Abstract
Recent studies of complex systems indicate that real networks are far from random, instead having a highly robust, large-scale architecture that is governed by strict organizational principles. Here, we will focus on cellular networks, discussing their scale-free and hierarchical features. We will first discuss a few central network models, before illustrating the major network characteristics using examples primarily from bacterial metabolic networks. Additionally, as the interactions in real networks have unequal strengths, we discuss the interplay between network topology and reaction fluxes in cellular metabolic networks, as provided by the flux balance method. We find that the utilization of the metabolic networks is both globally and locally highly inhomogeneous, dominated by “hot-spots” that represent connected set of high-flux pathways.
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References
Albert, R. & Barabási, A.-L. (2002). Statistical mechanics of complex networks. Rev. Mod. Phys. 74, p47–97.
Albert, R., Jeong, H. & Barabási, A.-L (1999). Diameter of the World-Wide Web. Nature, 401, p130–1.
Albert, R., Jeong, H. & Barabási, A.-L. (2000). Attack and error tolerance of complex networks. Nature, 406, p378–82.
Almaas, E., Kovacs, B., Vicsek, T., Oltvai, Z.N. & Barabási, A.-L. (2004). Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature, 427, p839– 843.
Anderson, M.H., Ensher, J.R., Matthews, M.R. Wieman, C.E.&Cornell, E.A. (1995). Observation of Bose-Einstein condensation in a dilute atomic vapor. Science, 269, p198– 201.
Anderson, P. W. (1972). More Is Different. Science, 177, p393–6.
Barabási, A.-L. & Albert, R., (1999). Emergence of scaling in random networks. Science, 286, p509–12.
Barrat, A., Barthelemy, M., Pastor-Satorras, R. & Vespignani, A. (2004). The architecture of complex weighted networks. Proc. Natl. Acad. Sci. USA, 101, p3747.
Barthelemy, M., Gondran, B. & Guichard, E. (2003). Spatial structure of the Internet traffic. Physica A, 319, p633–42.
Bianconi G.&Barabási. A.-L. (2001). Bose-Einstein condensation in complex networks. Phys. Rev. Lett., 86, 5632.
Bradley, C.C., Sackett, C.A., Tollett, J.J. & Hulet, R.G. (1995). Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions. Phys. Rev. Lett., 75, p1687– 90.
Bollobas, B. (1985). Random Graphs. Academic Press, London.
Bornholdt, S. & Schuster, H. G. (2003). Handbook of graphs and networks: From the genome to the Internet. Wiley-VCH, Berlin, Germany.
Broder, A., Kumar, R., Maghoul, F., Raghavan, P, Rajalopagan, S., Stata, R., Tomkins, A. & Wiener, J. (2000). Graph structure in the web. Comput. Netw., 33, p309–20.
Burge, C.B. (2001). Chipping away at the transcriptome. Nature Genet., 27, p232–4.
Caron, H., van Schaik, B., van der Mee, M., Baas, F., Riggins, G., van Sluis, P., Hermus, M.C., van Asperen, R., Boon, K., Voute, P.A., Heisterkamp, S., van Kampen, A. & Versteeg, R. (2001). The human transcriptome map: Clustering of highly expressed genes in chromosomal domains. Science, 291, p1289–92.
Dandekar, T., Schuster, S., Snel, B., Huynen, M. & Bork, P. (1999). Pathway alignment: application to the comparative analysis of glycolytic enzymes. Biochem. J. 343, p115– 124.
Derrida, B. & Flyvbjerg, H. (1987). Statistical properties of randomly broken objects and of multivalley structures in disordered-systems. J. Phys. A: Math. Gen., 20, p5273–88 (1987).
Dorogovtsev, S.N., Goltsev, A.V. & Mendes, J.F.F. (2002). Pseudofractal scale-free web. Phys. Rev. E, 65, 066122.
Dorogovtsev, S.N. & Mendes, J.F.F. (2003) Evolution of networks: From biological nets to the Internet and WWW. Oxford University Press, Oxford.
Edwards, J. S., Ibarra, R. U. & Palsson, B. O. (2001). In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nat Biotechnol 19, p125–30.
Edwards, J. S. & Palsson, B. O. (2000). The Escherichia coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities. Proc Natl Acad Sci U S A 97, p5528–33.
Edwards, J. S., Ramakrishna, R. & Palsson, B. O. (2002). Characterizing the metabolic phenotype: A phenotype phase plane analysis. Biotechn. Bioeng. 77, 27–36.
