S.Liang et al. Figure 4 The binding affinity as a function of the buried solvent accessible surface area of interface for EMPIRE with or without the reference state (target 1ATN). Only top-ranked 500 decoys are shown. The solid line denotes the result from linear regression on the data given by EMPIRE without the reference state (with a correlation coefficient of 0.54). There is no correlation for the data given by EMPIRE (with the reference state). incorporating the reference state in EMPIRE, near-native structures become a part of low energy conformations. Figure 4 further shows that there is a correlation between the buried solvent accessible surface area and binding af- finity for EMPIRE without reference state. The correlation coefficient is 0.54. The use of the reference state in EMPIRE effectively removes this correlation (the correla- tion coefficient becomes 0.02). Thus, removing the unreal- istic dependence of binding affinity on the buried solvent accessible surface area of interface is the main reason for the success of EMPIRE. DISCUSSION In this article, we successfully construct an empirical energy function for docking prediction by adding a simple reference state to a scoring function originally developed for protein design. The new scoring function, called EMPIRE, is tested in RosettaDock with or without further energy minimization. The success rates (3 or more in top five ranked decoys that are ‘‘near-native’’) are 69% with the original decoys and 72% with further energy minimi- zation, respectively. This can be compared to 63% made by RosettaDock.41,71 EMPIRE is further tested in ZDOCK 2.3 decoy set. It successfully ranks 20 near-native complex structures in top 250 PROTEINS 1. We have also applied EMPIRE to the ZDOCK 2.1 decoy set. This leads to 14 successful predictions. The reduction of the number of successful predictions is expected because the ZDOCK 2.1 decoy set has a much smaller number of near-native-structures (27 per complex) than the ZDOCK 2.3 decoy set (46 per complex in average). On the other hand, RDOCK, a structural refinement and scor- ing protocol, performs much better on the ZDOCK 2.1 decoys than on the ZDOCK 2.3 decoys.59 The number of successful prediction for RDOCKþZDOCK 2.1 (top 1) is 18, compared to 20 for EMPIREþZDOCK 2.3. For each target, a higher number of near-native struc- tures corresponds well with the improved ability of EMPIRE in detecting near-native structures. In fact, for all targets with 24 or more near-native structures in their decoys (1.2%), there is at least one near-native structure ranked within top 10 after energy minimization. This is true regardless if a complex is an enzyme-inhibitor, anti- body-antigen, or other complex. That is, a lower success rate in ranking near-native structures of antibody-antigen complexes than that of enzyme-inhibitor complexes reflects a smaller number of near-native structures in ZDOCK docking decoy sets of the former complexes. This suggests the robustness of the EMPIRE energy function in identification of near-native structures. It is of interest to note that RosettaDock is somewhat better than EMPIRE in detecting near-native structures for antibody-antigen complexes (EMPIRE recognizes more near-native struc- tures within top five in four antibody-antigen complexes and less so in six complexes than RosettaDock, Table I). This may be related to the fact that many of these anti- body-antigen complexes are used in training the weights of energy terms of RosettaDock.41,71 The success of the EMPIRE score function highlights the importance of removing nonspecific interactions. Pro- teins interact with each other via recognizing specific interfaces, rather than according to the size of interfaces. However, an unrealistic correlation between binding affin- ity and the interface area is often observed for structurally refined complexes (Fig. 4). This unrealistic correlation is possibly caused by local energy minimization with an ap- proximate energy function. In general, more minimization leads to higher binding affinity. Although binding affin- ities of near-native decoys may increase faster than those of non-native decoys with a similar interface area during minimization, binding affinities of decoys with a large interface will increase even faster. EMPIRE attempts to remove this artifact empirically by subtracting an interface reference state. The removal of the unrealistic dependence of binding affinities on interface areas is an empirical approach. One issue with this approach is that the performance of EMPIRE will depend on refinement protocol. This is because longer energy minimization will further increase binding affinities of docking decoys and the rate of increase depends on interface areas and other factors. As a DOI 10.1002/prot