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  1. titletitle The Architecture of Complexity: From the WWW to network biology www.nd.edu/~networks

  2. Bio-Map GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

  3. Connect with probability p p=1/6 N=10 k ~ 1.5 Poisson distribution Erdös-Rényi model(1960) Pál Erdös(1913-1996) - Democratic - Random

  4. WWW Expected P(k) ~ k- Found World Wide Web Nodes: WWW documents Links: URL links Over 3 billion documents ROBOT:collects all URL’s found in a document and follows them recursively R. Albert, H. Jeong, A-L Barabasi, Nature, 401 130 (1999).

  5. What does it mean? Airlines Poisson distribution Power-law distribution Random Network Scale-free Network

  6. Internet INTERNET BACKBONE Nodes: computers, routers Links: physical lines (Faloutsos, Faloutsos and Faloutsos, 1999)

  7. Internet-Map

  8. Swedish sex-web Nodes: people (Females; Males) Links: sexual relationships 4781 Swedes; 18-74; 59% response rate. Liljeros et al. Nature 2001

  9. Many real world networks have the same architecture: Scale-free networks WWW, Internet (routers and domains), electronic circuits, computer software, movie actors, coauthorship networks, sexual web, instant messaging, email web, citations, phone calls, metabolic, protein interaction, protein domains, brain function web, linguistic networks, comic book characters, international trade, bank system, encryption trust net, energy landscapes, earthquakes, astrophysical network…

  10. BA model Scale-free model (1) Networks continuously expand by the addition of new nodes WWW : addition of new documents (2) New nodes prefer to link to highly connected nodes. WWW : linking to well known sites P(k) ~k-3 GROWTH: add a new node with m links PREFERENTIAL ATTACHMENT:the probability that a node connects to a node with k links is proportional to k. Barabási & Albert, Science286, 509 (1999)

  11. Bio-Map GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

  12. METABOLISM Bio-chemical reactions Citrate Cycle

  13. Boehring-Mennheim

  14. Metab-movie Nodes: chemicals (substrates) Links: bio-chemical reactions Metabolic Network

  15. Meta-P(k) Metabolic network Archaea Bacteria Eukaryotes Organisms from all three domains of life are scale-free networks! H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000)

  16. Bio-Map GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

  17. PROTEOME protein-protein interactions

  18. Prot P(k) Topology of the protein network Nodes: proteins Links: physical interactions (binding) H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)

  19. Perfect copy Mistake: gene duplication Origin of the scale-free topology: Gene Duplication Proteins with more interactions are more likely to get a new link: Π(k)~k (preferential attachment). Wagner (2001); Vazquez et al. 2003; Sole et al. 2001; Rzhetsky & Gomez (2001); Qian et al. (2001); Bhan et al. (2002).

  20. Robustness 1 node failure S fc 0 1 Fraction of removed nodes, f Robustness Complex systems maintain their basic functions even under errors and failures (cell  mutations; Internet  router breakdowns)

  21. Robust-SF Robustness of scale-free networks 1 S 0 1 f Attacks Failures   3 : fc=1 (R. Cohen et al PRL, 2000) fc Albert, Jeong, Barabasi, Nature 406 378 (2000)

  22. Prot- robustness Yeast protein network - lethality and topological position - Highly connected proteins are more essential (lethal)... H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)

  23. Traditional view of modularity: Modularity in Cellular Networks • Hypothesis: Biological function are carried by discrete functional modules. • Hartwell, L.-H., Hopfield, J. J., Leibler, S., & Murray, A. W. (1999). • Question: Is modularity a myth, or a structural property of biological networks? (are biological networks fundamentally modular?)

  24. (a) Scale-free (b) Modular Modular vs. Scale-free Topology

  25. 3. Clustering coefficient scales # links between k neighbors C(k)= k(k-1)/2 Hierarchical Networks

  26. Scaling of the clustering coefficient C(k) The metabolism forms a hierachical network. Ravasz, Somera, Mongru, Oltvai, A-L. B,Science 297, 1551 (2002).

