Putative regulatory sites unraveled by network-embedded thermodynamic analysis of metabolome data

Mechanistic analysis of multi-omics datasets to generate kinetic parameters for constraint-based metabolic models

BACKGROUND

Constraint-based modeling uses mass balances, flux capacity, and reaction directionality constraints to predict fluxes through metabolism. Although transcriptional regulation and thermodynamic constraints have been integrated into constraint-based modeling, kinetic rate laws have not been extensively used.

RESULTS

In this study, an in vivo kinetic parameter estimation problem was formulated and solved using multi-omic data sets for Escherichia coli. To narrow the confidence intervals for kinetic parameters, a series of kinetic model simplifications were made, resulting in fewer kinetic parameters than the full kinetic model. These new parameter values are able to account for flux and concentration data from 20 different experimental conditions used in our training dataset. Concentration estimates from the simplified kinetic model were within one standard deviation for 92.7% of the 790 experimental measurements in the training set. Gibbs free energy changes of reaction were calculated to identify reactions that were often operating close to or far from equilibrium. In addition, enzymes whose activities were positively or negatively influenced by metabolite concentrations were also identified. The kinetic model was then used to calculate the maximum and minimum possible flux values for individual reactions from independent metabolite and enzyme concentration data that were not used to estimate parameter values. Incorporating these kinetically-derived flux limits into the constraint-based metabolic model improved predictions for uptake and secretion rates and intracellular fluxes in constraint-based models of central metabolism.

CONCLUSIONS

This study has produced a method for in vivo kinetic parameter estimation and identified strategies and outcomes of kinetic model simplification. We also have illustrated how kinetic constraints can be used to improve constraint-based model predictions for intracellular fluxes and biomass yield and identify potential metabolic limitations through the integrated analysis of multi-omics datasets.

The integrated response of primary metabolites to gene deletions and the environment

Intracellular metabolites arise from the molecular integration of genomic and environmental factors that jointly determine metabolic activity. However, it is not clear how the interplay of genotype, nutrients, growth, and fluxes affect metabolite concentrations globally. Here we used quantitative metabolomics to assess the combined effect of environment and genotype on the metabolite composition of a yeast cell. We analyzed a panel of 34 yeast single-enzyme knockout mutants grown on three archetypical carbon sources, generating a dataset of 400 unique metabolome samples. The different carbon sources globally affected the concentrations of intermediates, both directly, by changing the thermodynamic potentials (Δ(r)G) as a result of the substrate influx, and indirectly, by cellular regulation. In contrast, enzyme deletion elicited only local accumulation of the metabolic substrate immediately upstream of the lesion. Key biosynthetic precursors and cofactors were generally robust under all tested perturbations in spite of changes in fluxes and growth rate.

Systematic applications of metabolomics in metabolic engineering

The goals of metabolic engineering are well-served by the biological information provided by metabolomics: information on how the cell is currently using its biochemical resources is perhaps one of the best ways to inform strategies to engineer a cell to produce a target compound. Using the analysis of extracellular or intracellular levels of the target compound (or a few closely related molecules) to drive metabolic engineering is quite common. However, there is surprisingly little systematic use of metabolomics datasets, which simultaneously measure hundreds of metabolites rather than just a few, for that same purpose. Here, we review the most common systematic approaches to integrating metabolite data with metabolic engineering, with emphasis on existing efforts to use whole-metabolome datasets. We then review some of the most common approaches for computational modeling of cell-wide metabolism, including constraint-based models, and discuss current computational approaches that explicitly use metabolomics data. We conclude with discussion of the broader potential of computational approaches that systematically use metabolomics data to drive metabolic engineering.

Evaluation of control mechanisms for Saccharomyces cerevisiae central metabolic reactions using metabolome data of eight single-gene deletion mutants

We performed metabolome and metabolite-metabolite correlation analyses for eight single-gene deletion mutants of Saccharomyces cerevisiae to evaluate the physiology of glucose metabolism. The irreversible enzyme reactions can become bottlenecks when intracellular metabolism is perturbed by direct interference from the central metabolic pathway by gene deletions or by a deletion of transcriptional regulator. Metabolome data reveal that transcriptional factor, gcr2, regulates the reaction that converts 3-phosphoglycerate into phosphoenolpyruvate. Metabolome data also suggest that the reaction catalyzed by pyruvate kinase makes one of the rate-limiting reactions throughout the glycolytic pathway.

Impact of stoichiometry representation on simulation of genotype-phenotype relationships in metabolic networks

Genome-scale metabolic networks provide a comprehensive structural framework for modeling genotype-phenotype relationships through flux simulations. The solution space for the metabolic flux state of the cell is typically very large and optimization-based approaches are often necessary for predicting the active metabolic state under specific environmental conditions. The objective function to be used in such optimization algorithms is directly linked with the biological hypothesis underlying the model and therefore it is one of the most relevant parameters for successful modeling. Although linear combination of selected fluxes is widely used for formulating metabolic objective functions, we show that the resulting optimization problem is sensitive towards stoichiometry representation of the metabolic network. This undesirable sensitivity leads to different simulation results when using numerically different but biochemically equivalent stoichiometry representations and thereby makes biological interpretation intrinsically subjective and ambiguous. We hereby propose a new method, Minimization of Metabolites Balance (MiMBl), which decouples the artifacts of stoichiometry representation from the formulation of the desired objective functions, by casting objective functions using metabolite turnovers rather than fluxes. By simulating perturbed metabolic networks, we demonstrate that the use of stoichiometry representation independent algorithms is fundamental for unambiguously linking modeling results with biological interpretation. For example, MiMBl allowed us to expand the scope of metabolic modeling in elucidating the mechanistic basis of several genetic interactions in Saccharomyces cerevisiae.

