Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments

Rethinking 13C-metabolic flux analysis - The Bayesian way of flux inference

Metabolic reaction rates (fluxes) play a crucial role in comprehending cellular phenotypes and are essential in areas such as metabolic engineering, biotechnology, and biomedical research. The state-of-the-art technique for estimating fluxes is metabolic flux analysis using isotopic labelling (13C-MFA), which uses a dataset-model combination to determine the fluxes. Bayesian statistical methods are gaining popularity in the field of life sciences, but the use of 13C-MFA is still dominated by conventional best-fit approaches. The slow take-up of Bayesian approaches is, at least partly, due to the unfamiliarity of Bayesian methods to metabolic engineering researchers. To address this unfamiliarity, we here outline similarities and differences between the two approaches and highlight particular advantages of the Bayesian way of flux analysis. With a real-life example, re-analysing a moderately informative labelling dataset of E. coli, we identify situations in which Bayesian methods are advantageous and more informative, pointing to potential pitfalls of current 13C-MFA evaluation approaches. We propose the use of Bayesian model averaging (BMA) for flux inference as a means of overcoming the problem of model uncertainty through its tendency to assign low probabilities to both, models that are unsupported by data, and models that are overly complex. In this capacity, BMA resembles a tempered Ockham's razor. With the tempered razor as a guide, BMA-based 13C-MFA alleviates the problem of model selection uncertainty and is thereby capable of becoming a game changer for metabolic engineering by uncovering new insights and inspiring novel approaches.

High throughput 13C-metabolic flux analysis of 3-hydroxypropionic acid producing Pichia pastoris reveals limited availability of acetyl-CoA and ATP due to tight control of the glycolytic flux

BACKGROUND

Production of 3-hydroxypropionic acid (3-HP) through the malonyl-CoA pathway has yielded promising results in Pichia pastoris (Komagataella phaffii), demonstrating the potential of this cell factory to produce this platform chemical and other acetyl-CoA-derived products using glycerol as a carbon source. However, further metabolic engineering of the original P. pastoris 3-HP-producing strains resulted in unexpected outcomes, e.g., significantly lower product yield and/or growth rate. To gain an understanding on the metabolic constraints underlying these observations, the fluxome (metabolic flux phenotype) of ten 3-HP-producing P. pastoris strains has been characterized using a high throughput ¹³C-metabolic flux analysis platform. Such platform enabled the operation of an optimised workflow to obtain comprehensive maps of the carbon flux distribution in the central carbon metabolism in a parallel-automated manner, thereby accelerating the time-consuming strain characterization step in the design-build-test-learn cycle for metabolic engineering of P. pastoris.

RESULTS

We generated detailed maps of the carbon fluxes in the central carbon metabolism of the 3-HP producing strain series, revealing the metabolic consequences of different metabolic engineering strategies aimed at improving NADPH regeneration, enhancing conversion of pyruvate into cytosolic acetyl-CoA, or eliminating by-product (arabitol) formation. Results indicate that the expression of the POS5 NADH kinase leads to a reduction in the fluxes of the pentose phosphate pathway reactions, whereas an increase in the pentose phosphate pathway fluxes was observed when the cytosolic acetyl-CoA synthesis pathway was overexpressed. Results also show that the tight control of the glycolytic flux hampers cell growth due to limited acetyl-CoA biosynthesis. When the cytosolic acetyl-CoA synthesis pathway was overexpressed, the cell growth increased, but the product yield decreased due to higher growth-associated ATP costs. Finally, the six most relevant strains were also cultured at pH 3.5 to assess the effect of a lower pH on their fluxome. Notably, similar metabolic fluxes were observed at pH 3.5 compared to the reference condition at pH 5.

CONCLUSIONS

This study shows that existing fluoxomics workflows for high-throughput analyses of metabolic phenotypes can be adapted to investigate P. pastoris, providing valuable information on the impact of genetic manipulations on the metabolic phenotype of this yeast. Specifically, our results highlight the metabolic robustness of P. pastoris's central carbon metabolism when genetic modifications are made to increase the availability of NADPH and cytosolic acetyl-CoA. Such knowledge can guide further metabolic engineering of these strains. Moreover, insights into the metabolic adaptation of P. pastoris to an acidic pH have also been obtained, showing the capability of the fluoxomics workflow to assess the metabolic impact of environmental changes.

One-shot 13 C15 N-metabolic flux analysis for simultaneous quantification of carbon and nitrogen flux

Metabolic flux is the final output of cellular regulation and has been extensively studied for carbon but much less is known about nitrogen, which is another important building block for living organisms. For the tuberculosis pathogen, this is particularly important in informing the development of effective drugs targeting the pathogen's metabolism. Here we performed ¹³ C¹⁵ N dual isotopic labeling of Mycobacterium bovis BCG steady state cultures, quantified intracellular carbon and nitrogen fluxes and inferred reaction bidirectionalities. This was achieved by model scope extension and refinement, implemented in a multi-atom transition model, within the statistical framework of Bayesian model averaging (BMA). Using BMA-based ¹³ C¹⁵ N-metabolic flux analysis, we jointly resolve carbon and nitrogen fluxes quantitatively. We provide the first nitrogen flux distributions for amino acid and nucleotide biosynthesis in mycobacteria and establish glutamate as the central node for nitrogen metabolism. We improved resolution of the notoriously elusive anaplerotic node in central carbon metabolism and revealed possible operation modes. Our study provides a powerful and statistically rigorous platform to simultaneously infer carbon and nitrogen metabolism in any biological system.

Using Kinetic Modelling to Infer Adaptations in Saccharomyces cerevisiae Carbohydrate Storage Metabolism to Dynamic Substrate Conditions

Microbial metabolism is strongly dependent on the environmental conditions. While these can be well controlled under laboratory conditions, large-scale bioreactors are characterized by inhomogeneities and consequently dynamic conditions for the organisms. How Saccharomyces cerevisiae response to frequent perturbations in industrial bioreactors is still not understood mechanistically. To study the adjustments to prolonged dynamic conditions, we used published repeated substrate perturbation regime experimental data, extended it with proteomic measurements and used both for modelling approaches. Multiple types of data were combined; including quantitative metabolome, ¹³C enrichment and flux quantification data. Kinetic metabolic modelling was applied to study the relevant intracellular metabolic response dynamics. An existing model of yeast central carbon metabolism was extended, and different subsets of enzymatic kinetic constants were estimated. A novel parameter estimation pipeline based on combinatorial enzyme selection supplemented by regularization was developed to identify and predict the minimum enzyme and parameter adjustments from steady-state to dynamic substrate conditions. This approach predicted proteomic changes in hexose transport and phosphorylation reactions, which were additionally confirmed by proteome measurements. Nevertheless, the modelling also hints at a yet unknown kinetic or regulation phenomenon. Some intracellular fluxes could not be reproduced by mechanistic rate laws, including hexose transport and intracellular trehalase activity during substrate perturbation cycles.

