Metabolite and isotopomer balancing in the analysis of metabolic cycles: I. Theory

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

Fructose metabolism in Chromohalobacter salexigens: interplay between the Embden-Meyerhof-Parnas and Entner-Doudoroff pathways

BACKGROUND

The halophilic bacterium Chromohalobacter salexigens metabolizes glucose exclusively through the Entner-Doudoroff (ED) pathway, an adaptation which results in inefficient growth, with significant carbon overflow, especially at low salinity. Preliminary analysis of C. salexigens genome suggests that fructose metabolism could proceed through the Entner-Doudoroff and Embden-Meyerhof-Parnas (EMP) pathways. In order to thrive at high salinity, this bacterium relies on the biosynthesis and accumulation of ectoines as major compatible solutes. This metabolic pathway imposes a high metabolic burden due to the consumption of a relevant proportion of cellular resources, including both energy molecules (NADPH and ATP) and carbon building blocks. Therefore, the existence of more than one glycolytic pathway with different stoichiometries may be an advantage for C. salexigens. The aim of this work is to experimentally characterize the metabolism of fructose in C. salexigens.

RESULTS

Fructose metabolism was analyzed using in silico genome analysis, RT-PCR, isotopic labeling, and genetic approaches. During growth on fructose as the sole carbon source, carbon overflow was not observed in a wide range of salt concentrations, and higher biomass yields were reached. We unveiled the initial steps of the two pathways for fructose incorporation and their links to central metabolism. While glucose is metabolized exclusively through the Entner-Doudoroff (ED) pathway, fructose is also partially metabolized by the Embden-Meyerhof-Parnas (EMP) route. Tracking isotopic label from [1-¹³C] fructose to ectoines revealed that 81% and 19% of the fructose were metabolized through ED and EMP-like routes, respectively. Activities of enzymes from both routes were demonstrated in vitro by ³¹P-NMR. Genes encoding predicted fructokinase and 1-phosphofructokinase were cloned and the activities of their protein products were confirmed. Importantly, the protein encoded by csal1534 gene functions as fructose bisphosphatase, although it had been annotated previously as pyrophosphate-dependent phosphofructokinase. The gluconeogenic rather than glycolytic role of this enzyme in vivo is in agreement with the lack of 6-phosphofructokinase activity previously described.

CONCLUSIONS

Overall, this study shows that C. salexigens possesses a greater metabolic flexibility for fructose catabolism, the ED and EMP pathways contributing to a fine balancing of energy and biosynthetic demands and, subsequently, to a more efficient metabolism.

The challenge and potential of photosynthesis: unique considerations for metabolic flux measurements in photosynthetic microorganisms

Photosynthetic microorganisms have the potential for sustainable production of chemical feedstocks and products but have had limited success due to a lack of tools and deeper understanding of metabolic pathway regulation. The application of instationary metabolic flux analysis (INST-MFA) to photosynthetic microorganisms has allowed researchers to quantify fluxes and identify bottlenecks and metabolic inefficiencies to improve strain performance or gain insight into cellular physiology. Additionally, flux measurements can also highlight deviations between measured and predicted fluxes, revealing weaknesses in metabolic models and highlighting areas where a lack of understanding still exists. In this review, we outline the experimental steps necessary to successfully perform photosynthetic flux experiments and analysis. We also discuss the challenges unique to photosynthetic microorganisms and how to account for them, including: light supply, quenching, concentration, extraction, analysis, and flux calculation. We hope that this will enable a larger number of researchers to successfully apply isotope assisted metabolic flux analysis (¹³C-MFA) to their favorite photosynthetic organism.

Tracking the metabolic pulse of plant lipid production with isotopic labeling and flux analyses: Past, present and future

Metabolism is comprised of networks of chemical transformations, organized into integrated biochemical pathways that are the basis of cellular operation, and function to sustain life. Metabolism, and thus life, is not static. The rate of metabolites transitioning through biochemical pathways (i.e., flux) determines cellular phenotypes, and is constantly changing in response to genetic or environmental perturbations. Each change evokes a response in metabolic pathway flow, and the quantification of fluxes under varied conditions helps to elucidate major and minor routes, and regulatory aspects of metabolism. To measure fluxes requires experimental methods that assess the movements and transformations of metabolites without creating artifacts. Isotopic labeling fills this role and is a long-standing experimental approach to identify pathways and quantify their metabolic relevance in different tissues or under different conditions. The application of labeling techniques to plant science is however far from reaching it potential. In light of advances in genetics and molecular biology that provide a means to alter metabolism, and given recent improvements in instrumentation, computational tools and available isotopes, the use of isotopic labeling to probe metabolism is becoming more and more powerful. We review the principal analytical methods for isotopic labeling with a focus on seminal studies of pathways and fluxes in lipid metabolism and carbon partitioning through central metabolism. Central carbon metabolic steps are directly linked to lipid production by serving to generate the precursors for fatty acid biosynthesis and lipid assembly. Additionally some of the ideas for labeling techniques that may be most applicable for lipid metabolism in the future were originally developed to investigate other aspects of central metabolism. We conclude by describing recent advances that will play an important future role in quantifying flux and metabolic operation in plant tissues.

