The small world of metabolism

Discovering functions and revealing mechanisms at molecular level from biological networks

With the increasingly accumulated data from high-throughput technologies, study on biomolecular networks has become one of key focuses in systems biology and bioinformatics. In particular, various types of molecular networks (e.g., protein-protein interaction (PPI) network; gene regulatory network (GRN); metabolic network (MN); gene coexpression network (GCEN)) have been extensively investigated, and those studies demonstrate great potentials to discover basic functions and to reveal essential mechanisms for various biological phenomena, by understanding biological systems not at individual component level but at a system-wide level. Recent studies on networks have created very prolific researches on many aspects of living organisms. In this paper, we aim to review the recent developments on topics related to molecular networks in a comprehensive manner, with the special emphasis on the computational aspect. The contents of the survey cover global topological properties and local structural characteristics, network motifs, network comparison and query, detection of functional modules and network motifs, function prediction from network analysis, inferring molecular networks from biological data as well as representative databases and software tools.

On the processing of metabolic information through metabolite-gene communication networks: an approach for modelling causality

Gene-metabolite correlation networks of three independent biological systems were interrogated using an approach to define, and subsequently model, causality. The major goal of this work was to analyse how information from those metabolites, that displayed a rapid response to perturbation of the biological system, is processed through the response network to provide signal-specific adaptation of metabolism. For this purpose, comparison of network topologies was carried out on three different groups of system elements: transcription factors, other genes and metabolites, with special emphasis placed on those features which are possible sites of metabolic regulation or response propagation. The degree of connectivity in all three analysed gene-metabolite networks followed power-law and exponential functions, whilst a comparison of connectivities of the various cellular entities suggested, that metabolites are less involved in the regulation of the sulfur stress response than in the ripening of tomatoes (in which metabolites seem to have an even greater regulatory role than transcription factors). These findings reflect different degree of metabolic regulation for distinct biological processes. Implementing causality into the network allowed classification of metabolite-gene associations into those with causal directionality from gene to metabolite and from metabolite to gene. Several metabolites were positioned relatively early in the causal hierarchy and possessed many connections to the downstream elements. Such metabolites were considered to have higher regulatory potential. For the biological example of hypo-sulfur stress response in Arabidopsis, the highest regulatory potential scores were established for fructose and sucrose, isoleucine, methionine and sinapic acid. Further developments in profiling techniques will allow greater cross-systems comparisons, necessary for reliability and universality checks of inferred regulatory capacities of the particular metabolites.

Computational approaches to the topology, stability and dynamics of metabolic networks

Cellular metabolism is characterized by an intricate network of interactions between biochemical fluxes, metabolic compounds and regulatory interactions. To investigate and eventually understand the emergent global behavior arising from such networks of interaction is not possible by intuitive reasoning alone. This contribution seeks to describe recent computational approaches that aim to asses the topological and functional properties of metabolic networks. In particular, based on a recently proposed method, it is shown that it is possible to acquire a quantitative picture of the possible dynamics of metabolic systems, without assuming detailed knowledge of the underlying enzyme-kinetic rate equations and parameters. Rather, the method builds upon a statistical exploration of the comprehensive parameter space to evaluate the dynamic capabilities of a metabolic system, thus providing a first step towards the transition from topology to function of metabolic pathways. Utilizing this approach, the role of feedback mechanisms in the maintenance of stability is discussed using minimal models of cellular pathways.

Modular decomposition of metabolic reaction networks based on flux analysis and pathway projection

MOTIVATION

The rational decomposition of biochemical networks into sub-structures has emerged as a useful approach to study the design of these complex systems. A biochemical network is characterized by an inhomogeneous connectivity distribution, which gives rise to several organizational features, including modularity. To what extent the connectivity-based modules reflect the functional organization of the network remains to be further explored. In this work, we examine the influence of physiological perturbations on the modular organization of cellular metabolism.

RESULTS

Modules were characterized for two model systems, liver and adipocyte primary metabolism, by applying an algorithm for top-down partition of directed graphs with non-uniform edge weights. The weights were set by the engagement of the corresponding reactions as expressed by the flux distribution. For the base case of the fasted rat liver, three modules were found, carrying out the following biochemical transformations: ketone body production, glucose synthesis and transamination. This basic organization was further modified when different flux distributions were applied that describe the liver's metabolic response to whole body inflammation. For the fully mature adipocyte, only a single module was observed, integrating all of the major pathways needed for lipid storage. Weaker levels of integration between the pathways were found for the early stages of adipocyte differentiation. Our results underscore the inhomogeneous distribution of both connectivity and connection strengths, and suggest that global activity data such as the flux distribution can be used to study the organizational flexibility of cellular metabolism.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Introduction to systems biology

The developments in the molecular biosciences have made possible a shift to combined molecular and system-level approaches to biological research under the name of Systems Biology. It integrates many types of molecular knowledge, which can best be achieved by the synergistic use of models and experimental data. Many different types of modeling approaches are useful depending on the amount and quality of the molecular data available and the purpose of the model. Analysis of such models and the structure of molecular networks have led to the discovery of principles of cell functioning overarching single species. Two main approaches of systems biology can be distinguished. Top-down systems biology is a method to characterize cells using system-wide data originating from the Omics in combination with modeling. Those models are often phenomenological but serve to discover new insights into the molecular network under study. Bottom-up systems biology does not start with data but with a detailed model of a molecular network on the basis of its molecular properties. In this approach, molecular networks can be quantitatively studied leading to predictive models that can be applied in drug design and optimization of product formation in bioengineering. In this chapter we introduce analysis of molecular network by use of models, the two approaches to systems biology, and we shall discuss a number of examples of recent successes in systems biology.

