He hybrid-resolution approach. doi:10.1371/journal.pone.0056645.gAngular Distance in Protein-Protein DockingFigure 4. Average hit count for the standard 66 rotational sampling and the hybrid-resolution approach. doi:10.1371/journal.pone.0056645.gprediction with the highest score becomes the center of the second cluster, and these steps are repeated until no predictions remain in the list. The resulting set of cluster centers represents a pruned set of predictions, which are spaced by at least the threshold. The clustering NMS-E628 process is finalized by determining how many predictions of the original set are NMS-E628 web within the threshold distance of each cluster center. For the pruning using angular distance we also explored a `translation-restricted’ variant of the algorithm. Predictions that have a translational difference of more than half the receptor size are not allowed to be in the same 23727046 cluster, as they are highly unlikely to belong to the same funnel. The translational difference is obtained from the three translational coordinates in the rigidbody docking, and the receptor size is defined as the average of the lengths of the protein in the directions of the three Cartesian axes. Because the translational difference is needed only for pairs of predictions that have angular distances under the angular threshold, this extension to the algorithm only increases the computational time moderately. An alternative approach to score-based pruning is to rank and prune based on the density of predictions. We explored two versions of density-based pruning. First we followed the ClusPro algorithm [31], which determines for each prediction the number of neighbors within a threshold distance, ranks accordingly, and uses this rank for a pruning step. Second, we used R to hierarchically cluster the predictions, and varied the height at which the branches are cut to find the best performance. For both density-based algorithms we used the top scoring 2000 predictions as starting point, and tested both RMSD and angular distance. The ZDOCK score was used to rank predictions that have identical densities. For the hierarchical clustering we used the complete linkage method, and the defined the medoid as the prediction that represents a cluster.Funnel AnalysisWe analyze the energy funnel around each prediction using angular distances and RMSD’s. For each prediction, we plot the docking scores of the N most similar predictions as a function of either angular distance or RMSD from the prediction. Using linear regression, we then determine the slope and intersect of the best-fit line of the plot and use them to characterize the energy funnel around the prediction in question. In addition, we calculate the average docking score of the N most similar predictions.Angular DistanceIn this work we use the angular distance as a measure of the similarity of two docking predictions. In our docking algorithm, the rotation of the ligand from its original coordinates is described by three successive rotations, represented by the Euler angles. The total angle resulting from the three successive rotations, however, is not simply the sum of the three Euler angles, nor is it the Pythagorean distance (as the three rotations are not orthogonal). The Euler representation is equivalent to the axis-angle representation, which rotates the object about a single vector in the 3D space. Because the direction of this vector can be described using two variables, the axis-angle representation has t.He hybrid-resolution approach. doi:10.1371/journal.pone.0056645.gAngular Distance in Protein-Protein DockingFigure 4. Average hit count for the standard 66 rotational sampling and the hybrid-resolution approach. doi:10.1371/journal.pone.0056645.gprediction with the highest score becomes the center of the second cluster, and these steps are repeated until no predictions remain in the list. The resulting set of cluster centers represents a pruned set of predictions, which are spaced by at least the threshold. The clustering process is finalized by determining how many predictions of the original set are within the threshold distance of each cluster center. For the pruning using angular distance we also explored a `translation-restricted’ variant of the algorithm. Predictions that have a translational difference of more than half the receptor size are not allowed to be in the same 23727046 cluster, as they are highly unlikely to belong to the same funnel. The translational difference is obtained from the three translational coordinates in the rigidbody docking, and the receptor size is defined as the average of the lengths of the protein in the directions of the three Cartesian axes. Because the translational difference is needed only for pairs of predictions that have angular distances under the angular threshold, this extension to the algorithm only increases the computational time moderately. An alternative approach to score-based pruning is to rank and prune based on the density of predictions. We explored two versions of density-based pruning. First we followed the ClusPro algorithm [31], which determines for each prediction the number of neighbors within a threshold distance, ranks accordingly, and uses this rank for a pruning step. Second, we used R to hierarchically cluster the predictions, and varied the height at which the branches are cut to find the best performance. For both density-based algorithms we used the top scoring 2000 predictions as starting point, and tested both RMSD and angular distance. The ZDOCK score was used to rank predictions that have identical densities. For the hierarchical clustering we used the complete linkage method, and the defined the medoid as the prediction that represents a cluster.Funnel AnalysisWe analyze the energy funnel around each prediction using angular distances and RMSD’s. For each prediction, we plot the docking scores of the N most similar predictions as a function of either angular distance or RMSD from the prediction. Using linear regression, we then determine the slope and intersect of the best-fit line of the plot and use them to characterize the energy funnel around the prediction in question. In addition, we calculate the average docking score of the N most similar predictions.Angular DistanceIn this work we use the angular distance as a measure of the similarity of two docking predictions. In our docking algorithm, the rotation of the ligand from its original coordinates is described by three successive rotations, represented by the Euler angles. The total angle resulting from the three successive rotations, however, is not simply the sum of the three Euler angles, nor is it the Pythagorean distance (as the three rotations are not orthogonal). The Euler representation is equivalent to the axis-angle representation, which rotates the object about a single vector in the 3D space. Because the direction of this vector can be described using two variables, the axis-angle representation has t.

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