Carbon flux analysis by 13C nuclear magnetic resonance to determine the effect of CO2 on anaerobic succinate production by Corynebacterium glutamicum

Wild-type Corynebacterium glutamicum produces a mixture of lactic, succinic, and acetic acids from glucose under oxygen deprivation. We investigated the effect of CO2 on the production of organic acids in a two-stage process: cells were grown aerobically in glucose, and subsequently, organic acid production by nongrowing cells was studied under anaerobic conditions. The presence of CO2 caused up to a 3-fold increase in the succinate yield (1 mol per mol of glucose) and about 2-fold increase in acetate, both at the expense of l-lactate production; moreover, dihydroxyacetone formation was abolished. The redistribution of carbon fluxes in response to CO2 was estimated by using (13)C-labeled glucose and (13)C nuclear magnetic resonance (NMR) analysis of the labeling patterns in end products. The flux analysis showed that 97% of succinate was produced via the reductive part of the tricarboxylic acid cycle, with the low activity of the oxidative branch being sufficient to provide the reducing equivalents needed for the redox balance. The flux via the pentose phosphate pathway was low (~5%) regardless of the presence or absence of CO2. Moreover, there was significant channeling of carbon to storage compounds (glycogen and trehalose) and concomitant catabolism of these reserves. The intracellular and extracellular pools of lactate and succinate were measured by in vivo NMR, and the stoichiometry (H(+):organic acid) of the respective exporters was calculated. This study shows that it is feasible to take advantage of natural cellular regulation mechanisms to obtain high yields of succinate with C. glutamicum without genetic manipulation.

Role of central metabolism in the osmoadaptation of the halophilic bacterium Chromohalobacter salexigens

Bacterial osmoadaptation involves the cytoplasmic accumulation of compatible solutes to counteract extracellular osmolarity. The halophilic and highly halotolerant bacterium Chromohalobacter salexigens is able to grow up to 3 m NaCl in a minimal medium due to the de novo synthesis of ectoines. This is an osmoregulated pathway that burdens central metabolic routes by quantitatively drawing off TCA cycle intermediaries. Consequently, metabolism in C. salexigens has adapted to support this biosynthetic route. Metabolism of C. salexigens is more efficient at high salinity than at low salinity, as reflected by lower glucose consumption, lower metabolite overflow, and higher biomass yield. At low salinity, by-products (mainly gluconate, pyruvate, and acetate) accumulate extracellularly. Using [1-(13)C]-, [2-(13)C]-, [6-(13)C]-, and [U-(13)C6]glucose as carbon sources, we were able to determine the main central metabolic pathways involved in ectoines biosynthesis from glucose. C. salexigens uses the Entner-Doudoroff pathway rather than the standard glycolytic pathway for glucose catabolism, and anaplerotic activity is high to replenish the TCA cycle with the intermediaries withdrawn for ectoines biosynthesis. Metabolic flux ratios at low and high salinity were similar, revealing a certain metabolic rigidity, probably due to its specialization to support high biosynthetic fluxes and partially explaining why metabolic yields are so highly affected by salinity. This work represents an important contribution to the elucidation of specific metabolic adaptations in compatible solute-accumulating halophilic bacteria.

Metabolic modeling of dynamic brain ¹³C NMR multiplet data: concepts and simulations with a two-compartment neuronal-glial model

Metabolic modeling of dynamic (13)C labeling curves during infusion of (13)C-labeled substrates allows quantitative measurements of metabolic rates in vivo. However metabolic modeling studies performed in the brain to date have only modeled time courses of total isotopic enrichment at individual carbon positions (positional enrichments), not taking advantage of the additional dynamic (13)C isotopomer information available from fine-structure multiplets in (13)C spectra. Here we introduce a new (13)C metabolic modeling approach using the concept of bonded cumulative isotopomers, or bonded cumomers. The direct relationship between bonded cumomers and (13)C multiplets enables fitting of the dynamic multiplet data. The potential of this new approach is demonstrated using Monte-Carlo simulations with a brain two-compartment neuronal-glial model. The precision of positional and cumomer approaches are compared for two different metabolic models (with and without glutamine dilution) and for different infusion protocols ([1,6-(13)C(2)]glucose, [1,2-(13)C(2)]acetate, and double infusion [1,6-(13)C(2)]glucose + [1,2-(13)C(2)]acetate). In all cases, the bonded cumomer approach gives better precision than the positional approach. In addition, of the three different infusion protocols considered here, the double infusion protocol combined with dynamic bonded cumomer modeling appears the most robust for precise determination of all fluxes in the model. The concepts and simulations introduced in the present study set the foundation for taking full advantage of the available dynamic (13)C multiplet data in metabolic modeling.

Delineation of substrate selection and anaplerosis in tricarboxylic acid cycle of the heart by 13C NMR spectroscopy and mass spectrometry

(13)C NMR and mass spectrometry (MS) provide complementary information regarding the (13)C labeling of intermediary metabolites. Currently, these two techniques are rarely used together because of the complexity of modeling the distribution of both positional and mass isotopomers. In this study, we developed a matrix-based model for the assessment of (13)C label distribution in the tricarboxylic acid cycle and related metabolites. The model was applied to the analysis of NMR- and MS-measured (13)C isotopomers for quantification of substrate utilization and anaplerotic fluxes in isolated perfused rat hearts. NMR and MS data were acquired from two groups of rat hearts perfused with substrates in complementary labeling patterns, i.e. the (13)C-PAL + GLC group (0.6 mM [(13) C(16) ]palmitate + 5.5 mM glucose) and the PAL + (13)C-GLC group (0.6 mM palmitate + 5.5 mM [(13)C(6) ]glucose). Relative flux parameters were obtained by fitting the model to the NMR data, MS data and their combination, respectively. Our results suggest that, although both NMR and MS can provide accurate quantification of substrate selection in oxidative metabolism, the accuracy of estimation of anaplerotic fluxes relies on the combination of these two experimental methods.

