Quantitative assignment of reaction directionality in constraint-based models of metabolism: application to Escherichia coli

2'-Fucosyllactose helps butyrate producers outgrow competitors in infant gut microbiota simulations

A reduced capacity for butyrate production by the early infant gut microbiota is associated with negative health effects, such as inflammation and the development of allergies. Here, we develop new hypotheses on the effect of the prebiotic galacto-oligosaccharides (GOS) or 2'-fucosyllactose (2'-FL) on butyrate production by the infant gut microbiota using a multiscale, spatiotemporal mathematical model of the infant gut. The model simulates a community of cross-feeding gut bacteria in metabolic detail. It represents the community as a grid of bacterial populations that exchange metabolites, using 20 different subspecies-specific metabolic networks taken from the AGORA database. The simulations predict that both GOS and 2'-FL promote the growth of Bifidobacterium, whereas butyrate producing bacteria are only consistently abundant in the presence of propane-1,2-diol, a product of 2'-FL metabolism. In absence of prebiotics or in presence of only GOS, however, Bacteroides vulgatus and Cutibacterium acnes outcompete butyrate producers by consuming intermediate metabolites.

Architect: A tool for aiding the reconstruction of high-quality metabolic models through improved enzyme annotation

Constraint-based modeling is a powerful framework for studying cellular metabolism, with applications ranging from predicting growth rates and optimizing production of high value metabolites to identifying enzymes in pathogens that may be targeted for therapeutic interventions. Results from modeling experiments can be affected at least in part by the quality of the metabolic models used. Reconstructing a metabolic network manually can produce a high-quality metabolic model but is a time-consuming task. At the same time, current methods for automating the process typically transfer metabolic function based on sequence similarity, a process known to produce many false positives. We created Architect, a pipeline for automatic metabolic model reconstruction from protein sequences. First, it performs enzyme annotation through an ensemble approach, whereby a likelihood score is computed for an EC prediction based on predictions from existing tools; for this step, our method shows both increased precision and recall compared to individual tools. Next, Architect uses these annotations to construct a high-quality metabolic network which is then gap-filled based on likelihood scores from the ensemble approach. The resulting metabolic model is output in SBML format, suitable for constraints-based analyses. Through comparisons of enzyme annotations and curated metabolic models, we demonstrate improved performance of Architect over other state-of-the-art tools, notably with higher precision and recall on the eukaryote C. elegans and when compared to UniProt annotations in two bacterial species. Code for Architect is available at https://github.com/ParkinsonLab/Architect. For ease-of-use, Architect can be readily set up and utilized using its Docker image, maintained on Docker Hub.

The topology of genome-scale metabolic reconstructions unravels independent modules and high network flexibility

The topology of metabolic networks is recognisably modular with modules weakly connected apart from sharing a pool of currency metabolites. Here, we defined modules as sets of reversible reactions isolated from the rest of metabolism by irreversible reactions except for the exchange of currency metabolites. Our approach identifies topologically independent modules under specific conditions associated with different metabolic functions. As case studies, the E.coli iJO1366 and Human Recon 2.2 genome-scale metabolic models were split in 103 and 321 modules respectively, displaying significant correlation patterns in expression data. Finally, we addressed a fundamental question about the metabolic flexibility conferred by reversible reactions: “Of all Directed Topologies (DTs) defined by fixing directions to all reversible reactions, how many are capable of carrying flux through all reactions?”. Enumeration of the DTs for iJO1366 model was performed using an efficient depth-first search algorithm, rejecting infeasible DTs based on mass-imbalanced and loopy flux patterns. We found the direction of 79% of reversible reactions must be defined before all directions in the network can be fixed, granting a high degree of flexibility.

Genome-scale metabolic reconstructions represent all biochemical reactions that an organism can accomplish. These reconstructions are complex and often difficult to study in great detail. A way to overcome this limitation is to focus on specific pathways or subsystems. We present a novel method to identify metabolic modules based on the network topology. The method relies on reaction directions and ignores currency metabolites, which artificially connect distant metabolic reactions. In this way, topologically independent modules are built, where inputs and outputs are controlled by irreversible reactions. The method is automatic and unbiased, and, the result is a set of condition specific modules with defined metabolic functions. As a proof-of-concept we generated biologically relevant modules for the E.coli and Human genome-scale metabolic reconstructions supported by transcriptomic data. Finally, we applied the novel approach to study the network flexibility conferred by reversible reactions. In the case of the E. coli model, we found that the direction of 79% of structurally reversible reactions (those not directionally constrained by surrounding irreversible reactions) must be fixed to determine all the reaction directions in the network. Therefore, reversible reactions operate practically independent of each other.

Enhancing in silico strain design predictions through next generation metabolic modeling approaches

The reconstruction and analysis of metabolic models has garnered increasing attention due to the multitude of applications in which these have proven to be practical. The growing number of generated metabolic models has been accompanied by an exponentially expanding arsenal of tools used to analyze them. In this work, we discussed the biological relevance of a number of promising modeling frameworks, focusing on the questions and hypotheses each method is equipped to address. To this end, we critically analyzed the steady-state modeling approaches focusing on resource allocation and incorporation of thermodynamic considerations which produce promising results and aid in the generation and experimental validation of numerous predictions. For smaller networks involving more complex regulation, we addressed kinetic modeling techniques which show encouraging results in addressing questions outside the scope of steady-state modeling. Finally, we discussed the potential application of the discussed frameworks within the field of strain design. Adoption of such methodologies is believed to significantly enhance the accuracy of in silico predictions and hence decrease the number of design-build-test cycles required.

