An elementary metabolite unit (EMU) based method of isotopically nonstationary flux analysis

Nonstationary metabolic flux analysis (NMFA) is at present a very computationally intensive exercise, especially for large reaction networks. We applied elementary metabolite unit (EMU) theory to NMFA, dramatically reducing computational difficulty. We also introduced block decoupling, a new method that systematically and comprehensively divides EMU systems of equations into smaller subproblems to further reduce computational difficulty. These improvements led to a 5000-fold reduction in simulation times, enabling an entirely new and more complicated set of problems to be analyzed with NMFA. We simulated a series of nonstationary and stationary GC/MS measurements for a large E. coli network that was then used to estimate parameters and their associated confidence intervals. We found that fluxes could be successfully estimated using only nonstationary labeling data and external flux measurements. Addition of near-stationary and stationary time points increased the precision of most parameters. Contrary to prior reports, the precision of nonstationary estimates proved to be comparable to the precision of estimates based solely on stationary data. Finally, we applied EMU-based NMFA to experimental nonstationary measurements taken from brown adipocytes and successfully estimated fluxes and some metabolite concentrations. By using NFMA instead of traditional MFA, the experiment required only 6 h instead of 50 (the time necessary for most metabolite labeling to reach 99% of isotopic steady state).     

Dynamic metabolic flux analysis (DMFA): a framework for determining fluxes at metabolic non-steady state

Metabolic flux analysis (MFA) is a key tool for measuring in vivo metabolic fluxes in systems at metabolic steady state. Here, we present a new method for dynamic metabolic flux analysis (DMFA) of systems that are not at metabolic steady state. The advantages of our DMFA method are: (1) time-series of metabolite concentration data can be applied directly for estimating dynamic fluxes, making data smoothing and estimation of average extracellular rates unnecessary; (2) flux estimation is achieved without integration of ODEs, or iterations; (3) characteristic metabolic phases in the fermentation data are identified automatically by the algorithm, rather than selected manually/arbitrarily. We demonstrate the application of the new DMFA framework in three example systems. First, we evaluated the performance of DMFA in a simple three-reaction model in terms of accuracy, precision and flux observability. Next, we analyzed a commercial glucose-limited fed-batch process for 1,3-propanediol production. The DMFA method accurately captured the dynamic behavior of the fed-batch fermentation and identified characteristic metabolic phases. Lastly, we demonstrate that DMFA can be used without any assumed metabolic network model for data reconciliation and detection of gross measurement errors using carbon and electron balances as constraints.     

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.     

应用最大熵原理通过酶控制通量预测突变体的通量分布

在代谢工程和系统生物学领域, 计算机模拟比以往更为有效的应用于生物过程的分析和优化。胞内代谢通量可以用代谢通量分析和基元模式分析来估算。由于测定数据的不足和误差, 以及基元途径的冗余, 经常很难得到准确的代谢通量分布数据。本研究提出一种基于最大熵原理的算法来计算基元模式系数。欠定和不确定条件下, 通过胞外代谢通量数据估算胞内代谢通量分布。为了检验算法的可行性, 对杂交瘤细胞、枯草芽孢杆菌和大肠杆菌的胞内代谢通量分布做了估算。本研究提出的基于最大熵原理的优化算法避免了对细胞状态的生理学假设。与其他目标函数相比, 可以更为可靠和可行的估算胞内代谢通量分布。     

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.     

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.     

Determination of metabolic flux changes during fed-batch cultivation from measurements of intracellular amino acids by LC-MS/MS

Metabolic flux analysis using (13)C-labeled substrates is a well-developed method for investigating cellular behavior in steady-state culture condition. To extend its application, in particular to typical industrial conditions, such as batch and fed-batch cultivations, a novel method of (13)C metabolic flux analysis is proposed. An isotopomer balancing model was developed to elucidate flux distributions in the central metabolism and all amino acids synthetic pathways. A lysine-producing strain of Escherichia coli was cultivated by fed-batch mode in a growth medium containing yeast extract. Mass distribution data was derived from both intracellular free amino acids and proteinogenic amino acids measured by LC-MS/MS, and a correction parameter for the protein turnover effect on the mass distributions of intracellular amino acids was introduced. Metabolic flux distributions were determined in both exponential and stationary phases. Using this new approach, a culture phase-dependent metabolic shift was detected in the fed-batch culture. The approach presented here has great potential for investigating cellular behavior in industrial processes, independent of cultivation modes, metabolic phase and growth medium.     