Metabolic analysis of wild-type Escherichia coli and a pyruvate dehydrogenase complex (PDHC)-deficient derivative reveals the role of PDHC in the fermentative metabolism of glucose

Pyruvate is located at a metabolic junction of assimilatory and dissimilatory pathways and represents a switch point between respiratory and fermentative metabolism. In Escherichia coli, the pyruvate dehydrogenase complex (PDHC) and pyruvate formate-lyase are considered the primary routes of pyruvate conversion to acetyl-CoA for aerobic respiration and anaerobic fermentation, respectively. During glucose fermentation, the in vivo activity of PDHC has been reported as either very low or undetectable, and the role of this enzyme remains unknown. In this study, a comprehensive characterization of wild-type E. coli MG1655 and a PDHC-deficient derivative (Pdh) led to the identification of the role of PDHC in the anaerobic fermentation of glucose. The metabolism of these strains was investigated by using a mixture of (13)C-labeled and -unlabeled glucose followed by the analysis of the labeling pattern in protein-bound amino acids via two-dimensional (13)C,(1)H NMR spectroscopy. Metabolite balancing, biosynthetic (13)C labeling of proteinogenic amino acids, and isotopomer balancing all indicated a large increase in the flux of the oxidative branch of the pentose phosphate pathway (ox-PPP) in response to the PDHC deficiency. Because both ox-PPP and PDHC generate CO(2) and the calculated CO(2) evolution rate was significantly reduced in Pdh, it was hypothesized that the role of PDHC is to provide CO(2) for cell growth. The similarly negative impact of either PDHC or ox-PPP deficiencies, and an even more pronounced impairment of cell growth in a strain lacking both ox-PPP and PDHC, provided further support for this hypothesis. The three strains exhibited similar phenotypes in the presence of an external source of CO(2), thus confirming the role of PDHC. Activation of formate hydrogen-lyase (which converts formate to CO(2) and H(2)) rendered the PDHC deficiency silent, but its negative impact reappeared in a strain lacking both PDHC and formate hydrogen-lyase. A stoichiometric analysis of CO(2) generation via PDHC and ox-PPP revealed that the PDHC route is more carbon- and energy-efficient, in agreement with its beneficial role in cell growth.

Combining genomics, metabolome analysis, and biochemical modelling to understand metabolic networks

Now that complete genome sequences are available for a variety of organisms, the elucidation of gene functions involved in metabolism necessarily includes a better understanding of cellular responses upon mutations on all levels of gene products, mRNA, proteins, and metabolites. Such progress is essential since the observable properties of organisms – the phenotypes – are produced by the genotype in juxtaposition with the environment. Whereas much has been done to make mRNA and protein profiling possible, considerably less effort has been put into profiling the end products of gene expression, metabolites. To date, analytical approaches have been aimed primarily at the accurate quantification of a number of pre-defined target metabolites, or at producing fingerprints of metabolic changes without individually determining metabolite identities. Neither of these approaches allows the formation of an in-depth understanding of the biochemical behaviour within metabolic networks. Yet, by carefully choosing protocols for sample preparation and analytical techniques, a number of chemically different classes of compounds can be quantified simultaneously to enable such understanding. In this review, the terms describing various metabolite-oriented approaches are given, and the differences among these approaches are outlined. Metabolite target analysis, metabolite profiling, metabolomics, and metabolic fingerprinting are considered. For each approach, a number of examples are given, and potential applications are discussed.

Recent developments in parameter estimation and structure identification of biochemical and genomic systems

The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.

Dynamics of Positional Enrichment: Theoretical Development and Application to Carbon Labeling in Zymomonas mobilis

Positional enrichment analysis has become an important technique for assessing detailed flux distributions and the fates of specific atoms in metabolic pathway systems. The typical approach to positional enrichment analysis is performed by supplying specifically labeled substrate to a cell system, letting the system reach steady state, and measuring where label had arrived and accumulated. The data are then evaluated mathematically with the help of a linear stoichiometric flux distribution model. While this procedure has proven to yield new and valuable insights, it does not address the transient dynamics between providing label and its ultimate steady-state distribution, which is often of great interest to the experimentalist (pulse labeling experiments). We show here that an extension of a recent mathematical method for dynamic labeling analysis is able to shed light on these transitions, thereby revealing insights not obtained with traditional positional enrichment analyses. The method traces the dynamics of one or more carbons through fully regulated metabolic pathways, which, in principle, may be arbitrarily complex. After a brief review of the earlier method and description of the theoretical extension, we illustrate the method with an analysis of the pentose phosphate pathway in Zymomonas mobilis, which has been used for traditional positional enrichment analyses in the past. We show how different labeling schemes result in distinctly different transients, which nevertheless eventually lead to a steady-state labeling profile that coincides exactly with the corresponding profile from traditional analysis. Thus, over the domain of commonality, the proposed method leads to results equivalent to those from state-of-the-art existing methods. However, these steady-state results constitute only a small portion of the insights obtainable with the proposed method. Our method can also be used as an "inverse" technique for elucidating the topology and regulation of pathway systems, if appropriate time series data are available. While such dynamic data are still rather rare, they are now being generated with increasing frequency and we believe it is desirable, and indeed necessary, to accompany this trend with an adequate, rigorous method of analysis.

