BOKEI: Bayesian optimization using knowledge of correlated torsions and expected improvement for conformer generation

A key challenge in conformer sampling is finding low-energy conformations with a small number of energy evaluations. We recently demonstrated the Bayesian Optimization Algorithm (BOA) is an effective method for finding the lowest energy conformation of a small molecule. Our approach balances between exploitation and exploration, and is more efficient than exhaustive or random search methods. Here, we extend strategies used on proteins and oligopeptides (e.g. Ramachandran plots of secondary structure) and study correlated torsions in small molecules. We use bivariate von Mises distributions to capture correlations, and use them to constrain the search space. We validate the performance of our new method, Bayesian Optimization with Knowledge-based Expected Improvement (BOKEI), on a dataset consisting of 533 diverse small molecules, using (i) a force field (MMFF94); and (ii) a semi-empirical method (GFN2), as the objective function. We compare the search performance of BOKEI, BOA with Expected Improvement (BOA-EI), and a genetic algorithm (GA), using a fixed number of energy evaluations. In more than 60% of the cases examined, BOKEI finds lower energy conformations than global optimization with BOA-EI or GA. More importantly, we find correlated torsions in up to 15% of small molecules in larger data sets, up to 8 times more often than previously reported. The BOKEI patterns not only describe steric clashes, but also reflect favorable intramolecular interactions such as hydrogen bonds and π-π stacking. Increasing our understanding of the conformational preferences of molecules will help improve our ability to find low energy conformers efficiently, which will have impact in a wide range of computational modeling applications.