## 3 Results and Discussion
### All-Atom Model
The displacement field in Figure 6a (6 A) is more homogeneous over the whole structure, while in Figure 6d (15 A), the large displacements are localized in a specific region; therefore, the amplitude of the vectors almost vanishes over the body, leading to insignificant relative motion for most of the structure. In this case, only localized vectors indicated in red circles can be seen,  
Figure 4: 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**) 10 modes, (**b**) 50 modes, (**c**) 300 modes, (**d**) 1000 modes, (**e**) 2000 modes, and (**f**) 2994 modes. pointed at the bottom part of the figures. The increasing number of generated links locks the global motions, leading to more localized modal shapes (see Figure 5). Figure 5: The mode collectivity index \(\kappa\) for all cutoff values according to the respective natural frequency range. The red dashed lines indicate the modes represented in Figure 6 for 6, 8, 12, and 15 Å cases related to the most significant collective motions. Figure 6: Representation of the modes with the highest collectivity index displayed in Figure 5. Cases represented are for: (**a**) 6 Å, (**b**) 8 Å, (**c**) 12 Å and (**d**) 15 Å. The participation of modes at higher frequencies in conventional mechanical and civil structures is not a common feature. Usually, a few initial modes are enough for a proper description of the dynamics of the system. Figure 7 displays the entire frequency spectra of the lysozyme for all cases. The lowest frequency for the 6 A case is found to correspond to 0.025 THz, while a convergence towards 0.36 THz is found for the model with a cutoff value of 30 A. The increment of the cutoff creates higher frequency values for approximately the first 150 modes. After this point, a switch happens and the lower cutoffs assume the higher frequencies, as can be appreciated from Figure 7. This is because the larger axial rigidities in the models with lower cutoff values cause higher natural frequencies for the initial modes, but this also causes a smaller difference between the lower and higher values, shortening the total frequency range. The difference between the initial and the final eigenvalues are concentrated in one order of magnitude. For example, the lowest frequency for the 12 A case corresponds to 0.18 THz, while the highest one is found at 1.6 THz. It is essential to observe that the frequencies shown below are highly dependable on the adopted model's stiffness (see Table 1). Another important aspect concerns the spectral frequency density. The distribution is generally associated with a Gaussian curve for globular proteins, as suggested by other authors [8; 58]. The lysozyme is an enzyme densely packed in a spherical form. A large part of the known proteins exhibits a globular shape and a sequence of 20 basic amino acids form the \(\alpha\)-helices and \(\beta\)-sheets that can be assumed as randomly spread in the body. [PERSON] stated that \"there is, statistically speaking, a large degree of homogeneity between different proteins. Thus, the vibrational spectrum ought to be essentially the same for all proteins\" [58]. Therefore, we expect to obtain similar dynamic properties that allow us to compare different proteins using the same baseline. NMA was applied by [PERSON] to extract the spectra of vibrational modes of many proteins showing a normal distribution at least for the lower frequencies [58]. The analysis of [PERSON] et al. [8] and [PERSON] et al. [10] made use of the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) respectively, and also provided evidence for these characteristic curves considering the equilibrium position of the C\({}^{\alpha}\) atoms. The all-atom models generate the spectra presented in Figure 7. The increasing cutoff leads to the distribution of frequencies towards a normal distribution for the lower cutoff values. The 12 A and 15 A match this description with a well-behaved Gaussian density distribution.