Figure 4
Shannon information (entropy) values of the ligand/domain compositions and the functional diversity of binding site communities The x-axes represent the community size using a log-scale. The y-axis of (A) represents the functional diversity of the communities. The average functional diversity of a community is measured by the average number of distinct GO-BP (\(\overline{{{\boldsymbol{N}}}_{{\rm{BP}}}}\)) and GO-MF (\(\overline{{{\boldsymbol{N}}}_{{\rm{MF}}}}\)) terms of included proteins. The average functional diversity of all proteins in the network, 4.9, is denoted as the blue dotted line. The y-axes of subplot (B) and (D) represent the Shannon information values of ligand and domain compositions of communities. The Shannon information values were calculated as follows: \({\boldsymbol{S}}=-\sum _{{\boldsymbol{i}}}{{\boldsymbol{p}}}_{{\boldsymbol{i}}}\,\mathrm{ln}\,{{\boldsymbol{p}}}_{{\boldsymbol{i}}}\), where i is the ligand or the domain index. The y-axis of subplot (C) represents the variance of the distances between ligands in a community: \({\rm{Var}}({\boldsymbol{C}})=\frac{1}{{{\boldsymbol{n}}}^{2}}{\sum }_{i}{\sum }_{{\boldsymbol{j}} > {\boldsymbol{i}}}{(1-{{\boldsymbol{T}}}_{{\boldsymbol{ij}}})}^{2}\), where T ij is the Tanimoto coefficient53 between ligands i and j. The variances of the binding sites communities are plotted with red crosses and the green dots correspond to the variances of the same number of randomly selected ligands.