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.     

Synergy between (13)C-metabolic flux analysis and flux balance analysis for understanding metabolic adaptation to anaerobiosis in E. coli

Genome-based Flux Balance Analysis (FBA) and steady-state isotopic-labeling-based Metabolic Flux Analysis (MFA) are complimentary approaches to predicting and measuring the operation and regulation of metabolic networks. Here, genome-derived models of Escherichia coli (E. coli) metabolism were used for FBA and 13C-MFA analyses of aerobic and anaerobic growths of wild-type E. coli (K-12 MG1655) cells. Validated MFA flux maps reveal that the fraction of maintenance ATP consumption in total ATP production is about 14% higher under anaerobic (51.1%) than aerobic conditions (37.2%). FBA revealed that an increased ATP utilization is consumed by ATP synthase to secrete protons from fermentation. The TCA cycle is shown to be incomplete in aerobically growing cells and submaximal growth is due to limited oxidative phosphorylation. An FBA was successful in predicting product secretion rates in aerobic culture if both glucose and oxygen uptake measurement were constrained, but the most-frequently predicted values of internal fluxes yielded from sampling the feasible space differ substantially from MFA-derived fluxes.     

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.     

A transient isotopic labeling methodology for 13C metabolic flux analysis of photoautotrophic microorganisms

Metabolic flux analysis is increasingly recognized as an integral component of systems biology. However, techniques for experimental measurement of system-wide metabolic fluxes in purely photoautotrophic systems (growing on CO(2) as the sole carbon source) have not yet been developed due to the unique problems posed by such systems. In this paper, we demonstrate that an approach that balances positional isotopic distributions transiently is the only route to obtaining system-wide metabolic flux maps for purely autotrophic metabolism. The outlined transient (13)C-MFA methodology enables measurement of fluxes at a metabolic steady-state, while following changes in (13)C-labeling patterns of metabolic intermediates as a function of time, in response to a step-change in (13)C-label input. We use mathematical modeling of the transient isotopic labeling patterns of central intermediates to assess various experimental requirements for photoautotrophic MFA. This includes the need for intracellular metabolite concentration measurements and isotopic labeling measurements as a function of time. We also discuss photobioreactor design and operation in order to measure fluxes under precise environmental conditions. The transient MFA technique can be used to measure and compare fluxes under different conditions of light intensity, nitrogen sources or compare strains with various mutations or gene deletions and additions.     

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.     

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     

On‐line adaptive metabolic flux analysis: Application to PHB production by mixed microbial cultures

In this work, an algorithm for on‐line adaptive metabolic flux analysis (MFA) is proposed and applied to polyhydroxybutyrate (PHB) production by mixed microbial cultures (MMC). In this process, population dynamics constitutes an important source of perturbation to MFA calculations because some stoichiometric and energetic parameters of the underlying metabolic network are continuously changing over time. The proposed algorithm is based on the application of the observer‐based estimator (OBE) to the central MFA equation, whereby the role of the OBE is to force the accumulation of intracellular metabolites to converge to zero by adjusting the values of unknown network parameters. The algorithm was implemented in a reactor equipped with on‐line analyses of dissolved oxygen and carbon dioxide through respirometric and titrimetric measurements. The oxygen and carbon dioxide fluxes were measured directly, whereas acetate, PHB, and sludge production fluxes were estimated indirectly using a projection of latent structures model calibrated a priori with off‐line measurements. The algorithm was implemented in a way that the network parameters associated with biosynthesis were adjusted on‐line. The algorithm proofed to converge exponentially with the steady state error always below 1 mmol/L. The estimated fluxes passed the consistency index test for experimental error variances as low as 1%. The comparison of measured and estimated respiratory coefficient and of the theoretical and estimated yield of sludge on acetate further confirmed the metabolic consistency of the parameters that were estimated on‐line. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

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.     

