  We consider continuum dielectric models as minimal models to understand the
effect of a surrounding globular protein and solvent on the quantum dynamics of
electronic excitations in a biological chromophore. We derive expressions for
the frequency dependent spectral density which describes the coupling of the
electronic levels in the chromophore to its environment. The magnitude and
frequency dependence of the spectral density determines whether or not the
quantum dynamics is coherent or incoherent, and thus whether on not one can
observe quantum interference effects such as Rabi oscillations. We find the
contributions to the spectral density from each component of the chromophore
environment: the bulk solvent, protein, and water bound to the protein. The
relative importance of each component to the quantum dynamics of the
chromophore is determined by the dynamics' time scale. Our results provide a
natural explanation and model for the different time scales observed in the
spectral density extracted from the solvation dynamics probed by ultra-fast
laser spectroscopy techniques such as the dynamic Stokes shift and three pulse
photon echo spectroscopy. Our results are used to define under what conditions
the dynamics of the excited chromophore is dominated by the surrounding protein
and when it is dominated by dielectric fluctuations in the solvent. We show
that even when the chromophore is shielded from the solvent by the protein
ultra-fast solvation can be dominated by the solvent. We suggest that the
ultra-fast solvation recently seen in some biological chromophores should not
necessarily be assigned to ultra-fast protein dynamics. Spectral densities
estimated from our continuum models and extracted from experiment suggest that
most quantum dynamics of electronic excitations is incoherent.