The view of microbes as energy converters illustrates the trade-off between growth rate and yield

The application of thermodynamics to microbial growth has a long tradition that originated in the middle of the 20th century. This approach reflects the view that self-replication is a thermodynamic process that is not fundamentally different from mechanical thermodynamics. The key distinction is that a free energy gradient is not converted into mechanical (or any other form of) energy but rather into new biomass. As such, microbes can be viewed as energy converters that convert a part of the energy contained in environmental nutrients into chemical energy that drives self-replication. Before the advent of high-throughput sequencing technologies, only the most central metabolic pathways were known. However, precise measurement techniques allowed for the quantification of exchanged extracellular nutrients and heat of growing microbes with their environment. These data, together with the absence of knowledge of metabolic details, drove the development of so-called black-box models, which only consider the observable interactions of a cell with its environment and neglect all details of how exactly inputs are converted into outputs. Now, genome sequencing and genome-scale metabolic models (GEMs) provide us with unprecedented detail about metabolic processes inside the cell. However, mostly due to computational complexity issues, the derived modelling approaches make surprisingly little use of thermodynamic concepts. Here, we review classical black-box models and modern approaches that integrate thermodynamics into GEMs. We also illustrate how the description of microbial growth as an energy converter can help to understand and quantify the trade-off between microbial growth rate and yield.

New thermodynamic activity-based approach allows predicting the feasibility of glycolysis

Thermodynamic feasibility analyses help evaluating the feasibility of metabolic pathways. This is an important information used to develop new biotechnological processes and to understand metabolic processes in cells. However, literature standard data are uncertain for most biochemical reactions yielding wrong statements concerning their feasibility. In this article we present activity-based equilibrium constants for all the ten glycolytic reactions, accompanied by the standard reaction data (standard Gibbs energy of reaction and standard enthalpy of reaction). We further developed a thermodynamic activity-based approach that allows to correctly determine the feasibility of glycolysis under different chosen conditions. The results show for the first time that the feasibility of glycolysis can be explained by thermodynamics only if (1) correct standard data are used and if (2) the conditions in the cell at non-equilibrium states are accounted for in the analyses. The results here will help to determine the feasibility of other metabolisms and to understand metabolic processes in cells in the future.

Physicochemical and metabolic constraints for thermodynamics-based stoichiometric modelling under mesophilic growth conditions

Metabolic engineering in the post-genomic era is characterised by the development of new methods for metabolomics and fluxomics, supported by the integration of genetic engineering tools and mathematical modelling. Particularly, constraint-based stoichiometric models have been widely studied: (i) flux balance analysis (FBA) (in silico), and (ii) metabolic flux analysis (MFA) (in vivo). Recent studies have enabled the incorporation of thermodynamics and metabolomics data to improve the predictive capabilities of these approaches. However, an in-depth comparison and evaluation of these methods is lacking. This study presents a thorough analysis of two different in silico methods tested against experimental data (metabolomics and ¹³C-MFA) for the mesophile Escherichia coli. In particular, a modified version of the recently published matTFA toolbox was created, providing a broader range of physicochemical parameters. Validating against experimental data allowed the determination of the best physicochemical parameters to perform the TFA (Thermodynamics-based Flux Analysis). An analysis of flux pattern changes in the central carbon metabolism between ¹³C-MFA and TFA highlighted the limited capabilities of both approaches for elucidating the anaplerotic fluxes. In addition, a method based on centrality measures was suggested to identify important metabolites that (if quantified) would allow to further constrain the TFA. Finally, this study emphasised the need for standardisation in the fluxomics community: novel approaches are frequently released but a thorough comparison with currently accepted methods is not always performed.

Biotechnology has benefitted from the development of high throughput methods characterising living systems at different levels (e.g. concerning genes or proteins), allowing the industrial production of chemical commodities. Recently, focus has been placed on determining reaction rates (or metabolic fluxes) in the metabolic network of certain microorganisms, in order to identify bottlenecks hindering their exploitation. Two main approaches are commonly used, termed metabolic flux analysis (MFA) and flux balance analysis (FBA), based on measuring and estimating fluxes, respectively. While the influence of thermodynamics in living systems was accepted several decades ago, its application to study biochemical networks has only recently been enabled. In this sense, a multitude of different approaches constraining well-established modelling methods with thermodynamics has been suggested. However, physicochemical parameters are generally not properly adjusted to the experimental conditions, which might affect their predictive capabilities. In this study, we have explored the reliability of currently available tools by investigating the impact of varying said parameters in the simulation of metabolic fluxes and metabolite concentration values. Additionally, our in-depth analysis allowed us to highlight limitations and potential solutions that should be considered in future studies.

pyTFA and matTFA: a Python package and a Matlab toolbox for Thermodynamics-based Flux Analysis

Summary

pyTFA and matTFA are the first published implementations of the original TFA paper. Specifically, they include explicit formulation of Gibbs energies and metabolite concentrations, which enables straightforward integration of metabolite concentration measurements.

Motivation

High-throughput analytic technologies provide a wealth of omics data that can be used to perform thorough analyses for a multitude of studies in the areas of Systems Biology and Biotechnology. Nevertheless, most studies are still limited to constraint-based Flux Balance Analyses (FBA), neglecting an important physicochemical constraint: thermodynamics. Thermodynamics-based Flux Analysis (TFA) in metabolic models enables the integration of quantitative metabolomics data to study their effects on the net-flux directionality of reactions in the network. In addition, it allows us to estimate how far each reaction operates from thermodynamic equilibrium, which provides critical information for guiding metabolic engineering decisions.

Results

We present a Python package (pyTFA) and a Matlab toolbox (matTFA) that implement TFA. We show an example of application on both a reduced and a genome-scale model of E. coli., and demonstrate TFA and data integration through TFA reduce the feasible flux space with respect to FBA.

Availability and implementation

Documented implementation of TFA framework both in Python (pyTFA) and Matlab (matTFA) are available on www.github.com/EPFL-LCSB/.

