ACES: Optimized Alchemically Enhanced Sampling

Abstract

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an “enhanced sampling state” by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting “dummy state” with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

AMBER Free Energy Tools: A New Framework for the Design of Optimized Alchemical Transformation Pathways

“…To generate the benchmark reference number for test systems, we introduced the alchemical enhanced sampling method (ACES) that will be described in detail elsewhere. , Initial structures and the equilibration procedure were performed in the same way as for relative binding free energy simulations, but were repeated in 16 independent runs and with nonuniform λ scheduling which led to 25 λ windows (0, 0.176834, 0.229764, 0.269379, 0.302697, 0.33229, 0.359436, 0.384886, 0.40913, 0.432518, 0.455318, 0.477748, 0.5, 0.522252, 0.544682, 0.567482, 0.59087, 0.615114, 0.640564, 0.66771, 0.697303, 0.730621, 0.770236, 0.823166, 1). These 25 λ points correspond to uniform spacing of the S 2 (λ) smoothstep function (eq ) that is used for the nonlinear mixing weights in eq .…”

“…These issues will be explored in the next paper in this series. 54 For the present paper, the dummy state was created by scaling (i.e., "turning off") electrostatic interactions, and in some cases also torsion angle and 1−4 LJ terms, but keeping other bonded and normal LJ terms in place. Hence, the new form of the softcore potential will affect mainly the U nb SC/(CC + I) term, which, as results presented later in the paper will show, has a profound effect on the free energy estimates.…”

“…In fact, the proper choice of potential energy interactions in the dummy state, together with well-established generalized ensemble methods such as Hamiltonian replica exchange, − can lead to powerful new alchemical enhanced sampling methods. These issues will be explored in the next paper in this series . For the present paper, the dummy state was created by scaling (i.e., “turning off”) electrostatic interactions, and in some cases also torsion angle and 1–4 LJ terms, but keeping other bonded and normal LJ terms in place.…”

Broadening the Scope of Binding Free Energy Calculations Using a Separated Topologies Approach

“…We scaled down the LJ parameters, which, combined with Hamiltonian Replica Exchange (HREX), − can enhance the sampling of slow degrees of freedom, as has been shown in the implementation REST2 and ACES . Instead of running different replicas at different temperatures, as in temperature replica exchange, all replicas are run at the same temperature while the potential energy of every replica is scaled differently.…”

“…The single and the hybrid topology approaches are based on having a common core, distinct from the Separated Topologies approach, as described below. The common core is often defined as the maximum common substructure between the two ligands , (or between multiple ligands , ); however, additional mapping ideas are possible . The RBFE approach is less computationally demanding and has lower statistical uncertainties than absolute binding free energy (ABFE) calculations.…”