Duplication Models for Biological Networks
By Fan Chung, Linyuan Lu, T. Dewey, David J. Galas. J. Comput. Biol., 2002
334 citations recorded by the source corpus.
Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit power-law graphs (number of nodes with degree k, N(k)~k-β), yet the exponents, β, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce power-law graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.
Subfields: Molecular Biology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/939f9ae38c7adca13c78783ed5a9618a9357bcb7
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In Molecular Biology
In Statistical and Nonlinear Physics
Citations in the corpus
- Random Dot Product Graph Models for Social Networks (2007, methodology): “In a similar vein, the copying model [7, 8], also attempts to model the growth process of a complex networks.”
- The Structure and Function of Complex Networks (2003, neutral): “s by copying, this produces exponents 2 ≤ α ≤ 3, which is the range observed in most real-world networks—see Table II. Some further analytic results for copying models have been given by Chung et al. [90]. It is not clear whether the copying mechanism really is at work in the growth of the World Wid”
- Turning a hobby into a job: How duplicated genes find new functions (2008, background): “Several studies have suggested that the extant features of networks, such as those of protein–protein interactions and transcriptional regulation, are compatible with a node (gene) duplication mode”
- Distribution of subgraphs of random regular graphs (2008, background): “Such graphs arise in a variety of applications such asWeb connectivity [2,5,6,9,24,26,28,29], communication networks [1,3], biological networks [22], collaboration graphs [27], etc.”
- Graph theory and networks in Biology. (2006, background): “ number of basic properties of the model and its suitability to model the PPI network of S. cerevisae are discussed in this paper also. The same basic model has also been studied more analytically in [37]. In this paper, it was shown that if q < 1/2, then the degree distribution of the DD network”