Visual exploration of isotope labeling networks in 3D

Isotope labeling networks (ILNs) are graphs explaining the flow of isotope labeled molecules in a metabolic network. Moreover, they are the structural backbone of metabolic flux analysis (MFA) by isotopic tracers which has been established as a standard experimental tool in fluxomics. To configure an isotope labeling experiment (ILE) for MFA, the structure of the corresponding ILN must be understood to a certain extent even by a practitioner. Graph algorithms help to analyze the network structure but produce rather abstract results. Here, the major obstruction is the high dimension of these networks and the large number of network components which, consequently, are hard to figure out manually. At the interface between theory and experiment, the three-dimensional interactive visualization tool CumoVis has been developed for exploring the network structure in a step by step manner. Navigation and orientation within ILNs are supported by exploiting the natural 3D structure of an underlying metabolite network with stacked labeled particles on top of each metabolite node. Network exploration is facilitated by rotating, zooming, forward and backward path tracing and, most important, network component reduction. All features of CumoVis are explained with an educational example and a realistic network describing carbon flow in the citric acid cycle.

Accurate assessment of amino acid mass isotopomer distributions for metabolic flux analysis

Metabolic flux analysis based on stable-isotope labeling experiments and analysis of mass isotopomer distributions (MID) of cellular metabolites is a tool of great significance for metabolic engineering and study of human disease. This method relies on accurate and precise measurements of mass isotopomers by gas chromatography/mass spectrometry. To improve flux estimates, we assessed potential errors in determining MID of tert-butyldimethylsilyl-derivatized amino acids, which were attributed to (i) the choice of integration algorithm, (ii) concentration effects, and (iii) overlapping fragments. We report 29 amino acid fragments that are useful for flux analysis and another 18 fragments that should be rejected, most importantly Val-302, Leu-200, Leu-302, Ile-302, Ser-302, and Asp-316. In addition, we provide a protocol to minimize errors for determining MID to less than 0.4 mol % for accepted fragments.

Flux quantification in central carbon metabolism of Catharanthus roseus hairy roots by 13C labeling and comprehensive bondomer balancing

Methods for accurate and efficient quantification of metabolic fluxes are desirable in plant metabolic engineering and systems biology. Toward this objective, we introduce the application of "bondomers", a computationally efficient and intuitively appealing alternative to the commonly used isotopomer concept, to flux evaluation in plants, by using Catharanthus roseus hairy roots as a model system. We cultured the hairy roots on (5% w/w U-(13)C, 95% w/w naturally abundant) sucrose, and acquired two-dimensional [(13)C, (1)H] and [(1)H, (1)H] NMR spectra of hydrolyzed aqueous extract from the hairy roots. Analysis of these spectra yielded a data set of 116 bondomers of beta-glucans and proteinogenic amino acids from the hairy roots. Fluxes were evaluated from the bondomer data by using comprehensive bondomer balancing. We identified most fluxes in a three-compartmental model of central carbon metabolism with good precision. We observed parallel pentose phosphate pathways in the cytosol and the plastid with significantly different fluxes. The anaplerotic fluxes between phosphoenolpyruvate and oxaloacetate in the cytosol and between malate and pyruvate in the mitochondrion were relatively high (60.1+/-2.5 mol per 100 mol sucrose uptake, or 22.5+/-0.5 mol per 100 mol mitochondrial pyruvate dehydrogenase flux). The development of a comprehensive flux analysis tool for this plant hairy root system is expected to be valuable in assessing the metabolic impact of genetic or environmental changes, and this methodology can be extended to other plant systems.

Challenges in engineering microbes for biofuels production

Economic and geopolitical factors (high oil prices, environmental concerns, and supply instability) have been prompting policy-makers to put added emphasis on renewable energy sources. For the scientific community, recent advances, embodied in new insights into basic biology and technology that can be applied to metabolic engineering, are generating considerable excitement. There is justified optimism that the full potential of biofuel production from cellulosic biomass will be obtainable in the next 10 to 15 years.

Expanding the metabolic engineering toolbox: more options to engineer cells

Metabolic engineering exploits an integrated, systems-level approach for optimizing a desired cellular property or phenotype; and great strides have been made within this scope and context during the past fifteen years. However, due to limitations in the concepts and techniques, these have relied on a focused, pathway-oriented view. Recent advances in 'omics' technologies and computational systems biology have brought the foundational systems approach of metabolic engineering into focus. At the same time, protein engineering and synthetic biology have expanded the breadth and precision of the methods available to metabolic engineers to improve strain properties. Examples are presented that illustrate this broader perspective of tools and concepts, including a recent approach for global transcriptional machinery engineering (gTME), which has demonstrated the ability to elicit multigenic transcriptional changes that have improved phenotypes compared with single-gene perturbations.

