Improved reweighting protocols for variationally enhanced sampling simulations with multiple walkers.

In molecular dynamics simulations utilizing enhanced-sampling techniques, reweighting is a central component for recovering the targeted ensemble averages of the "unbiased" system by calculating and applying a bias-correction function c ( t ). We present enhanced reweighting protocols for variationally enhanced sampling (VES) simulations by exploiting a recent reweighting method, originally introduced in the metadynamics framework [Giberti et al. J. Chem. Theory Comput ., 2020, 16 , 100-107], which was modified and extended to multiple-walker simulations: these may be implemented either as "independent" walkers (associated with one unique correction function per walker) or "cooperative" ones that all share one correction function, which is the hitherto only explored option. When each case is combined with the two possibilities of determining c ( t ) by time integration up to either t or over the entire simulation period , altogether four reweighting options result. Their relative merits were assessed by well-tempered VES simulations of two model problems: locating the free-energy difference between two metastable molecular conformations of the N -acetyl-L-alanine methylamide dipeptide, and the recovery of an a priori known distribution when one water molecule in the liquid phase is perturbed by a periodic free-energy function. The most rapid convergence occurred for large cooperative walkers, regardless of the upper integration limit, but integrating up to t proved advantageous for small walker ensembles. That novel reweighting method compared favorably to the standard VES reweighting, as well as to current state-of-the-art reweighting options introduced for metadynamics simulations that estimate c ( t ) by integration over the collective variables. For further gains in computational speed and accuracy, we also introduce analytical solutions for c ( t ), as well as offering further insight in t o its features by approximative analytical expressions in the "high-temperature" regime.