  We fit the Fourier transforms of solvent accessibility and hydrophobicity
profiles of a representative set of proteins to a joint multi-variable
Gaussian. This allows us to separate the intrinsic tendencies of sequence and
structure profiles from the interactions that correlate them; for example, the
$\alpha$-helix periodicity in sequence hydrophobicity is dictated by the
solvent accessibility of structures. The distinct intrinsic tendencies of
sequence and structure profiles are most pronounced at long periods, where
sequence hydrophobicity fluctuates more, while solvent accessibility
fluctuations are less than average. Interestingly, correlations between the two
profiles can be interpreted as the Boltzmann weight of the solvation energy at
room temperature.
