Bioinformatics Vol. 17 no. 10 2001
Pages 988-996
© 2001 Oxford University Press
Birth of scale-free molecular networks and the number of distinct DNA and protein domains per genome
1 Columbia Genome Center
2 Department of Medical Informatics,
Columbia University, New York, NY 10032, USA
Received on April 20, 2001
; revised on July 13, 2001
; accepted on July 13, 2001
Motivation: Current growth in the field of genomics has provided a number of exciting approaches to the modeling of evolutionary mechanisms within the genome. Separately, dynamical and statistical analyses of networks such as the World Wide Web and the social interactions existing between humans have shown that these networks can exhibit common fractal properties—including the property of being scale-free. This work attempts to bridge these two fields and demonstrate that the fractal properties of molecular networks are linked to the fractal properties of their underlying genomes.
Results: We suggest a stochastic model capable of describing the evolutionary growth of metabolic or signal-transduction networks. This model generates networks that share important statistical properties (so-called scale-free behavior) with real molecular networks. In particular, the frequency of vertices connected to exactly k other vertices follows a power-law distribution. The shape of this distribution remains invariant to changes in network scale: a small subgraph has the same distribution as the complete graph from which it is derived. Furthermore, the model correctly predicts that the frequencies of distinct DNA and protein domains also follow a power-law distribution. Finally, the model leads to a simple equation linking the total number of different DNA and protein domains in a genome with both the total number of genes and the overall network topology.
Availability: MatLab (MathWorks, Inc.) programs described in this manuscript are available on request from the authors.
Contact: ar345{at}columbia.edu
* To whom correspondence should be addressed.
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  J. Zhang, Y. Ji, and L. Zhang Extracting three-way gene interactions from microarray data Bioinformatics, November 1, 2007; 23(21): 2903 - 2909. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 A. S. Novozhilov, G. P. Karev, and E. V. Koonin Biological applications of the theory of birth-and-death processes Brief Bioinform, March 1, 2006; 7(1): 70 - 85. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Y. Louzoun, L. Muchnik, and S. Solomon Copying nodes versus editing links: the source of the difference between genetic regulatory networks and the WWW Bioinformatics, March 1, 2006; 22(5): 581 - 588. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
A. Beyer and T. Wilhelm Dynamic simulation of protein complex formation on a genomic scale Bioinformatics, April 15, 2005; 21(8): 1610 - 1616. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 M. Middendorf, E. Ziv, and C. H. Wiggins From The Cover: Inferring network mechanisms: The Drosophila melanogaster protein interaction network PNAS, March 1, 2005; 102(9): 3192 - 3197. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
A. Vazquez, R. Dobrin, D. Sergi, J.-P. Eckmann, Z. N. Oltvai, and A.-L. Barabasi The topological relationship between the large-scale attributes and local interaction patterns of complex networks PNAS, December 28, 2004; 101(52): 17940 - 17945. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 I. K. Jordan, L. Marino-Ramirez, Y. I. Wolf, and E. V. Koonin Conservation and Coevolution in the Scale-Free Human Gene Coexpression Network Mol. Biol. Evol., November 1, 2004; 21(11): 2058 - 2070. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 H. Yu, X. Zhu, D. Greenbaum, J. Karro, and M. Gerstein TopNet: a tool for comparing biological sub-networks, correlating protein properties with topological statistics Nucleic Acids Res., January 14, 2004; 32(1): 328 - 337. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
H. Qin, H. H. S. Lu, W. B. Wu, and W.-H. Li Evolution of the yeast protein interaction network PNAS, October 28, 2003; 100(22): 12820 - 12824. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Aldana and P. Cluzel A natural class of robust networks PNAS, July 22, 2003; 100(15): 8710 - 8714. [Abstract] [Full Text] [PDF]
|
|