An interval approach for dealing with flux distributions and elementary modes activity patterns

This work introduces the use of an interval representation of fluxes. This representation can be useful in two common situations: (a) when fluxes are uncertain due to the lack of accurate measurements and (b) when the flux distribution is partially unknown. In addition, the interval representation can be used for other purposes such as dealing with inconsistency or representing a range of behaviour. Two main problems are addressed. On the one hand, the translation of a metabolic flux distribution into an elementary modes or extreme pathways activity pattern is analysed. In general, there is not a unique solution for this problem but a range of solutions. To represent the whole solution region in an easy way, it is possible to compute the alpha-spectrum (i.e., the range of possible values for each elementary mode or extreme pathway activity). Herein, a method is proposed which, based on the interval representation of fluxes, makes it possible to compute the alpha-spectrum from an uncertain or even partially unknown flux distribution. On the other hand, the concept of the flux-spectrum is introduced as a variant of the metabolic flux analysis methodology that presents some advantages: applicable when measurements are insufficient (underdetermined case), integration of uncertain measurements, inclusion of irreversibility constraints and an alternative procedure to deal with inconsistency. Frequently, when applying metabolic flux analysis the available measurements are insufficient and/or uncertain and the complete flux distribution cannot be uniquely calculated. The method proposed here allows the determination of the ranges of possible values for each non-calculable flux, resulting in a flux region called flux-spectrum. In order to illustrate the proposed methods, the example of the metabolic network of CHO cells cultivated in stirred flasks is used.

Isotopomer analysis of myocardial substrate metabolism: a systems biology approach

The increasing accessibility of mass isotopomer data via GC-MS and NMR technology has necessitated the use of a systematic and reliable method to take advantage of such data for flux analysis. Here we applied a nonlinear, optimization-based method to study substrate metabolism in cardiomyocytes using (13)C data from perfused mouse hearts. The myocardial metabolic network used in this study accounts for 257 reactions and 240 metabolites, which are further compartmentalized into extracellular space, cytosol, and mitochondrial matrix. Analysis of the perfused mouse heart showed that the steady-state ATP production rate was 16.6 +/- 2.3 micromol/min . gww, with 30% of the ATP coming from glycolysis. Of the four substrates available in the perfusate (glucose, pyruvate, lactate, and oleate), exogenous glucose forms the majority of cytosolic pyruvate. Pyruvate decaboxylation is significantly higher than carboxylation, suggesting that anaplerosis is low in the perfused heart. Exchange fluxes were predicted to be high for reversible enzymes in the citric acid cycle (CAC), but low in the glycolytic pathway. Pseudoketogenesis amounted to approximately 50% of the net ketone body uptake. Sensitivity analysis showed that the estimated flux distributions were relatively insensitive to experimental errors. The application of isotopomer data drastically improved the estimation of reaction fluxes compared to results computed with respect to reaction stoichiometry alone. Further study of 12 commonly used (13)C glucose mixtures showed that the mixtures of 20% [U-(13)C(6)] glucose, 80% [3 (13)C] glucose and 20% [U-(13)C(6)] glucose, 80% [4 (13)C] were best for resolving fluxes in the current network.

Bayesian-based selection of metabolic objective functions

MOTIVATION

A critical component of in silico analysis of underdetermined metabolic systems is the identification of the appropriate objective function. A common assumption is that the objective of the cell is to maximize growth. This objective function has been shown to be consistent in a few limited experimental cases, but may not be universally appropriate. Here a method is presented to quantitatively determine the most probable objective function.

RESULTS

The genome-scale metabolism of Escherichia coli growing on succinate was used as a case-study for analysis. Five different objective functions, including maximization of growth rate, were chosen based on biological plausibility. A combination of flux balance analysis and linear programming was used to simulate cellular metabolism, which was then compared to independent experimental data using a Bayesian objective function discrimination technique. After comparing rates of oxygen uptake and acetate production, minimization of the production rate of redox potential was determined to be the most probable objective function. Given the appropriate reaction network and experimental data, the discrimination technique can be applied to any bacterium to test a variety of different possible objective functions.

SUPPLEMENTARY INFORMATION

Additional files, code and a program for carrying out model discrimination are available at http://www.engr.uconn.edu/~srivasta/modisc.html.

Metabolic networks in motion: 13C-based flux analysis

Many properties of complex networks cannot be understood from monitoring the components—not even when comprehensively monitoring all protein or metabolite concentrations—unless such information is connected and integrated through mathematical models. The reason is that static component concentrations, albeit extremely informative, do not contain functional information per se. The functional behavior of a network emerges only through the nonlinear gene, protein, and metabolite interactions across multiple metabolic and regulatory layers. I argue here that intracellular reaction rates are the functional end points of these interactions in metabolic networks, hence are highly relevant for systems biology. Methods for experimental determination of metabolic fluxes differ fundamentally from component concentration measurements; that is, intracellular reaction rates cannot be detected directly, but must be estimated through computer model-based interpretation of stable isotope patterns in products of metabolism.

Metabolic engineering

Metabolic engineering is a powerful methodology aimed at intelligently designing new biological pathways, systems, and ultimately phenotypes through the use of recombinant DNA technology. Built largely on the theoretical and computational analysis of chemical systems, the field has evolved to incorporate a growing number of genome scale experimental tools. This combination of rigorous analysis and quantitative molecular biology methods has endowed metabolic engineering with an effective synergism that crosses traditional disciplinary bounds. As such, there are a growing number of applications for the effective employment of metabolic engineering, ranging from the initial industrial fermentation applications to more recent medical diagnosis applications. In this review we highlight many of the contributions metabolic engineering has provided through its history, as well as give an overview of new tools and applications that promise to have a large impact on the field's future.

