Arianna Bottinelli, Bruno Bassetti, Marco Cosentino Lagomarsino, Marco Gherardi
Proteins participating in a protein-protein interaction network can be grouped into homology classes following their common ancestry. Furthermore, homology class number and size have a high degree of universality, depending on genome size only and not on genome-specific features. These "genomic laws" can be regarded as evolutionary constraints on the growth mechanism of genomes. We define a statistical model describing the joint growth of the network and the partitioning of nodes into homology classes under the constraint of a stochastic class-expansion/innovation model based on the "Chinese restaurant process", and we study this model through a combined mean-field and simulation approach. Additionally, we define model variants that allow to study the age dependency of interactions under different prescriptions of duplication-divergence growth. Comparing with empirical data, we show that the model reproduces the observed universal behavior allowing a variant-independent fit of parameters. This analysis also indicates that an age-dependent duplication move appears to be necessary for reproducing the basic network topological observables together with the age correlation between interacting nodes visible in empirical data.
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http://arxiv.org/abs/1206.2818
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