13C metabolic flux analysis: Classification and characterization from the perspective of mathematical modeling and application in physiological research of neural cell

¹³C metabolic flux analysis (¹³C-MFA) has emerged as a forceful tool for quantifying in vivo metabolic pathway activity of different biological systems. This technology plays an important role in understanding intracellular metabolism and revealing patho-physiology mechanism. Recently, it has evolved into a method family with great diversity in experiments, analytics, and mathematics. In this review, we classify and characterize the various branch of ¹³C-MFA from a unified perspective of mathematical modeling. By linking different parts in the model to each step of its workflow, the specific technologies of ¹³C-MFA are put into discussion, including the isotope labeling model (ILM), isotope pattern measuring technique, optimization algorithm and statistical method. Its application in physiological research in neural cell has also been reviewed.

Computational Framework for Machine-Learning-Enabled 13C Fluxomics

¹³C metabolic flux analysis (MFA) has emerged as a powerful tool for synthetic biology. This optimization-based approach suffers long computation time and unstable solutions depending on the initial guess. Here, we develop a machine-learning-based framework for ¹³C fluxomics. Specifically, training and test data sets are generated by metabolic network decomposition and flux sampling, in which flux ratios at metabolic nodes and simulated labeling patterns of metabolites are used as training targets and features, respectively. To improve prediction accuracy and simplify the model, automated processes are developed for flux ratio selection based on solvability and feature screening based on importance. We found that predictive performance can be significantly improved using both amino acids and central carbon metabolites in comparison with amino acids alone. Together with measured external fluxes, the predicted flux ratios determine the mass balance system, yielding global flux distributions. This approach is validated by flux estimation using both simulated and experimental data in comparison with canonical ¹³C MFA. The approach represents a reliable fluxomics method readily applicable to high-throughput metabolic phenotyping, which highlights the advances of intelligent learning algorithms in synthetic biology, specifically in the Test and Learn stage of the Design-Build-Test-Learn cycle.

Glucose metabolism in Pseudomonas aeruginosa is cyclic when producing Polyhydroxyalkanoates and Rhamnolipids

Pseudomonas aeruginosa is an important chassis for production of polyhydroxyalkanoates (PHA) and rhamnolipids (RHL). Advances in the understanding of the biosynthesis metabolism of these biocompounds are crucial for increasing yield. ¹³C-Metabolic Flux Ratio Analysis (¹³C-MFA) is a technique to estimate in vivo metabolic fluxes ratios. PHA and RHL are essentially non-growth associated products of biotechnological interest and both contain hydroxyalkanoates (HAs), whose labeling patterns could be accessed by GC-MS. In this study, to reveal the relative contributions of the Entner-Doudoroff (ED) pathway and the non-oxidative Pentose Phosphate (PP) pathway to PHA and RHL production, ¹³C-MFA was performed in Pseudomonas aeruginosa LFM634 when supplied with labeled glucose. This bacterial strain lacks both functional EMP and the oxidative PP branch. Labeling patterns in HAs were measured. Experiments with [U-¹³C] glucose indicated a low flux though PP pathway. An optimal design of labeling experiment showed that [6-¹³C] glucose would be the best substrate to enable an estimation of the ED flux with high accuracy. Results of experiments performed with this isotope indicated that about two-thirds of glyceraldehyde 3-phosphate is recycled through a cyclic ED architecture, suggesting that P. aeruginosa utilizes that cycle to regulate the NADPH/Acetyl-CoA ratio for PHA and RHL biosynthesis.

Compartment-specific metabolome labeling enables the identification of subcellular fluxes that may serve as promising metabolic engineering targets in CHO cells

¹³C labeling data are used to calculate quantitative intracellular flux patterns reflecting in vivo conditions. Given that approaches for compartment-specific metabolomics exist, the benefits they offer compared to conventional non-compartmented ¹³C flux studies remain to be determined. Using compartment-specific labeling information of IgG1-producing Chinese hamster ovary cells, this study investigated differences of flux patterns exploiting and ignoring metabolic labeling data of cytosol and mitochondria. Although cellular analysis provided good estimates for the majority of intracellular fluxes, half of the mitochondrial transporters, and NADH and ATP balances, severe differences were found for some reactions. Accurate flux estimations of almost all iso-enzymes heavily depended on the sub-cellular labeling information. Furthermore, key discrepancies were found for the mitochondrial carriers v_AGC1 (Aspartate/Glutamate antiporter), v_DIC (Malate/H⁺ symporter), and v_OGC (α-ketoglutarate/malate antiporter). Special emphasis is given to the flux of cytosolic malic enzyme (v_ME): it could not be estimated without the compartment-specific malate labeling information. Interesting enough, cytosolic malic enzyme is an important metabolic engineering target for improving cell-specific IgG1 productivity. Hence, compartment-specific ¹³C labeling analysis serves as prerequisite for related metabolic engineering studies.

Robustifying Experimental Tracer Design for13C-Metabolic Flux Analysis

¹³C metabolic flux analysis (MFA) has become an indispensable tool to measure metabolic reaction rates (fluxes) in living organisms, having an increasingly diverse range of applications. Here, the choice of the¹³C labeled tracer composition makes the difference between an information-rich experiment and an experiment with only limited insights. To improve the chances for an informative labeling experiment, optimal experimental design approaches have been devised for¹³C-MFA, all relying on some a priori knowledge about the actual fluxes. If such prior knowledge is unavailable, e.g., for research organisms and producer strains, existing methods are left with a chicken-and-egg problem. In this work, we present a general computational method, termed robustified experimental design (R-ED), to guide the decision making about suitable tracer choices when prior knowledge about the fluxes is lacking. Instead of focusing on one mixture, optimal for specific flux values, we pursue a sampling based approach and introduce a new design criterion, which characterizes the extent to which mixtures are informative in view of all possible flux values. The R-ED workflow enables the exploration of suitable tracer mixtures and provides full flexibility to trade off information and cost metrics. The potential of the R-ED workflow is showcased by applying the approach to the industrially relevant antibiotic producer Streptomyces clavuligerus, where we suggest informative, yet economic labeling strategies.

Utilizing tandem mass spectrometry for metabolic flux analysis

Metabolic flux analysis (MFA) aims at revealing the metabolic reaction rates in a complex biochemical network. To do so, MFA uses the input of stable isotope labeling patterns of the intracellular metabolites. Elementary metabolic unit (EMU) is the computational framework to simulate the metabolite labeling patterns in a network, which was originally designed for simulating mass isotopomer distributions (MIDs) at the MS1 level. Recently, the EMU framework is expanded to simulate tandem mass spectrometry data. Tandem mass spectrometry has emerged as a new experimental approach to provide information on the positional isotope labeling of metabolites and therefore greatly improves the precision of MFA. In this review, we will discuss the new EMU framework that can accommodate the tandem mass isotopomer distributions (TMIDs) data. We will also analyze the improvement on the MFA precision by using TMID. Our analysis shows that combining the MIDs of the parent and daughter ions and the TMID for the MFA is more powerful than using TMID alone.