One of the challenging tasks in systems biology is to quantitatively predict the metabolic behavior of the cell under given genetic and environmental constraints. To this end, genome-scale metabolic reconstructions and simulation tools are indispensable. The choice of the objective function to be used for simulating genome-scale metabolic models is dependent on the biological context and one of the most relevant parameters for successful modeling. Formulation of the intended objective function often requires the use of multiple fluxes, e.g. the sum of fluxes through ATP-producing reactions. We demonstrate that the existing tools confound biological interpretation of the simulations due to undesired dependence on the representation of stoichiometry and propose a new tool – Minimization of Metabolites Balance (MiMBl). MiMBl allows casting of the desired biological objective functions into linear optimization models and gives consistent simulation results when using numerically different but biochemically equivalent stoichiometry representations. We demonstrate relevance of MiMBl for addressing biological questions through improved predictions of genetic interactions within the yeast metabolic network. Genetic interactions imply functional relationship between the genes and therefore allow assessing different hypotheses for the underlying biological principles. MiMBl explains several of the genetic interactions as outcome of flux re-routing for minimal metabolite turnover adjustments.

Expanding the concepts and tools of metabolic engineering to elucidate cancer metabolism

The metabolic engineer's toolbox, comprising stable isotope tracers, flux estimation and analysis, pathway identification, and pathway kinetics and regulation, among other techniques, has long been used to elucidate and quantify pathways primarily in the context of engineering microbes for producing small molecules of interest. Recently, these tools are increasingly finding use in cancer biology due to their unparalleled capacity for quantifying intracellular metabolism of mammalian cells. Here, we review basic concepts that are used to derive useful insights about the metabolism of tumor cells, along with a number of illustrative examples highlighting the fundamental contributions of these methods to elucidating cancer cell metabolism. This area presents unique opportunities for metabolic engineering to expand its portfolio of applications into the realm of cancer biology and help develop new cancer therapies based on a new class of metabolically derived targets.

Quantitative assignment of reaction directionality in a multicompartmental human metabolic reconstruction

Reaction directionality is a key constraint in the modeling of genome-scale metabolic networks. We thermodynamically constrained reaction directionality in a multicompartmental genome-scale model of human metabolism, Recon 1, by calculating, in vivo, standard transformed reaction Gibbs energy as a function of compartment-specific pH, electrical potential, and ionic strength. We show that compartmental pH is an important determinant of thermodynamically determined reaction directionality. The effects of pH on transport reaction thermodynamics are only seen to their full extent when metabolites are represented as pseudoisomer groups of multiple protonated species. We accurately predict the irreversibility of 387 reactions, with detailed propagation of uncertainty in input data, and manually curate the literature to resolve conflicting directionality assignments. In at least half of all cases, a prediction of a reversible reaction directionality is due to the paucity of compartment-specific quantitative metabolomic data, with remaining cases due to uncertainty in estimation of standard reaction Gibbs energy. This study points to the pressing need for 1), quantitative metabolomic data, and 2), experimental measurement of thermochemical properties for human metabolites.

Shrinking the metabolic solution space using experimental datasets

Constraint-based models of metabolism have been used in a variety of studies on drug discovery, metabolic engineering, evolution, and multi-species interactions. These genome-scale models can be generated for any sequenced organism since their main parameters (i.e., reaction stoichiometry) are highly conserved. Their relatively low parameter requirement makes these models easy to develop; however, these models often result in a solution space with multiple possible flux distributions, making it difficult to determine the precise flux state in the cell. Recent research efforts in this modeling field have investigated how additional experimental data, including gene expression, protein expression, metabolite concentrations, and kinetic parameters, can be used to reduce the solution space. This mini-review provides a summary of the data-driven computational approaches that are available for reducing the solution space and thereby improve predictions of intracellular fluxes by constraint-based models.

A scalable algorithm to explore the Gibbs energy landscape of genome-scale metabolic networks

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample (10(6)) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.

Integrated pathway modules using time-course metabolic profiles and EST data from Milnesium tardigradum

Background

Tardigrades are multicellular organisms, resistant to extreme environmental changes such as heat, drought, radiation and freezing. They outlast these conditions in an inactive form (tun) to escape damage to cellular structures and cell death. Tardigrades are apparently able to prevent or repair such damage and are therefore a crucial model organism for stress tolerance. Cultures of the tardigrade Milnesium tardigradum were dehydrated by removing the surrounding water to induce tun formation. During this process and the subsequent rehydration, metabolites were measured in a time series by GC-MS. Additionally expressed sequence tags are available, especially libraries generated from the active and inactive state. The aim of this integrated analysis is to trace changes in tardigrade metabolism and identify pathways responsible for their extreme resistance against physical stress.

Results

In this study we propose a novel integrative approach for the analysis of metabolic networks to identify modules of joint shifts on the transcriptomic and metabolic levels. We derive a tardigrade-specific metabolic network represented as an undirected graph with 3,658 nodes (metabolites) and 4,378 edges (reactions). Time course metabolite profiles are used to score the network nodes showing a significant change over time. The edges are scored according to information on enzymes from the EST data. Using this combined information, we identify a key subnetwork (functional module) of concerted changes in metabolic pathways, specific for de- and rehydration. The module is enriched in reactions showing significant changes in metabolite levels and enzyme abundance during the transition. It resembles the cessation of a measurable metabolism (e.g. glycolysis and amino acid anabolism) during the tun formation, the production of storage metabolites and bioprotectants, such as DNA stabilizers, and the generation of amino acids and cellular components from monosaccharides as carbon and energy source during rehydration.

