Hydration Free Energy Calculations Research Articles

Evaluation of the SAFT-γ Mie force field with solvation free energy calculations

Solvation free energies can be essential in the process of evaluating and developing force fields. In addition, they can be used to obtain a diversity of other thermodynamic properties such as Henry's law constants and partition coefficients, for instance. In this paper, we study the solvation of asphaltene-like molecules (polyaromatic hydrocarbons) in both aqueous and organic solvents by using a coarse-grained model known as the SAFT-γ Mie force field. This model relies on a top-down approach in which the force-field parameters are obtained using an equation of state. The use of solvation free energy calculations to evaluate this force field can help in improving the model and increasing the scale in which these simulations can be applied. The results presented here were obtained by carrying out molecular dynamics simulations, with the expanded ensemble method being applied to sample an alchemical path. For this, we employed a softcore variant of the Mie potential. From the output of these simulations, we estimated free-energy differences by means of the Multistate Bennett Acceptance Ratio method. The results with organic solvents exhibited low absolute deviations from experimental data. In turn, hydration free energy calculations required a binary interaction parameter to be estimated from molecular dynamics data, which displays a flaw in the top-down parameterization approach. Fortunately, however, a single binary parameter could be used for all pairs of polyaromatic hydrocarbons with water, proving that the SAFT-γ Mie force field exhibits a suitable transferability property that deserves further investigation.

Statistical efficiency of methods for computing free energy of hydration.

The hydration free energy (HFE) is a critical property for predicting and understanding chemical and biological processes in aqueous solution. There are a number of computational methods to derive HFE, generally classified into the equilibrium or non-equilibrium methods, based on the type of calculations used. In the present study, we compute the hydration free energies of 34 small, neutral, organic molecules with experimental HFE between +2 and -16 kcal/mol. The one-sided non-equilibrium methods Jarzynski Forward (JF) and Backward (JB), the two-sided non-equilibrium methods Jarzynski mean based on the average of JF and JB, Crooks Gaussian Intersection (CGI), and the Bennett Acceptance Ratio (BAR) are compared to the estimates from the two-sided equilibrium method Multistate Bennett Acceptance Ratio (MBAR), which is considered as the reference method for HFE calculations, and experimental data from the literature. Our results show that the estimated hydration free energies from all the methods are consistent with MBAR results, and all methods provide a mean absolute error of ∼0.8 kcal/mol and root mean square error of ∼1 kcal for the 34 organic molecules studied. In addition, the results show that one-sided methods JF and JB result in systematic deviations that cannot be corrected entirely. The statistical efficiency ε of the different methods can be expressed as the one over the simulation time times the average variance in the HFE. From such an analysis, we conclude that ε(MBAR) > ε(BAR) ≈ ε(CGI) > ε(JX), where JX is any of the Jarzynski methods. In other words, the non-equilibrium methods tested here for the prediction of HFE have lower computational efficiency than the MBAR method.

Reproducibility of Free Energy Calculations across Different Molecular Simulation Software Packages.

Alchemical free energy calculations are an increasingly important modern simulation technique to calculate free energy changes on binding or solvation. Contemporary molecular simulation software such as AMBER, CHARMM, GROMACS, and SOMD include support for the method. Implementation details vary among those codes, but users expect reliability and reproducibility, i.e., for a given molecular model and set of force field parameters, comparable free energy differences should be obtained within statistical bounds regardless of the code used. Relative alchemical free energy (RAFE) simulation is increasingly used to support molecule discovery projects, yet the reproducibility of the methodology has been less well tested than its absolute counterpart. Here we present RAFE calculations of hydration free energies for a set of small organic molecules and demonstrate that free energies can be reproduced to within about 0.2 kcal/mol with the aforementioned codes. Absolute alchemical free energy simulations have been carried out as a reference. Achieving this level of reproducibility requires considerable attention to detail and package-specific simulation protocols, and no universally applicable protocol emerges. The benchmarks and protocols reported here should be useful for the community to validate new and future versions of software for free energy calculations.

