Prediction Of Solvation Free Energies Research Articles

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State.

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Something for nothing: improved solvation free energy prediction with $${\Delta }$$-learning

Something for nothing: improved solvation free energy prediction with $${\Delta }$$-learning

Persistent Dirac for molecular representation

Molecular representations are of fundamental importance for the modeling and analysing molecular systems. The successes in drug design and materials discovery have been greatly contributed by molecular representation models. In this paper, we present a computational framework for molecular representation that is mathematically rigorous and based on the persistent Dirac operator. The properties of the discrete weighted and unweighted Dirac matrix are systematically discussed, and the biological meanings of both homological and non-homological eigenvectors are studied. We also evaluate the impact of various weighting schemes on the weighted Dirac matrix. Additionally, a set of physical persistent attributes that characterize the persistence and variation of spectrum properties of Dirac matrices during a filtration process is proposed to be molecular fingerprints. Our persistent attributes are used to classify molecular configurations of nine different types of organic-inorganic halide perovskites. The combination of persistent attributes with gradient boosting tree model has achieved great success in molecular solvation free energy prediction. The results show that our model is effective in characterizing the molecular structures, demonstrating the power of our molecular representation and featurization approach.

Development and test of highly accurate endpoint free energy methods. 1: Evaluation of ABCG2 charge model on solvation free energy prediction and optimization of atom radii suitable for more accurate solvationfreeenergy prediction by the PBSA method.

Accurate estimation of solvation free energy (SFE) lays the foundation for accurate prediction of binding free energy. The Poisson-Boltzmann (PB) or generalized Born (GB) combined with surface area (SA) continuum solvation method (PBSA and GBSA) have been widely used in SFE calculations because they can achieve good balance between accuracy and efficiency. However, the accuracy of these methods can be affected by several factors such as the charge models, polar and nonpolar SFE calculation methods and the atom radii used in the calculation. In this work, the performance of the ABCG2 (AM1-BCC-GAFF2) charge model as well as other two charge models, that is, RESP (Restrained Electrostatic Potential) and AM1-BCC (Austin Model 1-bond charge corrections), on the SFE prediction of 544 small molecules in water by PBSA/GBSA was evaluated. In order to improve the performance of the PBSA prediction based on the ABCG2 charge, we further explored the influence of atom radii on the prediction accuracy and yielded a set of atom radius parameters for more accurate SFE prediction using PBSA based on the ABCG2/GAFF2 by reproducing the thermodynamic integration (TI) calculation results. The PB radius parameters of carbon, oxygen, sulfur, phosphorus, chloride, bromide and iodine, were adjusted. New atom types, on, oi, hn1, hn2, hn3, were introduced to further improve the fitting performance. Then, we tuned the parameters in the nonpolar SFE model using the experimental SFE data and the PB calculation results. By adopting the new radius parameters and new nonpolar SFE model, the root mean square error (RMSE) of the SFE calculation for the 544 molecules decreased from 2.38 to 1.05 kcal/mol. Finally, the new radius parameters were applied in the prediction of protein-ligand binding free energies using the MM-PBSA method. For the eight systems tested, we could observe higher correlation between the experiment data and calculation results and smaller prediction errors for the absolute binding free energies, demonstrating that our new radius parameters can improve the free energy calculation using the MM-PBSA method.

Explainable Solvation Free Energy Prediction Combining Graph Neural Networks with Chemical Intuition.

