Tsai et al. applied in situ elastic NS to study the effect of glycerol and hydration on the dynamic processes of lysozyme powder. Glycerol was shown with a stabilization and destabilization effect when the temperature is below and above the dynamical transition temperature (Td), as evidenced by the changes of <u 2 > at different temperature regimes. Cicerone et al. provided the first direct evidence correlating β relaxation processes with protein stability. They utilized elastic and inelastic coherent NS to investigate the stability of horseradish peroxidase and yeast alcohol dehydrogenase in the binary glasses of trehalose and glycerol. By adding a small mole fraction of antiplasticizers, i.e., glycerol, the stability of these enzymes was improved with the suppression of the short-time scale dynamics and protein motions even though the 𝜏α is lowered. Such a relationship between protein stability and βfast relaxation was further validated using inelastic NS measurement. The degradation rates of either chemical or physical degradation processes of 11 proteins correlate linearly with <u 2 > -1 , indicating that βfast relaxation plays an important role in protein stabilization. These observations suggest that protein stability is more directly coupled with highfrequency β relaxation processes, rather than α relaxation. Later, another study leveraged molecular dynamics simulation and NS to evaluate the impact of sugar and water on the protein motion in the lyophilized glassy matrixes. Trehalose was reported to rigidify the lysozyme as evidenced by the inverse relationship between protein flexibility and stability in NS measurements. Interestingly, this study highlighted the importance of hydration levels in the solid state. Lysozyme was found to have a greater tendency to interact with water rather than trehalose in the hydrated matrix. Furthermore, the presence of trehalose significantly slows down the relaxation of hydrogen bonds between lysozyme and water and the formation of hydrogen bonds to fill the void space. Furthermore, some studies have utilized NS to study the impact of buffer composition on the internal protein dynamics in the lyophilized powder. For example, human butyrylcholinesterase lyophilized in three different buffers demonstrated distinct protein internal motions, where salt-free and sample with Tris-HCl sample showed similar small-amplitude motions but sample containing sodium phosphate demonstrated highly reduced mean-square displacements at ambient temperature. Neutron spectroscopy can yield highly valuable details regarding the microscopic aspects of molecular motions, including atomic motion geometry across various length scales, through the analysis of scattering wave-vector dependencies. Nevertheless, the frequency range accessible through neutron spectroscopy is limited, primarily enabling the study of protein dynamics on a timescale ranging from picoseconds to nanoseconds. While neutron scattering can provide valuable information in conjunction with vibrational spectroscopy methods, it does have certain drawbacks. Larger sample sizes are required due to the weak neutron sources and low efficient neutron detector. In addition, The highly specific and accurate nondestructive tool of neutron activation analysis makes it expensive and impractical for routine use. 3.2.3.4. Solid-state nuclear magnetic resonance (ssNMR) Figure . Illustration of molecular dynamics in proteins characterized by ssNMR spectroscopy. NMR spectroscopy plays a significant role in the investigation of protein dynamics since it allows for the determination of dynamics at the level of individual atoms. The movement of a molecule, whether it involves small-scale bond vibrations or large-scale domain motions, causes atoms and bonds to reorient in space. Consequently, this reorientation alters the spatial arrangement of electrons as well as various interatomic distances and orientations. These variations in bond angles, distances, and electronic environments can result in the fluctuations of spin interactions. Chemical shift, chemical shift anisotropy (CSA), relaxation time, and dipolar coupling measurement from NMR are commonly used to probe these dynamic changes. Solid-state NMR (ssNMR) has a natural advantage over solution-state NMR in detecting motions that occur over timescales exceeding tens of nanoseconds, even when there are no isotropic differences in chemical shifts, 172 as shown in Figure . Especially, magic-angle spinning (MAS) NMR was used to probe motions on the nanosecond-microsecond-millisecond timescales by spin-relaxation experiments. It has been widely used for side chain dynamics characterization. For example, the line shape and spin relaxation measurements via ssNMR parameters can probe specific site motion. Side chain motion of dry streptomyces subtilisin inhibitor protein power has been observed and quantified by 2 H ssNMR. Comparison solution N relaxation data and solid-state 1 H