Global mapping of gene/protein interactions in PubMed abstracts: a framework and an experiment with P53 interactions

Gene/protein interactions provide critical information for a thorough understanding of cellular processes. Recently, considerable interest and effort has been focused on the construction and analysis of genome-wide gene networks. The large body of biomedical literature is an important source of gene/protein interaction information. Recent advances in text mining tools have made it possible to automatically extract such documented interactions from free-text literature. In this paper, we propose a comprehensive framework for constructing and analyzing large-scale gene functional networks based on the gene/protein interactions extracted from biomedical literature repositories using text mining tools. Our proposed framework consists of analyses of the network topology, network topology-gene function relationship, and temporal network evolution to distill valuable information embedded in the gene functional interactions in the literature. We demonstrate the application of the proposed framework using a testbed of P53-related PubMed abstracts, which shows that the literature-based P53 networks exhibit small-world and scale-free properties. We also found that high degree genes in the literature-based networks have a high probability of appearing in the manually curated database and genes in the same pathway tend to form local clusters in our literature-based networks. Temporal analysis showed that genes interacting with many other genes tend to be involved in a large number of newly discovered interactions.

Systems biology and its impact on anti-infective drug development

Systems biology offers the potential for more effective selection of novel targets for anti-infective drugs. In contrast to conventional reductionist biology, a systems approach allows targets to be viewed in a wider context of the entire physiology of the cell, with the potential to identify key susceptible nodes and to predict synergistic effects of blocking multiple pathways. In addition to the holistic perspective provided by systems biology, the emphasis on quantitative analysis is likely to add further rigour to the process of target selection. Systems biology also offers the potential to incorporate different levels of information into the selection process. Consideration of data from microbial population biology may be important in the context of predicting future drug-resistance profiles associated with targeting a particular pathway, for example. This chapter provides an overview of major themes in the developing field of systems biology, summarising the core technologies and the strategies used to translate datasets into useful quantitative models capable of predicting complex biological behaviour.

Hydrophobic, hydrophilic, and charged amino acid networks within protein

The native three-dimensional structure of a single protein is determined by the physicochemical nature of its constituent amino acids. The 20 different types of amino acids, depending on their physicochemical properties, can be grouped into three major classes: hydrophobic, hydrophilic, and charged. The anatomy of the weighted and unweighted networks of hydrophobic, hydrophilic, and charged residues separately for a large number of proteins were studied. Results showed that the average degree of the hydrophobic networks has a significantly larger value than that of hydrophilic and charged networks. The average degree of the hydrophilic networks is slightly higher than that of the charged networks. The average strength of the nodes of hydrophobic networks is nearly equal to that of the charged network, whereas that of hydrophilic networks has a smaller value than that of hydrophobic and charged networks. The average strength for each of the three types of networks varies with its degree. The average strength of a node in a charged network increases more sharply than that of the hydrophobic and hydrophilic networks. Each of the three types of networks exhibits the "small-world" property. Our results further indicate that the all-amino-acids networks and hydrophobic networks are of assortative type. Although most of the hydrophilic and charged networks are of the assortative type, few others have the characteristics of disassortative mixing of the nodes. We have further observed that all-amino-acids networks and hydrophobic networks bear the signature of hierarchy, whereas the hydrophilic and charged networks do not have any hierarchical signature.

Bacterial regulatory networks are extremely flexible in evolution

Over millions of years the structure and complexity of the transcriptional regulatory network (TRN) in bacteria has changed, reorganized and enabled them to adapt to almost every environmental niche on earth. In order to understand the plasticity of TRNs in bacteria, we studied the conservation of currently known TRNs of the two model organisms Escherichia coli K12 and Bacillus subtilis across complete genomes including Bacteria, Archaea and Eukarya at three different levels: individual components of the TRN, pairs of interactions and regulons. We found that transcription factors (TFs) evolve much faster than the target genes (TGs) across phyla. We show that global regulators are poorly conserved across the phylogenetic spectrum and hence TFs could be the major players responsible for the plasticity and evolvability of the TRNs. We also found that there is only a small fraction of significantly conserved transcriptional regulatory interactions among different phyla of bacteria and that there is no constraint on the elements of the interaction to co-evolve. Finally our results suggest that majority of the regulons in bacteria are rapidly lost implying a high-order flexibility in the TRNs. We hypothesize that during the divergence of bacteria certain essential cellular processes like the synthesis of arginine, biotine and ribose, transport of amino acids and iron, availability of phosphate, replication process and the SOS response are well conserved in evolution. From our comparative analysis, it is possible to infer that transcriptional regulation is more flexible than the genetic component of the organisms and its complexity and structure plays an important role in the phenotypic adaptation.

How scale-free are biological networks

The concept of scale-free network has emerged as a powerful unifying paradigm in the study of complex systems in biology and in physical and social studies. Metabolic, protein, and gene interaction networks have been reported to exhibit scale-free behavior based on the analysis of the distribution of the number of connections of the network nodes. Here we study 10 published datasets of various biological interactions and perform goodness-of-fit tests to determine whether the given data is drawn from the power-law distribution. Our analysis did not identify a single interaction network that has a nonzero probability of being drawn from the power-law distribution.

