Properties Of Metabolic Networks Research Articles

Alteration of the Individual Metabolic Network of the Brain Based on Jensen-Shannon Divergence Similarity Estimation in Elderly Patients With Type 2 Diabetes Mellitus.

The aim of this study was to investigate the interactive effect between aging and type 2 diabetes mellitus (T2DM) on brain glucose metabolism, individual metabolic connectivity, and network properties. Using a 2 × 2 factorial design, 83 patients with T2DM (40 elderly and 43 middle-aged) and 69 sex-matched healthy control subjects (HCs) (34 elderly and 35 middle-aged) underwent 18F-fluorodeoxyglucose positron emission tomography/magnetic resonance scanning. Jensen-Shannon divergence was applied to construct individual metabolic connectivity and networks. The topological properties of the networks were quantified using graph theoretical analysis. The general linear model was used to mainly estimate the interaction effect between aging and T2DM on glucose metabolism, metabolic connectivity, and network. There was an interaction effect between aging and T2DM on glucose metabolism, metabolic connectivity, and regional metabolic network properties (all P < 0.05). The post hoc analyses showed that compared with elderly HCs and middle-aged patients with T2DM, elderly patients with T2DM had decreased glucose metabolism, increased metabolic connectivity, and regional metabolic network properties in cognition-related brain regions (all P < 0.05). Age and fasting plasma glucose had negative correlations with glucose metabolism and positive correlations with metabolic connectivity. Elderly patients with T2DM had glucose hypometabolism, strengthened functional integration, and increased efficiency of information communication mainly located in cognition-related brain regions. Metabolic connectivity pattern changes might be compensatory changes for glucose hypometabolism.

Functional prediction of environmental variables using metabolic networks

In this manuscript, we propose a novel approach to assess relationships between environment and metabolic networks. We used a comprehensive dataset of more than 5000 prokaryotic species from which we derived the metabolic networks. We compute the scope from the reconstructed graphs, which is the set of all metabolites and reactions that can potentially be synthesized when provided with external metabolites. We show using machine learning techniques that the scope is an excellent predictor of taxonomic and environmental variables, namely growth temperature, oxygen tolerance, and habitat. In the literature, metabolites and pathways are rarely used to discriminate species. We make use of the scope underlying structure—metabolites and pathways—to construct the predictive models, giving additional information on the important metabolic pathways needed to discriminate the species, which is often absent in other metabolic network properties. For example, in the particular case of growth temperature, glutathione biosynthesis pathways are specific to species growing in cold environments, whereas tungsten metabolism is specific to species in warm environments, as was hinted in current literature. From a machine learning perspective, the scope is able to reduce the dimension of our data, and can thus be considered as an interpretable graph embedding.

The Contribution of Metabolomics to Systems Biology: Current Applications Bridging Genotype and Phenotype in Plant Science.

Metabolomics is a valuable approach used to acquire comprehensive information about the set of metabolites in a cell or tissue, enabling a functional screen of the cellular activities in biological systems. Although metabolomics provides a more immediate and dynamic picture of phenotypes in comparison to the other omics, it is also the most complicated to measure because no single analytical technology can capture the extraordinary complexity of metabolite diversity in terms of structure and physical properties. Metabolomics has been extensively employed for a wide range of applications in plant science, which will be described in detail in this chapter. Among them, metabolomics is used for discriminating patterns of plant responses to genetic and environmental perturbations, as diagnostics and prediction tool to elucidate the function of genes for important and complex agronomic traits in crop species, and flux measurements are used to dissect the structure and regulatory properties of metabolic networks.

An extended and generalized framework for the calculation of metabolic intervention strategies based on minimal cut sets.

