Molecular recognition between proteins and ligands plays an important role in many biological processes, such as membrane receptor signaling and enzyme catalysis. Predicting the structures of protein-ligand complexes and finding ligands by virtual screening of small molecule databases are two long-standing goals in molecular biophysics and medicinal chemistry.^{1, 2} Solving both problems requires the development of an accurate and efficient scoring function to assess protein-ligand interactions.

Much effort has been devoted to developing scoring functions for modeling protein-ligand interactions.^{3–12} These scoring functions can be divided into three categories^{13}: potential or free energy functions based primarily on a molecular mechanics force field^{14–26}, knowledge-based statistical potentials based on distributions of intermolecular features in large databases of protein-ligand complex structures^{27–40}, and empirical-regression functions fitted to experimental binding constants of a training set of protein-ligand complexes.^{41–50}

Energy functions based on molecular mechanics force field generally estimate the binding affinity by summing van der Waals, electrostatic, desolvation, and/or entropy terms. The weights for various terms are sometimes obtained by fitting the energy function to experimental binding constants for a training set of protein-ligand complexes. Because of the rugged energy landscape, minimization is often required prior to energy evaluation. The identification of the global minimum in the energy landscape generally requires extensive conformational and configurational sampling.

Statistical potentials are based on distributions of intermolecular structural features extracted from large databases, such as Protein Data Bank (PDB)^{51} and Cambridge Structural Database (CSD).^{52} Statistical potentials have been widely used because of their relative simplicity, accuracy, and computational efficiency.^{53–98} During the last decade, several statistical potentials have been developed to describe protein-ligand interactions, such as PMF,^{27} SMoG2001,^{33} and DrugScore.^{30, 35} Still, many aspects of statistical potentials for protein-ligand interactions have not yet been systematically explored.

Here, we are interested in the following questions. First, can a statistical potential be used for distinguishing between ligands and nonbinding molecules, in addition to recognizing native binding modes? Second, can the accuracy of a statistical potential be improved by adding “negative” information, such as geometric decoys of the true ligands? Third, what is the accuracy of scoring complexes with modeled protein structures relative to that with crystallographic structures? Finally, what are the differences between the reference states for protein-ligand and protein-protein statistical potentials?

We describe two distance-dependent atomic statistical potentials derived from PDB - one for predicting the binding pose of a known ligand (PoseScore), and the other one for identifying ligands through virtual screening (RankScore). We proceed in three steps. First, distance distributions for the protein-ligand atom-type pairs were calculated from a sample of native complex structures (structures in the training and testing sets are excluded). Second, the distance-dependent atomic potential was derived from these distance distributions, and trained to find the optimal set of parameters for binding pose prediction (PoseScore) and ligand enrichment (RankScore), respectively. Third, PoseScore and RankScore were evaluated with the aid of two widely used docking benchmarks.^{11, 99} The performance of PoseScore and RankScore was compared to that of a number of other scoring functions.

We begin by describing the theory used to derive PoseScore and RankScore, criteria to evaluate the accuracy of each statistical potential, as well as the procedures and data sets used to derive, train, and test the statistical potentials (Methods). We then describe the accuracy of PoseScore and RankScore for docking against crystal structures of proteins in comparison to 14 and 7 other scoring functions, respectively (Results). We proceed by describing (i) the effect of including both native and non-native conformations of small molecules in the derivation of the statistical potentials, (ii) the accuracy of scoring against modeled protein structures, as well as (iii) the distribution of atomic protein-ligand distances. Finally, we discuss the implications of the results, relative successes and failures, and answer the questions raised above (Discussion and Conclusions).