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Statistical mechanics approach to complex networks: from abstract to

Statistical mechanics approach to complex networks: from abstract to. biological networks. Vittoria Colizza Supervisor: Prof. Amos Maritan. biological networks. Protein-protein Interaction Networks. Outline. PIN Methods Topological analysis Renormalization

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Statistical mechanics approach to complex networks: from abstract to

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  1. Statistical mechanics approach to complex networks: from abstract to biological networks Vittoria Colizza Supervisor:Prof. Amos Maritan

  2. biological networks Protein-protein Interaction Networks

  3. Outline • PIN • Methods • Topological analysis • Renormalization • Topology / functionality correlations • Function prediction • mixed Global Optimization Model • Maximum Entropy Estimate Model • Conclusions & Perspectives SISSA - PHD - October, 18th 2004

  4. Protein Interaction Networks Involved in almost every cellular process : • DNA replication, transcription and translation • intracellular communication • cell cycle control • the workings of complex molecular motors • ….. SISSA - PHD - October, 18th 2004

  5. Protein Interaction Networks Undirected network: • nodes proteins • links direct interaction S.Maslov & K.Sneppen, Science296, 910 (2002) SISSA - PHD - October, 18th 2004

  6. Interaction-detection Methods • experimental techniquesphysical bindings • yeast two-hybrid systems • mass spectrometry analysis of purifiedcomplexes • interaction prediction methodsfunctional associations • correlated mRNA expression profiles • genetic interaction-detection methods • in silico approaches – gene fusion, gene neighborhood, phylogenetic profiles SISSA - PHD - October, 18th 2004

  7. Yeast two-hybrid system (Y2H) • simple, rapid, sensitive, inexpensive  suitable for large-scale applications • virtually every protein-protein interaction, even transient, unstable or weak ints. • no cooperative binding • some kinds of proteins not suitable, e.g. transcription factors • false negative ints. (artificially made hybrids) • false positive ints. (spatio-temporal constraints) SISSA - PHD - October, 18th 2004

  8. Protein Complex analysis • identification of whole complexes cooperative binding • in vivotechnique; one artificially made protein • physiological settings • several components as tagged baits for test • tagging procedure interference with complex formation • false negative ints. (weakly associated proteins) SISSA - PHD - October, 18th 2004

  9. Topological analysis Saccharomyces cerevisiae • network (I): Y2H binary interactions from 2 distinct experiments • network (II): interactions from complex analysis (tandem affinity purification,TAP) • network (III): mixedcollection of interactions from different exp. techniques (Database of Interacting Proteins,DIP) P.Uetz et al. Nature403, 623 (2000) T.Ito et al. Proc. Natl. Acad. Sci. USA98, 4569 (2001) A.C.Gavin et al. Nature415, 141 (2002) Database of Interacting Proteins (DIP) http://dip.doe-mbi.ucla.edu/ SISSA - PHD - October, 18th 2004

  10. Topological analysis SISSA - PHD - October, 18th 2004

  11. H.Jeong, S.P.Mason, A.-L. Barabasi & Z.N.Oltvai, Nature411, 41 (2001) degree distrib. P(k) SISSA - PHD - October, 18th 2004

  12. SISSA - PHD - October, 18th 2004

  13. clustering coeff. C(k) SISSA - PHD - October, 18th 2004

  14. neighb. degree knn(k) SISSA - PHD - October, 18th 2004

  15. rich-club phenomenon SISSA - PHD - October, 18th 2004

  16. Y2H network no correlations only 3-points correlations (complexes) TAP network hierarchical structure, degree correlations DIP network SISSA - PHD - October, 18th 2004

  17. Topological analysis through network renormalization SISSA - PHD - October, 18th 2004

  18. Network renormalization • investigation of critical behaviors of complex networks through RG approach • coarse-graining: decimation of less relevant details to elucidate critical properties • ‘simplification’ simpler and more understandable versions of large-scale networks  network visualization ? SISSA - PHD - October, 18th 2004

  19. G=0,1G’ not only 0,1 weighted networks SISSA - PHD - October, 18th 2004

  20. PIN renormalization SISSA - PHD - October, 18th 2004

  21. power-law + exp. cut-off PIN renormalization pure power-law no pure power-law (+ exp. cut-off) power-law (+ exp. cut-off) SISSA - PHD - October, 18th 2004

  22. Functional characterization Change in the view of protein function: individual task cooperative behaviour protein interactions functional relationships MIPS Comprehensive Yeast Genome Database (CYGD). http://mips.gsf.de/proj/yeast/CYGD/db SISSA - PHD - October, 18th 2004

