What to Make of Zero: Resolving the Statistical Noise from Conformational Reorganization in Alchemical Binding Free Energy Estimates with Metadynamics Sampling

Abstract

We introduce the self-relative binding free energy (self-RBFE) approach to evaluate the intrinsic statistical variance of dualtopology alchemical binding free energy estimators. The self-RBFE is the relative binding free energy between a ligand and a copy of the same ligand, and its true value is zero. Nevertheless, because the two copies of the ligand move independently, the self-RBFE value produced by a finitelength simulation fluctuates and can be used to measure the variance of the model. The results of this validation provide evidence that a significant fraction of the errors observed in benchmark studies reflect the statistical fluctuations of unconverged estimates rather than the models' accuracy. Furthermore, we find that ligand reorganization is a significant contributing factor to the statistical variance of binding free energy estimates and that metadynamics-accelerated conformational sampling of the torsional degrees of freedom of the ligand can drastically reduce the time to convergence.

Adsorption of Flavonoids in a Transcriptional Regulator TtgR: Relative Binding Free Energies and Intermolecular Interactions

“…We have conducted AFE simulations in aqueous solutions and TtgR-ligand complexes to calculate the relative binding free energies of the seven flavonoids. Among the recent advancements in AFE methods, − we have invoked the ACES approach to enhance conformational and alchemical sampling and produce reliable free energy estimates . As illustrated in Figure , the common cores incorporate the basic skeleton of the flavonoids, while the softcore regions undergo transformation between two ligands in each AFE simulation.…”

“…AFE simulations have been used extensively in drug discovery for the prediction of ligand–protein binding, and have been the subject of several reviews. − We conducted AFE simulations to compute the relative binding free energies of the flavonoids using the Amber 2022 package and AMBER Drug Discovery Boost Tools that leverage high-performance GPU acceleration. , The version differences in the Amber program for standard MD simulations and AFE simulations are expected to have minimal impact on the prediction results. The relative binding free energy between ligands 1 and 2 in TtgR is defined as the difference between their absolute binding free energies, ΔΔ G bind = Δ G bind,2 – Δ G bind,1 .…”

Alchemical Enhanced Sampling with Optimized Phase Space Overlap

“…A vast literature of methods has evolved that seek to improve the design of alchemical transformation pathways − and their sampling. ,− For more extensive discussion, we refer the reader to several excellent reviews. ,,,− Recently, an AlChemically Enhanced Sampling (ACES) method has been introduced that enables focused enhanced sampling of select regions involving the ligand undergoing alchemical transformation and/or the nearby residues. The foundation of the method is to create an artificial noninteracting “enhanced-sampled” state that can be rigorously connected to the corresponding real state end-point through Hamiltonian replica exchange. − The enhanced sampled state is a selection of atoms (the ligand, a subset of the ligand, and/or nearby protein residues) whose intermolecular interactions with the environment are removed.…”