Identification of metabolic fluxes in hepatic cells from transient 13C-labeling experiments: Part II. Flux estimation

This contribution addresses the identification of metabolic fluxes and metabolite concentrations in mammalian cells from transient (13)C-labeling experiments. Whilst part I describes experimental set-up and acquisition of required metabolite and (13)C-labeling data, part II focuses on setting up network models and the estimation of intracellular fluxes. Metabolic fluxes were determined in glycolysis, pentose-phosphate pathway (PPP), and citric acid cycle (TCA) in a hepatoma cell line grown in aerobic batch cultures. In glycolytic and PPP metabolite pools isotopic stationarity was observed within 30 min, whereas in the TCA cycle the labeling redistribution did not reach isotopic steady state even within 180 min. In silico labeling dynamics were in accordance with in vivo (13)C-labeling data. Split ratio between glycolysis and PPP was 57%:43%; intracellular glucose concentration was estimated at 101.6 nmol per 10(6) cells. In contrast to isotopic stationary (13)C-flux analysis, transient (13)C-flux analysis can also be applied to industrially relevant mammalian cell fed-batch and batch cultures.     

Analysis of metabolic fluxes for hyaluronic acid (HA) production by Streptococcus zooepidemicus

Summary A detailed metabolic flux analysis (MFA) for hyaluronic acid (HA) production by Streptococcus zooepidemicus was carried out. A metabolic network was constructed for the metabolism of S. zooepidemicus. Fluxes through these reactions were estimated by MFA using accumulation rates of biomass and product, consumption rate of glucose in batch fermentation and dissolved oxygen-controlled fermentation. The changes of the fluxes were observed at different stages of batch fermentation and in different dissolved oxygen tension (DOT)-controlled fermentation processes. The effects of metabolic nodes on HA accumulation under various culture conditions were investigated. The results showed that high concentration of glucose in the medium did not affect metabolic flux distribution, but did influence the uptake rate of glucose. HA synthesis was influenced by DOT via flux redistribution in the principal node. Adenosine triphosphate (ATP) and reduced nicotinamide adenine dinucleotide (NADH) produced in the fermentation process are associated with cell growth and HA synthesis.     

Eukaryotic metabolism: measuring compartment fluxes

Metabolic compartmentation represents a major characteristic of eukaryotic cells. The analysis of compartmented metabolic networks is complicated by separation and parallelization of pathways, intracellular transport, and the need for regulatory systems to mediate communication between interdependent compartments. Metabolic flux analysis (MFA) has the potential to reveal compartmented metabolic events, although it is a challenging task requiring demanding experimental techniques and sophisticated modeling. At present no ready-made solution can be provided to cope with the complexity of compartmented metabolic networks, but new powerful tools are emerging. This review gives an overview of different strategies to approach this issue, focusing on different MFA methods and highlighting the additional information that should be included to improve the outcome of an experiment and associate estimation procedures.     

The thermodynamic meaning of metabolic exchange fluxes

Metabolic flux analysis (MFA) deals with the experimental determination of steady-state fluxes in metabolic networks. An important feature of the ¹³C MFA method is its capability to generate information on both directions of bidirectional reaction steps given by exchange fluxes. The biological interpretation of these exchange fluxes and their relation to thermodynamic properties of the respective reaction steps has never been systematically investigated. As a central result, it is shown here that for a general class of enzyme reaction mechanisms the quotients of net and exchange fluxes measured by ¹³C MFA are coupled to Gibbs energies of the reaction steps. To establish this relation the concept of apparent flux ratios of enzymatic isotope-labeling networks is introduced and some computing rules for these flux ratios are given. Application of these rules reveals a conceptional pitfall of ¹³C MFA, which is the inherent dependency of measured exchange fluxes on the chosen tracer atom. However, it is shown that this effect can be neglected for typical biochemical reaction steps under physiological conditions. In this situation, the central result can be formulated as a two-sided inequality relating fluxes, pool sizes, and standard Gibbs energies. This relation has far-reaching consequences for metabolic flux analysis, quantitative metabolomics, and network thermodynamics.