Comparative study on solvation free energy expressions in reference interaction site model integral equation theory

The performance of the recently proposed partial wave (PW) free energy functional is compared with those of two previous expressions, Gaussian fluctuation (GF) and hypernetted chain (HNC), within the reference interaction site model framework. The applications to the calculations of ambient and supercritical water, solvation free energies of organic molecules, and partition coefficients clearly show that the PW and GF free energy expressions provide more reliable results than the HNC functional, indicating rather associative situations of geometry in ordinary liquids of medium-sized molecules.     

Coupled reference interaction site model/simulation approach for thermochemistry of solvation: theory and prospects

We present a new methodology for computing solvation free energy, which is based upon the reference interaction site model (RISM)/hypernetted chain (HNC) solvation free energy expression, but which substitutes radial distribution functions taken from simulations for those calculated by simultaneous solution of the RISM and HNC equations. Consequently, solvation free energy can be obtained from a single molecular dynamics or Monte Carlo simulation. Here we describe in detail the coupled RISM/simulation approach, and offer some error analysis. Finally we give the results of its application to a set of small test molecules in aqueous solution. The success shown in some of our results demonstrates that the coupled RISM/simulation approach is worth considering further as a potentially useful tool in studies of solvated systems, such as aqueous molecular biosystems.     

Continuum solvation models in the linear interaction energy method

The linear interaction energy (LIE) method in combination with two different continuum solvent models has been applied to calculate protein-ligand binding free energies for a set of inhibitors against the malarial aspartic protease plasmepsin II. Ligand-water interaction energies are calculated from both Poisson-Boltzmann (PB) and Generalized Born (GB) continuum models using snapshots from explicit solvent simulations of the ligand and protein-ligand complex. These are compared to explicit solvent calculations, and we find close agreement between the explicit water and PB solvation models. The GB model overestimates the change in solvation energy, and this is caused by consistent underestimation of the effective Born radii in the protein-ligand complex. The explicit solvent LIE calculations and LIE-PB, with our standard parametrization, reproduce absolute experimental binding free energies with an average unsigned error of 0.5 and 0.7 kcal/mol, respectively. The LIE-GB method, however, requires a constant offset to approach the same level of accuracy.     

Calculation of relative solvation free energy differences by thermodynamic perturbation method: Dependence of free energy results on simulation length

Molecular dynamics (MD) simulations in conjunction with the thermodynamic cycle perturbation approach has been used to calculate relative solvation free energies for acetone to acetaldehyde, acetone to pyruvic acid, acetone to 1,1,1-trifluoroacetone, acetone to 1,1,1-trichloroacetone, acetone to 2,3-butanedione, acetone to cyclopropanone, and formaldehyde hydrate to formaldehyde. To evaluate the dependence of relative solvation free energy convergence on MD simulation length and starting configuration two studies were performed. In the first study, each simulation started from the same well-equilibrated configuration and the length was varied from 153 to 1530 ps. In the second study, the relative solvation free energy differences were calculated starting from three different configurations and using 510 ps of MD simulation for each mutation. These results clearly indicate that, even for molecules with limited conformational flexibility, a simulation length of 510 ps or greater is required to obtain satisfactory convergence and, for the mutations of large structural changes between reactant and product, such as cyclopropanone to acetone, require much longer simulation lengths to achieve satisfactory convergence. These results also show that performing one long simulation is better than averaging results from three shortest simulations of the same length using different starting conformations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1018–1027, 1999     

Ab initio quantum mechanics-based free energy perturbation method for calculating relative solvation free energies

A free energy perturbation (FEP) method was developed that uses ab initio quantum mechanics (QM) for treating the solute molecules and molecular mechanics (MM) for treating the surroundings. Like our earlier results using AM1 semi empirical QMs, the ab initio QM/MM-based FEP method was shown to accurately calculate relative solvation free energies for a diverse set of small molecules that differ significantly in structure, aromaticity, hydrogen bonding potential, and electron density. Accuracy was similar to or better than conventional FEP methods. The QM/MM-based methods eliminate the need for time-consuming development of MM force field parameters, which are frequently required for drug-like molecules containing structural motifs not adequately described by MM. Future automation of the method and parallelization of the code for Linux 128/256/512 clusters is expected to enhance the speed and increase its use for drug design and lead optimization.     

