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

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 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.