Four-dimensional docking: a fast and accurate account of discrete receptor flexibility in ligand docking

Abstract

Many available methods aimed at incorporating the receptor flexibility in ligand docking are computationally expensive, require a high level of user intervention, and were tested only on benchmarks of limited size and diversity. Here we describe the four-dimensional (4D) docking approach that allows seamless incorporation of receptor conformational ensembles in a single docking simulation and reduces the sampling time while preserving the accuracy of traditional ensemble docking. The approach was tested on a benchmark of 99 therapeutically relevant proteins and 300 diverse ligands (half of them experimental or marketed drugs). The conformational variability of the binding pockets was represented by the available crystallographic data, with the total of 1113 receptor structures. The 4D docking method reproduced the correct ligand binding geometry in 77.3% of the benchmark cases, matching the success rate of the traditional approach but employed on average only one-fourth of the time during the ligand sampling phase.

Figure 1

The extent of induced fit for the ERR and its treatment. (A) Schematic representation of the two different ensemble docking approaches compared in the present study. (B) Three different crystal structures of the EER Ligand Binding Domain are represented after superimposition without ligands. The variations of Phe435, AF-2 helix, and the binding pocket shape are highlighted.

Figure 1

The extent of induced fit for the ERR and its treatment. (A) Schematic representation of the two different ensemble docking approaches compared in the present study. (B) Three different crystal structures of the EER Ligand Binding Domain are represented after superimposition without ligands. The variations of Phe435, AF-2 helix, and the binding pocket shape are highlighted.

Figure 2

Evaluating the time required for 4D docking convergence as a function of the number of conformers in a 4D ensemble and their conformational variation. (A) The 4D docking time in case of identical copies of the cognate receptor (cyan blue curve). (B) The 4D docking time with two types of conformers: a cognate conformer and multiple copies of an extra conformer. The pocket variants are provided by a Type I inhibitor bound structure (pink curve) and by a Type II inhibitor bound structure (yellow curve). (C) The 4D docking time to all available different pocket conformers (orange curve). Each point represents the median value of all the possible combinations of n<=5 conformers. In each panel, the MRC docking ideal case (white curve) is reported for comparison. Each reported value is averaged over 100 runs.

Figure 3

The 4D docking protocol (blue markers, upper left quadrant) combines the accuracy of the MRC docking (orange markers, upper right quadrant) with the speed of single conformer cross-docking (yellow marker, lower left quadrant).

Figure 4

A diagram of the accuracy versus the ensemble size. The histograms compare the MRC (orange) and 4D (blue) results considering, instead of the whole validation set, three subsets divided according to the number of structures in each ensemble (between 3 and 8, between 9 and 14, and between 15 and 29, respectively) to the performance of the single rigid conformer docking (yellow histogram). A dashed line represents the accuracy trend. (A) The cognate receptor structure is included in the ensemble docking calculations. (B) The cognate receptor structure is not included in the ensemble docking calculations.

Figure 4

A diagram of the accuracy versus the ensemble size. The histograms compare the MRC (orange) and 4D (blue) results considering, instead of the whole validation set, three subsets divided according to the number of structures in each ensemble (between 3 and 8, between 9 and 14, and between 15 and 29, respectively) to the performance of the single rigid conformer docking (yellow histogram). A dashed line represents the accuracy trend. (A) The cognate receptor structure is included in the ensemble docking calculations. (B) The cognate receptor structure is not included in the ensemble docking calculations.

Figure 5

4D docking results summary. The fraction of ligands that can be correctly reproduced by both single rigid conformer cross-docking and 4D docking, the fraction that can be correctly reproduced only by 4D docking without including the cognate receptor in the structural ensemble, and the fraction that can be correctly reproduced only by 4D docking and only when the cognate receptor is included in the structural ensemble are reported in blue, cyan blue, and yellow, respectively. The fraction of ligands which can be correctly sampled but not ranked in the top position and the fraction that cannot be selected at all, are reported in orange and red, respectively.