Decomposition of the solvation free energies of deoxyribonucleoside triphosphates using the free energy perturbation method

Free energy perturbation (FEP) calculations using the Amber 95 force field and the TIP3P water model were carried out to evaluate the solvation free energy of deoxyribonucleoside triphosphates in aqueous solution. Solvation free energies of -307.5, -311.5, -314.1, and -317.0 kcal/mol were calculated for the (Mg x dTTP)2-, (Mg x dATP)2-, (Mg x dCTP)2-, and (Mg x dGTP)2- complexes, respectively. Structural origins of the relative solvation free energies of deoxyribonucleoside phosphates were examined by calculating the contribution of the interaction of the base moiety with its surroundings. We showed that for each nucleobase the magnitude of this contribution is unaffected by substituting the 5'-OH group of the corresponding nucleoside with the charged mono- or triphosphate groups. This free energy contribution was further decomposed into the sum of free energies originating from the interactions of the base with itself, its substituent, water, and Na+ ions. Although the sum of these components was nearly constant over a wide range of solutes the individual free energy constituents varied significantly. Furthermore, this decomposition showed a high degree of additivity. Computational conditions necessary for obtaining additive free energy decomposition for the systems studied here within the framework of the FEP method included the use of a single mutation pathway and a subdivision of the FEP protocol into 51 or more windows.     

New generation of the reference interaction site model self-consistent field method: introduction of spatial electron density distribution to the solvation theory

The authors propose the new generation of the reference interaction site model self-consistent field (RISM-SCF) method for the solvation effect on the electronic structure of a solute molecule, in which the procedure proposed by Gill et al. [J. Chem. Phys. 96, 7178 (1992)] is adopted. Main improvements are the introduction of spatial electron density distribution and the removal of the grid dependency that is inherent in the original RISM-SCF. The procedure also provides very stable determination of the effective charges even if a buried atom exists in the target molecule and eventually extends the applicability of the RISM-SCF. To demonstrate the superiority of our method, sample calculations for H2O, C2H5OH, and HLi in aqueous solution are presented.     

New approach to free energy of solvation applying continuum models to molecular dynamics simulation

A new approach to the calculation of the free energy of solvation from trajectories obtained by molecular dynamics simulation is presented. The free energy of solvation is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent nonpolar (repulsion and dispersion) interactions, and the electrostatic solvation of the solute. The electrostatic term is calculated based on ideas developed for the broadly used continuum models, the cavitational contribution from the excluded volume by the Claverie-Pierotti model, and the Van der Waals term directly from the molecular dynamics simulation. The proposed model is tested for diluted aqueous solutions of simple molecules containing a variety of chemically important functions: methanol, methylamine, water, methanethiol, and dichloromethane. These solutions were treated by molecular dynamics simulations using SPC/E water and the OPLS force field for the organic molecules. Obtained free energies of solvation are in very good agreement with experimental data.     

Relative solvation free energies calculated using an ab initio QM/MM-based free energy perturbation method: dependence of results on simulation length

Molecular dynamics (MD) simulations in conjunction with thermodynamic perturbation approach was used to calculate relative solvation free energies of five pairs of small molecules, namely; (1) methanol to ethane, (2) acetone to acetamide, (3) phenol to benzene, (4) 1,1,1 trichloroethane to ethane, and (5) phenylalanine to isoleucine. Two studies were performed to evaluate the dependence of the convergence of these calculations on MD simulation length and starting configuration. In the first study, each transformation started from the same well-equilibrated configuration and the simulation length was varied from 230 to 2,540 ps. The results indicated that for transformations involving small structural changes, a simulation length of 860 ps is sufficient to obtain satisfactory convergence. In contrast, transformations involving relatively large structural changes, such as phenylalanine to isoleucine, require a significantly longer simulation length (>2,540 ps) to obtain satisfactory convergence. In the second study, the transformation was completed starting from three different configurations and using in each case 860 ps of MD simulation. The results from this study suggest that performing one long simulation may be better than averaging results from three different simulations using a shorter simulation length and three different starting configurations.     

