Ion solvation thermodynamics from simulation with a polarizable force field

Thermodynamic measurements of the solvation of salts and electrolytes are relatively straightforward, but it is not possible to separate total solvation free energies into distinct cation and anion contributions without reference to an additional extrathermodynamic assumption. The present work attempts to resolve this difficulty using molecular dynamics simulations with the AMOEBA polarizable force field and perturbation techniques to directly compute absolute solvation free energies for potassium, sodium, and chloride ions in liquid water and formamide. Corresponding calculations are also performed with two widely used nonpolarizable force fields. The simulations with the polarizable force field accurately reproduce in vacuo quantum mechanical results, experimental ion-cluster solvation enthalpies, and experimental solvation free energies for whole salts, while the other force fields do not. The results indicate that calculations with a polarizable force field can capture the thermodynamics of ion solvation and that the solvation free energies of the individual ions differ by several kilocalories from commonly cited values.     

Polarizable solute in polarizable and flexible solvents: simulation study of electron transfer reaction systems

A polarizable solute model, based on the empirical valence bond approach, is developed and applied to electron transfer (ET) reactions in polarizable and flexible water solvents. The polarization effect is investigated in comparison with a nonpolarizable solute and solvent model. With free energy curves constructed by a molecular dynamics simulation, the activation energy barrier and the reorganization energy related to ET processes are investigated. The present simulation results show that the activation energy barrier becomes larger in the polarizable model than in the nonpolarizable model and that this makes the ET rate slower than that with the nonpolarizable model. It is shown that the effect of the electronic energy difference of solute molecule on free energy profiles is remarkable and that, corresponding to this effect, the reorganization energy is significantly modified. These results indicate that the process of solvent polarization by the polarized solute to enhance the solute-solvent interaction is a key factor and that treating the polarization of both solute and solvent at the same time is essential. Also, the polarization effect on the diffusive motion of the solute molecule in the polarization solvent is studied. The polarized solute molecule shows slower diffusive motion compared with that in the nonpolarizable model.     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

Predicting hydration free energies with chemical accuracy: the SAMPL4 challenge

An implicit solvent model described by a non-simple dielectric medium is used for the prediction of hydration free energies on the dataset of 47 molecules in the SAMPL4 challenge. The solute is represented by a minimal parameter set model based on a new all atom force-field, named the liquid simulation force-field. The importance of a first solvation shell correction to the hydration free energy prediction is discussed and two different approaches are introduced to address it: either with an empirical correction to a few functional groups (alcohol, ether, ester, amines and aromatic nitrogen), or an ab initio correction based on the formation of a solute/explicit water complex. Both approaches give equally good predictions with an average unsigned error <1 kcal/mol. Chemical accuracy is obtained.     

Combining a polarizable force-field and a coarse-grained polarizable solvent model. II. Accounting for hydrophobic effects

A revised and improved version of our efficient polarizable force-field/coarse grained solvent combined approach (Masella, Borgis, and Cuniasse, J. Comput. Chem. 2008, 29, 1707) is described. The polarizable pseudo-particle solvent model represents the macroscopic solvent polarization by induced dipoles placed on mobile pseudo-particles. In this study, we propose a new formulation of the energy term handling the nonelectrostatic interactions among the pseudo-particles. This term is now able to reproduce the energetic and structural response of liquid water due to the presence of a hydrophobic spherical cavity. Accordingly, the parameters of the energy term handling the nonpolar solute/solvent interactions have been refined to reproduce the free-solvation energy of small solutes, based on a standard thermodynamic integration scheme. The reliability of this new approach has been checked for the properties of solvated methane and of the solvated methane dimer, as well as by performing 10 × 20 ns molecular dynamics (MD) trajectories for three solvated proteins. A long-time stability of the protein structures along the trajectories is observed. Moreover, our method still provides a measure of the protein solvation thermodynamic at the same accuracy as standard Poisson-Boltzman continuum methods. These results show the relevance of our approach and its applicability to massively coupled MD schemes to accurately and intensively explore solvated macromolecule potential energy surfaces.     