Genetically constrained metabolic flux analysis

Significant progress has been made in using existing metabolic databases to estimate metabolic fluxes. Traditional metabolic flux analysis generally starts with a predetermined metabolic network. This approach has been employed successfully to analyze the behaviors of recombinant strains by manually adding or removing the corresponding pathway(s) in the metabolic map. The current work focuses on the development of a new framework that utilizes genomic and metabolic databases, including available genetic/regulatory network structures and gene chip expression data, to constrain metabolic flux analysis. The genetic network consisting of the sensing/regulatory circuits will activate or deactivate a specific set of genes in response to external stimulus. The activation and/or repression of this set of genes will result in different gene expression levels that will in turn change the structure of the metabolic map. Hence, the metabolic map will automatically "adapt" to the external stimulus as captured by the genetic network. This adaptation selects a subnetwork from the pool of feasible reactions and so performs what we term "environmentally driven dimensional reduction." The Escherichia coli oxygen and redox sensing/regulatory system, which controls the metabolic patterns connected to glycolysis and the TCA cycle, was used as a model system to illustrate the proposed approach.

Metabolic network simulation using logical loop algorithm and Jacobian matrix

A novel method to accomplish efficient numerical simulation of metabolic networks for flux analysis was developed. The only inputs required are the set of stoichiometric balances and the atom mapping matrices of all components of the reaction network. The latter are used to automatically calculate isotopomer mapping matrices. Using the symbolic toolbox of MATLAB the analytical solution of the stoichiometric balance equation system, isotopomer balances and the analytical Jacobian matrix of the total set of stoichiometric and isotopomer balances are created automatically. The number of variables in the isotopomer distribution equation system is significantly reduced applying modified isotopomer mapping matrices. These allow lumping of several consecutive isotopomer reactions into a single one. The solution of the complete system of equations is improved by implementing an iterative logical loop algorithm and using the analytical Jacobian matrix. This new method provided quick and robust convergence to the root of such equation systems in all cases tested. The method was applied to a network of lysine producing Corynebacterium glutamicum. The resulting equation system with the dimension of 546 x 546 was directly derived from 12 isotopomer balance equations. The results obtained yielded identical labeling patterns for metabolites as compared to the relaxation method.

A critical perspective of the use of (13)C-isotopomer analysis by GCMS and NMR as applied to cardiac metabolism

The aim of this article is to provide a guide for metabolic physiologists and bioengineers to the combined use of gas chromatography-mass spectrometry (GCMS) and nuclear magnetic resonance (NMR) in stable isotope investigations in any biological systems. Building on our past experience with these two techniques, as applied separately to the investigation of citric acid metabolism in the ex vivo perfused rat heart we initiated a collaborative study for their critical evaluation. This article, which expands on our previous work (Mol. Cel. Biol., 2003), directly compares GCMS- and NMR-determined 13C-isotopomer and flux data obtained from ex vivo rat heart perfusion studies with 13C-substrates. Overall we have found excellent agreement between the 13C-enrichments of GCMS- and NMR-determined citric acid cycle metabolites (citrate, 2-ketoglutarate, succinate and malate) and glutamate; however the unlabeled component (M) was consistently underestimated by NMR. Despite this discrepancy there was reasonably good agreement in the relative fluxes of 13C-substrates through the citric acid cycle determined by the two techniques. Nevertheless, further investigations appear necessary before maximal advantage can be taken of the complementary 13C-isotopomer and flux data of GCMS and NMR for probing the dynamics of cellular metabolism.

Carbohydrate cycling in micro-organisms: what can (13)C-NMR tell us?

The extension of (13)C-nuclear magnetic resonance (NMR) techniques to study cellular metabolism over recent years has provided valuable data supporting the occurrence, diversity and extent of carbon cycling in the carbohydrate metabolism of micro-organisms. The occurrence of such cycles, resulting from the simultaneous operation of different and sometimes opposite individual steps, is inherently related to the network organisation of cellular metabolism. These cycles are tentatively classified here as 'reversibility', 'metabolic' and 'substrate' cycles on the basis of their balance in carbon and cofactors. Current hypotheses concerning the physiological relevance of carbohydrate cycles are discussed in light of the (13)C-NMR data. They most likely represent system-level mechanisms for coherent and timely partitioning of carbon resources to fit with the various biosynthetic, energetic or redox needs of cells and/or additional strategies in the adaptive capacity of micro-organisms to face variation in environmental conditions.

Metabolic engineering of Lactococcus lactis: the impact of genomics and metabolic modelling

Lactic acid bacteria display a relatively simple and well described metabolism where the sugar source is converted mainly to lactic acid. Here we will shortly describe metabolic engineering strategies that led to the efficient re-routing of the lactococcal pyruvate metabolism to end-products other than lactic acid, including diacetyl and alanine. Moreover, we will review current metabolic engineering approaches that aim at increasing the flux through complex biosynthetic pathways, leading to exopolysaccharides and folic acid. Finally, the (future) impact of the developments in the area of genomics and corresponding high-throughput technologies will be discussed.

Metabolic flux analysis using mass spectrometry

Detailed knowledge on carbon flux distributions is crucial for the understanding and targeted optimization of cellular systems. Analytical methods to identify the topology of metabolic networks and to quantify fluxes through its different pathways are therefore in the core of metabolic engineering. An elegant approach for metabolic flux analysis is provided by tracer experiments. In such studies tracer substrates with stable isotopes such as 13C are applied and the labeling pattern of metabolites is subsequently measured. Detailed flux distributions can be obtained by a combination of tracer experiments and stoichiometric balancing. In recent years, mass spectrometry (MS) has emerged as an interesting method for labeling measurements in metabolic flux analysis and provided valuable insights into the cellular metabolism. The present review provides an overview on current experimental and modeling tools for metabolic flux analysis by MS. The application of MS for flux analysis is illustrated by examples from the literature for various biological systems, including bacteria, fungi, tissue cultures and in vivo studies in humans.

