## 4 Results and Discussion
### Results of the Dynamics-Based Alignment  
We performed an alignment based on the dynamical information entailed into the first 10 lowest frequency modes obtained by the NMA on the \(\beta\)-Gaussian network model of each pair of proteins in the dataset. The alignment consists of the optimization of a score function that maximizes the RMSIP of the two sets of normal modes. For each pair of dynamically aligned proteins, matching regions in the two structures are identified as the subset of residues giving the best overlap. The number of residues belonging to these cores shows great variability (Figure S2), and their RMSD values range from 0.6 to 4.0 A; these results are indicative of heterogeneity in dynamics within the dataset.  
The distance matrix obtained from the pairwise dynamics-based alignments of all proteins of this dataset is used as a measure of similarity in dynamics. This can be compared to the MEROPS classification by computing the average distance between protein pairs that fall into the same family. Following such a procedure, it is apparent that the average distance in dynamics is lower within each family, with respect to the total average (Figure 4). In other words, proteins belonging to the same family are significantly closer in dynamics than they are to members of other families.  
The distance matrix is used as the input for the division of the dataset into dynamically homogeneous protein clusters. The outcome of the hierarchical clustering is graphically  
Figure 4: Average distances (in terms of dynamics) between proteins of the dataset belonging to the same family. Only those subfamilies including more than one representative member are displayed here. The histograms show that proteins are significantly closer in dynamics within the same family than they are to members of other families.  
Figure 3: Cartoon representation of chymotrypsin from _Bos taurus_ (PDB ID: 2 CGA). Colors are used to differentiate the structural elements; in particular, the two \(\beta\)-barrels are distinguishable in yellow. The catalytic triad is represented in licorice and colored in red.  
expressed by the dendrogram in Figure S3. On the basis of the resolution-relevance plot, nine clusters were identified (Figure 2); this corresponds to a threshold of \(\approx\)0.58 in the clustering dendrogram. The resulting clusters appear to be quite homogeneous in terms of protease classification (Figure S4). Importantly, the dynamics-based clustering automatically tends to group proteins belonging to the same subfamily. Figure 5a shows that in most of the cases (17 of the 19 subfamilies represented in the dataset), all the members of each subfamily fall into the same cluster, thus suggesting that these proteins share a similar conformational dynamics and strengthening the idea of homogeneity in dynamics between homologous proteins [77; 78]. On the other hand, each cluster groups several subfamilies, and only 4 clusters out of 9 include proteins belonging to only one subfamily (Figure 5b). Therefore, the clustering procedure proves able to effectively group different protein subfamilies that, despite the different evolutionary origin, share similar dynamics.