Validity of natural isotope abundance correction for metabolic flux analysis

A pervasive issue in stable isotope tracing and metabolic flux analysis is the presence of naturally occurring isotopes such as ¹³C. For mass isotopomer distributions (MIDs) measured by mass spectrometry, it is common practice to correct for natural occurrence of isotopes within metabolites of interest using a linear transform based on binomial distributions. The resulting corrected MIDs are often used to fit metabolic network models and infer metabolic fluxes, which implicitly assumes that corrected MIDs will yield the same flux solution as the actual observed MIDs. Although this assumption can be empirically verified in special cases by simulation studies, there seems to be no published proof of this important property for the general case. In this paper, we prove that this property holds for the case of noise-free MID data obtained at steady state. On the other hand, for noisy MID data, the flux solution will generally differ between the two representations. These results provide a theoretical foundation for the common practice of MID correction in metabolic flux analysis.

Modeling Plant Metabolism: From Network Reconstruction to Mechanistic Models

Mathematical modeling of plant metabolism enables the plant science community to understand the organization of plant metabolism, obtain quantitative insights into metabolic functions, and derive engineering strategies for manipulation of metabolism. Among the various modeling approaches, metabolic pathway analysis can dissect the basic functional modes of subsections of core metabolism, such as photorespiration, and reveal how classical definitions of metabolic pathways have overlapping functionality. In the many studies using constraint-based modeling in plants, numerous computational tools are currently available to analyze large-scale and genome-scale metabolic networks. For ¹³C-metabolic flux analysis, principles of isotopic steady state have been used to study heterotrophic plant tissues, while nonstationary isotope labeling approaches are amenable to the study of photoautotrophic and secondary metabolism. Enzyme kinetic models explore pathways in mechanistic detail, and we discuss different approaches to determine or estimate kinetic parameters. In this review, we describe recent advances and challenges in modeling plant metabolism.

Analysing central metabolism in ultra-high resolution: At the crossroads of carbon and nitrogen

BACKGROUND

Cancer cell metabolism can be characterised by adaptive metabolic alterations, which support abnormal proliferative cell growth with high energetic demand. De novo nucleotide biosynthesis is essential for providing nucleotides for RNA and DNA synthesis, and drugs targeting this biosynthetic pathway have proven to be effective anticancer therapeutics. Nevertheless, cancers are often able to circumvent chemotherapeutic interventions and become therapy resistant. Our understanding of the changing metabolic profile of the cancer cell and the mode of action of therapeutics is dependent on technological advances in biochemical analysis.

SCOPE OF REVIEW

This review begins with information about carbon- and nitrogen-donating pathways to build purine and pyrimidine moieties in the course of nucleotide biosynthesis. We discuss the application of stable isotope resolved metabolomics to investigate the dynamics of cancer cell metabolism and outline the benefits of high-resolution accurate mass spectrometry, which enables multiple tracer studies.

CONCLUSION

With the technological advances in mass spectrometry that allow for the analysis of the metabolome in high resolution, the application of stable isotope resolved metabolomics has become an important technique in the investigation of biological processes. The literature in the area of isotope labelling is dominated by 13C tracer studies. Metabolic pathways have to be considered as complex interconnected networks and should be investigated as such. Moving forward to simultaneous tracing of different stable isotopes will help elucidate the interplay between carbon and nitrogen flow and the dynamics of de novo nucleotide biosynthesis within the cell.

Dynamic 13C Flux Analysis Captures the Reorganization of Adipocyte Glucose Metabolism in Response to Insulin

Cellular metabolism is dynamic, but quantifying non-steady metabolic fluxes by stable isotope tracers presents unique computational challenges. Here, we developed an efficient 13C-tracer dynamic metabolic flux analysis (13C-DMFA) framework for modeling central carbon fluxes that vary over time. We used B-splines to generalize the flux parameterization system and to improve the stability of the optimization algorithm. As proof of concept, we investigated how 3T3-L1 cultured adipocytes acutely metabolize glucose in response to insulin. Insulin rapidly stimulates glucose uptake, but intracellular pathways responded with differing speeds and magnitudes. Fluxes in lower glycolysis increased faster than those in upper glycolysis. Glycolysis fluxes rose disproportionally larger and faster than the tricarboxylic acid cycle, with lactate a primary glucose end product. The uncovered array of flux dynamics suggests that glucose catabolism is additionally regulated beyond uptake to help shunt glucose into appropriate pathways. This work demonstrates the value of using dynamic intracellular fluxes to understand metabolic function and pathway regulation.

Reversible jump MCMC for multi-model inference in Metabolic Flux Analysis

Motivation

The validity of model based inference, as used in systems biology, depends on the underlying model formulation. Often, a vast number of competing models is available, that are built on different assumptions, all consistent with the existing knowledge about the studied biological phenomenon. As a remedy for this, Bayesian Model Averaging (BMA) facilitates parameter and structural inferences based on multiple models simultaneously. However, in fields where a vast number of alternative, high-dimensional and non-linear models are involved, the BMA-based inference task is computationally very challenging.

Results

Here we use BMA in the complex setting of Metabolic Flux Analysis (MFA) to infer whether potentially reversible reactions proceed uni- or bidirectionally, using 13C labeling data and metabolic networks. BMA is applied on a large set of candidate models with differing directionality settings, using a tailored multi-model Markov Chain Monte Carlo (MCMC) approach. The applicability of our algorithm is shown by inferring the in vivo probability of reaction bidirectionalities in a realistic network setup, thereby extending the scope of 13C MFA from parameter to structural inference.

Supplementary information

Supplementary data are available at Bioinformatics online.

Unveiling the metabolic fate of monosaccharides in cell membranes with glycomic and glycoproteomic analyses

Cell membrane protein glycosylation is dependent on the metabolic state of the cell as well as exogenous nutrients available. Although the metabolism and interconversion of monosaccharides have been well-studied, their incorporation into cell surface glycans and their corresponding glycoproteins remains relatively unknown. In this study, we developed a method to investigate quantitatively the incorporation pathways of dietary saccharides into specific glycans and glycoproteins on the cell membrane by treating intestinal Caco-2 and hepatic KKU-M213 cells with ¹³C-labeled monosaccharides and characterizing the resulting cell surface glycans and glycopeptides by LC-MS/MS. Time-course studies using uniformly labeled glucose revealed that the rate of incorporation was both glycan-specific and protein-dependent. Comparative studies using different dietary saccharides and multiple cell lines revealed the variance of monosaccharide utilization and interconversion in different tissues and organisms. The robust isotope-labeling and glycan profiling methods can provide a useful tool for differentiating glycosylation pathways and enhance the understanding of how dietary sugar intake affects health.