Conclusions

The functional module identifies relationships among changed metabolites (e.g. spermidine) and reactions and provides first insights into important altered metabolic pathways. With sparse and diverse data available, the presented integrated metabolite network approach is suitable to integrate all existing data and analyse it in a combined manner.

System-level insights into yeast metabolism by thermodynamic analysis of elementary flux modes

One of the most obvious phenotypes of a cell is its metabolic activity, which is defined by the fluxes in the metabolic network. Although experimental methods to determine intracellular fluxes are well established, only a limited number of fluxes can be resolved. Especially in eukaryotes such as yeast, compartmentalization and the existence of many parallel routes render exact flux analysis impossible using current methods. To gain more insight into the metabolic operation of S. cerevisiae we developed a new computational approach where we characterize the flux solution space by determining elementary flux modes (EFMs) that are subsequently classified as thermodynamically feasible or infeasible on the basis of experimental metabolome data. This allows us to provably rule out the contribution of certain EFMs to the in vivo flux distribution. From the 71 million EFMs in a medium size metabolic network of S. cerevisiae, we classified 54% as thermodynamically feasible. By comparing the thermodynamically feasible and infeasible EFMs, we could identify reaction combinations that span the cytosol and mitochondrion and, as a system, cannot operate under the investigated glucose batch conditions. Besides conclusions on single reactions, we found that thermodynamic constraints prevent the import of redox cofactor equivalents into the mitochondrion due to limits on compartmental cofactor concentrations. Our novel approach of incorporating quantitative metabolite concentrations into the analysis of the space of all stoichiometrically feasible flux distributions allows generating new insights into the system-level operation of the intracellular fluxes without making assumptions on metabolic objectives of the cell.

Fluxes in metabolic pathways are a highly informative aspect of an organism's phenotype. The experimental determination of such fluxes is well established and has proven very useful. To address some of the limitations of experimental flux analysis, such as when the cell is divided in multiple compartments, stoichiometric modeling provides a valuable addition. The approach that we take is based on stoichiometric modeling where we consider the thermodynamic feasibility of many different possible routes through the metabolic network of Saccharomyces cerevisiae using experimentally determined metabolite concentrations. We show that next to conclusions on single biochemical reactions in the metabolic network, we obtain system-level insights on thermodynamically infeasible flux patterns. We found that the compartmental concentrations of and NADH are the causes for the system-level infeasibilities. With the current advances in quantitative metabolomics and biochemical thermodynamics, we envision that the presented method will help gaining more insight into complex metabolic systems.

Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods

Reconstructed microbial metabolic networks facilitate a mechanistic description of the genotype-phenotype relationship through the deployment of constraint-based reconstruction and analysis (COBRA) methods. As reconstructed networks leverage genomic data for insight and phenotype prediction, the development of COBRA methods has accelerated following the advent of whole-genome sequencing. Here, we describe a phylogeny of COBRA methods that has rapidly evolved from the few early methods, such as flux balance analysis and elementary flux mode analysis, into a repertoire of more than 100 methods. These methods have enabled genome-scale analysis of microbial metabolism for numerous basic and applied uses, including antibiotic discovery, metabolic engineering and modelling of microbial community behaviour.

Label-free shotgun proteomics and metabolite analysis reveal a significant metabolic shift during citrus fruit development

Label-free LC-MS/MS-based shot-gun proteomics was used to quantify the differential protein synthesis and metabolite profiling in order to assess metabolic changes during the development of citrus fruits. Our results suggested the occurrence of a metabolic change during citrus fruit maturation, where the organic acid and amino acid accumulation seen during the early stages of development shifted into sugar synthesis during the later stage of citrus fruit development. The expression of invertases remained unchanged, while an invertase inhibitor was up-regulated towards maturation. The increased expression of sucrose-phosphate synthase and sucrose-6-phosphate phosphatase and the rapid sugar accumulation suggest that sucrose is also being synthesized in citrus juice sac cells during the later stage of fruit development.

Chemical basis of metabolic network organization

Although the metabolic networks of the three domains of life consist of different constituents and metabolic pathways, they exhibit the same scale-free organization. This phenomenon has been hypothetically explained by preferential attachment principle that the new-recruited metabolites attach preferentially to those that are already well connected. However, since metabolites are usually small molecules and metabolic processes are basically chemical reactions, we speculate that the metabolic network organization may have a chemical basis. In this paper, chemoinformatic analyses on metabolic networks of Kyoto Encyclopedia of Genes and Genomes (KEGG), Escherichia coli and Saccharomyces cerevisiae were performed. It was found that there exist qualitative and quantitative correlations between network topology and chemical properties of metabolites. The metabolites with larger degrees of connectivity (hubs) are of relatively stronger polarity. This suggests that metabolic networks are chemically organized to a certain extent, which was further elucidated in terms of high concentrations required by metabolic hubs to drive a variety of reactions. This finding not only provides a chemical explanation to the preferential attachment principle for metabolic network expansion, but also has important implications for metabolic network design and metabolite concentration prediction.