A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6

Successive parameterizations of the GROMOS force field have been used successfully to simulate biomolecular systems over a long period of time. The continuing expansion of computational power with time makes it possible to compute ever more properties for an increasing variety of molecular systems with greater precision. This has led to recurrent parameterizations of the GROMOS force field all aimed at achieving better agreement with experimental data. Here we report the results of the latest, extensive reparameterization of the GROMOS force field. In contrast to the parameterization of other biomolecular force fields, this parameterization of the GROMOS force field is based primarily on reproducing the free enthalpies of hydration and apolar solvation for a range of compounds. This approach was chosen because the relative free enthalpy of solvation between polar and apolar environments is a key property in many biomolecular processes of interest, such as protein folding, biomolecular association, membrane formation, and transport over membranes. The newest parameter sets, 53A5 and 53A6, were optimized by first fitting to reproduce the thermodynamic properties of pure liquids of a range of small polar molecules and the solvation free enthalpies of amino acid analogs in cyclohexane (53A5). The partial charges were then adjusted to reproduce the hydration free enthalpies in water (53A6). Both parameter sets are fully documented, and the differences between these and previous parameter sets are discussed.     

Monte Carlo simulations of the solution structure of simple alcohols in water-acetonitrile mixtures

Monte Carlo simulations have been performed to explore the solution structure of ethyl, isopropyl, isobutyl, and tertiary butyl alcohols in pure water, pure acetonitrile, and different mixtures of the two solvents. The explicit solvent studies in NpT ensembles at T = 298 K illustrate that the solute "discriminates" the solvent's components and that the composition of the first solvation shell differs from that of the bulk solution. Since the polarizable continuum dielectric method (PCM) does not presently model the solvation of molecules with both polar and apolar sites in mixed protic solvents, we suggest a direction for further program development wherein a continuum dielectric method would accept more than one solvent and the solute sites would be solvated by user-defined solvent components. The prevailing solvation model will be determined upon the lowest free energy calculated for a particular solvation pattern of the solute having a specific conformational/tautomeric state. Characterization of equilibrium hydrogen-bond formation becomes a complicated problem that depends on the chemical properties of the solute and its conformation, as well as upon the varying nature of the first solvation shell. For example, while the number of hydrogen bonds to secondary and tertiary alcohol solutes are nearly constant in pure water and in water-acetonitrile mixtures with at least 50% water content, the number of hydrogen bonds to primary alcohols gradually decreases for most of their conformations when acetonitrile content is increased. Nonetheless, the calculations indicate that O-H...O(water) hydrogen bonds are still possible in a small fraction of the arrangements for the solution models with water content of 30% or less. The isopentene solute does not form any observable hydrogen bonds, despite having an electron-rich, double-bond site.     

On the transferability of hydration-parametrized continuum electrostatics models to solvated binding calculations

Using molecular mechanics force field partial atomic charges, we show the nonuniqueness of the parametrization of continuum electrostatics models with respect to solute atomic radii and interior dielectric constant based on hydration (vacuum-to-water transfer) free energy data available for small molecules. Moreover, parameter sets that are optimal and equivalent for hydration free energy calculations lead to large variations of calculated absolute and relative electrostatic binding free energies. Hence, parametrization of solvation effects based on hydration data, although a necessary condition, is not sufficient to guarantee its transferability to the calculation of binding free energies in solution.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.     

A systematic approach to calibrate a transferable polarizable force field parameter set for primary alcohols

In this work, parameters are optimized for a charge‐on‐spring based polarizable force field for linear alcohols. We show that parameter transferability can be obtained using a systematic approach in which the effects of parameter changes on physico‐chemical properties calculated from simulation are predicted. Our previously described QM/MM calculations are used to attribute condensed‐phase polarizabilities, and starting from the non‐polarizable GROMOS 53A5/53A6 parameter set, van der Waals and Coulomb interaction parameters are optimized to reproduce pure‐liquid (thermodynamic, dielectric, and transport) properties, as well as hydration free energies. For a large set of models, which were obtained by combining small perturbations of 10 distinct parameters, values for pure‐liquid properties of the series methanol to butanol were close to experiment. From this large set of models, we selected 34 models without special repulsive van der Waals parameters to distinguish between hydrogen‐bonding and non‐hydrogen‐bonding atom pairs, to make the force field simple and transparent. © 2017 Wiley Periodicals, Inc.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999     

Theoretical studies on the effects of methods and parameterization on the calculated free energy of hydration for small molecules

Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In‐solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree–Fock levels with two basis sets (6‐31G* and 6‐311++G**). Good linear correlation has been obtained for calculated and experimental gas‐phase dipole moments, with an increase by ～30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6‐31G* and 6‐311++G** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas‐phase and in‐solution molecular electrostatic potentials at in‐solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all‐atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6‐31G* level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Force field evaluation for biomolecular simulation: free enthalpies of solvation of polar and apolar compounds in various solvents.

