A Protein Solvation Model Based on Residue Burial

The influence of solvent on the individual amino acids of a protein depends not simply on their surface exposure but rather on the degree of their burial within the structure. This property can be related to a simple geometrical measure termed circular variance. Circular variance depends on the spatial distribution of neighboring residues and varies from zero to one as a residue becomes buried. Its only adjustable parameter is a cutoff distance for selecting neighbors. Here, we show that circular variance can be used to build a fast and effective model of protein solvation energies. For this, we combine a coarse-grain protein representation with statistical potentials derived by Boltzmann inversion of circular variance probability distributions for different classes of pseudoatom within a large protein structure database. The method is shown to work well for distinguishing native protein structures from decoy structures generated in a variety of ways. It can also be used to detect specific residues in unfavorable solvent environments. Compared to surface accessibility, circular variance calculations are faster, less sensitive to small conformational changes, and able to account for the longer-range interactions that characterize the electrostatic component of solvent effects. The resulting solvation energies can be used alone or as part of a more general coarse-grain protein model.