Hierarchy of metabolic compounds based on their synthesising capacity

The concept of scopes is applied to analyse large metabolic networks. Scopes are defined as sets of metabolites that can be synthesised by a metabolic network when it is provided with given seeds (Sets of initial metabolic compounds). Thus, scopes represent synthesising capacities of the seeds in the network. A hierarchy is discussed in the sense that compounds, which are part of the scope of another compound, possess scopes themselves that are subsets of the former scope. This hierarchy is analysed by means of a directed acyclic graph. Using a simple chemical model, it is found that this hierarchy contains specific structures that can, to a large extent, be explained by the chemical composition of the participating compounds. In this way, it represents a new kind of map of metabolic networks, arranging the metabolic compounds according to their chemical capacity.     

Minimal cut sets in biochemical reaction networks

MOTIVATION: Structural studies of metabolic networks yield deeper insight into topology, functionality and capabilities of the metabolisms of different organisms. Here, we address the analysis of potential failure modes in metabolic networks whose occurrence will render the network structurally incapable of performing certain functions. Such studies will help to identify crucial parts in the network structure and to find suitable targets for repressing undesired metabolic functions. RESULTS: We introduce the concept of minimal cut sets for biochemical networks. A minimal cut set (MCS) is a minimal (irreducible) set of reactions in the network whose inactivation will definitely lead to a failure in certain network functions. We present an algorithm which enables the computation of the MCSs in a given network related to user-defined objective reactions. This algorithm operates on elementary modes. A number of potential applications are outlined, including network verifications, phenotype predictions, assessing structural robustness and fragility, metabolic flux analysis and target identification in drug discovery. Applications are illustrated by the MCSs in the central metabolism of Escherichia coli for growth on different substrates. AVAILABILITY: Computation and analysis of MCSs is an additional feature of the FluxAnalyzer (freely available for academic users upon request, special contracts for industrial companies; see web page below). Supplementary information: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer     

Structural analysis of metabolic networks based on flux centrality

Metabolic reactions are fundamental to living organisms, and a large number of reactions simultaneously occur at a given time in living cells transforming diverse metabolites into each other. There has been an ongoing debate on how to classify metabolites with respect to their importance for metabolic performance, usually based on the analysis of topological properties of genome scale metabolic networks. However, none of these studies have accounted quantitatively for flux in metabolic networks, thus lacking an important component of a cell’s biochemistry.We therefore analyzed a genome scale metabolic network of Escherichia coli by comparing growth under 19 different growth conditions, using flux balance analysis and weighted network centrality investigation. With this novel concept of flux centrality we generated metabolite rankings for each particular growth condition. In contrast to the results of conventional analysis of genome scale metabolic networks, different metabolites were top-ranking dependent on the growth condition. At the same time, several metabolites were consistently among the high ranking ones. Those are associated with pathways that have been described by biochemists as the most central part of metabolism, such as glycolysis, tricarboxylic acid cycle and pentose phosphate pathway. The values for the average path length of the analyzed metabolite networks were between 10.5 and 12.6, supporting recent findings that the metabolic network of E. coli is not a small-world network.     

A transcriptional analysis of carotenoid, chlorophyll and plastidial isoprenoid biosynthesis genes during development and osmotic stress responses in Arabidopsis thaliana

Background

Multiple pathway databases are available that describe the human metabolic network and have proven their usefulness in many applications, ranging from the analysis and interpretation of high-throughput data to their use as a reference repository. However, so far the various human metabolic networks described by these databases have not been systematically compared and contrasted, nor has the extent to which they differ been quantified. For a researcher using these databases for particular analyses of human metabolism, it is crucial to know the extent of the differences in content and their underlying causes. Moreover, the outcomes of such a comparison are important for ongoing integration efforts.

Results

We compared the genes, EC numbers and reactions of five frequently used human metabolic pathway databases. The overlap is surprisingly low, especially on reaction level, where the databases agree on 3% of the 6968 reactions they have combined. Even for the well-established tricarboxylic acid cycle the databases agree on only 5 out of the 30 reactions in total. We identified the main causes for the lack of overlap. Importantly, the databases are partly complementary. Other explanations include the number of steps a conversion is described in and the number of possible alternative substrates listed. Missing metabolite identifiers and ambiguous names for metabolites also affect the comparison.

