BMC Syst Biol. 2012 May 01;6:34. doi: 10.1186/1752-0509-6-34.
Revisiting the variation of clustering coefficient of biological networks suggests new modular structure.
BMC systems biology
Dapeng Hao, Cong Ren, Chuanxing Li
PMID: 22548803
PMCID: PMC3465239 DOI: 10.1186/1752-0509-6-34
Abstract
BACKGROUND: A central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling). Although several studies have suggested other possible origins of this signature, it is still widely used nowadays to identify hierarchical modularity, especially in the analysis of biological networks. Therefore, a further and systematical investigation of this signature for different types of biological networks is necessary.
RESULTS: We analyzed a variety of biological networks and found that the commonly used signature of hierarchical modularity is actually the reflection of spoke-like topology, suggesting a different view of network architecture. We proved that the existence of super-hubs is the origin that the clustering coefficient of a node follows a particular scaling law with degree k in metabolic networks. To study the modularity of biological networks, we systematically investigated the relationship between repulsion of hubs and variation of clustering coefficient. We provided direct evidences for repulsion between hubs being the underlying origin of the variation of clustering coefficient, and found that for biological networks having no anti-correlation between hubs, such as gene co-expression network, the clustering coefficient doesn't show dependence of degree.
CONCLUSIONS: Here we have shown that the variation of clustering coefficient is neither sufficient nor exclusive for a network to be hierarchical. Our results suggest the existence of spoke-like modules as opposed to "deterministic model" of hierarchical modularity, and suggest the need to reconsider the organizational principle of biological hierarchy.
References
- Proc Natl Acad Sci U S A. 2007 Sep 25;104(39):15224-9 - PubMed
- Science. 2002 May 3;296(5569):910-3 - PubMed
- Nucleic Acids Res. 2004 Jan 1;32(Database issue):D41-4 - PubMed
- BMC Evol Biol. 2005 Mar 23;5:24 - PubMed
- Mol Microbiol. 2001 Feb;39(4):1022-35 - PubMed
- Nature. 2008 May 1;453(7191):98-101 - PubMed
- Proteomics. 2004 Apr;4(4):928-42 - PubMed
- Nat Rev Mol Cell Biol. 2009 Nov;10(11):791-803 - PubMed
- Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 2):026112 - PubMed
- Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 2):057101 - PubMed
- PLoS Biol. 2007 Jun;5(6):e154 - PubMed
- Nucleic Acids Res. 2004 Jan 1;32(Database issue):D449-51 - PubMed
- Bioinform Biol Insights. 2008 Apr 17;2:203-13 - PubMed
- Proc Biol Sci. 2001 Sep 7;268(1478):1803-10 - PubMed
- Nat Rev Genet. 2004 Feb;5(2):101-13 - PubMed
- Nucleic Acids Res. 2006 Jan 1;34(Database issue):D535-9 - PubMed
- Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 2):026126 - PubMed
- Proc Natl Acad Sci U S A. 2002 Jun 11;99(12):7821-6 - PubMed
- Phys Rev Lett. 2002 Nov 11;89(20):208701 - PubMed
- Science. 2002 Aug 30;297(5586):1551-5 - PubMed
- Curr Opin Struct Biol. 2003 Apr;13(2):193-202 - PubMed
- Science. 1999 Oct 15;286(5439):509-12 - PubMed
- BMC Bioinformatics. 2010 May 19;11:265 - PubMed
- Methods Mol Biol. 2009;541:145-60 - PubMed
- Science. 2003 Sep 26;301(5641):1866-7 - PubMed
- Eur J Hum Genet. 2011 Jul;19(7):783-8 - PubMed
- BMC Bioinformatics. 2010 Oct 15;11 Suppl 7:S9 - PubMed
- Nature. 1999 Dec 2;402(6761 Suppl):C47-52 - PubMed
- Nature. 2000 Oct 5;407(6804):651-4 - PubMed
- mBio. 2010 Oct 05;1(4): - PubMed
- Mol Biol Cell. 1998 Dec;9(12):3273-97 - PubMed
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