The prediction of a molecule's solvation Gibbs free (ΔGsolv) energy in a given solvent is an important task which has traditionally been carried out via quantum chemical continuum methods or force field-based molecular simulations. Machine learning (ML) and graph neural networks in particular have emerged as powerful techniques for elucidating structure-property relationships. This work presents a graph neural network (GNN) for the prediction of ΔGsolv which, in addition to encoding typical atom and bond-level features, incorporates chemically intuitive, solvation-relevant parameters into the featurization process: semiempirical partial atomic charges and solvent dielectric constant. Solute-solvent interactions are included via an interaction map layer which can be visualized to examine solubility-enhancing or -decreasing interactions learnt by the model. On a test set of small organic molecules, our GNN predicts ΔGsolv in water and cyclohexane with an accuracy comparable to polarizable and ab initio generated force field methods [mean absolute error (MAE) = 0.4 and 0.2 kcal mol-1, respectively], without the need for any molecular simulation. For the FreeSolv data set of hydration free energies, the test MAE is 0.7 kcal mol-1. Interpretability and applicability of the model is highlighted through several examples including rationalizing the increased solubility of modified diaminoanthraquinones in organic solvents. The clear explanations afforded by our GNN allow for easy understanding of the model's predictions, giving the experimental chemist confidence in employing ML models toward more optimized synthetic routes.

A constrained variational model of biomolecular solvation and its numerical implementation

Variational based solvation models of biomolecules with smooth interface have drawn attentions in the past decade since they have been developed as an efficient and reliable representation of solute-solvent interfaces in the framework of implicit solvent models. This work aims at providing solid mathematical supports for a promising geometric flow based computational solvation model with smooth interface (GFBSS) and its involved computational treatments. For this purpose, we improve the GFBSS model by explicitly including two physical constraints: (1) a novel experimental based domain decomposition, and (2) a two-sided obstacle for the characteristic function describing the optimal diffuse solute-solvent boundary. It is shown that the resulting constrained model is mathematically well-posed. Further, to overcome the challenges arising from including these constraints, we propose a family of generalized constrained energy functionals whose variations satisfy a q-Laplacian type equation for nonpolar molecules. The solvation free energies predicted by the generalized models converge to that of the proposed constrained one. Most importantly, the numerical difference between the generalized models and the previous unconstrained GFBSS model is negligible. It implies that the newly proposed constrained solvation model and the previous unconstrained one are equivalent to each other in terms of the solvation free energy calculation and prediction. Our model validation, its numerical implementation, and solvation energy convergence have been demonstrated using several common biomolecular modeling tasks.

Application of Artificial Intelligence for the Prediction of Solvation Free Energies for Covid-19 Drug Discovery

Solvation free energy is a key indicator of the effectiveness of a drug molecule. There are several applications of predicting the solvation free energies of chemical compounds using quantum mechanical methods. However, these methods take a long time and are costly. For that reason, the application of recently developed artificial intelligence techniques for the prediction of solvation free energies is becoming increasingly valuable in drug discovery to address time and the high-cost issues with traditional quantum mechanical approaches. In this paper, we present application of two different artificial intelligence models for predicting solute-solvent free solvation energy for Covid-19 drug design. The research involves building, training, evaluating and comparing the performances of the two models on a large dataset, then predicting solvation free energies for 138 known APIs and 28 organic solvents that could potentially be used as a Covid-19 medicine. The potential repurposing of 138 drugs for Covid-19 from solubility perspective is novel. We demonstrate the application of the AI models and derive several conclusions regarding suitability of the APIs and their efficacy. We conclude our research by providing insights on how our work can be put to future use towards drug development.

MLSolvA: solvation free energy prediction from pairwise atomistic interactions by machine learning

Recent advances in machine learning technologies and their applications have led to the development of diverse structure–property relationship models for crucial chemical properties. The solvation free energy is one of them. Here, we introduce a novel ML-based solvation model, which calculates the solvation energy from pairwise atomistic interactions. The novelty of the proposed model consists of a simple architecture: two encoding functions extract atomic feature vectors from the given chemical structure, while the inner product between the two atomistic feature vectors calculates their interactions. The results of 6239 experimental measurements achieve outstanding performance and transferability for enlarging training data owing to its solvent-non-specific nature. An analysis of the interaction map shows that our model has significant potential for producing group contributions on the solvation energy, which indicates that the model provides not only predictions of target properties but also more detailed physicochemical insights.

Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state.