The metabolic networks of the three domains of life exhibit the same scale-free organization, which has been hypothetically explained in terms of preferential attachment principle. Here we reveal that the scale-free organization of metabolic networks may have a chemical basis. Through a chemoinformatic analysis on metabolic networks of Kyoto Encyclopedia of Genes and Genomes (KEGG), Escherichia coli and Saccharomyces cerevisiae, it was found that the metabolites with higher degrees of connectivity (hubs) are of relatively stronger polarity. The reason underlying this phenomenon is that to drive a variety of reactions, metabolic hubs have to be highly concentrated. Since the intracellular environments are hydrophilic, metabolic hubs have to be strong-polar to reach high concentrations. This finding has direct implications for metabolic network design and provides a chemical explanation to the preferential attachment principle, which has been validated by numerical simulations of metabolic network expansion. In addition, the correlations between metabolite concentration, metabolic network topology and metabolite chemical properties also suggest that we can use chemical and topological properties of metabolites to predict their intracellular concentrations. A support vector regression model has been successfully established to predict the metabolite concentrations for Escherichia coli.

A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimization problem and use strong duality to demonstrate that a biochemical analogue of Tellegen's theorem holds at optimality. Each optimal flux is dependent on a free parameter that we relate to an elementary kinetic parameter when mass action kinetics is assumed.

Systems-biology approaches for predicting genomic evolution

Is evolution predictable at the molecular level? The ambitious goal to answer this question requires an understanding of the mutational effects that govern the complex relationship between genotype and phenotype. In practice, it involves integrating systems-biology modelling, microbial laboratory evolution experiments and large-scale mutational analyses - a feat that is made possible by the recent availability of the necessary computational tools and experimental techniques. This Review investigates recent progresses in mapping evolutionary trajectories and discusses the degree to which these predictions are realistic.

A database of thermodynamic properties of the reactions of glycolysis, the tricarboxylic acid cycle, and the pentose phosphate pathway

A database of thermodynamic properties is developed, which extends a previous database of glycolysis and tricarboxylic acid cycle by adding the reactions of the pentose phosphate pathway. The raw data and documented estimations of solution properties are made electronically available. The database is determined by estimation of a set of parameters representing species-level free energies of formation. The resulting calculations provide thermodynamic and network-based estimates of thermodynamic properties for six reactions of the pentose phosphate pathway for which estimates are not available in the preexisting literature. Optimized results are made available in ThermoML format. Because calculations depend on estimated hydrogen and metal cation dissociation constants, an uncertainty and sensitivity analysis is performed, revealing 23 critical dissociation constants to which the computed thermodynamic properties are particularly sensitive. DATABASE URL: http://www.biocoda.org/thermo

Optimization of a blueprint for in vitro glycolysis by metabolic real-time analysis

Recruiting complex metabolic reaction networks for chemical synthesis has attracted considerable attention but frequently requires optimization of network composition and dynamics to reach sufficient productivity. As a design framework to predict optimal levels for all enzymes in the network is currently not available, state-of-the-art pathway optimization relies on high-throughput phenotype screening. We present here the development and application of a new in vitro real-time analysis method for the comprehensive investigation and rational programming of enzyme networks for synthetic tasks. We used this first to rationally and rapidly derive an optimal blueprint for the production of the fine chemical building block dihydroxyacetone phosphate (DHAP) via Escherichia coli's highly evolved glycolysis. Second, the method guided the three-step genetic implementation of the blueprint, yielding a synthetic operon with the predicted 2.5-fold-increased glycolytic flux toward DHAP. The new analytical setup drastically accelerates rational optimization of synthetic multienzyme networks.

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.

Elimination of thermodynamically infeasible loops in steady-state metabolic models

The constraint-based reconstruction and analysis (COBRA) framework has been widely used to study steady-state flux solutions in genome-scale metabolic networks. One shortcoming of current COBRA methods is the possible violation of the loop law in the computed steady-state flux solutions. The loop law is analogous to Kirchhoff's second law for electric circuits, and states that at steady state there can be no net flux around a closed network cycle. Although the consequences of the loop law have been known for years, it has been computationally difficult to work with. Therefore, the resulting loop-law constraints have been overlooked. Here, we present a general mixed integer programming approach called loopless COBRA (ll-COBRA), which can be used to eliminate all steady-state flux solutions that are incompatible with the loop law. We apply this approach to improve flux predictions on three common COBRA methods: flux balance analysis, flux variability analysis, and Monte Carlo sampling of the flux space. Moreover, we demonstrate that the imposition of loop-law constraints with ll-COBRA improves the consistency of simulation results with experimental data. This method provides an additional constraint for many COBRA methods, enabling the acquisition of more realistic simulation results.

Mathematical models of cell factories: moving towards the core of industrial biotechnology

Industrial biotechnology involves the utilization of cell factories for the production of fuels and chemicals. Traditionally, the development of highly productive microbial strains has relied on random mutagenesis and screening. The development of predictive mathematical models provides a new paradigm for the rational design of cell factories. Instead of selecting among a set of strains resulting from random mutagenesis, mathematical models allow the researchers to predict in silico the outcomes of different genetic manipulations and engineer new strains by performing gene deletions or additions leading to a higher productivity of the desired chemicals. In this review we aim to summarize the main modelling approaches of biological processes and illustrate the particular applications that they have found in the field of industrial microbiology.