N -15 N dipolar couplings suggested little or no protein backbone dynamic but evidence of ns-us fast motions in the flexible loops and termini. In addition, the combination use of R1, R1ρ, and S 2 data for both 1 Hα- Cα and 1 H- N have also been studied as a powerful tool to characterize three timescales of motion (slow and global motion, intermediate, and fast motion), such as application in backbone dynamics of HET fibrils. Moreover, ssNMR often is used to investigate the motion of secondary structure elements. Such as the loop and helix dynamics in an intramembrane protease were characterized by relaxation dispersion and conformational changes by ssNMR in the liposomes. Transient unfolding of a β-sheet in the excited state of a macroglobulin mutant D76N beta-2 was found by MAS ssNMR probing the intrinsic dynamics of both wildtype and mutant forms of proteins both correlating to its increased aggregation propensity. 179 ssNMR is also particularly powerful for large protein complexes characterization. Zinke et al. found that bacteriophage tail tube-bending mediated by highly flexible hinge regions through N R1 and 15 N R1ρ relaxation rates and cryo-EM characterization. 180 Aside from extensive application in the dynamic characterization of neat solid protein molecules, ssNMR also remains a powerful technique for the investigation of protein conformation and dynamics in lyophilized powders. By utilizing ssNMR relaxation measurements, one can track the mobility of protein side chains, surface groups, excipients, and bound water molecules, correlating these findings to the stability of proteins in freeze-dried solids. The commonly used methods are measurements of the spinlattice relaxation time in the laboratory (T1) and rotating frame (T1ρ) by ssNMR, where T1 and T1ρ characterizes the amplitude of the high-frequency (MHz) and low-frequency (kHz) motions, respectively. Many ssNMR studies have described that β-relaxations are more critical to protein stability instead of α relaxations under certain circumstances. Relaxation parameters on different time scales can be used to evaluate spin diffusion over different length scales. 1 H T1, typically 1-10 s, corresponds to a spin diffusion over ∼20-100 nm, while 1 H T1ρ, ranging from 1 to 10 ms, estimates spin diffusion over ∼ a1-20 nm length scale. For instance, Lam et al. measured the T1 values of pure lysozyme, trehalose, lactose, trehalose-lysozyme, and lactose-lysozyme at different hydration levels by ssNMR. The increase of T1 values induced by both sugars was found well correlated with the enhancement of protein stability. In contrast, the change in aggregation and activity of proteins was attributed to the hydration in the formulations, as reflected by the increased relaxation rates, R1, or reduced relaxation time, T1 values, with increasing water contents. Moreover, Yoshioka et al. measured the T1ρ for both protein and sugar (trehalose, sucrose, and isomaltose) carbons in freeze-dried lysozyme formulations. It was found that the relaxation time constant (𝜏c) and temperature coefficient of β-relaxation were both decreased in the presence of sucrose while increased in the presence of isomaltose, indicating the significant impact of sugars on the β-mobility of the lysozyme. Another study by Yoshioka et al. also demonstrated that the degradation rate of lyophilized insulin is determined by β-relaxation rather than global matrix mobility. Compared to the insulin-dextran formulation, the addition of trehalose was shown able to prolong the T1ρ of the insulin carbonyl carbon at 12% relative humidity. Meanwhile, the insulin-trehalose glasses presented a substantially lower degradation rate than the insulin-dextran system at a temperature below the Tg, suggesting β-relaxation is likely the determinant process for protein degradation. Later, Mensink et al. and Lay-Fortenbery et al. investigated the impact of various sugars on the lyophilized proteins' stability. The relaxation T1 correlated well with the stability of protein as shown in Though ssNMR offers detailed insights into the local movements of specific groups within proteins for examination of protein dynamics, such as methyl groups, it does not provide comprehensive information about larger-scale global motions in existing pharmaceutical applications. In addition, ssNMR relaxation measurement is also sensitive to the moisture or water content in the lyophilized sample which impacts its application in dynamic quantification and corresponding stability correlation. Considering water as the dominant relaxation resource in the lyocake and its significant impact on protein relaxation properties through 1 H-1 H spin diffusion, interpreting the relaxation values without controlled low moisture levels can be misleading. Furthermore, there is so-far limited application in high-resolution structural characterization using ssNMR as the orientations of proteins in amorphous solids are considerably more random.