Predicting absolute ligand binding free energies to a simple model site

Abstract

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.

Fig. 1. The model hydrophobic binding site in the L99A mutant of T4 lysozyme

The enclosed molecular surface of the cavity is shown (brown) as is the crystallographic geometry of a bound benzene ligand (green), within the context of the overall structure of T4 lysozyme (green ribbons, PDB code 181L). The sidechain of Met102 is also shown for reference.

Fig. 2. Calculated binding free energies compared with experiment

Calculated and experimental binding free energies are shown with error bars; the calculated error bars represent one standard deviation. The two points shown as larger diamonds are the non-ligands phenol and 2-fluorobenzaldehyde; for these, only a lower limit on the experimental binding free energy is known, as denoted by a large experimental error bar to the right. The diagonal x = y line denotes perfect agreement with experiment. (a) Calculated $\mathrm{\Delta }{G}_{\mathit{single}}^o$, single-orientation binding free energies, including only the contribution from the single best docking orientation. (b) $\mathrm{\Delta }{G}_{\mathit{calc}.}^o$, binding free energies, including all relevant ligand orientations, and contributions from releasing Val111 from its kinetic confinement.

Fig. 3. Val111 reorients on ligand binding

Val111 is observed to adopt a different sidechain rotamer from the apo crystallographic structure in co-crystal structures with several different ligands. Shown here is the benzene-bound structure (PDB code 181L), green, which is virtually identical to the apo structure of the protein. Also shown is the p-xylene bound structure (PDB code 187L) in magenta. The sticks at left show the reorientation of the Val111 sidechain on binding to p-xylene by roughly 120° relative to the benzene-bound and apo structures.

Fig. 4. DOCK scores for the best-ranked pose for each molecule versus experimental binding free energies

The correlation coefficient (R) is −0.69, meaning that compounds that DOCK predicts should bind strongly tend to bind weakly. Additionally, the two nonbinders have similar DOCK scores to a number of the binders.

Fig. 5. Comparison of calculated and experimental binding free energies with the protein held rigid

(a) Binding free energies with the protein completely rigid. The RMS error relative to experiment is 19.78±0.06 kcal/mol and the correlation coefficient (R) is −0.05±0.09. (b) Binding free energies with the whole protein minimized separately for each ligand. The RMS error relative to experiment is 4.92±0.07 kcal/mol and the correlation coefficient (R) is 0.82±0.09. (c) Binding free energies with only the binding site minimized for each ligand. The RMS error relative to experiment is 4.06±0.06 kcal/mol and the correlation coefficient (R) is 0.32±0.08. The x = y indicates perfect agreement with experiment.

Fig. 6. Five compounds for which binding predictions were made

(a) 1,2-dichlorobenzene; (b) n-methylaniline; (c) 1-methylpyrrole; (d) 1,2-benzenedithiol; and (e) thieno[2,3-c]pyridine.

Fig. 7. Predicted and experimental ligand orientations

Stereo images comparing the experimental and predicted poses for three ligands bound to L99A. (a) The two observed configurations of 1,2-dichlorobenzene, structure determined to 1.70 Å resolution. (b) 1-methylpyrrole, structure determined to 1.94 Å A resolution and (c) n-methylaniline, structure determined to 2.07 Å resolution. The crystallographic carbon atoms of protein residue M102 and each ligand are colored grey. The carbon atoms of the docking predictions are colored yellow, and the carbon atoms of the free energy predictions are colored magenta. The carbon atoms of the second free energy prediction in (c) are colored cyan. The F_o−F_c density maps are contoured at 3σ (green mesh). PDB codes are 2OTY, 2OU0, and 2OTZ, respectively.

Fig. 8. Representative ITC data

Data and fit for T4 lysozyme L99A (0.063 mM) titrated with 1,2-dichlorobenzene (~ 0.6 mM). An initial injection of 2.5μL was followed by 29 injections of 10μL of the ligand solution made every 2.5 min into the 1.4 mL reaction cell. After subtraction of blank runs, titrations were fit as described under Experimental Procedures to obtain the results in Table 4