Nontargeted elucidation of metabolic pathways using stable-isotope tracers and mass spectrometry

Systems level tools for the quantitative analysis of metabolic networks are required to engineer metabolism for biomedical and industrial applications. While current metabolomics techniques enable high-throughput quantification of metabolites, these methods provide minimal information on the rates and connectivity of metabolic pathways. Here we present a new method, nontargeted tracer fate detection (NTFD), that expands upon the concept of metabolomics to solve the above problems. Through the combined use of stable isotope tracers and chromatography coupled to mass spectrometry, our computational analysis enables the quantitative detection of all measurable metabolites derived from a specific labeled compound. Without a priori knowledge of a reaction network or compound library, NTFD provides information about relative flux magnitudes into each metabolite pool by determining the mass isotopomer distribution for all labeled compounds. This novel method adds a new dimension to the metabolomics tool box and provides a framework for global analysis of metabolic fluxes.

Parameter balancing in kinetic models of cell metabolism

Kinetic modeling of metabolic pathways has become a major field of systems biology. It combines structural information about metabolic pathways with quantitative enzymatic rate laws. Some of the kinetic constants needed for a model could be collected from ever-growing literature and public web resources, but they are often incomplete, incompatible, or simply not available. We address this lack of information by parameter balancing, a method to complete given sets of kinetic constants. Based on Bayesian parameter estimation, it exploits the thermodynamic dependencies among different biochemical quantities to guess realistic model parameters from available kinetic data. Our algorithm accounts for varying measurement conditions in the input data (pH value and temperature). It can process kinetic constants and state-dependent quantities such as metabolite concentrations or chemical potentials, and uses prior distributions and data augmentation to keep the estimated quantities within plausible ranges. An online service and free software for parameter balancing with models provided in SBML format (Systems Biology Markup Language) is accessible at www.semanticsbml.org. We demonstrate its practical use with a small model of the phosphofructokinase reaction and discuss its possible applications and limitations. In the future, parameter balancing could become an important routine step in the kinetic modeling of large metabolic networks.

Limitations in xylose-fermenting Saccharomyces cerevisiae, made evident through comprehensive metabolite profiling and thermodynamic analysis

Little is known about how the general lack of efficiency with which recombinant Saccharomyces cerevisiae strains utilize xylose affects the yeast metabolome. Quantitative metabolomics was therefore performed for two xylose-fermenting S. cerevisiae strains, BP000 and BP10001, both engineered to produce xylose reductase (XR), NAD(+)-dependent xylitol dehydrogenase and xylulose kinase, and the corresponding wild-type strain CEN.PK 113-7D, which is not able to metabolize xylose. Contrary to BP000 expressing an NADPH-preferring XR, BP10001 expresses an NADH-preferring XR. An updated protocol of liquid chromatography/tandem mass spectrometry that was validated by applying internal (13)C-labeled metabolite standards was used to quantitatively determine intracellular pools of metabolites from the central carbon, energy, and redox metabolism and of eight amino acids. Metabolomic responses to different substrates, glucose (growth) or xylose (no growth), were analyzed for each strain. In BP000 and BP10001, flux through glycolysis was similarly reduced (∼27-fold) when xylose instead of glucose was metabolized. As a consequence, (i) most glycolytic metabolites were dramatically (≤ 120-fold) diluted and (ii) energy and anabolic reduction charges were affected due to decreased ATP/AMP ratios (3- to 4-fold) and reduced NADP(+) levels (∼3-fold), respectively. Contrary to that in BP000, the catabolic reduction charge was not altered in BP10001. This was due mainly to different utilization of NADH by XRs in BP000 (44%) and BP10001 (97%). Thermodynamic analysis complemented by enzyme kinetic considerations suggested that activities of pentose phosphate pathway enzymes and the pool of fructose-6-phosphate are potential factors limiting xylose utilization. Coenzyme and ATP pools did not rate limit flux through xylose pathway enzymes.

IGERS: inferring Gibbs energy changes of biochemical reactions from reaction similarities

Mathematical analysis and modeling of biochemical reaction networks requires knowledge of the permitted directionality of reactions and membrane transport processes. This information can be gathered from the standard Gibbs energy changes (DeltaG(0)) of reactions and the concentration ranges of their reactants. Currently, experimental DeltaG(0) values are not available for the vast majority of cellular biochemical processes. We propose what we believe to be a novel computational method to infer the unknown DeltaG(0) value of a reaction from the known DeltaG(0) value of the chemically most similar reaction. The chemical similarity of two arbitrary reactions is measured by the relative number (T) of co-occurring changes in the chemical attributes of their reactants. Testing our method across a validated reference set of 173 biochemical reactions with experimentally determined DeltaG(0) values, we found that a minimum reaction similarity of T = 0.6 is required to infer DeltaG(0) values with an error of <10 kJ/mol. Applying this criterion, our method allows us to assign DeltaG(0) values to 458 additional reactions of the BioPath database. We believe our approach permits us to minimize the number of DeltaG(0) measurements required for a full coverage of a given reaction network with reliable DeltaG(0) values.

Ultrahigh performance liquid chromatography-tandem mass spectrometry method for fast and robust quantification of anionic and aromatic metabolites

Quantification of metabolites is of pivotal relevance in biology, where it complements more established omics techniques such as transcriptomics and proteomics. Here, we present a 25 min ion-pairing ultrahigh performance liquid chromatography-tandem mass spectrometry method that was developed for comprehensive coverage of central metabolism (glycolysis, pentose phosphate pathway, and tricarboxylic acid cycle) and closely related biosynthetic reactions. We demonstrate quantification of 138 compounds, including carboxylic acids, amino acids, sugar phosphates, nucleotides, and functionalized aromatics. Biologically relevant isomers such as sugar phosphates are individually quantified by combining chromatographic separation and fragmentation. The obtained sensitivity and robustness enabled the detection of more than half all tested compounds in each of eight diverse biological samples of 0.5-50 mg dry cell weight. We recommend this method for routine and yet comprehensive quantification of primary metabolites in a wide variety of biological matrices.

