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.     

Birth and death of protein domains: A simple model of evolution explains power law behavior

Background  

Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution.     

Analysis of metabolic network based on conservation of molecular structure

Recent work has revealed much about chemical reactions inside hundreds of organisms as well as universal characteristics of metabolic networks, which shed light on the evolution of the networks. However, characteristics of individual metabolites have been neglected. For example, some carbohydrates have structures that are decomposed into small molecules by metabolic reactions, but coenzymes such as ATP are mostly preserved. Such differences in metabolite characteristics are important for understanding the universal characteristics of metabolic networks. To quantify the structure conservation of metabolites, we defined the "structure conservation index" (SCI) for each metabolite as the fraction of metabolite atoms restored to their original positions through metabolic reactions. As expected, coenzymes and coenzyme-like metabolites that have reaction loops in the network show a higher SCI. Using the index, we found that the sum of metabolic fluxes is negatively correlated with the structure preservation of metabolite. Also, we found that each reaction path around high SCI metabolites changes independently, while changes in reaction paths involving low SCI metabolites coincide through evolution processes. These correlations may provide a clue to universal properties of metabolic networks.     

Metabolic pathway analysis web service (Pathway Hunter Tool at CUBIC)

MOTIVATION: Pathway Hunter Tool (PHT), is a fast, robust and user-friendly tool to analyse the shortest paths in metabolic pathways. The user can perform shortest path analysis for one or more organisms or can build virtual organisms (networks) using enzymes. Using PHT, the user can also calculate the average shortest path (Jungnickel, 2002 Graphs, Network and Algorithm. Springer-Verlag, Berlin), average alternate path and the top 10 hubs in the metabolic network. The comparative study of metabolic connectivity and observing the cross talk between metabolic pathways among various sequenced genomes is possible. RESULTS: A new algorithm for finding the biochemically valid connectivity between metabolites in a metabolic network was developed and implemented. A predefined manual assignment of side metabolites (like ATP, ADP, water, CO(2) etc.) and main metabolites is not necessary as the new concept uses chemical structure information (global and local similarity) between metabolites for identification of the shortest path.     

Observing local and global properties of metabolic pathways: 'load points' and 'choke points' in the metabolic networks

MOTIVATION: The local and global aspects of metabolic network analyses allow us to identify enzymes or reactions that are crucial for the survival of the organism(s), therefore directing us towards the discovery of potential drug targets. RESULTS: We demonstrate a new method ('load points') to rank the enzymes/metabolites in the metabolic network and propose a model to determine and rank the biochemical lethality in metabolic networks (enzymes/metabolites) through 'choke points'. Based on an extended form of the graph theory model of metabolic networks, metabolite structural information was used to calculate the k-shortest paths between metabolites (the presence of more than one competing path between substrate and product). On the basis of these paths and connectivity information, load points were calculated and used to empirically rank the importance of metabolites/enzymes in the metabolic network. The load point analysis emphasizes the role that the biochemical structure of a metabolite, rather than its connectivity (hubs), plays in the conversion pathway. In order to identify potential drug targets (based on the biochemical lethality of metabolic networks), the concept of choke points and load points was used to find enzymes (edges) which uniquely consume or produce a particular metabolite (nodes). A non-pathogenic bacterial strain Bacillus subtilis 168 (lactic acid producing bacteria) and a related pathogenic bacterial strain Bacillus anthracis Sterne (avirulent but toxigenic strain, producing the toxin Anthrax) were selected as model organisms. The choke point strategy was implemented on the pathogen bacterial network of B.anthracis Sterne. Potential drug targets are proposed based on the analysis of the top 10 choke points in the bacterial network. A comparative study between the reported top 10 bacterial choke points and the human metabolic network was performed. Further biological inferences were made on results obtained by performing a homology search against the human genome. AVAILABILITY: The load and choke point modules are introduced in the Pathway Hunter Tool (PHT), the basic version of which is available on http://www.pht.uni-koeln.de.     

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/     

Stability of Metabolic Correlations under Changing Environmental Conditions in Escherichia coli – A Systems Approach

Background

Biological systems adapt to changing environments by reorganizing their cellular and physiological program with metabolites representing one important response level. Different stresses lead to both conserved and specific responses on the metabolite level which should be reflected in the underlying metabolic network.

Methodology/Principal Findings

Starting from experimental data obtained by a GC-MS based high-throughput metabolic profiling technology we here develop an approach that: (1) extracts network representations from metabolic condition-dependent data by using pairwise correlations, (2) determines the sets of stable and condition-dependent correlations based on a combination of statistical significance and homogeneity tests, and (3) can identify metabolites related to the stress response, which goes beyond simple observations about the changes of metabolic concentrations. The approach was tested with Escherichia coli as a model organism observed under four different environmental stress conditions (cold stress, heat stress, oxidative stress, lactose diauxie) and control unperturbed conditions. By constructing the stable network component, which displays a scale free topology and small-world characteristics, we demonstrated that: (1) metabolite hubs in this reconstructed correlation networks are significantly enriched for those contained in biochemical networks such as EcoCyc, (2) particular components of the stable network are enriched for functionally related biochemical pathways, and (3) independently of the response scale, based on their importance in the reorganization of the correlation network a set of metabolites can be identified which represent hypothetical candidates for adjusting to a stress-specific response.