The Design of FluxML: A Universal Modeling Language for 13C Metabolic Flux Analysis

¹³C metabolic flux analysis (MFA) is the method of choice when a detailed inference of intracellular metabolic fluxes in living organisms under metabolic quasi-steady state conditions is desired. Being continuously developed since two decades, the technology made major contributions to the quantitative characterization of organisms in all fields of biotechnology and health-related research. ¹³C MFA, however, stands out from other "-omics sciences," in that it requires not only experimental-analytical data, but also mathematical models and a computational toolset to infer the quantities of interest, i.e., the metabolic fluxes. At present, these models cannot be conveniently exchanged between different labs. Here, we present the implementation-independent model description language FluxML for specifying ¹³C MFA models. The core of FluxML captures the metabolic reaction network together with atom mappings, constraints on the model parameters, and the wealth of data configurations. In particular, we describe the governing design processes that shaped the FluxML language. We demonstrate the utility of FluxML to represent many contemporary experimental-analytical requirements in the field of ¹³C MFA. The major aim of FluxML is to offer a sound, open, and future-proof language to unambiguously express and conserve all the necessary information for model re-use, exchange, and comparison. Along with FluxML, several powerful computational tools are supplied for easy handling, but also to maintain a maximum of flexibility. Altogether, the FluxML collection is an "all-around carefree package" for ¹³C MFA modelers. We believe that FluxML improves scientific productivity as well as transparency and therewith contributes to the efficiency and reproducibility of computational modeling efforts in the field of ¹³C MFA.

A Pareto approach to resolve the conflict between information gain and experimental costs: Multiple-criteria design of carbon labeling experiments

Science revolves around the best way of conducting an experiment to obtain insightful results. Experiments with maximal information content can be found by computational experimental design (ED) strategies that identify optimal conditions under which to perform the experiment. Several criteria have been proposed to measure the information content, each emphasizing different aspects of the design goal, i.e., reduction of uncertainty. Where experiments are complex or expensive, second sight is at the budget governing the achievable amount of information. In this context, the design objectives cost and information gain are often incommensurable, though dependent. By casting the ED task into a multiple-criteria optimization problem, a set of trade-off designs is derived that approximates the Pareto-frontier which is instrumental for exploring preferable designs. In this work, we present a computational methodology for multiple-criteria ED of information-rich experiments that accounts for virtually any set of design criteria. The methodology is implemented for the case of ¹³C metabolic flux analysis (MFA), which is arguably the most expensive type among the ‘omics’ technologies, featuring dozens of design parameters (tracer composition, analytical platform, measurement selection etc.). Supported by an innovative visualization scheme, we demonstrate with two realistic showcases that the use of multiple criteria reveals deep insights into the conflicting interplay between information carriers and cost factors that are not amendable to single-objective ED. For instance, tandem mass spectrometry turns out as best-in-class with respect to information gain, while it delivers this information quality cheaper than the other, routinely applied analytical technologies. Therewith, our Pareto approach to ED offers the investigator great flexibilities in the conception phase of a study to balance costs and benefits.

Designing experiments is obligatory in the biosciences to valorize their scientific outcome. When the experiments are expensive, unfortunately, in practice often the costs emerge to be showstoppers. In this situation the question arises: How to get the most out of the experiment for your invest in terms of time and money? We approach this question by formulating the design task as a multiple-criteria optimization problem. Its solution produces a set of Pareto-optimal design proposals that feature the trade-off between information gain, as measured by different metrics, and the costs. Then, exploration of the design proposals allows us to make the best decision on information-economic experiments under given circumstances. Implemented in the field of isotope-based metabolic flux analysis, practical application of the Pareto approach provides detailed insight into the tight interplay of plenty of information carriers and cost factors. Supported by an innovative tailored visual representation scheme, the investigator is enabled to explore the options before conducting the experiment. With a practical showcase at hand, our computational study highlights the benefits of incorporating multiple information criteria apart from the costs, balancing the shortcomings of conventional single-objective experimental design strategies.

Isotopically nonstationary metabolic flux analysis (INST-MFA): putting theory into practice

Typically, ¹³C flux analysis relies on assumptions of both metabolic and isotopic steady state. If metabolism is steady but isotope labeling is not allowed to fully equilibrate, isotopically nonstationary metabolic flux analysis (INST-MFA) can be used to estimate fluxes. This requires solution of differential equations that describe the time-dependent labeling of network metabolites, while iteratively adjusting the flux and pool size parameters to match the transient labeling measurements. INST-MFA holds a number of unique advantages over approaches that rely solely upon steady-state isotope enrichments. First, INST-MFA can be applied to estimate fluxes in autotrophic systems, which consume only single-carbon substrates. Second, INST-MFA is ideally suited to systems that label slowly due to the presence of large intermediate pools or pathway bottlenecks. Finally, INST-MFA provides increased measurement sensitivity to estimate reversible exchange fluxes and metabolite pool sizes, which represents a potential framework for integrating metabolomic analysis with ¹³C flux analysis. This review highlights the unique capabilities of INST-MFA, describes newly available software tools that automate INST-MFA calculations, presents several practical examples of recent INST-MFA applications, and discusses the technical challenges that lie ahead.

13C-assisted metabolic flux analysis to investigate heterotrophic and mixotrophic metabolism in Cupriavidus necator H16

INTRODUCTION

Cupriavidus necator H16 is a gram-negative bacterium, capable of lithoautotrophic growth by utilizing hydrogen as an energy source and fixing carbon dioxide (CO2) through Calvin-Benson-Bassham (CBB) cycle. The potential to utilize synthesis gas (Syngas) and the prospects of rerouting carbon from polyhydroxybutyrate synthesis to value-added compounds makes C. necator an excellent chassis for industrial application.

OBJECTIVES

In the context of lack of sufficient quantitative information of the metabolic pathways and to advance in rational metabolic engineering for optimized product synthesis in C. necator H16, we carried out a metabolic flux analysis based on steady-state 13C-labelling.

METHODS

In this study, steady-state carbon labelling experiments, using either d-[1-13C]fructose or [1,2-13C]glycerol, were undertaken to investigate the carbon flux through the central carbon metabolism in C. necator H16 under heterotrophic and mixotrophic growth conditions, respectively.

RESULTS

We found that the CBB cycle is active even under heterotrophic condition, and growth is indeed mixotrophic. While Entner-Doudoroff (ED) pathway is shown to be the major route for sugar degradation, tricarboxylic acid (TCA) cycle is highly active in mixotrophic condition. Enhanced flux is observed in reductive pentose phosphate pathway (redPPP) under the mixotrophic condition to supplement the precursor requirement for CBB cycle. The flux distribution was compared to the mRNA abundance of genes encoding enzymes involved in key enzymatic reactions of the central carbon metabolism.

CONCLUSION

This study leads the way to establishing 13C-based quantitative fluxomics for rational pathway engineering in C. necator H16.

