Addressing Intersite Coupling Unlocks Large Combinatorial Chemical Spaces for Alchemical Free Energy Methods

Alchemical free energy methods are playing a growing role in molecular design, both for computer-aided drug design of small molecules and for computational protein design. Multisite λ dynamics (MSλD) is a uniquely scalable alchemical free energy method that enables more efficient exploration of combinatorial alchemical spaces encountered in molecular design, but simulations have typically been limited to a few hundred ligands or sequences. Here, we focus on coupling between sites to enable scaling to larger alchemical spaces. We first discuss updates to the biasing potentials that facilitate MSλD sampling to include coupling terms and show that this can provide more thorough sampling of alchemical states. We then harness coupling between sites by developing a new free energy estimator based on the Potts models underlying direct coupling analysis, a method for predicting contacts from sequence coevolution, and find it yields more accurate free energies than previous estimators. The sampling requirements of the Potts model estimator scale with the square of the number of sites, a substantial improvement over the exponential scaling of the standard estimator. This opens up exploration of much larger alchemical spaces with MSλD for molecular design.