Single-Particle and Collective Dynamics of Protein Hydration Water: A Molecular Dynamics Study

We present an analysis based on molecular dynamics simulations of water single particle and collective density fluctuations in a protein crystal at 150 and 300 K. For the collective dynamics, the calculations predict the existence of two sound modes. The first one around 35 meV is highly dispersive and the second one around 9 meV is weakly dispersive in the $k$ range studied here ($0.5<k<4.2{\AA }^{-1}$). We provide evidence that the boson peak around 4 meV in the single particle spectra arises from translational motion, is present in the coherent spectra, and is distinct from the two sound modes.

Figure 1

Snapshot from a MD simulation of the RNase crystal. The simulation box corresponds to one crystal unit cell containing 2 protein molecules (light atoms) and 817 water molecules (dark atoms). The box is replicated infinitely in three dimensions using periodic boundary conditions.

Figure 2

Coherent dynamical structure factors $S_c(k,E)$ and corresponding longitudinal spectra $C_L(k,E)$ for the protein hydration water in simulations of the RNase crystal at 150 K for selected values of the momentum transfer ($k=0.5$ to $1.9{\AA }^{-1}$, increasing from bottom to top at intervals of $0.1{\AA }^{-1}$).

Figure 3

Contour plots of the longitudinal current spectra $C_L(k,E)$ for the protein hydration water from the simulations of the RNase crystal at 150 K (a) and 300 K (b).

Figure 4

Hydration water single particle dynamics in the RNase crystal. (a) Water protons $S_s(k,E)$ at 300 and 150 K. (b) Decomposition of the water proton $I_s(k,t)$ into rotational and translational contributions; (c) the corresponding $S_s(k,E)$ and (d) dynamical susceptibility spectra ${\chi }^{\prime \prime }(k,E)$ at 150 K.

Figure 5

(a) Water incoherent structure factors $S_s(k,E)$ and (b) dynamical susceptibilities ${\chi }^{\prime \prime }(k,E)$ from the simulations at 150 K of systems 1 to 4 where increasing numbers of protein backbone atoms were held fixed, and the results from the system in which all the protein atoms were held fixed.

Figure 6

Coherent dynamical structure factors (left) and corresponding longitudinal spectra (right) of the hydration water from MD simulations of the RNase crystal at 150 K, for the unconstrained system (dashed lines) and the system with the protein atoms fixed (solid lines). From bottom to top: spectra for $k=0.5$, 1.5, 2.5, and $3.5{\AA }^{-1}$. Note the damping of the boson peak intensity ($\approx 3–4\mathrm{m}\mathrm{e}\mathrm{V}$) in $S(k,E)$ as the protein motion is hindered, while the 10 meV and $\approx 30\mathrm{m}\mathrm{e}\mathrm{V}$ Brillouin peaks (sound modes) are not affected.