Hybrid QSPR models for the prediction of the free energy of solvation of organic solute/solvent pairs

Predicting drug solubility in organic solvents mixtures: A machine-learning approach supported by high-throughput experimentation

A novel approach based on supervised machine-learning is proposed to predict the solubility of drugs and drug-like molecules in mixtures of organic solvents. Similar to quantitative structure-property relationship (QSPR) models, different solvent types are identified by molecular descriptors, which, in this study, are considered as UNIFAC subgroups. To overcome the potential lack of UNIFAC subgroups for the complex Active Pharmaceutical Ingredients (APIs) currently developed in the pharmaceutical industry, the API molecule is considered as a unique entity in the proposed modelling approach. Therefore, API solubility is predicted as a function of temperature, functional subgroups of the solvents and composition of the solvent mixture; in turn, regressors' correlation is handled through Partial Least-Squares (PLS) regression. The method is developed and tested with experimental data of a real API and 14 organic solvents that are industrially employed for crystallisation. Solubility predictions are accurate and precise for single solvents, binary mixtures and ternary mixtures of organic solvents at different compositions and temperatures, with a determination coefficient R2 ≥ 0.90. To further test the applicability of the model, the proposed approach is applied to 9 literature organic solubility datasets of drugs and drug-like compounds and compared to benchmark solubility models in the literature. Results show that the proposed approach provides satisfactory predictions: the majority of validation and calibration data have R2 = 0.95-0.99; the ratio between RMSE (root mean squared error) of the proposed method and the range of measured solubility values is from 1 to 3 orders of magnitude smaller than the RMSE ratio obtained by the benchmark models.

Explainable Supervised Machine Learning Model To Predict Solvation Gibbs Energy

Many challenges persist in developing accurate computational models for predicting solvation free energy (ΔGsol). Despite recent developments in Machine Learning (ML) methodologies that outperformed traditional quantum mechanical models, several issues remain concerning explanatory insights for broad chemical predictions with an acceptable speed-accuracy trade-off. To overcome this, we present a novel supervised ML model to predict the ΔGsol for an array of solvent-solute pairs. Using two different ensemble regressor algorithms, we made fast and accurate property predictions using open-source chemical features, encoding complex electronic, structural, and surface area descriptors for every solvent and solute. By integrating molecular properties and chemical interaction features, we have analyzed individual descriptor importance and optimized our model though explanatory information form feature groups. On aqueous and organic solvent databases, ML models revealed the predictive relevance of solutes with increasing polar surface area and decreasing polarizability, yielding better results than state-of-the-art benchmark Neural Network methods (without complex quantum mechanical or molecular dynamic simulations). Both algorithms successfully outperformed previous ΔGsol predictions methods, with a maximum absolute error of 0.22 ± 0.02 kcal mol-1, further validated in an external benchmark database and with solvent hold-out tests. With these explanatory and statistical insights, they allow a thoughtful application of this method for predicting other thermodynamic properties, stressing the relevance of ML modeling for further complex computational chemistry problems.

Predicting Solvation Free Energies Using Electronegativity-Equalization Atomic Charges and a Dense Neural Network: A Generalized-Born Approach

I propose a dense Neural Network, ESE-GB-DNN, for evaluation of solvation free energies ΔG°solv for molecules and ions in water and nonaqueous solvents. As input features, it employs generalized-Born monatomic and diatomic terms, as well as atomic surface areas and the molecular volume. The electrostatics calculation is based on a specially modified version of electronegativity-equalization atomic charges. ESE-GB-DNN evaluates ΔG°solv in a simple and highly efficient way, yet it offers a high accuracy, often challenging that of standard DFT-based methods. For neutral solutes, ESE-GB-DNN yields an RMSE between 0.7 and 1.3 kcal/mol, depending on the solvent class. ESE-GB-DNN performs particularly well for nonaqueous solutions of ions, with an RMSE of about 0.7 kcal/mol. For ions in water, the RMSE is larger (2.9 kcal/mol).

Dense Neural Network for Calculating Solvation Free Energies from Electronegativity-Equalization Atomic Charges

I propose a dense Neural Network for evaluation of solvation free energies ΔG°solv for molecules and ions in water and nonaqueous solvents, Easy Solvation Energy with Electronegativity Equalization charges and Dense Neural Network (ESE-EE-DNN). As input features, it uses the Conductor-like Screening Model (COSMO) electrostatic energy, atomic cavity surface areas, total cavity volume, and induced surface charges. For the COSMO calculation, electronegativity-equalization atomic charges are employed. ESE-EE-DNN exhibits fairly high accuracy, similar or even superior to that of mainstream density functional theory-based methods. For neutral solutes in water, polar protic, polar aprotic, and nonpolar solvents, ESE-EE-DNN yields a root-mean-square error (RMSE) of 1.25, 1.36, 0.70, and 0.71 kcal/mol, respectively. ESE-EE-DNN is particularly advantageous for ionic solutes, with an RMSE of 2.82 and 1.42 kcal/mol for aqueous and nonaqueous ion solutions, correspondingly. ESE-EE-DNN is very efficient due to a fast evaluation of the electronegativity-equalization charges.

