Do all roads lead to Rome? Convergence issues in umbrella sampling simulations

Molecular dynamics (MD) simulations are widely applied to estimate absolute binding free energies of protein-ligand and protein-protein complexes. A routinely used method for binding free energy calculations with MD is umbrella sampling (US), which calculates the potential of mean force (PMF) along a reaction coordinate. In this work, we investigate the convergence of US along standard distance-based reaction coordinates for various protein-protein and protein-ligand complexes, following commonly used guidelines for the setup. We show that repeating the complete US workflow can lead to differences of 2-20 kcal/mol in computed binding free energies. We attribute those discrepancies to small differences in the binding pathways. We then demonstrate that adaptive-biasing approaches, which are constructed to sample multiple pathways in a single simulation, such as the accelerated weight histogram (AWH) method, can achieve convergence between independent simulations. To the best of our knowledge, this is the first attempt to systematically assess the shortcomings of the widely accepted protocols for US of protein-protein and protein-ligand binding affinities. We anticipate therefore that our results will provide an incentive for a critical reassessment of the validity of PMFs computed with US, as well as adopt adaptive-biasing approaches for computing binding affinities.