Recently, the GROMOS biomolecular force field parameter set 53A6--which has been parametrized to reproduce experimentally determined free enthalpies of hydration and solvation in cyclohexane of amino acid side-chain analogs--was presented. To investigate the transferability of the new parameter set, we calculated free enthalpies of solvation of a range of polar and apolar compounds in different solvents (methanol, dimethyl sulfoxide (DMSO), acetonitrile, and acetone) from molecular dynamics simulations using the GROMOS 53A6 force field. For methanol and DMSO, parameters were used that are available in the 53A6 parameter set. For acetonitrile, a recently developed model was taken and for acetone, two models available in literature were used. We found that trends in and values for the solvation free enthalpies are in satisfactory agreement with experiment, except for the solvation in acetone for which deviations from experiment can be explained in terms of the properties of the models used.     

Amine hydration: a united-atom force-field solution.

The free energies of hydration for ammonia and mono-, di-, and trimethylated amines experimentally show an unexpected trend that has, in the past, been difficult to reproduce computationally. Absolute and relative free energies of hydration of these compounds were calculated using the OPLS all-atom and the united-atom GROMOS force fields. Both force fields reproduce the relative free energy of hydration, but the absolute free energies of hydration were only reproduced within kBT when using the recently developed GROMOS parameter set 53A6. Relative free energies of solvation in chloroform could also be reproduced indicating a proper partitioning of the compounds between polar and apolar media. Overall we conclude that it is possible to resolve the amine hydration problem using a simple united-atom force field.     

Electrostatic polarization is crucial for reproducing pKa shifts of carboxylic residues in Turkey ovomucoid third domain

We have computed pKa shifts for carboxylic residues of the serine protease inhibitor turkey ovomucoid third domain (residues Asp7, Glu10, Glu19, Asp27, and Glu43). Both polarizable and nonpolarizable empirical force fields were employed. Hydration was represented by the surface generalized Born and Poisson-Boltzmann continuum model. The calculations were carried out in the most physically straightforward fashion, by directly comparing energies of the protonated and deprotonated protein forms, without any additional parameter fitting or adjustment. Our studies have demonstrated that (i) the Poisson-Boltzmann solvation model is more than adequate in reproducing pKa shifts, most likely due to its intrinsically many-body formalism; (ii) explicit treatment of electrostatic polarization included in our polarizable force field (PFF) calculations appears to be crucial in reproducing the acidity constant shifts. The average error of the PFF results was found to be as low as 0.58 pKa units, with the best fixed-charges average deviation being 3.28 units. Therefore, the pKa shifts phenomena and the governing electrostatics are clearly many-body controlled in their intrinsic nature; (iii) our results confirm previously reported conclusions that pKa shifts for protein residues are controlled by the immediate environment of the residues in question, as opposed to long-range interactions in proteins. We are confident that our confirmation of the importance of explicit inclusion of polarization in empirical force fields for protein studies will be useful far beyond the immediate goal of accurate calculation of acidity constants.     

Calculations of the free energy of interaction of the c-Fos-c-Jun coiled coil: effects of the solvation model and the inclusion of polarization effects

The leucine zipper region of activator protein-1 (AP-1) comprises the c-Jun and c-Fos proteins and constitutes a well-known coiled coil protein-protein interaction motif. We have used molecular dynamics (MD) simulations in conjunction with the molecular mechanics/Poisson-Boltzmann generalized-Born surface area [MM/PB(GB)SA] methods to predict the free energy of interaction of these proteins. In particular, the influence of the choice of solvation model, protein force field, and water potential on the stability and dynamic properties of the c-Fos-c-Jun complex were investigated. Use of the AMBER polarizable force field ff02 in combination with the polarizable POL3 water potential was found to result in increased stability of the c-Fos-c-Jun complex. MM/PB(GB)SA calculations revealed that MD simulations using the POL3 water potential give the lowest predicted free energies of interaction compared to other nonpolarizable water potentials. In addition, the calculated absolute free energy of binding was predicted to be closest to the experimental value using the MM/GBSA method with independent MD simulation trajectories using the POL3 water potential and the polarizable ff02 force field, while all other binding affinities were overestimated.     

