Following the previously proposed equilibrate-state sampling based adaptive sampling regime Optimum Bennett Acceptance Ratio (OBAR), we introduce its nonequilibrium extension, the Optimum Crooks' Equation (OCE) in the current work. The efficiency of the NonEquilibrium Work (NEW) stratification is improved by adaptively manipulating the significance of each nonequilibrium realization followed by importance sampling. As is exhibited in the equilibrium case, the nonequilibrium extension outperforms the simple equal time rule used in nonequilibrium stratification in the sense of minimizing the total variance of the free energy estimate. The speedup of this non-equal time rule is more than 1-fold. The Time Derivative of total Variance (TDV) proposed for the OBAR criterion is extended to determine the importance of each nonequilibrium transformation, which is linearly dependent on the variance. The TDV in the nonequilibrium case gives a totally different importance rank from the standard errors of the free energy differences and OBAR TDV due to the duration of nonequilibrium pulling being added into the OCE equation. The performance of the OCE workflow is demonstrated in the solvation of several small molecules with a series of lambda increments and relaxation times between successive perturbations. To the best of our knowledge, such a nonequilibrium adaptive sampling regime in alchemical transformation is unprecedented.

The equilibrium and nonequilibrium adaptive alchemical free energy simulation methods optimum Bennett's acceptance ratio and optimum crooks' equation (OCE), based on the statistically optimal bidirectional reweighting estimator named Bennett's Acceptance Ratio or Crooks' equation, perform initial sampling in the staging alchemical transformation and then determine the importance rank of different states via the time‐derivative of the variance. The method is proven to give speedups compared with the equal time rule. In the current work, we extend the time derivative of variance guided adaptive sampling method to the configurational space, falling in the term of steered MD (SMD). The SMD approach biasing physically meaningful collective variable (CV) such as one dihedral or one distance to pulling the system from one conformational state to another. By minimizing the variance of the free energy differences along the pathway in an optimized way, a new type of adaptive SMD (ASMD) is introduced. As exhibits in the alchemical case, this adaptive sampling method outperforms the traditional equal‐time SMD in nonequilibrium stratification. Also, the method gives much more efficient calculation of potential of mean force than the selection criterion‐based ASMD scheme, which is proven to be more efficient than traditional SMD. The OCE workflow is periodicity‐of‐CV dependent while ASMD is not. The performance is demonstrated in a dihedral flipping case and two distance pulling cases, accounting for periodic and nonperiodic CVs, respectively. © 2019 Wiley Periodicals, Inc.

<p>Previously we proposed the equilibrium and nonequilibrium adaptive alchemical free energy simulation methods Optimum Bennett’s Acceptance Ratio (OBAR) and Optimum Crooks’ Equation (OCE). They are based on the statistically optimal bidirectional reweighting estimator named Bennett’s Acceptance Ratio (BAR) or Crooks’ Equation (CE). They perform initial sampling in the staging alchemical transformation and then determine the importance rank of different states via the time-derivative of the variance (TDV). The method is proven to give speedups compared with the equal time rule. In the current work, we extended the time derivative of variance guided adaptive sampling method to the configurational space, falling in the term of Steered MD (SMD). The SMD approach biasing physically meaningful collective variable (CV) such as one dihedral or one distance to pulling the system from one conformational state to another. By minimizing the variance of the free energy differences along the pathway in an optimized way, a new type of adaptive SMD (ASMD) is introduced. As exhibits in the alchemical case, this adaptive sampling method outperforms the traditional equal-time SMD in nonequilibrium stratification. Also, the method gives much more efficient calculation of potential of mean force than the selection criterion based ASMD scheme, which is proven to be more efficient than traditional SMD. The variance-linearly-dependent minus time derivative of overall variance proposed for OBAR and OCE criterion is extended to determine the importance rank of the nonequilibrium pulling in the configurational space. It is shown that the importance rank given by the standard deviation of the free energy difference is wrong, but by correcting it with the simulation time we obtain the true importance rank in nonequilibrium stratification. The OCE workflow is periodicity-of-CV dependent while ASMD is not. In the non-periodic CV case, the end-state discrimination in the SD rank is eliminated in the TDV rank, while in the periodic CV case the correction introduced in the TDV rank is not that significant. The performance is demonstrated in a dihedral flipping case and two distance pulling cases, accounting for periodic and non-periodic CVs, respectively. </p>