  The low-frequency collective vibrational modes in proteins as well as the
protein-water interface have been suggested as dominant factors controlling the
efficiency of biochemical reactions and biological energy transport. It is thus
crucial to uncover the mystery of hydration structure and dynamics as well as
their coupling to collective motions of proteins in aqueous solutions. Here we
report dielectric properties of aqueous bovine serum albumin protein solutions
as a model system using an extremely sensitive dielectric spectrometer with
frequencies spanning from megahertz to terahertz. The dielectric relaxation
spectra reveal several polarization mechanisms at the molecular level with
different time constants and dielectric strengths, reflecting the complexity of
protein-water interactions. Combining the effective-medium approximation and
molecular dynamics simulations, we have determined collective vibrational modes
at terahertz frequencies and the number of water molecules in the tightly-bound
and loosely-bound hydration layers. High-precision measurements of the number
of hydration water molecules indicate that the dynamical influence of proteins
extends beyond the first solvation layer, to around 7 {\AA} distance from the
protein surface, with the largest slowdown arising from water molecules
directly hydrogen-bonded to the protein. Our results reveal critical
information of protein dynamics and protein-water interfaces, which determine
biochemical functions and reactivity of proteins.
