Elastic potential grids: accurate and efficient representation of intermolecular interactions for fully flexible docking.

Protein–ligand docking is the major workhorse in computeraided structure-based lead finding and optimization. Predicted protein–ligand complex configurations are used for studying protein–ligand interactions, estimating binding affinities, and as a final filter step in virtual screening. Early methods on protein–ligand docking treated either both proteins and ligands as rigid molecules or allowed for conformational flexibility of only the ligand, following a “rigid receptor hypothesis”. However, pronounced plasticity upon ligand binding has been observed for several pharmacologically important proteins, such as HIV-1 protease, aldose reductase, FK506 binding protein, renin, and dihydrofolate reductase (DHFR). Protein plasticity comprises a range of possible movements, from single side chains to drastic structural rearrangements as seen in calmodulin. Not surprisingly, if docking is performed with the assumption of a rigid active site in those cases, a dramatic decrease in docking accuracy is observed: Whereas a docking success rate of 76% was reported for docking a ligand back to the protein structure derived from the ligand’s co-crystal structure (“re-docking”), this rate dropped to only 49% if the ligands were docked against protein structures derived from other ligands’ co-crystal structures (“cross docking”). Similar drop-offs have also been reported by others. Furthermore, the drop in docking accuracy was found to be mirrored by the degree to which the protein moves upon ligand binding 32] so that docking to an empty form (“apo docking”) usually shows the largest deterioration. This clearly highlights the importance of developing strategies for taking protein plasticity into account in addition to the conformational flexibility of the ligand (henceforth referred to as “fully flexible docking”) to prevent mis-dockings of ligands to flexible proteins. At present, three major routes to include protein plasticity during docking can be identified. The classification correlates with various types of protein movements observed upon ligand binding. First, plasticity is considered implicitly following a soft-docking strategy with attenuated repulsive forces between protein and ligand. While this is simple to implement and does not compromise docking efficiency, the range of possible movements that can be covered is rather limited. Second, only side chain conformational changes in the binding pocket are modeled. These approaches assume that the protein has a rigid backbone structure, thus neglecting critical backbone shifts responsible for mis-docking of ligands. Third, large-scale conformational changes including backbone motions are taken into account. There are several types of approaches in this category: perform parallel docking into multiple protein conformations; structurally combine multiple conformations; model protein motions in reduced coordinates; apply molecular dynamics or Monte Carlo based sampling to either generate protein–ligand configurations 50] or optimize pre-computed configurations. Docking accuracy and computational efficiency determine the scope and quality of a docking approach. As for the first, fully flexible docking should ultimately become as accurate as “re-docking” pursued with a “rigid receptor hypothesis”. Preserving computational efficiency is equally important, given the short timeframe usually available for a docking run. In particular, evaluating the interaction energy between protein and ligand is expensive. A widely used approach to increase the calculation speed is based on potential fields that are pre-calculated just once in the binding pocket region of the protein, by scanning interactions between the protein and ligand atom probes. The potential field values are stored at the intersections of a regular 3D grid, providing a lookup table. The approach is applicable to all distance-dependent pairwise interactions, such as electrostatic and van der Waals interactions and interactions described by statistical pair potentials. In subsequent docking runs, interaction energies between protein and ligand are then determined in constant time from the lookup table by means of interpolation. This provides a significant rate increase relative to individually evaluating the pair interactions. However, this regular 3D grid-based approach is incompatible with fully flexible docking, because the lookup table values would need to be recalculated for every new protein conformation considered. In the present study, we therefore developed an accurate representation of intermolecular interactions that makes use of the high efficiency in evaluating protein–ligand interaction energies from lookup tables even in the case of a moving protein. The new lookup table function for potential fields that we introduce is based on irregular, deformable 3D grids (Figure 1). The underlying idea is to adapt a 3D grid with pre-calculated potential field values, which were derived from an initial protein conformation, to another conformation by moving intersection points in space, but keeping the potential field values constant. As in the case of a regular 3D grid, interaction energies between ligand and protein are then determined from this lookup table. In contrast to the established approach, however, new protein conformations can now be sampled [a] S. Kazemi, D. M. Kr ger, Prof. Dr. H. Gohlke Institut f r Pharmazeutische und Medizinische Chemie Heinrich-Heine-Universit t Universit tsstr. 1, 40225 D sseldorf (Germany) Fax: (+49)211-81-13847 E-mail : [email protected] [b] Dr. F. Sirockin Novartis Pharma AG, 4002 Basel (Switzerland) Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/cmdc.200900146.