydrogenase flux ratios measured by glutamate isotopomers and the production of isotopomers of several metabolites showed that the metabolic processes described could not take place simultaneously in the same macrocompartments (cells). Results revealed a heterogeneous metabolism in an asynchronous cell population that may be interpreted on the basis of different metabolic phenotypes of subpopulations in relation to different cell cycle phases.     

鸟苷产生菌的代谢途径分析

代谢工程要解决的主要问题就是改变某些途径中的碳架物质流量或改变碳架物质流在不同途径中的流量分布,其目标就是修饰初级代谢,将碳架物质流导入目的产物的载流途径以获得产物的最大转化率。利用途径分析方法对枯草芽孢杆菌生产鸟苷的途径进行了分析,建立了3种基础模型,鸟苷理论摩尔产率分别是0．625、0．75和0．667,确定了枯草芽孢杆菌生产鸟苷的最佳途径的通量分布。     

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.     

Quantification and identification of isotopomer distributions of metabolites in crude cell extracts using 1H TOCSY

Isotopomer analysis is a very powerful technique for determining site enrichment with stable isotopes. Such information helps determine the relative flux through metabolic pathways. We have developed ¹H NMR detection methods to isotopomer analysis of human rhabdomyosarcoma cells grown in the presence of uniformly ¹³C-labeled glucose. We show that TOCSY can be used both to identify the isotopomer distributions in a substantial number of key compounds and to determine the site-specific enrichment with good precision. Effects of differential relaxation have been specifically addressed. We have identified and quantified isotopomer distributions in Ala, Lactate, (glycolysis markers), nucleotide riboses (pentose phosphate markers), Asp, Glu and Gln (citric acid cycle and anaplerosis markers) as well as in nucleotide pyrimidine rings. Due to the high sensitivity of proton experiments, a reasonable throughput was achieved using a cold probe on only 3–5 mg dry cell weight. This methodology can be applied to biological system using different labeled precursors to examine their metabolic phenotypes and their response to external perturbations. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

13C代谢流量分析发展30年

13C代谢流量分析(13C metabolic flux analysis,13C-MFA),是通过标记实验分析蛋白氨基酸或胞内代谢物同位素标记异构体的分布情况,从而准确定量胞内反应速率.该技术在系统理解细胞代谢特性、指导代谢工程改造和揭示病理生理学等方面起着重要作用,引起研究者的广泛重视.文中重点综述了代谢流分析30...     

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.     

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.     

Photobioreactor design for isotopic non‐stationary 13C‐metabolic flux analysis (INST 13C‐MFA) under photoautotrophic conditions

Adaptive metabolic behavior of photoautotrophic microorganisms toward genetic and environmental perturbations can be interpreted in a quantitative depiction of carbon flow through a biochemical reaction network using isotopic non‐stationary ¹³C‐metabolic flux analysis (INST ¹³C‐MFA). To evaluate ¹³C‐metabolic flux maps for Chlamydomonas reinhardtii, an original experimental framework was designed allowing rapid, reliable collection of high‐quality isotopomer data against time. It involved (i) a short‐time ¹³C labeling injection device based on mixing control in a torus‐shaped photobioreactor with plug‐flow hydrodynamics allowing a sudden step‐change in the ¹³C proportion in the substrate feed and (ii) a rapid sampling procedure using an automatic fast filtration method coupled to a manual rapid liquid nitrogen quenching step. ¹³C‐substrate labeling enrichment was controlled through the total dissolved inorganic carbon concentration in the pulsed solution. First results were obtained from steady‐state continuous culture measurements allowing the characterization of the kinetics of label incorporation into light‐limited growing cells cultivated in a photobioreactor operating at the maximal biomass productivity for an incident photon flux density of 200 µmol m^?2 s^?1. ¹³C label incorporation was measured for 21 intracellular metabolites using IC‐MS/MS in 58 samples collected across a labeling experiment duration of 7 min. The fastest labeling rate was observed for 2/3‐phosphoglycerate with an apparent isotopic stationary state reached after 300 s. The labeling rate was consistent with the optimized mixing time of about 4.9 s inside the reactor and the shortest reliable sampling period assessed at 5 s. Biotechnol. Bioeng. 2012; 109: 3030–3040. © 2012 Wiley Periodicals, Inc.     

An improved method for statistical analysis of metabolic flux analysis using isotopomer mapping matrices with analytical expressions

Analytical expressions were derived for calculating the sensitivities of isotopomer distribution vectors, the weighted output matrix with respect to the fluxes, and the covariance matrix for the metabolic flux analysis based on isotopomers mapping matrices (IMM). These expressions allow us to implement efficient statistical analysis, avoiding the time-consuming Monte Carlo techniques for estimating the confidence interval of the fluxes. The analytical expressions are also useful in implementing a faster design of experiment, which requires repetitive computation of the covariance matrix that is not straightforward to make in practice with the numerical techniques based on the conventional IMM. The proposed method was applied for analyzing the central carbon metabolism of the mixotrophically cultivated Synechocystis sp. PCC6803, and the confidence intervals of all its fluxes were computed based on the isotopomer distribution measured using NMR and GC-MS. It was found that the best feasible mixture for labeling experiment is 70% unlabeled, 10% [U-13C] and 20% [1,2-13C2] labeled glucose to obtain the most reliable metabolic fluxes.