Hydrophobic Term Modeling in Protein Energetics

The hydrophobic term was introduced by us in a previous version of our energy model.^{14 (link)} The original term was taken from a scoring function employed in docking calculations, ChemScore.^{50 (link)} The hydrophobic term rewards contacts between nonpolar heavy atoms and stabilizes hydrophobic contacts. As the effect of hydrophobic term is much smaller in one side chain than in a loop, in the VSGB 2.0 model we replaced the linear function with a polynomial and refit the parameters based on the loop predictions at lengths of 11–13 residues.
$$E_{\mathit{hydrophobic}}=\mathit{coeff}·\sum _{ij}{E}_{\mathit{hydrophobic}}^{ij}$$
$$E_{\mathit{hydrophobic}}^{ij}=\{\begin{array}{l}0.0(1\le \mathit{scale})\hfill \\ 0.25·{\mathit{scale}}^3-0.75·\mathit{scale}+0.5(-1.0<\mathit{scale}<1.0)\hfill \\ 1.0(\mathit{scale}\le -1.0)\hfill \end{array}$$ where
The coefficient in Eq. 11 was fit by a line search algorithm and the optimal value we obtained is −0.30. (Comparison of the linear function and polynomial is shown in Fig. S1 in supporting information.)
The hydrophobic term is intended to model the interaction of hydrophobic surfaces presented by various protein and ligand groups with water; when these groups make contacts (in the extreme case forming the hydrophobic core of the protein), unfavorable interactions with water are eliminated, and this effect drives hydrophobic packing. The atom-atom contact term described above represents an alternative to models which attempt to directly compute cavitation and van der Waals interactions of the solute atoms with the solvent. Our empirical investigations, initially described in ref. 14 (link) but continued over the past several years with extensive experiments on large data sets, suggest that the model of Eq. 12 and 13 provides superior predictions as compared to more standard approaches penalizing exposed hydrophobic surface area, which are generally derived from small molecules in bulk solution, a very different situation from hydrophobic groups embedded in an active site cavity, or otherwise positioned in confined spaces within a protein environment. Therefore, in the VSGB 2.0 model, we have eliminated the G_cav and G_vdw terms discussed above in Eq. 2 and 3, and replaced them with the hydrophobic term presented in this section. The quality of results for long loop prediction, which involve no further adjustment of the energy model, will serve as an unbiased test of the validity of this approach.