Large-scale organization of metabolic networks Jeong et al.Complex network in cellKey findingsIntroductionSlide 5Network modelsErdos-Renyi random graphPowerPoint PresentationSlide 9Slide 10Empirical graphsScale-free networksSlide 13What does this tell us?DataMetabolic networksExample of a metabolic network http://www.avatar.se/strbio2001/metabolic/what.htmlResultsTopologySlide 20Small-world propertySlide 22Slide 23Slide 24Hubs in networkSlide 26Slide 27Hubs across networksSlide 29Slide 30SummaryLarge-scale organization of metabolic networksJeong et al.CS 466Saurabh SinhaComplex network in cell•Cellular processes generating mass & energy, transfering information, specifying cell fate•Integrated through complex network of several constituents and reactions•Can we look at such networks and learn something about biology and evolution?Key findings•“Metabolic” networks analyzed•Compared among 43 species from all three domains of life (archaea, bacteria, eukarya)•Noticed the same topologic scaling properties across all species•Metabolic organization identical for living organisms, and is “robust”•May extrapolate to other cellular networksIntroduction•Fundamental design principles of cellular networks?•Example: Dynamic interactions of various constituents impart “robustness” to cellular processes–If one reaction did not happen optimally, does not necessarily mess up the whole processIntroduction•Constituents of networks: DNA, RNA, proteins, small molecules•High throughput biology has helped develop databases of networks, e.g., metabolic networks•Maps are extremely complex•Fundamental features of network topology?Network modelsErdos-Renyi random graph•Start with a fixed number of nodes, no edges•Each pair of nodes connected by an edge with probability p•This leads to a “statistically homogeneous” graph or network•Most nodes have same degreehttp://arxiv.org/pdf/cond-mat/0010278Erdos-Renyi random graph•Degree distribution is Poisson with strong peak at mean <k>•Therefore, probability of finding a highly connected node decays exponentiallyhttp://arxiv.org/pdf/cond-mat/0010278Empirical graphs•World-wide web, internet, social networks have been studied•Serious deviations from random structure of E-R model•Better described by “scale-free” networksScale-free networks•Degree distribution P(k) follows power law distribution–P(k) ~ k-x•Scale-free networks are extremely heterogeneous:–a few highly connected nodes (hubs)–rest of the (less connected) nodes connect to hubs•Generated by a process where new nodes are preferentially attached to already high-degree nodeshttp://arxiv.org/pdf/cond-mat/0010278What does this tell us?•Difference between Erdos-Renyi and scale-free graphs arise from simple principles of how the graphs were created•Therefore, understanding topological properties can tell us how the cellular networks were createdDataMetabolic networks•Core metabolic network of 43 different organisms (WIT database)•6 archaea, 32 bacteria, 5 eukarya •Nodes = substrates, edges = metabolic reactions, additional nodes = enzymes•Based on firmly established data from biochemical literature•Sufficient data for statistical analysisExample of a metabolic network http://www.avatar.se/strbio2001/metabolic/what.htmlGreen boxes: known enzymesResultsTopology•Is the topology described by E-R model or by scale-free model?•Observed that degree distribution follows a power law. Therefore, scale-free networkshttp://arxiv.org/pdf/cond-mat/0010278A. fulgidusE. coliC. elegans AverageSmall-world property•General feature of many complex networks: any two nodes can be connected by relatively short paths•In metabolic network, a path is the biological “pathway” connecting two substrates•Characterized by “network diameter”–Shortest path, over all pairs of nodesSmall-world property•For non-biological networks, the average degree is usually fixed•This implies that network diameter increases logarithmically with new nodes being added•Is this true of metabolic networks ?•That is, more complex bacterium (more substrates and enzymes) will have larger diameter ?Small-world property•More complex bacterium (more substrates and enzymes) will have larger diameter ?•Observed: diameter same across all 43 species ! •A possible explanation: average degree must be higher for more complex organisms•This is also verified.http://arxiv.org/pdf/cond-mat/0010278network diameter for differentorganismsaverage degree over different organismsHubs in network•Power-law connectivity implies that a few “hub” nodes dominate the overall connectivity•Sequential removal of hubs => diameter rises sharply•Observed: metabolic networks show this phenomenon toohttp://arxiv.org/pdf/cond-mat/0010278Diameter after removing M substratesHubs in network•At the same time, scale-free networks are robust to random errors•In metabolic network, removal of randomly chosen substrates did not affect average distance between remaining nodes•Fault tolerance to removal of metabolic enzymes also demonstrated through biological experimentsHubs across networks•Do the same substrates act as hubs in all organisms?•Rank all substrates by their degrees•Ranking of the top substrates is practically same across all species•For every substrate present in all species, compute rank “r” (in terms of degree) in each speciesHubs across networks•Compute mean <r> and standard deviation r of rank of each substrate•Observed: r increases with <r>•The top-ranking nodes (hubs) have relatively little variance across specieshttp://arxiv.org/pdf/cond-mat/0010278Summary•Other biological networks also hypothesized to be scale-free.•Evolutionary selection of a robust and error tolerant