Prediction Of Hydration Free Energies Research Articles

Mechanism Analysis and Property Prediction of Extended Surfactants Based on the Respectively Optimized Force Field.

Extended surfactants represent a novel class of anionic-nonionic surfactants with exceptional performance and unique application value in chemically enhanced oil recovery. Although molecular dynamics (MD) simulations can efficiently screen these surfactants, the current research is limited. Here, it is proven for the first time that existing generic force fields (GAFF and CHARMM) cannot accurately describe extended surfactants, and traditional approaches are insufficient for obtaining precise charge parameters. The concept of the respectively optimized force field (ROFF) with the purports of specialization and accuracy is proposed to construct high-accuracy models for MD simulations, and a new approach is developed to simulate the interface model. By combining the newly specialized alkane model, ROFF-based surfactant models, and the innovative simulation protocol, high accuracy and reliability can be obtained in predicting hydration free energies, minimum of area per molecule, and critical micelle concentration of extended surfactants. Key properties of the newly designed extended surfactants in conventional oil-water interfaces and oil reservoir environments are comprehensively predicted by using advanced analytical and characterization methods. Furthermore, the more rigorous mechanism underlying the special amphiphilicity of the extended surfactant is revealed, potentially offering significant improvements over previous empirical perspectives.

Machine Learning Prediction of Hydration Free Energy with Physically Inspired Descriptors

We present machine learning models for predicting experimental hydration free energies of molecules without any atom-, bond-, or geometry-specific input feature. Four types of physically inspired descriptors are adopted for predictions. The first type is composed of the total dipole moment, anisotropic polarizability, and vibrational analysis results of the solute molecule. The second and third types are derived from the electrostatic potential distribution of the solute. The last type includes the solvent accessible surface area and shape similarities. Several machine learning regression models are built on the basis of the FreeSolv database with ∼600 samples, showing a better performance in comparison with that of most traditional approaches and other prediction methods based on molecular fingerprints. In particular, the present descriptors are capable of predicting hydration free energies of new compounds with elements or fragments that are never seen in the training set. The importance of these descriptors, the impact of dissociation energies of specific covalent bonds, and the outliers with relatively large prediction errors are also discussed.

Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction.

Hydration free energies of small molecules are commonly used as benchmarks for solvation models. However, errors in predicting hydration free energies are partially due to the force fields used and not just the solvation model. To address this, we have used the 3D reference interaction site model (3D-RISM) of molecular solvation and existing benchmark explicit solvent calculations with a simple element count correction (ECC) to identify problems with the non-bond parameters in the general AMBER force field (GAFF). 3D-RISM was used to calculate hydration free energies of all 642 molecules in the FreeSolv database, and a partial molar volume correction (PMVC), ECC, and their combination (PMVECC) were applied to the results. The PMVECC produced a mean unsigned error of 1.01±0.04kcal/mol and root mean squared error of 1.44±0.07kcal/mol, better than the benchmark explicit solvent calculations from FreeSolv, and required less than 15 s of computing time per molecule on a single CPU core. Importantly, parameters for PMVECC showed systematic errors for molecules containing Cl, Br, I, and P. Applying ECC to the explicit solvent hydration free energies found the same systematic errors. The results strongly suggest that some small adjustments to the Lennard-Jones parameters for GAFF will lead to improved hydration free energy calculations for all solvent models.

Fragmentation Method for Computing Quantum Mechanics and Molecular Mechanics Gradients for Force Matching: Validation with Hydration Free Energy Predictions Using Adaptive Force Matching.

A fragmentation approach referred to as a simple overlapping region method for force matching (SORForM) is presented. SORForM is designed to enable efficient computation of quantum mechanical (QM) forces for large molecules and is validated in the framework of adaptive force matching (AFM) to develop solute models in water. The SORForM method divides a molecule into overlapping QM regions with each region containing a gradient zone and a buffer zone. The buffer zone ensures that the atoms in the gradient zone have their surroundings unchanged with fragmentation. The performance of the method is validated with mefenamic acid and linalyl acetate by comparing the hydration free energies of AFM models developed with and without SORForM. The AFM hydration free energies are also compared with that of the experiments. The models developed with B3LYP-D3(BJ) and def2-TZVP are in excellent agreement with experiments. Our work shows that PBE-D3(BJ) provides less satisfactory results when compared to B3LYP-D3(BJ). The def2-TZVP basis set is found to greatly improve the agreement with experiments when compared to a double-zeta quality basis set.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional.