Supplementary information

Supplementary data are available at Bioinformatics online.

iMet: A graphical user interface software tool to merge metabolic networks

Nowadays, studying microorganisms has become faster and deeper than the last decades, thanks to the modeling of genome-scale metabolic networks. Completed genome sequencing projects of microorganisms and annotating these sequences have provided a worthwhile platform for reconstructing and modeling genome-scale metabolic networks. The genome-scale metabolic network reconstruction is a laborious and time-consuming task which needs an extensive study and search in different types of databases. Furthermore, it also requires an iterative process of creating and curating the obtained network, particularly with experimental methods. Hence, different types of reconstructions and models of a targeted microorganism can be found with different qualities, as the goal and need of researchers differ. Due to these circumstances, scientists have to continue with only one of the reconstructed metabolic networks of each microorganism and ignore the rest in their in silico works. It is clear that having a tool which merges different metabolic networks of a single organism can be a useful and effective way to study them with minimal cost and time. To meet this need, we have developed iMet, the standalone graphical user interface (GUI) software tool to merge multiple reconstructed metabolic networks of microorganisms. As a case study, we merged three reconstructed metabolic networks of a cyanobacterium using iMet, and then all of them (including the new merged one) became modeled. The results of our evaluations including Flux Balance Analysis (FBA), revealed enhancing metabolic network coverage as well as increasing yield of desired products in the new obtained model.

Evolution of hierarchy in bacterial metabolic networks

Flow hierarchy is a useful way to characterize the movement of information and matter throughout a network. Hierarchical network organizations are shown to arise when there is a cost of maintaining links in the network. A similar constraint exists in metabolic networks, where costs come from reduced efficiency of nonspecific enzymes or from producing unnecessary enzymes. Previous analyses of bacterial metabolic networks have been used to predict the minimal nutrients that a bacterium needs to grow, its mutualistic relationships with other bacteria, and its major ecological niche. We use metabolic network inference to obtain metabolite flow graphs of 2935 bacterial metabolic networks and find that flow hierarchy evolves independently of modularity and other network properties. By inferring the ancestral metabolic networks and estimating the hierarchical character of the inferred network, we show that hierarchical structure first increased and later decreased over evolutionary history. Furthermore, hierarchical structure in the network is associated with slower growth rates; bacteria with hierarchy scores above the median grow on average 2.25 times faster than those with hierarchy scores below the median.

Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0

Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods.

Pareto Optimality Explanation of the Glycolytic Alternatives in Nature

The Entner-Doudoroff (ED) and Embden-Meyerhof-Parnas (EMP) glycolytic pathways are largely conserved across glycolytic species in nature. Is this a coincidence, convergent evolution or there exists a driving force towards either of the two pathway designs? We addressed this question by first employing a variant of the optStoic algorithm to exhaustively identify over 11,916 possible routes between glucose and pyruvate at different pre-determined stoichiometric yields of ATP. Subsequently, we analyzed the thermodynamic feasibility of all the pathways at physiological metabolite concentrations and quantified the protein cost of the feasible solutions. Pareto optimality analysis between energy efficiency and protein cost reveals that the naturally evolved ED and EMP pathways are indeed among the most protein cost-efficient pathways in their respective ATP yield categories and remain thermodynamically feasible across a wide range of ATP/ADP ratios and pathway intermediate metabolite concentration ranges. In contrast, pathways with higher ATP yield (>2) while feasible, are bound within stringent and often extreme operability ranges of cofactor and intermediate metabolite concentrations. The preponderance of EMP and ED is thus consistent with not only optimally balancing energy yield vs. enzyme cost but also with ensuring operability for wide metabolite concentration ranges and ATP/ADP ratios.

An upper limit on Gibbs energy dissipation governs cellular metabolism

The principles governing cellular metabolic operation are poorly understood. Because diverse organisms show similar metabolic flux patterns, we hypothesized that a fundamental thermodynamic constraint might shape cellular metabolism. Here, we develop a constraint-based model for Saccharomyces cerevisiae with a comprehensive description of biochemical thermodynamics including a Gibbs energy balance. Non-linear regression analyses of quantitative metabolome and physiology data reveal the existence of an upper rate limit for cellular Gibbs energy dissipation. By applying this limit in flux balance analyses with growth maximization as the objective function, our model correctly predicts the physiology and intracellular metabolic fluxes for different glucose uptake rates as well as the maximal growth rate. We find that cells arrange their intracellular metabolic fluxes in such a way that, with increasing glucose uptake rates, they can accomplish optimal growth rates but stay below the critical rate limit on Gibbs energy dissipation. Once all possibilities for intracellular flux redistribution are exhausted, cells reach their maximal growth rate. This principle also holds for Escherichia coli and different carbon sources. Our work proposes that metabolic reaction stoichiometry, a limit on the cellular Gibbs energy dissipation rate, and the objective of growth maximization shape metabolism across organisms and conditions.

OptMDFpathway: Identification of metabolic pathways with maximal thermodynamic driving force and its application for analyzing the endogenous CO2 fixation potential of Escherichia coli

Constraint-based modeling techniques have become a standard tool for the in silico analysis of metabolic networks. To further improve their accuracy, recent methodological developments focused on integration of thermodynamic information in metabolic models to assess the feasibility of flux distributions by thermodynamic driving forces. Here we present OptMDFpathway, a method that extends the recently proposed framework of Max-min Driving Force (MDF) for thermodynamic pathway analysis. Given a metabolic network model, OptMDFpathway identifies both the optimal MDF for a desired phenotypic behavior as well as the respective pathway itself that supports the optimal driving force. OptMDFpathway is formulated as a mixed-integer linear program and is applicable to genome-scale metabolic networks. As an important theoretical result, we also show that there exists always at least one elementary mode in the network that reaches the maximal MDF. We employed our new approach to systematically identify all substrate-product combinations in Escherichia coli where product synthesis allows for concomitant net CO₂ assimilation via thermodynamically feasible pathways. Although biomass synthesis cannot be coupled to net CO₂ fixation in E. coli we found that as many as 145 of the 949 cytosolic carbon metabolites contained in the genome-scale model iJO1366 enable net CO₂ incorporation along thermodynamically feasible pathways with glycerol as substrate and 34 with glucose. The most promising products in terms of carbon assimilation yield and thermodynamic driving forces are orotate, aspartate and the C4-metabolites of the tricarboxylic acid cycle. We also identified thermodynamic bottlenecks frequently limiting the maximal driving force of the CO₂-fixing pathways. Our results indicate that heterotrophic organisms like E. coli hold a possibly underestimated potential for CO₂ assimilation which may complement existing biotechnological approaches for capturing CO₂. Furthermore, we envision that the developed OptMDFpathway approach can be used for many other applications within the framework of constrained-based modeling and for rational design of metabolic networks.

