Optimal designs for pairwise calculation: An application to free energy perturbation in minimizing prediction variability

Abstract

Pairwise‐based methods such as the free energy perturbation (FEP) method have been widely deployed to compute the binding free energy differences between two similar host–guest complexes. The calculated pairwise free energy difference is either directly adopted or transformed to absolute binding free energy for molecule rank ordering. We investigated, through both analytic derivations and simulations, how the selection of pairs in the experiment could impact the overall prediction precision. Our studies showed that (1) the estimated absolute binding free energy (truenormalΔG^) derived from calculated pairwise differences (ΔΔG) through weighted least squares fitting is more precise in prediction than the pairwise difference values when the number of pairs is more than the number of ligands and (2) prediction precision is influenced by both the total number of pairs and the specifically selected pairs, the latter being critically important when the number of calculated pairs is limited. Furthermore, we applied optimal experimental design in pair selection and found that the optimally selected pairs can outperform randomly selected pairs in prediction precision. In an illustrative example, we showed that, upon weighing ligand structure similarity into design optimization, the weighted optimal designs are more efficient than the literature reported designs. This work provides a new approach to assess retrospective pairwise‐based prediction results, and a method to design new prospective pairwise‐based experiments for molecular lead optimization. © 2019 Wiley Periodicals, Inc.

Best Practices for Alchemical Free Energy Calculations [Article v1.0]

“…In this way the top-ranking examples can be readily identified and submitted to additional calculations in a second round. Alternatively, if the goal is to achieve the smallest possible error with minimal computational expense, certain graph topologies provide benefits [94,95]…”

“…Based on the input ligand series, a perturbation map or network can be planned. Recent heuristics have shown the more connected the perturbation network the better, however, there is a way to optimize network structure while minimizing the number of perturbations that need to be computed reducing the resulting computational cost [94,95]. Sometimes the introduction of intermediates that are not part of the original congeneric series are essential to avoid ring breaking, or deal with perturbations that would otherwise result in large numbers of atoms being inserted or deleted.…”

“…5 B. Methods in experimental design have been applied to the construction of the perturbation maps. Yang et al [94] optimized the perturbation map by selecting a fixed number of calculations from the pairwise perturbations so that the resulting set of calculations minimize the total variance. Xu [95] optimized the perturbation map by allocating different amounts of simulation time to different pairwise perturbations so as to minimize the total variance, given the total simulation time of all the perturbation calculations.…”

“…An alternative approach computes the free energy change between a target and reference compound as a weighted average over all unique paths in the network, with the weights derived from the propagated uncertainties of each node [16]. Approaches as illustrated by Yang et al for perturbation map design can also be used to compute relative free energies between target and reference compounds [94].…”

Machine learning-accelerated quantum mechanics-based atomistic simulations for industrial applications

“…The ability to efficiently calculate the associated binding free energy [22][23][24] can provide valuable contributions to the ligand optimization phase, allowing to rank ligands, optimize selectivity, and estimate off-target interactions. With recent advances in the free energy methods and underlying simulation models, the calculation of free energies from atomistic MD simulations has become a reliable tool with several examples of successful industrial applications [25][26][27][28][29]. Multi-scale approaches in which atomistic force fields are combined with coarse-grained models that were built for specific applications can further reduce the computational cost and allow to study even larger systems such as membrane-bound ion channels [30].…”