LAO+: Focused, Multi-Replica Accelerated Orthogonal Sampling for Robust Binding Free Energy Predictions

Abstract

We introduce Lambda-ABF-OPES+ ($\text{LAO+}$), a multi-replica framework for absolute binding free energy (ABFE) calculations that accelerates both the alchemical transformation and the slow ``orthogonal'' motions coupled to it. At the core of $\text{LAO+}$ is a partitioned $λ$-dynamics scheme that concentrates sampling on the abrupt rehydration of the binding pocket, the main bottleneck of ligand decoupling, while Hamiltonian replica exchange relays configurations along the entire alchemical path. This drives a fourfold gain in convergence speed for the rate-limiting leg over our previous $\text{LAO}$ method, which was itself up to ninefold faster than Lambda-ABF, an overall gain of up to $\sim$36-fold. Applied to 28 protein--ligand complexes across five targets, $\text{LAO+}$ achieves a root-mean-square error of 0.83~kcal~mol$^{-1}$ and a correlation of 0.87 with experiment from only 63~ns of sampling per ligand. Moreover, dedicated reservoir replicas accelerate any slow degree of freedom that can be described by a collective variable. We demonstrate this by recovering hidden protein and ligand conformational states, for example in T4 lysozyme, BRD4 and JNK1. Together, these advances make accurate ABFE calculations practical for drug discovery.