Assessing Significance of Connectivity and Conservation in Protein Interaction Networks

  • Mehmet Koyutürk
  • Ananth Grama
  • Wojciech Szpankowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3909)


Computational and comparative analysis of protein-protein interaction (PPI) networks enable understanding of the modular organization of the cell through identification of functional modules and protein complexes. These analysis techniques generally rely on topological features such as connectedness, based on the premise that functionally related proteins are likely to interact densely and that these interactions follow similar evolutionary trajectories. Significant recent work in our lab, and in other labs has focused on efficient algorithms for identification of modules and their conservation. Application of these methods to a variety of networks has yielded novel biological insights. In spite of algorithmic advances, development of a comprehensive infrastructure for interaction databases is in relative infancy compared to corresponding sequence analysis tools such as BLAST and CLUSTAL. One critical component of this infrastructure is a measure of the statistical significance of a match or a dense subcomponent. Corresponding sequence-based measures such as E-values are key components of sequence matching tools. In the absence of an analytical measure, conventional methods rely on computer simulations based on ad-hoc models for quantifying significance. This paper presents the first such effort, to the best of our knowledge, aimed at analytically quantifying statistical significance of dense components and matches in reference model graphs. We consider two reference graph models – a G(n,p) model in which each pair of nodes has an identical likelihood, p, of sharing an edge, and a two-level G(n,p) model, which accounts for high-degree hub nodes generally occurring in PPI networks. We argue that by choosing conservatively the value of p, the G(n,p) model will dominate that of the power-law graph that is often used to model PPI networks. We also propose a method for evaluating statistical significance based on the results derived from this analysis, and demonstrate the use of these measures for assessing significant structures in PPI networks. Experiments performed on a rich collection of PPI networks show that the proposed model provides a reliable means of evaluating statistical significance of dense patterns in these networks.