Conclusions

Our results show that each of the five networks compared provides us with a valuable piece of the puzzle of the complete reconstruction of the human metabolic network. To enable integration of the networks, next to a need for standardizing the metabolite names and identifiers, the conceptual differences between the databases should be resolved. Considerable manual intervention is required to reach the ultimate goal of a unified and biologically accurate model for studying the systems biology of human metabolism. Our comparison provides a stepping stone for such an endeavor.     

Chemical basis of metabolic network organization

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

Evolutionary changes of metabolic networks and their biosynthetic capacities

The metabolic networks of different species show a large variety in their structural design. In this work, the evolution of functional properties of metabolism in relation with metabolic network structure is investigated. The metabolism of ancestral species is inferred from the metabolism of contemporary species using a Bayesian network model for metabolism evolution. Subsequently, these networks are analysed with the recently developed method of network expansion. This method allows for a structural analysis of metabolic networks as well as a quantification of network functions in terms of their synthesising capacities when they are provided with certain external resources. The evolutionary dynamics of one particular network function: the metabolic expansion of glucose is investigated.     

Inferring meaningful pathways in weighted metabolic networks

An approach is presented for computing meaningful pathways in the network of small molecule metabolism comprising the chemical reactions characterized in all organisms. The metabolic network is described as a weighted graph in which all the compounds are included, but each compound is assigned a weight equal to the number of reactions in which it participates. Path finding is performed in this graph by searching for one or more paths with lowest weight. Performance is evaluated systematically by computing paths between the first and last reactions in annotated metabolic pathways, and comparing the intermediate reactions in the computed pathways to those in the annotated ones. For the sake of comparison, paths are computed also in the un-weighted raw (all compounds and reactions) and filtered (highly connected pool metabolites removed) metabolic graphs, respectively. The correspondence between the computed and annotated pathways is very poor (<30%) in the raw graph; increasing to approximately 65% in the filtered graph; reaching approximately 85% in the weighted graph. Considering the best-matching path among the five lightest paths increases the correspondence to 92%, on average. We then show that the average distance between pairs of metabolites is significantly larger in the weighted graph than in the raw unfiltered graph, suggesting that the small-world properties previously reported for metabolic networks probably result from irrelevant shortcuts through pool metabolites. In addition, we provide evidence that the length of the shortest path in the weighted graph represents a valid measure of the "metabolic distance" between enzymes. We suggest that the success of our simplistic approach is rooted in the high degree of specificity of the reactions in metabolic pathways, presumably reflecting thermodynamic constraints operating in these pathways. We expect our approach to find useful applications in inferring metabolic pathways in newly sequenced genomes.     

Stoichiometric design of metabolic networks: multifunctionality,clusters, optimization,weak and strong robustness

Starting from a limited set of reactions describing changes in the carbon skeleton of biochemical compounds complete sets of metabolic networks are constructed. The networks are characterized by the number and types of participating reactions. Elementary networks are defined by the condition that a specific chemical conversion can be performed by a set of given reactions and that this ability will be lost by elimination of any of these reactions. Groups of networks are identified with respect to their ability to perform a certain number of metabolic conversions in an elementary way which are called the network’s functions. The number of the network functions defines the degree of multifunctionality. Transitions between networks and mutations of networks are defined by exchanges of single reactions. Different mutations exist such as gain or loss of function mutations and neutral mutations. Based on these mutations neighbourhood relations between networks are established which are described in a graph theoretical way. Basic properties of these graphs are determined such as diameter, connectedness, distance distribution of pairs of vertices. A concept is developed to quantify the robustness of networks against changes in their stoichiometry where we distinguish between strong and weak robustness. Evolutionary algorithms are applied to study the development of network populations under constant and time dependent environmental conditions. It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured. Under changing environmental conditions multifunctional networks prove to be optimal and will be selected.     

The evolution of connectivity in metabolic networks

Processes in living cells are the result of interactions between biochemical compounds in highly complex biochemical networks. It is a major challenge in biology to understand causes and consequences of the specific design of these networks. A characteristic design feature of metabolic networks is the presence of hub metabolites such as ATP or NADH that are involved in a high number of reactions. To study the emergence of hub metabolites, we implemented computer simulations of a widely accepted scenario for the evolution of metabolic networks. Our simulations indicate that metabolic networks with a large number of highly specialized enzymes may evolve from a few multifunctional enzymes. During this process, enzymes duplicate and specialize, leading to a loss of biochemical reactions and intermediary metabolites. Complex features of metabolic networks such as the presence of hubs may result from selection of growth rate if essential biochemical mechanisms are considered. Specifically, our simulations indicate that group transfer reactions are essential for the emergence of hubs.     

