To Design Scalable Free Energy Perturbation Networks, Optimal Is Not Enough

Drug discovery is accelerated with computational methods such as alchemical simulations to estimate ligand affinities. In particular, relative binding free energy (RBFE) simulations are beneficial for lead optimization. To use RBFE simulations to compare prospective ligands in silico, researchers first plan the simulation experiment, represented by graphs where nodes represent ligands and graph edges represent alchemical transformations between ligands. Recent work demonstrated that optimizing the statistical architecture of these perturbation graphs improves the accuracy of the resultant changes in the free energy of ligand binding. Therefore, to improve the success rate of computational drug discovery, we present the open-source software package High Information Mapper (HiMap) --- a modernized take on its predecessor, Lead Optimization Mapper (LOMAP). HiMap removes heuristics decisions from design selection and instead finds statistically optimal graphs over ligands clustered with machine learning. Beyond optimal design generation, we present theoretical insights for designing alchemical perturbation maps. Some of these results include that for n number of nodes, the precision of perturbation maps is stable at n·ln(n) edges. We additionally find that optimal designs will converge more rapidly than radial and LOMAP designs. Moreover, we derive bounds for how clustering reduces cost for designs with a constant expected error, invariant of the size of the design. These results inform how to best design perturbation maps for computational drug discovery and have broader implications for experimental design.