Hydration Free Energies in the FreeSolv Database Calculated with Polarized Iterative Hirshfeld Charges.

Computer simulations of biomolecular systems often use force fields, which are combinations of simple empirical atom-based functions to describe the molecular interactions. Even though polarizable force fields give a more detailed description of intermolecular interactions, nonpolarizable force fields, developed several decades ago, are often still preferred because of their reduced computation cost. Electrostatic interactions play a major role in biomolecular systems and are therein described by atomic point charges. In this work, we address the performance of different atomic charges to reproduce experimental hydration free energies in the FreeSolv database in combination with the GAFF force field. Atomic charges were calculated by two atoms-in-molecules approaches, Hirshfeld-I and Minimal Basis Iterative Stockholder (MBIS). To account for polarization effects, the charges were derived from the solute's electron density computed with an implicit solvent model, and the energy required to polarize the solute was added to the free energy cycle. The calculated hydration free energies were analyzed with an error model, revealing systematic errors associated with specific functional groups or chemical elements. The best agreement with the experimental data is observed for the AM1-BCC and the MBIS atomic charge methods. The latter includes the solvent polarization and presents a root-mean-square error of 2.0 kcal mol-1 for the 613 organic molecules studied. The largest deviation was observed for phosphorus-containing molecules and the molecules with amide, ester and amine functional groups.

Free-Energy Calculations of Ionic Hydration Consistent with the Experimental Hydration Free Energy of the Proton

Computational free-energy correction strategies and the choice of experimental proton hydration free energy, ΔGs*(H+), are analyzed to investigate the apparent controversy in experimental thermodynamics of ionic hydration. Without corrections, the hydration free-energy (ΔGhyd) calculations match experiments with ΔGs*(H+) = -1064 kJ/mol as reference. Using the Galvani surface potential the resulting (real) ΔGhyd are consistent with ΔGs*(H+) = -1098 kJ/mol. When applying, in an ad hoc manner, the discrete solvent correction, ΔGhyd matching the "consensus" ΔGs*(H+) of -1112 kJ/mol are obtained. This analysis rationalizes reports on ΔGhyd calculations for ions using different experimental references. For neutral amino acid side chains ΔGhyd are independent of the water model, whereas there are large differences in ΔGhyd due to the water model for charged species, suggesting that long-range ordering of water around ions yields an important contribution to the ΔGhyd. These differences are reduced significantly when applying consistent corrections, but to obtain the most accurate results it is recommended to use the water model belonging to the force field.

Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database.

Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.

Prediction of cyclohexane-water distribution coefficients for the SAMPL5 data set using molecular dynamics simulations with the OPLS-AA force field.

All-atom molecular dynamics simulations were used to predict water-cyclohexane distribution coefficients [Formula: see text] of a range of small molecules as part of the SAMPL5 blind prediction challenge. Molecules were parameterized with the transferable all-atom OPLS-AA force field, which required the derivation of new parameters for sulfamides and heterocycles and validation of cyclohexane parameters as a solvent. The distribution coefficient was calculated from the solvation free energies of the compound in water and cyclohexane. Absolute solvation free energies were computed by an established protocol using windowed alchemical free energy perturbation with thermodynamic integration. This protocol resulted in an overall root mean square error in [Formula: see text] of almost 4 log units and an overall signed error of -3 compared to experimental data. There was no substantial overall difference in accuracy between simulating in NVT and NPT ensembles. The signed error suggests a systematic error but the experimental [Formula: see text] data on their own are insufficient to uncover the source of this error. Preliminary work suggests that the major source of error lies in the hydration free energy calculations.

