A Quadrupolar Fullerene Model System for Benchmarking Enhanced Sampling of Trapped Waters in Free Energy Calculations

Enhanced sampling methods, such as hybrid Monte Carlo/molecular dynamics (MC/MD), grand canonical MC/MD, non-equilibrium candidate MC/MD, etc., are widely used to sample slow rearrangement of water molecules in binding free energy calculations. However, direct comparison of the accuracies of these methods is oftentimes challenging due to differences in studied systems, simulation parameters and system setup across studies. To overcome this challenge, we introduce a novel and well-defined model system for benchmarking water sampling methods: a closed, custom-defined C90 fullerene. Unlike conventional fullerenes with nonpolar, hydrophobic cavities, our custom-defined fullerene incorporates partial charges creating a polar cavity that energetically favors water binding. Due to a significant free energy barrier imposed by the fullerene wall, water exchange between the cavity and bulk solvent is essentially impossible on MD timescales. To allow solvent water to equilibrate in the cavity, we introduce a solvent inlet, by performing Hamiltonian replica exchange (i.e., HREX) simulations, which reveal that our polar fullerene cavity can accommodate a maximum of two waters. From these HREX simulations, we also identify the binding sites of waters and their occupancies inside the cavity, which show that fullerene conformations with 2 or 1 waters inside the cavity are dominant, with nearly equal free energies. We further validate a non-equilibrium switching (NES) protocol for calculating the free energy of displacing a water from the conformations with 2 waters inside the cavity. Our NES results agree within statistical error with those obtained from HREX. Our findings establish the polar fullerene as a well-defined reproducible test system for rigorously benchmarking current as well as future enhanced sampling techniques targeting slow water sampling in confined environments.