  Since the pioneering works of Pethig, Grant and Wuthrich on 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
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 is 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 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.