We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This allows for a coarse-grained description of the solvent based on an inhomogeneous density of PC-SAFT segments. The solute, on the other hand, is described in full detail by atomistic Lennard-Jones interaction sites. The approach is entirely predictive as it only takes the PC-SAFT parameters of the solvent and the force-field parameters of the solute as input. No adjustable parameters or empirical corrections are involved. The framework is applied to study self-solvation of n-alkanes and to the calculation of residual chemical potentials in binary solvent mixtures. Our DFT approach accurately predicts solvation free energies of small molecular solutes in three different non-polar solvents, namely n-hexane, cyclohexane, and benzene. Additionally, we show that the calculated solvation free energies agree well with those obtained by molecular dynamics simulations and with the residual chemical potential calculated by the bulk PC-SAFT equation of state. We observe higher deviations for the solvation free energy of systems with significant solute-solvent Coulomb interactions.

Improved prediction of solvation free energies by machine-learning polarizable continuum solvation model

Theoretical estimation of solvation free energy by continuum solvation models, as a standard approach in computational chemistry, is extensively applied by a broad range of scientific disciplines. Nevertheless, the current widely accepted solvation models are either inaccurate in reproducing experimentally determined solvation free energies or require a number of macroscopic observables which are not always readily available. In the present study, we develop and introduce the Machine-Learning Polarizable Continuum solvation Model (ML-PCM) for a substantial improvement of the predictability of solvation free energy. The performance and reliability of the developed models are validated through a rigorous and demanding validation procedure. The ML-PCM models developed in the present study improve the accuracy of widely accepted continuum solvation models by almost one order of magnitude with almost no additional computational costs. A freely available software is developed and provided for a straightforward implementation of the new approach.

Transfer learning for solvation free energies: From quantum chemistry to experiments

Data scarcity, bias, and experimental noise are all frequently encountered problems in the application of deep learning to chemical and material science disciplines. Transfer learning has proven effective in compensating for the lack in data. The use of quantum calculations in machine learning enables the generation of a diverse dataset and ensures that learning is less affected by noise inherent to experimental databases. In this work, we propose a transfer learning approach for the prediction of solvation free energies that combines fundamentals from quantum calculations with the higher accuracy of experimental measurements using two new databases CombiSolv-QM and CombiSolv-Exp. The employed model architecture is based on the directed-message passing neural network for the molecular embedding of solvent and solute molecules. A significant advantage of models pre-trained on quantum calculations is demonstrated for small experimental datasets and for out-of-sample predictions. The improved out-of-sample performance is shown for new solvents, for new solute elements, and for the extension to higher molar mass solutes. The overall performance of the pre-trained models is limited by the noise in the experimental test data, known as the aleatoric uncertainty. On a random test split, a mean absolute error of 0.21 kcal/mol is achieved. This is a significant improvement compared to the mean absolute error of the quantum calculations (0.40 kcal/mol). The error can be further reduced to 0.09 kcal/mol if the model performance is assessed on a more accurate subset of the experimental data.

Learning Atomic Interactions through Solvation Free Energy Prediction Using Graph Neural Networks.

Solvation free energy is a fundamental property that influences various chemical and biological processes, such as reaction rates, protein folding, drug binding, and bioavailability of drugs. In this work, we present a deep learning method based on graph networks to accurately predict solvation free energies of small organic molecules. The proposed model, comprising three phases, namely, message passing, interaction, and prediction, is able to predict solvation free energies in any generic organic solvent with a mean absolute error of 0.16 kcal/mol. In terms of accuracy, the current model outperforms all of the proposed machine learning-based models so far. The atomic interactions predicted in an unsupervised manner are able to explain the trends of free energies consistent with chemical wisdom. Further, the robustness of the machine learning-based model has been tested thoroughly, and its capability to interpret the predictions has been verified with several examples.

Graphical Gaussian process regression model for aqueous solvation free energy prediction of organic molecules in redox flow batteries.

