Studies of liquid water in its supercooled region have led to many insights
into the structure and behavior of water. While bulk water freezes at its
homogeneous nucleation temperature of approximately 235 K, for protein
hydration water, the binding of water molecules to the protein avoids
crystallization. Here we study the dynamics of the hydrogen bond (HB) network
of a percolating layer of water molecules, comparing measurements of a hydrated
globular protein with the results of a coarse-grained model that has been shown
to successfully reproduce the properties of hydration water. With dielectric
spectroscopy we measure the temperature dependence of the relaxation time of
protons charge fluctuations. These fluctuations are associated to the dynamics
of the HB network of water molecules adsorbed on the protein surface. With
Monte Carlo (MC) simulations and mean--field (MF) calculations we study the
dynamics and thermodynamics of the model. In both experimental and model
analyses we find two dynamic crossovers: (i) one at about 252 K, and (ii) one
at about 181 K. The agreement of the experiments with the model allows us to
relate the two crossovers to the presence of two specific heat maxima at
ambient pressure. The first is due to fluctuations in the HB formation, and the
second, at lower temperature, is due to the cooperative reordering of the HB
network