Stepping Up Enhanced Rate Calculations with EATR-Flooding

Several recent methods have shown that it is possible to compute rate constants of very slow biomolecular processes using simulations where a time-dependent bias is added along one or several collective variables (CVs). We previously reported the exponential average time-dependent rate (EATR) method, which can improve upon these approaches by accounting for how efficiently the external biasing potential modifies the observed rate using a learned CV-quality factor γ. This results in more accurate rate estimates using the same data when biasing a suboptimal coordinate. As formulated, however, EATR depended on the biasing potential varying over time to properly determine the biasing efficiency, which limits the method's applicability to quasi-static biasing schemes such as "flooding" or on-the-fly probability enhanced sampling (OPES). Here, we present the EATR-flooding approach, which generalizes our method by replacing the need for a time-dependent bias by instead varying (stepping up) the strength of the biasing potential across multiple sets of simulations. We implement this approach in an open source Python library, and demonstrate that this approach is accurate without substantial loss of efficiency compared to standard EATR for a coarse-grained protein system, and also show good performance on a fully atomistic cavity-ligand model. Two additional appealing features of EATR-flooding are an internal check for overbiasing and the fact that only a single γ parameter is predicted for a given choice of CVs, as compared to our earlier results where the estimated γ empirically varied with the biasing rate. Finally, we believe EATR-flooding applies not only to OPES simulations but more generally to CV biasing enhanced sampling approaches, making it broadly useful.