The concept of minimal cut sets (MCS) provides a flexible framework for analyzing properties of metabolic networks and for computing metabolic intervention strategies. In particular, it has been used to support the targeted design of microbial strains for bio-based production processes. Herein we present a number of major extensions that generalize the existing MCS approach and broaden its scope for applications in metabolic engineering. We first introduce a modified approach to integrate gene-protein-reaction associations (GPR) in the metabolic network structure for the computation of gene-based intervention strategies. In particular, we present a set of novel compression rules for GPR associations, which effectively speedup the computation of gene-based MCS by a factor of up to one order of magnitude. These rules are not specific for MCS and as well applicable to other computational strain design methods. Second, we enhance the MCS framework by allowing the definition of multiple target (undesired) and multiple protected (desired) regions. This enables precise tailoring of the metabolic solution space of the designed strain with unlimited flexibility. Together with further generalizations such as individual cost factors for each intervention, direct combinations of reaction/gene deletions and additions as well as the possibility to search for substrate co-feeding strategies, the scope of the MCS framework could be broadly extended. We demonstrate the applicability and performance benefits of the described developments by computing (gene-based) Escherichia coli strain designs for the bio-based production of 2,3-butanediol, a chemical, that has recently received much attention in the field of metabolic engineering. With our extended framework, we could identify promising strain designs that were formerly unpredictable, including those based on substrate co-feeding.

Distinct relationships of amyloid-beta and tau deposition to cerebral glucose metabolic networks in Alzheimer’s disease

Extracellular accumulation of amyloid-beta peptides and intracellular neurofibrillary tangles (NFTs) of hyperphosphorylated tau proteins are the two cardinally pathological hallmarks of Alzheimer’s disease (AD). However, their exact roles in the mechanisms of AD progression are not well established. Given that AD is a disconnection syndrome and hypometabolism is one of its most important neurodegenerative indicators, we hypothesized amyloid-beta and tau burden may disturb the glucose metabolic network of AD. Here we investigated the relationship of these two factors to regional metabolic network properties using multimodal positron emission tomography (PET) imaging data. Participants included six groups covering from cognitively normal controls, patients with early cognitive impairment (MCI), late MCI, mild AD, moderate AD to severe AD who underwent amyloid-beta PET, tau PET and fluorodeoxyglucose (FDG) PET. Glucose metabolic network of each group was constructed and relations of amyloid-beta and tau to regional metabolic network measurements were investigated. Results revealed distinct associations of these two hallmarks to metabolic networks: amyloid-beta were positively related to metabolic network measurements at relative early phases of AD, while tau burden showed a negative relationship at late phase of AD. These results supported the notion that amyloid-beta and tau accumulation may contribute independently to mechanisms of AD. Furthermore, these findings might also provide connectivity evidence for the speculation that amyloid-beta deposition is protective to neuronal activity.

Statistical mechanics for metabolic networks during steady state growth

Which properties of metabolic networks can be derived solely from stoichiometry? Predictive results have been obtained by flux balance analysis (FBA), by postulating that cells set metabolic fluxes to maximize growth rate. Here we consider a generalization of FBA to single-cell level using maximum entropy modeling, which we extend and test experimentally. Specifically, we define for Escherichia coli metabolism a flux distribution that yields the experimental growth rate: the model, containing FBA as a limit, provides a better match to measured fluxes and it makes a wide range of predictions: on flux variability, regulation, and correlations; on the relative importance of stoichiometry vs. optimization; on scaling relations for growth rate distributions. We validate the latter here with single-cell data at different sub-inhibitory antibiotic concentrations. The model quantifies growth optimization as emerging from the interplay of competitive dynamics in the population and regulation of metabolism at the level of single cells.

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming.

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. The software is implemented in Matlab, and is provided as supplementary information . hyunseob.song@pnnl.gov. Supplementary data are available at Bioinformatics online.

The Landscape of Evolution: Reconciling Structural and Dynamic Properties of Metabolic Networks in Adaptive Diversifications.

The network of the interactions among genes, proteins, and metabolites delineates a range of potential phenotypic diversifications in a lineage, and realized phenotypic changes are the result of differences in the dynamics of the expression of the elements and interactions in this deterministic network. Regulatory mechanisms, such as hormones, mediate the relationship between the structural and dynamic properties of networks by determining how and when the elements are expressed and form a functional unit or state. Changes in regulatory mechanisms lead to variable expression of functional states of a network within and among generations. Functional properties of network elements, and the magnitude and direction of evolutionary change they determine, depend on their location within a network. Here, we examine the relationship between network structure and the dynamic mechanisms that regulate flux through a metabolic network. We review the mechanisms that control metabolic flux in enzymatic reactions and examine structural properties of the network locations that are targets of flux control. We aim to establish a predictive framework to test the contributions of structural and dynamic properties of deterministic networks to evolutionary diversifications.

Integration and Validation of the Genome-Scale Metabolic Models of Pichia pastoris: A Comprehensive Update of Protein Glycosylation Pathways, Lipid and Energy Metabolism.