When analyzing metabolic networks, one often searches for metabolic pathways with certain (desired) properties, for example, conversion routes that maximize the yield of a product from a given substrate. While those problems can be solved with established methods of constraint-based modeling, no algorithm is currently available for genome-scale models to identify the pathway that has the highest possible thermodynamic driving force among all solutions with predefined stoichiometric properties. This gap is closed with our new approach OptMDFpathway which is based on the recently introduced concept of Max-min Driving Force (MDF). OptMDFpathway offers various applications, especially in the context of metabolic design of cell factories. To demonstrate the power and usefulness of OptMDFpathway, we employed it to analyze the endogenous CO₂ fixation potential of Escherichia coli. While E. coli cannot assimilate CO₂ into biomass, net CO₂ fixation can take place along linear pathways from substrate to product and we show that thermodynamically feasible pathways with net CO₂ assimilation exist for 145 (34) products when choosing glycerol (glucose) as substrate. Our results indicate that heterotrophic organisms like E. coli hold a possibly underestimated potential for CO₂ assimilation which may complement existing biotechnological approaches for capturing CO₂.

Toward Synthetic Biology Strategies for Adipic Acid Production: An in Silico Tool for Combined Thermodynamics and Stoichiometric Analysis of Metabolic Networks

Adipic acid, a nylon-6,6 precursor, has recently gained popularity in synthetic biology. Here, 16 different production routes to adipic acid were evaluated using a novel tool for network-embedded thermodynamic analysis of elementary flux modes. The tool distinguishes between thermodynamically feasible and infeasible modes under determined metabolite concentrations, allowing the thermodynamic feasibility of theoretical yields to be assessed. Further, patterns that always caused infeasible flux distributions were identified, which will aid the development of tailored strain design. A review of cellular efflux mechanisms revealed that significant accumulation of extracellular product is only possible if coupled with ATP hydrolysis. A stoichiometric analysis demonstrated that the maximum theoretical product carbon yield heavily depends on the metabolic route, ranging from 32 to 99% on glucose and/or palmitate in Escherichia coli and Saccharomyces cerevisiae metabolic models. Equally important, metabolite concentrations appeared to be thermodynamically restricted in several pathways. Consequently, the number of thermodynamically feasible flux distributions was reduced, in some cases even rendering whole pathways infeasible, highlighting the importance of pathway choice. Only routes based on the shikimate pathway were thermodynamically favorable over a large concentration and pH range. The low pH capability of S. cerevisiae shifted the thermodynamic equilibrium of some pathways toward product formation. One identified infeasible-pattern revealed that the reversibility of the mitochondrial malate dehydrogenase contradicted the current state of knowledge, which imposes a major restriction on the metabolism of S. cerevisiae. Finally, the evaluation of industrially relevant constraints revealed that two shikimate pathway-based routes in E. coli were the most robust.

Modeling metabolism of the human gut microbiome

The human gut microbiome plays an important part in human health. The complexity of the microbiome makes it difficult to determine the detailed metabolic functions and cross-talk occurs between the individual species. In silico systems biology studies of the microbiome can help to identify metabolite exchanges among gut microbes. Constraint-based reconstruction and analysis methods use biochemically accurate genome-scale metabolic networks of microorganisms to simulate metabolism between species in a given microbiome and help generate novel hypotheses on microbial interactions. Here, we review metabolic modeling studies that have investigated metabolic functions of the gut microbiome.

Thermodynamic Constraints Improve Metabolic Networks

In pursuit of establishing a realistic metabolic phenotypic space, the reversibility of reactions is thermodynamically constrained in modern metabolic networks. The reversibility constraints follow from heuristic thermodynamic poise approximations that take anticipated cellular metabolite concentration ranges into account. Because constraints reduce the feasible space, draft metabolic network reconstructions may need more extensive reconciliation, and a larger number of genes may become essential. Notwithstanding ubiquitous application, the effect of reversibility constraints on the predictive capabilities of metabolic networks has not been investigated in detail. Instead, work has focused on the implementation and validation of the thermodynamic poise calculation itself. With the advance of fast linear programming-based network reconciliation, the effects of reversibility constraints on network reconciliation and gene essentiality predictions have become feasible and are the subject of this study. Networks with thermodynamically informed reversibility constraints outperformed gene essentiality predictions compared to networks that were constrained with randomly shuffled constraints. Unconstrained networks predicted gene essentiality as accurately as thermodynamically constrained networks, but predicted substantially fewer essential genes. Networks that were reconciled with sequence similarity data and strongly enforced reversibility constraints outperformed all other networks. We conclude that metabolic network analysis confirmed the validity of the thermodynamic constraints, and that thermodynamic poise information is actionable during network reconciliation.

Quantification of Microbial Phenotypes

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

The Influence of Crowding Conditions on the Thermodynamic Feasibility of Metabolic Pathways

Intracellular reactions are carried out in a crowded medium where the macromolecules occupy ∼40% of the total volume. This decrease in the available volume affects the activity of the reactants. Scaled particle theory is used for the estimation of the activity coefficients of the metabolites, and thereby for the assessment of the impact of the presence of background molecules, on the estimation of the Gibbs free energy change (ΔrG) of the reactions. The lactic acid pathway and the central carbon metabolism of Actinobacillus succinogenes for the production of succinic acid from glycerol have been used as illustrative case studies. Results suggest the importance of maintaining intracellular crowded regions to favor the feasibility of a pathway that in other circumstances would be infeasible. Moreover, the crowding conditions may change the directionality of reactions and can modify the feasible range of fluxes estimated for a metabolic system compared with those obtained at standard biological conditions.