The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using the Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model for electrostatic interaction, the nonpolar interaction contribution of the solvent and the conformational entropy of the solute in the solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of the conformational entropy of the solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal mol-1 for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.

A fast and high-quality charge model for the next generation general AMBER force field.

The General AMBER Force Field (GAFF) has been broadly used by researchers all over the world to perform in silico simulations and modelings on diverse scientific topics, especially in the field of computer-aided drug design whose primary task is to accurately predict the affinity and selectivity of receptor-ligand binding. The atomic partial charges in GAFF and the second generation of GAFF (GAFF2) were originally developed with the quantum mechanics derived restrained electrostatic potential charge, but in practice, users usually adopt an efficient charge method, Austin Model 1-bond charge corrections (AM1-BCC), based on which, without expensive ab initio calculations, the atomic charges could be efficiently and conveniently obtained with the ANTECHAMBER module implemented in the AMBER software package. In this work, we developed a new set of BCC parameters specifically for GAFF2 using 442 neutral organic solutes covering diverse functional groups in aqueous solution. Compared to the original BCC parameter set, the new parameter set significantly reduced the mean unsigned error (MUE) of hydration free energies from 1.03 kcal/mol to 0.37 kcal/mol. More excitingly, this new AM1-BCC model also showed excellent performance in the solvation free energy (SFE) calculation on diverse solutes in various organic solvents across a range of different dielectric constants. In this large-scale test with totally 895 neutral organic solvent-solute systems, the new parameter set led to accurate SFE predictions with the MUE and the root-mean-square-error of 0.51 kcal/mol and 0.65 kcal/mol, respectively. This newly developed charge model, ABCG2, paved a promising path for the next generation GAFF development.

Solvation Thermodynamics in Different Solvents: Water-Chloroform Partition Coefficients from Grid Inhomogeneous Solvation Theory.

Reliable information on partition coefficients plays a key role in drug development, as solubility decisively affects bioavailability. In a physicochemical context, the partition coefficient of a solute between two different solvents can be described as a function of solvation free energies. Hence, substantial scientific efforts have been made toward accurate predictions of solvation free energies in various solvents. The grid inhomogeneous solvation theory (GIST) facilitates the calculation of solvation free energies. In this study, we introduce an extended version of the GIST algorithm, which enables the calculation for chloroform in addition to water. Furthermore, GIST allows localization of enthalpic and entropic contributions. We test our approach by calculating partition coefficients between water and chloroform for a set of eight small molecules. We report a Pearson correlation coefficient of 0.96 between experimentally determined and calculated partition coefficients. The capability to reliably predict partition coefficients between water and chloroform and the possibility to localize their contributions allow the optimization of a compound’s partition coefficient. Therefore, we presume that this methodology will be of great benefit for the efficient development of pharmaceuticals.

Prediction of solvation free energy and partition coefficient of polychlorinated biphenyls using thermodynamic integration

Partition coefficient of Polychlorinated biphenyls (PCBs) is important property for environment governance. We employed the all-atom molecular dynamics (MD) simulation to calculate solvation free energies of the PCBs in water and 1-octanol, respectively. The solvation free energy was predicted using thermodynamics integration (TI) approach. Two methods were compared to calculate the integrations of free energy in the TI approach. To improve the accuracy of our calculations, optimized atomic partial charges were applied for the PCBs in our MD simulations, leading to good computational predictions in partition coefficients. Our computational studies provided reliable data for separation process design.

Prediction of Solvation Free Energies of Ionic Solutes in Neutral Solvents.

