Constraint-based Metabolic Models Research Articles

Robustness analysis of a constraint-based metabolic model links cell growth and proteomics of Thermoanaerobacter tengcongensis under temperature perturbation

The integration of omic data with metabolic networks has been demonstrated to be an effective approach to elucidate the underlying metabolic mechanisms in life. Because the metabolic pathways of Thermoanaerobacter tengcongensis (T. tengcongensis) are incomplete, we used a 1-(13)C-glucose culture to monitor intracellular isotope-labeled metabolites by GC/MS and identified the gap gene in glucose catabolism, Re-citrate synthase. Based on genome annotation and biochemical information, we reconstructed the metabolic network of glucose metabolism and amino acid synthesis in T. tengcongensis, including 253 reactions, 227 metabolites, and 236 genes. Furthermore, we performed constraint based modeling (CBM)-derived robustness analysis on the model to study the dynamic changes of the metabolic network. By perturbing the culture temperature from 75 to 55 °C, we collected the bacterial growth rates and differential proteomes. Assuming that protein abundance changes represent metabolic flux variations, we proposed that the robustness analysis of the CBM model could decipher the effect of proteome change on the bacterial growth under perturbation. For approximately 73% of the reactions, the predicted cell growth changes due to such reaction flux variations matched the observed cell growth data. Our study, therefore, indicates that differential proteome data can be integrated with metabolic network modeling and that robustness analysis is a strong method for representing the dynamic change in cell phenotypes under perturbation.

Gap detection for genome-scale constraint-based models.

Constraint-based metabolic models are currently the most comprehensive system-wide models of cellular metabolism. Several challenges arise when building an in silico constraint-based model of an organism that need to be addressed before flux balance analysis (FBA) can be applied for simulations. An algorithm called FBA-Gap is presented here that aids the construction of a working model based on plausible modifications to a given list of reactions that are known to occur in the organism. When applied to a working model, the algorithm gives a hypothesis concerning a minimal medium for sustaining the cell in culture. The utility of the algorithm is demonstrated in creating a new model organism and is applied to four existing working models for generating hypotheses about culture media. In modifying a partial metabolic reconstruction so that biomass may be produced using FBA, the proposed method is more efficient than a previously proposed method in that fewer new reactions are added to complete the model. The proposed method is also more accurate than other approaches in that only biologically plausible reactions and exchange reactions are used.

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.

Elucidating and reprogramming Escherichia coli metabolisms for obligate anaerobic n-butanol and isobutanol production

Elementary mode (EM) analysis based on the constraint-based metabolic network modeling was applied to elucidate and compare complex fermentative metabolisms of Escherichia coli for obligate anaerobic production of n-butanol and isobutanol. The result shows that the n-butanol fermentative metabolism was NADH-deficient, while the isobutanol fermentative metabolism was NADH redundant. E. coli could grow and produce n-butanol anaerobically as the sole fermentative product but not achieve the maximum theoretical n-butanol yield. In contrast, for the isobutanol fermentative metabolism, E. coli was required to couple with either ethanol- or succinate-producing pathway to recycle NADH. To overcome these "defective" metabolisms, EM analysis was implemented to reprogram the native fermentative metabolism of E. coli for optimized anaerobic production of n-butanol and isobutanol through multiple gene deletion (~8-9 genes), addition (~6-7 genes), up- and downexpression (~6-7 genes), and cofactor engineering (e.g., NADH, NADPH). The designed strains were forced to couple both growth and anaerobic production of n-butanol and isobutanol, which is a useful characteristic to enhance biofuel production and tolerance through metabolic pathway evolution. Even though the n-butanol and isobutanol fermentative metabolisms were quite different, the designed strains could be engineered to have identical metabolic flux distribution in "core" metabolic pathways mainly supporting cell growth and maintenance. Finally, the model prediction in elucidating and reprogramming the native fermentative metabolism of E. coli for obligate anaerobic production of n-butanol and isobutanol was validated with published experimental data.

