## 3 Results and Discussion
### All-Atom Model
However, one must observe that this scenario, i.e., the all-atom calculation, uses 1000 nodes, instead of only 129 nodes as in the coarse-grained approach. Therefore, an overall correlation of 0.70 obtained over 1000 locations should be more informative than the same correlation obtained over 129 points. Moreover, it has also been found that, when small portions are analyzed in separate domains, the agreement between numerical and experimental can be superior to 0.85 locally. The analyzed data in terms of computed B-factors indicates the local flexibility according to the complete summation of modal shapes, as reported in Equation (5). However, the computed B-factors considering all the \(3N-6\) modes do not necessarily provide information about the individual modal motions or whether which modes represent the protein flexibility. As a matter of fact, the B-factors profile results from a summation of 2994 non-rigid modes. Each mode's contribution is weighted with the inverse of the squared angular frequency, as shown in Equation (5), but it is generally unknown how many modes are vital to providing accurate results when comparing the numerical profile to the experimental values. For this reason, the effect of the number of modes has been investigated for the 12 A case. The results are displayed in Figure 4. Figure 4a reports the computed B-factors  
Figure 3: The Pearson correlation coefficient between the different numerical B-factors and with the experimental ones for the all-atom scheme. by adopting only the lowest 10 modes. The following plots, i.e., Figure 4b-f, show the cases when 50, 300, 1000, 2000, and all 2994 modes are considered, respectively. As can be observed from these graphs, the initial low-frequency modes are not sufficient to accurately represent the curve of experimental B-factors, compared to the complete solution shown in Figure 4f. The profile starts to display a better correlation when more than 300 modes are taken into account. Still, small peaks reach a more precise representation for more than 2000 modes. These graphs demonstrate that, although the low-frequency modes are the most involved in the B-factors' definition due to their lower frequency values, the application of just the initial modes for such calculation is not necessarily adequate when using the all-atom representation. Higher modes might have a nonnegligible influence in terms of local flexibility, thus modifying the overall trend of the B-factor curve. The collectivity index reported in Equation (8) was also used to assess the degree of the collectivity of each vibrational mode. Figure 5 shows the distribution of the collectivity indexes across all the obtained mode shape for each selected cutoff value. It can be noted that, as the sphere of influence due to the selected cutoff increases, the collectivity indexes of the lysozyme motions experience a downward shift towards lower values. This observation also indicates that the modal shapes are not equivalent among the cutoffs. The vertical red dashed lines in Figure 5 indicate the five modes with the highest collectivity index for each displacement fields shown. The cases with cutoff values equal to 6, 8, 12, and 15 A are presented. Figure 6 shows the protein structure, densely packed in black colors. The colored vectors represent the normalized displacement related to modal shapes according to increasing cutoffs. The visual verification of the collective motions can be seen in Figure 6a-d. In the 6 A and 8 A cases, the first significant mode is very similar to previously reported binding cleft opening and closing at 0.12 THz [6; 15; 57]. However, as the cutoff increases, the modes do not present the same mechanism. At first sight, it seems that the relationship between modes is just similar for close cutoff cases. As the difference increases, the mode shapes are different and cannot be related in a one-by-one fashion.