  We cast the problem of protein transfer free energy within the formalism of
density functional theory (DFT), treating the protein as a source of external
potential that acts upon the solvent. Solvent excluded volume,
solvent-accessible surface area, and temperature-dependence of the transfer
free energy all emerge naturally within this formalism, and may be compared
with simplified "back of the envelope" models, which are also developed here.
Depletion contributions to osmolyte induced stability range from 5-$10\kB T$
for typical protein lengths. The general DFT transfer theory developed here may
be simplified to reproduce a Langmuir isotherm condensation mechanism on the
protein surface in the limits of short-ranged interactions, and dilute solute.
Extending the equation of state to higher solute densities results in
non-monotonic behavior of the free energy driving protein or polymer collapse.
Effective interaction potentials between protein backbone or sidechains and
TMAO are obtained, assuming a simple backbone/sidechain 2-bead model for the
protein with an effective 6-12 potential with the osmolyte. The transfer free
energy $\delta g$ shows significant entropy: $d(\delta g)/dT \approx 20 \kB$
for a 100 residue protein. The application of DFT to effective solvent forces
for use in implicit-solvent molecular dynamics is also developed. The simplest
DFT expressions for implicit-solvent forces contain both depletion interactions
and an "impeded-solvation" repulsive force at larger distances.