Genome-scale metabolic flux analysis of Streptomyces lividans growing on a complex medium

Constraint-based metabolic modeling comprises various excellent tools to assess experimentally observed phenotypic behavior of micro-organisms in terms of intracellular metabolic fluxes. In combination with genome-scale metabolic networks, micro-organisms can be investigated in much more detail and under more complex environmental conditions. Although complex media are ubiquitously applied in industrial fermentations and are often a prerequisite for high protein secretion yields, such multi-component conditions are seldom investigated using genome-scale flux analysis. In this paper, a systematic and integrative approach is presented to determine metabolic fluxes in Streptomyces lividans TK24 grown on a nutritious and complex medium. Genome-scale flux balance analysis and randomized sampling of the solution space are combined to extract maximum information from exometabolome profiles. It is shown that biomass maximization cannot predict the observed metabolite production pattern as such. Although this cellular objective commonly applies to batch fermentation data, both input and output constraints are required to reproduce the measured biomass production rate. Rich media hence not necessarily lead to maximum biomass growth. To eventually identify a unique intracellular flux vector, a hierarchical optimization of cellular objectives is adopted. Out of various tested secondary objectives, maximization of the ATP yield per flux unit returns the closest agreement with the maximum frequency in flux histograms. This unique flux estimation is hence considered as a reasonable approximation for the biological fluxes. Flux maps for different growth phases show no active oxidative part of the pentose phosphate pathway, but NADPH generation in the TCA cycle and NADPH transdehydrogenase activity are most important in fulfilling the NADPH balance. Amino acids contribute to biomass growth by augmenting the pool of available amino acids and by boosting the TCA cycle, particularly when using glutamate and aspartate. Depletion of glutamate and aspartate causes a distinct shift in fluxes of the central carbon and nitrogen metabolism. In the current work, hurdles encountered in flux analysis at a genome-scale level are addressed using hierarchical flux balance analysis and uniform sampling of the constrained solution space. This general framework can now be adopted in further studies of S. lividans, e.g., as a host for heterologous protein production.

Exploring the gap between dynamic and constraint-based models of metabolism

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of Escherichia coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identified by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.

Optimality criteria for the prediction of metabolic fluxes in yeast mutants.

Constraint-based models of cellular metabolism, such as flux balance analysis (FBA), use convex analysis and optimization to study metabolic networks at a genome scale. The availability of reaction lists for numerous organisms, along with a variety of network analysis and optimization tools, is making these approaches increasingly popular for metabolic engineering and biomedical applications, as well as for addressing fundamental biological questions. It is therefore very important to assess the predictive capacity of these models and to understand how to interpret them in a biologically relevant manner. Typically, model assessment is limited to gauging the ability to predict phenotypes, such as viability under different environmental and genetic conditions. These types of assessments, for the most part, focus only on the growth phenotype of the cells, but ignore the underlying flux predictions. While this may be sufficient for certain types of study, the question of whether flux balance models can reliably predict intracellular and transport fluxes is crucial for more detailed analysis, and remains largely unanswered. Here we compare FBA model predictions of yeast metabolic fluxes to a previously published set of experimentally determined fluxes for 13 different single gene deletion mutants across a variety of possible objective functions. We find that the specific optimization criteria used to determine fluxes have a significant impact on the accuracy of the predicted fluxes. Interestingly, while different optimization methods provide very different levels of agreement relative to experimental fluxes, they tend to provide similar predictions with respect to the effect of the perturbation on growth. This demonstrates that assessment of models at the level of flux predictions is a critical step in assessing the biological validity of different models and optimization criteria.

Applications of system-level models of metabolism for analysis of bacterial physiology and identification of new drug targets

For nearly all of the 20th century, biologists gained considerable insights into the fundamental principles of cellular dynamics by examining select modules of biochemical processes. This form of analysis provides detailed information about the workings of the examined pathways. However, any attempt to alter the normal function of bacteria (perhaps for industrial or medicinal goals) requires a detailed global understanding of cellular mechanisms. The reductionist mode of analysis cannot provide the required information for developing the needed perspective on the complex interactions of biochemical pathways. Thankfully, the increasing availability of microbial genomic, transcriptomic, proteomic and other high-throughput data permits system-level analyses of microbiology. During the past two decades, systems biologists have developed constraint-based genome-scale models (GSM) of metabolism for a variety of pathogens. These models are important tools for assessing the metabolic capabilities of various genotypes. Simultaneously, new computational methods have been developed that use these network reconstructions to answer an array of important immunological questions. The objective of this article is to briefly review some of the uses of GSMs for studying bacterial metabolism under different conditions and to discuss how the calculated solutions can be used for rational design of drugs.

Functional integration of a metabolic network model and expression data without arbitrary thresholding.