Reference Model Random Graph Degree Distribution Maximum Clique Protein Interaction Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aiello, W., Chung, F., Lu, L.: A random graph model for power law graphs. In: Proc. ACM Symp. Theory of Computing, pp. 171–180 (2000)Google Scholar
  2. 2.
    Bader, G.D., Donalson, I., Wolting, C., Quellette, B.F., Pawson, T., Hogue, C.W.: BIND-the Biomolecular Interaction Network Database. Nuc. Acids Res. 29(1), 242–245 (2001)CrossRefGoogle Scholar
  3. 3.
    Bader, G.D., Hogue, C.W.V.: An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics 4(2) (2003)Google Scholar
  4. 4.
    Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bollobás, B.: Random Graphs. Cambridge University Press, Cambridge (2001)MATHGoogle Scholar
  6. 6.
    Brun, C., Herrmann, C., Guénoche, A.: Clustering proteins from interaction networks for the prediction of cellular functions. BMC Bioinformatics 5(95) (2004)Google Scholar
  7. 7.
    Chung, F., Lu, L., Vu, V.: Spectra of random graphs with given expected degrees. PNAS 100(11), 6313–6318 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    del Sol, A., Fujihashi, H., O’Meara, P.: Topology of small-world networks of protein-protein complex structures. Bioinformatics 21(8), 1311–1315 (2005)CrossRefGoogle Scholar
  9. 9.
    Han, J.-D.J., Dupuy, D., Bertin, N., Cusick, M.E., Vidal, M.: Effect of sampling on topology predictions of protein interaction networks. Nat. Biotech. 23(7), 839–844 (2005)CrossRefGoogle Scholar
  10. 10.
    Hartuv, E., Shamir, R.: A clustering algorithm based on graph connectivity. Information Processing Letters 76, 171–181 (2000)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Hu, H., Yan, X., Huang, Y., Han, J., Zhou, X.J.: Mining coherent dense subgraphs across massive biological networks for functional discovery. Bioinformatics 21, i213–i221 (2005)Google Scholar
  12. 12.
    Itzkovitz, S., Milo, R., Kashtan, N., Ziv, G., Alon, U.: Subgraphs in random networks. Physical Review E 68(026127) (2003)Google Scholar
  13. 13.
    Jeong, H., Mason, S.P., Barabási, A., Oltvai, Z.N.: Lethality and centrality in protein networks. Nature 411, 41–42 (2001)CrossRefGoogle Scholar
  14. 14.
    Kelley, B.P., Sharan, R., Karp, R.M., Sittler, T., Root, D.E., Stockwell, B.R., Ideker, T.: Conserved pathways withing bacteria and yeast as revealed by global protein network alignment. PNAS 100(20), 11394–11399 (2003)CrossRefGoogle Scholar
  15. 15.
    Koyutürk, M., Grama, A., Szpankowski, W.: An efficient algorithm for detecting frequent subgraphs in biological networks. In: Bioinformatics (ISMB 2004), pp. i200–i207 (2004)Google Scholar
  16. 16.
    Koyutürk, M., Grama, A., Szpankowski, W.: Pairwise local alignment of protein interaction networks guided by models of evolution. In: Miyano, S., Mesirov, J., Kasif, S., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2005. LNCS (LNBI), vol. 3500, pp. 48–65. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Koyutürk, M., Kim, Y., Subramaniam, S., Szpankowski, W., Grama, A.: Detecting conserved interaction patterns in biological networks (submitted)Google Scholar
  18. 18.
    Künkele, K.-P., Juin, P., Pompa, C., Nargang, F.E., Henry, J.-P., Neuperr, W., Lill, R., Thieffry, M.: The isolated complex of the translocase of the outer membrane of mitochondria. J. Biol. Chem. 273(47), 31032–31039 (1998)CrossRefGoogle Scholar
  19. 19.
    Pereira-Leal, J.B., Enright, A.J., Ouzounis, C.A.: Detection of functional modules from protein interaction networks. Proteins 54(1), 49–57 (2004)CrossRefGoogle Scholar
  20. 20.
    Pržulj, N.: Graph theory analysis of protein-protein interactions. In: Jurisica, I., Wigle, D. (eds.) Knowledge Discovery in Proteomics. CRC Press, Boca Raton (2004)Google Scholar
  21. 21.
    Pržulj, N., Corneil, D.G., Jurisica, I.: Modeling interactome: scale-free or geometric?. Bioinformatics 20(18), 3508–3515 (2004)CrossRefGoogle Scholar
  22. 22.
    Pržulj, N., Wigle, D.A., Jurisica, I.: Functional topology in a network of protein interactions. Bioinformatics 20(3), 340–348 (2004)CrossRefGoogle Scholar
  23. 23.
    Rives, A.W., Galitski, T.: Modular organization of cellular networks. PNAS 100(3), 1128–1133 (2003)CrossRefGoogle Scholar
  24. 24.
    Scholtens, D., Vidal, M., Gentleman, R.: Local modeling of global interactome networks. Bioinformatics 21(17), 3548–3557 (2005)CrossRefGoogle Scholar
  25. 25.
    Shannon, P., Markiel, A., Ozier, O., Baliga, N.S., Wang, J.T., Ramage, D., Amin, N., Schwikowski, B., Ideker, T.: Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Res. 13(11), 2498–2504 (2003)CrossRefGoogle Scholar
  26. 26.
    Sharan, R., Ideker, T., Kelley, B.P., Shamir, R., Karp, R.M.: Identification of protein complexes by comparative analysis of yeast and bacterial protein interaction data. In: RECOMB 2004, pp. 282–289 (2004)Google Scholar
  27. 27.
    Sharan, R., Suthram, S., Kelley, R.M., Kuhn, T., McCuine, S., Uetz, P., Sittler, T., Karp, R.M., Ideker, T.: Conserved patterns of protein interaction in multiple species. PNAS 102(6), 1974–1979 (2005)CrossRefGoogle Scholar
  28. 28.
    Spirin, V., Mirny, L.A.: Protein complexes and functional modules in molecular networks. PNAS 100(21), 12123–12128 (2003)CrossRefGoogle Scholar
  29. 29.
    Stoer, M., Wagner, F.: A simple min-cut algorithm. J. ACM 44(4), 585–591 (1997)MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Szpankowski, W.: Average Case Analysis of Algorithms on Sequences. John Wiley & Sons, New York (2001)MATHGoogle Scholar
  31. 31.
    Tatusov, R., Fedorova, N., Jackson, J., Jacobs, A., Kiryutin, B., Koonin, E.: The cog database: An updated version includes eukaryotes. BMC Bioinformatics 4(41) (2003)Google Scholar
  32. 32.
    Thomas, A., Cannings, R., Monk, N.A., Cannings, C.: On the structure of protein-protein interaction networks. Biochem. Soc. Trans. 31(6), 1491–1496 (2003)CrossRefGoogle Scholar
  33. 33.
    Tornow, S., Mewes, H.W.: Functional modules by relating protein interaction networks and gene expression. Nuc. Acids Res. 31(21), 6283–6289 (2003)CrossRefGoogle Scholar
  34. 34.
    Wagner, A.: The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. Mol. Bio. Evol. 18(7), 1283–1292 (2001)Google Scholar
  35. 35.
    Wagner, A.: How the global structure of protein interaction networks evolves. Proc. R. Soc. Lond. Biol. Sci. 270(1514), 457–466 (2003)CrossRefGoogle Scholar
  36. 36.
    Waterman, M.: Introduction to Computational Biology. Chapman & Hall, London (1995)MATHGoogle Scholar
  37. 37.
    Waterman, M.S., Vingrons, M.: Rapid and accurate estimates of statistical significance for sequence data base searches. PNAS 91, 4625–4628 (1994)MATHCrossRefGoogle Scholar
  38. 38.
    Xenarios, I., Salwinski, L., Duan, X.J., Higney, P., Kim, S., Eisenberg, D.: DIP: The Database of Interacting Proteins. A research tool for studying cellular networks of protein interactions. Nuc. Acids Res. 30, 303–305 (2002)CrossRefGoogle Scholar
  39. 39.
    Yook, S.H., Oltvai, Z.N., Barabási, A.L.: Functional and topological characterization of protein interaction networks. Proteomics 4(4), 928–942 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mehmet Koyutürk
    • 1
  • Ananth Grama
    • 1
  • Wojciech Szpankowski
    • 1
  1. 1.Dept. of Computer SciencesPurdue UniversityWest LafayetteUSA

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