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5kBT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

Accurate MP2-based force fields predict hydration free energies for simple alkanes and alcohols in good agreement with experiments.

Force fields for four small molecules, methane, ethane, methanol, and ethanol, were created by force matching MP2 gradients computed with triple-zeta-quality basis sets using the Adaptive Force Matching method. Without fitting to any experimental properties, the force fields created were able to predict hydration free energies, enthalpies of hydration, and diffusion constants in excellent agreements with experiments. The root mean square error for the predicted hydration free energies is within 1 kJ/mol of experimental measurements of Ben-Naim et al. [J. Chem. Phys. 81(4), 2016–2027 (1984)]. The good prediction of hydration free energies is particularly noteworthy, as it is an important fundamental property. Similar hydration free energies of ethane relative to methane and of ethanol relative to methanol are attributed to a near cancellation of cavitation penalty and favorable contributions from dispersion and Coulombic interactions as a result of the additional methyl group.

Predicting Hydration Free Energies of the FreeSolv Database of Drug-like Molecules with Molecular Density Functional Theory.

We assess the performance of molecular density functional theory (MDFT) to predict hydration free energies of the small drug-like molecules benchmark, FreeSolv. The MDFT in the hypernetted chain approximation (HNC) coupled with a pressure correction predicts experimental hydration free energies of the FreeSolv database within 1 kcal/mol with an average computation time of 2 cpu·min per molecule. This is the same accuracy as for simulation-based free energy calculations that typically require hundreds of cpu·h or tens of gpu·h per molecule.

Pressure-dependent electronic structure calculations using integral equation-based solvation models

Recent methodological progress in quantum-chemical calculations using the “embedded cluster reference interaction site model” (EC-RISM) integral equation theory is reviewed in the context of applying it as a solvation model for calculating pressure-dependent thermodynamic and spectroscopic properties of molecules immersed in water. The methodology is based on self-consistent calculations of electronic and solvation structure around dissolved molecules where pressure enters the equations via an appropriately chosen solvent response function and the pure solvent density. Besides specification of a dispersion-repulsion force field for solute-solvent interactions, the EC-RISM approach derives the electrostatic interaction contributions directly from the wave function. We further develop and apply the method to a variety of benchmark cases for which computational or experimental reference data are either available in the literature or are generated specifically for this purpose in this work. Starting with an enhancement to predict hydration free energies at non-ambient pressures, which is the basis for pressure-dependent molecular population estimation, we demonstrate the performance on the calculation of the autoionization constant of water. Spectroscopic problems are addressed by studying the biologically relevant small osmolyte TMAO (trimethylamine N-oxide). Pressure-dependent NMR shifts are predicted and compared to experiments taking into account proper computational referencing methods that extend earlier work. The experimentally observed IR blue-shifts of certain vibrational bands of TMAO as well as of the cyanide anion are reproduced by novel methodology that allows for weighing equilibrium and non-equilibrium solvent relaxation effects. Taken together, the model systems investigated allow for an assessment of the reliability of the EC-RISM approach for studying pressure-dependent biophysical processes.

Enthalpy-Entropy Interplay in π-Stacking Interaction of Benzene Dimer in Water.

Aromatic groups can engage in an interesting class of noncovalent interactions termed π-π interactions, which play a pivotal role in stabilizing a variety of molecular architectures, including nucleic acids, proteins, and supramolecular assemblies. When the aromatic compounds interact with each other in an aqueous environment, their association is facilitated by the hydrophobic effect-the trend of nonpolar solutes to aggregate in a polar solution. To develop an in-depth understanding of hydrophobic association, we investigate in the present work π-π interactions in water, employing as a paradigm the benzene dimer. Using DFT-CES, a mean-field QM/MM method recently developed by our group, we describe the benzene solute at a quantum-mechanical level. Full consideration of detailed solute-electron density enables an optimal description of the solute-solvent interactions, leading to an accurate prediction of hydration free energies. In π-stacking of benzene, we find an entropic stabilization associated with the shrinkage of the solvent-excluded volume, which agrees with the theory of hydrophobic effect at subnanoscales. However, at the equilibrium binding distance of the benzene dimer, we find that the entropic stabilization nearly cancels out due to the enthalpic cost required for dewetting the internal space. Such an enthalpy-entropy compensation leads the association free energy to be predominantly dictated by the solute-solute interaction enthalpy. The present work offers new insight into the mechanistic role of water and the primary thermodynamic driving force of hydrophobic association.