Beyond topology: coevolution of structure and flux in metabolic networks

Interactions between the structure of a metabolic network and its functional properties underlie its evolutionary diversification, but the mechanism by which such interactions arise remains elusive. Particularly unclear is whether metabolic fluxes that determine the concentrations of compounds produced by a metabolic network, are causally linked to a network's structure or emerge independently of it. A direct empirical study of populations where both structural and functional properties vary among individuals’ metabolic networks is required to establish whether changes in structure affect the distribution of metabolic flux. In a population of house finches (Haemorhous mexicanus), we reconstructed full carotenoid metabolic networks for 442 individuals and uncovered 11 structural variants of this network with different compounds and reactions. We examined the consequences of this structural diversity for the concentrations of plumage‐bound carotenoids produced by flux in these networks. We found that concentrations of metabolically derived, but not dietary carotenoids, depended on network structure. Flux was partitioned similarly among compounds in individuals of the same network structure: within each network, compound concentrations were closely correlated. The highest among‐individual variation in flux occurred in networks with the strongest among‐compound correlations, suggesting that changes in the magnitude, but not the distribution of flux, underlie individual differences in compound concentrations on a static network structure. These findings indicate that the distribution of flux in carotenoid metabolism closely follows network structure. Thus, evolutionary diversification and local adaptations in carotenoid metabolism may depend more on the gain or loss of enzymatic reactions than on changes in flux within a network structure.     

Biosynthetic potentials of metabolites and their hierarchical organization

A major challenge in systems biology is to understand how complex and highly connected metabolic networks are organized. The structure of these networks is investigated here by identifying sets of metabolites that have a similar biosynthetic potential. We measure the biosynthetic potential of a particular compound by determining all metabolites than can be produced from it and, following a terminology introduced previously, call this set the scope of the compound. To identify groups of compounds with similar scopes, we apply a hierarchical clustering method. We find that compounds within the same cluster often display similar chemical structures and appear in the same metabolic pathway. For each cluster we define a consensus scope by determining a set of metabolites that is most similar to all scopes within the cluster. This allows for a generalization from scopes of single compounds to scopes of a chemical family. We observe that most of the resulting consensus scopes overlap or are fully contained in others, revealing a hierarchical ordering of metabolites according to their biosynthetic potential. Our investigations show that this hierarchy is not only determined by the chemical complexity of the metabolites, but also strongly by their biological function. As a general tendency, metabolites which are necessary for essential cellular processes exhibit a larger biosynthetic potential than those involved in secondary metabolism. A central result is that chemically very similar substances with different biological functions may differ significantly in their biosynthetic potentials. Our studies provide an important step towards understanding fundamental design principles of metabolic networks determined by the structural and functional complexity of metabolites.     

The connectivity structure,giant strong component and centrality of metabolic networks

MOTIVATION: Structural and functional analysis of genome-based large-scale metabolic networks is important for understanding the design principles and regulation of the metabolism at a system level. The metabolic network is conventionally considered to be highly integrated and very complex. A rational reduction of the metabolic network to its core structure and a deeper understanding of its functional modules are important. RESULTS: In this work, we show that the metabolites in a metabolic network are far from fully connected. A connectivity structure consisting of four major subsets of metabolites and reactions, i.e. a fully connected sub-network, a substrate subset, a product subset and an isolated subset is found to exist in metabolic networks of 65 fully sequenced organisms. The largest fully connected part of a metabolic network, called 'the giant strong component (GSC)', represents the most complicated part and the core of the network and has the feature of scale-free networks. The average path length of the whole network is primarily determined by that of the GSC. For most of the organisms, GSC normally contains less than one-third of the nodes of the network. This connectivity structure is very similar to the 'bow-tie' structure of World Wide Web. Our results indicate that the bow-tie structure may be common for large-scale directed networks. More importantly, the uncovered structure feature makes a structural and functional analysis of large-scale metabolic network more amenable. As shown in this work, comparing the closeness centrality of the nodes in the GSC can identify the most central metabolites of a metabolic network. To quantitatively characterize the overall connection structure of the GSC we introduced the term 'overall closeness centralization index (OCCI)'. OCCI correlates well with the average path length of the GSC and is a useful parameter for a system-level comparison of metabolic networks of different organisms. SUPPLEMENTARY INFORMATION: http://genome.gbf.de/bioinformatics/     

