Torsion angle preference and energetics of small-molecule ligands bound to proteins

Small organic molecules can assume conformations in the protein-bound state that are significantly different from those in solution. We have analyzed the conformations of 21 common torsion motifs of small molecules extracted from crystal structures of protein-ligand complexes and compared them with their torsion potentials calculated by an ab initio DFT method. We find a good correlation between the potential energy of the torsion motifs and their conformational distribution in the protein-bound state: The most probable conformations of the torsion motifs agree well with the calculated global energy minima, and the lowest torsion-energy state becomes increasingly dominant as the torsion barrier height increases. The torsion motifs can be divided into 3 groups based on torsion barrier heights: high (>4 kcal/mol), medium (2-4 kcal/mol), and low (<2 kcal/mol). The calculated torsion energy profiles are predictive for the most preferred bound conformation for the high and medium barrier groups, the latter group common in druglike molecules. In the high-barrier group of druglike ligands, >95% of conformational torsions occur in the energy region <4 kcal/mol. The conformations of the torsion motifs in the protein-bound state can be modeled by a Boltzmann distribution with a temperature factor much higher than room temperature. This high-temperature factor, derived by fitting the theoretical model to the experimentally observed conformation occurrence of torsions, can be interpreted as the perturbation that proteins inflict on the conformation of the bound ligand. Using this model, it is calculated that the average strain energy of a torsion motif in ligands bound to proteins is approximately 0.6 kcal/mol, a result which can be related to the lower binding efficiency of larger ligands with more rotatable bonds. The above results indicate that torsion potentials play an important role in dictating ligand conformations in both the free and the bound states.