U of I CS 466 - Large-scale organization of metabolic networks

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Large-scale organization ofmetabolic networksJeong et al.CS 466Saurabh SinhaComplex network in cell• Cellular processes generating mass &energy, transfering information,specifying cell fate• Integrated through complex network ofseveral constituents and reactions• Can we look at such networks and learnsomething about biology and evolution?Key findings• “Metabolic” networks analyzed• Compared among 43 species from all threedomains of life (archaea, bacteria, eukarya)• Noticed the same topologic scaling propertiesacross all species• Metabolic organization identical for livingorganisms, and is “robust”• May extrapolate to other cellular networksIntroduction• Fundamental design principles ofcellular networks?• Example: Dynamic interactions ofvarious constituents impart “robustness”to cellular processes– If one reaction did not happen optimally,does not necessarily mess up the wholeprocessIntroduction• Constituents of networks: DNA, RNA,proteins, small molecules• High throughput biology has helpeddevelop databases of networks, e.g.,metabolic networks• Maps are extremely complex• Fundamental features of networktopology?Network modelsErdos-Renyi random graph• Start with a fixed number of nodes, noedges• Each pair of nodes connected by anedge with probability p• This leads to a “statisticallyhomogeneous” graph or network• Most nodes have same degreehttp://arxiv.org/pdf/cond-mat/0010278Erdos-Renyi random graph• Degree distribution is Poisson withstrong peak at mean <k>• Therefore, probability of finding a highlyconnected node decays exponentiallyhttp://arxiv.org/pdf/cond-mat/0010278Empirical graphs• World-wide web, internet, socialnetworks have been studied• Serious deviations from randomstructure of E-R model• Better described by “scale-free”networksScale-free networks• Degree distribution P(k) follows power lawdistribution– P(k) ~ k-x• Scale-free networks are extremelyheterogeneous:– a few highly connected nodes (hubs)– rest of the (less connected) nodes connect to hubs• Generated by a process where new nodesare preferentially attached to already high-degree nodeshttp://arxiv.org/pdf/cond-mat/0010278What does this tell us?• Difference between Erdos-Renyi andscale-free graphs arise from simpleprinciples of how the graphs werecreated• Therefore, understanding topologicalproperties can tell us how the cellularnetworks were createdDataMetabolic networks• Core metabolic network of 43 differentorganisms (WIT database)• 6 archaea, 32 bacteria, 5 eukarya• Nodes = substrates, edges = metabolicreactions, additional nodes = enzymes• Based on firmly established data frombiochemical 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 modelor by scale-free model?• Observed that degree distributionfollows a power law. Therefore, scale-free networkshttp://arxiv.org/pdf/cond-mat/0010278A. fulgidusE. coliC. elegans AverageSmall-world property• General feature of many complexnetworks: any two nodes can beconnected by relatively short paths• In metabolic network, a path is thebiological “pathway” connecting twosubstrates• Characterized by “network diameter”– Shortest path, over all pairs of nodesSmall-world property• For non-biological networks, the averagedegree is usually fixed• This implies that network diameter increaseslogarithmically with new nodes being added• Is this true of metabolic networks ?• That is, more complex bacterium (moresubstrates and enzymes) will have largerdiameter ?Small-world property• More complex bacterium (more substratesand enzymes) will have larger diameter ?• Observed: diameter same across all 43species !• A possible explanation: average degree mustbe 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 afew “hub” nodes dominate the overallconnectivity• Sequential removal of hubs => diameterrises sharply• Observed: metabolic networks showthis phenomenon toohttp://arxiv.org/pdf/cond-mat/0010278Diameter after removing M substratesHubs in network• At the same time, scale-free networks arerobust to random errors• In metabolic network, removal of randomlychosen substrates did not affect averagedistance between remaining nodes• Fault tolerance to removal of metabolicenzymes also demonstrated throughbiological experimentsHubs across networks• Do the same substrates act as hubs inall organisms?• Rank all substrates by their degrees• Ranking of the top substrates ispractically same across all species• For every substrate present in allspecies, compute rank “r” (in terms ofdegree) in each speciesHubs across networks• Compute mean <r> and standarddeviation σr of rank of each substrate• Observed: σr increases with <r>• The top-ranking nodes (hubs) haverelatively little variance across specieshttp://arxiv.org/pdf/cond-mat/0010278Summary• Other biological networks alsohypothesized to be scale-free.• Evolutionary selection of a robust anderror tolerant


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