Proteome Network Emulating Models

  • Phuong Dao
  • Fereydoun Hormozdiari
  • Iman Hajirasouliha
  • Martin Ester
  • S. Cenk Sahinalp
Chapter

Abstract

The proteome network (or protein–protein interaction (PPI) network) of an organism represents each protein as a vertex and each pairwise interaction as an edge. In the past 10 years, we witnessed a significant amount of effort going into the development of the PPI networks and the computational tools for analyzing them. In particular, there have been several attempts to capture the topological features of PPI networks through random graph models, which have been successfully applied to the emulation of “small-world” networks, which are sparse, but highly connected. The available PPI networks have also been thought to have a small diameter with power-law degree distribution thus “scale-free” network emulators such as the Preferential Attachment Model have been investigated for the purposes of emulating PPI networks. The lack of success in this direction led to the development of further models, which either reject the “scale-freeness” of the PPI networks, such as the Geometric Random Network Model or guarantee scale freeness through means of expansion other than “Preferential Attachment” such as vertex (i.e., protein/gene duplication) – as in the case of the Pastor-Satorras Model or the more recent Generalized Duplication Model. In this study, we compare available PPI networks of various sizes with those generated by the random graph models and observe that the Generalized Duplication Model, with the “right” choice of the initial “seed” network, provides the best alternative in capturing all network feature distributions. One network feature distribution that remains difficult to capture, however, is the “dense graphlet” distribution: all available PPI networks seem to include (many) more dense graphlets such as cliques in comparison to the networks generated by all available models.

