Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms

MOTIVATION: Information from fully sequenced genomes makes it possible to reconstruct strain-specific global metabolic network for structural and functional studies. These networks are often very large and complex. To properly understand and analyze the global properties of metabolic networks, methods for rationally representing and quantitatively analyzing their structure are needed. RESULTS: In this work, the metabolic networks of 80 fully sequenced organisms are in silico reconstructed from genome data and an extensively revised bioreaction database. The networks are represented as directed graphs and analyzed by using the 'breadth first searching algorithm to identify the shortest pathway (path length) between any pair of the metabolites. The average path length of the networks are then calculated and compared for all the organisms. Different from previous studies the connections through current metabolites and cofactors are deleted to make the path length analysis physiologically more meaningful. The distribution of the connection degree of these networks is shown to follow the power law, indicating that the overall structure of all the metabolic networks has the characteristics of a small world network. However, clear differences exist in the network structure of the three domains of organisms. Eukaryotes and archaea have a longer average path length than bacteria. AVAILABILITY: The reaction database in excel format and the programs in VBA (Visual Basic for Applications) are available upon request. SUPPLEMENTARY MATERIAL: Bioinformatics Online.     

Evolution under Fluctuating Environments Explains Observed Robustness in Metabolic Networks

A high level of robustness against gene deletion is observed in many organisms. However, it is still not clear which biochemical features underline this robustness and how these are acquired during evolution. One hypothesis, specific to metabolic networks, is that robustness emerges as a byproduct of selection for biomass production in different environments. To test this hypothesis we performed evolutionary simulations of metabolic networks under stable and fluctuating environments. We find that networks evolved under the latter scenario can better tolerate single gene deletion in specific environments. Such robustness is underlined by an increased number of independent fluxes and multifunctional enzymes in the evolved networks. Observed robustness in networks evolved under fluctuating environments was “apparent,” in the sense that it decreased significantly as we tested effects of gene deletions under all environments experienced during evolution. Furthermore, when we continued evolution of these networks under a stable environment, we found that any robustness they had acquired was completely lost. These findings provide evidence that evolution under fluctuating environments can account for the observed robustness in metabolic networks. Further, they suggest that organisms living under stable environments should display lower robustness in their metabolic networks, and that robustness should decrease upon switching to more stable environments.     

Decoupling Environment-Dependent and Independent Genetic Robustness across Bacterial Species

The evolutionary origins of genetic robustness are still under debate: it may arise as a consequence of requirements imposed by varying environmental conditions, due to intrinsic factors such as metabolic requirements, or directly due to an adaptive selection in favor of genes that allow a species to endure genetic perturbations. Stratifying the individual effects of each origin requires one to study the pertaining evolutionary forces across many species under diverse conditions. Here we conduct the first large-scale computational study charting the level of robustness of metabolic networks of hundreds of bacterial species across many simulated growth environments. We provide evidence that variations among species in their level of robustness reflect ecological adaptations. We decouple metabolic robustness into two components and quantify the extents of each: the first, environmental-dependent, is responsible for at least 20% of the non-essential reactions and its extent is associated with the species'' lifestyle (specialized/generalist); the second, environmental-independent, is associated (correlation = ∼0.6) with the intrinsic metabolic capacities of a species—higher robustness is observed in fast growers or in organisms with an extensive production of secondary metabolites. Finally, we identify reactions that are uniquely susceptible to perturbations in human pathogens, potentially serving as novel drug-targets.     

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.     

Conservation of high-flux backbone in alternate optimal and near-optimal flux distributions of metabolic networks

Constraint-based flux balance analysis (FBA) has proven successful in predicting the flux distribution of metabolic networks in diverse environmental conditions. FBA finds one of the alternate optimal solutions that maximizes the biomass production rate. Almaas et al. have shown that the flux distribution follows a power law, and it is possible to associate with most metabolites two reactions which maximally produce and consume a given metabolite, respectively. This observation led to the concept of high-flux backbone (HFB) in metabolic networks. In previous work, the HFB has been computed using a particular optima obtained using FBA. In this paper, we investigate the conservation of HFB of a particular solution for a given medium across different alternate optima and near-optima in metabolic networks of E. coli and S. cerevisiae. Using flux variability analysis (FVA), we propose a method to determine reactions that are guaranteed to be in HFB regardless of alternate solutions. We find that the HFB of a particular optima is largely conserved across alternate optima in E. coli, while it is only moderately conserved in S. cerevisiae. However, the HFB of a particular near-optima shows a large variation across alternate near-optima in both organisms. We show that the conserved set of reactions in HFB across alternate near-optima has a large overlap with essential reactions and reactions which are both uniquely consuming (UC) and uniquely producing (UP). Our findings suggest that the structure of the metabolic network admits a high degree of redundancy and plasticity in near-optimal flow patterns enhancing system robustness for a given environmental condition.     

Comparative analysis of metabolic network of pathogens

Background

Metabolic networks are complex and system of highly connected chemical reactions and hence it needs a system level computational approach to identify the genotype- phenotype relationship. The study of essential genes and reactions and synthetic lethality of genes and reactions plays a crucial role in explaining functional links between genes and gene function predictions.