Metabolite concentrations, fluxes and free energies imply efficient enzyme usage

In metabolism, available free energy is limited and must be divided across pathway steps to maintain ΔG negative throughout. For each reaction, ΔG is log-proportional both to a concentration ratio (reaction quotient-to-equilibrium constant) and to a flux ratio (backward-to-forward flux). Here we use isotope labeling to measure absolute metabolite concentrations and fluxes in Escherichia coli, yeast, and a mammalian cell line. We then integrate this information to obtain a unified set of concentrations and ΔG for each organism. In glycolysis, we find that free energy is partitioned so as to mitigate unproductive backward fluxes associated with ΔG near zero. Across metabolism, we observe that absolute metabolite concentrations and ΔG are substantially conserved, and that most substrate (but not inhibitor) concentrations exceed the associated enzyme binding site affinity. The observed conservation of metabolite concentrations is consistent with an evolutionary drive to utilize enzymes efficiently given thermodynamic and osmotic constraints.

Computational Modeling of Human Metabolism and Its Application to Systems Biomedicine

Modern high-throughput techniques offer immense opportunities to investigate whole-systems behavior, such as those underlying human diseases. However, the complexity of the data presents challenges in interpretation, and new avenues are needed to address the complexity of both diseases and data. Constraint-based modeling is one formalism applied in systems biology. It relies on a genome-scale reconstruction that captures extensive biochemical knowledge regarding an organism. The human genome-scale metabolic reconstruction is increasingly used to understand normal cellular and disease states because metabolism is an important factor in many human diseases. The application of human genome-scale reconstruction ranges from mere querying of the model as a knowledge base to studies that take advantage of the model's topology and, most notably, to functional predictions based on cell- and condition-specific metabolic models built based on omics data.An increasing number and diversity of biomedical questions are being addressed using constraint-based modeling and metabolic models. One of the most successful biomedical applications to date is cancer metabolism, but constraint-based modeling also holds great potential for inborn errors of metabolism or obesity. In addition, it offers great prospects for individualized approaches to diagnostics and the design of disease prevention and intervention strategies. Metabolic models support this endeavor by providing easy access to complex high-throughput datasets. Personalized metabolic models have been introduced. Finally, constraint-based modeling can be used to model whole-body metabolism, which will enable the elucidation of metabolic interactions between organs and disturbances of these interactions as either causes or consequence of metabolic diseases. This chapter introduces constraint-based modeling and describes some of its contributions to systems biomedicine.

Predicting network functions with nested patterns

Identifying suitable patterns in complex biological interaction networks helps understanding network functions and allows for predictions at the pattern level: by recognizing a known pattern, one can assign its previously established function. However, current approaches fail for previously unseen patterns, when patterns overlap and when they are embedded into a new network context. Here we show how to conceptually extend pattern-based approaches. We define metabolite patterns in metabolic networks that formalize co-occurrences of metabolites. Our probabilistic framework decodes the implicit information in the networks' metabolite patterns to predict metabolic functions. We demonstrate the predictive power by identifying 'indicator patterns', for instance, for enzyme classification, by predicting directions of novel reactions and of known reactions in new network contexts, and by ranking candidate network extensions for gap filling. Beyond their use in improving genome annotations and metabolic network models, we expect that the concepts transfer to other network types.

Network thermodynamic curation of human and yeast genome-scale metabolic models

Genome-scale models are used for an ever-widening range of applications. Although there has been much focus on specifying the stoichiometric matrix, the predictive power of genome-scale models equally depends on reaction directions. Two-thirds of reactions in the two eukaryotic reconstructions Homo sapiens Recon 1 and Yeast 5 are specified as irreversible. However, these specifications are mainly based on biochemical textbooks or on their similarity to other organisms and are rarely underpinned by detailed thermodynamic analysis. In this study, a to our knowledge new workflow combining network-embedded thermodynamic and flux variability analysis was used to evaluate existing irreversibility constraints in Recon 1 and Yeast 5 and to identify new ones. A total of 27 and 16 new irreversible reactions were identified in Recon 1 and Yeast 5, respectively, whereas only four reactions were found with directions incorrectly specified against thermodynamics (three in Yeast 5 and one in Recon 1). The workflow further identified for both models several isolated internal loops that require further curation. The framework also highlighted the need for substrate channeling (in human) and ATP hydrolysis (in yeast) for the essential reaction catalyzed by phosphoribosylaminoimidazole carboxylase in purine metabolism. Finally, the framework highlighted differences in proline metabolism between yeast (cytosolic anabolism and mitochondrial catabolism) and humans (exclusively mitochondrial metabolism). We conclude that network-embedded thermodynamics facilitates the specification and validation of irreversibility constraints in compartmentalized metabolic models, at the same time providing further insight into network properties.

Obstructions to Sampling Qualitative Properties

Background

Sampling methods have proven to be a very efficient and intuitive method to understand properties of complicated spaces that cannot easily be computed using deterministic methods. Therefore, sampling methods became a popular tool in the applied sciences.

Results

Here, we show that sampling methods are not an appropriate tool to analyze qualitative properties of complicated spaces unless RP = NP. We illustrate these results on the example of the thermodynamically feasible flux space of genome-scale metabolic networks and show that with artificial centering hit and run (ACHR) not all reactions that can have variable flux rates are sampled with variables flux rates. In particular a uniform sample of the flux space would not sample the flux variabilities completely.

Conclusion

We conclude that unless theoretical convergence results exist, qualitative results obtained from sampling methods should be considered with caution and if possible double checked using a deterministic method.

Sequence-based Network Completion Reveals the Integrality of Missing Reactions in Metabolic Networks

Genome-scale metabolic models are central in connecting genotypes to metabolic phenotypes. However, even for well studied organisms, such as Escherichia coli, draft networks do not contain a complete biochemical network. Missing reactions are referred to as gaps. These gaps need to be filled to enable functional analysis, and gap-filling choices influence model predictions. To investigate whether functional networks existed where all gap-filling reactions were supported by sequence similarity to annotated enzymes, four draft networks were supplemented with all reactions from the Model SEED database for which minimal sequence similarity was found in their genomes. Quadratic programming revealed that the number of reactions that could partake in a gap-filling solution was vast: 3,270 in the case of E. coli, where 72% of the metabolites in the draft network could connect a gap-filling solution. Nonetheless, no network could be completed without the inclusion of orphaned enzymes, suggesting that parts of the biochemistry integral to biomass precursor formation are uncharacterized. However, many gap-filling reactions were well determined, and the resulting networks showed improved prediction of gene essentiality compared with networks generated through canonical gap filling. In addition, gene essentiality predictions that were sensitive to poorly determined gap-filling reactions were of poor quality, suggesting that damage to the network structure resulting from the inclusion of erroneous gap-filling reactions may be predictable.

