Untangling influences of hydrophobicity on protein sequences and structures.

We perform a statistical analysis of solvent accessibility and hydrophobicity profiles of a representative set of proteins. The joint probability distribution is well fitted to a multivariable Gaussian, which takes a relatively simple form when expressed in terms of the Fourier transforms of the profiles. This allows us to quantify the asymmetric manner by which these profiles influence each other. For example, the alpha-helix periodicity in sequence hydrophobicity is dictated by the solvent accessibility of structures, and not vice versa, possibly indicating the faster evolution of sequences compared to structures. The decorrelated hydrophobicity and solvent accessibility profiles show distinct behaviors at long periods, where sequence hydrophobicity fluctuates less, while solvent accessibility fluctuates more than average. The correlations between the two profiles can be interpreted as the Boltzmann weight of the solvation energy at room temperature, consistent with earlier observations.