## 3 Results and Discussion
### Coarse-Grained Model  
The mass-weighted experimental B-factors in the CM of each residue were used as reference values to compute the axial rigidity \(EA\) of the elastic connections generated for the coarse-grained model. Similar to what occurs in the all-atom model, this procedure is performed to establish a comparison between the B-factors' numerical and experimental values, and the resulting value of \(EA\) leads to a not negligible influence on the obtained frequency values. Table 2 shows the axial rigidity and average stiffness values for each cutoff value. Again, the mean rigidity is found to decrease as the number of connections increases. The work of [PERSON] et al. (2015) considers the mass of each residue centered at the C\({}^{\alpha}\) location and with a constant value throughout the protein structure. In Table 2, we can see that using the CM, the axial rigidity is lower for smaller cutoffs. This effect results from a reduced standard deviation of the B-factors when using a CM-based description, which in turn allows reducing the individual rigidity values to obtain the same averaged B-factor. As an example, the 8 A case was found to provide a standard deviation of 28% lower for the B-factor curves using the CM, with respect to the C\({}^{\alpha}\) representation. On the other side, for higher cutoffs, e.g., 20 A, the variation is reduced, leading to almost the same values for both methods. From this observation, it can be concluded that the proposed change has a more significant impact on the rigidity values for the cases with a lower number of connections. The construction of a model based on the CM locations stabilizes the structural state decreasing the oscillations in flexible regions. On the other side, for higher cutoffs, the difference using the CM and the C\({}^{\alpha}\) scenarios is lower. In terms of flexibility, the higher number of connections imposes more restrictions on the system, making the actual position of the nodes less critical. The normalized B-factors are presented in Figure 8a for all cutoffs applying the data provided in Table 2, with respect to the model based on the CM locations. The comparison is also made with the results of [PERSON] et al. (2015), concerning the model based on the C\({}^{\alpha}\) sites, as reported in Figure 8b. From these figures, it is possible to observe less variance between the different numerical curves for the CM-based model. An example can be given by observing what happens at node 117. The peak at 8 A is not seen for the other C\({}^{\alpha}\)-based cutoffs when compared to the CM-based models. Therefore, the application of the CM modeling technique appears to smooth the jump between the different horizons and provide more robustness to the model, i.e., less dependence on the specific cutoff value. Furthermore, it seems that the application of the CM-based scheme also allows smoothing the highest peaks that are found in the C\({}^{\alpha}\)-based numerical B-factors (see Figure S1 in the Supplementary Material). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Cutoff (Å)**} & **Axial Rigidity** & **N\({}^{\circ}\) of** & **Average** & **Axial Rigidity** \\  & **EA-CM (N)** & **Connections** & **(N/m)** & **EA-C\({}^{\alpha}\) (N)**[15] \\ \hline
8 & \(4.56\times 10^{-10}\) & 627 & 0.783 & \(8.31\times 10^{-10}\) \\
10 & \(1.95\times 10^{-10}\) & 1109 & 0.283 & \(2.35\times 10^{-10}\) \\
12 & \(1.13\times 10^{-10}\) & 1771 & 0.142 & \(1.24\times 10^{-10}\) \\
15 & \(0.69\times 10^{-10}\) & 2938 & 0.0723 & \(0.71\times 10^{-1 The Pearson correlation coefficient between the numerical and experimental B-factors is then used to confirm the previous comments and it also allows us to establish the agreement between the curves quantitatively. In Figure 9a, the correlation coefficient among each numerical solution and with the C\({}^{\alpha}\) experimental B-factors are reported. The same output is presented in Figure 9b for the CM-based scenario.