Flux balance analysis (FBA) has been used extensively to analyze genome-scale, constraint-based models of metabolism in a variety of organisms. The predictive accuracy of such models has recently been improved through the integration of high-throughput expression profiles of metabolic genes and proteins. However, extensions of FBA often require that such data be discretized a priori into sets of genes or proteins that are either 'on' or 'off'. This procedure requires selecting relatively subjective expression thresholds, often requiring several iterations and refinements to capture the expression dynamics and retain model functionality. We present a method for mapping expression data from a set of environmental, genetic or temporal conditions onto a metabolic network model without the need for arbitrary expression thresholds. Metabolic Adjustment by Differential Expression (MADE) uses the statistical significance of changes in gene or protein expression to create a functional metabolic model that most accurately recapitulates the expression dynamics. MADE was used to generate a series of models that reflect the metabolic adjustments seen in the transition from fermentative- to glycerol-based respiration in Saccharomyces cerevisiae. The calculated gene states match 98.7% of possible changes in expression, and the resulting models capture functional characteristics of the metabolic shift. MADE is implemented in Matlab and requires a mixed-integer linear program solver. Source code is freely available at http://www.bme.virginia.edu/csbl/downloads/.

An Automated Phenotype-Driven Approach (GeneForce) for Refining Metabolic and Regulatory Models

Integrated constraint-based metabolic and regulatory models can accurately predict cellular growth phenotypes arising from genetic and environmental perturbations. Challenges in constructing such models involve the limited availability of information about transcription factor—gene target interactions and computational methods to quickly refine models based on additional datasets. In this study, we developed an algorithm, GeneForce, to identify incorrect regulatory rules and gene-protein-reaction associations in integrated metabolic and regulatory models. We applied the algorithm to refine integrated models of Escherichia coli and Salmonella typhimurium, and experimentally validated some of the algorithm's suggested refinements. The adjusted E. coli model showed improved accuracy (∼80.0%) for predicting growth phenotypes for 50,557 cases (knockout mutants tested for growth in different environmental conditions). In addition to identifying needed model corrections, the algorithm was used to identify native E. coli genes that, if over-expressed, would allow E. coli to grow in new environments. We envision that this approach will enable the rapid development and assessment of genome-scale metabolic and regulatory network models for less characterized organisms, as such models can be constructed from genome annotations and cis-regulatory network predictions.

Characterizing the Metabolism of Dehalococcoides with a Constraint-Based Model

Dehalococcoides strains respire a wide variety of chloro-organic compounds and are important for the bioremediation of toxic, persistent, carcinogenic, and ubiquitous ground water pollutants. In order to better understand metabolism and optimize their application, we have developed a pan-genome-scale metabolic network and constraint-based metabolic model of Dehalococcoides. The pan-genome was constructed from publicly available complete genome sequences of Dehalococcoides sp. strain CBDB1, strain 195, strain BAV1, and strain VS. We found that Dehalococcoides pan-genome consisted of 1118 core genes (shared by all), 457 dispensable genes (shared by some), and 486 unique genes (found in only one genome). The model included 549 metabolic genes that encoded 356 proteins catalyzing 497 gene-associated model reactions. Of these 497 reactions, 477 were associated with core metabolic genes, 18 with dispensable genes, and 2 with unique genes. This study, in addition to analyzing the metabolism of an environmentally important phylogenetic group on a pan-genome scale, provides valuable insights into Dehalococcoides metabolic limitations, low growth yields, and energy conservation. The model also provides a framework to anchor and compare disparate experimental data, as well as to give insights on the physiological impact of “incomplete” pathways, such as the TCA-cycle, CO2 fixation, and cobalamin biosynthesis pathways. The model, referred to as iAI549, highlights the specialized and highly conserved nature of Dehalococcoides metabolism, and suggests that evolution of Dehalococcoides species is driven by the electron acceptor availability.

Validation of a constraint-based model of Pichia pastoris metabolism under data scarcity

BackgroundConstraint-based models enable structured cellular representations in which intracellular kinetics are circumvented. These models, combined with experimental data, are useful analytical tools to estimate the state exhibited (the phenotype) by the cells at given pseudo-steady conditions.ResultsIn this contribution, a simplified constraint-based stoichiometric model of the metabolism of the yeast Pichia pastoris, a workhorse for heterologous protein expression, is validated against several experimental available datasets. Firstly, maximum theoretical growth yields are calculated and compared to the experimental ones. Secondly, possibility theory is applied to quantify the consistency between model and measurements. Finally, the biomass growth rate is excluded from the datasets and its prediction used to exemplify the capability of the model to calculate non-measured fluxes.ConclusionsThis contribution shows how a small-sized network can be assessed following a rational, quantitative procedure even when measurements are scarce and imprecise. This approach is particularly useful in lacking data scenarios.

