Near-Native Selections from Docking Decoys result, EMPIRE will work best with a fixed minimization step that leads to a nativelike binding affinity. This high- lights the approximate nature of the EMPIRE energy func- tion. The RDOCK refinement protocol59 obviously has the same problem. The number of steps in its refinement procedure is precisely defined. We examined the dependence of reference parameters on minimization steps. This is done by varying c2 in Eq. (3) at an interval of 0.001 to make the best near-native prediction for docking decoys with different refinement procedures. The best performances are a total of 14, 21, 20, and 24 targets successfully predicted (NP ¼ 1) after sidechain modeling, and sidechain modeling plus 50, 100, and 200 steps of energy minimization, respectively. Thus, optimizing c2 can increase the prediction success rate for decoys refined by 100 or 200 steps of energy minimization, compared to c2 obtained from native structures and exper- imental-binding affinities. As a result, a stronger interface reference value would be needed to counter the increase of binding affinities for over optimized decoy sets. Indeed, we find that the best c2 value for the decoy set refined by 200 steps of energy minimization yields binding affinities that are close to the experimental values. Although this value yields the highest success rate (24 targets), we prefer 50 steps of minimization and the parameters independ- ently generated from native structures and experimental- binding affinities. This is to avoid overoptimization. One interesting result is that EMPIRE performs well for some difficult targets (1BTH to 3HHR in Table I). We found that this is mainly because of the improvement of correlation between rmsd values and energy scores after the introduction of the reference state. Figure 5 displays the rmsd values of decoys as a function of their energy scores with and without the reference state in EMPIRE for a difficult target 1GOT. The correlation coefficient between rmsd values and energy scores increases from 0.12 to 0.41 after the reference state is used in EMPIRE. Without the interface reference state, the selected decoys with the lowest interaction energy have a overwhelmingly larger interface than the near-native docking decoys. Some docking decoys were made from the docking between an unbound structure and a bound one (Table II). EMPIRE performs better on those targets than the decoys from unbound–unbound docking. For example, near-native structures for unbound–bound-docked en- zyme-inhibitor targets are all ranked number 1. The dif- ference between unbound-unbound and unbound-bound docking is largely because there are more near-native structures in unbound-bound decoys. The most time-consuming part of calculations in this study is sidechain optimization via simulated annealing. Sidechain modeling for 2000 decoys typically takes 1–3 weeks on a single 2.6 GHz AMD Opteron CPU. We use our in-house sidechain optimization since its simplified version is one of the most accurate sidechain prediction algorithms.65 For sidechain modeling, EMPIRE is 1–2 DOI 10.1002/prot Figure 5 As in Figure 1, but compares the binding affinity for EMPIRE with or without the reference state (target 1GOT). Only top-ranked 500 decoys are shown. The solid lines denote the result from linear regression on the data with a correlation coefficient of 0.12 for EMPIRE without the reference state and 0.41 for EMPIRE. times slower than its simplified version but the prediction accuracy is similar. In this study, we use the same energy function for intraprotein and interprotein interactions (except the reference state) that allows a consistent evalua- tion of the energy function. An executable version of the EMPIRE score function and its corresponding webserver are freely available at http://sparks.informatics.iupui.edu. ACKNOWLEDGMENTS We gratefully thank Professors Jeffrey J. Gray and David Baker for providing us the RosettaDock docking decoy sets, Professor Ziping Weng, Dr. Rong Chen, and Ms. Li Li for ZDOCK decoys. REFERENCES 1. Camacho CJ, Vajda S. Protein–protein association kinetics and pro- tein docking. Curr Opin Struct Biol 2002;12:36–40. 2. Vajda S, Vakser I, Sternberg M, Janin J. Modeling of protein inter- actions in genomes. Proteins 2002;47:444–446. 3. Smith GR, Sternberg MJE. Prediction of protein–protein interac- tions by docking methods. Curr Opin Struct Biol 2002;12:28–35. 4. Halperin I, Ma B, Wolfson H, Nussinov R. Principles of docking: an overview of search algorithms and a guide to scoring functions. Proteins 2002;47:409–443. PROTEINS 251