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Structure, Function and Evolution of Metabolic Networks (I)

Structure, Function and Evolution of Metabolic Networks (I). Jing Zhao College of Pharmacy, Second Military Medical University Shanghai Center for Bioinformation and Technology 2009.5.25. Spring school on multiscale methods and modeling in biophysics and system biology, Shanghai, China.

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Structure, Function and Evolution of Metabolic Networks (I)

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  1. Structure, Function andEvolution of MetabolicNetworks (I) Jing Zhao College of Pharmacy, Second Military Medical University Shanghai Center for Bioinformation and Technology 2009.5.25 Spring school on multiscale methods and modeling in biophysics and system biology, Shanghai, China

  2. Outline • Reconstruction of metabolic networks • Network metrics and topological features • Modularity and network decomposition • Topological diversity of networks with a given degree sequence

  3. I. Reconstruction of metabolic networks Zhao J, Yu H, Luo J, Cao Z, Li Y: Complex networks theory for analyzing metabolic networks. Chinese Science Bulletin 2006, 51(13):1529-1537.

  4. What is network?

  5. Examples: Internet

  6. Examples: Scientific collaborations

  7. Examples: protein-protein interaction network

  8. Metabolism

  9. Examples: metabolic network

  10. How to get genome-specific metabolic reactions? • Identifying ORFs from the genomic sequence; • (ii) Predicting all the enzyme genes of this organism by sequence similarity alignment; • (iii) Comparing the predicted enzymes within this organism against the collection of known • reference pathways to determine all the reactions of this organism.

  11. Two refined metabolism database for human being manually reconstructed: • BiGG database • Duarte, N. C.; Becker, S. A.; Jamshidi, N.; Thiele, I.; Mo, M. L.; Vo, T. D.; Srivas, R.; Palsson, B. O., Global reconstruction of the human metabolic network based on genomic and bibliomic data.PNAS 2007, 104, (6), 1777-1782. • The Edinburgh human metabolic network • Ma, H.; Sorokin, A.; Mazein, A.; Selkov, A.; Selkov, E.; Demin, O.; Goryanin, I., The Edinburgh human metabolic network reconstruction and its functional analysis.Molecular Systems Biology 2007, 3, 135.

  12. Statistics for BiGG database

  13. Process for reconstructing the Edinburgh human metabolic network

  14. Different graph representations of a simple metabolic network

  15. Currency metabolites Ma H, Zeng A-P: Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics 2003, 19(2):270-277.

  16. Currency metabolites

  17. Currency metabolites • Definition: • currency metabolites have high degree • they make not meaningful shortcuts • i.e. tie together distant parts of the network • i.e. tie different modules together Algorithm: Remove vertices in order of (currently) highest degree. The set of removed vertices that gives the network the highest modularity is the set of currency metabolites. Huss M, Holme P: Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks. IET Systems Biology 2007, 1:280-285.

  18. Human currency metabolites Huss M, Holme P: Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks. IET Systems Biology 2007, 1:280-285.

  19. Steps for reconstructing a metabolic network • Get reaction list • Generate substrate - product pair list • Delete currency metabolites • Generate metabolic network • Useful tool: • Text2pajek.exe

  20. II. Network metrics and topological features Zhao J, Yu H, Luo J, Cao Z, Li Y: Complex networks theory for analyzing metabolic networks. Chinese Science Bulletin 2006, 51(13):1529-1537.

  21. network science Measures of network structure. How does a network that is too large to draw .look. like? Real-world networks have both randomness and structure. How can we quantify network structure? Models of evolving networks. How do networks get their structure? What .microscopic. properties are responsible for the macro-structure of the network. Models of network changing events. Malicious attacks; overload breakdowns. Classication and functional prediction. How can we classify vertices and predict their function in the network? How does the network structure affect dynamic systems of the network? Running dynamic simulations on top of the network and see how dynamic properties correlates with the network structure.

  22. As for biochemical networks, what questions can we ask? • how can the large-scale organization be characterized? • are there any universal features over different species? • do the differences tell us something about evolution? • can we identify functional modules? • . . the functions of molecules?

  23. Degree distribution vs. scale-free networks Degree distribution p(k) : the occurrence frequency of nodes with degree k, (k=1,2,…). Random network Scale-free network hub Barabasi, A.L., Albert, R., Emergence of scaling in random networks, Science, 1999, 286:509-512

  24. BA model for network evolution: (1) Growth: the continuous addition of new nodes. (2) Preferential attachment: “the rich get richer” principle. • The high-degree nodes should appear in the earlier stage of network formation. Thirteen hub metabolites in E.coli metabolic network Wagner, A., Fell, D.A., The small world inside large metabolic networks, Proc R Soc Lond B, 2001, 268:1803-1810.

  25. Performance of scale-free networks: error tolerance: high resistance to random perturbations attack vulnerability : the removal of a few hub nodes will destroy the whole network. Albert, R., Jeong, H., Barabasi, A.-L., Error and attack tolerance of complex networks, Nature, 2000, 406:378-382.

  26. Jeong, H., Mason, S.P., Barabasi, A.L., Oltvai, Z.N., Lethality and centrality in protein networks, Nature, 2001, 411:41-42.

  27. Notice: Computation of the exponent cumulative distribution :  Log-log plot of the degree distribution (A) and cumulative degree distribution (B) for a network of 20000 nodes constructed by Barabasi-Albert preferential attachment model.