Imaging and Modeling of Myocardial Metabolism

Current imaging methods have focused on evaluation of myocardial anatomy and function. However, since myocardial metabolism and function are interrelated, metabolic myocardial imaging techniques, such as positron emission tomography, single photon emission tomography, and magnetic resonance spectroscopy present novel opportunities for probing myocardial pathology and developing new therapeutic approaches. Potential clinical applications of metabolic imaging include hypertensive and ischemic heart disease, heart failure, cardiac transplantation, as well as cardiomyopathies. Furthermore, response to therapeutic intervention can be monitored using metabolic imaging. Analysis of metabolic data in the past has been limited, focusing primarily on isolated metabolites. Models of myocardial metabolism, however, such as the oxygen transport and cellular energetics model and constraint-based metabolic network modeling, offer opportunities for evaluation interactions between greater numbers of metabolites in the heart. In this review, the roles of metabolic myocardial imaging and analysis of metabolic data using modeling methods for expanding our understanding of cardiac pathology are discussed.

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

Constraint-based modeling is an approach for quantitative prediction of net reaction flux in genome-scale biochemical networks. In vivo, the second law of thermodynamics requires that net macroscopic flux be forward, when the transformed reaction Gibbs energy is negative. We calculate the latter by using (i) group contribution estimates of metabolite species Gibbs energy, combined with (ii) experimentally measured equilibrium constants. In an application to a genome-scale stoichiometric model of Escherichia coli metabolism, iAF1260, we demonstrate that quantitative prediction of reaction directionality is increased in scope and accuracy by integration of both data sources, transformed appropriately to in vivo pH, temperature and ionic strength. Comparison of quantitative versus qualitative assignment of reaction directionality in iAF1260, assuming an accommodating reactant concentration range of 0.02–20 mM, revealed that quantitative assignment leads to a low false positive, but high false negative, prediction of effectively irreversible reactions. The latter is partly due to the uncertainty associated with group contribution estimates. We also uncovered evidence that the high intracellular concentration of glutamate in E. coli may be essential to direct otherwise thermodynamically unfavorable essential reactions, such as the leucine transaminase reaction, in an anabolic direction.

Systems-Level Engineering of Nonfermentative Metabolism in Yeast

We designed and experimentally validated an in silico gene deletion strategy for engineering endogenous one-carbon (C1) metabolism in yeast. We used constraint-based metabolic modeling and computer-aided gene knockout simulations to identify five genes (ALT2, FDH1, FDH2, FUM1, and ZWF1), which, when deleted in combination, predicted formic acid secretion in Saccharomyces cerevisiae under aerobic growth conditions. Once constructed, the quintuple mutant strain showed the predicted increase in formic acid secretion relative to a formate dehydrogenase mutant (fdh1 fdh2), while formic acid secretion in wild-type yeast was undetectable. Gene expression and physiological data generated post hoc identified a retrograde response to mitochondrial deficiency, which was confirmed by showing Rtg1-dependent NADH accumulation in the engineered yeast strain. Formal pathway analysis combined with gene expression data suggested specific modes of regulation that govern C1 metabolic flux in yeast. Specifically, we identified coordinated transcriptional regulation of C1 pathway enzymes and a positive flux control coefficient for the branch point enzyme 3-phosphoglycerate dehydrogenase (PGDH). Together, these results demonstrate that constraint-based models can identify seemingly unrelated mutations, which interact at a systems level across subcellular compartments to modulate flux through nonfermentative metabolic pathways.

FBA-SimVis: interactive visualization of constraint-based metabolic models

Summary: FBA-SimVis is a VANTED plug-in for the constraint-based analysis of metabolic models with special focus on the visual exploration of metabolic flux data resulting from model analysis. The program provides a user-friendly environment for model reconstruction, constraint-based model analysis, and interactive visualization of the simulation results. With the ability to quantitatively analyse metabolic fluxes in an interactive and visual manner, FBA-SimVis supports a comprehensive understanding of constraint-based metabolic flux models in both overview and detail.Availability: Software with manual and tutorials are freely available at http://fbasimvis.ipk-gatersleben.de/Contact: grafahr@ipk-gatersleben.deSupplementary information: Examples and supplementary data are available at http://fbasimvis.ipk-gatersleben.de/

Proteomic and network analysis characterize stage-specific metabolism in Trypanosoma cruzi.

BackgroundTrypanosoma cruzi is a Kinetoplastid parasite of humans and is the cause of Chagas disease, a potentially lethal condition affecting the cardiovascular, gastrointestinal, and nervous systems of the human host. Constraint-based modeling has emerged in the last decade as a useful approach to integrating genomic and other high-throughput data sets with more traditional, experimental data acquired through decades of research and published in the literature.ResultsWe present a validated, constraint-based model of the core metabolism of Trypanosoma cruzi strain CL Brener. The model includes four compartments (extracellular space, cytosol, mitochondrion, glycosome), 51 transport reactions, and 93 metabolic reactions covering carbohydrate, amino acid, and energy metabolism. In addition, we make use of several replicate high-throughput proteomic data sets to specifically examine metabolism of the morphological form of T. cruzi in the insect gut (epimastigote stage).ConclusionThis work demonstrates the utility of constraint-based models for integrating various sources of data (e.g., genomics, primary biochemical literature, proteomics) to generate testable hypotheses. This model represents an approach for the systematic study of T. cruzi metabolism under a wide range of conditions and perturbations, and should eventually aid in the identification of urgently needed novel chemotherapeutic targets.