A bioinformatician's view of the metabolome

The study of a collection of metabolites as a whole (metabolome), as opposed to isolated small molecules, is a fast-growing field promising to take us one step further towards understanding cell biology, and relating the genetic capabilities of an organism to its observed phenotype. The new sciences of metabolomics and metabonomics can exploit a variety of existing experimental and computational methods, but they also require new technology that can deal with both the amount and the diversity of the data relating to the rich world of metabolites. More specifically, the collaboration between bioinformaticians and chemoinformaticians promises to advance our view of cognate molecules, by shedding light on their atomic structure and properties. Modelling of the interactions of metabolites with other entities in the cell, and eventually complete modelling of reaction pathways will be essential for analysis of the experimental data, and prediction of an organism's response to environmental challenges.

Small-world network approach to identify key residues in protein-protein interaction

We show that protein complexes can be represented as small-world networks, exhibiting a relatively small number of highly central amino-acid residues occurring frequently at protein-protein interfaces. We further base our analysis on a set of different biological examples of protein-protein interactions with experimentally validated hot spots, and show that 83% of these predicted highly central residues, which are conserved in sequence alignments and nonexposed to the solvent in the protein complex, correspond to or are in direct contact with an experimentally annotated hot spot. The remaining 17% show a general tendency to be close to an annotated hot spot. On the other hand, although there is no available experimental information on their contribution to the binding free energy, detailed analysis of their properties shows that they are good candidates for being hot spots. Thus, highly central residues have a clear tendency to be located in regions that include hot spots. We also show that some of the central residues in the protein complex interfaces are central in the monomeric structures before dimerization and that possible information relating to hot spots of binding free energy could be obtained from the unbound structures.

A three-level problem-centric strategy for selecting NMR precursor labeling and analytes

We have developed a sequential set of computational screens that may prove useful for evaluating analyte sets for their ability to accurately report on metabolic fluxes. The methodology is problem-centric in that the screens are used in the context of a particular metabolic engineering problem. That is, flux bounds and alternative flux routings are first identified for a particular problem, and then the information is used to inform the design of nuclear magnetic resonance (NMR) experiments. After obtaining the flux bounds via MILP, analytes are first screened for whether the predicted NMR spectra associated with various analytes can differentiate between different extreme point (or linear combinations of extreme point) flux solutions. The second screen entails determining whether the analytes provide unique flux values or multiple flux solutions. Finally, the economics associated with using different analytes is considered in order to further refine the analyte selection process in terms of an overall utility index, where the index summarizes the cost-benefit attributes by quantifying benefit (contrast power) per cost (e.g., NMR instrument time required). We also demonstrate the use of an alternative strategy, the Analytical Hierarchy Process, for ranking analytes based on the individual experimentalist's-generated weights assigned for the relative value of flux scenario contrast, unique inversion of NMR data to fluxes, etc.

Exploration of biological network centralities with CentiBiN

Background

The elucidation of whole-cell regulatory, metabolic, interaction and other biological networks generates the need for a meaningful ranking of network elements. Centrality analysis ranks network elements according to their importance within the network structure and different centrality measures focus on different importance concepts. Central elements of biological networks have been found to be, for example, essential for viability.

Results

CentiBiN (Centralities in Biological Networks) is a tool for the computation and exploration of centralities in biological networks such as protein-protein interaction networks. It computes 17 different centralities for directed or undirected networks, ranging from local measures, that is, measures that only consider the direct neighbourhood of a network element, to global measures. CentiBiN supports the exploration of the centrality distribution by visualising central elements within the network and provides several layout mechanisms for the automatic generation of graphical representations of a network. It supports different input formats, especially for biological networks, and the export of the computed centralities to other tools.

Conclusion

CentiBiN helps systems biology researchers to identify crucial elements of biological networks. CentiBiN including a user guide and example data sets is available free of charge at . CentiBiN is available in two different versions: a Java Web Start application and an installable Windows application.

The origins and evolution of functional modules: lessons from protein complexes

Modularity is an attribute of a system that can be decomposed into a set of cohesive entities that are loosely coupled. Many cellular networks can be decomposed into functional modules-each functionally separable from the other modules. The protein complexes in physical protein interaction networks are a good example of this, and here we focus on their origins and evolution. We investigate the emergence of protein complexes and physical interactions between proteins by duplication, and review other mechanisms. We dissect the dataset of protein complexes of known three-dimensional structure, and show that roughly 90% of these complexes contain contacts between identical proteins within the same complex. Proteins that are shared across different complexes occur frequently, and they tend to be essential genes more often than members of a single protein complex. We also provide a perspective on the evolutionary mechanisms driving the growth of other modular cellular networks such as transcriptional regulatory and metabolic networks.

Virtual identification of essential proteins within the protein interaction network of yeast

Topological analysis of large scale protein-protein interaction networks (PINs) is important for understanding the organizational and functional principles of individual proteins. The number of interactions that a protein has in a PIN has been observed to be correlated with its indispensability. Essential proteins generally have more interactions than the nonessential ones. We show here that the lethality associated with removal of a protein from the yeast proteome correlates with different centrality measures of the nodes in the PIN, such as the closeness of a protein to many other proteins, or the number of pairs of proteins which need a specific protein as an intermediary in their communications, or the participation of a protein in different protein clusters in the PIN. These measures are significantly better than random selection in identifying essential proteins in a PIN. Centrality measures based on graph spectral properties of the network, in particular the subgraph centrality, show the best performance in identifying essential proteins in the yeast PIN. Subgraph centrality gives important structural information about the role of individual proteins, and permits the selection of possible targets for rational drug discovery through the identification of essential proteins in the PIN.

