Hydrophobic Interactions

PIPER is an FFT based docking program that uses a pairwise interaction potential as part of its scoring function E=E_attr+w₁E_rep+w₂E_elec+w₃E_pair, where E_attr and E_rep denote the attractive and repulsive contributions to the van der Waals interaction energy E_vdw, E_elec is an electrostatic energy term, and E_pair represents the desolvation contributions.^{4 (link)}E_pair has been parameterized on a set of complexes that included a substantial number of enzyme-inhibitor pairs and multi-subunit proteins, and hence the resulting potential assumes good shape and electrostatic complementarity. The coefficients w₁, w₂, and w₃ specify the weights of the corresponding terms, and are optimally selected for different types of docking problems (see below). In order to evaluate the energy function E by FFT, it must be written in the form of correlation functions. The terms E_vdw and E_elec satisfy this condition, and E_pair can be expressed as a sum of a few correlation functions using the eigenvalue-eigenvector decomposition of the matrix of interaction energy coefficients.^{4 (link)}Unless specified otherwise in Advanced Options, ClusPro 2.0 simultaneously generates four types of models using the scoring schemes called (1) balanced, (2) electrostatic-favored, (3) hydrophobic-favored, and (4) van der Waals + electrostatics. The balanced option works generally well for enzyme-inhibitor complexes, whereas options (2) and (3) are suggested for complexes where the association is primarily driven by electrostatic and hydrophobic interactions, respectively. The fourth option, van der Waals + electrostatics, means that w₃=0, i.e., the pairwise potential E_pair is not used. The need for this option occurs for proteins that are very different from the ones used for the parameterization of E_pair. Two specific cases can be selected as Advanced Options. In the “Antibody Mode”, ClusPro 2.0 uses a recently developed asymmetric potential for docking antibody and antigen pairs.^{26 (link)} The “Other Mode” targets the so-called “other” type of complexes that primarily occur in signal transduction pathways,^{27 (link)} and generally have substantially less perfect shape and electrostatic complementarity than the enzyme-inhibitor complexes. Due to the diverse nature implied by the “other” classification, this mode chooses 500 conformations from three diverse sets of weighting coefficients to give 1500 conformations. Our initial research using a diversity of coefficients is indicative that the “other” type of complexes can likely be further classified into subtypes for which a particular coefficient set works well. While it is difficult to perform automated selection of the best scoring function, users frequently have some information on the type of the particular complex considered. If such information is not available, it may be useful to select the function that yields large clusters of docked structures with relatively low energies. As will be shown, this simple albeit somewhat ambiguous rule provided good model selection in the current rounds of CAPRI.

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.