The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.

[1]  Ricard V. Solé,et al.  A Model of Large-Scale proteome Evolution , 2002, Adv. Complex Syst..

[2]  Jean-Pierre Eckmann,et al.  Curvature of co-links uncovers hidden thematic layers in the World Wide Web , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Albert-László Barabási,et al.  Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network , 2004, BMC Bioinformatics.

[4]  S. N. Dorogovtsev,et al.  Pseudofractal scale-free web. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  김삼묘,et al.  “Bioinformatics” 특집을 내면서 , 2000 .

[6]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[7]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[8]  David J. Galas,et al.  A duplication growth model of gene expression networks , 2002, Bioinform..

[9]  Natalia Ivanova,et al.  The ERGOTM genome analysis and discovery system , 2003, Nucleic Acids Res..

[10]  Nicola J. Rinaldi,et al.  Transcriptional Regulatory Networks in Saccharomyces cerevisiae , 2002, Science.

[11]  Kensuke Fukuda,et al.  Similarities between communication dynamics in the Internet and the autonomic nervous system , 2003 .

[12]  P. Bourgine,et al.  Topological and causal structure of the yeast transcriptional regulatory network , 2002, Nature Genetics.

[13]  S. Mangan,et al.  The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks. , 2003, Journal of molecular biology.

[14]  S. Mangan,et al.  Structure and function of the feed-forward loop network motif , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[16]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[17]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[18]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[19]  Reuven Cohen,et al.  Tomography of scale-free networks and shortest path trees. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[21]  Andrey Rzhetsky,et al.  Birth of scale-free molecular networks and the number of distinct DNA and protein domains per genome , 2001, Bioinform..

[22]  S. Teichmann,et al.  Gene regulatory network growth by duplication , 2004, Nature Genetics.

[23]  G. Bianconi,et al.  Number of loops of size h in growing scale-free networks. , 2002, Physical review letters.

[24]  Ioannis Xenarios,et al.  DIP: The Database of Interacting Proteins: 2001 update , 2001, Nucleic Acids Res..

[25]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[26]  M. Gerstein,et al.  Protein family and fold occurrence in genomes: power-law behaviour and evolutionary model. , 2001, Journal of molecular biology.

[27]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[28]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[29]  A. Vespignani,et al.  Modeling of Protein Interaction Networks , 2001, Complexus.

[30]  David Bawden,et al.  Book Review: Evolution and Structure of the Internet: A Statistical Physics Approach. , 2006 .

[31]  Peter F. Stadler,et al.  Relevant cycles in Chemical reaction Networks , 2001, Adv. Complex Syst..

[32]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[33]  R. Milo,et al.  Subgraphs in random networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  A. Wagner.  The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. , 2001, Molecular biology and evolution.

[35]  S. Shen-Orr,et al.  Superfamilies of Evolved and Designed Networks , 2004, Science.

[36]  D. Fell,et al.  The small world inside large metabolic networks , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[37]  S. Havlin,et al.  Optimization of robustness of complex networks , 2004, cond-mat/0404331.

[38]  S. Basu,et al.  Spatiotemporal control of gene expression with pulse-generating networks. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[39]  E. Davidson,et al.  Developmental gene regulatory network architecture across 500 million years of echinoderm evolution , 2003, Proceedings of the National Academy of Sciences of the United States of America.