MotivationGenome-scale metabolic models (GEMs) are tools that allow predicting a phenotype from a genotype under certain environmental conditions. GEMs have been developed in the last ten years for a broad range of organisms, and are used for multiple purposes such as discovering new properties of metabolic networks, predicting new targets for metabolic engineering, as well as optimizing the cultivation conditions for biochemicals or recombinant protein production. Pichia pastoris is one of the most widely used organisms for heterologous protein expression. There are different GEMs for this methylotrophic yeast of which the most relevant and complete in the published literature are iPP668, PpaMBEL1254 and iLC915. However, these three models differ regarding certain pathways, terminology for metabolites and reactions and annotations. Moreover, GEMs for some species are typically built based on the reconstructed models of related model organisms. In these cases, some organism-specific pathways could be missing or misrepresented.ResultsIn order to provide an updated and more comprehensive GEM for P. pastoris, we have reconstructed and validated a consensus model integrating and merging all three existing models. In this step a comprehensive review and integration of the metabolic pathways included in each one of these three versions was performed. In addition, the resulting iMT1026 model includes a new description of some metabolic processes. Particularly new information described in recently published literature is included, mainly related to fatty acid and sphingolipid metabolism, glycosylation and cell energetics. Finally the reconstructed model was tested and validated, by comparing the results of the simulations with available empirical physiological datasets results obtained from a wide range of experimental conditions, such as different carbon sources, distinct oxygen availability conditions, as well as producing of two different recombinant proteins. In these simulations, the iMT1026 model has shown a better performance than the previous existing models.

Impact of kinetic isotope effects in isotopic studies of metabolic systems.

BackgroundIsotope labeling experiments (ILEs) are increasingly used to investigate the functioning of metabolic systems. Some enzymes are subject to kinetic isotope effects (KIEs) which modulate reaction rates depending on the isotopic composition of their substrate(s). KIEs may therefore affect both the propagation of isotopes through metabolic networks and their operation, and ultimately jeopardize the biological value of ILEs. However, the actual impact of KIEs on metabolism has never been investigated at the system level.ResultsFirst, we developed a framework which integrates KIEs into kinetic and isotopic models of metabolism, thereby accounting for their system-wide effects on metabolite concentrations, metabolic fluxes, and isotopic patterns. Then, we applied this framework to assess the impact of KIEs on the central carbon metabolism of Escherichia coli in the context of 13C-ILEs, under different situations commonly encountered in laboratories. Results showed that the impact of KIEs strongly depends on the label input and on the variable considered but is significantly lower than expected intuitively from measurements on isolated enzymes. The global robustness of both the metabolic operation and isotopic patterns largely emerge from intrinsic properties of metabolic networks, such as the distribution of control across the network and bidirectional isotope exchange.ConclusionsThese results demonstrate the necessity of investigating the impact of KIEs at the level of the entire system, contradict previous hypotheses that KIEs would have a strong effect on isotopic distributions and on flux determination, and strengthen the biological value of 13C-ILEs. The proposed modeling framework is generic and can be used to investigate the impact of all the isotopic tracers (2H, 13C, 15N, 18O, etc.) on different isotopic datasets and metabolic systems. By allowing the integration of isotopic and metabolomics data collected under stationary and/or non-stationary conditions, it may also assist interpretations of ILEs and facilitate the development of more accurate kinetic models with improved explicative and predictive capabilities.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0213-8) contains supplementary material, which is available to authorized users.

Phenotypic constraints promote latent versatility and carbon efficiency in metabolic networks.

System-level properties of metabolic networks may be the direct product of natural selection or arise as a by-product of selection on other properties. Here we study the effect of direct selective pressure for growth or viability in particular environments on two properties of metabolic networks: latent versatility to function in additional environments and carbon usage efficiency. Using a Markov chain Monte Carlo (MCMC) sampling based on flux balance analysis (FBA), we sample from a known biochemical universe random viable metabolic networks that differ in the number of directly constrained environments. We find that the latent versatility of sampled metabolic networks increases with the number of directly constrained environments and with the size of the networks. We then show that the average carbon wastage of sampled metabolic networks across the constrained environments decreases with the number of directly constrained environments and with the size of the networks. Our work expands the growing body of evidence about nonadaptive origins of key functional properties of biological networks.

