A procedure for detection and quantitation of cavity volumes in proteins. Application to measure the strength of the hydrophobic driving force in protein folding

Accurate identification of cavities is important in the study of protein structure, stability, design, and ligand binding. Identification and quantitation of cavities is a nontrivial problem because most cavities are connected to the protein exterior. We describe a computational procedure for quantitating cavity volumes and apply this to derive an estimate of the hydrophobic driving force in protein folding. A grid-based Monte Carlo procedure is used to position water molecules on the surface of a protein. A Voronoi procedure is used to identify and quantitate empty space within the solvated protein. Additional cavities not detected by other existing procedures can be identified. Most of these are close to surface concavities. Residue volumes for both the interior and the surface residues as well as cavity volumes are in good agreement with volumes calculated from fully hydrated protein structures obtained from molecular dynamic simulations. We show that the loss of stability because of cavity-creating mutations correlates better with cavity volumes determined by this procedure than with cavity volumes determined by other methods. Available structural and thermodynamic data for a number of cavity-containing mutants were analyzed to obtain estimates of 26.1 $cal.mol^{-1}.\AA^{-3}$ and 18.5 $cal.mol^{-1}.\AA^{-2}$ for the relative contributions of cavity formation and the hydrophobic effect to the observed stability changes. The present estimate for the hydrophobic driving force is at the lower end of estimates derived from model compound studies and considerably lower than previous estimates of approximately 50 $cal.mol^{-1}.\AA^{-2}$ derived from protein mutational data. In the absence of structural rearrangement, on average, deletion of a single methylene group is expected to result in losses in stability of 0.41 and 0.70 $kcal.mol^{-1}$ resulting from decrease in hydrophobicity and packing, respectively