Protein side chain modeling with orientation-dependent atomic force fields derived by series expansions

We describe the development of new force fields for protein side chain modeling called optimized side chain atomic energy (OSCAR). The distance-dependent energy functions (OSCAR-d) and side-chain dihedral angle potential energy functions were represented as power and Fourier series, respectively. The resulting 802 adjustable parameters were optimized by discriminating the native side chain conformations from non-native conformations, using a training set of 12,000 side chains for each residue type. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. Then, the OSCAR-d were multiplied by an orientation-dependent function to yield OSCAR-o. A total of 1087 parameters of the orientation-dependent energy functions (OSCAR-o) were optimized by maximizing the energy gap between the native conformation and subrotamers calculated as low energy by OSCAR-d. When OSCAR-o with optimized parameters were used to model side chain conformations simultaneously for 218 recently released protein structures, the prediction accuracies were 88.8% for χ₁, 79.7% for χ_{1 + 2}, 1.24 ̊ overall root mean square deviation (RMSD), and 0.62 ̊ RMSD for core residues, respectively, compared with the next-best performing side-chain modeling program which achieved 86.6% for χ₁, 75.7% for χ_{1 + 2}, 1.40 ̊ overall RMSD, and 0.86 ̊ RMSD for core residues, respectively. The continuous energy functions obtained in this study are suitable for gradient-based optimization techniques for protein structure refinement. A program with built-in OSCAR for protein side chain prediction is available for download at.