Flux estimation using isotopic tracers: common ground for metabolic physiology and metabolic engineering

Metabolic physiologists and metabolic engineers share the need to estimate flux. However, the physiologist often works with systems that do not maintain steady state for long. Many sites cannot be sampled, and calculating mass and isotopic balance for the entire system may not be feasible. To deal with these constraints, metabolic physiologists have developed specialized isotopic techniques that may be unfamiliar to metabolic engineers. A selection of these techniques is presented here, not because it is anticipated that they would be used by engineers exactly as in the physiologist's setting, but because they illustrate novel applications of tracer methodology. Creative engineers may find new adaptations of these tools in metabolic engineering and opportunities to increase redundancy. Physiologists, entering into a dialog with engineers, may see more clearly the potential of comprehensive models and revisit the impediments to a more complete analysis of human metabolic systems.     

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.     

Rational design of 13C-labeling experiments for metabolic flux analysis in mammalian cells

ABSTRACT: BACKGROUND: 13C-Metabolic flux analysis (13C-MFA) is a standard technique to probe cellular metabolism and elucidate in vivo metabolic fluxes. 13C-Tracer selection is an important step in conducting 13C-MFA, however, current methods are restricted to trial-and-error approaches, which commonly focus on an arbitrary subset of the tracer design space. To systematically probe the complete tracer design space, especially for complex systems such as mammalian cells, there is a pressing need for new rational approaches to identify optimal tracers. RESULTS: Recently, we introduced a new framework for optimal 13C-tracer design based on elementary metabolite units (EMU) decomposition, in which a measured metabolite is decomposed into a linear combination of so-called EMU basis vectors. In this contribution, we applied the EMU method to a realistic network model of mammalian metabolism with lactate as the measured metabolite. The method was used to select optimal tracers for the two free fluxes in the system, the oxidative pentose phosphate pathway (oxPPP) flux and anaplerosis by pyruvate carboxylase (PC). Our approach was based on sensitivity analysis of EMU basis vector coefficients with respect to free fluxes. Through efficient grouping of coefficient sensitivities, simple tracer selection rules were derived for high-resolution quantification of the fluxes in the mammalian network model. The approach resulted in a significant reduction of the number of possible tracers and the feasible tracers were evaluated using numerical simulations. Two optimal, novel tracers were identified that have not been previously considered for 13C-MFA of mammalian cells, specifically [2,3,4,5,6-13C]glucose for elucidating oxPPP flux and [3,4-13C]glucose for elucidating PC flux. We demonstrate that 13C-glutamine tracers perform poorly in this system in comparison to the optimal glucose tracers. CONCLUSIONS: In this work, we have demonstrated that optimal tracer design does not need to be a pure simulation-based trial-and-error process; rather, rational insights into tracer design can be gained through the application of the EMU basis vector methodology. Using this approach, rational labeling rules can be established a priori to guide the selection of optimal 13C-tracers for high-resolution flux elucidation in complex metabolic network models.     

Selection of tracers for 13C-metabolic flux analysis using elementary metabolite units (EMU) basis vector methodology

Metabolic flux analysis (MFA) is a powerful technique for elucidating in vivo fluxes in microbial and mammalian systems. A key step in (13)C-MFA is the selection of an appropriate isotopic tracer to observe fluxes in a proposed network model. Despite the importance of MFA in metabolic engineering and beyond, current approaches for tracer experiment design are still largely based on trial-and-error. The lack of a rational methodology for selecting isotopic tracers prevents MFA from achieving its full potential. Here, we introduce a new technique for tracer experiment design based on the concept of elementary metabolite unit (EMU) basis vectors. We demonstrate that any metabolite in a network model can be expressed as a linear combination of so-called EMU basis vectors, where the corresponding coefficients indicate the fractional contribution of the EMU basis vector to the product metabolite. The strength of this approach is the decoupling of substrate labeling, i.e. the EMU basis vectors, from the dependence on free fluxes, i.e. the coefficients. In this work, we demonstrate that flux observability inherently depends on the number of independent EMU basis vectors and the sensitivities of coefficients with respect to free fluxes. Specifically, the number of independent EMU basis vectors places hard limits on how many free fluxes can be determined in a model. This constraint is used as a guide for selecting feasible substrate labeling. In three example models, we demonstrate that by maximizing the number of independent EMU basis vectors the observability of a system is improved. Inspection of sensitivities of coefficients with respect to free fluxes provides additional constraints for proper selection of tracers. The present contribution provides a fresh perspective on an important topic in metabolic engineering, and gives practical guidelines and design principles for a priori selection of isotopic tracers for (13)C-MFA studies.     

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.     

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.     

