Development of a method to improve the protein-ligand docking results with delaunay tessellation

In drug design studies, scoring functions are used to evaluate protein-ligand interactions and to determine the correct pose for molecular docking processes. Their ability to discriminate the native conformation from the poses is crucial. The data set used in the Comparative Assessment of Scoring Functions (CASF) evaluation in the PDBbind database serves as a benchmark to test these scoring functions. Vina scoring function was found to be the most successful using the benchmark set by CASF. A subset of this benchmark set constitutes approximately 100 binding poses for each of 57 proteins which were obtained by the CASF team using molecular mechanics methods. In this study, tetrahedra at the interface of protein and ligand are created by Delaunay tessellation using atoms' coordinates to examine the complexes in this set, and the averages of the aspect ratios of these tetrahedra are calculated. The high average aspect ratio of tetrahedra means that tetrahedra are less irregular which may indicate that the atoms are distributed in 3 dimensions uniformly. Based on the results of the analysis and previous studies, the following null hypothesis is made: the probability of finding that the average aspect ratio of tetrahedra at the protein-ligand interface is the highest among the three conformations that are the native conformation and two low energy poses identified by Vina is 1/3. To test this hypothesis, 48 proteins which Vina performed well were analyzed with a method that makes use of binding energy values of the poses and the native complex obtained by using Vina scoring function along with the average aspect ratio calculations. The null hypothesis created in this way is rejected (p-value 0.007). This finding shows that the atoms in the interface of protein-ligand complexes tend to be distributed homogenously.