Molecular dynamics simulation of acetamide solvation using interaction energy components: Application to structural and energy properties

Molecular dynamics simulation of an aqueous solution of acetamide was performed using Lennard–Jones 12-6-1 potentials to describe the solute–solvent interactions, and TIP3P to describe the water–water interactions. The Morokuma decomposition scheme and the ESIE solute atomic charges were used to reproduce the molecular parameters of the solute–water interaction potential. The results showed that the functions that use the EX-PL-DIS-ES interaction model lead to good values of the structural and energy properties (in particular, the hydration shell and the solvation energies) when they are compared with those from using AMBER-derived parameters, and with the available theoretical and experimental data.     

A method for calculating the Gibbs energy of nonspecific solvation

A method for calculating the Gibbs energy of nonspecific solvation of nonelectrolytes was suggested. The new equation for the Gibbs energy of nonspecific solvation contains one solvent parameter that characterize nonspecific solvent-solute interactions and two experimental Gibbs energies of solvation in two standard solvents. The method is applicable to a wide range of solutes and solvents. It was successfully used to describe some 800 Gibbs energies of solvation for systems without specific solvent-solute interactions.     

Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton

Thermochemical cycles that involve pKa, gas-phase acidities, aqueous solvation free energies of neutral species, and gas-phase clustering free energies have been used with the cluster pair approximation to determine the absolute aqueous solvation free energy of the proton. The best value obtained in this work is in good agreement with the value reported by Tissandier et al. (Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787), who applied the cluster pair approximation to a less diverse and smaller data set of ions. We agree with previous workers who advocated the value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton. Considering the uncertainties associated with the experimental gas-phase free energies of ions that are required to use the cluster pair approximation as well as analyses of various subsets of data, we estimate an uncertainty for the absolute aqueous solvation free energy of the proton of no less than 2 kcal/mol. Using a value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton, we expand and update our previous compilation of absolute aqueous solvation free energies; this new data set contains conventional and absolute aqueous solvation free energies for 121 unclustered ions (not including the proton) and 147 conventional and absolute aqueous solvation free energies for 51 clustered ions containing from 1 to 6 water molecules. When tested against the same set of ions that was recently used to develop the SM6 continuum solvation model, SM6 retains its previously determined high accuracy; indeed, in most cases the mean unsigned error improves when it is tested against the more accurate reference data.     

Shared solvation of sodium ions in alcohol-water solutions explains the non-ideality of free energy of solvation

In order to explain the discrepancies between theories and experiments regarding the non-ideality in the free energy of solvation, here we present a microscopic picture of sodium ions dissolved in water-alcohol mixed solvents. We used X-ray absorption spectroscopy to probe the K-edge of sodium ions in mixed solvents of water and alcohols (methanol, ethanol) and in the respective pure solvents. In the mixed solvents a shared solvation of the sodium ions is observed. We find that specifically the water component plays a key role in stabilizing the solvation shell in mixed solvents, which was revealed by a selective photochemical process occurring only in the pure alcohol solvents.     

Electrostatic solvation free energy of amino acid side chain analogs: implications for the validity of electrostatic linear response in water

Electrostatic free energies of solvation for 15 neutral amino acid side chain analogs are computed. We compare three methods of varying computational complexity and accuracy for three force fields: free energy simulations, Poisson-Boltzmann (PB), and linear response approximation (LRA) using AMBER, CHARMM, and OPLS-AA force fields. We find that deviations from simulation start at low charges for solutes. The approximate PB and LRA produce an overestimation of electrostatic solvation free energies for most of molecules studied here. These deviations are remarkably systematic. The variations among force fields are almost as large as the variations found among methods. Our study confirms that success of the approximate methods for electrostatic solvation free energies comes from their ability to evaluate free energy differences accurately.     

Incorporating the excluded solvent volume and surface charges for computing solvation free energy

Gauss's law or Poisson's equation is conventionally used to calculate solvation free energy. However, the near‐solute dielectric polarization from Gauss's law or Poisson's equation differs from that obtained from molecular dynamics (MD) simulations. To mimic the near‐solute dielectric polarization from MD simulations, the first‐shell water was treated as two layers of surface charges, the densities of which are proportional to the electric field at the solvent molecule that is modeled as a hard sphere. The intermediate water was treated as a bulk solvent. An equation describing the solvation free energy of ions using this solvent scheme was derived using the TIP3P water model. © 2013 Wiley Periodicals, Inc.     