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes.

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree–Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard–Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute–solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

Predicting hydration free energies of amphetamine-type stimulants with a customized molecular model

Amphetamine-type stimulants (ATS) are a group of incitation and psychedelic drugs affecting the central nervous system. Physicochemical data for these compounds are essential for understanding the stimulating mechanism, for assessing their environmental impacts, and for developing new drug detection methods. However, experimental data are scarce due to tight regulation of such illicit drugs, yet conventional methods to estimate their properties are often unreliable. Here we introduce a tailor-made multiscale procedure for predicting the hydration free energies and the solvation structures of ATS molecules by a combination of first principles calculations and the classical density functional theory. We demonstrate that the multiscale procedure performs well for a training set with similar molecular characteristics and yields good agreement with a testing set not used in the training. The theoretical predictions serve as a benchmark for the missing experimental data and, importantly, provide microscopic insights into manipulating the hydrophobicity of ATS compounds by chemical modifications.

Building Water Models: A Different Approach.

Simplified classical water models are currently an indispensable component in practical atomistic simulations. Yet, despite several decades of intense research, these models are still far from perfect. Presented here is an alternative approach to constructing widely used point charge water models. In contrast to the conventional approach, we do not impose any geometry constraints on the model other than the symmetry. Instead, we optimize the distribution of point charges to best describe the “electrostatics” of the water molecule. The resulting “optimal” 3-charge, 4-point rigid water model (OPC) reproduces a comprehensive set of bulk properties significantly more accurately than commonly used rigid models: average error relative to experiment is 0.76%. Close agreement with experiment holds over a wide range of temperatures. The improvements in the proposed model extend beyond bulk properties: compared to common rigid models, predicted hydration free energies of small molecules using OPC are uniformly closer to experiment, with root-mean-square error <1 kcal/mol.

Update to the General Amber Force Field for Small Solutes with an Emphasis on Free Energies of Hydration

An approach to a straightforward reparametrization of the general AMBER force field (GAFF) for small organic solutes and druglike compounds is presented. The parametrization is based on specific pair interactions between the solvent and the solute, namely, the interactions between the constituting atoms of the solute and the oxygen of water were tuned in order to reproduce experimental hydration free energies for small model compounds. The key of the parametrization was to abandon the Lorentz-Berthelot combination rules for the van der Waals interactions. These parameters were then used for larger solutes in order to validate the newly derived pair interactions. In total close to 600 hydration free energies are computed, ranging from simple alkanes to multifunctional drug compounds, and compared to experimental data. The results show that the proposed parameters work well in describing the interactions between the solute and the solvent and that the agreement in absolute numbers is good. This modified version of GAFF is a good candidate for computing and predicting hydration free energies on a large scale, which has been a long-sought goal of computational chemists and can be used in rational drug design.

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).

Blind prediction of solvation free energies from the SAMPL4 challenge.

Here, we give an overview of the small molecule hydration portion of the SAMPL4 challenge, which focused on predicting hydration free energies for a series of 47 small molecules. These gas-to-water transfer free energies have in the past proven a valuable test of a variety of computational methods and force fields. Here, in contrast to some previous SAMPL challenges, we find a relatively wide range of methods perform quite well on this test set, with RMS errors in the 1.2kcal/mol range for several of the best performing methods. Top-performers included a quantum mechanical approach with continuum solvent models and functional group corrections, alchemical molecular dynamics simulations with a classical all-atom force field, and a single-conformation Poisson-Boltzmann approach. While 1.2kcal/mol is still a significant error, experimental hydration free energies covered a range of nearly 20kcal/mol, so methods typically showed substantial predictive power. Here, a substantial new focus was on evaluation of error estimates, as predicting when a computational prediction is reliable versus unreliable has considerable practical value. We found, however, that in many cases errors are substantially underestimated, and that typically little effort has been invested in estimating likely error. We believe this is an important area for further research.