A mathematical approach to emergent properties of metabolic networks: Partial coupling relations, hyperarcs and flux ratios

Emergent properties in systems biology are those which arise only when the biological system passes a certain level of complexity. In this study, we introduce some of the emergent properties which appear in the constraint-based analysis of metabolic networks. These properties generally appear as a result of existence of hfdeyperarcs and irreversible reactions in networks. Here, we present examples of metabolic networks in which there exist at least two reactions whose fluxes cannot be written as products and/or ratios of the stoichiometric coefficients of the network. We show that any such network contains at least one hyperarc. Additionally, we prove that partial coupling cannot appear in consistent metabolic networks with less than four reactions, or with less than three irreversible reactions, or without hyperarc(s).

(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis

BackgroundMetabolic control analysis (MCA) and supply–demand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supply–demand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect.ResultsThis study integrates control engineering and classical MCA augmented with supply–demand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the ‘integral control’ (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of ‘integral control’ should rarely be expected to lead to the ‘perfect adaptation’: although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily.ConclusionsA proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the ‘perfect’ regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

Basic concepts and principles of stoichiometric modeling of metabolic networks

Metabolic networks supply the energy and building blocks for cell growth and maintenance. Cells continuously rewire their metabolic networks in response to changes in environmental conditions to sustain fitness. Studies of the systemic properties of metabolic networks give insight into metabolic plasticity and robustness, and the ability of organisms to cope with different environments. Constraint-based stoichiometric modeling of metabolic networks has become an indispensable tool for such studies. Herein, we review the basic theoretical underpinnings of constraint-based stoichiometric modeling of metabolic networks. Basic concepts, such as stoichiometry, chemical moiety conservation, flux modes, flux balance analysis, and flux solution spaces, are explained with simple, illustrative examples. We emphasize the mathematical definitions and their network topological interpretations.

A MATLAB toolbox for structural kinetic modeling

Structural kinetic modeling (SKM) enables the analysis of dynamical properties of metabolic networks solely based on topological information and experimental data. Current SKM-based experiments are hampered by the time-intensive process of assigning model parameters and choosing appropriate sampling intervals for Monte-Carlo experiments. We introduce a toolbox for the automatic and efficient construction and evaluation of structural kinetic models (SK models). Quantitative and qualitative analyses of network stability properties are performed in an automated manner. We illustrate the model building and analysis process in detailed example scripts that provide toolbox implementations of previously published literature models. The source code is freely available for download at http://bioinformatics.uni-potsdam.de/projects/skm. girbig@mpimp-golm.mpg.de.

Evolutionary significance of metabolic network properties

Complex networks have been successfully employed to represent different levels of biological systems, ranging from gene regulation to protein–protein interactions and metabolism. Network-based research has mainly focused on identifying unifying structural properties, such as small average path length, large clustering coefficient, heavy-tail degree distribution and hierarchical organization, viewed as requirements for efficient and robust system architectures. However, for biological networks, it is unclear to what extent these properties reflect the evolutionary history of the represented systems. Here, we show that the salient structural properties of six metabolic networks from all kingdoms of life may be inherently related to the evolution and functional organization of metabolism by employing network randomization under mass balance constraints. Contrary to the results from the common Markov-chain switching algorithm, our findings suggest the evolutionary importance of the small-world hypothesis as a fundamental design principle of complex networks. The approach may help us to determine the biologically meaningful properties that result from evolutionary pressure imposed on metabolism, such as the global impact of local reaction knockouts. Moreover, the approach can be applied to test to what extent novel structural properties can be used to draw biologically meaningful hypothesis or predictions from structure alone.

JMassBalance: mass-balanced randomization and analysis of metabolic networks

Summary: Analysis of biological networks requires assessing the statistical significance of network-based predictions by using a realistic null model. However, the existing network null model, switch randomization, is unsuitable for metabolic networks, as it does not include physical constraints and generates unrealistic reactions. We present JMassBalance, a tool for mass-balanced randomization and analysis of metabolic networks. The tool allows efficient generation of large sets of randomized networks under the physical constraint of mass balance. In addition, various structural properties of the original and randomized networks can be calculated, facilitating the identification of the salient properties of metabolic networks with a biologically meaningful null model.Availability and Implementation: JMassBalance is implemented in Java and freely available on the web at http://mathbiol.mpimp-golm.mpg.de/massbalance/.Contact: basler@mpimp-golm.mpg.de