A new quantum method for electrostatic solvation energy of protein

A new method that incorporates the conductorlike polarizable continuum model (CPCM) with the recently developed molecular fractionation with conjugate caps (MFCC) approach is developed for ab initio calculation of electrostatic solvation energy of protein. The application of the MFCC method makes it practical to apply CPCM to calculate electrostatic solvation energy of protein or other macromolecules in solution. In this MFCC-CPCM method, calculation of protein solvation is divided into calculations of individual solvation energies of fragments (residues) embedded in a common cavity defined with respect to the entire protein. Besides computational efficiency, the current approach also provides additional information about contribution to protein solvation from specific fragments. Numerical studies are carried out to calculate solvation energies for a variety of peptides including alpha helices and beta sheets. Excellent agreement between the MFCC-CPCM result and those from the standard full system CPCM calculation is obtained. Finally, the MFCC-CPCM calculation is applied to several real proteins and the results are compared to classical molecular mechanics Poisson-Boltzmann (MM/PB) and quantum Divid-and-Conque Poisson-Boltzmann (D&C-PB) calculations. Large wave function distortion energy (solute polarization energy) is obtained from the quantum calculation which is missing in the classical calculation. The present study demonstrates that the MFCC-CPCM method is readily applicable to studying solvation of proteins.     

Stochastic dynamics simulation of alanine dipeptide: Including solvation interaction determined by boundary element method

A merger of the Poisson–Boltzmann equation and stochastic dynamics simulation is examined using illustrative calculations of alanine dipeptide. The boundary element method (BEM) is used to calculate the hydration forces acting on the solute molecule based on the surroundings. Computational efficiency is achieved by the use of a simple hydration model and a coarse boundary element. Nonetheless, the conformational distribution obtained from this new method is reasonable compared with other theoretical and computational results. Detailed analysis has been accomplished in terms of the hydration interactions and solvation energies. The results indicate that the new simulation method provides an obvious improvement over the conventional stochastic dynamics simulation technique. The further improvement of the hydration model and future application to large molecules are also discussed. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1440–1449, 1997     

Prediction of molecular solvation free energy based on the optimization of atomic solvation parameters with genetic algorithm

We propose an improved solvent contact model to estimate the solvation free energy of an organic molecule from individual atomic contributions. The modification of the solvation model involves the optimization of three kinds of parameters in the solvation free energy function: atomic fragmental volume, maximum atomic occupancy, and atomic solvation parameters. All of these atomic parameters for 24 atom types are developed by the operation of a standard genetic algorithm in such a way as to minimize the difference between experimental and calculated solvation free energies. The data set for experimental solvation free energies is divided into a training set of 131 compounds and a test set of 24 compounds. Linear regressions with the optimized atomic parameters yield fits with the squared correlation coefficients (r2) of 0.89 and 0.86 for the training set and for the test set, respectively. Overall, the results indicate that the improved solvent contact model with the newly developed atomic parameters would be a useful tool for rapid calculation of molecular solvation free energies in aqueous solution.     

Continuous medium theory for nonequilibrium solvation: I. How to correctly evaluate solvation free energy of nonequilibrium

Considering the influences of electrostatic potential Phi upon the change of solute charge distribution deltarho and rho upon the change deltaPhi at the same time, a more reasonable integral formula of dG = (1/2) integral (V) (rhodeltaPhi + Phideltarho)dV is used to calculate the change of the electrostatic free energy in charging the solute-solvent system to a nonequilibrium state, instead of the one of dG = integral (V) PhideltarhodV used before. This modification improves the expressions of electrostatic free energy and solvation free energy, in which no quantity of the intermediate equilibrium state is explicitly involved. Detailed investigation reveals that the solvation free energy of nonequilibrium only contains the interaction energy between the field due to the solute charge in vacuum, and the dielectric polarization at the nonequilibrium state. The solvent reorganization energies of forward and backward electron transfer reactions have been redefined because the derivations lead to a remarkable feature that these quantities are direction-dependent, unlike the theoretical models developed before. The deductions are given in the electric field-displacement form. Relevant discussions on the reliability of theoretical models suggested in this work have also been presented.