A. Rzhetsky et Sm. Gomez, Birth of scale-free molecular networks and the number of distinct DNA and protein domains per genome, BIOINFORMAT, 17(10), 2001, pp. 988-996
Motivation: Current growth in the field of genomics has provided a number o
f 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 ha
ve shown that these networks can exhibit common fractal properties-includin
g 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 evolutiona
ry growth of metabolic or signal-transduction networks. This model generate
s networks that share important statistical properties (so-called scale-fre
e behavior) With real molecular networks. In particular, the frequency of v
ertices, connected to, exactly k other vertices, follows a power-law. distr
ibution. The shape of this distribution remains. invariant to changes in ne
twork scale: a small, subgraph has the same distribution as the complete gr
aph from which it is derived. Furthermore, the model correctly predicts tha
t the frequencies of distinct DNA and protein domains also follow a power-l
aw 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.