Cross-platform comparison of methods for quantitative metabolomics of primary metabolism

Quantitative metabolomics is under intense development, and no commonly accepted standard analytical technique has emerged, yet. The employed analytical methods were mostly chosen based on educated guesses. So far, there has been no systematic cross-platform comparison of different separation and detection methods for quantitative metabolomics. Generally, the chromatographic separation of metabolites followed by their selective detection in a mass spectrometer (MS) is the most promising approach in terms of sensitivity and separation power. Using a defined mixture of 91 metabolites (covering glycolysis, pentose phosphate pathway, the tricarboxylic acid (TCA) cycle, redox metabolism, amino acids, and nucleotides), we compared six separation methods designed for the analysis of these mostly very polar primary metabolites, two methods each for gas chromatography (GC), liquid chromatography (LC), and capillary electrophoresis (CE). For analyses on a single platform, LC provides the best combination of both versatility and robustness. If a second platform can be used, it is best complemented by GC. Only liquid-phase separation systems can handle large polar metabolites, such as those containing multiple phosphate groups. As assessed by supplementing the defined mixture with (13)C-labeled yeast extracts, matrix effects are a common phenomenon on all platforms. Therefore, suitable internal standards, such as (13)C-labeled biomass extracts, are mandatory for quantitative metabolomics with any methods.

Tradeoff between enzyme and metabolite efficiency maintains metabolic homeostasis upon perturbations in enzyme capacity

Substrate metabolite concentrations are inversely related to the in vivo capacity of their converting enzymes.

Local metabolite responses represent a passive mechanism to achieve metabolic homeostasis upon perturbations in enzyme capacity.

Enzyme capacity and metabolite concentration control the metabolic reaction rate.

Physiological behavior emerges from complex dynamic interactions between transcripts, enzymes, and metabolites, the constituents of metabolism, and its regulatory network (Sauer, 2006). Although large data sets can be generated on all these variables, data integration, in particular across different omics levels, is becoming the key challenge (Stitt and Fernie, 2003; Sauer et al, 2007). In this study, we identify a general relationship between substrates of an enzymatic reaction and enzymatic capacity in central carbon metabolism that allows the prediction of changes in metabolite concentration based on changes in enzyme capacity and vise versa. To elucidate whether general relationships exist between metabolite concentrations and enzyme capacities (i.e. the outcome of enzyme abundance combined with activity), we propose three hypothetical and alternative governing principles. The first hypothesis postulates a minimization of metabolite concentration at a given flux. In this case, no correlation between alterations in metabolite concentrations and enzyme capacities is expected. The second hypothesis postulates a tradeoff between metabolite concentration and enzyme capacity. In this case, a negative correlation between differences in concentrations of substrate metabolites and differences in enzyme capacity is expected. The third hypothesis postulates a minimization of enzyme capacity at a given flux. In this case, we expect a positive correlation between differences in concentrations of product metabolites and differences in enzyme capacity. As hypotheses I–III imply different relationships between enzyme capacities and metabolite concentrations, identification of the prevailing situation in microbial metabolism requires quantitative in vivo metabolite concentration and enzyme capacity data upon moderate changes in enzyme capacity. As a first test, we chose wild type Saccharomyces cerevisiae and an otherwise isogenic mutant with a complete deletion of the transcription factor Gcr2p, an activator of glycolysis (Chambers et al, 1995). This mutant exhibits altered transcript abundances, enzyme activities, and metabolite concentrations within closely connected reactions in glycolysis and in the tricarboxylic acid cycle (Uemura and Fraenkel, 1990, 1999; Sasaki and Uemura, 2005). To quantify the relationship between metabolite concentrations and enzyme capacities, we determined transcript, enzyme, and metabolite abundances in wild type and GCR2 mutant in batch culture on glucose minimal medium. Transcript and enzyme abundances are used as surrogates for enzyme capacities. The most significant correlation was observed for fold-changes in substrate metabolite concentrations with fold-changes in enzyme abundance. Not unexpectedly, enzyme abundances were a significantly better approximation for enzyme capacities than transcript abundances. A further improved correlation was achieved by considering all diverging enzymes that react upon a given substrate metabolite simultaneously rather than considering them as a separate reaction (Figure 4). The high correlation between substrate metabolite and enzyme fold-changes suggests a tradeoff between enzyme capacity and metabolite concentrations in central metabolism. To test the general validity for central carbon metabolism of the above-identified tradeoff between reaction substrate metabolite concentrations and enzyme abundances, we performed four independent validations: a statistical, a literature based, and two experimental ones. Statistically, we verified that the correlation between substrate metabolites and enzymes could not have been found by chance. On the basis of the literature data, we performed the above correlation analysis with literature data. All available data followed the proposed correlation, thus providing further evidence for the general validity of this relationship. As a more serious challenge of the identified correlation, we designed an experiment where the absolute flux alterations are large and additionally the flux directions are altered. We expected the substrate metabolites to occur at higher concentrations in the mutant than in the wild type. This expectation was fulfilled by the experimental data in all cases, thereby further corroborating the negative correlation between enzyme capacity and metabolite concentrations. So far, our experimental evidence was based on perturbing multiple enzyme abundances through a transcription factor mutant. To ensure that our findings are also valid for single-reaction perturbations, we modulated individual abundances of the four glycolytic enzymes Pgi1p, Tpi1p, Eno2p, and Cdc19p using strains whose endogenous genomic promotor was replaced by a Tet-controlled promotor (Mnaimneh et al, 2004) (Figure 7). Thus, we determined intracellular metabolites concentrations during exponential growth in the strains with modulated enzyme abundance. Our above-identified correlation predicts metabolite concentrations to increase only for the substrate of the such perturbed reaction and all other metabolite concentrations to remain constant. This prediction was verified. We demonstrate here that global or local alterations in enzyme abundance correlate negatively with enzyme reaction substrate concentration at least in central carbon metabolism. This implies a tradeoff between enzyme and metabolite efficiency in metabolic networks. These findings can be interpreted as a passive network mechanism to maintain close-to-wild-type homeostasis of central carbon metabolism upon perturbations that alter the enzyme capacity. The alterations are compensated by converse changes in reaction substrate concentrations, thereby minimizing the difference in metabolic flux that is caused by the alteration.

