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Detecting Hierarchical Modularity in Biological Networks

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Part of the book series: Methods in Molecular Biology ((MIMB,volume 541))

Abstract

Spatially or chemically isolated modules that carry out discrete functions are considered fundamental building blocks of cellular organization. However, detecting them in highly integrated biological networks requires a thorough understanding of the organization of these networks. In this chapter I argue that many biological networks are organized into many small, highly connected topologic modules that combine in a hierarchical manner into larger, less cohesive units. On top of a scale-free degree distribution, these networks show a power law scaling of the clustering coefficient with the node degree, a property that can be used as a signature of hierarchical organization. As a case study, I identify the hierarchical modules within the Escherichia coli metabolic network, and show that the uncovered hierarchical modularity closely overlaps with known metabolic functions.

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References

  1. Hartwell, L. H., Hopfield, J. J., Leibler, S., and Murray, A. W., From molecular to modular cell biology. Nature, 1999, 402:C47–C52.

    Article  PubMed  CAS  Google Scholar 

  2. Kitano, H., Systems biology: A brief overview. Science, 2002, 295:1662–1664.

    Article  PubMed  CAS  Google Scholar 

  3. Wolf, Y., Karev, G., and Koonin, E., Scale-free networks in biology: New insights into the fundamentals of evolution? Bioessays, 2002, 24:105–109.

    Article  PubMed  Google Scholar 

  4. Lauffenburger, D., Cell signaling pathways as control modules: Complexity for simplicity. Proc. Natl. Acad. Sci. USA, 2000, 97:5031–5033.

    Article  PubMed  CAS  Google Scholar 

  5. Rao, C. V., and Arkin, A. P., Control motifs for intracellular regulatory networks. Annu. Rev. Biomed. Eng., 2000, 3:391–419.

    Article  Google Scholar 

  6. Holter, N. S., Maritan, A., Cieplak, M., Fedoroff, N. V., and Banavar, J. R., Dynamic modeling of gene expression data. Proc. Natl. Acad. Sci. USA, 2001, 98:1693–1698.

    Article  PubMed  CAS  Google Scholar 

  7. Hasty, J., McMillen, D., Isaacs, F., and Collins, J. J., Computational studies of gene regulatory networks: In numero molecular biology. Nat. Rev. Genet., 2001, 2:268–279.

    Article  PubMed  CAS  Google Scholar 

  8. Shen-Orr, S., Milo, R., Mangan, S., and Alon, U., Network motifs in the transcriptional regulation network of E. coli. Nat. Genet., 2002, 31:64–68.

    Article  PubMed  CAS  Google Scholar 

  9. Alon, U., Surette, M. G., Barkai, N., and Leibler, S., Robustness in bacterial chemotaxis. Nature, 1999, 397:168–171.

    Article  PubMed  CAS  Google Scholar 

  10. Flajolet, M., Rotondo, G., Daviet, L., Bergametti, F., Inchauspe, G., Tiollais, P., Transy, C., and Legrain, P., A genomic approach to the Hepatitis C virus. Gene, 2000, 242:369–379.

    Article  PubMed  CAS  Google Scholar 

  11. McGraith, S., Holtzman, T., Moss, B., and Fields, S., Genome-wide analysis of vaccinia virus protein-protein interactions. Proc. Natl. Acad. Sci. USA, 2000, 97:4879–4884.

    Article  Google Scholar 

  12. Rain, J. C., Selig, L., De Reuse, H., Battaglia, V., Reverdy, C., Simon, S., Lenzen, G., Petel, F., Wojcik, J., and Schachter, V., The protein-protein interaction map of Helicobacter pylori. Nature, 2001, 409:211–215.

    Article  PubMed  CAS  Google Scholar 

  13. Ito, T., Chiba, T., Ozawa, R., Yoshida, M., Hattori, M., and Sakaki, Y., A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc. Natl. Acad. Sci. USA, 2001, 98:4569–4574.

    Article  PubMed  CAS  Google Scholar 

  14. Ito, T., Tashiro, K., Muta, S., Ozawa, R., Chiba, T., Nishizawa, M., Yamamoto, K., Kuhara, S., and Sakaki, Y., Toward a protein-protein interaction map of the budding yeast: A comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins. Proc. Natl. Acad. Sci. USA, 2000, 97:1143–1147.