NExT: integration of thermodynamic constraints and metabolomics data into a metabolic network

Thermodynamic constraints are widely used in metabolic modelling such that calculated flux phenotypes are closer to real cell behavior. If metabolic data is also included in the analysis, a check of the thermodynamic consistency of the data can be realized and subsequently use the metabolic data to further constrain the solution space, giving a more specific representation of the cell metabolism under the studied conditions. Here NExT, a software based on network-embedded thermodynamic analysis, is presented, to integrate thermodynamics constraints and metabolomics data in the estimation of intracellular fluxes. New irreversible reactions can be inferred by calculating the thermodynamically feasible range of metabolite concentrations and Gibbs energy of reactions.

Generic flux coupling analysis

Flux coupling analysis (FCA) has become a useful tool for aiding metabolic reconstructions and guiding genetic manipulations. Originally, it was introduced for constraint-based models of metabolic networks that are based on the steady-state assumption. Recently, we have shown that the steady-state assumption can be replaced by a weaker lattice-theoretic property related to the supports of metabolic fluxes. In this paper, we further extend our approach and develop an efficient algorithm for generic flux coupling analysis that works with any kind of qualitative pathway model. We illustrate our method by thermodynamic flux coupling analysis (tFCA), which allows studying steady-state metabolic models with loop-law thermodynamic constraints. These models do not satisfy the lattice-theoretic properties required in our previous work. For a selection of genome-scale metabolic network reconstructions, we discuss both theoretically and practically, how thermodynamic constraints strengthen the coupling results that can be obtained with classical FCA. A prototype implementation of tFCA is available at http://hoverboard.io/L4FC.

Prediction of intracellular metabolic states from extracellular metabolomic data

Metabolic models can provide a mechanistic framework to analyze information-rich omics data sets, and are increasingly being used to investigate metabolic alternations in human diseases. An expression of the altered metabolic pathway utilization is the selection of metabolites consumed and released by cells. However, methods for the inference of intracellular metabolic states from extracellular measurements in the context of metabolic models remain underdeveloped compared to methods for other omics data. Herein, we describe a workflow for such an integrative analysis emphasizing on extracellular metabolomics data. We demonstrate, using the lymphoblastic leukemia cell lines Molt-4 and CCRF-CEM, how our methods can reveal differences in cell metabolism. Our models explain metabolite uptake and secretion by predicting a more glycolytic phenotype for the CCRF-CEM model and a more oxidative phenotype for the Molt-4 model, which was supported by our experimental data. Gene expression analysis revealed altered expression of gene products at key regulatory steps in those central metabolic pathways, and literature query emphasized the role of these genes in cancer metabolism. Moreover, in silico gene knock-outs identified unique control points for each cell line model, e.g., phosphoglycerate dehydrogenase for the Molt-4 model. Thus, our workflow is well-suited to the characterization of cellular metabolic traits based on extracellular metabolomic data, and it allows the integration of multiple omics data sets into a cohesive picture based on a defined model context.

Investigating host-pathogen behavior and their interaction using genome-scale metabolic network models

Genome Scale Metabolic Modeling methods represent one way to compute whole cell function starting from the genome sequence of an organism and contribute towards understanding and predicting the genotype-phenotype relationship. About 80 models spanning all the kingdoms of life from archaea to eukaryotes have been built till date and used to interrogate cell phenotype under varying conditions. These models have been used to not only understand the flux distribution in evolutionary conserved pathways like glycolysis and the Krebs cycle but also in applications ranging from value added product formation in Escherichia coli to predicting inborn errors of Homo sapiens metabolism. This chapter describes a protocol that delineates the process of genome scale metabolic modeling for analysing host-pathogen behavior and interaction using flux balance analysis (FBA). The steps discussed in the process include (1) reconstruction of a metabolic network from the genome sequence, (2) its representation in a precise mathematical framework, (3) its translation to a model, and (4) the analysis using linear algebra and optimization. The methods for biological interpretations of computed cell phenotypes in the context of individual host and pathogen models and their integration are also discussed.

Software platforms to facilitate reconstructing genome-scale metabolic networks

System-level analyses of microbial metabolism are facilitated by genome-scale reconstructions of microbial biochemical networks. A reconstruction provides a structured representation of the biochemical transformations occurring within an organism, as well as the genes necessary to carry out these transformations, as determined by the annotated genome sequence and experimental data. Network reconstructions also serve as platforms for constraint-based computational techniques, which facilitate biological studies in a variety of applications, including evaluation of network properties, metabolic engineering and drug discovery. Bottom-up metabolic network reconstructions have been developed for dozens of organisms, but until recently, the pace of reconstruction has failed to keep up with advances in genome sequencing. To address this problem, a number of software platforms have been developed to automate parts of the reconstruction process, thereby alleviating much of the manual effort previously required. Here, we review four such platforms in the context of established guidelines for network reconstruction. While many steps of the reconstruction process have been successfully automated, some manual evaluation of the results is still required to ensure a high-quality reconstruction. Widespread adoption of these platforms by the scientific community is underway and will be further enabled by exchangeable formats across platforms.

Counting and correcting thermodynamically infeasible flux cycles in genome-scale metabolic networks

Thermodynamics constrains the flow of matter in a reaction network to occur through routes along which the Gibbs energy decreases, implying that viable steady-state flux patterns should be void of closed reaction cycles. Identifying and removing cycles in large reaction networks can unfortunately be a highly challenging task from a computational viewpoint. We propose here a method that accomplishes it by combining a relaxation algorithm and a Monte Carlo procedure to detect loops, with ad hoc rules (discussed in detail) to eliminate them. As test cases, we tackle (a) the problem of identifying infeasible cycles in the E. coli metabolic network and (b) the problem of correcting thermodynamic infeasibilities in the Flux-Balance-Analysis solutions for 15 human cell-type-specific metabolic networks. Results for (a) are compared with previous analyses of the same issue, while results for (b) are weighed against alternative methods to retrieve thermodynamically viable flux patterns based on minimizing specific global quantities. Our method, on the one hand, outperforms previous techniques and, on the other, corrects loopy solutions to Flux Balance Analysis. As a byproduct, it also turns out to be able to reveal possible inconsistencies in model reconstructions.

