A Distributional Model of Bound Ligand Conformational Strain: From Small Molecules up to Large Peptidic Macrocycles

Abstract

The internal conformational strain incurred by ligands upon binding a target site has a critical impact on binding affinity, and expectations about the magnitude of ligand strain guide conformational search protocols. Estimates for bound ligand strain begin with modeled ligand atomic coordinates from X-ray co-crystal structures. By deriving low-energy conformational ensembles to fit X-ray diffraction data, calculated strain energies are substantially reduced compared with prior approaches. We show that the distribution of expected global strain energy values is dependent on molecular size in a superlinear manner. The distribution of strain energy follows a rectified normal distribution whose mean and variance are related to conformational complexity. The modeled strain distribution closely matches calculated strain values from experimental data comprising over 3000 protein-ligand complexes. The distributional model has direct implications for conformational search protocols as well as for directions in molecular design.

Figure 1

Alternative methods for estimating bound ligand strain for grazoprevir bound to NS3/4A protease variant R155K. (A) Deposited ligand model coordinates (green), showing the experimental electron density contour from the 2|F_o| – |F_c| map at 1.0σ, with real-space fit metrics calculated using the modeled atom-specific B-factors. (B) The energy-surrogate conformer (yellow), with force field energy values for the modeled coordinates, the energy-surrogate, the global minimum, and the calculated strain. (C) Conformer ensemble from xGen (orange), with real-space fit metrics calculated using a constant B-factor and conformer-level occupancy weighting. (D) The lowest-energy xGen surrogate conformer (yellow), with the range of energy values for the ensemble and energy-surrogates along with the calculated strain.

Figure 2

Molecular size, flexibility, and degree of ligand binding site contact. (A) Cumulative histogram of molecular size. (B) Cumulative histogram of total molecular flexibility, which includes exocyclic rotatable bonds plus rotatable macrocyclic bonds. (C) Smoothed histogram of the ligand binding contact, defined as the fraction of ligand atoms within 1.0 Å of any protein atom (distance measured between VdW surfaces). (D) Relationship between molecular size and binding site contact.

Figure 3

Examples spanning different molecular sizes and ligand binding site contact (energy values in kcal/mol). PDB ligand coordinates are shown with green carbons, and xGen fitted ensembles are shown with orange carbons. (A) Biotin bound to the S45A mutant of streptavidin. (B) Inhibitor bound to the kinase domain of human DDR1. (C) Antagonist bound to heat-labile Enterotoxin B. (D) Sanglifehrin A analog bound to cyclophilin. (E) Cyclosporin A bound to a Leishmania donovani cyclophilin (ΔG from Venugopal et al.). (F) Endothelin in complex with human endothelin receptor type-B (ΔG from Shihoya et al.).

Figure 4

The xGen approach constructs ensembles to fit electron density from conformational trios, each of which is anchored by a conformer that arose from an X-ray density-aware conformational search (slate). These balanced conformers are optimized toward a density-weighted fit (orange) and an energy-weighted fit (salmon). Conformer trios are identified whose density-favored member and energy-favored member are near optimal and where both are geometrically close to a central balanced conformer.

Figure 5

Relationship between strain energy and molecular size for the Brueckner Set with an approximately linear upper bound on strain (blue dashed line).

Figure 6

Relationship of ligand strain to molecular size.

Figure 7

Relationship between the square of heavy atom count (X axis) and conformational complexity modeled as the product of atom count and number of rotatable bonds (Y axis).

Figure 8

Relationship between strain energy and molecular size for the High-Contact Set, modeled using the proposed size-dependent rectified normal distribution.

Figure 9

Relationship between strain energy and molecular size for the Low-Contact Set, modeled using the proposed size-dependent rectified normal distribution.

Figure 10

Typical example of strained cyclohexane conformation contributing to high nominal strain in an uncorrected PDB structure (green) being resolved by re-refinement (orange).

Figure 11

Relationship of ligand efficiency to ligand size and ligand strain-per-atom.

Figure 12

Relationship of LEFF to ligand size (violet) and LEFF adjusted upward to account for the modeled high-strain upper bound at each molecular size (red).

Figure 13

A full conformer neighborhood: a single balanced-pool conformer (slate), the full set of density-pool (orange) and min-pool conformers (salmon) within 0.65 Å sRMSD of the balanced conformer.