An efficient protocol for obtaining accurate hydration free energies using quantum chemistry and reweighting from molecular dynamics simulations

The non-Boltzmann Bennett (NBB) free energy estimator method is applied to 21 molecules from the blind subset of the SAMPL4 challenge. When NBB is applied with the SMD implicit solvent model, and the OLYP/DZP level of quantum chemistry, highly accurate hydration free energy calculations are obtained with respect to experiment (RMSD=0.89kcal·mol−1). Other quantum chemical methods are also tested, and the effects of solvent model, density functional, basis set are explored in this benchmarking study, providing a framework for improvements in calculating hydration free energies. We provide a practical guide for using the best QM-NBB protocols that are consistently more accurate than either pure QM or pure MM alone. In situations where high accuracy hydration free energy predictions are needed, the QM-NBB method with SMD implicit solvent should be the first choice of quantum chemists.

Evaluating Parametrization Protocols for Hydration Free Energy Calculations with the AMOEBA Polarizable Force Field.

Hydration free energy (HFE) calculations are often used to assess the performance of biomolecular force fields and the quality of assigned parameters. The AMOEBA polarizable force field moves beyond traditional pairwise additive models of electrostatics and may be expected to improve upon predictions of thermodynamic quantities such as HFEs over and above fixed-point-charge models. The recent SAMPL4 challenge evaluated the AMOEBA polarizable force field in this regard but showed substantially worse results than those using the fixed-point-charge GAFF model. Starting with a set of automatically generated AMOEBA parameters for the SAMPL4 data set, we evaluate the cumulative effects of a series of incremental improvements in parametrization protocol, including both solute and solvent model changes. Ultimately, the optimized AMOEBA parameters give a set of results that are not statistically significantly different from those of GAFF in terms of signed and unsigned error metrics. This allows us to propose a number of guidelines for new molecule parameter derivation with AMOEBA, which we expect to have benefits for a range of biomolecular simulation applications such as protein-ligand binding studies.

Hydration Free Energies of Molecular Ions from Theory and Simulation.

We present a theoretical/computational framework for accurate calculation of hydration free energies of ionized molecular species. The method is based on a molecular theory, 3D-RISM, combined with a recently developed pressure correction (PC+). The 3D-RISM/PC+ model can provide ∼3 kcal/mol hydration free energy accuracy for a large variety of ionic compounds, provided that the Galvani potential of water is taken into account. The results are compared with direct atomistic simulations. Several methodological aspects of hydration free energy calculations for charged species are discussed.

Accuracy enhancement in the estimation of molecular hydration free energies by implementing the intramolecular hydrogen bond effects.

BackgroundThe formation of intramolecular hydrogen bonds (IHBs) may induce the remarkable changes in molecular physicochemical properties. Within the framework of the extended solvent-contact model, we investigate the effect of implementing the IHB interactions on the accuracy in estimating the molecular hydration free energies.ResultsThe performances of hydration free energy functions including and excluding the IHB parameters are compared using the molecules distributed for SAMPL4 blind prediction challenge and those in Free Solvation Database (FSD). The calculated hydration free energies with IHB effects are found to be in considerably better agreement with the experimental data than those without them. For example, the root mean square error of the estimation decreases from 2.56 to 1.66 and from 1.73 to 1.54 kcal/mol for SAMPL4 and FSD molecules, respectively, due to the extension of atomic parameter space to cope with IHBs.ConclusionsThese improvements are made possible by reducing the overestimation of attractive interactions between water and the solute molecules involving IHBs. The modified hydration free energy function is thus anticipated to be useful for estimating the desolvation cost for various organic molecules.Electronic supplementary materialThe online version of this article (doi:10.1186/s13321-015-0106-2) contains supplementary material, which is available to authorized users.

A Python tool to set up relative free energy calculations in GROMACS.

