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

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Protein-protein Interaction Networks biological networks

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

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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

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Protein Interaction Networks Undirected network: nodes proteins links direct interaction interaction SISSA - PHD - October, 18th 2004 S.Maslov & K.Sneppen, Science 296, 910 (2002)

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Interaction-detection Methods experimental techniques physical bindings yeast two-hybrid systemsyeast two-hybrid systems mass spectrometry analysis of purified complexesmass spectrometry analysis of purified complexes interaction prediction methods functional associations correlated mRNA expression profilescorrelated mRNA expression profiles genetic interaction-detection methodsgenetic interaction-detection methods in silico approaches – gene fusion, gene neighborhood, phylogenetic profilesin silico approaches – gene fusion, gene neighborhood, phylogenetic profiles SISSA - PHD - October, 18th 2004

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Yeast two-hybrid system (Y2H) simple, rapid, sensitive, inexpensive suitable for large- scale applications simple, rapid, sensitive, inexpensive suitable for large- scale applications virtually every protein-protein interaction, even transient, unstable or weak ints. 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

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

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Topological analysis Saccharomyces cerevisiae network (I): Y2H binary interactions from 2 distinct experiments network (I): Y2H binary interactions from 2 distinct experiments network (II): interactions from complex analysis (tandem affinity purification, TAP) network (II): interactions from complex analysis (tandem affinity purification, TAP) network (III): mixed collection of interactions from different exp. techniques (Database of Interacting Proteins, DIP) network (III): mixed collection of interactions from different exp. techniques (Database of Interacting Proteins, DIP) SISSA - PHD - October, 18th 2004 P.Uetz et al. Nature 403, 623 (2000) T.Ito et al. Proc. Natl. Acad. Sci. USA 98, 4569 (2001) A.C.Gavin et al. Nature 415, 141 (2002) Database of Interacting Proteins (DIP)

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Topological analysis SISSA - PHD - October, 18th 2004 (I)(II)(III) # proteins # links

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degree distrib. P(k) SISSA - PHD - October, 18th 2004 H.Jeong, S.P.Mason, A.-L. Barabasi & Z.N.Oltvai, Nature 411, 41 (2001)

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SISSA - PHD - October, 18th 2004

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

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

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

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Y2H network TAP network DIP network no correlations only 3-points correlations(complexes) hierarchicalstructure,degreecorrelations

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

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

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

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PIN renormalization SISSA - PHD - October, 18th 2004

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

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Functional characterization SISSA - PHD - October, 18th 2004 Change in the view of protein function: individual task cooperative behaviour protein interactions interactions functional relationships functional relationships MIPS Comprehensive Yeast Genome Database (CYGD).

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Function prediction SISSA - PHD - October, 18th 2004 about 30% of encoded proteins per sequenced genome are still uncharacterized about 30% of encoded proteins per sequenced genome are still uncharacterized network-based methods for function prediction: 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. Yeast 18, 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

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Function prediction SISSA - PHD - October, 18th 2004 Basic strategy: close proteins closely related functional annotations annotations Rate (link f common) (I)(II)(III) exp NM1 NM2

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

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

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

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mixed GOM & MEE models SISSA - PHD - October, 18th 2004 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

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mixed Global Optimization Model SISSA - PHD - October, 18th 2004 II neighbors experimental reasons: direct interaction/ mediated interaction mediated interaction evolution by duplication/divergence topological redundancies M.P.Samanta & S.Liang. Proc. Natl. Acad. Sci. USA, 100,12579 (2003) A.Edwards et al. Trends Genet. 18, 529 (2002) A.Force et al. Genetics 151, 1531 (1999) M.Lynch and A.Force. Genetics 154, 459 (2000)

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mixed Global Optimization Model SISSA - PHD - October, 18th 2004 I neighbors GOM 1 II neighbors GOM 2

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mixed Global Optimization Model SISSA - PHD - October, 18th 2004 random initial functional assignment indipendent optimization of GOM 1 and GOM 2 frustration multiple optimal solutions functional assignment: function(s) with highest frequency of occurrence mixed GOM functional assignment: merging GOM 1 and GOM 2 GOM 1 and GOM 2 role of topological redundancies: S ij = # paths of length 2 connecting proteins i and j S ij = # paths of length 2 connecting proteins i and j

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Maximum Entropy Estimate Model SISSA - PHD - October, 18th 2004 k -points correlation functions ( i, j ) ( i, j ) measure of the functional correlations

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

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

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

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Results: Statistical reliability SISSA - PHD - October, 18th 2004 (I)(II) totally overlapping success success unsuccess unsuccess36% 79% 79% 21% 21%51% 80% 80% 20% 20% partly overlapping success GOM 1 success GOM 1 success GOM 2 success GOM 2 success GOM 1 & GOM 2 success GOM 1 & GOM 2 unsuccess unsuccess37% 8% 8% 4% 4% 74% 74% 14% 14%26% 9% 9% 1% 1% 75% 75% 15% 15% not overlapping success GOM 1 success GOM 1 success GOM 2 success GOM 2 success GOM 1 & GOM 2 success GOM 1 & GOM 2 unsuccess unsuccess27% 20% 20% 23% 23% 34% 34% 23% 23%23% 20% 20% 24% 24% 42% 42% 14% 14%

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Results: Statistical reliability SISSA - PHD - October, 18th 2004 P: ensemble of predicted functions T: ensemble of true functions MR: majority rule random: random guessing guessing

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

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Results: Robustness SISSA - PHD - October, 18th 2004 random rewiring degree of dissimilarity f l dissimilarity f l function prediction on original & on original & rewired networks rewired networks prediction overlap:

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Conclusions & Perspectives SISSA - PHD - October, 18th 2004 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)

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

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