## 3 Results and Discussion
### Coarse-Grained Model
From the analysis of the obtained Pearson coefficients, the previous arguments are confirmed. For example, the correlation among the generated numerical models with 20 A and 8 A cutoff increases from 0.816 for the C\({}^{\alpha}\)-based models to 0.882 for the CM-based ones. The remaining values of the correlation coefficients among the various numerical solutions show similar behavior. Therefore, it follows that using the CM locations as the nodes of the truss-like structure leads to fewer dependencies of the results on the specific cutoff value. Additionally, the difference between experimental and numerical values also has less influence in the CM-based scenario. For example, the coefficient gap between 8 A and 20 A is 60% lower for the CM-based approach. Similar to Figure 4, the effect of the number of modes for evaluating the numerical B-factors has been investigated for the 12 A case of the coarse-grained model. Figure 10a reports the computed B-factors by adopting only the lowest 5 modes. The following plots, i.e., Figure 10b-f, show the case when 10, 35, 130, 250, and all 381 modes are considered, respectively. Similar to what was found for the all-atom model, the initial low-frequency modes are not sufficient to represent the curve of experimental B-factors alone. However, the convergence towards the final profile obtained with all 381 modes in the coarse-grained representation is faster, and a lower number of modes is needed to reach the final curve. Note that, after adding the first 130 modes, the profile basically does not show any additional significant changes. Figure 8: (**a**) The center of mass (CM) of each amino acid is taken to calculate the numerical B-factors. The experimental value is also weighted according to the mass of each atom composing the residue. (**b**) The results from [PERSON] et al. [15] considering the C\({}^{\alpha}\) location. Figure 9: The Pearson coefficient comparing different numerical solutions and with the experimental B-factors. (**a**) Adopting the C\({}^{\alpha}\) scheme. (**b**) Adopting the CM-based strategy. Figure 11 displays the collectivity index for the coarse-grained structure for the CM-based scenario. Smaller cutoffs produce index values around 0.9 for a large portion of the frequency spectrum, meaning that highly collective motions can be detected when using the coarse-grained strategy. On the other side, as the cutoff increases, the curves' overall behavior translates downwards (similarly to what is found in the all-atom models), reducing the collectivity of the motions. The same behavior was found considering the C\({}^{\alpha}\)-based configuration (see Figure S2 in the Supplementary Material). Figure 11: The mode collectivity index \(\kappa\) for the coarse-grained model with the CM-based configuration. The \(x\)-axis represents the frequency spectrum for each cutoff. The red dashed lines indicate the most collective modes described in Figure 12 for 8, 10, 12, and 15 Å cases. Figure 10: The numerical and experimental B-factor for the 12 Å case. The plots vary the number of modes added for the B-factor calculation. At (**a**) 5 modes, (**b**) 10 modes, (**c**) 35 modes, (**d**) 130 modes, (**e**) 250 modes and (**f**) 381 modes. The highest collectivity values are marked with a dashed-red line and the respective mode shapes are represented in Figure 12. The illustrated nine cases indicate the protein regions with high (red) and low (blue) flexibility. Cutoffs of 15 A and 20 A have a diffuse distribution of motions without global motions. This is caused because, for higher cutoff values, the protein's inner regions are highly constrained by many connections, allowing only local movements at the structure's external parts. On the other side, for the 8 A case, the complete system has the freedom to vibrate for a wide range of frequencies, demonstrating many cooperative modes. Finally, Figure 13 shows the frequency spectrum for all modes and selected cutoffs for the CM-based scheme.