  28. How many triangles are there in the network? Clustering coefficient vs. Hierarchical modular networks N(v): the number of links between neighbours of node v d(v) :the degree of node v

  29. Ravasz E, Somera A L, Mongru D A, Oltvai Z N, Barabasi A L, Hierarchical organization of modularity in metabolic networks, Science,2002,297: 1551-1556

  30. Complex systems usually have a hierarchical structure, the entities of one level being compounded into new entities at the next higher lever, as cells into tissues, tissues into organs, and organs into functional systems. The whole is greater than the sum of its parts! At each new level of complexity in biology new and unexpected qualities appear, qualities which apparently cannot be reduced to the properties of the component parts. Life’s complex Pyramid: from the particular to the universal Oltvai, Z.N., Barabási, A.-L., Life’s Complexity Pyramid, SCIENCE, 2002, 298:763-764.

  31. Mean path length vs. small-world networks Small-world network:small mean path length; high clustering coefficient Small-world cell networks=>the cell may react quickly to changes of the surroundings Watts, D.J., Strogatz, S.H., Collective dynamics of `small-world' networks, Nature, 1998, 393:440-442.

  32. Assortativity coefficient vs. degree-degree correlation Are high-degree vertices connected to other high-degree vertices? Or are these vertices primarily connected to low-degree vertices? ji , ki: the degrees of the nodes at the ends of the ith edge M: number of edges in the network r>0: assortative network r<0: disassortative network Newman , M.E.J., Assortative mixing in networks, Phys Rev Lett, 2002, 89:208701.

  33. Newman , M.E.J., Assortative mixing in networks, Phys Rev Lett, 2002, 89:208701.

  34. The average connectivity <knn> of the nearest neighbors of a node depending on its connectivity k for the 1998 snapshot of the Internet, the generalized BA model and the fitness model. Romualdo Pastor-Satorras, Alexei Vázquez, and Alessandro Vespignani, Dynamical and Correlation Properties of the Internet,PHYSI CAL REV IEW LETTERS, VOLUME 87, NUMBER 25(2002)

  35. Correlation profiles of protein interaction network in yeast. Z-scores for connectivity correlations : Z(K0,K1) = (P(K0,K1) − Pr(K0,K1))/r(K0,K1) where r(K0,K1) is the standard deviation of Pr(K0,K1) in 1000 realizations of a randomized network. Maslov, S., Sneppen, K., Specificity and Stability in Topology of Protein Networks, Science, 2002, 296:910-913.

  36. Rich-club coefficient and rich-club phenomenon rich-club coefficient: Notice: Rich-club Assortative mixing Colizza V, Flammini A, Serrano MA, Vespignani A: Detecting rich-club ordering in complex networks. Nat Phys 2006, 2(2):110-115.

  37. Centrality: Which nodes are important for communication on the network? Assumption: Information transmission or material transportation on the network are along shortest paths.

  38. Betweenness centrality Node betweenness measures the degree to which a vertex is participating in the communication between pairs of other vertices :the number of shortest paths from s to t : the number of shortest paths from s to t with v as an inner vertex Holme P, Kim BJ, Yoon CN, Han SK: Attack vulnerability of complex networks. Phys Rev E 2002, 65:056109.

  39. Edge betweenness measures the degree to which an edge is participating in the communication between pairs of other vertices :the number of shortest paths from s to t : the number of shortest paths from s to t with v as an inner vertex Holme P, Kim BJ, Yoon CN, Han SK: Attack vulnerability of complex networks. Phys Rev E 2002, 65:056109.

  40. Nodes and edges of high betweenness centrality could be bottlenecks of the network, thus could be important enzymes or metabolites. • Edges of high betweenness centrality could be bridges of modules. Rahman, S.A., Schomburg, D., Observing local and global properties of metabolic pathways: 'load points' and 'choke points' in the metabolic networks, Bioinformatics, 2006, 22:1767-1774. Girvan M, Newman MEJ: Community structure in social and biological networks. Proc Natl Acad Sci 2002, 99(12):7821-7826.

  41. Closeness centrality Closeness centrality measures the degree to which a vertex is close to other vertices on average. “Service facility locating problem”: Find the location of a shopping mall that the average driving distance to the mall is minimal. Solution: the nodes which have the biggest closeness centrality

  42. Center: “Emergency facility locating problem”: find the optimal location of a firehouse such that the worst-case response distance of a fire engine is minimal.

  43. k-core 1, 2 and 3-core. Two basic properties of cores: first, cores may be disconnected subgraphs; second, cores are nested: for i>j, an i-core is a subgraph of a j-core of the same graph. => The probability of nodes both being essential and evolutionary conserved successively increases toward the innermost cores. Wuchty, S., Almaas, E., Peeling the yeast protein network, Proteomics, 2005, 5:444-449.

  44. Reciprocity metric aij= 1 if there is an arc from nodes i to j, aij= 0 otherwise L: the number of total arcs in the network N: the number of total nodes in the network ρ = -1 for purely unidirectional networks ρ = 1 for purely bidirectional networks

  45. Network null models • Network structures are always relative • Network structures: how the network differs from a random network, or a null model • One has to be clear about what to compare with a null model • Null model 1: random graphs (Poisson random graphs, • Erdos-Renyi graphs) • Null model 2: random graphs constrained to the set of • degrees of the original graph

  46. Null Models : random rewiring Maslov, S., Sneppen, K., Specificity and Stability in Topology of Protein Networks, Science, 2002, 296:910-913. Maslov S, Sneppen K, Zaliznyak A: Detection of topological patterns in complex networks: correlation profile of the internet. Physica A: Statistical and Theoretical Physics 2004, 333:529-540.

  47. Z-score

  48. Graph analysis and visualization software: Pajek: http://vlado.fmf.uni-lj.si/pub/networks/pajek/ txt2pajek.exe; pajek.exe UCINET: http://www.analytictech.com/downloaduc6.htm NetMiner: http://www.netminer.com/NetMiner/home_01.jsp

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