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.

Results

Metabolite coupling in the studied networks was found to be dominated by a relatively small group of highly interacting pairs of metabolites. As would be expected, metabolites with high individual metabolite connectivity also tended to be those with the highest metabolite coupling, as the most connected metabolites couple more often. For metabolite pairs that are not highly coupled, we show that the number of reactions a pair of metabolites shares across a metabolic network closely approximates a line on a log-log scale. We also show that the preferential coupling of two metabolites with each other is spread across the spectrum of metabolites and is not unique to the most connected metabolites. We provide a measure for determining which metabolite pairs couple more often than would be expected based on their individual connectivity in the network and show that these metabolites often derive their principal biological functions from existing in pairs. Thus, analysis of metabolite coupling provides information beyond that which is found from studying the individual connectivity of individual metabolites.

Conclusion

The coupling of metabolites is an important topological property of metabolic networks. By computing coupling quantitatively for the first time in genome-scale metabolic networks, we provide insight into the basic structure of these networks.

Metabolite fingerprinting in transgenic Nicotiana tabacum altered by the Escherichia coli glutamate dehydrogenase gene

With about 200 000 phytochemicals in existence, identifying those of biomedical significance is a mammoth task. In the postgenomic era, relating metabolite fingerprints, abundances, and profiles to genotype is also a large task. Ion analysis using Fourier transformed ion cyclotron resonance mass spectrometry (FT-ICR-MS) may provide a high-throughput approach to measure genotype dependency of the inferred metabolome if reproducible techniques can be established. Ion profile inferred metabolite fingerprints are coproducts. We used FT-ICR-MS-derived ion analysis to examine gdhA (glutamate dehydrogenase (GDH; EC 1.4.1.1)) transgenic Nicotiana tabacum (tobacco) carrying out altered glutamate, amino acid, and carbon metabolisms, that fundamentally alter plant productivity. Cause and effect between gdhA expression, glutamate metabolism, and plant phenotypes was analyzed by 13NH4+ labeling of amino acid fractions, and by FT-ICR-MS analysis of metabolites. The gdhA transgenic plants increased ¹³N labeling of glutamate and glutamine significantly. FT-ICR-MS detected 2 012 ions reproducible in 2 to 4 ionization protocols. There were 283 ions in roots and 98 ions in leaves that appeared to significantly change abundance due to the measured GDH activity. About 58% percent of ions could not be used to infer a corresponding metabolite. From the 42% of ions that inferred known metabolites we found that certain amino acids, organic acids, and sugars increased and some fatty acids decreased. The transgene caused increased ammonium assimilation and detectable ion variation. Thirty-two compounds with biomedical significance were altered in abundance by GDH including 9 known carcinogens and 14 potential drugs. Therefore, the GDH transgene may lead to new uses for crops like tobacco.

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.

Scale-freeness and biological networks

The notion of scale-freeness and its prevalence in both natural and artificial networks have recently attracted much attention. The concept of scale-freeness is enthusiastically applied to almost any conceivable network, usually with affirmative conclusions. Well-known scale-free examples include the internet, electric lines among power plants, the co-starring of movie actors, the co-authorship of researchers, food webs, and neural, protein-protein interactional, genetic, and metabolic networks. The purpose of this review is to clarify the relationship between scale-freeness and power-law distribution, and to assess critically the previous related works, especially on biological networks. In addition, I will focus on the close relationship between power-law distribution and lognormal distribution to show that power-law distribution is not a special characteristic of natural selection.

Metabolic PathFinding: inferring relevant pathways in biochemical networks

Our knowledge of metabolism can be represented as a network comprising several thousands of nodes (compounds and reactions). Several groups applied graph theory to analyse the topological properties of this network and to infer metabolic pathways by path finding. This is, however, not straightforward, with a major problem caused by traversing irrelevant shortcuts through highly connected nodes, which correspond to pool metabolites and co-factors (e.g. H2O, NADP and H+). In this study, we present a web server implementing two simple approaches, which circumvent this problem, thereby improving the relevance of the inferred pathways. In the simplest approach, the shortest path is computed, while filtering out the selection of highly connected compounds. In the second approach, the shortest path is computed on the weighted metabolic graph where each compound is assigned a weight equal to its connectivity in the network. This approach significantly increases the accuracy of the inferred pathways, enabling the correct inference of relatively long pathways (e.g. with as many as eight intermediate reactions). Available options include the calculation of the k-shortest paths between two specified seed nodes (either compounds or reactions). Multiple requests can be submitted in a queue. Results are returned by email, in textual as well as graphical formats (available in http://www.scmbb.ulb.ac.be/pathfinding/).

Robustness of the p53 network and biological hackers

The p53 protein interaction network is crucial in regulating the metazoan cell cycle and apoptosis. Here, the robustness of the p53 network is studied by analyzing its degeneration under two modes of attack. Linear Programming is used to calculate average path lengths among proteins and the network diameter as measures of functionality. The p53 network is found to be robust to random loss of nodes, but vulnerable to a targeted attack against its hubs, as a result of its architecture. The significance of the results is considered with respect to mutational knockouts of proteins and the directed attacks mounted by tumour inducing viruses.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edges--that is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Maximal planar networks with large clustering coefficient and power-law degree distribution