Modeling and simulation: tools for metabolic engineering

Mathematical modeling is one of the key methodologies of metabolic engineering. Based on a given metabolic model different computational tools for the simulation, data evaluation, systems analysis, prediction, design and optimization of metabolic systems have been developed. The currently used metabolic modeling approaches can be subdivided into structural models, stoichiometric models, carbon flux models, stationary and nonstationary mechanistic models and models with gene regulation. However, the power of a model strongly depends on its basic modeling assumptions, the simplifications made and the data sources used. Model validation turns out to be particularly difficult for metabolic systems. The different modeling approaches are critically reviewed with respect to their potential and benefits for the metabolic engineering cycle. Several tools that have emerged from the different modeling approaches including structural pathway synthesis, stoichiometric pathway analysis, metabolic flux analysis, metabolic control analysis, optimization of regulatory architectures and the evaluation of rapid sampling experiments are discussed.

Mathematical modeling of plant metabolic pathways

The understanding of the control of metabolic flux in plants requires integrated mathematical formulations of gene and protein expression, enzyme kinetics, and developmental biology. Plants have a large number of metabolically active compartments, and non-steady-state conditions are frequently encountered. Consequently steady-state metabolic flux balance and isotopic flux balance modeling approaches have limited utility in probing plant metabolic systems. Transient isotopic flux analysis and kinetic modeling are powerful proven techniques for the quantification of metabolic fluxes in compartmentalized, dynamic metabolic systems. These tools are now widely used to address metabolic flux responses to environmental and genetic perturbations in plant metabolism. Continued developments in isotopic and kinetic modeling, quantifying metabolite exchange between compartments, and transcriptional and posttranscriptional regulatory mechanisms governing enzyme level and activity will enable simulation of large sections of plant metabolism under non-steady-state conditions. Metabolic control analysis will continue to make substantial contributions to the understanding of quantitative distribution of control of flux. From the synergy between mathematical models and experiments, creative methods for controlling the distribution of flux by genetic or environmental means will be discovered and rationally implemented.

Metabolomics--the link between genotypes and phenotypes

Metabolites are the end products of cellular regulatory processes, and their levels can be regarded as the ultimate response of biological systems to genetic or environmental changes. In parallel to the terms 'transcriptome' and proteome', the set of metabolites synthesized by a biological system constitute its 'metabolome'. Yet, unlike other functional genomics approaches, the unbiased simultaneous identification and quantification of plant metabolomes has been largely neglected. Until recently, most analyses were restricted to profiling selected classes of compounds, or to fingerprinting metabolic changes without sufficient analytical resolution to determine metabolite levels and identities individually. As a prerequisite for metabolomic analysis, careful consideration of the methods employed for tissue extraction, sample preparation, data acquisition, and data mining must be taken. In this review, the differences among metabolite target analysis, metabolite profiling, and metabolic fingerprinting are clarified, and terms are defined. Current approaches are examined, and potential applications are summarized with a special emphasis on data mining and mathematical modelling of metabolism.

Using isotopomer path tracing to quantify metabolic fluxes in pathway models containing reversible reactions

As a more complete picture of the genetic and enzymatic composition of cells becomes available, there is a growing need to describe how cellular regulatory elements interact with the cellular environment to affect cell physiology. One means for describing intracellular regulatory mechanisms is concurrent measurement of multiple metabolic pathways and their interactions by metabolic flux analysis. Flux of carbon through a metabolic pathway responds to all cellular regulatory systems, including changes in enzyme and substrate concentrations, enzyme activation or inhibition, and ultimately genetic control. The extent to which metabolic flux analysis can describe cellular physiology depends on the number of pathways in the model and the quality of the data. Intracellular information is obtainable from isotopic tracer experiments, the most extensive being the determination of the isotopomer distribution, or specific labeling pattern, of intracellular metabolites. We present a rapid and novel solution method that determines the flux of carbon through complex pathway models using isotopomer data. This time-consuming problem was solved with the introduction of isotopomer path tracing, which drastically reduces the number of isotopomer variables to the number of isotopomers observed experimentally. We propose a partitioned solution method that takes advantage of the nearly linear relationship between fluxes and isotopomers. Whereas the stoichiometric matrix and the isotopomer matrix are invertible, simulated annealing and the Newton-Raphson method are used for the nonlinear components. Reversible reactions are described by a new parameter, the association factor, which scales hyperbolically with the rate of metabolite exchange. Automating the solution method permits a variety of models to be compared, thus enhancing the accuracy of results. A simplified example that contains all of the complexities of a comprehensive pathway model is presented.

13C metabolic flux analysis

Metabolic flux analysis using 13C-labeled substrates has become an important tool in metabolic engineering. It allows the detailed quantification of all intracellular fluxes in the central metabolism of a microorganism. The method has strongly evolved in recent years by the introduction of new experimental procedures, measurement techniques, and mathematical data evaluation methods. Many of these improvements require advanced skills in the application of nuclear magnetic resonance and mass spectrometry techniques on the one hand and computational and statistical experience on the other hand. This minireview summarizes these recent developments and sketches the major practical problems. An outlook to possible future developments concludes the text.

