Matrix of the distances between the biological relevant units of the proteins in the set. Multipole-based distance matrix calculated from Cα atoms that are part of the biologically relevant portion of the proteins in the set. The proteins in the set are identified by their pdb id. The groups inside the TPK family are labeled according to the classification produced by Manning et al. [28, 29]. In this calculations all multipoles up to l_max = 4 are retained in Eq. (7). Here, and in all other distance matrix representations, darker colors map into bigger distances. The upper six raws and left six columns represent inter-family distances while the rest of the matrix contains only distances between the kinase family members.

Correlation coefficient between multipole and rmsd distances. Correlation coefficient of the multipole and rmsd-based distances (r) as a function of the level of detail of the multipole representation (highest multipole rank l_max retained in the description). All different pairs of distances from the 31 protein set are included in the comparison. The rmsd distances used in this calculation were determined after the spatial superposition of structures. Only aligned residues are included in the calculation of distances.

Comparison between multipole and rmsd distances (Case 1). The distance matrices between aligned portions of proteins in the multipolar (a) and Cartesian coordinate (b) representations. Multipoles up to order four are retained in (a). The rmsd distances are calculated after prior spatial superimposition. The shading is in both cases proportional to the distance, however the scale is normalized to the entire range of values taken in each case. The order of the 31 proteins along the two axis is as described in the text and the same as in Figure 1.

Distances in a subset of representative proteins. The distance between all pairs of a subset of representatives: 1bo1, 1ia9, 1e8x, 1cja, 1nw1, 1j7u, 1cdk, 1csn and 1ir3. The upper dashed curve is the rmsd. The lowest continuous curve represents the multipoles-based distance rescaled by a factor of 10 with respect to the mean value and shifted to ease comparison. The multiplication factor compensates for the difference in the scale of numerical values of the two measures. In this figure l_max = 12.

Correlation coefficient between multipole and rmsd distances for a subset of pairs closer in rmsd. Correlation coefficient as a function of the level of detail (highest multipole rank l_max in the representation). In this calculations only six structures from the smaller set, those occupying the right side in Figure 4 are included: 1cja, 1nw1, 1j7u, 1cdk, 1csn and 1ir3. The distance between pairs of structures in this set are on average smaller than for the whole set in Figure 4.

Comparison between multipole and rmsd distances in the "canonical" frame (Case 2). Multipole (a) and rmsd (b) distance matrices when in both representations proteins in each pair are positioned in the "canonical" reference frame.

Comparison between multipole and rmsd distances with superposition (Case 2). Multipole (a) and rmsd (b) distance matrices when in both representations proteins in each pair are superimposed by minimizing the rmsd distance.