Prediction of hydration free energies for the SAMPL4 diverse set of compounds using molecular dynamics simulations with the OPLS-AA force field

All-atom molecular dynamics computer simulations were used to blindly predict the hydration free energies of a range of small molecules as part of the SAMPL4 challenge. Compounds were parametrized on the basis of the OPLS-AA force field using three different protocols for deriving partial charges: (1) using existing OPLS-AA atom types and charges with minor adjustments of partial charges on equivalent connecting atoms and derivation of new parameters for a number of distinct chemical groups (N-alkyl imidazole, nitrate) that were not present in the published force field; (2) calculation of quantum mechanical charges via geometry optimization, followed by electrostatic potential (ESP) fitting, using Jaguar at the LMP2/cc-pVTZ(-F) level; and (3) via geometry optimization and CHelpG charges (Gaussian09at the HF/6-31G* level), followed by two-stage RESP fitting. The absolute hydration free energy was computed by an established protocol including alchemical free energy perturbation with thermodynamic integration. The use of standard OPLS-AA charges (protocol 1) with a number of newly parametrized charges and the use of histidine derived parameters for imidazole yielded an overall root mean square deviation of the prediction from the experimental data of 1.75kcal/mol. The precision of our results appears to be mainly limited by relatively poor reproducibility of the Lennard-Jones contribution towards the solvation free energy, for which we observed large variability that could be traced to a strong dependence on the initial system conditions.

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 <1kcal/mol. Chemical accuracy is obtained.

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3kcal/mol, the hybrid approach yields an improved RMSD of 1.6kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.

Assessing the Accuracy of Inhomogeneous Fluid Solvation Theory in Predicting Hydration Free Energies of Simple Solutes

Accurate prediction of hydration free energies is a key objective of any free energy method that is applied to modeling and understanding interactions in the aqueous phase. Inhomogeneous fluid solvation theory (IFST) is a statistical mechanical method for calculating solvation free energies by quantifying the effect of a solute acting as a perturbation to bulk water. IFST has found wide application in understanding hydration phenomena in biological systems, but quantitative applications have not been comprehensively assessed. In this study, we report the hydration free energies of six simple solutes calculated using IFST and independently using free energy perturbation (FEP). This facilitates a validation of IFST that is independent of the accuracy of the force field. The results demonstrate that IFST shows good agreement with FEP, with an R2 coefficient of determination of 0.99 and a mean unsigned difference of 0.7 kcal/mol. However, sampling is a major issue that plagues IFST calculations and the results suggest that a histogram method may require prohibitively long simulations to achieve convergence of the entropies, for bin sizes which effectively capture the underlying probability distributions. Results also highlight the sensitivity of IFST to the reference interaction energy of a water molecule in bulk, with a difference of 0.01 kcal/mol changing the predicted hydration free energies by approximately 2.4 kcal/mol for the systems studied here. One of the major advantages of IFST over perturbation methods such as FEP is that the systems are spatially decomposed to consider the contribution of specific regions to the total solvation free energies. Visualizing these contributions can yield detailed insights into solvation thermodynamics. An insight from this work is the identification and explanation of regions with unfavorable free energy density relative to bulk water. These regions contribute unfavorably to the hydration free energy. Further work is necessary before IFST can be extended to yield accurate predictions of binding free energies, but the work presented here demonstrates its potential.

A Reparametrized Implicit Solvent Model for Accurate Computation of Hydration Free Energies

While solvation plays an important role in many chemical and biological processes, detailed solvent behavior is typically of much less interest than the effect of the solvent on the solute. Although explicit solvent treatment provides a very accurate description of the considered system, it is not necessary for many applications and can be replaced by implicit solvent models. A typical application is the computation of hydration free energies for small molecules. However a recent study [1] showed that there is still a gap between the accuracy of implicit models typically used in biomolecular simulations and explicit solvent treatment. To address this issue we have reparametrized an implicit solvent model consisting of a generalized Born term to model polar solvation and an extended nonpolar term that models cavity formation and Lennard-Jones interactions with water. When fitted to experimental hydration free energies of a large set of 499 small molecules, the model is able to reproduce hydration free energies with a similar error than those derived from explicit solvent computation, while still offering some degrees of freedom in the fit parameters. To test the transferability of the resulting model, we have applied it to the prediction of hydration free energies of Glycine-X-Glycine tri-peptides. This model will be part of the SIMONA [2] simulation package.[1] Knight, J. L. & Brooks III, C. L. Surveying implicit solvent models for estimating small molecule absolute hydration free energies. Journal of Computational Chemistry 32, 2909-2923 (2011).[2] Strunk, T. et al. SIMONA 1.0: An efficient and versatile framework for stochastic simulations of molecular and nanoscale systems. Journal of Computational Chemistry (2012).doi:10.1002/jcc.23089