In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called random Apollonian networks (RANs) as they can be considered as a variation of Apollonian networks. We obtain the analytic results of power-law exponent gamma=3 and clustering coefficient C= (46/3)-36 ln 3/2 approximately 0.74, which agree with the simulation results very well. We prove that the increasing tendency of average distance of RANs is a little slower than the logarithm of the number of nodes in RANs. Since most real-life networks are both scale-free and small-world networks, RANs may perform well in mimicking the reality. The RANs possess hierarchical structure as C(k) approximately k(-1) that are in accord with the observations of many real-life networks. In addition, we prove that RANs are maximal planar networks, which are of particular practicability for layout of printed circuits and so on. The percolation and epidemic spreading process are also studied and the comparisons between RANs and Barabási-Albert (BA) as well as Newman-Watts (NW) networks are shown. We find that, when the network order N (the total number of nodes) is relatively small (as N approximately 10(4)), the performance of RANs under intentional attack is not sensitive to N , while that of BA networks is much affected by N. And the diseases spread slower in RANs than BA networks in the early stage of the susceptible-infected process, indicating that the large clustering coefficient may slow the spreading velocity, especially in the outbreaks.

Evolutionary cores of domain co-occurrence networks

BACKGROUND

The modeling of complex systems, as disparate as the World Wide Web and the cellular metabolism, as networks has recently uncovered a set of generic organizing principles: Most of these systems are scale-free while at the same time modular, resulting in a hierarchical architecture. The structure of the protein domain network, where individual domains correspond to nodes and their co-occurrences in a protein are interpreted as links, also falls into this category, suggesting that domains involved in the maintenance of increasingly developed, multicellular organisms accumulate links. Here, we take the next step by studying link based properties of the protein domain co-occurrence networks of the eukaryotes S. cerevisiae, C. elegans, D. melanogaster, M. musculus and H. sapiens.

RESULTS

We construct the protein domain co-occurrence networks from the PFAM database and analyze them by applying a k-core decomposition method that isolates the globally central (highly connected domains in the central cores) from the locally central (highly connected domains in the peripheral cores) protein domains through an iterative peeling process. Furthermore, we compare the subnetworks thus obtained to the physical domain interaction network of S. cerevisiae. We find that the innermost cores of the domain co-occurrence networks gradually grow with increasing degree of evolutionary development in going from single cellular to multicellular eukaryotes. The comparison of the cores across all the organisms under consideration uncovers patterns of domain combinations that are predominately involved in protein functions such as cell-cell contacts and signal transduction. Analyzing a weighted interaction network of PFAM domains of yeast, we find that domains having only a few partners frequently interact with these, while the converse is true for domains with a multitude of partners. Combining domain co-occurrence and interaction information, we observe that the co-occurrence of domains in the innermost cores (globally central domains) strongly coincides with physical interaction. The comparison of the multicellular eukaryotic domain co-occurrence networks with the single celled of S. cerevisiae (the overlap network) uncovers small, connected network patterns.

CONCLUSION

We hypothesize that these patterns, consisting of the domains and links preserved through evolution, may constitute nucleation kernels for the evolutionary increase in proteome complexity. Combining co-occurrence and physical interaction data we argue that the driving force behind domain fusions is a collective effect caused by the number of interactions and not the individual interaction frequency.

Uncovering transcriptional regulation of metabolism by using metabolic network topology

Cellular response to genetic and environmental perturbations is often reflected and/or mediated through changes in the metabolism, because the latter plays a key role in providing Gibbs free energy and precursors for biosynthesis. Such metabolic changes are often exerted through transcriptional changes induced by complex regulatory mechanisms coordinating the activity of different metabolic pathways. It is difficult to map such global transcriptional responses by using traditional methods, because many genes in the metabolic network have relatively small changes at their transcription level. We therefore developed an algorithm that is based on hypothesis-driven data analysis to uncover the transcriptional regulatory architecture of metabolic networks. By using information on the metabolic network topology from genome-scale metabolic reconstruction, we show that it is possible to reveal patterns in the metabolic network that follow a common transcriptional response. Thus, the algorithm enables identification of so-called reporter metabolites (metabolites around which the most significant transcriptional changes occur) and a set of connected genes with significant and coordinated response to genetic or environmental perturbations. We find that cells respond to perturbations by changing the expression pattern of several genes involved in the specific part(s) of the metabolism in which a perturbation is introduced. These changes then are propagated through the metabolic network because of the highly connected nature of metabolism.

Revealing metabolic phenotypes in plants: inputs from NMR analysis

Assessing the performance of the plant metabolic network, with its varied biosynthetic capacity and its characteristic subcellular compartmentation, remains a considerable challenge. The complexity of the network is such that it is not yet possible to build large-scale predictive models of the fluxes it supports, whether on the basis of genomic and gene expression analysis or on the basis of more traditional measurements of metabolites and their interconversions. This limits the agronomic and biotechnological exploitation of plant metabolism, and it undermines the important objective of establishing a rational metabolic engineering strategy. Metabolic analysis is central to removing this obstacle and currently there is particular interest in harnessing high-throughput and/or large-scale analyses to the task of defining metabolic phenotypes. Nuclear magnetic resonance (NMR) spectroscopy contributes to this objective by providing a versatile suite of analytical techniques for the detection of metabolites and the fluxes between them. The principles that underpin the analysis of plant metabolism by NMR are described, including a discussion of the measurement options for the detection of metabolites in vivo and in vitro, and a description of the stable isotope labelling experiments that provide the basis for metabolic flux analysis. Despite a relatively low sensitivity, NMR is suitable for high-throughput system-wide analyses of the metabolome, providing methods for both metabolite fingerprinting and metabolite profiling, and in these areas NMR can contribute to the definition of plant metabolic phenotypes that are based on metabolic composition. NMR can also be used to investigate the operation of plant metabolic networks. Labelling experiments provide information on the operation of specific pathways within the network, and the quantitative analysis of steady-state labelling experiments leads to the definition of large-scale flux maps for heterotrophic carbon metabolism. These maps define multiple unidirectional fluxes between branch-points in the metabolic network, highlighting the existence of substrate cycles and discriminating in favourable cases between fluxes in the cytosol and plastid. Flux maps can be used to define a functionally relevant metabolic phenotype and the extensive application of such maps in microbial systems suggests that they could have important applications in characterising the genotypes produced by plant genetic engineering.

