Anomalous diffusion of adsorbed water: a neutron scattering study of hydrated myoglobin

The neutron scattering spectrum of bound H2O has been determined from the excess scattering of H2O-hydrated myoglobin relative to a sample hydrated with D2O. The resulting vibrational difference spectrum shows the well known translational and librational bands of bulk water. Significant discrepancies arise at low frequencies indicating that the diffusive motion is strongly retarded by interactions with the protein surface. By Fourier deconvolution of constant Q-spectra we obtain the intermediate scattering function and the time-resolved mean square displacement of the water protons on a 15 ps timescale. We observe a sublinear increase in the squared displacements with time suggesting anomalous diffusion. Furthermore, the fourth moment 〈r4(t)〉 exceeds the value expected for a Gaussian distribution, which indicates either strong heterogeneity or anisotropic motions. The data are discussed in relation to simulations and theoretical results on strongly coupled liquids.