Aug 2026· Journal of Chemical Theory and Computation· Vol 22 16, pp.
8423-8432
· 0 citations· 42 references
Medicine
TL;DR
This work presents an efficient strategy, λ-resolved free energy (λFE), to generate databases that solve the challenge of resolving physical charging free energies at any intermediate charge state from a single alchemical free-energy simulation.
Abstract
One way to compute solvation free energies is through standard alchemical free energy (AFE) methods. But they can be expensive, and they do not give useful atomwise or site-specific decompositions. Alternatively, these challenges are partly addressed by bottom-up methods, like semi-explicit assembly (SEA), that start from atomic units and handle larger molecules using additivity rules. The latter methods require databases only on elementary monatomics. Here, we present an efficient strategy, λ-resolved free energy (λFE), to generate such databases. By resolving physical charging free energies at any intermediate charge state from a single alchemical free-energy simulation, λFE eliminates the need for separate alchemical charging calculations for atom types that differ only in their charge. This approach is significantly less costly and is robust across a range of charges, LJ parameters, system sizes, and three water models (TIP3P, TIP4P/EW, and TIP4P/2005). Combined with a cubic polynomial fit to the alchemical charging free energies, λFE yields a closed-form expression for absolute charging free energies of monatomic ions with any charge from a single alchemical simulation.
Alchemical free energy perturbation (FEP) is one of the most rigorous methods for predicting protein-ligand binding affinities, yet charged-ligand calculations suffer from finite-size electrostatic artifacts introduced by periodic boundary conditions, which can bias results by several kcal·mol-1. Existing approaches each have limitations: finite-size correction methods rely on approximate dielectric models and Poisson-Boltzmann (PB) calculations, while alchemical co-ion methods introduce alchemically transformed particles, causing spurious interactions and sampling difficulties. Here we present Electrostatic Interaction Decoupling (EID), a postprocessing approach that combines an exact algebraic isolation of the ligand-environment linear electrostatic interaction under the neutral-environment condition with an analytical correction for the residual periodic-boundary offset. By separating the physical ligand-environment interaction from artifact-contaminated terms, EID corrects charge-changing FEP results without PB/continuum-electrostatics calculations or alchemically transformed particles. In benchmarks across four charged protein-ligand systems, EID achieved improved predictive accuracy and more consistent cross-system performance than both comparison methods. Because EID operates as a postprocessing step requiring no additional simulations or PB calculations, it provides a rigorous, immediately deployable solution for charge-changing free energy calculations.
Runduo Liu, Wanyi Huang, Yufen Yao et al.· Journal of Chemical Theory a...· 0 citations
Accurate solvation free energies from molecular dynamics simulations require efficient sampling of coupled slow variables, including solvent coordinates, solute conformational modes, and the alchemical coordinate $\lambda$. Here, we develop a $\lambda$-dynamics framework that combines mass scaling, on-the-fly probability enhanced sampling (OPES), and driven adiabatic free energy dynamics (d-AFED) to address these sampling challenges within a unified protocol. For rigid organic solutes, Hamiltonian replica exchange with mass scaling is first used to quantify the effect of octanol solvent relaxation. Reducing all octanol atomic masses by a factor of ten accelerates convergence by more than fivefold while preserving equilibrium solvation free energies. These calculations then provide reference benchmarks for $\lambda$-OPES, a dual-bias $\lambda$-dynamics strategy that combines the"standard"and"explore"variants of OPES to promote transitions along the alchemical coordinate. This approach reaches convergence on timescales comparable to replica exchange, but without predefined $\lambda$ windows or multiple parallel simulations. For flexible $N$-acetyl amino-acid amide solutes, $\lambda$-OPES is coupled with d-AFED on selected backbone and side-chain dihedrals to enable simultaneous alchemical and conformational enhanced sampling. This combined strategy improves agreement with experimental octanol-water partition coefficients and reduces the mean absolute error from 0.75 log units with $\lambda$-OPES alone to 0.30 log units with $\lambda$-OPES-d-AFED. Overall, this work establishes an integrated enhanced sampling protocol for solvation free energy calculations across rigid organic solutes and flexible peptide-like solutes, and provides a foundation for the application of alchemical free energy methods to larger and more conformationally complex systems.