Concept-based annotation of enzyme classes

MOTIVATION

Given the explosive growth of biomedical data as well as the literature describing results and findings, it is getting increasingly difficult to keep up to date with new information. Keeping databases synchronized with current knowledge is a time-consuming and expensive task-one which can be alleviated by automatically gathering findings from the literature using linguistic approaches. We describe a method to automatically annotate enzyme classes with disease-related information extracted from the biomedical literature for inclusion in such a database.

RESULTS

Enzyme names for the 3901 enzyme classes in the BRENDA database, a repository for quantitative and qualitative enzyme information, were identified in more than 100,000 abstracts retrieved from the PubMed literature database. Phrases in the abstracts were assigned to concepts from the Unified Medical Language System (UMLS) utilizing the MetaMap program, allowing for the identification of disease-related concepts by their semantic fields in the UMLS ontology. Assignments between enzyme classes and diseases were created based on their co-occurrence within a single sentence. False positives could be removed by a variety of filters including minimum number of co-occurrences, removal of sentences containing a negation and the classification of sentences based on their semantic fields by a Support Vector Machine. Verification of the assignments with a manually annotated set of 1500 sentences yielded favorable results of 92% precision at 50% recall, sufficient for inclusion in a high-quality database.

AVAILABILITY

Source code is available from the author upon request.

SUPPLEMENTARY INFORMATION

ftp.uni-koeln.de/institute/biochemie/pub/brenda/info/diseaseSupp.pdf.

Structural comparison of metabolic networks in selected single cell organisms

Background

There has been tremendous interest in the study of biological network structure. An array of measurements has been conceived to assess the topological properties of these networks. In this study, we compared the metabolic network structures of eleven single cell organisms representing the three domains of life using these measurements, hoping to find out whether the intrinsic network design principle(s), reflected by these measurements, are different among species in the three domains of life.

Results

Three groups of topological properties were used in this study: network indices, degree distribution measures and motif profile measure. All of which are higher-level topological properties except for the marginal degree distribution. Metabolic networks in Archaeal species are found to be different from those in S. cerevisiae and the six Bacterial species in almost all measured higher-level topological properties. Our findings also indicate that the metabolic network in Archaeal species is similar to the exponential random network.

Conclusion

If these metabolic network properties of the organisms studied can be extended to other species in their respective domains (which is likely), then the design principle(s) of Archaea are fundamentally different from those of Bacteria and Eukaryote. Furthermore, the functional mechanisms of Archaeal metabolic networks revealed in this study differentiate significantly from those of Bacterial and Eukaryotic organisms, which warrant further investigation.

Process strategies to enhance pyruvate production with recombinant Escherichia coli: from repetitive fed-batch to in situ product recovery with fully integrated electrodialysis

Using the pyruvate production strain Escherichia coli YYC202 ldhA::Kan different process alternatives are studied with the aim of preventing potential product inhibition by appropriate product separation. This strain is completely blocked in its ability to convert pyruvate into acetyl-CoA or acetate, resulting in acetate auxotrophy during growth in glucose minimal medium. Continuous experiments with cell retention, repetitive fed-batch, and an in situ product recovery (ISPR) process with fully integrated electrodialysis were tested. Although the continuous approach achieved a high volumetric productivity (QP) of 110 g L(-1) d(-1), this approach was not pursued because of long-term production strain instabilities. The highest pyruvate/glucose molar yield of up to 1.78 mol mol(-1) together with high QP 145 g L(-1) d(-1) and high pyruvate titers was achieved by the repetitive fed-batch approach. To separate pyruvate from fermentation broth a fully integrated continuous process was developed. In this process electrodialysis was used as a separation unit. Under optimum conditions a (calculated) final pyruvate titer of >900 mmol L(-1) (79 g L(-1)) was achieved.

A more efficient search strategy for aging genes based on connectivity

MOTIVATION

Many aging genes have been found from unbiased screens in model organisms. Genetic interventions promoting longevity are usually quantitative, while in many other biological fields (e.g. development) null mutations alone have been very informative. Therefore, in the case of aging the task is larger and the need for a more efficient genetic search strategy is especially strong.

RESULTS

The topology of genetic and metabolic networks is organized according to a scale-free distribution, in which hubs with large numbers of links are present. We have developed a computational model of aging genes as the hubs of biological networks. The computational model shows that, after generalized damage, the function of a network with scale-free topology can be significantly restored by a limited intervention on the hubs. Analyses of data on aging genes and biological networks support the applicability of the model to biological aging. The model also might explain several of the properties of aging genes, including the high degree of conservation across different species. The model suggests that aging genes tend to have a higher number of connections and therefore supports a strategy, based on connectivity, for prioritizing what might otherwise be a random search for aging genes.