Understanding metabolism with flux analysis: From theory to application

Quantitative and qualitative knowledge of metabolic rates (i.e. fluxes) over a metabolic network and in specific cellular compartments gives insights into the regulation of metabolism and helps to understand the contribution of metabolic alterations to pathology. In this review we introduce methodology to resolve metabolic fluxes from stable isotope labeling and relevant techniques in model development, model simplification, flux uncertainty analysis and experimental design that together is termed metabolic flux analysis. Finally we discuss applications using metabolic flux analysis to elucidate mechanisms pertinent to tumor cell metabolism. We hope that this review gives the readers a brief introduction of how flux analysis is conducted, how technical issues related to it are addressed, and how its application has contributed to our knowledge of tumor cell metabolism.

A comprehensive evaluation of constraining amino acid biosynthesis in compartmented models for metabolic flux analysis

Recent advances in the availability and applicability of genetic tools for non-conventional yeasts have raised high hopes regarding the industrial applications of such yeasts; however, quantitative physiological data on these yeasts, including intracellular flux distributions, are scarce and have rarely aided in the development of novel yeast applications. The compartmentation of eukaryotic cells adds to model complexity. Model constraints are ideally based on biochemical evidence, which is rarely available for non-conventional yeast and eukaryotic cells. A small-scale model for ¹³C-based metabolic flux analysis of central yeast carbon metabolism was developed that is universally valid and does not depend on localization information regarding amino acid anabolism. The variable compartmental origin of traced metabolites is a feature that allows application of the model to yeasts with uncertain genomic and transcriptional backgrounds. The presented test case includes the baker's yeast Saccharomyces cerevisiae and the methylotrophic yeast Hansenula polymorpha. Highly similar flux solutions were computed using either a model with undefined pathway localization or a model with constraints based on curated (S. cerevisiae) or computationally predicted (H. polymorpha) localization information, while false solutions were found with incorrect localization constraints. These results indicate a potentially adverse effect of universally assuming Saccharomyces-like constraints on amino acid biosynthesis for non-conventional yeasts and verify the validity of neglecting compartmentation constraints using a small-scale metabolic model. The model was specifically designed to investigate the intracellular metabolism of wild-type yeasts under various growth conditions but is also expected to be useful for computing fluxes of other eukaryotic cells.

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Compartmentation influences computed intracellular fluxes.

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Improper localization constraints potentially produce false flux solutions.

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Minimal compartmentation constraints result in high-quality flux computations.

Metabolic flux analysis of heterotrophic growth in Chlamydomonas reinhardtii

Despite the wealth of knowledge available for C. reinhardtii, the central metabolic fluxes of growth on acetate have not yet been determined. In this study, ¹³C-metabolic flux analysis (¹³C-MFA) was used to determine and quantify the metabolic pathways of primary metabolism in C. reinhardtii cells grown under heterotrophic conditions with acetate as the sole carbon source. Isotopic labeling patterns of compartment specific biomass derived metabolites were used to calculate the fluxes. It was found that acetate is ligated with coenzyme A in the three subcellular compartments (cytosol, mitochondria and plastid) included in the model. Two citrate synthases were found to potentially be involved in acetyl-coA metabolism; one localized in the mitochondria and the other acting outside the mitochondria. Labeling patterns demonstrate that Acetyl-coA synthesized in the plastid is directly incorporated in synthesis of fatty acids. Despite having a complete TCA cycle in the mitochondria, it was also found that a majority of the malate flux is shuttled to the cytosol and plastid where it is converted to oxaloacetate providing reducing equivalents to these compartments. When compared to predictions by flux balance analysis, fluxes measured with ¹³C-MFA were found to be suboptimal with respect to biomass yield; C. reinhardtii sacrifices biomass yield to produce ATP and reducing equivalents.

The importance of accurately correcting for the natural abundance of stable isotopes

The use of isotopically labeled tracer substrates is an experimental approach for measuring in vivo and in vitro intracellular metabolic dynamics. Stable isotopes that alter the mass but not the chemical behavior of a molecule are commonly used in isotope tracer studies. Because stable isotopes of some atoms naturally occur at non-negligible abundances, it is important to account for the natural abundance of these isotopes when analyzing data from isotope labeling experiments. Specifically, a distinction must be made between isotopes introduced experimentally via an isotopically labeled tracer and the isotopes naturally present at the start of an experiment. In this tutorial review, we explain the underlying theory of natural abundance correction of stable isotopes, a concept not always understood by metabolic researchers. We also provide a comparison of distinct methods for performing this correction and discuss natural abundance correction in the context of steady state 13C metabolic flux, a method increasingly used to infer intracellular metabolic flux from isotope experiments.

Exo-MFA - A 13C metabolic flux analysis framework to dissect tumor microenvironment-secreted exosome contributions towards cancer cell metabolism

Dissecting the pleiotropic roles of tumor micro-environment (TME) on cancer progression has been brought to the foreground of research on cancer pathology. Extracellular vesicles such as exosomes, transport proteins, lipids, and nucleic acids, to mediate intercellular communication between TME components and have emerged as candidates for anti-cancer therapy. We previously reported that cancer-associated fibroblast (CAF) derived exosomes (CDEs) contain metabolites in their cargo that are utilized by cancer cells for central carbon metabolism and promote cancer growth. However, the metabolic fluxes involved in donor cells towards packaging of metabolites in extracellular vesicles and exosome-mediated metabolite flux upregulation in recipient cells are still not known. Here, we have developed a novel empirical and computational technique, exosome-mediated metabolic flux analysis (Exo-MFA) to quantify flow of cargo from source cells to recipient cells via vesicular transport. Our algorithm, which is based on ¹³C metabolic flux analysis, successfully predicts packaging fluxes to metabolite cargo in CAFs, dynamic changes in rate of exosome internalization by cancer cells, and flux of cargo release over time. We find that cancer cells internalize exosomes rapidly leading to depletion of extracellular exosomes within 24h. However, metabolite cargo significantly alters intracellular metabolism over the course of 24h by regulating glycolysis pathway fluxes via lactate supply. Furthermore, it can supply up to 35% of the TCA cycle fluxes by providing TCA intermediates and glutamine. Our algorithm will help gain insight into (i) metabolic interactions in multicellular systems (ii) biogenesis of extracellular vesicles and their differential packaging of cargo under changing environments, and (iii) regulation of cancer cell metabolism by its microenvironment.

Synergizing 13C Metabolic Flux Analysis and Metabolic Engineering for Biochemical Production

Metabolic engineering of industrial microorganisms to produce chemicals, fuels, and drugs has attracted increasing interest as it provides an environment-friendly and renewable route that does not depend on depleting petroleum sources. However, the microbial metabolism is so complex that metabolic engineering efforts often have difficulty in achieving a satisfactory yield, titer, or productivity of the target chemical. To overcome this challenge, ¹³C Metabolic Flux Analysis (¹³C-MFA) has been developed to investigate rigorously the cell metabolism and quantify the carbon flux distribution in central metabolic pathways. In the past decade, ¹³C-MFA has been widely used in academic labs and the biotechnology industry to pinpoint the key issues related to microbial-based chemical production and to guide the development of the appropriate metabolic engineering strategies for improving the biochemical production. In this chapter we introduce the basics of ¹³C-MFA and illustrate how ¹³C-MFA has been applied to synergize with metabolic engineering to identify and tackle the rate-limiting steps in biochemical production.

