Content-based network model with duplication and divergence

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. 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 logperiodic 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.