QM/MM linear response method distinguishes ligand affinities for closely related metalloproteins

Abstract

Design of selective ligands for closely related targets is becoming one of the most important tasks in the drug development. New tools, more precise than fast scoring functions and less demanding than sophisticated Free Energy Perturbation methods, are necessary to help accomplish this goal. The methods of intermediate complexity, characterizing individual contributions to the binding energy, have been an area of intense research in the past few years. Our recently developed quantum mechanical/molecular mechanical (QM/MM) modification of the Linear Response (LR) method describes the binding free energies as the sum of empirically weighted contributions of the QM/MM interaction energies and solvent-accessible surface areas for the time-averaged structures of hydrated complexes, obtained by molecular dynamics (MD) simulations. The method was applied to published data on 27 inhibitors of matrix metalloproteinase-3 (MMP-3). The two descriptors explained 90% of variance in the inhibition constants with RMSE of 0.245 log units. The QM/MM treatment is indispensable for characterization of the systems lacking suitable force-field expressions. In this case, it provided characteristics of H-bonds of the inhibitors to Glu202, charges of binding site atoms, and accurate coordination geometries of the ligands to catalytic zinc. The geometries were constrained during the MD simulations, which characterized conformational flexibility of the complexes and helped in the elucidation of the binding differences for related compounds. A comparison of the presented QM/MM LR results with those previously published for inhibition of MMP-9 by the same set of ligands showed that the QM/MM LR approach was able to distinguish subtle differences in binding affinities for MMP-3 and MMP-9, which did not exceed one order of magnitude. This precision level makes the approach a useful tool for design of selective ligands to similar targets, because the results can be safely extrapolated to maximize selectivity.

Fig. 1

The results of QM/MM optimization for the 27 hydroxamate complexes with MMP-3 (Table I). Average Mulliken charges were: 0.351 (H1), 0.438 (H2), O.633 (C1), 0.585 (C2), −0.217 (N1), −0.586 (N2), −0.583 (N3), −0.577 (N4), −0.633 (O1), −0.639 (O2), and 1.160 (Zn). Average bond lengths, in Å, were: 1.323 (C1-N1), 1.260 (C1=O1), 1.305 (C2-O3), 1.237 (C2=O4), 1.023 (N1-H1), 1.376 (N1-O2), 2.180 (N2-Zn), 2.158 (N3-Zn), 2.158 (N4-Zn), 2.072 (O1-Zn), 2.135 (O2-Zn), 1.406 (O2-H2), and 1.055 (03-H2). The maximum standard deviations were 11.0 % for charges and 2.3 % for distances.

Fig. 2

Movements of the backbone of MMP-3 and the inhibitor molecules during the MD simulations characterized by the average RMSD±SD Å from initial conformation.

Fig. 3

Experimental vs. calculated inhibition potencies of hydroxamates against MMP-3 as obtained by FlexX docking with the zinc binding-based selection of modes in Step 1 (green), MM minimization in Step 1 (cyan), QM/MM minimization in Step 2 (blue), MD simulation with constrained zinc bonds in Step 3 (red), and QM/MM energy calculations for the time averaged structures from MD simulation in Step 4 (black). All correlation results are summarized in Table II. The identity line is drawn for visual aid.

Fig. 4

Binding site superposition of MMP-3 (PDB file 1B3D) and MMP-9 (PDB file 1GKC) using c-α carbon atoms. MMP-9 is shown in atom colors while, for MMP-3, the colors identify individual subsites: S1 (orange), S1’ (magenta), S2 (green), S2’ (blue) and S3 (red). The sequences of the S1 and S2’ sites, with the conserved residues in black, are also shown.

Fig. 5

Inhibitory potencies of MMP-3 vs. those of MMP-9: experimental (full points) and predicted (open points) values for MMP-3, predicted values for MMP-9 (crosses scattered around the dotted identity line). The full line represents the correlation between the experimental MMP-3 and MMP-9 values.