Quantification of Microbial Phenotypes

Metabolite profiling technologies have improved to generate close to quantitative metabolomics data, which can be employed to quantitatively describe the metabolic phenotype of an organism. Here, we review the current technologies available for quantitative metabolomics, present their advantages and drawbacks, and the current challenges to generate fully quantitative metabolomics data. Metabolomics data can be integrated into metabolic networks using thermodynamic principles to constrain the directionality of reactions. Here we explain how to estimate Gibbs energy under physiological conditions, including examples of the estimations, and the different methods for thermodynamics-based network analysis. The fundamentals of the methods and how to perform the analyses are described. Finally, an example applying quantitative metabolomics to a yeast model by 13C fluxomics and thermodynamics-based network analysis is presented. The example shows that (1) these two methods are complementary to each other; and (2) there is a need to take into account Gibbs energy errors. Better estimations of metabolic phenotypes will be obtained when further constraints are included in the analysis.

Interaction of storage carbohydrates and other cyclic fluxes with central metabolism: A quantitative approach by non-stationary 13C metabolic flux analysis

13C labeling experiments in aerobic glucose limited cultures of Saccharomyces cerevisiae at four different growth rates (0.054; 0.101, 0.207, 0.307 h-1) are used for calculating fluxes that include intracellular cycles (e.g., storage carbohydrate cycles, exchange fluxes with amino acids), which are rearranged depending on the growth rate. At low growth rates the impact of the storage carbohydrate recycle is relatively more significant than at high growth rates due to a higher concentration of these materials in the cell (up to 560-fold) and higher fluxes relative to the glucose uptake rate (up to 16%). Experimental observations suggest that glucose can be exported to the extracellular space, and that its source is related to storage carbohydrates, most likely via the export and subsequent extracellular breakdown of trehalose. This hypothesis is strongly supported by 13C-labeling experimental data, measured extracellular trehalose, and the corresponding flux estimations.

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.

Conserved moieties are transferred between metabolites in internal reactions of a metabolic network but are not synthesised, degraded or exchanged with the environment. The total amount of a conserved moiety in the metabolic network is therefore constant over time. Metabolites that share a conserved moiety have interdependent concentrations because their total amount is constant. Identification of conserved moieties results in a concise description of all concentration dependencies in a metabolic network. The problem of identifying conserved moieties has previously been formulated in terms of the stoichiometry of metabolic reactions. Methods based on this formulation are computationally intractable for large networks. We show that reaction stoichiometry alone gives insufficient information to identify conserved moieties. By first incorporating additional data on the fate of atoms in metabolic reactions, we developed and implemented a computationally tractable algorithm to identify conserved moieties and their atomic structure.

SUMOFLUX: A Generalized Method for Targeted 13C Metabolic Flux Ratio Analysis

Metabolic fluxes are a cornerstone of cellular physiology that emerge from a complex interplay of enzymes, carriers, and nutrients. The experimental assessment of in vivo intracellular fluxes using stable isotopic tracers is essential if we are to understand metabolic function and regulation. Flux estimation based on 13C or 2H labeling relies on complex simulation and iterative fitting; processes that necessitate a level of expertise that ordinarily preclude the non-expert user. To overcome this, we have developed SUMOFLUX, a methodology that is broadly applicable to the targeted analysis of 13C-metabolic fluxes. By combining surrogate modeling and machine learning, we trained a predictor to specialize in estimating flux ratios from measurable 13C-data. SUMOFLUX targets specific flux features individually, which makes it fast, user-friendly, applicable to experimental design and robust in terms of experimental noise and exchange flux magnitude. Collectively, we predict that SUMOFLUX's properties realistically pave the way to high-throughput flux analyses.

Bridging the gap between non-targeted stable isotope labeling and metabolic flux analysis

BACKGROUND

Metabolism gained increasing interest for the understanding of diseases and to pinpoint therapeutic intervention points. However, classical metabolomics techniques only provide a very static view on metabolism. Metabolic flux analysis methods, on the other hand, are highly targeted and require detailed knowledge on metabolism beforehand.

RESULTS

We present a novel workflow to analyze non-targeted metabolome-wide stable isotope labeling data to detect metabolic flux changes in a non-targeted manner. Furthermore, we show how similarity-analysis of isotopic enrichment patterns can be used for pathway contextualization of unidentified compounds. We illustrate our approach with the analysis of changes in cellular metabolism of human adenocarcinoma cells in response to decreased oxygen availability. Starting without a priori knowledge, we detect metabolic flux changes, leading to an increased glutamine contribution to acetyl-CoA production, reveal biosynthesis of N-acetylaspartate by N-acetyltransferase 8-like (NAT8L) in lung cancer cells and show that NAT8L silencing inhibits proliferation of A549, JHH-4, PH5CH8, and BEAS-2B cells.

CONCLUSIONS

Differential stable isotope labeling analysis provides qualitative metabolic flux information in a non-targeted manner. Furthermore, similarity analysis of enrichment patterns provides information on metabolically closely related compounds. N-acetylaspartate and NAT8L are important players in cancer cell metabolism, a context in which they have not received much attention yet.

Natural isotope correction of MS/MS measurements for metabolomics and (13)C fluxomics

Fluxomics and metabolomics are crucial tools for metabolic engineering and biomedical analysis to determine the in vivo cellular state. Especially, the application of (13)C isotopes allows comprehensive insights into the functional operation of cellular metabolism. Compared to single MS, tandem mass spectrometry (MS/MS) provides more detailed and accurate measurements of the metabolite enrichment patterns (tandem mass isotopomers), increasing the accuracy of metabolite concentration measurements and metabolic flux estimation. MS-type data from isotope labeling experiments is biased by naturally occurring stable isotopes (C, H, N, O, etc.). In particular, GC-MS(/MS) requires derivatization for the usually non-volatile intracellular metabolites introducing additional natural isotopes leading to measurements that do not directly represent the carbon labeling distribution. To make full use of LC- and GC-MS/MS mass isotopomer measurements, the influence of natural isotopes has to be eliminated (corrected). Our correction approach is analyzed for the two most common applications; (13)C fluxomics and isotope dilution mass spectrometry (IDMS) based metabolomics. Natural isotopes can have an impact on the calculated flux distribution which strongly depends on the substrate labeling and the actual flux distribution. Second, we show that in IDMS based metabolomics natural isotopes lead to underestimated concentrations that can and should be corrected with a nonlinear calibration. Our simulations indicate that the correction for natural abundance in isotope based fluxomics and quantitative metabolomics is essential for correct data interpretation.

