Three Classes of Motion in the Dynamic Neutron-Scattering Susceptibility of a Globular Protein

A simplified description of the 295 K dynamics of a globular protein over a wide frequency range (1–1000 GHz) is obtained by combining neutron scattering of lysozyme with molecular dynamics simulation. The molecular dynamics simulation agrees quantitatively with experiment for both the protein and the hydration water and shows that, whereas the hydration water molecules subdiffuse, the protein atoms undergo confined motion decomposable into three distinct classes: localized diffusion, methyl group rotations, and jumps. Each of the three classes gives rise to a characteristic neutron susceptibility signal.

Figure 1

(a) Susceptibility spectra of hydrated lysozyme ($q=1{\AA }^{-1}$) obtained from neutron-scattering experiments on the National Institute of Standards and Technology high-flux backscattering spectrometer (HFBS, triangles), the Oak Ridge National Laboratory’s Spallation Neutron Source backscattering spectrometer (BASIS, spheres), the National Institute of Standards and Technology disk-chopper time-of-flight spectrometer (TOF, squares) [8, 15], and from MD simulation (thick solid line). To improve the statistics, the experimental spectra were summed over the $q$ range from 0.3 to $1.7{\AA }^{-1}$ with an average $q=1{\AA }^{-1}$. The experimental data on the $y$ axis were multiplied by an arbitrary constant for ease of comparison of the shape of the two spectra. Experimental intensity is difficult to obtain on an absolute scale, and even more so when combining several instruments. Hence, only the shape of the spectra can be compared. (b) $q$ dependence of the average main relaxation time ($\tau$) of water molecules presented on a double logarithmic scale. Simulation results are denoted as empty symbols: hydration water (squares) and bulk water (spheres). The solid squares are experimental data for hydration water [14]. The dashed lines are linear fits to the simulation data yielding slopes of 2.5 for the hydration water and 2.0 for the bulk. The susceptibility spectra of hydration and bulk water at different $q$ values, from which $\tau$ is estimated, are presented in Fig. 3s in Ref. 16.

Figure 2

Typical examples of scatter plot projections of hydrogen-atom trajectories from MD. (a) Diffusion in a single cluster (the $\delta$ hydrogen atom of TRP63). (b)–(d) Diffusion in clusters plus jumping between (b) two clusters (a $\gamma$ hydrogen atom of ARG150), (c) three clusters (a methyl hydrogen atom of VAL2 ), and (d) four clusters (a $\gamma$ hydrogen atom of LYS226).

Figure 3

(a) MD neutron susceptibility spectrum of the whole protein (${\chi }^{\prime \prime }$), the localized diffusion ($\chi ^{\prime \prime }{}_{\mathrm{ld}}$) summed over Type I and II hydrogen atoms, the methyl group rotations ($\chi ^{\prime \prime }{}_{\mathrm{me}}$), and the jumps ($\chi ^{\prime \prime }{}_{\mathrm{jump}}$). (b) $⟨x^2⟩$ of the same hydrogen atom as in Fig. 2a, the ballistic region at $t<0.1\mathrm{ps}$ is not shown.