Free energy calculations based on molecular dynamics (MD) simulations have seen a tremendous growth in the last decade. However, it is still difficult and tedious to set them up in an automated manner, as the majority of the present-day MD simulation packages lack that functionality. Relative free energy calculations are a particular challenge for several reasons, including the problem of finding a common substructure and mapping the transformation to be applied. Here we present a tool, alchemical-setup.py, that automatically generates all the input files needed to perform relative solvation and binding free energy calculations with the MD package GROMACS. When combined with Lead Optimization Mapper (LOMAP;Liu et al. in J Comput Aided Mol Des 27(9):755-770, 2013), recently developed in our group, alchemical-setup.py allows fully automated setup of relative free energy calculations in GROMACS. Taking a graph of the planned calculations and a mapping, both computed by LOMAP, our tool generates the topology and coordinate files needed to perform relative free energy calculations for a given set of molecules, and provides a set of simulation input parameters. The tool was validated by performing relative hydration free energy calculations for a handful of molecules from the SAMPL4 challenge (Mobley et al. in J Comput Aided Mol Des 28(4):135-150, 2014). Good agreement with previously published results and the straightforward way in which free energy calculations can be conducted make alchemical-setup.py a promising tool for automated setup of relative solvation and binding free energy calculations.

Rapid Alchemical Free Energy Calculation Employing a Generalized Born Implicit Solvent Model

Generalized Born (GB) implicit solvent models are typically used in postprocessing of molecular dynamics trajectories obtained from explicit solvent simulations to estimate binding free energies or effects of mutations in proteins. The possibility to employ a GB implicit solvent model for the calculation of rigorous free energy changes associated with alchemical transformations has been explored. During free energy perturbation (FEP) simulations, Lennard-Jones, Coulomb, and Born radii parameters are transformed gradually in a single-topology series. The FEP calculations are embedded in a replica exchange scheme allowing rapid convergence. The method was tested on the calculation of relative hydration free energies, relative binding free energies of a ligand-receptor system, and in silico alanine scanning of a peptide-protein complex. In all cases, good agreement with available experimental data was obtained. On medium sized protein-ligand systems and using a cluster of graphical processing units, the approach allows the calculation of relative free energy changes associated with a chemical modification of a binding partner within a few minutes of computer time and opens the possibility for systematic in silico studies.

Hydration free energies calculated using the AMBER ff03 charge model for natural and unnatural amino acids and multiple water models

In this work, we assess calculated hydration free energies of natural and unnatural amino acids compared to experimental hydration free energies of corresponding side-chain analogs using the ff03 charge model. Fine-grid, explicit water thermodynamic integration calculations using two widely used explicit water models (TIP3P and TIP4P-Ew) were performed on 19 natural amino acids and compared with experimental hydration free energies of corresponding side-chain analogs to establish expected accuracy levels for this charge model. Next, parameters previously derived for 17 unnatural amino acids and several new parameters optimized in this work were assessed using the same methodology. We found that the ff03 charge model is correlated with experimental hydration free energies but underestimates the solubilities of several polar natural and unnatural amino acids. Comparisons are presented with other forcefields and water models recently presented in the literature for both natural and modified amino acids.

Box size effects are negligible for solvation free energies of neutral solutes.

Hydration free energy calculations in explicit solvent have become an integral part of binding free energy calculations and a valuable test of force fields. Most of these simulations follow the conventional norm of keeping edge length of the periodic solvent box larger than twice the Lennard-Jones (LJ) cutoff distance, with the rationale that this should be sufficient to keep the interactions between copies of the solute to a minimum. However, for charged solutes, hydration free energies can exhibit substantial box size-dependence even at typical box sizes. Here, we examine whether similar size-dependence affects hydration of neutral molecules. Thus, we focused on two strongly polar molecules with large dipole moments, where any size-dependence should be most pronounced, and determined how their hydration free energies vary as a function of simulation box size. In addition to testing a variety of simulation box sizes, we also tested two LJ cut-off distances, 0.65 and 1.0nm. We show from these simulations that the calculated hydration free energy is independent of the box-size as well as the LJ cut-off distance, suggesting that typical hydration free energy calculations of neutral compounds indeed need not be particularly concerned with finite-size effects as long as standard good practices are followed.

FreeSolv: a database of experimental and calculated hydration free energies, with input files.

