Abstract
The proteome network (or protein–protein interaction (PPI) network) of an organism represents each protein as a vertex and each pairwise interaction as an edge. In the past 10 years, we witnessed a significant amount of effort going into the development of the PPI networks and the computational tools for analyzing them. In particular, there have been several attempts to capture the topological features of PPI networks through random graph models, which have been successfully applied to the emulation of “small-world” networks, which are sparse, but highly connected. The available PPI networks have also been thought to have a small diameter with power-law degree distribution thus “scale-free” network emulators such as the Preferential Attachment Model have been investigated for the purposes of emulating PPI networks. The lack of success in this direction led to the development of further models, which either reject the “scale-freeness” of the PPI networks, such as the Geometric Random Network Model or guarantee scale freeness through means of expansion other than “Preferential Attachment” such as vertex (i.e., protein/gene duplication) – as in the case of the Pastor-Satorras Model or the more recent Generalized Duplication Model. In this study, we compare available PPI networks of various sizes with those generated by the random graph models and observe that the Generalized Duplication Model, with the “right” choice of the initial “seed” network, provides the best alternative in capturing all network feature distributions. One network feature distribution that remains difficult to capture, however, is the “dense graphlet” distribution: all available PPI networks seem to include (many) more dense graphlets such as cliques in comparison to the networks generated by all available models.
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By large cliques we mean its size should be bigger than 5 or 6 nodes.
References
W. Aiello, F. Chung, and L. Lu. A random graph model for power law graphs. In Proceedings of ACM STOC, pages 171–180, 2000.
Noga Alon, Raphael Yuster, and Uri Zwick. Color-coding. J. ACM, 42(4):844–856, 1995.
A.-L. Barabási and R. A. Albert. Emergence of scaling in random networks. Science, 286: 509–512, 1999.
G. Bebek, P. Berenbrink, C. Cooper, T. Friedetzky, J. Nadeau, and S.C. Sahinalp. The degree distribution of the general duplication models. Theoretical Computer Science, 369(1–3): 239–249, 2006.
G. Bebek, P. Berenbrink, C. Cooper, T. Friedetzky, J. Nadeau, and S.C. Sahinalp. Topological properties of proteome networks. In Proceedings of RECOMB satellite meeting on System Biology. LNBI,Springer, 2005.
A. Bhan, D. J. Galas, and T. G. Dewey. A duplication growth model of gene expression networks. Bioinformatis, 18:1486–1493, 2002.
B. Bollobás, O Riordan, J. Spencer, and G. Tusanády. The degree sequence of a scale-free random graph process. Random Struct. Algorithms, 18:279–290, 2001.
F. Chung, L. Lu, and D.J. Galas. Duplication models for biological networks. Journal of Computational Biology, 10:677–687, 2003.
C. Cooper and A. Frieze. A general model of webgraphs. Random Struct. Algorithms, 22: 311–335, 2003.
M. Rasajskim, D. J. Higham, and N. Przulj. Fitting a geometric graph to a protein-protein interaction network. Bioinformatics, 8:1093–1099, 2008.
E. De Silva and M.P.H. Stumpf. Complex networks and simple models in biology. Journal of the Royal Society Interface, 2:419–430, 2005.
M. Faloutsos, P. Faloutsos, and C. Faloutsos. On power-law relationships of the internet topology. In SIGCOMM, pages 251–262, 1999.
R. Ferrer i Cancho, and C. Janssen. The small world of human language. In Proceedings of Royal Society of London B, volume 268, pages 2261–2266, 2001.
Michael R. Garey and David S.Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.
J. Han, D. Dupuy, N. Bertin, M. Cusick, and M. Vidal. Effect of sampling on topology predictions of protein-protein interaction networks. Nature Biotech, 23:839–844, 2005.
F. Hormozdiari, P. Berenbrink, N. Przulj, and S.C. Sahinalp. Not all scale free networks are born equal: the role of the seed graph in ppi network emulation. In Proceedings of RECOMB satellite meeting on System Biology, 2006.
B. Kahng S. Redner J. Kim, P.L. Krapivsky. Infinite-order percolation and giant fluctuations in a protein interaction network. Phys. Rev. E 66, 2002.