Identifying essential genes in Escherichia coli from a metabolic optimization principle

Understanding the organization of reaction fluxes in cellular metabolism from the stoichiometry and the topology of the underlying biochemical network is a central issue in systems biology. In this task, it is important to devise reasonable approximation schemes that rely on the stoichiometric data only, because full-scale kinetic approaches are computationally affordable only for small networks (e.g., red blood cells, ≈50 reactions). Methods commonly used are based on finding the stationary flux configurations that satisfy mass-balance conditions for metabolites, often coupling them to local optimization rules (e.g., maximization of biomass production) to reduce the size of the solution space to a single point. Such methods have been widely applied and have proven able to reproduce experimental findings for relatively simple organisms in specific conditions. Here, we define and study a constraint-based model of cellular metabolism where neither mass balance nor flux stationarity are postulated and where the relevant flux configurations optimize the global growth of the system. In the case of Escherichia coli , steady flux states are recovered as solutions, although mass-balance conditions are violated for some metabolites, implying a nonzero net production of the latter. Such solutions furthermore turn out to provide the correct statistics of fluxes for the bacterium E. coli in different environments and compare well with the available experimental evidence on individual fluxes. Conserved metabolic pools play a key role in determining growth rate and flux variability. Finally, we are able to connect phenomenological gene essentiality with “frozen” fluxes (i.e., fluxes with smaller allowed variability) in E. coli metabolism.

Iterative reconstruction of a global metabolic model of Acinetobacter baylyi ADP1 using high-throughput growth phenotype and gene essentiality data

BackgroundGenome-scale metabolic models are powerful tools to study global properties of metabolic networks. They provide a way to integrate various types of biological information in a single framework, providing a structured representation of available knowledge on the metabolism of the respective species.ResultsWe reconstructed a constraint-based metabolic model of Acinetobacter baylyi ADP1, a soil bacterium of interest for environmental and biotechnological applications with large-spectrum biodegradation capabilities. Following initial reconstruction from genome annotation and the literature, we iteratively refined the model by comparing its predictions with the results of large-scale experiments: (1) high-throughput growth phenotypes of the wild-type strain on 190 distinct environments, (2) genome-wide gene essentialities from a knockout mutant library, and (3) large-scale growth phenotypes of all mutant strains on 8 minimal media. Out of 1412 predictions, 1262 were initially consistent with our experimental observations. Inconsistencies were systematically examined, leading in 65 cases to model corrections. The predictions of the final version of the model, which included three rounds of refinements, are consistent with the experimental results for (1) 91% of the wild-type growth phenotypes, (2) 94% of the gene essentiality results, and (3) 94% of the mutant growth phenotypes. To facilitate the exploitation of the metabolic model, we provide a web interface allowing online predictions and visualization of results on metabolic maps.ConclusionThe iterative reconstruction procedure led to significant model improvements, showing that genome-wide mutant phenotypes on several media can significantly facilitate the transition from genome annotation to a high-quality model.

Context-Specific Metabolic Networks Are Consistent with Experiments

Reconstructions of cellular metabolism are publicly available for a variety of different microorganisms and some mammalian genomes. To date, these reconstructions are “genome-scale” and strive to include all reactions implied by the genome annotation, as well as those with direct experimental evidence. Clearly, many of the reactions in a genome-scale reconstruction will not be active under particular conditions or in a particular cell type. Methods to tailor these comprehensive genome-scale reconstructions into context-specific networks will aid predictive in silico modeling for a particular situation. We present a method called Gene Inactivity Moderated by Metabolism and Expression (GIMME) to achieve this goal. The GIMME algorithm uses quantitative gene expression data and one or more presupposed metabolic objectives to produce the context-specific reconstruction that is most consistent with the available data. Furthermore, the algorithm provides a quantitative inconsistency score indicating how consistent a set of gene expression data is with a particular metabolic objective. We show that this algorithm produces results consistent with biological experiments and intuition for adaptive evolution of bacteria, rational design of metabolic engineering strains, and human skeletal muscle cells. This work represents progress towards producing constraint-based models of metabolism that are specific to the conditions where the expression profiling data is available.