  We investigate the presence of structural collective motions on a picosecond
time scale for the heme protein, cytochrome c, as a function of oxidation and
hydration, using terahertz (THz) time-domain spectroscopy and molecular
dynamics simulations. The THz response dramatically increases with oxidation,
with the largest increase for lowest hydrations and highest frequencies. For
both oxidation states the THz response rapidly increases with hydration
saturating above ~25% (g H2O/g protein). Quasi-harmonic vibrational modes and
dipole-dipole correlation functions are calculated from molecular dynamics
trajectories. The collective mode density of states alone reproduces the
measured hydration dependence providing strong evidence of the existence of
these motions. The large oxidation dependence is reproduced only by the
dipole-dipole correlation function, indicating the contrast arises from
diffusive motions consistent with structural changes occurring in the vicinity
of a buried internal water molecule.
