  The paper presents an analytical theory and numerical simulations of the
dipolar response of hydrated proteins. The effective dielectric constant of the
solvated protein, representing the average dipole moment induced at the protein
by a uniform external field, shows a remarkable variation among the proteins
studied by numerical simulations. It changes from 0.5 for ubiquitin to 640 for
cytochrome c. The former value implies a negative dipolar susceptibility of
ubiquitin, that is a dia-electric dipolar response and negative
dielectrophoresis. It means that a protein carrying an average dipole of ~240 D
is expected to repel from the region of a stronger electric field. This outcome
is the result of a negative cross-correlation between the protein and water
dipoles, compensating for the positive variance of the protein dipole in the
overall dipolar susceptibility. This phenomenon can be characterized as
overscreening of protein's dipole by the hydration shell. In contrast to the
neutral ubiquitin, charged proteins studied here show para-electric dipolar
response and positive dielectrophoresis. The protein-water dipolar
cross-correlations are long-ranged, extending approximately 2 nm from the
protein surface into the bulk. The analysis of numerical simulations suggests
that the polarization of the protein-water interface is strongly affected by
the distribution of the protein surface charge. This component of the protein
dipolar response gains in importance for high frequencies, above the protein
Debye peak, when the response of the protein dipole becomes dynamically
arrested. The interface response found in simulations suggests a possibility of
a positive increment of the high-frequency dielectric constant of the solution
compared to the dielectric constant of the solvent, in support of the observed
THz absorbance of protein solutions.
