Figure 1
Basic statistics of domain occurrence networks. (a) All domains co-occurring in a single protein are represented as a fully connected unweighted clique in the network. (b) Determining the number of domains each protein contains in H. sapiens, M. musculus, D. melanogaster, C. elegans, and S. cerevisiae, we observe power-laws P(N) ~ N-δin frequency distributions thus obtained (see Table 1 for detailed values). This inhomogeneity in domain architectures suggests that the vast majority of proteins in all organisms considered contains only one domain. (c) Counting the occurrence of each domain in the proteomes of the organisms under consideration, we find a positive power-law dependence from the mean number of co-occurring domains – the degree – ⟨k⟩ ~ Nε, suggesting that on average frequent occurrence of a domain coincide with the participation in various domain architectures (see Table 1 for detailed values). (d). The domain networks of H. sapiens, M. musculus, D. melanogaster, C. elegans, and S. cerevisiae display scale-free behavior, a network feature which is characterized by the power-law in the degree distribution P(k) ~ k-θ[15] (see Table 1 for detailed values). (e) The network's inherent modularity is indicated by the presence of a power-law dependence between the clustering coefficient and the degree as a generalized Zipf-law ⟨C(k)⟩ = α(β + k)-γ(see Table 1 for detailed values). With respect to (b,c,d,e), we observe that the organisms specific distributions differ by their individual power-law exponents, indicating their levels of evolutionary development.