A universal framework for 13C metabolic flux analysis

A general methodology is presented for the modeling, simulation, design, evaluation, and statistical analysis of (13)C-labeling experiments for metabolic flux analysis. The universal software framework 13C-FLUX was implemented to support all steps of this process. Guided by the example of anaplerotic flux determination in Corynebacterium glutamicum, the technical details of the model setup, experimental design, and data evaluation are discussed. It is shown how the network structure, the input substrate composition, the assumptions about fluxes, and the measurement configuration are specified within 13C-FLUX. Based on the network model, different experimental designs are computed depending on the goal of the investigations. Finally, a specific experiment is evaluated and the various statistical methods used to analyze the results are briefly explained. The appendix gives some details about the software implementation and availability.

Metabolic engineering as an integrating platform for strain development

Integration of the analytical framework and experimental tools of metabolic engineering with emerging technologies such as DNA microarrays and directed evolution stands to dramatically improve the approaches by which strain improvement and biocatalyst design are pursued in the future. Progress in genomics and applied molecular biology, together with increasing emphasis on renewable resource utilization for chemical production, has advanced metabolic engineering to the forefront of biotechnological interest.

A MILP-based flux alternative generation and NMR experimental design strategy for metabolic engineering

A mixed-integer linear program (MILP) is described that can enumerate all the ways fluxes can distribute in a metabolic network while still satisfying the same constraints and objective function. The multiple solutions can be used to (1) generate alternative flux scenarios that can account for limited experimental observations, (2) forecast the potential responses to mutation (e.g., new reaction pathways may be used), and (3) (as illustrated) design (13)C NMR experiments such that different potential flux patterns in a mutant can be distinguished. The experimental design is enabled by using the MILP results as an input to an isotopomer mapping matrices (IMM)-based program, which accounts for the network circulation of (13)C from a precursor such as glucose. The IMM-based program can interface to common plotting programs with the result that the user is provided with predicted NMR spectra that are complete with splittings and Lorentzian line-shape features. The example considered is the trafficking of carbon in an Escherichia coli mutant, which has pyruvate kinase activity deleted for the purpose of eliminating acetate production. Similar yields and extracellular measurements would be manifested by the flux alternatives. The MILP-IMM results suggest how NMR experiments can be designed such that the spectra of glutamate for two flux distribution scenarios differ significantly.

In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data

A significant goal in the post-genome era is to relate the annotated genome sequence to the physiological functions of a cell. Working from the annotated genome sequence, as well as biochemical and physiological information, it is possible to reconstruct complete metabolic networks. Furthermore, computational methods have been developed to interpret and predict the optimal performance of a metabolic network under a range of growth conditions. We have tested the hypothesis that Escherichia coli uses its metabolism to grow at a maximal rate using the E. coli MG1655 metabolic reconstruction. Based on this hypothesis, we formulated experiments that describe the quantitative relationship between a primary carbon source (acetate or succinate) uptake rate, oxygen uptake rate, and maximal cellular growth rate. We found that the experimental data were consistent with the stated hypothesis, namely that the E. coli metabolic network is optimized to maximize growth under the experimental conditions considered. This study thus demonstrates how the combination of in silico and experimental biology can be used to obtain a quantitative genotype-phenotype relationship for metabolism in bacterial cells.

Large-scale prediction of phenotype: concept

The capability to gather organism wide data has far outstripped the ability to understand it. Transforming large-scale data into a "better" cell requires tools that integrate physiology with its environment. One such tool is large-scale mathematical models that marry stoichiometry and kinetics with metabolic regulation and control. It is straightforward to determine stoichiometry (at least for central pathways), and kinetics can be roughly approximated where need be. However, the molecular details of the "metabolic wiring" managing the cell are often missing. Presented here is a surrogate for these missing details based on a simple premise; over evolutionary time, biological systems have developed objective-based programs that frugally manage gene expression and enzyme activity. Mathematically, this notion can be represented as sets of nonlinear control or "management" problems which, when solved in parallel with the model balances, offer a prediction of how gene expression and enzyme activity are modulated, in the absence of specific mechanistic details. We present a model of Escherichia coli central carbon metabolism, describing batch aerobic growth on glucose, in which transcription, translation, and activity of the gene products of 45 genes is "managed" using this approach. The model consists of 122 species (metabolites, enzymes, mRNA pools, and biomass) and describes 46 reactions (17 reversible). The model is identified (kinetic parameters as well as management structure) from metabolic flux ratio (METAFoR) analysis and physiological measurements. Simulations of a pyruvate kinase knockout strain are compared with experiments and it is shown the model is capable of accurately capturing the metabolic reprogramming resulting from the deletion. Analysis of the mRNA expression pattern, translational pattern and enzyme activity pattern of the wild-type versus mutant indicates a combination of expression and specific activity shifts are responsible for observed differences. While being only a first step toward large-scale physiological modeling, this work is important in two ways. First, it strengthens the hypothesis that unknown mechanism can be reasonably approximated using objective-based management criteria. Second, it provides a dynamic means to couple large-scale analysis technologies with physiology at the single-gene, single-protein level.

Environmental biotechnology informatics

Environmental biotechnology informatics is in its infancy and is growing fast. Computer and information science can assist environmental biotechnology by developing biological databases and building mathematical models of biological systems. Funding and training limitations in this field may, however, hinder its future growth.