References

  1. 1.
    W. Aiello, F. Chung, and L. Lu. A random graph model for power law graphs. In Proceedings of ACM STOC, pages 171–180, 2000.Google Scholar
  2. 2.
    Noga Alon, Raphael Yuster, and Uri Zwick. Color-coding. J. ACM, 42(4):844–856, 1995.Google Scholar
  3. 3.
    A.-L. Barabási and R. A. Albert. Emergence of scaling in random networks. Science, 286: 509–512, 1999.PubMedCrossRefGoogle Scholar
  4. 4.
    G. Bebek, P. Berenbrink, C. Cooper, T. Friedetzky, J. Nadeau, and S.C. Sahinalp. The degree distribution of the general duplication models. Theoretical Computer Science, 369(1–3): 239–249, 2006.CrossRefGoogle Scholar
  5. 5.
    G. Bebek, P. Berenbrink, C. Cooper, T. Friedetzky, J. Nadeau, and S.C. Sahinalp. Topological properties of proteome networks. In Proceedings of RECOMB satellite meeting on System Biology. LNBI,Springer, 2005.Google Scholar
  6. 6.
    A. Bhan, D. J. Galas, and T. G. Dewey. A duplication growth model of gene expression networks. Bioinformatis, 18:1486–1493, 2002.CrossRefGoogle Scholar
  7. 7.
    B. Bollobás, O Riordan, J. Spencer, and G. Tusanády. The degree sequence of a scale-free random graph process. Random Struct. Algorithms, 18:279–290, 2001.Google Scholar
  8. 8.
    F. Chung, L. Lu, and D.J. Galas. Duplication models for biological networks. Journal of Computational Biology, 10:677–687, 2003.PubMedCrossRefGoogle Scholar
  9. 9.
    C. Cooper and A. Frieze. A general model of webgraphs. Random Struct. Algorithms, 22: 311–335, 2003.CrossRefGoogle Scholar
  10. 10.
    M. Rasajskim, D. J. Higham, and N. Przulj. Fitting a geometric graph to a protein-protein interaction network. Bioinformatics, 8:1093–1099, 2008.Google Scholar
  11. 11.
    E. De Silva and M.P.H. Stumpf. Complex networks and simple models in biology. Journal of the Royal Society Interface, 2:419–430, 2005.CrossRefGoogle Scholar
  12. 12.
    M. Faloutsos, P. Faloutsos, and C. Faloutsos. On power-law relationships of the internet topology. In SIGCOMM, pages 251–262, 1999.Google Scholar
  13. 13.
    R. Ferrer i Cancho, and C. Janssen. The small world of human language. In Proceedings of Royal Society of London B, volume 268, pages 2261–2266, 2001.Google Scholar
  14. 14.
    Michael R. Garey and David S.Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.Google Scholar
  15. 15.
    J. Han, D. Dupuy, N. Bertin, M. Cusick, and M. Vidal. Effect of sampling on topology predictions of protein-protein interaction networks. Nature Biotech, 23:839–844, 2005.CrossRefGoogle Scholar
  16. 16.
    F. Hormozdiari, P. Berenbrink, N. Przulj, and S.C. Sahinalp. Not all scale free networks are born equal: the role of the seed graph in ppi network emulation. In Proceedings of RECOMB satellite meeting on System Biology, 2006.Google Scholar
  17. 17.
    B. Kahng S. Redner J. Kim, P.L. Krapivsky. Infinite-order percolation and giant fluctuations in a protein interaction network. Phys. Rev. E 66, 2002.Google Scholar
  18. 18.
    H. Jeong, S. Mason, A.-L. Barabasi, and Z. N. Oltvai. Lethality and centrality in protein networks. Nature, 411:41, 2001.PubMedCrossRefGoogle Scholar
  19. 19.
    J. Kleinberg, R. Kumar, PP. Raphavan, S. Rajagopalan, and A. Tomkins. The web as a graph: Measurements, models and methods. In Proceedings of COCOON, pages 1–17, 1999.Google Scholar
  20. 20.
    R. Kumar, P. Raghavan, D. Sivakumar, A. Tomkins, and E. Upfal. Stochastic models for the web graph. In Proceedings of FOCS, pages 57–65, 2002.Google Scholar
  21. 21.
    D. G. Corneil, N. Przulj, and I. Jurisica. Modeling interactome: Scale-free or geometric? Bioinformatics, 150:216–231, 2005.Google Scholar
  22. 22.
    N. Alon, P. Dao, I. Hajirasouliha, F. Hormozdiari, and S.C. Sahinalp. Biomolecular network motif counting and discovery by color coding. Bioinformatics, 24: i32–i40, 2008.CrossRefGoogle Scholar
  23. 23.
    D. J. Higham, O. Kuchaiev, M. Rasajski and N. Przulj. Geometric de-noising of protein-protein interaction networks. Plos Computationtal Biology, 5, 2009.Google Scholar
  24. 24.
    Ohno. Evolution by gene duplication. Springer, 1970.Google Scholar
  25. 25.
    P. Dao, A. Schönhuth, F. Hormozdiari, I. Hajirasouliha, S.C. Sahinalp, and M. Ester. Quantifying systemic evolutionary changes by color coding confidence-sored ppi networks. In Proceedings of the WABI 2009, pages 37–48, 2009.Google Scholar
  26. 26.
    R. Pastor-Satorras, E. Smith, and R.V. Sole. Evolving protein interaction networks through gene duplication. Journal of Theoretical biology, 222:199–210, 2003.PubMedCrossRefGoogle Scholar
  27. 27.
    T. Przytycka and Y.K. Yu. Scale-free networks versus evolutionary drift. Computational Biology and Chemistry, 28:257–264, 2004.PubMedCrossRefGoogle Scholar
  28. 28.
    F. Moser, A. Schnhuth, J. Holman, M. Ester, R. Colak, F. Hormozdiar, and S.C. Sahinalp. Dense graphlet statistics of protein interaction and random networks. In Proceedings of the Pacific Symposium on Biocomputing 2009, pages 190–202, 2009.Google Scholar
  29. 29.
    A.-L. Barabsi, R.A. Albert. Topology of evolving networks: local events and universality. Phys. Rev. Lett., 85:5234, 2000.CrossRefGoogle Scholar
  30. 30.
    S. Redner. How popular is your paper? an empirical study of the citations distribution. European Physical journal B, 4:131–134, 1998.CrossRefGoogle Scholar
  31. 31.
    Erdös and Rényi. On random graphsI. Publicationes Mathematicae Debrecen, 6:290–297, 1959.Google Scholar
  32. 32.
    H. A. Simon. On a class of skew distribution functions. Biometrika, 42:425440, 1955.Google Scholar
  33. 33.
    A.N. Samukhin, S.N. Dorogovstev, J.F.F. Mendes. Structure of growing networks with preferential linking. Phys. Rev. Lett., 85:4633, 2000.PubMedCrossRefGoogle Scholar
  34. 34.
    J.F.F. Mendes, S.N. Dorogovstev. Evolution of networks with aging of sites. Phys. Rev. E, 62:1842, 2000.CrossRefGoogle Scholar
  35. 35.
    R. Tanaka and et al. Some protein interaction data do not exhibit power law statistics. FEBS Letters, 579:5140–5144, 2005.Google Scholar
  36. 36.
    A. Vázquez, A. Flammini, A. Maritan, and A. Vespignani. Modelling of protein interaction networks. Complexus, 1:38–44, 2003.CrossRefGoogle Scholar
  37. 37.
    A. Wagner. The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. Molecular Biology and Evolution, 18:1283–1292, 2001.PubMedGoogle Scholar
  38. 38.
    D.J. Watts. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, 1999.Google Scholar
  39. 39.
    D.J. Watts and S.H. Strogatz. Collective dynamics of small-world networks. Nature, 393: 440–442, 1998.PubMedCrossRefGoogle Scholar
  40. 40.
    I. Xenarios and et al. Dip, the database of interacting proteins: a research tool for studying cellular networks of protein interactions. Nucleic Acids Research, 30:303–305, 2002.Google Scholar
  41. 41.
    G. Yule. A mathematical theory of evolution based on the conclusions of dr. j.c. willis. Philos. Trans. Roy. Soc. London (Ser. B), 213, 1925.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Phuong Dao
    • 1
  • Fereydoun Hormozdiari
    • 2
  • Iman Hajirasouliha
    • 2
  • Martin Ester
    • 2
  • S. Cenk Sahinalp
    • 2
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Simon Fraser UniversityBurnabyCanada

Personalised recommendations