Computational Systems Biology pp 145-160 | Cite as
Detecting Hierarchical Modularity in Biological Networks
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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.
Key words
Networks modularity hierarchical organization clustering coefficient metabolismReferences
- 1.Hartwell, L. H., Hopfield, J. J., Leibler, S., and Murray, A. W., From molecular to modular cell biology. Nature, 1999, 402:C47–C52.PubMedCrossRefGoogle Scholar
- 2.Kitano, H., Systems biology: A brief overview. Science, 2002, 295:1662–1664.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle Scholar
- 4.Lauffenburger, D., Cell signaling pathways as control modules: Complexity for simplicity. Proc. Natl. Acad. Sci. USA, 2000, 97:5031–5033.PubMedCrossRefGoogle Scholar
- 5.Rao, C. V., and Arkin, A. P., Control motifs for intracellular regulatory networks. Annu. Rev. Biomed. Eng., 2000, 3:391–419.CrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle Scholar
- 9.Alon, U., Surette, M. G., Barkai, N., and Leibler, S., Robustness in bacterial chemotaxis. Nature, 1999, 397:168–171.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.CrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle Scholar
- 15.Schwikowski, B., Uetz, P., and Fields, S., A network of protein-protein interactions in yeast. Nat. Biotechnol., 2000, 18:257–1261.CrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.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.PubMedCrossRefGoogle Scholar
- 30.Fell, D. A., and Wagner, A., The small world of metabolism. Nat. Biotechnol., 2000, 189:1121–1122.CrossRefGoogle 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.CrossRefGoogle Scholar
- 32.Albert, R., and Barabási, A.-L., Statistical mechanics of complex networks. Rev. Mod. Phys., 2002, 74:67–97.CrossRefGoogle Scholar
- 33.Newman, M. E. J., The structure and function of complex networks. SIAM Rev., 2003, 45:167–256.CrossRefGoogle Scholar
- 34.Dorogovtsev, S. N., and Mendes, J. F. F., Evolution of networks. Adv. Phys., 2002, 51:1079–1187.CrossRefGoogle 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.CrossRefGoogle 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.PubMedCrossRefGoogle Scholar
- 43.Jeong, H., Mason, S., Barabási, A.-L., and Oltvai, Z. N., Lethality and centrality in protein networks. Nature, 2001, 411:41–42.PubMedCrossRefGoogle Scholar
- 44.Wagner, A., The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. Mol. Biol. Evol., 2001, 18:1283–1292.PubMedGoogle Scholar
- 45.Albert, R., Jeong, H., and Barabási, A.-L., Diameter of the world-wide web. Nature, 1999, 401:130–131.CrossRefGoogle Scholar
- 46.Barabási, A.-L., Albert, R., and Jeong, H., Mean-field theory for scale-free random networks. Physica A, 1999, 272:173–187.CrossRefGoogle Scholar
- 47.Barabási, A.-L., and Albert, R., Emergence of scaling in random networks. Science, 1999, 286:509–512.PubMedCrossRefGoogle Scholar
- 48.Newman, M. E. J., The structure of scientific collaboration networks. Proc. Natl. Acad. Sci. USA, 2001, 98:404–409.PubMedCrossRefGoogle 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.CrossRefGoogle Scholar
- 50.Newman, M. E. J., Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E, 2001, 64:016131.CrossRefGoogle 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.PubMedCrossRefGoogle 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.CrossRefGoogle 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.PubMedCrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
- 60.Albert, R., Jeong, H., and Barabási, A.-L., Error and attack tolerance of complex networks. Nature, 2000, 406:378–382.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle Scholar
- 62.Pastor-Satorras, R., and Vespignani, A., Epidemic spreading in scale-free networks. Phys. Rev. Lett., 2001, 86:3200–3203.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.PubMedCrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.PubMedCrossRefGoogle Scholar
- 70.Holme, P., Huss, M., and Jeong, H., Subnetwork hierarchies in biochemical pathways. Bioinformatics, 2003, 19:532–538.PubMedCrossRefGoogle Scholar