Dense Module Enumeration in Biological Networks

  • Koji Tsuda
  • Elisabeth Georgii
Part of the Methods in Molecular Biology book series (MIMB, volume 939)


Automatic discovery of functional complexes from protein interaction data is a rewarding but challenging problem. While previous approaches use approximations to extract dense modules, our approach exactly solves the problem of dense module enumeration. Furthermore, constraints from additional information sources such as gene expression and phenotype data can be integrated, so we can systematically detect dense modules with interesting profiles. Given a weighted protein interaction network, our method discovers all protein sets that satisfy a user-defined minimum density threshold. We employ a reverse search strategy, which allows us to exploit the density criterion in an efficient way.

Key words

Protein complex Dense module enumeration Reverse search Gene expression Protein interaction 


  1. 1.
    Sharan R, Ulitsky I, Shamir R (2007) Network-based prediction of protein function. Mol Syst Biol 3:88PubMedCrossRefGoogle Scholar
  2. 2.
    Ulitsky I, Shamir R (2007) Identification of functional modules using network topology and high-throughput data. BMC Syst Biol 1:8PubMedCrossRefGoogle Scholar
  3. 3.
    Bader GD, Hogue CW (2003) An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics 4:2PubMedCrossRefGoogle Scholar
  4. 4.
    Uno T (2007) An efficient algorithm for enumerating pseudo cliques. In: Proceedings of ISAAC 2007, pp. 402–414Google Scholar
  5. 5.
    Chen J, Yuan B (2006) Detecting functional modules in the yeast protein-protein interaction network. Bioinformatics 22(18):2283–2290PubMedCrossRefGoogle Scholar
  6. 6.
    van Dongen S (2000) Graph clustering by flow simulation. PhD thesis, University of UtrechtGoogle Scholar
  7. 7.
    Newman ME (2006) Modularity and community structure in networks. Proc Natl Acad Sci USA 103(23):8577–8582PubMedCrossRefGoogle Scholar
  8. 8.
    Everett L, Wang LS, Hannenhalli S (2006) Dense subgraph computation via stochastic search: application to detect transcriptional modules. Bioinformatics 22(14):e117–e123PubMedCrossRefGoogle Scholar
  9. 9.
    Palla G, Derenyi I, Farkas I, Vicsek T (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043):814–818PubMedCrossRefGoogle Scholar
  10. 10.
    Spirin V, Mirny LA (2003) Protein complexes and functional modules in molecular networks. Proc Natl Acad Sci USA 100(21):12123–12128PubMedCrossRefGoogle Scholar
  11. 11.
    Zeng Z, Wang J, Zhou L, Karypis G (2006) Coherent closed quasi-clique discovery from large dense graph databases. KDD '06: proceedings of the 12th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, New York, pp 797–802CrossRefGoogle Scholar
  12. 12.
    Hanisch D, Zien A, Zimmer R, Lengauer T (2002) Co-clustering of biological networks and gene expression data. Bioinformatics 18(suppl 1):S145–S154PubMedCrossRefGoogle Scholar
  13. 13.
    Tanay A, Sharan R, Kupiec M, Shamir R (2004) Revealing modularity and organization in the yeast molecular network by integrated analysis of highly heterogeneous genomewide data. Proc Natl Acad Sci USA 101(9):2981–2986PubMedCrossRefGoogle Scholar
  14. 14.
    Segal E, Wang H, Koller D (2003) Discovering molecular pathways from protein interaction and gene expression data. Bioinformatics 19(suppl 1):i264–i271PubMedCrossRefGoogle Scholar
  15. 15.
    Pei J, Jiang D, Zhang A (2005) Mining cross-graph quasi-cliques in gene expression and protein interaction data. ICDE '05: proceedings of the 21st international conference on data engineering (ICDE'05). IEEE Computer Society, Washington, DC, pp 353–354Google Scholar
  16. 16.
    Ideker T, Ozier O, Schwikowski B, Siegel AF (2002) Discovering regulatory and signalling circuits in molecular interaction networks. Bioinformatics 18(suppl 1):S233–S240PubMedCrossRefGoogle Scholar
  17. 17.
    Huang Y, Li H, Hu H, Yan X, Waterman MS, Huang H, Zhou XJ (2007) Systematic discovery of functional modules and context-specific functional annotation of human genome. Bioinformatics 23(13):i222–i229PubMedCrossRefGoogle Scholar
  18. 18.
    Yan X, Mehan MR, Huang Y, Waterman MS, Yu PS, Zhou XJ (2007) A graph-based approach to systematically reconstruct human transcriptional regulatory modules. Bioinformatics 23(13):i577–i586PubMedCrossRefGoogle Scholar
  19. 19.
    Hermjakob H, Montecchi-Palazzi L, Lewington C, Mudali S, Kerrien S, Orchard S, Vingron M, Roechert B, Roepstorff P, Valencia A, Margalit H, Armstrong J, Bairoch A, Cesareni G, Sherman D, Apweiler R (2004) IntAct: an open source molecular interaction database. Nucleic Acids Res 32(suppl 1):D452–D455PubMedCrossRefGoogle Scholar
  20. 20.
    Chatr-aryamontri A, Ceol A, Palazzi LM, Nardelli G, Schneider MV, Castagnoli L, Cesareni G (2007) MINT: the Molecular INTeraction database. Nucleic Acids Res 35(suppl 1):D572–D574PubMedCrossRefGoogle Scholar
  21. 21.
    Bader GD, Betel D, Hogue CWV (2003) BIND: the Biomolecular Interaction Network Database. Nucleic Acids Res 31(1):248–250PubMedCrossRefGoogle Scholar
  22. 22.
    Su AI, Wiltshire T, Batalov S, Lapp H, Ching KA, Block D, Zhang J, Soden R, Hayakawa M, Kreiman G, Cooke MP, Walker JR, Hogenesch JB (2004) A gene atlas of the mouse and human protein-encoding transcriptomes. Proc Natl Acad Sci U S A 101(16):6062–6067PubMedCrossRefGoogle Scholar
  23. 23.
    Avis D, Fukuda K (1996) Reverse search for enumeration. Discrete Appl Math 65:21–46CrossRefGoogle Scholar
  24. 24.
    Han J, Kamber M (2006) Data mining: concepts and techniques of the Morgan Kaufmann series in data management systems, 2nd edn. Morgan Kaufmann Publishers, San FranciscoGoogle Scholar
  25. 25.
    Georgii E, Dietmann S, Uno T, Pagel P, Tsuda K (2009) Enumeration of condition-dependent dense modules in protein interaction networks. Bioinformatics 25:933–940PubMedCrossRefGoogle Scholar
  26. 26.
    Georgii E, Tsuda K, Schölkopf B (2011) Multi-way set enumeration in weight tensors. Mach Learn 82:123–155CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.AIST Computational Biology Research CenterTokyoJapan
  2. 2.JST ERATO Minato ProjectSapporoJapan
  3. 3.School of ScienceHelsinki Institute for Information Technology HIIT Aalto UniversityAaltoFinland

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