    Article  PubMed  CAS  Google Scholar 

  15. Schwikowski, B., Uetz, P., and Fields, S., A network of protein-protein interactions in yeast. Nat. Biotechnol., 2000, 18:257–1261.

    Article  Google Scholar 

  16. Uetz, P., Giot, L., Cagney, G., Mansfield, T., Judson, R., Knight, J., Lockshorn, D., Narayan, V., Srinivasan, M., and Pochart, P., A comprehensive analysis of protein-protein interactions of Saccharomyces cerevisiae. Nature, 2000, 403:623–627.

    Article  PubMed  CAS  Google Scholar 

  17. Gavin, A., Bösche, M., Krause, R., Grandi, P., Marzioch, M., Bauer, A., Schultz, J., Rick, J., and Michon, A.-M., Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature, 2002, 415:141–147.

    Article  PubMed  CAS  Google Scholar 

  18. Ho, Y., Gruhler, A., Heilbut, A., Bader, G., Moore, L., Adams, S.-L., Millar, A., Taylor, P., Bennett, K., and Boutillier, K., Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry. Nature, 2002, 415:180–183.

    Article  PubMed  CAS  Google Scholar 

  19. Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., and Barabási, A.-L., The large-scale organization of metabolic networks. Nature, 2000, 407:651–654.

    Article  PubMed  CAS  Google Scholar 

  20. Walhout, A., Sordella, R., Lu, X., Hartley, J., Temple, G., Brasch, M., Thierry-Mieg, N., and Vidal, M., Protein interaction mapping in C. elegans using proteins involved in vulval development. Science, 2000, 287:116–122.

    Article  PubMed  CAS  Google Scholar 

  21. Giot, L., Bader, J. S., Brouwer, C., Chaudhuri, A., Kuang, B., Li, Y., Hao, Y. L., Ooi, C. E., Godwin, B., Vitols, E. et al., A protein interaction map of Drosophila melanogaster. Science, 2003, 302:1727–1735.

    Article  PubMed  CAS  Google Scholar 

  22. Thieffry, D., Huerta, A. M., Perez-Rueda, E., and Collado-Vides, J., From specific gene regulation to genomic networks: A global analysis of transcriptional regulation in Escherichia coli. Bioessays, 1998, 20:433–440.

    Article  PubMed  CAS  Google Scholar 

  23. Salgado, H., Santos-Zavaleta, A., Gama-Castro, S., Millán-Zárate, D., Díaz-Peredo, E., Sánchez-Solano, F., Pérez-Rueda, E., Bonavides-Martínez, C., and Collado-Vides, J., RegulonDB (version 3.2): Transcriptional regulation and operon organization in Escherichia coli K-12. Nuc. Acids Res., 2001, 29:72–74.

    Article  CAS  Google Scholar 

  24. Costanzo, M. C., Crawford, M. E., Hirschman, J. E., Kranz, J. E., Olsen, P., Robertson, L. S., Skrzypek, M. S., Braun, B. R., Hopkins, K. L., Kondu, P. et al., YPDTM, PombePDTM and WormPDTM:model organism volumes of the BioKnowledgeTM Library, an integrated resource for protein information. Nuc. Acids Res., 2001, 29:75–79.

    Article  CAS  Google Scholar 

  25. Mangan, S., and Alon, U., The structure and function of the feed-forward loop network motif. Proc. Natl. Acad. Sci. USA, 2003, 100:11980–11985.

    Article  PubMed  CAS  Google Scholar 

  26. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U., Network motifs: Simple building blocks of complex networks. Science, 2002, 298:824–827.

    Article  PubMed  CAS  Google Scholar 

  27. Lee, T. I., Rinaldi, N. J., Robert, F., Odom, D. T., Bar-Joseph, Z., Gerber, G. K., Hannett, N. M., Harbison, C. T., Thompson, C. M., Simon, I. et al., Transcriptional regulatory networks in Saccharomyces cerevisiae. Science, 2002, 298:799–804.

    Article  PubMed  CAS  Google Scholar 

  28. Overbeek, R., Larsen, N., Pusch, G., D'Souza, M., Selkov, E., Jr, Kyrpides, N., Fonstein, M., Maltsev, N., and Selkov, E., WIT: Integrated system for high-throughput genome sequence analysis and metabolic reconstruction. Science, 2000, 28:123–125.

