  The extent to which biological interfaces affect the dynamics of water plays
a key role in the exchange of matter and chemical interactions that are
essential for life. The density and the mobility of water molecules depend on
their proximity to biological interfaces and can play an important role in
processes such as protein folding and aggregation. In this work, we study the
dynamics of water near glutamine surfaces---a system of interest in studies of
neurodegenerative diseases. Combining molecular-dynamics simulations and
stochastic modelling, we study how the mean first-passage time and related
statistics of water molecules escaping subnanometer-sized regions vary from the
interface to the bulk. Our analysis reveals a dynamical complexity that
reflects underlying chemical and geometrical properties of the glutamine
surfaces. From the first-passage time statistics of water molecules, we infer
their space-dependent diffusion coefficient in directions normal to the
surfaces. Interestingly, our results suggest that the mobility of water varies
over a longer length scale than the chemical potential associated with the
water-protein interactions. The synergy of molecular dynamics and first-passage
techniques opens the possibility for extracting space-dependent diffusion
coefficients in more complex, inhomogeneous environments that are commonplace
in living matter.