H. Jeong, S. Mason, A.-L. Barabasi, and Z. N. Oltvai. Lethality and centrality in protein networks. Nature, 411:41, 2001.
J. Kleinberg, R. Kumar, PP. Raphavan, S. Rajagopalan, and A. Tomkins. The web as a graph: Measurements, models and methods. In Proceedings of COCOON, pages 1–17, 1999.
R. Kumar, P. Raghavan, D. Sivakumar, A. Tomkins, and E. Upfal. Stochastic models for the web graph. In Proceedings of FOCS, pages 57–65, 2002.
D. G. Corneil, N. Przulj, and I. Jurisica. Modeling interactome: Scale-free or geometric? Bioinformatics, 150:216–231, 2005.
N. Alon, P. Dao, I. Hajirasouliha, F. Hormozdiari, and S.C. Sahinalp. Biomolecular network motif counting and discovery by color coding. Bioinformatics, 24: i32–i40, 2008.
D. J. Higham, O. Kuchaiev, M. Rasajski and N. Przulj. Geometric de-noising of protein-protein interaction networks. Plos Computationtal Biology, 5, 2009.
Ohno. Evolution by gene duplication. Springer, 1970.
P. Dao, A. Schönhuth, F. Hormozdiari, I. Hajirasouliha, S.C. Sahinalp, and M. Ester. Quantifying systemic evolutionary changes by color coding confidence-sored ppi networks. In Proceedings of the WABI 2009, pages 37–48, 2009.
R. Pastor-Satorras, E. Smith, and R.V. Sole. Evolving protein interaction networks through gene duplication. Journal of Theoretical biology, 222:199–210, 2003.
T. Przytycka and Y.K. Yu. Scale-free networks versus evolutionary drift. Computational Biology and Chemistry, 28:257–264, 2004.
F. Moser, A. Schnhuth, J. Holman, M. Ester, R. Colak, F. Hormozdiar, and S.C. Sahinalp. Dense graphlet statistics of protein interaction and random networks. In Proceedings of the Pacific Symposium on Biocomputing 2009, pages 190–202, 2009.
A.-L. Barabsi, R.A. Albert. Topology of evolving networks: local events and universality. Phys. Rev. Lett., 85:5234, 2000.
S. Redner. How popular is your paper? an empirical study of the citations distribution. European Physical journal B, 4:131–134, 1998.
Erdös and Rényi. On random graphsI. Publicationes Mathematicae Debrecen, 6:290–297, 1959.
H. A. Simon. On a class of skew distribution functions. Biometrika, 42:425440, 1955.
A.N. Samukhin, S.N. Dorogovstev, J.F.F. Mendes. Structure of growing networks with preferential linking. Phys. Rev. Lett., 85:4633, 2000.
J.F.F. Mendes, S.N. Dorogovstev. Evolution of networks with aging of sites. Phys. Rev. E, 62:1842, 2000.
R. Tanaka and et al. Some protein interaction data do not exhibit power law statistics. FEBS Letters, 579:5140–5144, 2005.
A. Vázquez, A. Flammini, A. Maritan, and A. Vespignani. Modelling of protein interaction networks. Complexus, 1:38–44, 2003.
A. Wagner. The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. Molecular Biology and Evolution, 18:1283–1292, 2001.
D.J. Watts. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, 1999.
D.J. Watts and S.H. Strogatz. Collective dynamics of small-world networks. Nature, 393: 440–442, 1998.
I. Xenarios and et al. Dip, the database of interacting proteins: a research tool for studying cellular networks of protein interactions. Nucleic Acids Research, 30:303–305, 2002.
G. Yule. A mathematical theory of evolution based on the conclusions of dr. j.c. willis. Philos. Trans. Roy. Soc. London (Ser. B), 213, 1925.
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Dao, P., Hormozdiari, F., Hajirasouliha, I., Ester, M., Sahinalp, S.C. (2012). Proteome Network Emulating Models. In: Koyutürk, M., Subramaniam, S., Grama, A. (eds) Functional Coherence of Molecular Networks in Bioinformatics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0320-3_4
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