    CAS  Google Scholar 

  29. Karp, P. D., Riley, M., Saier, M., Paulsen, I., Paley, S., and Pellegrini-Toole, A., The EcoCyc and MetaCyc databases. Nucl. Acids Res., 2000, 28:56–59.

    Article  PubMed  CAS  Google Scholar 

  30. Fell, D. A., and Wagner, A., The small world of metabolism. Nat. Biotechnol., 2000, 189:1121–1122.

    Article  Google Scholar 

  31. Wagner, A., and Fell, D. A., The small world inside large metabolic networks. Proc. Roy. Soc. London Series B, 2001, 268:1803–1810.

    Article  CAS  Google Scholar 

  32. Albert, R., and Barabási, A.-L., Statistical mechanics of complex networks. Rev. Mod. Phys., 2002, 74:67–97.

    Article  Google Scholar 

  33. Newman, M. E. J., The structure and function of complex networks. SIAM Rev., 2003, 45:167–256.

    Article  Google Scholar 

  34. Dorogovtsev, S. N., and Mendes, J. F. F., Evolution of networks. Adv. Phys., 2002, 51:1079–1187.

    Article  Google Scholar 

  35. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., and Hwang, D.-U., Complex networks: Structure and dynamics. Phys. Rep., 2006, 424:175–308.

    Article  Google Scholar 

  36. Barabási, A.-L., Linked: The New Science of Networks, 2002, Perseus Publishing, Cambridge, MA.

    Google Scholar 

  37. Newman, M. E. J., Barabási, A.-L., and Watts, D. J. (eds.), The Structure and Dynamics of Complex Networks, 2003, Princeton University Press, Princeton.

    Google Scholar 

  38. Pastor-Satorras, R., Rubi, M., and Diaz-Guilera, A. (eds.), Statistical Mechanics of Complex Networks, Lecture Notes in Physics, 2003, 625, Springer Verlag, Berlin, Germany.

    Google Scholar 

  39. Mendes, J. F. F., Dorogovtsev, S. N., Povolotsky, A., Abreu, F. V., and Oliveira, J. G. (eds.), Science of Complex Networks. From Biology to the Internet and WWW, AIP Conference Proceedings, 2004, 776, American Institute of Physics, New York.

    Google Scholar 

  40. Ben-Naim, E., Frauenfelder, H., and Toroczkai, Z. (eds.), Complex Networks, Lecture Notes in Physics, 2004, 650, Springer Verlag, Berlin/Heidelberg, Germany.

    Google Scholar 

  41. Bornholdt, S., and Schuster, H. G. (eds.), Handbook of Graphs and Networks: From the Genome to the Internet, 2002, Wiley-VCH, Berlin.

    Google Scholar 

  42. Watts, D. J., and Strogatz, S. H., Collective dynamics of small-world networks. Nature, 1998, 393:440–442.

    Article  PubMed  CAS  Google Scholar 

  43. Jeong, H., Mason, S., Barabási, A.-L., and Oltvai, Z. N., Lethality and centrality in protein networks. Nature, 2001, 411:41–42.

    Article  PubMed  CAS  Google Scholar 

  44. Wagner, A., The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. Mol. Biol. Evol., 2001, 18:1283–1292.

    PubMed  CAS  Google Scholar 

  45. Albert, R., Jeong, H., and Barabási, A.-L., Diameter of the world-wide web. Nature, 1999, 401:130–131.

    Article  CAS  Google Scholar 

  46. Barabási, A.-L., Albert, R., and Jeong, H., Mean-field theory for scale-free random networks. Physica A, 1999, 272:173–187.

    Article  Google Scholar 

  47. Barabási, A.-L., and Albert, R., Emergence of scaling in random networks. Science, 1999, 286:509–512.

    Article  PubMed  Google Scholar 

  48. Newman, M. E. J., The structure of scientific collaboration networks. Proc. Natl. Acad. Sci. USA, 2001, 98:404–409.

    Article  PubMed  CAS  Google Scholar 

  49. Barabási, A.-L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., and Vicsek, T., Evolution of the social network of scientific collaborations. Physica A, 2002, 311:590–614.