Possible pitfalls of flux calculations based on (13)C-labeling

Metabolic engineers have enthusiastically adopted the (13)C-labeling technique as a powerful tool for elucidating fluxes in metabolic networks. This tracer technique makes it possible to determine fluxes that are unobservable using only metabolite balances and allows the elimination of doubtful cofactor balances that are indispensable in flux analysis based on metabolite balancing alone. The (13)C-labeling technique, however, relies on a number of assumptions that are not free from uncertainties. Two possible errors in the models that are needed to determine the metabolic fluxes from labeling data are omitted reactions and ignored occurrence of channeling. By means of two representative examples it is shown that these modeling errors may lead to serious errors in the calculated flux distributions despite the use of labeling data. A complicating fact is that the model errors are not always easily detected as poor models may still yield good fits of experimental data. Results of (13)C-labeling experiments should therefore be interpreted with appropriate caution.     

Metabolic fluxes and metabolic engineering

Metabolic engineering is the directed improvement of cellular properties through the modification of specific biochemical reactions or the introduction of new ones, with the use of recombinant DNA technology. As such, metabolic engineering emphasizes metabolic pathway integration and relies on metabolic fluxes as determinants of cell physiology and measures of metabolic control. The combination of analytical methods to quantify fluxes and their control with molecular biological techniques to implement genetic modifications is the essence of metabolic engineering. Strategies for metabolic flux determination are reviewed in this paper and it is shown how metabolic fluxes can be used in the systematic elucidation of metabolic control in the framework of reaction grouping and top-down metabolic control analysis.     

Green pathways: Metabolic network analysis of plant systems

Metabolic engineering of plants with enhanced crop yield and value-added compositional traits is particularly challenging as they probably exhibit the highest metabolic network complexity of all living organisms. Therefore, approaches of plant metabolic network analysis, which can provide systems-level understanding of plant physiology, appear valuable as guidance for plant metabolic engineers. Strongly supported by the sequencing of plant genomes, a number of different experimental and computational methods have emerged in recent years to study plant systems at various levels: from heterotrophic cell cultures to autotrophic entire plants. The present review presents a state-of-the-art toolbox for plant metabolic network analysis. Among the described approaches are different in silico modeling techniques, including flux balance analysis, elementary flux mode analysis and kinetic flux profiling, as well as different variants of experiments with plant systems which use radioactive and stable isotopes to determine in vivo plant metabolic fluxes. The fundamental principles of these techniques, the required data input and the obtained flux information are enriched by technical advices, specific to plants. In addition, pioneering and high-impacting findings of plant metabolic network analysis highlight the potential of the field.     

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.     

Optimization of 13C isotopic tracers for metabolic flux analysis in mammalian cells

Mammalian cells consume and metabolize various substrates from their surroundings for energy generation and biomass synthesis. Glucose and glutamine, in particular, are the primary carbon sources for proliferating cancer cells. While this combination of substrates generates static labeling patterns for use in (13)C metabolic flux analysis (MFA), the inability of single tracers to effectively label all pathways poses an obstacle for comprehensive flux determination within a given experiment. To address this issue we applied a genetic algorithm to optimize mixtures of (13)C-labeled glucose and glutamine for use in MFA. We identified tracer combinations that minimized confidence intervals in an experimentally determined flux network describing central carbon metabolism in tumor cells. Additional simulations were used to determine the robustness of the [1,2-(13)C(2)]glucose/[U-(13)C(5)]glutamine tracer combination with respect to perturbations in the network. Finally, we experimentally validated the improved performance of this tracer set relative to glucose tracers alone in a cancer cell line. This versatile method allows researchers to determine the optimal tracer combination to use for a specific metabolic network, and our findings applied to cancer cells significantly enhance the ability of MFA experiments to precisely quantify fluxes in higher organisms.     

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.     

Systems-level analysis of genome-scalein silico metabolic models using MetaFluxNet

The systems-level analysis of microbes with myriad of heterologous data generated by omics technologies has been applied to improve our understanding of cellular function and physiology and consequently to enhance production of various bioproducts. At the heart of this revolution residesin silico genome-scale metabolic model. In order to fully exploit the power of genome-scale model, a systematic approach employing user-friendly software is required. Metabolic flux analysis of genome-scale metabolic network is becoming widely employed to quantify the flux distribution and validate model-driven hypotheses. Here we describe the development of an upgraded MetaFluxNet which allows (1) construction of metabolic models connected to metabolic databases, (2) calculation of fluxes by metabolic flux analysis, (3) comparative flux analysis with flux-profile visualization, (4) the use of metabolic flux analysis markup language to enable models to be exchanged efficiently, and (5) the exporting of data from constraints-based flux analysis into various formats. MetaFluxNet also allows cellular physiology to be predicted and strategies for strain improvement to be developed from genome-based information on flux distributions. This integrated software environment promises to enhance our understanding on metabolic network at a whole organism level and to establish novel strategies for improving the properties of organisms for various biotechnological applications.     

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

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

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.     

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.     

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.     

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