Cutting the Gordian Knot: Identifiability of anaplerotic reactions in Corynebacterium glutamicum by means of (13) C-metabolic flux analysis

Corynebacterium glutamicum is the major workhorse for the microbial production of several amino and organic acids. As long as these derive from tricarboxylic acid cycle intermediates, the activity of anaplerotic reactions is pivotal for a high biosynthetic yield. To determine single anaplerotic activities (13) C-Metabolic Flux Analysis ((13) C-MFA) has been extensively used for C. glutamicum, however with different network topologies, inconsistent or poorly determined anaplerotic reaction rates. Therefore, in this study we set out to investigate whether a focused isotopomer model of the anaplerotic node can at all admit a unique solution for all fluxes. By analyzing different scenarios of active anaplerotic reactions, we show in full generality that for C. glutamicum only certain anaplerotic deletion mutants allow to uniquely determine the anaplerotic fluxes from (13) C-isotopomer data. We stress that the result of this analysis for different assumptions on active enzymes is directly transferable to other compartment-free organisms. Our results demonstrate that there exist biologically relevant metabolic network topologies for which the flux distribution cannot be inferred by classical (13) C-MFA.

The oxidative pentose phosphate pathway is the primary source of NADPH for lipid overproduction from glucose in Yarrowia lipolytica

Oleaginous microbes represent an attractive means of converting a diverse range of feedstocks into oils that can be transesterified to biodiesel. However, the mechanism of lipid overproduction in these organisms is incompletely understood, hindering the development of strategies for engineering superior biocatalysts for "single-cell oil" production. In particular, it is unclear which pathways are used to generate the large quantities of NADPH required for overproduction of the highly reduced fatty acid species. While early studies implicated malic enzyme as having a key role in production of lipogenic NADPH in oleaginous fungi, several recent reports have cast doubts as to whether malic enzyme may contribute to production of lipogenic NADPH in the model oleaginous yeast Yarrowia lipolytica. To address this problem we have used (13)C-Metabolic Flux Analysis to estimate the metabolic flux distributions during lipid accumulation in two Y. lipolytica strains; a control strain and a previously published engineered strain capable of producing lipids at roughly twice the yield. We observe a dramatic rearrangement of the metabolic flux distribution in the engineered strain which supports lipid overproduction. The NADPH-producing flux through the oxidative Pentose Phosphate Pathway is approximately doubled in the engineered strain in response to the roughly two-fold increase in fatty acid biosynthesis, while the flux through malic enzyme does not differ significantly between the two strains. Moreover, the estimated rate of NADPH production in the oxidative Pentose Phosphate Pathway is in good agreement with the estimated rate of NADPH consumption in fatty acid biosynthesis in both strains. These results suggest the oxidative Pentose Phosphate Pathway is the primary source of lipogenic NADPH in Y. lipolytica.

Simultaneous parameters identifiability and estimation of an E. coli metabolic network model

This work proposes a procedure for simultaneous parameters identifiability and estimation in metabolic networks in order to overcome difficulties associated with lack of experimental data and large number of parameters, a common scenario in the modeling of such systems. As case study, the complex real problem of parameters identifiability of the Escherichia coli K-12 W3110 dynamic model was investigated, composed by 18 differential ordinary equations and 35 kinetic rates, containing 125 parameters. With the procedure, model fit was improved for most of the measured metabolites, achieving 58 parameters estimated, including 5 unknown initial conditions. The results indicate that simultaneous parameters identifiability and estimation approach in metabolic networks is appealing, since model fit to the most of measured metabolites was possible even when important measures of intracellular metabolites and good initial estimates of parameters are not available.

Pool size measurements facilitate the determination of fluxes at branching points in non-stationary metabolic flux analysis: the case of Arabidopsis thaliana

Pool size measurements are important for the estimation of absolute intracellular fluxes in particular scenarios based on data from heavy carbon isotope experiments. Recently, steady-state fluxes estimates were obtained for central carbon metabolism in an intact illuminated rosette of Arabidopsis thaliana grown photoautotrophically (Szecowka et al., 2013; Heise et al., 2014). Fluxes were estimated therein by integrating mass-spectrometric data of the dynamics of the unlabeled metabolic fraction, data on metabolic pool sizes, partitioning of metabolic pools between cellular compartments and estimates of photosynthetically inactive pools, with a simplified model of plant central carbon metabolism. However, the fluxes were determined by treating the pool sizes as fixed parameters. Here we investigated whether and, if so, to what extent the treatment of pool sizes as parameters to be optimized in three scenarios may affect the flux estimates. The results are discussed in terms of benchmark values for canonical pathways and reactions, including starch and sucrose synthesis as well as the ribulose-1,5-bisphosphate carboxylation and oxygenation reactions. In addition, we discuss pathways emerging from a divergent branch point for which pool sizes are required for flux estimation, irrespective of the computational approach used for the simulation of the observable labeling pattern. Therefore, our findings indicate the necessity for development of techniques for accurate pool size measurements to improve the quality of flux estimates from non-stationary flux estimates in intact plant cells in the absence of alternative flux measurements.

CBFA: phenotype prediction integrating metabolic models with constraints derived from experimental data

Background

Flux analysis methods lie at the core of Metabolic Engineering (ME), providing methods for phenotype simulation that allow the determination of flux distributions under different conditions. Although many constraint-based modeling software tools have been developed and published, none provides a free user-friendly application that makes available the full portfolio of flux analysis methods.

Results

This work presents Constraint-based Flux Analysis (CBFA), an open-source software application for flux analysis in metabolic models that implements several methods for phenotype prediction, allowing users to define constraints associated with measured fluxes and/or flux ratios, together with environmental conditions (e.g. media) and reaction/gene knockouts. CBFA identifies the set of applicable methods based on the constraints defined from user inputs, encompassing algebraic and constraint-based simulation methods. The integration of CBFA within the OptFlux framework for ME enables the utilization of different model formats and standards and the integration with complementary methods for phenotype simulation and visualization of results.

Conclusions

A general-purpose and flexible application is proposed that is independent of the origin of the constraints defined for a given simulation. The aim is to provide a simple to use software tool focused on the application of several flux prediction methods.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0123-1) contains supplementary material, which is available to authorized users.

Metabolomic and (13)C-metabolic flux analysis of a xylose-consuming Saccharomyces cerevisiae strain expressing xylose isomerase

Over the past two decades, significant progress has been made in the engineering of xylose-consuming Saccharomyces cerevisiae strains for production of lignocellulosic biofuels. However, the ethanol productivities achieved on xylose are still significantly lower than those observed on glucose for reasons that are not well understood. We have undertaken an analysis of central carbon metabolite pool sizes and metabolic fluxes on glucose and on xylose under aerobic and anaerobic conditions in a strain capable of rapid xylose assimilation via xylose isomerase in order to investigate factors that may limit the rate of xylose fermentation. We find that during xylose utilization the flux through the non-oxidative Pentose Phosphate Pathway (PPP) is high but the flux through the oxidative PPP is low, highlighting an advantage of the strain employed in this study. Furthermore, xylose fails to elicit the full carbon catabolite repression response that is characteristic of glucose fermentation in S. cerevisiae. We present indirect evidence that the incomplete activation of the fermentation program on xylose results in a bottleneck in lower glycolysis, leading to inefficient re-oxidation of NADH produced in glycolysis.

