Jul 2026· Journal of Chemical Theory and Computation· Vol 22 15, pp.
7981-7992
· 0 citations· 47 references
Medicine
Abstract
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.
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.
Lakshmanji Verma, Ken A. Dill· Journal of Chemical Theory a...· 0 citations
The Poisson-Boltzmann (PB) theory is a cornerstone of implicit solvent models for electrostatic analysis, and has found a great success in various biomolecular applications. However, in calculating polar solvation energy, one should consider that the structure of the protein changes upon transition from vacuum to water phases. To address this, here we report for the first time a generalized PB framework capable of accommodating nonrigid conformational changes without suffering from self-energy artifacts. For regularized PB models, in which the charge singularities are captured by the Green's functions, self-energies in the water and vacuum states will be analytically canceled. For non-regularized PB solvers, such as APBS and DelPhi, a simple thermodynamic cycle is proposed for nonrigid proteins by adding a Coulombic correction in vacuum. 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
Interatomic potentials which accurately describe long-range electrostatics require atom-centered charges. One such method to determine these atom-centered charges from density functional theory (DFT) calculations is the density-derived atomic point (DDAP) charge method. DDAP fits atom-centered Gaussians to the ground-state DFT charge density and preserves the multipole moments that govern long-range electrostatics. While these charges accurately predict long-range behavior, in practice, they are limited by their reliance on fixed, heuristic parameters and a constrained solver that becomes numerically unstable for complex or covalent systems. In this work, we present opt-DDAP, which solves this limitation by reformulating the algorithm as a differentiable computational graph. This reformulation allows for the optimization of Gaussian basis parameters and the reciprocal-space cutoff using automatic differentiation. To ensure numerical robustness through this automatic differentiation process, we replace the conventional Lagrange-multiplier approach with a pseudoinverse solution followed by charge renormalization, maintaining stability even in the presence of ill-conditioned matrices. We validate the framework on NaCl vacancy supercells and on MoS2, demonstrating faithful reconstruction of both absolute and difference charge densities. The optimized charges are intended to serve as inputs to effective electrostatic models in machine learning and empirical interatomic potentials that incorporate long-range interactions.
M. H, Sudarshan Vijay· Journal of Chemical Theory a...· 0 citations
Electrostatic embedding improved every accuracy and correlation metric for TYK2 but performed comparably to the classical and mechanical-embedding baselines for CDK2, thrombin, p38 and JNK1, and standard single-molecule energy and charge benchmarks were not good predictors of this target-dependent outcome.
We present a statistical-mechanics framework for computing equilibrium binding constants $K$ in the dilute limit. From first principles, we derive a general expression relating $K$ to the relative populations of the bound and unbound states. Its transparency has twofold advantage: it makes the origin of the unbound-state volumetric term explicit, and it allows one to track exactly how an imposed volume restraint propagates through the expression. This makes $K$ directly computable, as restrained simulations can account for the volumetric contribution exactly, under the physically mild assumption of a homogeneous unbound state. The resulting estimators are computable from histograms of any suitably defined reaction coordinate, and determine unambiguously how the boundaries of the thermodynamic states of interest must be defined. We apply our framework to the cucurbit[7]uril/1-adamantanol host--guest complex and the galactonate--DgoT ligand--protein complex. Our results show that commonly used single-bin estimators depart from the theoretically correct one by $\approx 1$~kcal/mol in both systems. This shift originates in the definition of the bound state: by anchoring that definition to what state-of-the-art experiments resolve, the theory turns it from a hidden assumption into a controlled input, and provides a principled route to absolute binding affinities from molecular simulations.
Davide Mandelli, E. Ippoliti, C. Plate· 0 citations
We present an efficient plane-wave implementation of analytical nuclear forces for electronic excited states described by the Bethe-Salpeter equation (BSE). The formulation combines density-matrix perturbation theory with a Lagrangian approach, and avoids both explicit empty-state summations and the response calculations for each atomic displacement, required by conventional approaches based on density functional perturbation theory. Together with GPU acceleration, these advances make BSE forces calculations tractable for solid-state systems containing hundreds of atoms. We demonstrate the method on two point defects with distinct dielectric environments: the nitrogen-vacancy center in diamond, where BSE and time-dependent density functional theory (TDDFT) yield consistent excited-state relaxations, and the carbon-dimer defect in two-dimensional hexagonal boron nitride, where the screened electron-hole interaction included in the BSE stabilizes the localized defect excitation and corrects the relaxation pattern predicted by semilocal TDDFT. These results establish a scalable framework for BSE-level studies of excited-state relaxation and vibronic coupling in heterogeneous condensed systems.
Yu-Ming Jin, V. Yu, M. Govoni et al.· 2 citations· ⚡1