This work provides a curated database of experimental and calculated hydration free energies for small neutral molecules in water, along with molecular structures, input files, references, and annotations. We call this the Free Solvation Database, or FreeSolv. Experimental values were taken from prior literature and will continue to be curated, with updated experimental references and data added as they become available. Calculated values are based on alchemical free energy calculations using molecular dynamics simulations. These used the GAFF small molecule force field in TIP3P water with AM1-BCC charges. Values were calculated with the GROMACS simulation package, with full details given in references cited within the database itself. This database builds in part on a previous, 504-molecule database containing similar information. However, additional curation of both experimental data and calculated values has been done here, and the total number of molecules is now up to 643. Additional information is now included in the database, such as SMILES strings, PubChem compound IDs, accurate reference DOIs, and others. One version of the database is provided in the Supporting Information of this article, but as ongoing updates are envisioned, the database is now versioned and hosted online. In addition to providing the database, this work describes its construction process. The database is available free-of-charge via http://www.escholarship.org/uc/item/6sd403pz .

Hydration Free Energy from Orthogonal Space Random Walk and Polarizable Force Field.

The orthogonal space random walk (OSRW) method has shown enhanced sampling efficiency in free energy calculations from previous studies. In this study, the implementation of OSRW in accordance with the polarizable AMOEBA force field in TINKER molecular modeling software package is discussed and subsequently applied to the hydration free energy calculation of 20 small organic molecules, among which 15 are positively charged and five are neutral. The calculated hydration free energies of these molecules are compared with the results obtained from the Bennett acceptance ratio method using the same force field, and overall an excellent agreement is obtained. The convergence and the efficiency of the OSRW are also discussed and compared with BAR. Combining enhanced sampling techniques such as OSRW with polarizable force fields is very promising for achieving both accuracy and efficiency in general free energy calculations.

Prediction of hydration free energies for the SAMPL4 data set with the AMOEBA polarizable force field

Hydration free energy calculations are often used to validate molecular simulation methodologies and molecular mechanics force fields. We use the free-energy perturbation method together with the AMOEBA polarizable force field and the Poltype parametrization protocol to predict the hydration free energies of 52 molecules as part of the SAMPL4 blind challenge. For comparison, similar calculations are performed using the non-polarizable General Amber force field. Against our expectations, the latter force field gives the better results compared to experiment. One possible explanation is the sensitivity of the AMOEBA results to the conformation used for parametrization.

Fast prediction of hydration free energies for SAMPL4 blind test from a classical density functional theory

We report the performance of a classical density functional theory (CDFT) in the competition for the solvation free-energy category of the SAMPL4 blind prediction event. The theoretical calculations were carried out with the TIP3P water model and different combinations of solute configurations and molecular force fields. In comparison with the experimental data, the blind test yields an average unsigned error of 2.38kcal/mol and the root mean square deviation of 2.99kcal/mol. Whereas these numbers are significantly larger than the best results from explicit-solvent MD simulations, we find that the theoretical performance is sensitive to both the molecular force fields and solute configurations and that a comparable level of accuracy can be achieved by a judicious selection of the solute configurations and the force-field parameters. Most importantly, CDFT reduces the computational cost of MD simulation by almost 3 orders of magnitude, making it very attractive for large-scale hydration free-energy calculations (e.g., screening the aqueous solubility of drug-like molecules).

Modeling Organochlorine Compounds and the σ-Hole Effect Using a Polarizable Multipole Force Field

The charge distribution of halogen atoms on organochlorine compounds can be highly anisotropic and even display a so-called σ-hole, which leads to strong halogen bonds with electron donors. In this paper, we have systematically investigated a series of chloromethanes with one to four chloro substituents using a polarizable multipole-based molecular mechanics model. The atomic multipoles accurately reproduced the ab initio electrostatic potential around chloromethanes, including CCl4, which has a prominent σ-hole on the Cl atom. The van der Waals parameters for Cl were fitted to the experimental density and heat of vaporization. The calculated hydration free energy, solvent reaction fields, and interaction energies of several homo- and heterodimer of chloromethanes are in good agreement with experimental and ab initio data. This study suggests that sophisticated electrostatic models, such as polarizable atomic multipoles, are needed for accurate description of electrostatics in organochlorine compounds and halogen bonds, although further improvement is necessary for better transferability.