A Graph Modification Approach for Finding Core–Periphery Structures in Protein Interaction Networks

  • Sharon Bruckner
  • Falk Hüffner
  • Christian Komusiewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8701)

Abstract

The core–periphery model for protein interaction (PPI) networks assumes that protein complexes in these networks consist of a dense core and a possibly sparse periphery that is adjacent to vertices in the core of the complex. In this work, we aim at uncovering a global core–periphery structure for a given PPI network. We propose two exact graph-theoretic formulations for this task, which aim to fit the input network to a hypothetical ground truth network by a minimum number of edge modifications. In one model each cluster has its own periphery, and in the other the periphery is shared. We first analyze both models from a theoretical point of view, showing their NP-hardness. Then, we devise efficient exact and heuristic algorithms for both models and finally perform an evaluation on subnetworks of the S. cerevisiae PPI network.

References

  1. 1.
    Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. Journal of Computational Biology 6(3-4), 281–297 (1999)CrossRefGoogle Scholar
  2. 2.
    Berger, A.J.: Minimal forbidden subgraphs of reducible graph properties. Discussiones Mathematicae Graph Theory 21(1), 111–117 (2001)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Böcker, S., Baumbach, J.: Cluster editing. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds.) CiE 2013. LNCS, vol. 7921, pp. 33–44. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. Algorithmica 60(2), 316–334 (2011)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Borgatti, S.P., Everett, M.G.: Models of core/periphery structures. Social Networks 21(4), 375–395 (1999)CrossRefGoogle Scholar
  6. 6.
    Chatr-aryamontri, A., et al.: The BioGRID interaction database: 2013 update. Nucleic Acids Research 41(D1), D816–D823 (2013)Google Scholar
  7. 7.
    Chen, J., Meng, J.: A 2k kernel for the cluster editing problem. Journal of Computer and System Sciences 78(1), 211–220 (2012)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Du, Z., Li, L., Chen, C.-F., Yu, P.S., Wang, J.Z.: G-SESAME: web tools for GO-term-based gene similarity analysis and knowledge discovery. Nucleic Acids Research 37(suppl. 2), W345–W349 (2009)Google Scholar
  9. 9.
    Farrugia, A.: Vertex-partitioning into fixed additive induced-hereditary properties is NP-hard. The Electronic Journal of Combinatorics 11(1), R46 (2004)Google Scholar
  10. 10.
    Foldes, S., Hammer, P.L.: Split graphs. Congressus Numerantium 19, 311–315 (1977)MathSciNetGoogle Scholar
  11. 11.
    Fomin, F.V., Kratsch, S., Pilipczuk, M., Pilipczuk, M., Villanger, Y.: Subexponential fixed-parameter tractability of cluster editing. CoRR, abs/1112.4419 (2011)Google Scholar
  12. 12.
    Gavin, A.-C., et al.: Proteome survey reveals modularity of the yeast cell machinery. Nature 440(7084), 631–636 (2006)CrossRefGoogle Scholar
  13. 13.
    Hammer, P.L., Simeone, B.: The splittance of a graph. Combinatorica 1(3), 275–284 (1981)CrossRefMathSciNetMATHGoogle Scholar
  14. 14.
    Heggernes, P., Kratsch, D.: Linear-time certifying recognition algorithms and forbidden induced subgraphs. Nordic Journal of Computing 14(1-2), 87–108 (2007)MathSciNetMATHGoogle Scholar
  15. 15.
    Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? Journal of Computer and System Sciences 63(4), 512–530 (2001)CrossRefMathSciNetMATHGoogle Scholar
  16. 16.
    Kelley, R., Ideker, T.: Systematic interpretation of genetic interactions using protein networks. Nature Biotechnology 23(5), 561–566 (2005)CrossRefGoogle Scholar
  17. 17.
    Komusiewicz, C., Uhlmann, J.: Cluster editing with locally bounded modifications. Discrete Applied Mathematics 160(15), 2259–2270 (2012)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Leung, H.C., Xiang, Q., Yiu, S.-M., Chin, F.Y.: Predicting protein complexes from PPI data: a core-attachment approach. Journal of Computational Biology 16(2), 133–144 (2009)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Luo, F., Li, B., Wan, X.-F., Scheuermann, R.: Core and periphery structures in protein interaction networks. BMC Bioinformatics (Suppl. 4), S8 (2009)Google Scholar
  20. 20.
    Pu, S., Wong, J., Turner, B., Cho, E., Wodak, S.J.: Up-to-date catalogues of yeast protein complexes. Nucleic Acids Research 37(3), 825–831 (2009)CrossRefGoogle Scholar
  21. 21.
    Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Applied Mathematics 144(1-2), 173–182 (2004)CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Spirin, V., Mirny, L.A.: Protein complexes and functional modules in molecular networks. PNAS 100(21), 12123–12128 (2003)CrossRefGoogle Scholar
  23. 23.
    Wu, M., Li, X., Kwoh, C.-K., Ng, S.-K.: A core-attachment based method to detect protein complexes in PPI networks. BMC Bioinformatics 10(1), 169 (2009)CrossRefGoogle Scholar
  24. 24.
    Xu, X., Yuruk, N., Feng, Z., Schweiger, T.A.J.: SCAN: a structural clustering algorithm for networks. In: Proc. 13th KDD, pp. 824–833. ACM (2007)Google Scholar
  25. 25.
    Zotenko, E., Guimarães, K.S., Jothi, R., Przytycka, T.M.: Decomposition of overlapping protein complexes: a graph theoretical method for analyzing static and dynamic protein associations. Algorithms for Molecular Biology 1(7) (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sharon Bruckner
    • 1
  • Falk Hüffner
    • 2
  • Christian Komusiewicz
    • 2
  1. 1.Institut für MathematikFreie Universität BerlinGermany
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

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