Near-Native Selections from Docking Decoys optimization and energy minimization31,55,56–59 are important strategies for improving near-native selections from docking decoys. However, unrealistic nonspecific binding affinity proportional to the interface size is often observed for the structurally refined complexes. This makes it difficult to identify the near-native complexes with a small interface from non-native decoys with large interfaces.60 In this article, we extend an empirical energy function originally developed for protein design to protein–protein docking prediction. We find that this energy function to- gether with a simple reference state provides a significant improvement in docking-structure prediction for structur- ally refined docking decoys. The reference state works by removing the unrealistic dependence of binding affinity of docking decoys on the buried solvent accessible surface area of interface. METHODS RosettaDock set: A refined set of docking decoys The RosettaDock set consists of 54 protein–protein decoy sets [version 1.0 of Chen-Mintseris-Janin-Weng’s bench- mark61] downloaded from the website http://graylab. jhu.edu/docking/decoys/. The decoy sets are generated by random starting position of unbound monomer compo- nents superimposed on the native bound complex structure, followed by RosettaDock protocol to create a diffuse space distribution that covers a reasonable area (20 A˚ radius rmsd) with moderate density around the native position. Each decoy set has 1000 decoys/protein complex (For more detailed description, see Ref. 41). All structures in the Ros- settaDock set have optimized sidechain conformations and their energies were minimized to reduce steric clashes. ZDOCK set: An unrefined set of docking decoys The ZDOCK 2.3 decoy set is made of 48 protein–pro- tein complexes (downloaded from http://zlab.bu.edu/ rong/dock/software.shtml). Each protein complex con- tains 2000 docking decoys. The decoy sets were generated using fast Fourier transform (FFT) algorithm based on the PDE scoring function that combines pairwise shape com- plementarity (PSC) with desolvation energy (DE) and electrostatic energy (ELEC).40 These decoy sets are from direct docking of unbound structures without either side- chain optimization or energy minimization. The ZDOCK set is structurally refined in a procedure described below. Structural refinement of docking decoys from ZDOCK Sidechain optimization We used an empirical sidechain score for sidechain opti- mization that was originally developed for protein design.62 The score calculates the energy of a sidechain rotamer (R) of DOI 10.1002/prot a residue, the representative conformation of the amino acid, placed on its backbone position. The score function is a linear combination of multiple energetic terms: DGsidechainðRiÞ ¼ 0:143 Scontact þ 0:724 Voverlap þ 1:72 Ehbond þ 28:6 Eelec 0:0467 DSpho þ 0:0042 DSphi þ 1:14 DðFphiÞ30 þ 7:95 Vexclusion 0:919 lnðf1f2Þ 4:3 Nssbond DGref ; 1 ð Þ where Scontact, Voverlap, Ehbond, Eelec, DSpho, and DSphi are atom-contact surface area, overlap volume, hydrogen bonding energy, electrostatic interaction energy, buried hydrophobic solvent accessible surface, and buried hydro- philic solvent accessible surface between the rotamer of residue i and the rest of the protein, respectively; Fphi is the fraction of the buried surface of non-hydrogen-bonded hydrophilic atoms; D(Fphi)30 is the difference between the rotamer positioned in the protein environment and the isolated form; Vexclusion is the normalized solvent exclusion volume around charged atoms63; f1 is the observed fre- quency of the rotamer and f2 is the observed frequency of the amino acid residues in a given backbone conforma- tion; Nssbond is the flag of disulfide bridge (1 or 0); DGref is the reference value for the free energy difference between the rotamer in solvent and in a denatured protein.64 The weights of these energy terms together with the reference values (DGref) were optimized so that the native residues are predicted energetically favorable over other residue types at each position of the training proteins.62 Here, the contact surface area (Scontact) is applied to evaluate geo- metric complementarity between a rotamer and its protein environment65 while the buried solvent accessible surface area accounts for the effect of solvation. This sidechain score is used because its simplified version yields one of the most accurate sidechain prediction method.65 For sidechain modeling, we are only interested in the energy difference between different sidechain rotamers. Thus, the terms f2 and DGref will make no contribution for sidechain modeling because they are unchanged. They are not considered in the actual calculation. We use the back- bone-dependent rotamer library developed by Dunbrack and Cohen.66 The updated library was downloaded from http://dunbrack.fccc.edu/bbdep/index.php. Polar hydrogen atoms, absent in the Dunbrack library, are added to calcu- late electrostatic interactions. The program REDUCE67 is used to add hydrogen atoms to all proteins. Refinement algorithm A two-step refinement algorithm is developed for dock- ing decoys. Sidechain modeling. For a given complex structure, only sidechain conformations of interface residues are opti- mized. Interface residues are surface residues of monomers whose solvent accessible surface areas are decreased by PROTEINS 245