In situ ligand restraints from quantum-mechanical methods

Abstract

In macromolecular crystallographic structure refinement, ligands present challenges for the generation of geometric restraints due to their large chemical variability, their possible novel nature and their specific interaction with the binding pocket of the protein. Quantum-mechanical approaches are useful for providing accurate ligand geometries, but can be plagued by the number of minima in flexible molecules. In an effort to avoid these issues, the Quantum Mechanical Restraints (QMR) procedure optimizes the ligand geometry in situ, thus accounting for the influence of the macromolecule on the local energy minima of the ligand. The optimized ligand geometry is used to generate target values for geometric restraints during the crystallographic refinement. As demonstrated using a sample of >2330 ligand instances in >1700 protein-ligand models, QMR restraints generally result in lower deviations from the target stereochemistry compared with conventionally generated restraints. In particular, the QMR approach provides accurate torsion restraints for ligands and other entities.

Keywords: Quantum Mechanical Restraints; ligand restraints; macromolecular crystallography; quantum mechanics; refinement.

Figure 1

Workflow of the QMR procedure.

Figure 2

Changes in valence-angle r.m.s.d. (a) and torsion-angle r.m.s.d. (b).

Figure 3

Mean valence-angle r.m.s.d. (a) and mean torsion-angle r.m.s.d. (b) for ligands averaged in resolution bins. The highest resolution bin is 0.8–1.4 Å; the other bins have a 0.2 Å width. The number of ligands per bin is indicated above the orange line in (a). The error bars represent the standard error of the mean.

Figure 4

The chemical structure of berberine. Relevant atoms are annotated with PDB atom names.

Figure 5

BER D in PDB entry 3vw2 and electron density after benchmark refinement with GeoStd restraints. Blue, 2mF _obs − DF _model map at 1 r.m.s. and 1.5 Å carve; green/red, mF _obs − DF _model map at ±3 r.m.s. and 3 Å carve.

Figure 6

Superposition of the computed structures for ligand BER used for restraint generation in the GeoStd (orange) and QMR (teal) methods.

Figure 7

(a, b) BER D in PDB entry 3vw2 after refinement with QMR restraints (teal) and after refinement with GeoStd restraints (orange). The electron density is computed with the model from QMR refinement. Blue, 2mF _obs − DF _model map at 1 r.m.s. and 1.5 Å carve; green/red, mF _obs − DF _model map at ±3 r.m.s. and 2 Å carve. (c) Close-up of the central unsaturated six-membered ring.

Figure 8

The chemical structure of EYW {5-[(3aS,4S,6R)-2-oxidanylidene-1,3,3a,4,6,6a-hexahydrothieno[3,4-d]imidazol-4-yl]-N-[(3R)-pyrrolidin-3-yl]pentanamide}. Relevant atoms are annotated with PDB atom names.

Figure 9

EYW of chain A in PDB entry 6gh7 and electron density after refinements with GeoStd restraints. Blue, 2mF _obs − DF _model map at 1 r.m.s.; green/red, mF _obs − DF _model map at ±3 r.m.s.

Figure 10

Superposition of the idealized EYW structures from GeoStd (orange) and QMR (teal) restraints. (a) Entire molecule; superposition based on the alkane group. (b) Close-up of the pyrrolidine ring; superposition based on the N12, C1 and H1 atoms.

Figure 11

EYW A in PDB entry 6gh7 after refinement with QMR restraints (teal) and after refinement with GeoStd restraints (orange). The electron density is computed with the model from QMR refinement. Blue, 2mF _obs − DF _model map at 1 r.m.s. and 1.2 Å carve; green/red, mF _obs − DF _model map at ±3 r.m.s. and 3 Å carve.