Dissecting the energy metabolism in Mycoplasma pneumoniae through genome-scale metabolic modeling

A new genome-scale metabolic reconstruction of M. pneumonia is used in combination with external metabolite measurement and protein abundance measurements to quantitatively explore the energy metabolism of this genome-reduce human pathogen.

We established a detailed biomass composition for M. pneumoniae, thus allowing for growth simulations.

Using our metabolic model, we corrected the metabolic network topology and the functional annotation of key metabolic enzymes.

M. pneumoniae, unlike other laboratory-grown bacteria, uses a high fraction of energy (up to 89%) for cellular maintenance and not for growth.

Simulating different growth conditions as well as single and double mutant phenotypes, we analyzed pathway connectivity and the impact of gene deletions on the growth performance of M. pneumoniae, highlighting the limited adaptive capabilities of this minimal model organism.

Mycoplasma pneumoniae, a threatening pathogen with a minimal genome, is a model organism for bacterial systems biology for which substantial experimental information is available. With the goal of understanding the complex interactions underlying its metabolism, we analyzed and characterized the metabolic network of M. pneumoniae in great detail, integrating data from different omics analyses under a range of conditions into a constraint-based model backbone. Iterating model predictions, hypothesis generation, experimental testing, and model refinement, we accurately curated the network and quantitatively explored the energy metabolism. In contrast to other bacteria, M. pneumoniae uses most of its energy for maintenance tasks instead of growth. We show that in highly linear networks the prediction of flux distributions for different growth times allows analysis of time-dependent changes, albeit using a static model. By performing an in silico knock-out study as well as analyzing flux distributions in single and double mutant phenotypes, we demonstrated that the model accurately represents the metabolism of M. pneumoniae. The experimentally validated model provides a solid basis for understanding its metabolic regulatory mechanisms.

GIM3E: condition-specific models of cellular metabolism developed from metabolomics and expression data

MOTIVATION

Genome-scale metabolic models have been used extensively to investigate alterations in cellular metabolism. The accuracy of these models to represent cellular metabolism in specific conditions has been improved by constraining the model with omics data sources. However, few practical methods for integrating metabolomics data with other omics data sources into genome-scale models of metabolism have been developed.

RESULTS

GIM(3)E (Gene Inactivation Moderated by Metabolism, Metabolomics and Expression) is an algorithm that enables the development of condition-specific models based on an objective function, transcriptomics and cellular metabolomics data. GIM(3)E establishes metabolite use requirements with metabolomics data, uses model-paired transcriptomics data to find experimentally supported solutions and provides calculations of the turnover (production/consumption) flux of metabolites. GIM(3)E was used to investigate the effects of integrating additional omics datasets to create increasingly constrained solution spaces of Salmonella Typhimurium metabolism during growth in both rich and virulence media. This integration proved to be informative and resulted in a requirement of additional active reactions (12 in each case) or metabolites (26 or 29, respectively). The addition of constraints from transcriptomics also impacted the allowed solution space, and the cellular metabolites with turnover fluxes that were necessarily altered by the change in conditions increased from 118 to 271 of 1397.

AVAILABILITY

GIM(3)E has been implemented in Python and requires a COBRApy 0.2.x. The algorithm and sample data described here are freely available at: http://opencobra.sourceforge.net/

CONTACTS

brianjamesschmidt@gmail.com

Quantitative assessment of thermodynamic constraints on the solution space of genome-scale metabolic models

Constraint-based methods provide powerful computational techniques to allow understanding and prediction of cellular behavior. These methods rely on physiochemical constraints to eliminate infeasible behaviors from the space of available behaviors. One such constraint is thermodynamic feasibility, the requirement that intracellular flux distributions obey the laws of thermodynamics. The past decade has seen several constraint-based methods that interpret this constraint in different ways, including those that are limited to small networks, rely on predefined reaction directions, and/or neglect the relationship between reaction free energies and metabolite concentrations. In this work, we utilize one such approach, thermodynamics-based metabolic flux analysis (TMFA), to make genome-scale, quantitative predictions about metabolite concentrations and reaction free energies in the absence of prior knowledge of reaction directions, while accounting for uncertainties in thermodynamic estimates. We applied TMFA to a genome-scale network reconstruction of Escherichia coli and examined the effect of thermodynamic constraints on the flux space. We also assessed the predictive performance of TMFA against gene essentiality and quantitative metabolomics data, under both aerobic and anaerobic, and optimal and suboptimal growth conditions. Based on these results, we propose that TMFA is a useful tool for validating phenotypes and generating hypotheses, and that additional types of data and constraints can improve predictions of metabolite concentrations.

Consistent estimation of Gibbs energy using component contributions

Standard Gibbs energies of reactions are increasingly being used in metabolic modeling for applying thermodynamic constraints on reaction rates, metabolite concentrations and kinetic parameters. The increasing scope and diversity of metabolic models has led scientists to look for genome-scale solutions that can estimate the standard Gibbs energy of all the reactions in metabolism. Group contribution methods greatly increase coverage, albeit at the price of decreased precision. We present here a way to combine the estimations of group contribution with the more accurate reactant contributions by decomposing each reaction into two parts and applying one of the methods on each of them. This method gives priority to the reactant contributions over group contributions while guaranteeing that all estimations will be consistent, i.e. will not violate the first law of thermodynamics. We show that there is a significant increase in the accuracy of our estimations compared to standard group contribution. Specifically, our cross-validation results show an 80% reduction in the median absolute residual for reactions that can be derived by reactant contributions only. We provide the full framework and source code for deriving estimates of standard reaction Gibbs energy, as well as confidence intervals, and believe this will facilitate the wide use of thermodynamic data for a better understanding of metabolism.