  27. Can we identify the modules? li,j is 1 if there is a direct link between i and j, 0 otherwise

  28. Modules in the E. coli metabolism

  29. The structure of pyrimidine metabolism

  30. System level experimental analysis of essentiality in E. coli Whole-Genome Essentiality by Transposomics Aerobic growth: 620 essential 3,126 dispensable genes Gerdes et al. J Bact. 185, 5673-5684 (2003).

  31. Pyrimidine metabolism

  32. System level analysis of the full E coli metabolism Essentiality: Red: highly essential Green: dispensable Evolutionary conservation: Red: highly conserved Green: non-conserved (reference: 32 bacteria) Gerdes et al. J Bact. 185, 5673-5684 (2003).

  33. Characterizing the links Metabolism: Flux Balance Analysis (Palsson) Metabolic flux for each reaction Edwards, J. S. & Palsson, B. O, PNAS97, 5528 (2000). Edwards, J. S., Ibarra, R. U. & Palsson, B. O. Nat Biotechnol19, 125 (2001). Ibarra, R. U., Edwards, J. S. & Palsson, B. O. Nature420, 186 (2002).

  34. SUCC: Succinate uptake GLU : Glutamate uptake Central Metabolism, Emmerling et. al, J Bacteriol184, 152 (2002) Global flux organization in the E. coli metabolic network E. Almaas, B. Kovács, T. Vicsek, Z. N. Oltvai, A.-L. B. Nature, 2004.

  35. ~ k -0.27 Mass flows along linear pathways Mass flows along linear pathways Succinate rich substrate Glutamate rich substrate Inhomogeneity in the local flux distribution

  36. Pyramid Life’s Complexity Pyramid Z.N. Oltvai and A.-L. B. (2002).

  37. Http://www.nd.edu/~networks Zoltán N. Oltvai, Northwestern Med. School Hawoong Jeong, KAIST, Corea Réka Albert, Penn State Ginestra Bianconi, Friburg/Trieste Erzsébet Ravasz, Notre Dame Stefan Wuchty, Notre Dame Eivind Almaas, Notre Dame Baldvin Kovács, Budapest Tamás Vicsek, Budapest http://www.nd.edu/~networks

  38. Http://www.nd.edu/~networks http://www.nd.edu/~networks

  39. Bacon-map #876 Kevin Bacon #1 Rod Steiger Donald Pleasence #2 #3 Martin Sheen

  40. Bacon-list NO! 876 Kevin Bacon 2.786981 46 1811 Bonus: Why Kevin Bacon? Measure the average distance between Kevin Bacon and all other actors. No. of movies : 46 No. of actors : 1811 Average separation: 2.79 Kevin Bacon Is Kevin Bacon the most connected actor?

  41. Inhomogeneity in the local flux distribution

  42. SUMMARY Science collaboration WWW Language Hierarchical Networks Scale-free Citation pattern Cell Internet Modular C(N)=const. Hierarchical C(k)~k-β Scale-free P(k)~k-γ

  43. Traditional modeling: Network as a static graph Given a network with N nodes and L links  Create a graph with statistically identical topology RESULT: model the static network topology PROBLEM: Real networks are dynamical systems! Evolving networks OBJECTIVE: capture the network dynamics • identify the processes that contribute to the network topology • develop dynamical models that capture these processes METHOD :  BONUS: get the topology correctly.

  44. Meta+all P(k) Whole cellular network

  45. Protein network Nodes: proteins Links: physical interaction (binding) Proteomics : identify and determine the properties of the proteins. (related to structure of proteins)

  46. Nodes: chemicals (substrates) Links: chem. reaction Metabolic Network

  47. Whole cellular network

  48. Achilles Heel Achilles’ Heel of complex network failure attack Internet Protein network R. Albert, H. Jeong, A.L. Barabasi, Nature 406 378 (2000)

  49. Taxonomy using networks A: Archaea B: Bacteria E: Eukaryotes

  50. Watts-Strogatz Clustering: My friends will know each other with high probability! Probability to be connected C»p # of links between 1,2,…n neighbors C = n(n-1)/2 N nodes forms a regular lattice. With probability p, each edge is rewired randomly. (Nature 393, 440 (1998))