dorsal/arxiv
View SchemaContent based network model with duplication and divergence
| Authors | Yasemin Sengun, Ayse Erzan |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0510022 |
| URL | https://arxiv.org/abs/q-bio/0510022 |
| DOI | 10.1016/j.physa.2006.02.045 |
Abstract
We construct a minimal content-based realization of the duplication and divergence model of genomic networks introduced by Wagner [A. Wagner, Proc. Natl. Acad. Sci. {\bf 91}, 4387 (1994)] and investigate the scaling properties of the directed degree distribution and clustering coefficient. We find that the content based network exhibits crossover between two scaling regimes, with log-periodic oscillations for large degrees. These features are not present in the original gene duplication model, but inherent in the content based model of Balcan and Erzan. The scaling exponents $\gamma_1$ and $\gamma_2=\gamma_1-1/2$ of the Balcan-Erzan model turn out to be robust under duplication and point mutations, but get modified in the presence of splitting and merging of strings. The clustering coefficient as a function of the degree, $C(d)$, is found, for the Balcan-Erzan model, to behave in a way qualitatively similar to the out-degree distribution, however with a very small exponent $\alpha_1= 1-\gamma_1$ and an envelope for the oscillatory part, which is essentially flat, thus $\alpha_2= 0$. Under duplication and mutations including splitting and merging of strings, $C(d)$ is found to decay exponentially.
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"abstract": "We construct a minimal content-based realization of the duplication and\ndivergence model of genomic networks introduced by Wagner [A. Wagner, Proc.\nNatl. Acad. Sci. {\\bf 91}, 4387 (1994)] and investigate the scaling properties\nof the directed degree distribution and clustering coefficient. We find that\nthe content based network exhibits crossover between two scaling regimes, with\nlog-periodic oscillations for large degrees. These features are not present in\nthe original gene duplication model, but inherent in the content based model of\nBalcan and Erzan. The scaling exponents $\\gamma_1$ and $\\gamma_2=\\gamma_1-1/2$\nof the Balcan-Erzan model turn out to be robust under duplication and point\nmutations, but get modified in the presence of splitting and merging of\nstrings. The clustering coefficient as a function of the degree, $C(d)$, is\nfound, for the Balcan-Erzan model, to behave in a way qualitatively similar to\nthe out-degree distribution, however with a very small exponent $\\alpha_1=\n1-\\gamma_1$ and an envelope for the oscillatory part, which is essentially\nflat, thus $\\alpha_2= 0$. Under duplication and mutations including splitting\nand merging of strings, $C(d)$ is found to decay exponentially.",
"arxiv_id": "q-bio/0510022",
"authors": [
"Yasemin Sengun",
"Ayse Erzan"
],
"categories": [
"q-bio.MN"
],
"doi": "10.1016/j.physa.2006.02.045",
"title": "Content based network model with duplication and divergence",
"url": "https://arxiv.org/abs/q-bio/0510022"
},
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