Topological analysis of mass-balanced signaling networks: a framework to obtain network properties including crosstalk

Signal transduction networks have only been studied at a small scale because large-scale reconstructions and suitable in silico analysis methods have not been available. Since reconstructions of large signaling networks are progressing well there is now a need to develop a framework for analysing structural properties of signaling networks. One such framework is presented here, one that is based on systemically independent pathways and a mass-balanced representation of signaling events. This approach was applied to a prototypic signaling network and it allowed for: (1) a systemic analysis of all possible input/output relationships, (2) a quantitative evaluation of network crosstalk, or the interconnectivity of systemically independent pathways, (3) a measure of the redundancy in the signaling network, (4) the participation of reactions in signaling pathways, and (5) the calculation of correlated reaction sets. These properties emerge from network structure and can only be derived and studied within a defined mathematical framework. The calculations presented are the first of their kind for a signaling network, while similar analysis has been extensively performed for prototypic and genome-scale metabolic networks. This approach does not yet account for dynamic concentration profiles. Due to the scalability of the stoichiometric formalism used, the results presented for the prototypic signaling network can be obtained for large signaling networks once their reconstruction is completed.

Differential metabolic networks unravel the effects of silent plant phenotypes

Current efforts aim to functionally characterize each gene in model plants. Frequently, however, no morphological or biochemical phenotype can be ascribed for antisense or knock-out plant genotypes. This is especially the case when gene suppression or knockout is targeted to isoenzymes or gene families. Consequently, pleiotropic effects and gene redundancy are responsible for phenotype resistance. Here, techniques are presented to detect unexpected pleiotropic changes in such instances despite very subtle changes in overall metabolism. The method consists of the relative quantitation of >1,000 compounds by GC/time-of-flight MS, followed by classical statistics and multivariate clustering. Complementary to these tools, metabolic networks are constructed from pair-wise analysis of linear metabolic correlations. The topology of such networks reflects the underlying regulatory pathway structure. A differential analysis of network connectivity was applied for a silent potato plant line suppressed in expression of sucrose synthase isoform II. Metabolic alterations could be assigned to carbohydrate and amino acid metabolism even if no difference in average metabolite levels was found.

Modeling of the pyruvate production with Escherichia coli in a fed-batch bioreactor

A family of 10 competing, unstructured models has been developed to model cell growth, substrate consumption, and product formation of the pyruvate producing strain Escherichia coli YYC202 ldhA::Kan strain used in fed-batch processes. The strain is completely blocked in its ability to convert pyruvate into acetyl-CoA or acetate (using glucose as the carbon source) resulting in an acetate auxotrophy during growth in glucose minimal medium. Parameter estimation was carried out using data from fed-batch fermentation performed at constant glucose feed rates of q(VG)=10 mL h(-1). Acetate was fed according to the previously developed feeding strategy. While the model identification was realized by least-square fit, the model discrimination was based on the model selection criterion (MSC). The validation of model parameters was performed applying data from two different fed-batch experiments with glucose feed rate q(VG)=20 and 30 mL h(-1), respectively. Consequently, the most suitable model was identified that reflected the pyruvate and biomass curves adequately by considering a pyruvate inhibited growth (Jerusalimsky approach) and pyruvate inhibited product formation (described by modified Luedeking-Piret/Levenspiel term).

Network motifs in integrated cellular networks of transcription-regulation and protein-protein interaction

Genes and proteins generate molecular circuitry that enables the cell to process information and respond to stimuli. A major challenge is to identify characteristic patterns in this network of interactions that may shed light on basic cellular mechanisms. Previous studies have analyzed aspects of this network, concentrating on either transcription-regulation or protein-protein interactions. Here we search for composite network motifs: characteristic network patterns consisting of both transcription-regulation and protein-protein interactions that recur significantly more often than in random networks. To this end we developed algorithms for detecting motifs in networks with two or more types of interactions and applied them to an integrated data set of protein-protein interactions and transcription regulation in Saccharomyces cerevisiae. We found a two-protein mixed-feedback loop motif, five types of three-protein motifs exhibiting coregulation and complex formation, and many motifs involving four proteins. Virtually all four-protein motifs consisted of combinations of smaller motifs. This study presents a basic framework for detecting the building blocks of networks with multiple types of interactions.

The yeast coexpression network has a small-world, scale-free architecture and can be explained by a simple model

We investigated the gene coexpression network in Saccharomyces cerevisiae, in which genes are linked when they are coregulated. This network is shown to have a scale-free, small-world architecture. Such architecture is typical of biological networks in which the nodes are connected when they are involved in the same biological process. Current models for the evolution of intracellular networks do not adequately reproduce the features that we observe in the network. We therefore derive a new model for its evolution based on the observation that there is a positive correlation between the sequence similarity of paralogues and their probability of coexpression or sharing of transcription factor binding sites (TFBSs). The simple, neutralist's model consists of (1) coduplication of genes with their TFBSs, (2) deletion and duplication of individual TFBSs and (3) gene loss. A network is constructed by connecting genes that share multiple TFBSs. Our model reproduces the scale-free, small-world architecture of the coregulation network and the homology relations between coregulated genes without the need for selection either at the level of the network structure or at the level of gene regulation.