Methods

Flux balance analysis (FBA) has been developed as a powerful method for the in silico analyses of metabolic networks. In this study, we present the comparative analysis of the genomic scale metabolic networks of the four microorganisms i.e. Salmonella typhimurium, Mycobacterium tuberculosis, Staphylococcus aureus, and Helicobacter pylori. The fluxes of all reaction were obtained and the growth rate of the organism was calculated by setting the biomass reaction as the objective function.

Results & Conclusions

The average lethality fraction of all the four organisms studied ranged from 0.2 to 0.6. It was also observed that there are very few metabolites which are highly connected. Those metabolites that are highly connected are supposed to be the ‘global players’ similar to the hub protein in the protein–protein interaction network.

     

Low degree metabolites explain essential reactions and enhance modularity in biological networks

Background  

Recently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational and systems biology is to go beyond identification towards an explanation of specific modules and essential genes and reactions in terms of specific structural or evolutionary constraints.     

Temperature compensation through systems biology

Temperature has a strong influence on most individual biochemical reactions. Despite this, many organisms have the remarkable ability to keep certain physiological fluxes approximately constant over an extended temperature range. In this study, we show how temperature compensation can be considered as a pathway phenomenon rather than the result of a single-enzyme property. Using metabolic control analysis, it is possible to identify reaction networks that exhibit temperature compensation. Because most activation enthalpies are positive, temperature compensation of a flux can occur when certain control coefficients are negative. This can be achieved in networks with branching reactions or if the first irreversible reaction is regulated by a feedback loop. Hierarchical control analysis shows that networks that are dynamic through regulated gene expression or signal transduction may offer additional possibilities to bring the apparent activation enthalpies close to zero and lead to temperature compensation. A calorimetric experiment with yeast provides evidence that such a dynamic temperature adaptation can actually occur.     

Phylogenetic comparison of metabolic capacities of organisms at genome level

Horizontal gene transfer (HGT) has been shown to widely spread in organisms by comparative genomic studies. However, its effect on the phylogenetic relationship of organisms, especially at a system level of different cellular functions, is still not well understood. In this work, we have constructed phylogenetic trees based on the enzyme, reaction, and gene contents of metabolic networks reconstructed from annotated genome information of 82 sequenced organisms. Results from different phylogenetic distance definitions and based on three different functional subsystems (i.e., metabolism, cellular processes, information storage and processing) were compared. Results based on the three different functional subsystems give different pictures on the phylogenetic relationship of organisms, reflecting the different extents of HGT in the different functional systems. In general, horizontal transfer is prevailing in genes for metabolism, but less in genes for information processing. Nevertheless, the major results of metabolic network-based phylogenetic trees are in good agreement with the tree based on 16S rRNA and genome trees, confirming the three domain classification and the close relationship between eukaryotes and archaea at the level of metabolic networks. These results strongly support the hypothesis that although HGT is widely distributed, it is nevertheless constrained by certain pre-existing metabolic organization principle(s) during the evolution. Further research is needed to identify the organization principle and constraints of metabolic network on HGT which have large impacts on understanding the evolution of life and in purposefully manipulating cellular metabolism.     

A Bayesian Approach to the Evolution of Metabolic Networks on a Phylogeny

The availability of genomes of many closely related bacteria with diverse metabolic capabilities offers the possibility of tracing metabolic evolution on a phylogeny relating the genomes to understand the evolutionary processes and constraints that affect the evolution of metabolic networks. Using simple (independent loss/gain of reactions) or complex (incorporating dependencies among reactions) stochastic models of metabolic evolution, it is possible to study how metabolic networks evolve over time. Here, we describe a model that takes the reaction neighborhood into account when modeling metabolic evolution. The model also allows estimation of the strength of the neighborhood effect during the course of evolution. We present Gibbs samplers for sampling networks at the internal node of a phylogeny and for estimating the parameters of evolution over a phylogeny without exploring the whole search space by iteratively sampling from the conditional distributions of the internal networks and parameters. The samplers are used to estimate the parameters of evolution of metabolic networks of bacteria in the genus Pseudomonas and to infer the metabolic networks of the ancestral pseudomonads. The results suggest that pathway maps that are conserved across the Pseudomonas phylogeny have a stronger neighborhood structure than those which have a variable distribution of reactions across the phylogeny, and that some Pseudomonas lineages are going through genome reduction resulting in the loss of a number of reactions from their metabolic networks.     

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.     

Distributed robustness versus redundancy as causes of mutational robustness

A biological system is robust to mutations if it continues to function after genetic changes in its parts. Such robustness is pervasive on different levels of biological organization, from macromolecules to genetic networks and whole organisms. I here ask which of two possible causes of such robustness are more important on a genome-wide scale, for systems whose parts are genes, such as metabolic and genetic networks. The first of the two causes is redundancy of a system's parts: A gene may be dispensable if the genome contains redundant, back-up copies of the gene. The second cause, distributed robustness, is more poorly understood. It emerges from the distributed nature of many biological systems, where many (and different) parts contribute to system functions. I will here discuss evidence suggesting that distributed robustness is equally or more important for mutational robustness than gene redundancy. This evidence comes from the functional divergence of redundant genes, as well as from large-scale gene deletion studies. I also ask whether one can quantify the extent to which redundancy or distributed robustness contribute to mutational robustness.     