Emmerling, M., Dauner, M., Ponti, A., Fiaux, J., Hochuli, M., Szyperski, T., Wuthrich, K., Bailey, J.E. & Sauer, U. (2002). Metabolic flux responses to pyruvate kinase knockout in Escherichia coli. J Bacteriol., 184, p152–64.
Erdos, P. & Renyi, A. (1960). On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci., 5, p17–61.
Faloutsos, M., Faloutsos, P. & Faloutsos, C. (1999). On power-law relationships of the Internet topology. Comput. Commun. Rev., 29, p251–62.
Flajolet, M., Rotondo, G., Daviet, L., Bergametti, F., Inchauspe, G., Tiollais, P., Transy, C. & Legrain, P. (2000). A genomic approach to the hepatitis C virus. Gene, 242, p369–79.
Gavin, A.C., Bosche, M., Krause, R., Grandi, P., Marzioch, M., Bauer, A., Schultz, J., Rick, J.M., Michon, A.M., Cruciat, C.M., Remor, M., Hofert, C., Schelder, M., Brajenovic, M., Ruffner, H., Merino, A., Klein, K., Hudak, M., Dickson, D., Rudi, T., Gnau, V., Bauch, A., Bastuck, S., Huhse, B., Leutwein, C., Heurtier, M.A., Copley, R.R., Edelmann, A., Querfurth, E., Rybin, V., Drewes, G., Raida, M., Bouwmeester, T., Bork, P., Seraphin, B., Kuster, B., Neubauer, G. & Superti-Furga, G. (2002). Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature, 415, p141–7.
Greiner, M., Regal, C.A. & Jin, D.S. (2003). Emergence of a molecular Bose-Einstein condensate from a Fermi gas. Nature, 426, p537–40.
Hartwell, L.H., Hopfield, J.J., Leibler, S. & Murray, A.W. (1999). From molecular to modular cell biology. Nature, 402, C47–52.
Ho, Y., Gruhler, A., Heilbut, A., Bader, G.D., Moore, L., Adams, S.L., Millar, A., Taylor, P., Bennett, K., Boutilier, K., Yang, L.Y., Wolting, C., Donaldson, I., Schandorff, S., Shewnarane, J., Vo, M., Taggart, J., Goudreault, M., Muskat, B., Alfarano, C., Dewar, D., Lin, Z., Michalickova, K., Willems, A.R., Sassi, H., Nielsen, P.A., Rasmussen, K.J., Andersen, J.R., Johansen, L.E., Hansen, L.H., Jespersen, H., Podtelejnikov, A., Nielsen, E., Crawford, J., Poulsen, V., Sorensen, B.D., Matthiesen, J., Hendrickson, R.C., Gleeson, F., Pawson, T., Moran, M.F., Durocher, D., Mann, M., Hogue, C.W.V., Figeys, D. & Tyers, M. (2002). Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry. Nature, 415, p180–3.
Holme, P., Huss, M. & Jeong, H. (2003). Subnetwork hierarchies of biochemical pathways. Bioinformatics. 19, p532–9.
Ibarra, R. U., Edwards, J. S. & Palsson, B. O. (2002). Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature 420, p186–9.
Ito, T., Chiba, T., Ozawa, R., Yoshida, M., Hattori, M. & Sakaki, Y. (2001). A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc. Natl. Acad. Sci., 98, p4569–74.
Ito, T., Tashiro, K., Muta, S., Ozawa, R., Chiba, T., Nishizawa, M., Yamamoto, K., Kuhara, S. & Sakaki, Y. (2000). Towards 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., 97, p1143–47.
Jeong, H., Mason, S.P., Barabási, A.-L. & Oltvai, Z.N. (2001). Lethality and centrality in protein networks. Nature, 411, p41–2.
Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N. & Barabási, A.-L. (2000). The large-scale organization of metabolic networks. Nature, 407, p651–4.
Kochen, M. (ed.) (1989). The small-world. Ablex, Norwood, N.J.
Lauffenburger, D. (2000). Cell signaling pathways as control modules: Complexity for simplicity. Proc. Natl. Acad. Sci., 97, p5031–33.
Lawrence, S. & Giles, C. L. (1999). Accessibility of information on the web. Nature, 400, p107–9.
Legget, A.J. (2001) Bose-Einstein consdensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys., 73, p307–56.