Simulations of solvation free energies and solubilities in supercritical solvents

Computer simulations are used to study solvation free energies and solubilities in supercritical solvents. Solvation free energies are calculated using the particle insertion method. The equilibrium solvent configurations required for these calculations are based on molecular dynamics simulations employing model solvent potentials previously tuned to reproduce liquid-vapor coexistence properties of the fluids Xe, C(2)H(6), CO(2), and CHF(3). Solutes are represented by all-atom potentials based on ab initio calculations and the OPLS-AA parameter set. Without any tuning of the intermolecular potentials, such calculations are found to reproduce the solvation free energies of a variety of typical solid solutes with an average accuracy of +/-2 kJmol. Further calculations on simple model solutes are also used to explore general aspects of solvation free energies in supercritical solvents. Comparisons of solutes in Lennard-Jones and hard-sphere representations of Xe show that solvation free energies and thus solubilities are not significantly influenced by solvent density fluctuations near the critical point. The solvation enthalpy and entropy do couple to these fluctuations and diverge similarly to solute partial molar volumes. Solvation free energies are also found to be little affected by the local density augmentation characteristic of the compressible regime. In contrast to solute-solvent interaction energies, which often provide a direct measure of local solvent densities, solvation free energies are remarkably insensitive to the presence of local density augmentation.     

Hydration free energies of monovalent ions in transferable intermolecular potential four point fluctuating charge water: an assessment of simulation methodology and force field performance and transferability

Hydration free energies of nonpolarizable monovalent atomic ions in transferable intermolecular potential four point fluctuating charge (TIP4P-FQ) are computed using several commonly employed ion-water force fields including two complete model sets recently developed for use with the simple water model with four sites and Drude polarizability and TIP4P water models. A simulation methodology is presented which incorporates a number of finite-system free energy corrections within the context of constant pressure molecular dynamics simulations employing the Ewald method and periodic boundary conditions. The agreement of the computed free energies and solvation structures with previously reported results for these models in finite droplet systems indicates good transferability of ion force fields from these water models to TIP4Q-FQ even when ion polarizability is neglected. To assess the performance of the ion models in TIP4P-FQ, we compare with consensus values for single-ion hydration free energies arising from recently improved cluster-pair estimates and a reevaluation of commonly cited, experimentally derived single-ion hydration free energies; we couple the observed consistency of these energies with a justification of the cluster-pair approximation in assigning single-ion hydration free energies to advocate the use of these consensus energies as a benchmark set in the parametrization of future ion force fields.     

Ab initio parameterization of an all-atom polarizable and dissociable force field for water

A novel all-atom, dissociative, and polarizable force field for water is presented. The force field is parameterized based on forces, stresses, and energies obtained form ab initio calculations of liquid water at ambient conditions. The accuracy of the force field is tested by calculating structural and dynamical properties of liquid water and the energetics of small water clusters. The transferability of the force field to dissociated states is studied by considering the solvation of a proton and the ionization of water at extreme conditions of pressure and temperature. In the case of the solvated proton, the force field properly describes the presence of both Eigen and Zundel configurations. In the case of the pressure-induced ice VIII/ice X transition and the temperature-induced transition to a superionic phase, the force field is found to describe accurately the proton symmetrization and the melting of the proton sublattice, respectively.     

Interior and interfacial aqueous solvation of benzene dicarboxylate dianions and their methylated analogues: A combined molecular dynamics and photoelectron spectroscopy study

Aqueous solvation of benzene dicarboxylate dianions (BCD(2-)) was studied by means of photoelectron spectroscopy and molecular dynamics simulations. Photoelectron spectra of hydrated o- and p-BCD(2-) with up to 25 water molecules were obtained. An even-odd effect was observed for the p-BCD(2-) system as a result of the alternate solvation of the two negative charges. However, the high polarizability of the benzene ring makes the two carboxylate groups interact with each other in p-BCD(2-), suppressing the strength of this even-odd effect compared with the linear dicarboxylate dianions linked by an aliphatic chain. No even-odd effect was observed for the o-BCD(2-) system, because each solvent molecule can interact with the two carboxylate groups at the same time due to their proximity. For large solvated clusters, the spectral features of the solute decreased while the solvent features became dominant, suggesting that both o- and p-BCD(2-) are situated in the center of the solvated clusters. Molecular dynamics simulations with both nonpolarizable and polarizable force fields confirmed that all three isomers (o-, m-, and p-BCD(2-)) solvate in the aqueous bulk. However, upon methylation the hydrophobic forces overwhelm electrostatic interactions and, as a result, the calculations predict that the tetramethyl-o-BCD(2-) is located at the water surface with the carboxylate groups anchored in the liquid and the methylated benzene ring tilted away from the aqueous phase.