Content based network model with duplication and divergence

Original · EN

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. 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 γ₁ and γ₂=γ₁-1/2 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 α₁= 1-γ₁ and an envelope for the oscillatory part, which is essentially flat, thus α₂= 0. Under duplication and mutations including splitting and merging of strings, C(d) is found to decay exponentially.