## 4 Results and Discussion
### Comparison between the Dynamics-Based and the Structure-Based Clustering  
We compared the results from the dynamics-based clustering on the proteases of the PA clan with the structure-based distance tree calculated in the work of [PERSON] et al. [34]. There, the authors identified a common structural core of 72 residues for the set of PA clan proteases taken into account; according to the structural similarities of this common core, they built a distance tree between the members of the dataset. Five different clusters were identified, contrary to the nine cluster found in this work. Despite the two different approaches, the results present several similarities, showing a close relation between structure and dynamics. The S1A subfamily, which includes both bacterial and eukaryotic proteases, forms a clearly distinct and compact cluster both in terms of structure and dynamics. On the other hand, the S1D subfamily, which includes bacterial proteases, is split into two different groups in terms of structure, as well as dynamics: in both cases, the S1D _Achromobacter_ protease I (1 ARB) is close to the bacterial S1B proteases, while the S1D protease AL20 of _Nesterenkonia abyssinica_ (3 CP7) is close to the members of the bacterial S1E subfamily. This difference between members of the S1D subfamily has been explained on the basis of the different evolutionary history of the bacteria in which they are expressed [34]. Another common feature emerging from the two clustering approaches is the similarity between the S39 subfamily of positive-strand RNA viruses and the bacterial S1B proteases; interestingly, such a degree of similarity is higher than between S39 and the other viral proteases, as already reported on the basis of structural comparisons [79]. Moreover, the bacterial S6 family forms an independent group in both clustering approaches. This  
Figure 5: (**a**) Distribution of the members of each subfamily among the different clusters, expressed as a percentage with respect to the total number of members of the subfamily. In (**b**), each row represents the content of each cluster classified on the basis of the function (in percentage, with respect to the total population of the cluster). The results show that the dynamics-based clustering automatically tends to group proteins belonging to the same subfamily. peculiarity has been attributed to the presence of a long \(\beta\)-stalk structure at the C-terminus (Figure S5), which is absent in all the other proteases of the PA clan [34,80]; the protease domain alone, instead, shares high structural similarity with that of the S1A subfamily. However, the \(\beta\)-stalk domain was cut before the dynamics-based alignment, meaning that our analysis of the dynamics of the S6 protease domain alone is able to distinguish this subfamily from the other members of the PA clan. Importantly, the two types of clustering present also some differences. In the case of the structure-based analysis, the cysteine proteases tend to be grouped together; however, in the dynamics-based alignment, the similarity is only at the level of one of the two large groups into which the dataset is divided, as evident from the dendrogram in Figure S4. Within this group, C families are mixed with S families and appear to be more distributed among different clusters than in the distance tree built on the basis of the structural features. This is indicative of a clear differentiation of the C proteases in terms of dynamics, despite their structural similarity in the protein core. This can be explained not only by the fact that different classes of C proteases are involved in the processing of different viral polyproteins (therefore, requiring adaptation to the substrate), but also because some of them have additional functions, playing the role of inhibitors of host cell protein synthesis [81].