Comparison between elementary flux modes analysis and 13C-metabolic fluxes measured in bacterial and plant cells

Background13C metabolic flux analysis is one of the pertinent ways to compare two or more physiological states. From a more theoretical standpoint, the structural properties of metabolic networks can be analysed to explore feasible metabolic behaviours and to define the boundaries of steady state flux distributions. Elementary flux mode analysis is one of the most efficient methods for performing this analysis. In this context, recent approaches have tended to compare experimental flux measurements with topological network analysis.ResultsMetabolic networks describing the main pathways of central carbon metabolism were set up for a bacteria species (Corynebacterium glutamicum) and a plant species (Brassica napus) for which experimental flux maps were available. The structural properties of each network were then studied using the concept of elementary flux modes. To do this, coefficients of flux efficiency were calculated for each reaction within the networks by using selected sets of elementary flux modes. Then the relative differences - reflecting the change of substrate i.e. a sugar source for C. glutamicum and a nitrogen source for B. napus - of both flux efficiency and flux measured experimentally were compared. For both organisms, there is a clear relationship between these parameters, thus indicating that the network structure described by the elementary flux modes had captured a significant part of the metabolic activity in both biological systems. In B. napus, the extension of the elementary flux mode analysis to an enlarged metabolic network still resulted in a clear relationship between the change in the coefficients and that of the measured fluxes. Nevertheless, the limitations of the method to fit some particular fluxes are discussed.ConclusionThis consistency between EFM analysis and experimental flux measurements, validated on two metabolic systems allows us to conclude that elementary flux mode analysis could be a useful tool to complement 13C metabolic flux analysis, by allowing the prediction of changes in internal fluxes before carbon labelling experiments.

Properties of metabolic graphs: biological organization or representation artifacts?

BackgroundStandard graphs, where each edge links two nodes, have been extensively used to represent the connectivity of metabolic networks. It is based on this representation that properties of metabolic networks, such as hierarchical and small-world structures, have been elucidated and null models have been proposed to derive biological organization hypotheses. However, these graphs provide a simplistic model of a metabolic network's connectivity map, since metabolic reactions often involve more than two reactants. In other words, this map is better represented as a hypergraph. Consequently, a question that naturally arises in this context is whether these properties truly reflect biological organization or are merely an artifact of the representation.ResultsIn this paper, we address this question by reanalyzing topological properties of the metabolic network of Escherichia coli under a hypergraph representation, as well as standard graph abstractions. We find that when clustering is properly defined for hypergraphs and subsequently used to analyze metabolic networks, the scaling of clustering, and thus the hierarchical structure hypothesis in metabolic networks, become unsupported. Moreover, we find that incorporating the distribution of reaction sizes into the null model further weakens the support for the scaling patterns.ConclusionsThese results combined suggest that the reported scaling of the clustering coefficients in the metabolic graphs and its specific power coefficient may be an artifact of the graph representation, and may not be supported when biochemical reactions are atomically treated as hyperedges. This study highlights the implications of the way a biological system is represented and the null model employed on the elucidated properties, along with their support, of the system.

Mass-balanced randomization of metabolic networks

Motivation: Network-centered studies in systems biology attempt to integrate the topological properties of biological networks with experimental data in order to make predictions and posit hypotheses. For any topology-based prediction, it is necessary to first assess the significance of the analyzed property in a biologically meaningful context. Therefore, devising network null models, carefully tailored to the topological and biochemical constraints imposed on the network, remains an important computational problem.Results: We first review the shortcomings of the existing generic sampling scheme—switch randomization—and explain its unsuitability for application to metabolic networks. We then devise a novel polynomial-time algorithm for randomizing metabolic networks under the (bio)chemical constraint of mass balance. The tractability of our method follows from the concept of mass equivalence classes, defined on the representation of compounds in the vector space over chemical elements. We finally demonstrate the uniformity of the proposed method on seven genome-scale metabolic networks, and empirically validate the theoretical findings. The proposed method allows a biologically meaningful estimation of significance for metabolic network properties.Contact: basler@mpimp-golm.mpg.de; nikoloski@mpimp-golm.mpg.deSupplementary Information: Supplementary data are available at Bioinformatics online.