    Article  Google Scholar 

  50. Newman, M. E. J., Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E, 2001, 64:016131.

    Article  CAS  Google Scholar 

  51. Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N., and Barabási, A.-L., Hierarchical organization of modularity in metabolic networks. Science, 2002, 297:1551–1555.

    Article  PubMed  CAS  Google Scholar 

  52. Ravasz, E., and Barabási, A.-L., Hierarchical organization in complex networks. Phys. Rev. E, 2002, 67:026122.

    Google Scholar 

  53. Barabási, A.-L., Ravasz, E., and Vicsek, T., Deterministic scale-free networks. Physica A, 2001, 299:559–564.

    Article  Google Scholar 

  54. Schilling, C. H., Letscher, D., and Palsson, B. O., Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. J. Theor. Biol., 2000, 203:229–248.

    Article  PubMed  CAS  Google Scholar 

  55. Schuster, H. G., Complex Adaptive Systems, 2002, Scator Verlag, Saarbruskey, Germany.

    Google Scholar 

  56. Dorogovtsev, S. N., Goltsev, A. V., and Mendes, J. F. F., Pseudofractal Scale-free Web. Phys. Rev. E, 2002, 65:066122.

    Article  CAS  Google Scholar 

  57. Erdős, P., and Rényi, A., On random graphs I. Publ. Math. (Debrecen), 1959, 6:290–297.

    Google Scholar 

  58. Bollobás, B., Random Graphs, 1985, Academic Press, London.

    Google Scholar 

  59. Newman, M. E. J., Models of the small world. J. Stat. Phys., 2000, 101:819–841.

    Article  Google Scholar 

  60. Albert, R., Jeong, H., and Barabási, A.-L., Error and attack tolerance of complex networks. Nature, 2000, 406:378–382.

    Article  PubMed  CAS  Google Scholar 

  61. Cohen, R., Erez, K., Ben-Avraham, D., and Havlin, S., Breakdown of the internet under intentional attack. Phys. Rev. Lett., 2001, 86:3682–3685.

    Article  PubMed  CAS  Google Scholar 

  62. Pastor-Satorras, R., and Vespignani, A., Epidemic spreading in scale-free networks. Phys. Rev. Lett., 2001, 86:3200–3203.

    Article  PubMed  CAS  Google Scholar 

  63. Xenarios, I., Rice, D. W., Salwinski, L., Baron, M. K., Marcotte, E. M., and Eisenberg, D. M. S., DIP: The Database of Interacting Proteins. Nucl. Acids. Res., 2000, 28:289–291.

    Article  PubMed  CAS  Google Scholar 

  64. Xenarios, I., Fernandez, E., Salwinski, L., Duan, X., Thompson, M., Marcotte, E., and Eisenberg, D., DIP: The Database of Interacting Proteins: 2001 update. Nucl. Acids Res., 2001, 29:239–241.

    Article  PubMed  CAS  Google Scholar 

  65. Eisen, M. B., Spellman, P. T., Brown, P. O., and Botstein, D., Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA, 1998, 95:14863–14868.

    Article  PubMed  CAS  Google Scholar 

  66. Sokal, J., Numerical Taxonomy, 1973, Freeman, San Francisco.

    Google Scholar 

  67. Klemm, K., and Eguíluz, V. M., Growing scale-free networks with small-world behavior. Phys. Rev. E, 2002, 65:057102.

    Article  Google Scholar 

  68. Vázquez, A., Moreno, Z., Boguñá, M., Pastor-Satorras, R., and Vespignani, A., Topology and correlations in structured scale-free networks. Phys. Rev. E, 2003, 67:046111.

    Article  Google Scholar 

  69. Girvan, M., and Newman, M. E. J., Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA, 2002, 99:7821–7826.

    Article  PubMed  CAS  Google Scholar 

  70. Holme, P., Huss, M., and Jeong, H., Subnetwork hierarchies in biochemical pathways. Bioinformatics, 2003, 19:532–538.

    Article  PubMed  CAS  Google Scholar 

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Ravasz, E. (2009). Detecting Hierarchical Modularity in Biological Networks. In: Ireton, R., Montgomery, K., Bumgarner, R., Samudrala, R., McDermott, J. (eds) Computational Systems Biology. Methods in Molecular Biology, vol 541. Humana Press. https://doi.org/10.1007/978-1-59745-243-4_7

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  • DOI: https://doi.org/10.1007/978-1-59745-243-4_7

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