Gabriela B. Correa, C. Abreu, Nishanth N Nair et al.· 0 citations
Free energies of solvation (ΔGsol) in a prototypical liquid alkane, cyclohexane, have been computed for 101 organic molecules at 25 °C. Monte Carlo statistical mechanics (MC) was used with free-energy perturbation theory (FEP) and both OPLS united-atom (UA) and all-atom (AA) force fields. Updated OPLS-UA parameters are provided along with thermodynamic results for 23 liquid alkanes; the modifications make the UA and AA force fields fully compatible. The average errors for ΔGsol in comparison to experimental data are ca. 0.5 kcal/mol for both force fields. This supports general use of the UA model, since it reduces the required computation times by 5-10-fold. The largest errors are about 1 kcal/mol and occur for small molecules with relatively large dipole moments and for perfluorocarbons. The former case is attributable to the lack of solvent-polarization in the force fields, and the latter issue can be remedied by reducing the Lennard-Jones well depth for the interaction of saturated carbon and fluorine. Results for free energies of hydration are also provided for the 101 solutes in TIP4P water and the average error is again 0.5 kcal/mol. The combined results provide cyclohexane/water free energies of transfer with average errors of 0.7 kcal/mol. In conjunction with prior results for solvation in benzene and perfluorobenzene, the 0.5 kcal/mol level of accuracy seems general for the performance of current generation, nonpolarizable force fields. Implications for modeling hydrophobic effects and protein-ligand binding are also considered.
W. Jorgensen, J. Tirado-Rives· Journal of Chemical Theory a...· 0 citations
Charge-equilibration models predict how electrons redistribute over a molecule more cheaply than quantum chemistry, and each begins from a table of atomic electronegativities and hardnesses. A recent table replaces ionization energies and electron affinities with one geometric quantity: each main-group atom's fractional distance to the noble gas closing its row. Holding geometries, electrostatic damping and the molecule list fixed, we compare it with spectroscopic values, with its own kernel refitted, and with a quadratic control, over a primary set of fifty-two molecules and ions at the B3LYP/def2-TZVP level. Two structural consequences follow from the table construction rather than the equalization solver. Atoms at equal fractional distance receive identical electronegativities, so the dipole moments of chlorine monofluoride, iodine monobromide and sulfur dioxide vanish exactly, and the measured $0.72$ debye $\mathrm{HF}/\mathrm{HCl}$ gap is lost. Because the first period is excluded, hydrogen retains its spectroscopic electronegativity above every geometric value, reversing $\mathrm{O{-}H}$, $\mathrm{N{-}H}$ and hydrogen-halide polarity. Fitted alike, geometric and quadratic kernels agree to $0.0022$ electron per atom, so predictions are set by the fitted energy scales, not the kernel shape. Resolving the electronegativity scale period by period restores correct polarity in all five polyatomic heavy-atom-hydrogen tests.
Megan Simons, Jonathan Washburn, Elshad Allahyarov· 0 citations
The generalized PB theory is validated using a perturbed two-atom system and a diverse set of proteins with different structures in vacuum and water, demonstrating its accuracy and robustness, regardless of the choice of sharp-interface and diffuse-interface PB models and different numerical solvers.
Matthias Dogbatsey, Yuanzhen Shao, Emil Alexov et al.· 0 citations
This work employs a dual-coordinate approach where both solutes are explicitly present but do not interact with one another, and utilizes a harmonic ″anchor″ restraint to a central atom on each molecule to enforce spatial overlap without modifying the internal intramolecular dynamics of either solute.
Anna Katharina Picha, S. Boresch· Journal of Chemical Theory a...· 1 citation
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