Genotype networks,innovation, and robustness in sulfur metabolism

Background  

A metabolism is a complex network of chemical reactions. This network synthesizes multiple small precursor molecules of biomass from chemicals that occur in the environment. The metabolic network of any one organism is encoded by a metabolic genotype, defined as the set of enzyme-coding genes whose products catalyze the network's reactions. Each metabolic genotype has a metabolic phenotype. We define this metabolic phenotype as the spectrum of different sources of a chemical element that a metabolism can use to synthesize biomass. We here focus on the element sulfur. We study properties of the space of all possible metabolic genotypes in sulfur metabolism by analyzing random metabolic genotypes that are viable on different numbers of sulfur sources.     

Metabolite coupling in genome-scale metabolic networks

Background  

Biochemically detailed stoichiometric matrices have now been reconstructed for various bacteria, yeast, and for the human cardiac mitochondrion based on genomic and proteomic data. These networks have been manually curated based on legacy data and elementally and charge balanced. Comparative analysis of these well curated networks is now possible. Pairs of metabolites often appear together in several network reactions, linking them topologically. This co-occurrence of pairs of metabolites in metabolic reactions is termed herein "metabolite coupling." These metabolite pairs can be directly computed from the stoichiometric matrix, S. Metabolite coupling is derived from the matrix ŜŜ ^T, whose off-diagonal elements indicate the number of reactions in which any two metabolites participate together, where Ŝ is the binary form of S.     

Metabolic Pathfinding Using RPAIR Annotation

Metabolic databases contain information about thousands of small molecules and reactions, which can be represented as networks. In the context of metabolic reconstruction, pathways can be inferred by searching optimal paths in such networks. A recurrent problem is the presence of pool metabolites (e.g., water, energy carriers, and cofactors), which are connected to hundreds of reactions, thus establishing irrelevant shortcuts between nodes of the network. One solution to this problem relies on weighted networks to penalize highly connected compounds. A more refined solution takes the chemical structure of reactants into account in order to differentiate between side and main compounds of a reaction. Thanks to an intensive annotation effort at KEGG, decompositions of reactions into reactant pairs (RPAIR) categorized by their role (main, trans, cofac, ligase, and leave) are now available.The goal of this article is to evaluate the impact of RPAIR data on pathfinding in metabolic networks. To this end, we measure the impact of different parameters concerning the construction of the metabolic network: mapping of reactions and reactant pairs onto a graph, use of selected categories of reactant pairs, weighting schemes for compounds and reactions, removal of highly connected metabolites, and reaction directionality. In total, we tested 104 combinations of parameters and identified their optimal values for pathfinding on the basis of 55 reference pathways from three organisms.The best-performing metabolic network combines the biochemical knowledge encoded by KEGG RPAIR with a weighting scheme penalizing highly connected compounds. With this network, we could recover reference pathways from Escherichia coli with an average accuracy of 93% (32 pathways), from Saccharomyces cerevisiae with an average accuracy of 66% (11 pathways), and from humans with an average accuracy of 70% (12 pathways). Our pathfinding approach is available as part of the Network Analysis Tools.     

An environmental perspective on metabolism

In principle the knowledge of an organism's metabolic network allows to infer its biosynthetic capabilities. Handorf et al. [2005. Expanding metabolic networks: scopes of compounds, robustness, and evolution. J. Mol. Evol. 61, 498-512] developed a method of network expansion generating the set of all possible metabolites that can be produced from a set of compounds, given the structure of a metabolic network. Here we investigate the inverse problem: which chemical compounds or sets of compounds must be provided as external resources in order to sustain the growth or maintenance of an organism, given the structure of its metabolic network? Although this problem is highly combinatorial, we show that it is possible to calculate locally minimal nutrient sets that can be interpreted in terms of resource types. Using these types we predict broad nutritional requirements for 447 organisms, providing clues for possible environments from the knowledge of their metabolic networks.     

Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph

MOTIVATION: Metabolic networks are organized in a modular, hierarchical manner. Methods for a rational decomposition of the metabolic network into relatively independent functional subsets are essential to better understand the modularity and organization principle of a large-scale, genome-wide network. Network decomposition is also necessary for functional analysis of metabolism by pathway analysis methods that are often hampered by the problem of combinatorial explosion due to the complexity of metabolic network. Decomposition methods proposed in literature are mainly based on the connection degree of metabolites. To obtain a more reasonable decomposition, the global connectivity structure of metabolic networks should be taken into account. RESULTS: In this work, we use a reaction graph representation of a metabolic network for the identification of its global connectivity structure and for decomposition. A bow-tie connectivity structure similar to that previously discovered for metabolite graph is found also to exist in the reaction graph. Based on this bow-tie structure, a new decomposition method is proposed, which uses a distance definition derived from the path length between two reactions. An hierarchical classification tree is first constructed from the distance matrix among the reactions in the giant strong component of the bow-tie structure. These reactions are then grouped into different subsets based on the hierarchical tree. Reactions in the IN and OUT subsets of the bow-tie structure are subsequently placed in the corresponding subsets according to a 'majority rule'. Compared with the decomposition methods proposed in literature, ours is based on combined properties of the global network structure and local reaction connectivity rather than, primarily, on the connection degree of metabolites. The method is applied to decompose the metabolic network of Escherichia coli. Eleven subsets are obtained. More detailed investigations of the subsets show that reactions in the same subset are really functionally related. The rational decomposition of metabolic networks, and subsequent studies of the subsets, make it more amenable to understand the inherent organization and functionality of metabolic networks at the modular level. SUPPLEMENTARY INFORMATION: http://genome.gbf.de/bioinformatics/     

The small world inside large metabolic networks

The metabolic network of the catabolic, energy and biosynthetic metabolism of Escherichia coli is a paradigmatic case for the large genetic and metabolic networks that functional genomics efforts are beginning to elucidate. To analyse the structure of previously unknown networks involving hundreds or thousands of components by simple visual inspection is impossible, and quantitative approaches are needed to analyse them. We have undertaken a graph theoretical analysis of the E. coli metabolic network and find that this network is a small-world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans. Moreover, the connectivity of the metabolites follows a power law, another unusual but by no means rare statistical distribution. This provides an objective criterion for the centrality of the tricarboxylic acid cycle to metabolism. The small-world architecture may serve to minimize transition times between metabolic states, and contains evidence about the evolutionary history of metabolism.     

A vacuolar class III peroxidase and the metabolism of anticancer indole alkaloids in Catharanthus roseus: Can peroxidases,secondary metabolites and arabinogalactan proteins be partners in microcompartmentation of cellular reactions?

Plants possess a unique metabolic diversity commonly designated as secondary metabolism, of which the anticancer alkaloids from Catharanthus roseus are among the most studied. Recently, in a classical function-to-protein-to-gene approach, we have characterized the main class III peroxidase (Prx) expressed in C. roseus leaves, CrPrx1, implicated in a key biosynthetic step of the anticancer alkaloids. We have shown the vacuolar sorting determination of CrPrx1 using GFP fusions and we have obtained further evidence supporting the role of this enzyme in alkaloid biosynthesis, indicating the potential of CrPrx1 as a molecular tool for the manipulation of alkaloid metabolism. Here, we discuss how plant cells may regulate Prx reactions. In fact, Prxs form a large multigenic family whose members accept a broad range of substrates and, in their two subcellular localizations, the cell wall and the vacuole, Prxs co-locate with a large variety of secondary metabolites which can be accepted as substrates. How then, are Prx reactions regulated? Localization data obtained in our lab suggest that arabinogalactan proteins (AGPs) and Prxs may be associated in membrane microdomains, evocative of lipid rafts. Whether plasma membrane and/or tonoplast microcompartmentation involve AGPs and Prxs and whether this enables metabolic channeling determining Prx substrate selection are challenging questions ahead.Key words: class III peroxidases, CrPrx1, indole alkaloids, vacuole, secondary metabolites, arabinogalactan proteins, lipid rafts