The metabolic core and catalytic switches are fundamental elements in the self-regulation of the systemic metabolic structure of cells

Background

Experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a metabolic core formed by a set of enzymatic reactions which are always active under all environmental conditions, while the rest of catalytic processes are only intermittently active. The reactions of the metabolic core are essential for biomass formation and to assure optimal metabolic performance. The on-off catalytic reactions and the metabolic core are essential elements of a Systemic Metabolic Structure which seems to be a key feature common to all cellular organisms.

Methodology/Principal Findings

In order to investigate the functional importance of the metabolic core we have studied different catalytic patterns of a dissipative metabolic network under different external conditions. The emerging biochemical data have been analysed using information-based dynamic tools, such as Pearson''s correlation and Transfer Entropy (which measures effective functionality). Our results show that a functional structure of effective connectivity emerges which is dynamical and characterized by significant variations of bio-molecular information flows.

Conclusions/Significance

We have quantified essential aspects of the metabolic core functionality. The always active enzymatic reactions form a hub –with a high degree of effective connectivity- exhibiting a wide range of functional information values being able to act either as a source or as a sink of bio-molecular causal interactions. Likewise, we have found that the metabolic core is an essential part of an emergent functional structure characterized by catalytic modules and metabolic switches which allow critical transitions in enzymatic activity. Both, the metabolic core and the catalytic switches in which also intermittently-active enzymes are involved seem to be fundamental elements in the self-regulation of the Systemic Metabolic Structure.     

Robustness analysis of the Escherichia coli metabolic network

Genomic, biochemical, and strain-specific data can be assembled to define an in silico representation of the metabolic network for a select group of single cellular organisms. Flux-balance analysis and phenotypic phase planes derived therefrom have been developed and applied to analyze the metabolic capabilities and characteristics of Escherichia coli K-12. These analyses have shown the existence of seven essential reactions in the central metabolic pathways (glycolysis, pentose phosphate pathway, tricarboxylic acid cycle) for the growth in glucose minimal media. The corresponding seven gene products can be grouped into three categories: (1) pentose phosphate pathway genes, (2) three-carbon glycolytic genes, and (3) tricarboxylic acid cycle genes. Here we develop a procedure that calculates the sensitivity of optimal cellular growth to altered flux levels of these essential gene products. The results indicate that the E. coli metabolic network is robust with respect to the flux levels of these enzymes. The metabolic flux in the transketolase and the tricarboxylic acid cycle reactions can be reduced to 15% and 19%, respectively, of the optimal value without significantly influencing the optimal growth flux. The metabolic network also exhibited robustness with respect to the ribose-5-phosphate isomerase, and the ribose-5-phosephate isomerase flux was reduced to 28% of the optimal value without significantly effecting the optimal growth flux. The metabolic network exhibited limited robustness to the three-carbon glycolytic fluxes both increased and decreased. The development presented another dimension to the use of FBA to study the capabilities of metabolic networks.     

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.     

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/     

Spontaneous Reaction Silencing in Metabolic Optimization

Metabolic reactions of single-cell organisms are routinely observed to become dispensable or even incapable of carrying activity under certain circumstances. Yet, the mechanisms as well as the range of conditions and phenotypes associated with this behavior remain very poorly understood. Here we predict computationally and analytically that any organism evolving to maximize growth rate, ATP production, or any other linear function of metabolic fluxes tends to significantly reduce the number of active metabolic reactions compared to typical nonoptimal states. The reduced number appears to be constant across the microbial species studied and just slightly larger than the minimum number required for the organism to grow at all. We show that this massive spontaneous reaction silencing is triggered by the irreversibility of a large fraction of the metabolic reactions and propagates through the network as a cascade of inactivity. Our results help explain existing experimental data on intracellular flux measurements and the usage of latent pathways, shedding new light on microbial evolution, robustness, and versatility for the execution of specific biochemical tasks. In particular, the identification of optimal reaction activity provides rigorous ground for an intriguing knockout-based method recently proposed for the synthetic recovery of metabolic function.     

Constraints on reciprocal flux sensitivities in biochemical reaction networks

We identify a connection between the structural features of mass-action networks and the robustness of their steady-state fluxes against rate constant variations. We find that in all positive steady states of so-called injective networks—networks that arise, for example, in metabolic and gene regulation contexts—there are certain firm bounds on the flux control coefficients. In particular, the control coefficient of the flux of a reaction, with respect to variation in its own rate constant, is delimited in a precise way. Moreover, for each pair of reactions, the flux of at least one of them must have a precisely delimited control coefficient with respect to variation in the rate constant of the other. The derived bounds can, however, be violated in noninjective networks, so for them a more pronounced lack of robustness could be exhibited. These results, which indicate a mechanism by which some degree of robustness is induced in the injective setting, also shed light on how robustness might evolve.