Improved Duplication Models for Proteome Network Evolution

  • Gürkan Bebek
  • Petra Berenbrink
  • Colin Cooper
  • Tom Friedetzky
  • Joseph H. Nadeau
  • S. Cenk Sahinalp
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4023)

Abstract

Protein-protein interaction networks, particularly that of the yeast S. Cerevisiae, have recently been studied extensively. These networks seem to satisfy the small world property and their (1-hop) degree distribution seems to form a power law. More recently, a number of duplication based random graph models have been proposed with the aim of emulating the evolution of protein-protein interaction networks and satisfying these two graph theoretical properties. In this paper, we show that the proposed model of Pastor-Satorras et al. does not generate the power law degree distribution with exponential cutoff as claimed and the more restrictive model by Chung et al. cannot be interpreted unconditionally. It is possible to slightly modify these models to ensure that they generate a power law degree distribution. However, even after this modification, the more general k-hop degree distribution achieved by these models, for k > 1, are very different from that of the yeast proteome network. We address this problem by introducing a new network growth model that takes into account the sequence similarity between pairs of proteins (as a binary relationship) as well as their interactions. The new model captures not only the k-hop degree distribution of the yeast protein interaction network for all k > 0, but it also captures the 1-hop degree distribution of the sequence similarity network, which again seems to form a power law.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aiello, W., Chung, F., Lu, L.: A random graph model for power law graphs. In: Proc. ACM STOC, pp. 171–180. ACM Press, New York (2000)Google Scholar
  2. 2.
    Aiello, W., Chung, F., Lu, L.: Random evolution in massive graphs. In: Proc. FOCS, pp. 510–519 (2001)Google Scholar
  3. 3.
    Balakrishnan, R., Christie, K.R., Costanzo, M.C., Dolinski, K., Dwight, S.S., Engel, S.R., Fisk, D.G., Hirschman, J.E., Hong, E.L., Nash, R., Oughtred, R., Skrzypek, M., Theesfeld, C.L., Binkley, G., Lane, C., Schroeder, M., Sethuraman, A., Dong, S., Weng, S., Miyasato, S., Andrada, R., Botstein, D., Cherry, J.M.: Saccharomyces Genome Database (April 1, 2004), ftp://ftp.yeastgenome.org/yeast/
  4. 4.
    Barabási, A.-L., Albert, R.A.: Emergence of scaling in random networks. Science 286, 509–512 (1999)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bebek, G., Berenbrink, P., Cooper, C., Friedetzky, T., Nadeau, J.H., Sahinalp, S.C.: The degree distribution of the generalized duplication model. Theoretical Computer Science 369, 234–249 (2006)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Berger, N., Bollobás, B., Borgs, C., Chayes, J., Riordan, O.: Degree distribution of the FKP network model. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 725–738. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Bhan, A., Galas, D.J., Dewey, T.G.: A duplication growth model of gene expression networks. Bioinformatics 18, 1486–1493 (2002)CrossRefGoogle Scholar
  8. 8.
    Bollobás, B., Borgs, C., Chayes, J., Riordan, O.: Directed scale-free graphs. In: Proc. ACM-SIAM SODA, pp. 132–139. ACM Press, New York (2003)Google Scholar
  9. 9.
    Bollobás, B., Riordan, O., Spencer, J., Tusanády, G.: The degree sequence of a scale-free random graph process. Random Structures and Algorithms 18, 279–290 (2001)CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Chung, F., Lu, L., Dewey, T.G., Galas, D.J.: Duplication models for biological networks. Journal of Computational Biology 10, 677–687 (2003)CrossRefGoogle Scholar
  11. 11.
    Cooper, C., Frieze, A.: A general model of webgraphs. Random Structures and Algorithms 22(3), 311–335 (2003)CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    Deane, C.M., Salwinski, L., Xenarios, I., Eisenberg, D.: Protein interactions: Two methods for assessment of the reliability of high-throughput observations. Molecular and Cellular Proteomics 1, 349–356 (2002)CrossRefGoogle Scholar
  13. 13.
    Erdös, P., Rényi, A.: On random graphs I. Publicationes Mathematicae Debrecen 6, 290–297 (1959)MathSciNetMATHGoogle Scholar
  14. 14.
    Faloutsos, M., Faloutsos, P., Faloutsos, C.: On Power-Law Relationships of the Internet Topology. In: SIGCOMM (1999)Google Scholar
  15. 15.