Thermodynamics of biochemical networks and duality theorems

One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.

Fast thermodynamically constrained flux variability analysis

MOTIVATION

Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints.

RESULTS

We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected.

AVAILABILITY AND IMPLEMENTATION

Fast-tFVA is written in C++ and published under GPL. It uses the open source software SCIP and libSBML. There also exists a Matlab interface for easy integration into Matlab. Fast-tFVA is available from page.mi.fu-berlin.de/arnem/fast-tfva.html.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A compendium of inborn errors of metabolism mapped onto the human metabolic network

Inborn errors of metabolism (IEMs) are hereditary metabolic defects, which are encountered in almost all major metabolic pathways occurring in man. Many IEMs are screened for in neonates through metabolomic analysis of dried blood spot samples. To enable the mapping of these metabolomic data onto the published human metabolic reconstruction, we added missing reactions and pathways involved in acylcarnitine (AC) and fatty acid oxidation (FAO) metabolism. Using literary data, we reconstructed an AC/FAO module consisting of 352 reactions and 139 metabolites. When this module was combined with the human metabolic reconstruction, the synthesis of 39 acylcarnitines and 22 amino acids, which are routinely measured, was captured and 235 distinct IEMs could be mapped. We collected phenotypic and clinical features for each IEM enabling comprehensive classification. We found that carbohydrate, amino acid, and lipid metabolism were most affected by the IEMs, while the brain was the most commonly affected organ. Furthermore, we analyzed the IEMs in the context of metabolic network topology to gain insight into common features between metabolically connected IEMs. While many known examples were identified, we discovered some surprising IEM pairs that shared reactions as well as clinical features but not necessarily causal genes. Moreover, we could also re-confirm that acetyl-CoA acts as a central metabolite. This network based analysis leads to further insight of hot spots in human metabolism with respect to IEMs. The presented comprehensive knowledge base of IEMs will provide a valuable tool in studying metabolic changes involved in inherited metabolic diseases.

Basic and applied uses of genome-scale metabolic network reconstructions of Escherichia coli

The genome-scale model (GEM) of metabolism in the bacterium Escherichia coli K-12 has been in development for over a decade and is now in wide use. GEM-enabled studies of E. coli have been primarily focused on six applications: (1) metabolic engineering, (2) model-driven discovery, (3) prediction of cellular phenotypes, (4) analysis of biological network properties, (5) studies of evolutionary processes, and (6) models of interspecies interactions. In this review, we provide an overview of these applications along with a critical assessment of their successes and limitations, and a perspective on likely future developments in the field. Taken together, the studies performed over the past decade have established a genome-scale mechanistic understanding of genotype-phenotype relationships in E. coli metabolism that forms the basis for similar efforts for other microbial species. Future challenges include the expansion of GEMs by integrating additional cellular processes beyond metabolism, the identification of key constraints based on emerging data types, and the development of computational methods able to handle such large-scale network models with sufficient accuracy.

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.

An integrated open framework for thermodynamics of reactions that combines accuracy and coverage

Motivation: The laws of thermodynamics describe a direct, quantitative relationship between metabolite concentrations and reaction directionality. Despite great efforts, thermodynamic data suffer from limited coverage, scattered accessibility and non-standard annotations. We present a framework for unifying thermodynamic data from multiple sources and demonstrate two new techniques for extrapolating the Gibbs energies of unmeasured reactions and conditions.

Results: Both methods account for changes in cellular conditions (pH, ionic strength, etc.) by using linear regression over the ΔG^○ of pseudoisomers and reactions. The Pseudoisomeric Reactant Contribution method systematically infers compound formation energies using measured K′ and pK_a data. The Pseudoisomeric Group Contribution method extends the group contribution method and achieves a high coverage of unmeasured reactions. We define a continuous index that predicts the reversibility of a reaction under a given physiological concentration range. In the characteristic physiological range 3μM–3mM, we find that roughly half of the reactions in Escherichia coli's metabolism are reversible. These new tools can increase the accuracy of thermodynamic-based models, especially in non-standard pH and ionic strengths. The reversibility index can help modelers decide which reactions are reversible in physiological conditions.

Availability: Freely available on the web at: http://equilibrator.weizmann.ac.il. Website implemented in Python, MySQL, Apache and Django, with all major browsers supported. The framework is open-source (code.google.com/p/milo-lab), implemented in pure Python and tested mainly on Linux.

Contact:ron.milo@weizmann.ac.il

Supplementary Information:Supplementary data are available at Bioinformatics online.

A systems biology approach to drug targets in Pseudomonas aeruginosa biofilm

Antibiotic resistance is an increasing problem in the health care system and we are in a constant race with evolving bacteria. Biofilm-associated growth is thought to play a key role in bacterial adaptability and antibiotic resistance. We employed a systems biology approach to identify candidate drug targets for biofilm-associated bacteria by imitating specific microenvironments found in microbial communities associated with biofilm formation. A previously reconstructed metabolic model of Pseudomonas aeruginosa (PA) was used to study the effect of gene deletion on bacterial growth in planktonic and biofilm-like environmental conditions. A set of 26 genes essential in both conditions was identified. Moreover, these genes have no homology with any human gene. While none of these genes were essential in only one of the conditions, we found condition-dependent genes, which could be used to slow growth specifically in biofilm-associated PA. Furthermore, we performed a double gene deletion study and obtained 17 combinations consisting of 21 different genes, which were conditionally essential. While most of the difference in double essential gene sets could be explained by different medium composition found in biofilm-like and planktonic conditions, we observed a clear effect of changes in oxygen availability on the growth performance. Eight gene pairs were found to be synthetic lethal in oxygen-limited conditions. These gene sets may serve as novel metabolic drug targets to combat particularly biofilm-associated PA. Taken together, this study demonstrates that metabolic modeling of human pathogens can be used to identify oxygen-sensitive drug targets and thus, that this systems biology approach represents a powerful tool to identify novel candidate antibiotic targets.

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.