  23. Function prediction • about 30% of encoded proteins per sequenced genome are stilluncharacterized • network-based methods for function prediction: • Majority rule (MR) • Global optimization (GOM) • Topological redundancies • Functional clustering (PRODISTIN) • Mixed GOM • MEE model B.Schwikowski, P.Uetz & S.Fields. Nature Biotech.18, 1257 (2000) H.Hishigaki, K.Nakai, T.Ono & A.Tanigami. Yeast18, 523 (2001) A.Vazquez, A. Flammini, A. Maritan & A.Vespignani. Nature Biotech.21, 697 (2003) M.P.Samanta & S.Liang. Proc. Natl. Acad. Sci. USA, 100,12579 (2003) C.Brun et al. Genome Biol.5, R6 (2003) VC, P.De Los Rios, A.Flammini & A.Maritan. In preparation SISSA - PHD - October, 18th 2004

  24. Function prediction Basic strategy: close proteins closely related functional annotations Rate (link  f common) SISSA - PHD - October, 18th 2004

  25. Majority rule function assigned = most common function(s) among classified partners ? 2 3,4,10 12 ? ? links uncl./uncl. proteins completely neglected !!! SISSA - PHD - October, 18th 2004

  26. Global Optimization Model (GOM) links unclassified / unclassified proteins also taken into account ? 2,4 3,4,10 12 2 3,4,10 12 ? ? whole set of interactions of each uncharacterized protein  self-consistency SISSA - PHD - October, 18th 2004

  27. Global Optimization Model (GOM) functional assignment score global optimization: minimum E functional assignment proposed links uncl./class. proteins links uncl./uncl. proteins SISSA - PHD - October, 18th 2004

  28. mixed GOM & MEE models Designed to take full advantage of the observed correlations between the pattern of interactions among proteins & their functionalities more throughful investigation of the topology mixed GOM observed correlations between the functions of interacting proteins MEE model SISSA - PHD - October, 18th 2004

  29. mixed Global Optimization Model II neighbors • experimental reasons: direct interaction/ mediated interaction • evolution by duplication/divergence • topological redundancies A.Edwards et al. Trends Genet. 18, 529 (2002) A.Force et al. Genetics151, 1531 (1999) M.Lynch and A.Force. Genetics154, 459 (2000) M.P.Samanta & S.Liang. Proc. Natl. Acad. Sci. USA, 100,12579 (2003) SISSA - PHD - October, 18th 2004

  30. mixed Global Optimization Model I neighbors GOM1 II neighbors GOM2 SISSA - PHD - October, 18th 2004

  31. mixed Global Optimization Model • random initial functional assignment • indipendent optimization of GOM1 and GOM2 • frustration multiple optimal solutions • functional assignment: function(s) with highest frequency of occurrence • mixed GOMfunctional assignment:merging GOM1andGOM2 • role of topological redundancies: Sij= # paths of length 2 connecting proteins i and j SISSA - PHD - October, 18th 2004

  32. Maximum Entropy Estimate Model k-points correlation functions l(si,sj) measure of the functional correlations SISSA - PHD - October, 18th 2004

  33. (5,6) (5,6) (2,3) (2,3) (2) (2) (2) (2) (2,4) (2,4) (3,4) (2,3,4) (3,4) (2,3,4) (4) (4) (2) (2) Maximum Entropy Estimate Model SISSA - PHD - October, 18th 2004

  34. Maximum Entropy Estimate Model Info extracted from the partial knowledge of the network (maximum entropy estimate criterion)cost function SISSA - PHD - October, 18th 2004

  35. Results: Statistical reliability • Self-consistency • test: • fraction fn of class. • proteins set • unclassified • function prediction • rate of success in • recovering correct • functions of test • proteins SISSA - PHD - October, 18th 2004

  36. Results: Statistical reliability SISSA - PHD - October, 18th 2004

  37. MR: majority rule random: random guessing P: ensemble ofpredicted functions T: ensemble oftrue functions Results: Statistical reliability SISSA - PHD - October, 18th 2004

  38. Results: Statistical reliability mixed GOM / MEE comparison SISSA - PHD - October, 18th 2004

  39. Results: Robustness • random rewiring • degree of dissimilarityfl • function prediction on original & rewired networks • prediction overlap: SISSA - PHD - October, 18th 2004

  40. Conclusions & Perspectives • PIN: underlying architecture and organization • standard tools of the theory of complex networks • renormalization group approach • functional relevance and correlations • function prediction methods • Mixed GOM: topological extension of GOM; 2 parameters with a priori assigned values • MEE model: no free parameters, extracting info from given knowledge • improvement of predictive ability (success rate, robustness) SISSA - PHD - October, 18th 2004

  41. Acknowledgments • Amos Maritan • Alessandro Flammini • Paolo De Los Rios • Alessandro Vespignani • Jayanth Banavar • Andrea Rinaldo SISSA - PHD - October, 18th 2004

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