The prediction of solvation free energies is essential for a variety of applications. Solvation free energies of neutral systems can be predicted quite accurately. The accuracy of predictions for solvation free energies of ionic solutes dissolved in neutral solvents, however, has been reported to be worse by at least 1 order of magnitude. In this study, the performance of three approaches for solvation free energy prediction of several hundred ions dissolved in neutral solvents is evaluated. The applied methods are COSMO-RS, cluster continuum model (CCM) together with COSMO-RS, and COSMO-RS-ES. It is emphasized that the reference data for model evaluation are subject to large uncertainties stemming from the impossibility to measure the so-called elusive absolute free energies of solvation of a single ion. Consequently, such uncertainty must be considered during the evaluation of prediction methods. Therefore, a straightforward approach to account for the underlying uncertainty is applied here. Hereby, it is revealed that the true performance of the method is better than what is often reported. The average absolute deviation (AAD) of COSMO-RS is calculated to be 2.3 kcal mol-1, while applying the CCM and COSMO-RS-ES each results in AADs of 2.0 kcal mol-1. This accuracy allows for qualitative assessment of solvation free energy-dependent quantities, such as reaction rate constants.

Multisolvent Models for Solvation Free Energy Predictions Using 3D-RISM Hydration Thermodynamic Descriptors.

The potential to predict solvation free energies (SFEs) in any solvent using a machine learning (ML) model based on thermodynamic output, extracted exclusively from 3D-RISM simulations in water is investigated. The models on multiple solvents take into account both the solute and solvent description and offer the possibility to predict SFEs of any solute in any solvent with root mean squared errors less than 1 kcal/mol. Validations that involve exclusion of fractions or clusters of the solutes or solvents exemplify the model's capability to predict SFEs of novel solutes and solvents with diverse chemical profiles. In addition to being predictive, our models can identify the solute and solvent features that influence SFE predictions. Furthermore, using 3D-RISM hydration thermodynamic output to predict SFEs in any organic solvent reduces the need to run 3D-RISM simulations in all these solvents. Altogether, our multisolvent models for SFE predictions that take advantage of the solvation effects are expected to have an impact in the property prediction space.

Temperature‐dependent vapor–liquid equilibria and solvation free energy estimation from minimal data

AbstractWe present a new strategy to estimate the temperature‐dependent vapor–liquid equilibria and solvation free energies of dilute neutral molecules based on only their estimated solvation energy and enthalpy at 298 K. These two pieces of information coupled with matching conditions between the functional forms developed by Japas and Levelt Sengers for near critical conditions and by Harvey for low and moderate temperature conditions allow the fitting of a piecewise function that predicts the temperature‐dependent solvation energy for dilute solutes up to the critical temperature of the solvent. If the Abraham and Mintz parameters for the solvent and solute are available or can be estimated from group contributions, this method requires no experimental data and can still provide accurate estimates with an error of about 1.6 kJ/mol. This strategy, which requires minimal computational resources, is shown to compare well with other methods of temperature‐dependent solvation free energy prediction.

Chemically Interpretable Graph Interaction Network for Prediction of Pharmacokinetic Properties of Drug-Like Molecules

Solubility of drug molecules is related to pharmacokinetic properties such as absorption and distribution, which affects the amount of drug that is available in the body for its action. Computational or experimental evaluation of solvation free energies of drug-like molecules/solute that quantify solubilities is an arduous task and hence development of reliable computationally tractable models is sought after in drug discovery tasks in pharmaceutical industry. Here, we report a novel method based on graph neural network to predict solvation free energies. Previous studies considered only the solute for solvation free energy prediction and ignored the nature of the solvent, limiting their practical applicability. The proposed model is an end-to-end framework comprising three phases namely, message passing, interaction and prediction phases. In the first phase, message passing neural network was used to compute inter-atomic interaction within both solute and solvent molecules represented as molecular graphs. In the interaction phase, features from the preceding step is used to calculate a solute-solvent interaction map, since the solvation free energy depends on how (un)favorable the solute and solvent molecules interact with each other. The calculated interaction map that captures the solute-solvent interactions along with the features from the message passing phase is used to predict the solvation free energies in the final phase. The model predicts solvation free energies involving a large number of solvents with high accuracy. We also show that the interaction map captures the electronic and steric factors that govern the solubility of drug-like molecules and hence is chemically interpretable.