The metabolic world of Escherichia coli is not small

To elucidate the organizational and evolutionary principles of the metabolism of living organisms, recent studies have addressed the graph-theoretic analysis of large biochemical networks responsible for the synthesis and degradation of cellular building blocks [Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N. & Barabási, A. L. (2000) Nature 407, 651-654; Wagner, A. & Fell, D. A. (2001) Proc. R. Soc. London Ser. B 268, 1803-1810; and Ma, H.-W. & Zeng, A.-P. (2003) Bioinformatics 19, 270-277]. In such studies, the global properties of the network are computed by considering enzymatic reactions as links between metabolites. However, the pathways computed in this manner do not conserve their structural moieties and therefore do not correspond to biochemical pathways on the traditional metabolic map. In this work, we reassessed earlier results by digitizing carbon atomic traces in metabolic reactions annotated for Escherichia coli. Our analysis revealed that the average path length of its metabolism is much longer than previously thought and that the metabolic world of this organism is not small in terms of biosynthesis and degradation.

Characterization of topological structure on complex networks

Characterizing the topological structure of complex networks is a significant problem especially from the viewpoint of data mining on the World Wide Web. "Page rank" used in the commercial search engine Google is such a measure of authority to rank all the nodes matching a given query. We have investigated the page-rank distribution of the real Web and a growing network model, both of which have directed links and exhibit a power law distributions of in-degree (the number of incoming links to the node) and out-degree (the number of outgoing links from the node), respectively. We find a concentration of page rank on a small number of nodes and low page rank on high degree regimes in the real Web, which can be explained by topological properties of the network, e.g., network motifs, and connectivities of nearest neighbors.

Correlations in scale-free networks: tomography and percolation

We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabási-Albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes. We point out that the Barabási-Albert model displays dissortative behavior with respect to the nodes' degrees, while the node-randomized network shows assortative mixing. These kinds of correlations are visualized by discussing the shell structure of the networks around an arbitrary node. In spite of different correlation behaviors, all three constructions exhibit similar percolation properties. This result for percolation is also detected for a network with finite second moment and its corresponding randomized models.

Combinatorial complexity of pathway analysis in metabolic networks

Elementary flux mode analysis is a promising approach for a pathway-oriented perspective of metabolic networks. However, in larger networks it is hampered by the combinatorial explosion of possible routes. In this work we give some estimations on the combinatorial complexity including theoretical upper bounds for the number of elementary flux modes in a network of a given size. In a case study, we computed the elementary modes in the central metabolism of Escherichia coli while utilizing four different substrates. Interestingly, although the number of modes occurring in this complex network can exceed half a million, it is still far below the upper bound. Hence, to a certain extent, pathway analysis of central catabolism is feasible to assess network properties such as flexibility and functionality.

Centers of complex networks

The central vertices in complex networks are of particular interest because they might play the role of organizational hubs. Here, we consider three different geometric centrality measures, excentricity, status, and centroid value, that were originally used in the context of resource placement problems. We show that these quantities lead to useful descriptions of the centers of biological networks which often, but not always, correlate with a purely local notion of centrality such as the vertex degree. We introduce the notion of local centers as local optima of a centrality value "landscape" on a network and discuss briefly their role.

Signatures of small-world and scale-free properties in large computer programs

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the "information flow" within the program. We show that (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.

Analysis of metabolic networks using a pathway distance metric through linear programming

The solution of the shortest path problem in biochemical systems constitutes an important step for studies of their evolution. In this paper, a linear programming (LP) algorithm for calculating minimal pathway distances in metabolic networks is studied. Minimal pathway distances are identified as the smallest number of metabolic steps separating two enzymes in metabolic pathways. The algorithm deals effectively with circularity and reaction directionality. The applicability of the algorithm is illustrated by calculating the minimal pathway distances for Escherichia coli small molecule metabolism enzymes, and then considering their correlations with genome distance (distance separating two genes on a chromosome) and enzyme function (as characterised by enzyme commission number). The results illustrate the effectiveness of the LP model. In addition, the data confirm that propinquity of genes on the genome implies similarity in function (as determined by co-involvement in the same region of the metabolic network), but suggest that no correlation exists between pathway distance and enzyme function. These findings offer insight into the probable mechanism of pathway evolution.

Evolving protein interaction networks through gene duplication

The topology of the proteome map revealed by recent large-scale hybridization methods has shown that the distribution of protein-protein interactions is highly heterogeneous, with many proteins having few edges while a few of them are heavily connected. This particular topology is shared by other cellular networks, such as metabolic pathways, and it has been suggested to be responsible for the high mutational homeostasis displayed by the genome of some organisms. In this paper we explore a recent model of proteome evolution that has been shown to reproduce many of the features displayed by its real counterparts. The model is based on gene duplication plus re-wiring of the newly created genes. The statistical features displayed by the proteome of well-known organisms are reproduced and suggest that the overall topology of the protein maps naturally emerges from the two leading mechanisms considered by the model.

Bio-array images processing and genetic networks modelling

The new tools available for gene expression studies are essentially the bio-array methods using a large variety of physical detectors (isotopes, fluorescent markers, ultrasounds...). Here we present first rapidly an image-processing method independent of the detector type, dealing with the noise and with the peaks overlapping, the peaks revealing the detector activity (isotopic in the presented example), correlated with the gene expression. After this primary step of bio-array image processing, we can extract information about causal influence (activation or inhibition) a gene can exert on other genes, leading to clusters of genes co-expression in which we extract an interaction matrix M and an associated interaction graph G explaining the genetic regulatory dynamics correlated to the studied tissue function. We give two examples of such interaction matrices and graphs (the flowering genetic regulatory network of Arabidopsis thaliana and the lytic/lysogenic operon of the phage Mu) and after some theoretical rigorous results recently obtained concerning the asymptotic states generated by the genetic networks having a given interaction matrix and reciprocally concerning the minimal (in the sense of having a minimal number of non-zero coefficients) matrices having given stationary stable states.