Liljeros, F., Edling, C.R., Amaral, L.A.N., Stanley, H.E. Aberg, Y. (2001). The web of human sexual contacts. Nature, 411, p907–8.
Milgram, S. (1967). The small-world problem. Psychology Today, 2, p60–7.
Montoya, J.M. & Sole, R.V. (2002). Small-world patterns in food webs. J. Theor. Biol., 214, p405–12.
Newman, M.E.J. (2001). The structure of scientific collaboration networks. Proc. Natl. Acad. Sci., 98, p404–9.
Newman, M.E.J. (2002). Assortative mixing in networks. Phys. Rev. Lett., 89, 208701.
Newman, M.E.J. (2003). Mixing patterns in networks. Phys. Rev. E., 67, 026126.
Pandey, A. & Mann, M. (2000). Proteomics to study genes and genomes. Nature, 405, p837– 46.
Pastor-Satorras, R., Vazquez, A. & Vespignani, A. (2001). Phys. Rev. Lett., 87, 258701.
Pastor-Satorras, R. & Vespignani, A. (2004). Evolution and structure of the Internet: A statistical physics approach. Cambridge University Press, Cambridge.
Rain, J.-C., Selig, L., DeReuse, H., Battaglia, V., Reverdy, C., Simon, S., Lenzen, G., Petel, F., Wojcik, J., Schächter, V., Chemama, Y., Labigne, A. & Legrain, P. (2001). The protein-protein interaction map of Helicobacter pylori. Nature, 409, p211–15.
Rao, C.V. & Arkin, A.P. (2001). Control motifs for intracellular regulatory networks. Annu. Rev. Biomed. Eng., 3, p391.
Ravasz, E. & Barabási, A.-L. (2003). Hierarchical organization in complex networks. Phys. Rev. E,67, 026112.
Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N. & Barabási, A.-L. (2002). Hierarchical organization of modularity in metabolic networks. Science, 297, p1551–5.
Redner, S. (1998). How popular is your paper? An empirical study of the citation distribution. Eur. Phys. J. B 4, p131–134.
Schuster, S., Fell, D. A. & Dandekar, T. (2000). A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nature Biotechn. 18, p326–332.
Schwikowski, B., Uetz, P., & Fields, S. (2000). A network of protein-protein interactions in yeast. Nature Biotechn., 18, p1257–61.
Segre, D., Vitkup, D. & Church, G. M. (2002). Analysis of optimality in natural and perturbed metabolic networks. Proc. Natl. Acad. Sci., 99, p15112–7.
Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S. & Gilles, E. D. (2002). Metabolic network structure determines key aspects of functionality and regulation. Nature 420, p190–193.
Strogatz, S.H. (2001). Exploring complex networks. Nature, 410, p268–76.
Uetz, P., Giot, L., Cagney, G., Mansfield, T., Judson, R., Knight, J., Lockshorn, D., Narayan, V., Srinivasan, M., Pochart, P., Qureshi-Emili, A., Li, Y., Godwin, B., Conover, D., Kalbfleisch, T., Vijayadamodar, G., Yang, M.J., Johnston, M., Fields, S. & Rothberg, J.M. (2000). A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae. Nature, 403, p623–27.
Vázquez, A., Pastor-Satorras, R. & Vespignani, A. (2002). Large-scale topological and dynamical properties of the Internet. Phys. Rev. E, 65, 066130.
Walhout, A., Sordella, R., Lu, X., Hartley, J., Temple, G., Brasch, M., Thierry-Mieg, N., & Vidal, M. (2000). Protein interaction mapping in C. elegans using proteins involved in vulva development. Science, 287, p116–22.
Wasserman, S. & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge.
Watts, D.J. & Strogatz, S.H. (1998). Collective dynamics of small-world networks. Nature, 393, p440–2.
Yook, S.-H., Jeong, H., Barabási, A.-L. & Tu, Y. (2001). Weighted evolving networks. Phys. Rev. Lett., 86, p5835–38.
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ALMAAS, E., BARABÁSI, AL. (2006). THE ARCHITECTURE OF COMPLEXITY: FROM WWW TO CELLULAR METABOLISM. In: Skjeltorp, A.T., Belushkin, A.V. (eds) Dynamics of Complex Interconnected Systems: Networks and Bioprocesses. NATO Science Series II, vol 232. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5030-5_7
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DOI: https://doi.org/10.1007/1-4020-5030-5_7
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