OpenFLUX2: (13)C-MFA modeling software package adjusted for the comprehensive analysis of single and parallel labeling experiments

BACKGROUND

Steady-state (13)C-based metabolic flux analysis ((13)C-MFA) is the most powerful method available for the quantification of intracellular fluxes. These analyses include concertedly linked experimental and computational stages: (i) assuming the metabolic model and optimizing the experimental design; (ii) feeding the investigated organism using a chosen (13)C-labeled substrate (tracer); (iii) measuring the extracellular effluxes and detecting the (13)C-patterns of intracellular metabolites; and (iv) computing flux parameters that minimize the differences between observed and simulated measurements, followed by evaluating flux statistics. In its early stages, (13)C-MFA was performed on the basis of data obtained in a single labeling experiment (SLE) followed by exploiting the developed high-performance computational software. Recently, the advantages of parallel labeling experiments (PLEs), where several LEs are conducted under the conditions differing only by the tracer(s) choice, were demonstrated, particularly with regard to improving flux precision due to the synergy of complementary information. The availability of an open-source software adjusted for PLE-based (13)C-MFA is an important factor for PLE implementation.

RESULTS

The open-source software OpenFLUX, initially developed for the analysis of SLEs, was extended for the computation of PLE data. Using the OpenFLUX2, in silico simulation confirmed that flux precision is improved when (13)C-MFA is implemented by fitting PLE data to the common model compared with SLE-based analysis. Efficient flux resolution could be achieved in the PLE-mediated analysis when the choice of tracer was based on an experimental design computed to minimize the flux variances from different parts of the metabolic network. The analysis provided by OpenFLUX2 mainly includes (i) the optimization of the experimental design, (ii) the computation of the flux parameters from LEs data, (iii) goodness-of-fit testing of the model's adequacy, (iv) drawing conclusions concerning the identifiability of fluxes and construction of a contribution matrix reflecting the relative contribution of the measurement variances to the flux variances, and (v) precise determination of flux confidence intervals using a fine-tunable and convergence-controlled Monte Carlo-based method.

CONCLUSIONS

The developed open-source OpenFLUX2 provides a friendly software environment that facilitates beginners and existing OpenFLUX users to implement LEs for steady-state (13)C-MFA including experimental design, quantitative evaluation of flux parameters and statistics.

A depth-first search algorithm to compute elementary flux modes by linear programming

Background

The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (<400 reactions), existing approaches based on the Double Description method must iterate through a large number of combinatorial candidates, thus imposing an immense processor and memory demand.

Results

Based on an alternative elementarity test, we developed a depth-first search algorithm using linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations.

Conclusions

The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints.

Developing sustainable software solutions for bioinformatics by the " Butterfly" paradigm

Software design and sustainable software engineering are essential for the long-term development of bioinformatics software. Typical challenges in an academic environment are short-term contracts, island solutions, pragmatic approaches and loose documentation. Upcoming new challenges are big data, complex data sets, software compatibility and rapid changes in data representation. Our approach to cope with these challenges consists of iterative intertwined cycles of development (“ Butterfly” paradigm) for key steps in scientific software engineering. User feedback is valued as well as software planning in a sustainable and interoperable way. Tool usage should be easy and intuitive. A middleware supports a user-friendly Graphical User Interface (GUI) as well as a database/tool development independently. We validated the approach of our own software development and compared the different design paradigms in various software solutions.

Mathematical modeling of isotope labeling experiments for metabolic flux analysis

Isotope labeling experiments (ILEs) offer a powerful methodology to perform metabolic flux analysis. However, the task of interpreting data from these experiments to evaluate flux values requires significant mathematical modeling skills. Toward this, this chapter provides background information and examples to enable the reader to (1) model metabolic networks, (2) simulate ILEs, and (3) understand the optimization and statistical methods commonly used for flux evaluation. A compartmentalized model of plant glycolysis and pentose phosphate pathway illustrates the reconstruction of a typical metabolic network, whereas a simpler example network illustrates the underlying metabolite and isotopomer balancing techniques. We also discuss the salient features of commonly used flux estimation software 13CFLUX2, Metran, NMR2Flux+, FiatFlux, and OpenFLUX. Furthermore, we briefly discuss methods to improve flux estimates. A graphical checklist at the end of the chapter provides a reader a quick reference to the mathematical modeling concepts and resources.

High-throughput data pipelines for metabolic flux analysis in plants

In this chapter we illustrate the methodology for high-throughput metabolic flux analysis. Central to this is developing an end to end data pipeline, crucial for integrating the wet lab experiments and analytics, combining hardware and software automation, and standardizing data representation providing importers and exporters to support third party tools. The use of existing software at the start, data extraction from the chromatogram, and the end, MFA analysis, allows for the most flexibility in this workflow. Developing iMS2Flux provided a standard, extensible, platform independent tool to act as the "glue" between these end points. Most importantly this tool can be easily adapted to support different data formats, data verification and data correction steps allowing it to be central to managing the data necessary for high-throughput MFA. An additional tool was needed to automate the MFA software and in particular to take advantage of the course grained parallel nature of high-throughput analysis and available high performance computing facilities.In combination these methods show the development of high-throughput pipelines that allow metabolic flux analysis to join as a full member of the omics family.

Optimization of steady-state ¹³C-labeling experiments for metabolic flux analysis

While steady-state (13)C metabolic flux analysis is a powerful method for deducing multiple fluxes in the central metabolic network of heterotrophic and mixotrophic plant tissues, it is also time-consuming and technically challenging. Key steps in the design and interpretation of steady-state (13)C labeling experiments are illustrated with a generic protocol based on applications to plant cell suspension cultures.

¹³C-metabolic flux analysis for Escherichia coli

(13)C-Metabolic flux analysis ((13)C-MFA) is used here to study the effects of the knockout of such genes as pgi, zwf, gnd, ppc, pck, pyk, and lpdA on the metabolic changes in Escherichia coli cultivated under aerobic condition. The metabolic regulation mechanisms were clarified by integrating such information as fermentation data, gene expression, enzyme activities, and metabolite concentrations as well the result of (13)C-MFA.

Liquid chromatography tandem mass spectrometry for measuring ¹³C-labeling in intermediates of the glycolysis and pentose phosphate pathway

This chapter describes a procedure to analyze (13)C-labeled phosphorylated compounds by liquid chromatography tandem mass spectrometry. Phosphorylated compounds, intermediaries of the glycolysis and pentose phosphate pathway, are separated by anion exchange chromatography and their isotopic labeling is determined by mass spectrometry. A sensitivity in the fmole range is achieved using scheduled multiple reaction monitoring mode.