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.
Abstract
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.
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
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
We propose an improved model, termed the gradient-corrected PCM (GCPCM), for improving the energy accuracy of the polarizable continuum model (PCM). Our previous study revealed deficiencies of PCM in describing the reaction field, i.e., the electrostatic potential generated by the solvent. These deficiencies can be partially alleviated by introducing an empirical correction to the solvent charges. As a result, solute-solvent interactions are improved at the self-consistent field level, leading to enhanced energy accuracy. The performance of GCPCM was evaluated through single-point calculations and geometry optimizations of phenol and phenolate, calculations of the free energy profile for proton transfer in glycine, and analysis of solvent responses of the HOMO and LUMO orbital energies of Brooker's merocyanine. The results demonstrate that the characteristic destabilization of charged solutes observed in conventional PCM is effectively resolved. Furthermore, despite having a computational cost comparable to that of PCM, GCPCM shows the potential to achieve an energy accuracy similar to that of 3D-RISM-SCF. The development of GCPCM enables more convenient and accurate treatment of solvation effects, which is expected to allow researchers to focus on other important challenges, such as the accurate description of electronic states.
Y. Kanamaru, Norio Yoshida, Toru Matsui· Journal of Chemical Theory a...· 0 citations
Accurate modeling of nonbonded interactions remains challenging because conventional force fields often provide inadequate descriptions of polarization and charge transfer. Here, we introduce a polarizable split-charge equilibration (PSQ) framework that combines localized charge flow with dipolar polarization, thereby mitigating the unphysical long-range charge delocalization associated with polarizable charge-equilibration models. To enable practical large-scale simulations, we develop an efficient PSQ implementation through algorithmic optimization and parallelization, achieving performance comparable to conventional approaches despite the model’s greater formal complexity. We combine PSQ with the universal nonbond potential for van der Waals interactions and an explicit four-body hydrogen-bond term to form the PUxH framework. PUxH achieves near-chemical accuracy in predicting small-molecular pair interactions and accurately reproduces the bulk properties of water, ammonia, and benzene. Overall, PUxH provides a transferable, physically grounded, and computationally efficient framework for modeling nonbonded interactions in molecular and condensed-phase systems.
Taehwan Jang, Minho M. Kim, Hoon Ryu et al.· Journal of Physical Chemistr...· 0 citations
Using the method of solvation Conductor-like Polarizable Continuum Model (C-PCM) and the method of Amovilli-Menucci contained in the GAMESS-US package, were estimated the electrostatic, dispersion and repulsion free energies of organic molecules in 1-octanol and water. The calculations of solvation in water and 1-octanol were performed using the method C-PCM//PBE-VWN/6-31G (2p, 2d), to determine the electrostatic contribution to the solvation free energy. Consequently, using the concept of structure-property relationship was obtained a QSPR model to estimate the cavitation free energies of organic molecules with the experimental solvation free energies. Additionally, with the surface atomics (C, H, N and O) of the atoms that conform to the organic molecules calculated by the method GEPOL-GB, the electrostatic free energies, and non-bonding free energies, two QSPR models were constructed to predict the 1‑octanol/water partition coefficient (logP) for neutral organic molecules containing a single functional group from the following classes: alcohols, ketones, aldehydes, carboxylic acids, esters, ethers, amines, alkanes (linear and cyclic), and aromatic compounds. Model A, which uses electrostatic free energies and atomic surface areas, achieved a correlation coefficient of R² = 0.991, while Model B, which incorporates non-bonding free energies, achieved R² = 0.986. The applicability domain of the models is explicitly defined for monofunctional compounds at infinite dilution and 298.15 K.
J. G. Parra· Molecular Modeling Connect· 0 citations
Hydration plays an essential role in protein–protein interactions. Coarse-grained modeling provides an efficient way to treat hydrated protein complexes without the use of extra-large computational resources. To enhance the capabilities of coarse-grained modeling, we developed an integral equation theory based on the solution of the Ornstein–Zerinke equation to evaluate the hydration structure of peptides and proteins within the framework of coarse-grained modeling. Our current version is based on the SPICA force field, which considers distance-dependent interaction potentials between solvent particles and amino acid segments. Our approach involves two key procedures: an accurate estimation of the structure factor of the uniform fluid and the specific construction of bridge functions obtained from MD simulations. The use of a special hybrid closure allows us to reproduce not only the details of the structure factor, but also the isothermal compressibility obtained from the simulations. The developed bridge functions include two components: an analytical repulsive contribution, which is primarily responsible for the thermodynamic properties, and an attractive contribution obtained from MD simulations. The main assumption in the construction is that the contribution of individual amino acids to the attractive bridge function is additive. By parameterizing the bridge functions, we reproduced details of the hydration structure and accurately calculated the hydration energy for various peptides and proteins. Our method is computationally inexpensive and appears to be suitable for the rapid processing of hydrated proteins of any size.
G. N. Chuev, T. Mamedov, Dmitry O. Morozov· Biomolecules· 0 citations
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