Conclusions/Significance

Network-based tools allowed the identification of stress-dependent and general metabolic correlation networks. This correlation-network-based approach does not rely on major changes in concentration to identify metabolites important for stress adaptation, but rather on the changes in network properties with respect to metabolites. This should represent a useful complementary technique in addition to more classical approaches.     

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.     

Clustering under the line graph transformation: application to reaction network

Background  

Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. In general, the second network may be related to the first one by a technique called line graph transformation (i.e., edges in an initial network are transformed into nodes). Recently, the main topological properties of the metabolic networks have been properly described by means of a hierarchical model. While the chemical compound network has been classified as hierarchical network, a detailed study of the chemical reaction network had not been carried out.     

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/     

Topological properties of protein-protein and metabolic interaction networks of Drosophila melanogaster

Introduction The concept of networking and its omnipresent na- ture has been an issue of considerable curiosity, cap- tivating scientists worldwide over the past few years. Simple networking can be witnessed in the physical connectivity of computer terminals or routers. On broader perspective, many networks, such as social ties—familial and professional, World Wide Web, net- work of scientific papers connected by citations, elec- trical power grids, transportation systems, and biolog- ical n…     

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.     

Modeling for evolving biological networks with scale-free connectivity, hierarchical modularity, and disassortativity

We propose a growing network model that consists of two tunable mechanisms: growth by merging modules which are represented as complete graphs and a fitness-driven preferential attachment. Our model exhibits the three prominent statistical properties are widely shared in real biological networks, for example gene regulatory, protein-protein interaction, and metabolic networks. They retain three power law relationships, such as the power laws of degree distribution, clustering spectrum, and degree-degree correlation corresponding to scale-free connectivity, hierarchical modularity, and disassortativity, respectively. After making comparisons of these properties between model networks and biological networks, we confirmed that our model has inference potential for evolutionary processes of biological networks.     

Expanding Metabolic Networks: Scopes of Compounds, Robustness, and Evolution

A new method for the mathematical analysis of large metabolic networks is presented. Based on the fact that the occurrence of a metabolic reaction generally requires the existence of other reactions providing its substrates, series of metabolic networks are constructed. In each step of the corresponding expansion process those reactions are incorporated whose substrates are made available by the networks of the previous generations. The method is applied to the set of all metabolic reactions included in the KEGG database. Starting with one or more seed compounds, the expansion results in a final network whose compounds define the scope of the seed. Scopes of all metabolic compounds are calculated and it is shown that large parts of cellular metabolism can be considered as the combined scope of simple building blocks. Analyses of various expansion processes reveal crucial metabolites whose incorporation allows for the increase in network complexity. Among these metabolites are common cofactors such as NAD⁺, ATP, and coenzyme A. We demonstrate that the outcome of network expansion is in general very robust against elimination of single or few reactions. There exist, however, crucial reactions whose elimination results in a dramatic reduction of scope sizes. It is hypothesized that the expansion process displays characteristics of the evolution of metabolism such as the temporal order of the emergence of metabolic pathways. [Reviewing Editor : Dr. David Pollock]     

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.     

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.     

Though with constraints imposed by endosymbiosis,preferential attachment is still a plausible mechanism responsible for the evolution of the chloroplast metabolic network

Chloroplasts evolved as a result of endosymbiosis, during which sophisticated mechanisms evolved to translocate nucleus‐encoded plastid‐targeted enzymes into the chloroplast to form the chloroplast metabolic network. Given the constraints and complexity of endosymbiosis, will preferential attachment still be a plausible mechanism for chloroplast metabolic network evolution? We answer this question by analysing the metabolic network properties of the chloroplast and a cyanobacterium, Synechococcus sp. WH8102 (syw). First, we found that enzymes related to more ancient pathways are more connected, and synthetases have the highest connectivity. Most of the enzymes shared by the two densest cores between the chloroplast and syw are synthetases. Second, the highly conserved functional modules mainly consist of highly connected enzymes. Finally, isozymes and enzymes from endosymbiotic gene transfer (EGT) were distributed mainly in conserved modules and showed higher connectivity than nonisozymes or non‐EGT enzymes. These results suggest that even with severe evolutionary constraints imposed by endosymbiosis, preferential attachment is still a plausible mechanism responsible for the evolution of the chloroplast metabolic network. However, the current analysis may not completely differentiate whether the chloroplast network properties reflect the evolution of the chloroplast network through preferential attachment or has been inherited from its cyanobacterial ancestor. To fully differentiate these two possibilities, further analyses of the metabolic network structure properties of organisms at various intermediate evolutionary stages between cyanobacteria and the chloroplast are needed.     

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

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

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.