Absolute Binding Free Energies between T4 Lysozyme and 141 Small Molecules: Calculations Based on Multiple Rigid Receptor Configurations

Abstract

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. On the basis of T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root-mean-square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/surface area implicit solvent was comparable to that of previously reported free energy calculations.

Figure 1

Ligands used in YANK calculations to generate snapshots for BPMF calculations: i) methylpyrrole, ii) benzene, iii) p-xylene, iv) phenol, v) n-hexylbenzene, and vi) (±)-camphor.

Figure 2

Configurations of n-hexylbenzene sampled at 600 K without a receptor interaction grid. The secondary structure of T4 lysozyme is shown as a ribbon. The protein structure is from an alchemical pathway calculation of DL-camphor binding.

Figure 3

Ligand configurations sampled at 300 K with a full receptor interaction grid. Clockwise from the upper left: thianaphthene, o-xylene, 1-methylpyrrole, and ethanol. The secondary structure of T4 lysozyme is shown as a ribbon. The protein structure is from an alchemical pathway calculation of p-xylene binding.

Figure 4. Convergence of AlGDock calculations

The standard deviation of free energy estimates as a function of the number of replica exchange cycles, for (a) changing the ligand temperature from 300 K to 600 K, and (b) scaling the receptor-ligand interaction grid from 0 to 1 while decreasing the temperature. Values were calculated between dipropyl disulfide, thianaphthene, isobutylbenzene, dibutyl-disulfide, phenylacetylene, cyclohexane, 1-heptanol, 1-propanol, 1,1-diethylurea, p-xylene, and a snapshot of T4 lysozyme from an alchemical pathway calculation with n-hexylbenzene. The thick black line is the average of the standard deviation across the 10 complexes.

Figure 5. Comparing representative snapshots with discrete conformations

Principal components analysis was performed for the heavy atoms of helix F (residues 107 to 115) based on the crystal structures 2OTZ, 3DN3, and 1QUD, which represent closed (square), intermediate (circle), and open (diamond) conformations, respectively. The 576 representative snapshots (black dots) were then projected onto these eigenvectors.

Figure 6

Binding free energies for 24 ligands estimated using YANK (x-axis) and AlGDock (y-axis) based on the OBC2 implicit solvent model. Active molecules are shown as red circles and inactive molecules as blue circles. The labels correspond to different weighting schemes (see text for details). Error bars denote the standard deviation from three independent YANK calculations (x-axis) or from bootstrapping BPMFs (y-axis), with the range of error bars representing a single standard deviation. The function y = x is shown as a dashed line and the linear regression for all ligands as a solid line.

Figure 7

Configuration space comparison between YANK and AlGDock. Principal components analysis was performed on snapshots from all YANK simulations for heavy atoms within 5 Å of Val 111 in PDB ID 3DMZ. Two-dimensional histograms, weighted by Eq. 5, of YANK snapshots from (a) indole and (b) methanol were projected on the first two principal components. The histograms are plotted on a logarithmic scale. The black dots are projections of the 576 snapshots used in AlGDock calculations onto the same eigenvectors.

Figure 8

Configuration space comparison between YANK samples from (a) all active and (b) all inactive ligands. Principal components analysis was performed on snapshots from all YANK simulations for heavy atoms within 5 Å of Val 111 in PDB ID 3DMZ. Two-dimensional histograms, weighted by Eq. 5, of YANK snapshots were projected on the first two principal components. The histograms are plotted on a logarithmic scale.

Figure 9. Convergence of free energy estimates

Correlation coefficient and RMSE of AlGDock free energy with respect to YANK (a, b) and to final result (c, d). Snapshots were selected randomly (red line), with lowest docking scores (green line) or with lowest BPMFs (blue line). The x-axis of the inset plots is on a log scale. For clarity, data for randomly selected snapshots are only shown for more than 10.

Figure 10. Comparing different free energy estimates with experiment

AlGDock free energy estimates in PBSA implicit solvent were based on BPMFs calculated with either the (a) minimum interaction energy, (b) mean interaction energy, or (c) MBAR estimator, using weighting scheme (c). A comparison of the average UCSF DOCK 6 grid score with experiment is shown in (d). Note that the y axes have different limits. The outlier iodobenzene is excluded. For the same plot with iodobenzene, see Fig. S5 in the SI.

Figure 11

ROC curves for the DOCK 6 score and for AlGDock scores calculated using the (a) OBC2 or (b) PBSA implicit solvent models. Snapshots from YANK simulations with active ligands are weighted according to scheme (c).