Comprehensive Assessment of Torsional Strain in Crystal Structures of Small Molecules and Protein–Ligand Complexes using ab Initio Calculations

Abstract

The energetics of rotation around single bonds (torsions) is a key determinant of the three-dimensional shape that druglike molecules adopt in solution, the solid state, and in different biological environments, which in turn defines their unique physical and pharmacological properties. Therefore, accurate characterization of torsion angle preference and energetics is essential for the success of computational drug discovery and design. Here, we analyze torsional strain in crystal structures of druglike molecules in Cambridge structure database (CSD) and bioactive ligand conformations in protein data bank (PDB), expressing the total strain energy as a sum of strain energy from constituent rotatable bonds. We utilized cloud computing to generate torsion scan profiles of a very large collection of chemically diverse neutral fragments at DFT(B3LYP)/6-31G*//6-31G** or DFT(B3LYP)/6-31+G*//6-31+G** (for sulfur-containing molecule). With the data generated from these ab initio calculations, we performed rigorous analysis of strain due to deviation of observed torsion angles relative to their ideal gas-phase geometries. Contrary to the previous studies based on molecular mechanics, we find that in the crystalline state, molecules generally adopt low-strain conformations, with median per-torsion strain energy in CSD and PDB under one-tenth and one-third of a kcal/mol, respectively. However, for a small fraction (<5%) of motifs, external effects such as steric hindrance and hydrogen bonds result in strain penalty exceeding 2.5 kcal/mol. We find that due to poor quality of PDB structures in general, bioactive structures tend to have higher torsional strain compared to small-molecule crystal conformations. However, in the absence of structural fitting artifacts in PDB structures, protein-induced strain in bioactive conformations is quantitatively similar to those due to the packing forces in small-molecule crystal structures. This analysis allows us to establish strain energy thresholds to help identify biologically relevant conformers in a given ensemble. The work presented here is the most comprehensive study to date that demonstrates the utility and feasibility of gas-phase quantum mechanics (QM) calculations to study conformational preference and energetics of drug-size molecules. Potential applications of this study in computational lead discovery and structure-based design are discussed.

Towards chemical accuracy for alchemical free energy calculations with hybrid physics-based machine learning / molecular mechanics potentials

“…It is well-appreciated that general small molecule MM force fields often fail to accurately describe torsion energy profiles observed with higher-level quantum chemical calculations [73,74], a phenomenon driven by the significant effect substituents can have on torsion profiles via electronic effects [26,75]. To overcome this limitation, many MM force fields recommend refitting torsion potentials directly to quantum chemical calculations for individual molecules in a bespoke manner [1,27].…”

PSI4 1.4: Open-source software for high-throughput quantum chemistry

“…from laptops to supercomputers) and frequently changing. We also note an emerging challenge: (v) thermochemical, 7 machine learning, 8 forcefield fitting, 9 etc. applications can demand large numbers (10 5 -10 8 ) of QC computations that may form part of complex workflows.…”

Assessing Conformer Energies using Electronic Structure and Machine Learning Methods

“…[6][7][8][9][10][11][12] While experimental crystal structures and bioactive docked conformers are not always the lowest energy conformer, recent efforts have demonstrated only small energy differences when using quantum chemical methods instead of force fields. 13,14 Even for simple molecules such as 1,1'-biphenyl, use of large basis set coupled cluster methods are needed to accurately place the dihedral angle and barrier. 15 Other works have documented the need for accurate treatment of non-covalent interactions to model conformers in -conjugated oligomers.…”