    Ferrer i Cancho, R., Janssen, C.: The small world of human language. Procs. Roy. Soc. London B 268, 2261–2266 (2001)CrossRefGoogle Scholar
  16. 16.
    Force, A., Lynch, M., Pickett, F.B., Amores, A., Yan, Y., Postlethwait, J.: Preservation of duplicate genes by complementary degenerative mutations. Genetics 151, 1531–1545 (1999)Google Scholar
  17. 17.
    Han, J.D., Dupuy, D., Bertin, N., Cusick, M., Vidal, M.: Effects of sampling on the predicted topology of interactome networks. Nature Biotechnology 23, 839–844 (2005)CrossRefGoogle Scholar
  18. 18.
    Ispolatov, I., Krapivsky, P.L., Yuryev, A.: Duplication-divergence model of protein interaction network. Physical Review, E 71, 061911 (2005)Google Scholar
  19. 19.
    Ito, T., et al.: A Comprehensive two-hybrid analysis to explore the yeast protein interactome. PNAS 98(8), 4569 (2001)CrossRefGoogle Scholar
  20. 20.
    Jeong, H., Mason, S., Barabasi, A.-L., Oltvai, Z.N.: Lethality and centrality in protein networks. Nature 411, 41 (2001)CrossRefGoogle Scholar
  21. 21.
    Kleinberg, J., Kumar, R., Raphavan, P.P., Rajagopalan, S., Tomkins, A.: The Web as a graph: Measurements, models and methods. In: Proc. COCOON, Tokyo, Japan, pp. 1–17 (1999)Google Scholar
  22. 22.
    Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: Stochastic models for the web graph. In: Proc. FOCS, pp. 57–65 (2000)Google Scholar
  23. 23.
    Nadeau, J.H., Sankoff, D.: Comparable Rates of Gene Loss and Functional Divergence After Genome Duplications Early in Vertebrate Evolution. Genetics 147, 1259 (1997)Google Scholar
  24. 24.
    van Noort, V., Snel, B., Huymen, M.A.: The yeast coexpression network has a small-world scale-free architecture and can be explained by a simple model. EMBO Reports 5(3) (2004)Google Scholar
  25. 25.
    Ohno, S.: Evolution by gene duplication. Springer, Berlin (1970)Google Scholar
  26. 26.
    Pastor-Satorras, R., Smith, E., Sole, R.V.: Evolving protein interaction networks through gene duplication. J. Theor. Biol. 222, 199–210 (2003)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Pearson, W.R., Lipman, D.J.: Fasta. ftp://ftp.virginia.edu/pub/fasta/ (data of access)
  28. 28.
    Przulj, N., Corneil, D.G., Jurisica, I.: Modeling Interactome: Scale-Free or Geometric? Bioinformatics 20(18), 3508–3515 (2004)CrossRefGoogle Scholar
  29. 29.
    Redner, S.: How Popular is Your Paper? An Empirical Study of the Citation Distribution. Eur. Phys. Jour. B 4, 131–134 (1998)Google Scholar
  30. 30.
    Seoighe, C., Wolfe, K.H.: Yeast genome evolution in the post-genome era. Current Opinion in Mol. Biol. 2, 548–554 (1999)Google Scholar
  31. 31.
    Seoighe, C., Wolfe, K.H.: Updated map of duplicated regions in the yeast genome. Gene 238(1), 253–261 (1999)CrossRefGoogle Scholar
  32. 32.
    Simon, H.A.: On a class of skew distribution functions. Biometrika 42, 425–440 (1955)MathSciNetMATHGoogle Scholar
  33. 33.
    Uetz, P.L., et al.: A comprehensive analysis of protein-protein interactions in Saccharomyces Cerevisiae. Nature 403, 623–627 (2000)CrossRefGoogle Scholar
  34. 34.
    Vázquez, A., Flammini, A., Maritan, A., Vespignani, A.: Modelling of protein interaction networks. Complexus 1, 38–44 (2003)CrossRefGoogle Scholar
  35. 35.
    Wagner, A.: The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. Mol. Biol. Evol. 18, 1283–1292 (2001)Google Scholar
  36. 36.
    Watts, D.J., Strogatz, S.H.: Colective dynamics of small-world networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  37. 37.
    Wolfe, K.H., Shields, D.C.: Molecular evidence for an ancient duplication of the entire yeast genome. Nature 387, 708–713 (1997)CrossRefGoogle Scholar
  38. 38.
    Xenarios, I., et al.: DIP, the Database of Interacting Proteins: a research tool for studying cellular networks of protein interactions. Nucleic Acids Res. 30, 303–305 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Gürkan Bebek
    • 1
  • Petra Berenbrink
    • 2
  • Colin Cooper
    • 3
  • Tom Friedetzky
    • 4
  • Joseph H. Nadeau
    • 5
  • S. Cenk Sahinalp
    • 2
  1. 1.Department of EECS, Case Western Reserve University, Cleveland, OH 44106-7071USA
  2. 2.School of Computing Science, Simon Fraser University, Burnaby BC, V5A 1S6Canada
  3. 3.Department of Computer Science, King’s College, London WC2R 2LSUK
  4. 4.Department of Computer Science, Durham University, Durham, DH1 3LEUK
  5. 5.Genetics Department, Case Western Reserve University, Cleveland, OH 44106-4955USA

Personalised recommendations