Birth of scale-free molecular networks and the number of distinct DNA and protein domains per genome

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.