Dynamical Transition of Collective Motions in Dry Proteins

Water is widely assumed to be essential for protein dynamics and function. In particular, the well-documented “dynamical” transition at $\sim 200\mathrm{K}$, at which the protein changes from a rigid, nonfunctional form to a flexible, functional state, as detected in hydrogenated protein by incoherent neutron scattering, requires hydration. Here, we report on coherent neutron scattering experiments on perdeuterated proteins and reveal that a transition occurs in dry proteins at the same temperature resulting primarily from the collective heavy-atom motions. The dynamical transition discovered is intrinsic to the energy landscape of dry proteins.

Figure 1

Structures of (a) CYP and (b) GFP. Experimental $S(q,\mathrm{\Delta }t)$, normalized to the lowest temperatures ($\sim 10\mathrm{K}$) and summed over 15 values of $q$, ranging from 0.36 to $1.75{\AA }^{-1}$ for dry ($h=0.02$) (c) H-CYP, (d) H-GFP, (e) D-CYP, and (f) D-GFP. The elastic-scan data of dry CYP in panels (c) and (e) have been reported in Ref. [52] in a different form. The experimental results of $S(q,\mathrm{\Delta }t)$ are grouped in intervals of 8 K for clarity. The two dashed lines in each figure are linear fits in the low ($5–110\mathrm{K}$) and high ($220–295\mathrm{K}$) temperature regions, respectively, and the crossing point of the two fits determines the transition temperature. The same fitting procedure is also used in Fig. 2 to determine the transition temperature. In Fig. S3, we compared $S(q,\mathrm{\Delta }t)$ scaled by the values at the lowest temperatures at each $q$ with that scaled by the values collected on vanadium, exhibiting negligible differences. (g) Temperature dependence of incoherent $S(q,\mathrm{\Delta }t)$ derived from MD simulation of dry ($h=0.02$) H-CYP with or without methyl rotation being removed through postprocessing the MD trajectories. The detailed procedures for removing methyl rotations from the MD trajectories are presented in Ref. [23] (see Fig. S7). The MD-derived $S(q,\mathrm{\Delta }t)$ is approximated as the value of the intermediate scattering function when decaying to the instrument resolution, $I(q,\mathrm{\Delta }t)$ (see Eqs. S1 and S2 in the Supplemental Material [23], and Ref. [53]), the same as in Fig. S4 [23]. The MD-derived $S(q,\mathrm{\Delta }t)$ is also normalized to the lowest temperature (10 K), being consistent with experiment.

Figure 2

Experimental mean-squared atomic displacements $⟨x^2(\mathrm{\Delta }t)⟩$ derived from dry ($h=0.02$) (a) H-CYP, (b) H-GFP, (c) D-CYP, and (d) D-GFP. Detailed procedures to derive $⟨x^2(\mathrm{\Delta }t)⟩$ are presented in Ref. [23]. Error bars throughout the text represent 1 standard deviation.

Figure 3

Quasielastic neutron scattering spectra measured at 180 and 240 K for dry ($h=0.02$) (a) H-CYP and (b) D-CYP. To improve statistics, the spectra measured over the experimental $q$ window from 0.4 to $1.8{\AA }^{-1}$ were summed up. For comparison, the resolution function measured at 10 K is also presented. (c) The frequencies of longitudinal sound waves ${\nu }_L$ measured using Brillouin light scattering on lyophilized ($h=0.02$) H-GFP (the results are taken from Ref. [53]). (d) Longitudinal modulus estimated using the result of (c), with the density and refractive index of the protein assumed to be $1.4\mathrm{g}/{\mathrm{cm}}^3$ [59] and 1.4 [60], respectively. Arrows in (c) and (d) mark the kinks in the temperature dependence of the elastic properties.