What is the relationship between enzymes and metabolites, the two major constituents of metabolic networks? We propose three alternative relationships between enzyme capacity and metabolite concentration alterations based on a Michaelis–Menten kinetic; that is enzyme capacities, metabolite concentrations, or both could limit the metabolic reaction rates. These relationships imply different correlations between changes in enzyme capacity and metabolite concentration, which we tested by quantifying metabolite, transcript, and enzyme abundances upon local (single-enzyme modulation) and global (GCR2 transcription factor mutant) perturbations in Saccharomyces cerevisiae. Our results reveal an inverse relationship between fold-changes in substrate metabolites and their catalyzing enzymes. These data provide evidence for the hypothesis that reaction rates are jointly limited by enzyme capacity and metabolite concentration. Hence, alteration in one network constituent can be efficiently buffered by converse alterations in the other constituent, implying a passive mechanism to maintain metabolic homeostasis upon perturbations in enzyme capacity.

Modeling with a view to target identification in metabolic engineering: a critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy.

A database of thermodynamic quantities for the reactions of glycolysis and the tricarboxylic acid cycle

Analysis of biochemical systems requires reliable and self-consistent databases of thermodynamic properties for biochemical reactions. Here a database of thermodynamic properties for the reactions of glycolysis and the tricarboxylic acid cycle is developed from measured equilibrium data. Species-level free energies of formation are estimated on the basis of comparing thermodynamic model predictions for reaction-level equilibrium constants to previously reported data obtained under different experimental conditions. Matching model predictions to the data involves applying state corrections for ionic strength, pH, and metal ion binding for each input experimental biochemical measurement. By archiving all of the raw data, documenting all model assumptions and calculations, and making the computer package and data available, this work provides a framework for extension and refinement by adding to the underlying raw experimental data in the database and/or refining the underlying model assumptions. Thus the resulting database is a refinement of preexisting databases of thermodynamics in terms of reliability, self-consistency, transparency, and extensibility.

Thermodynamic analysis of regulation in metabolic networks using constraint-based modeling

Background

Geobacter sulfurreducens is a member of the Geobacter species, which are capable of oxidation of organic waste coupled to the reduction of heavy metals and electrode with applications in bioremediation and bioenergy generation. While the metabolism of this organism has been studied through the development of a stoichiometry based genome-scale metabolic model, the associated regulatory network has not yet been well studied. In this manuscript, we report on the implementation of a thermodynamics based metabolic flux model for Geobacter sulfurreducens. We use this updated model to identify reactions that are subject to regulatory control in the metabolic network of G. sulfurreducens using thermodynamic variability analysis.

Findings

As a first step, we have validated the regulatory sites and bottleneck reactions predicted by the thermodynamic flux analysis in E. coli by evaluating the expression ranges of the corresponding genes. We then identified ten reactions in the metabolic network of G. sulfurreducens that are predicted to be candidates for regulation. We then compared the free energy ranges for these reactions with the corresponding gene expression fold changes under conditions of different environmental and genetic perturbations and show that the model predictions of regulation are consistent with data. In addition, we also identify reactions that operate close to equilibrium and show that the experimentally determined exchange coefficient (a measure of reversibility) is significant for these reactions.

Conclusions

Application of the thermodynamic constraints resulted in identification of potential bottleneck reactions not only from the central metabolism but also from the nucleotide and amino acid subsystems, thereby showing the highly coupled nature of the thermodynamic constraints. In addition, thermodynamic variability analysis serves as a valuable tool in estimating the ranges of Δ_rG' of every reaction in the model leading to the prediction of regulatory sites in the metabolic network, thereby characterizing the regulatory network in both a model organism such as E. coli as well as a non model organism such as G. sulfurreducens.

Use of genome-scale metabolic models for understanding microbial physiology

The exploitation of microorganisms in industrial, medical, food and environmental biotechnology requires a comprehensive understanding of their physiology. The availability of genome sequences and accumulation of high-throughput data allows gaining understanding of microbial physiology at the systems level, and genome-scale metabolic models represent a valuable framework for integrative analysis of metabolism of microorganisms. Genome-scale metabolic models are reconstructed based on a combination of genome sequence information and detailed biochemical information, and these reconstructed models can be used for analyzing and simulating the operation of metabolism in response to different stimuli. Here we discuss the requirement for having detailed physiological insight in order to exploit microorganisms for production of fuels, chemicals and pharmaceuticals. We further describe the reconstruction process of genome-scale metabolic models and different algorithms that can be used to apply these models to gain improved insight into microbial physiology.

