Validation of Free Energy Methods in AMBER

Abstract

Herein we provide high-precision validation tests of the latest GPU-accelerated free energy code in AMBER. We demonstrate that consistent free energy results are obtained in both the gas phase and in solution. We first show, in the context of thermodynamic integration (TI), that the results are invariant with respect to "split" (e.g., stepwise decharge-vdW-recharge) versus "unified" protocols. This brought to light a subtle inconsistency in previous versions of AMBER that was traced to the improper treatment of 1-4 vdW and electrostatic interactions involving atoms across the softcore boundary. We illustrate that under the assumption that the ensembles produced by different legs of the alchemical transformation between molecules A and B in the gas phase and aqueous phase are very small, the inconsistency in the relative hydration free energy ΔΔG_hydr[A → B] = ΔG_aq[A → B] - ΔG_gas[A → B] is minimal. However, for general cases where the ensembles are shown to be substantially different, as expected in ligand-protein binding applications, these errors can be large. Finally, we demonstrate that results for relative hydration free energy simulations are independent of TI or multistate Bennett's acceptance ratio (MBAR) analysis, invariant to the specific choice of the softcore region, and in agreement with results derived from absolute hydration free energy values.

Figure 1:

Comparison of ΔG_(aq) and ΔG_(gas) values (designated generically as ΔG on the axis labels) using unified and split protocols for nine transformations tabulated in Tables S3 and S4. a) Simulations using pre-AMBER18 (pA18) with values listed in Table S3, and b) current updated AMBER18 (A18*) with values listed in Table S4.

Figure 2:

Free energy profiles (FEPs) for acetic acid along O=C-O-H torsion angle (ϕ) in the gas phase and in solution for both real (λ=0) and dummy (λ=1) states. a) FEPs computed using pA18. b) FEPs computed using A18*. Torsion angle (ϕ) values of 0° represent cis proton configuration, and 180° represent trans proton configuration.