Distinguishing dynamical features of water inside protein hydration layer: Distribution reveals what is hidden behind the average.

Since the pioneering works of Pethig, Grant, and Wüthrich on a protein hydration layer, many studies have been devoted to find out if there are any "general and universal" characteristic features that can distinguish water molecules inside the protein hydration layer from bulk. Given that the surface itself varies from protein to protein, and that each surface facing the water is heterogeneous, search for universal features has been elusive. Here, we perform an atomistic molecular dynamics simulation in order to propose and demonstrate that such defining characteristics can emerge if we look not at average properties but the distribution of relaxation times. We present results of calculations of distributions of residence times and rotational relaxation times for four different protein-water systems and compare them with the same quantities in the bulk. The distributions in the hydration layer are unusually broad and log-normal in nature due to the simultaneous presence of peptide backbones that form weak hydrogen bonds, hydrophobic amino acid side chains that form no hydrogen bond, and charged polar groups that form a strong hydrogen bond with the surrounding water molecules. The broad distribution is responsible for the non-exponential dielectric response and also agrees with large specific heat of the hydration water. Our calculations reveal that while the average time constant is just about 2-3 times larger than that of bulk water, it provides a poor representation of the real behaviour. In particular, the average leads to the erroneous conclusion that water in the hydration layer is bulk-like. However, the observed and calculated lower value of static dielectric constant of hydration layer remained difficult to reconcile with the broad distribution observed in dynamical properties. We offer a plausible explanation of these unique properties.