Modular rate laws for enzymatic reactions: thermodynamics, elasticities and implementation

MOTIVATION

Standard rate laws are a key requisite for systematically turning metabolic networks into kinetic models. They should provide simple, general and biochemically plausible formulae for reaction velocities and reaction elasticities. At the same time, they need to respect thermodynamic relations between the kinetic constants and the metabolic fluxes and concentrations.

RESULTS

We present a family of reversible rate laws for reactions with arbitrary stoichiometries and various types of regulation, including mass-action, Michaelis-Menten and uni-uni reversible Hill kinetics as special cases. With a thermodynamically safe parameterization of these rate laws, parameter sets obtained by model fitting, sampling or optimization are guaranteed to lead to consistent chemical equilibrium states. A reformulation using saturation values yields simple formulae for rates and elasticities, which can be easily adjusted to the given stationary flux distributions. Furthermore, this formulation highlights the role of chemical potential differences as thermodynamic driving forces. We compare the modular rate laws to the thermodynamic-kinetic modelling formalism and discuss a simplified rate law in which the reaction rate directly depends on the reaction affinity. For automatic handling of modular rate laws, we propose a standard syntax and semantic annotations for the Systems Biology Markup Language.

AVAILABILITY

An online tool for inserting the rate laws into SBML models is freely available at www.semanticsbml.org.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Network thermodynamics in the post-genomic era

Network models have been used to study the underlying processes and principles of biological systems for decades, providing many insights into the complexity of life. Biological systems require a constant flow of free energy to drive these processes that operate away from thermodynamic equilibrium. With the advent of high-throughput omics technologies, more and more thermodynamic knowledge about the biological components, processes and their interactions are surfacing that we can integrate using large-scale biological network models. This allows us to ask many fundamental questions about these networks, such as, how far away from equilibrium must the reactions in a network be displaced in order to allow growth, or what are the possible thermodynamic objectives of the cell.

Descriptive and predictive applications of constraint-based metabolic models

Constraint-based models of metabolism are becoming available for an increasing number of organisms. These models can be used in combination with existing experimental data to describe the behavior of an organism and to analyze experimental observations in the context of a model. Such a descriptive application of the models can also allow for the integration of various types of data. Additionally, these models can be used in a predictive fashion to hypothesize the outcomes of new experiments. Comparing model predictions with experimental results allows for the iterative improvement of developed models and increases our understanding of the organism being studied. A number of recent examples of both descriptive and predictive applications of constraint-based models are discussed.

Metabolic network topology reveals transcriptional regulatory signatures of type 2 diabetes

Type 2 diabetes mellitus (T2DM) is a disorder characterized by both insulin resistance and impaired insulin secretion. Recent transcriptomics studies related to T2DM have revealed changes in expression of a large number of metabolic genes in a variety of tissues. Identification of the molecular mechanisms underlying these transcriptional changes and their impact on the cellular metabolic phenotype is a challenging task due to the complexity of transcriptional regulation and the highly interconnected nature of the metabolic network. In this study we integrate skeletal muscle gene expression datasets with human metabolic network reconstructions to identify key metabolic regulatory features of T2DM. These features include reporter metabolites—metabolites with significant collective transcriptional response in the associated enzyme-coding genes, and transcription factors with significant enrichment of binding sites in the promoter regions of these genes. In addition to metabolites from TCA cycle, oxidative phosphorylation, and lipid metabolism (known to be associated with T2DM), we identified several reporter metabolites representing novel biomarker candidates. For example, the highly connected metabolites NAD+/NADH and ATP/ADP were also identified as reporter metabolites that are potentially contributing to the widespread gene expression changes observed in T2DM. An algorithm based on the analysis of the promoter regions of the genes associated with reporter metabolites revealed a transcription factor regulatory network connecting several parts of metabolism. The identified transcription factors include members of the CREB, NRF1 and PPAR family, among others, and represent regulatory targets for further experimental analysis. Overall, our results provide a holistic picture of key metabolic and regulatory nodes potentially involved in the pathogenesis of T2DM.

Type 2 diabetes mellitus is a complex metabolic disease recognized as one of the main threats to human health in the 21^st century. Recent studies of gene expression levels in human tissue samples have indicated that multiple metabolic pathways are dysregulated in diabetes and in individuals at risk for diabetes; which of these are primary, or central to disease pathogenesis, remains a key question. Cellular metabolic networks are highly interconnected and often tightly regulated; any perturbations at a single node can thus rapidly diffuse to the rest of the network. Such complexity presents a considerable challenge in pinpointing key molecular mechanisms and biomarkers associated with insulin resistance and type 2 diabetes. In this study, we address this problem by using a methodology that integrates gene expression data with the human cellular metabolic network. We demonstrate our approach by analyzing gene expression patterns in skeletal muscle. The analysis identified transcription factors and metabolites that represent potential targets for therapeutic agents and future clinical diagnostics for type 2 diabetes and impaired glucose metabolism. In a broader perspective, the study provides a framework for analysis of gene expression datasets from complex diseases in the context of changes in cellular metabolism.

Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism

The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.

Mass spectrometry-based metabolomics of yeast

Driven by the advent of metabolomics, recent years have seen renewed interest in the investigation of yeast metabolism. Here we provide a practical guide to metabolomic analysis of yeast using liquid chromatography-mass spectrometry (LC-MS). We begin with background on LC-MS and its utility in studying yeast metabolism. We then describe key issues involved at each step of a typical yeast metabolomics experiment: in experimental design, cell culture, metabolite extraction, LC-MS, and data processing and analysis. Throughout, we highlight interdependencies between the steps that are relevant to developing an integrated workflow which effectively leverages LC-MS to reveal yeast biology.