A reliable QSPR model for predicting drug release rate from metal-organic frameworks: a simple and robust drug delivery approach

During the drug release process, the drug is transferred from the starting point in the drug delivery system to the surface, and then to the release medium. Metal-organic frameworks (MOFs) potentially have unique features to be utilized as promising carriers for drug delivery, due to their suitable pore size, high surface area, and structural flexibility. The loading and release of various therapeutic drugs through the MOFs are effectively accomplished due to their tunable inorganic clusters and organic ligands. Since the drug release rate percentage (RES%) is a significant concern, a quantitative structure-property relationship (QSPR) method was applied to achieve an accurate model predicting the drug release rate from MOFs. Structure-based descriptors, including the number of nitrogen and oxygen atoms, along with two other adjusted descriptors, were applied for obtaining the best multilinear regression (BMLR) model. Drug release rates from 67 MOFs were applied to provide a precise model. The coefficients of determination (R2) for the training and test sets obtained were both 0.9999. The root mean square error for prediction (RMSEP) of the RES% values for the training and test sets were 0.006 and 0.005, respectively. To examine the precision of the model, external validation was performed through a set of new observations, which demonstrated that the model works to a satisfactory degree.

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 solvation free energy 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 (ΔG_solv) 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 ΔG_solv 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 ΔG_solv 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.

Prediction of Combined Sorbent and Catalyst Materials for SE-SMR, Using QSPR and Multitask Learning

The process of sorption enhanced steam methane reforming (SE-SMR) is an emerging technology for the production of low carbon hydrogen. The development of a suitable catalytic material, as well as a CO₂ adsorbent with high capture capacity, has slowed the upscaling of this process to date. In this study, to aid the development of a combined sorbent catalyst material (CSCM) for SE-SMR, a novel approach involving quantitative structure–property relationship analysis (QSPR) has been proposed. Through data-mining, two databases have been developed for the prediction of the last cycle capacity (g_CO2/g_sorbent) and methane conversion (%). Multitask learning (MTL) was applied for the prediction of CSCM properties. Patterns in the data of this study have also yielded further insights; colored scatter plots were able to show certain patterns in the input data, as well as suggestions on how to develop an optimal material. With the results from the actual vs predicted plots collated, raw materials and synthesis conditions were proposed that could lead to the development of a CSCM that has good performance with respect to both the last cycle capacity and the methane conversion.

Mechanistic Studies Yield Improved Protocols for Base-Catalyzed Anti-Markovnikov Alcohol Addition Reactions

The catalytic anti-Markovnikov addition of alcohols to simple alkenes is a longstanding synthetic challenge. We recently disclosed the use of organic superbase catalysis for the nucleophilic addition of alcohols to activated styrene derivatives. This article describes mechanistic studies on this reversible reaction, including thermodynamic and kinetic profiling as well as computational modeling. Our findings show the negative entropy of addition is counterbalanced by an enthalpy that is most favored in nonpolar solvents. However, a large negative alcohol rate order under these conditions indicates excess alcohol sequesters the active alkoxide ion pairs, slowing the reaction rate. These observations led to an unexpected solution to a thermodynamically challenging reaction: use of less alcohol enables faster addition, which in turn allows for lower reaction temperatures to counteract Le Chatelier's principle. Thus, our original method has been improved with new protocols that do not require excess alcohol stoichiometry, enable an expanded alkene substrate scope, and allow for the use of more practical catalyst systems. The generality of this insight for other challenging hydroetherification reactions is also demonstrated through new alkenol cyclization and oxa-Michael addition reactions.

Monte Carlo based QSGFEAR: prediction of Gibb's free energy of activation at different temperatures using SMILES based descriptors

Monte Carlo optimization based QSGFEAR model development using CII results in the formation of more reliable, robust and predictive models.

Predicting Solvent-Dependent Nucleophilicity Parameter with a Causal Structure Property Relationship

Solvent-dependent reactivity is a key aspect of synthetic science, which controls reaction selectivity. The contemporary focus on new, sustainable solvents highlights a need for reactivity predictions in different solvents. Herein, we report the excellent machine learning prediction of the nucleophilicity parameter N in the four most-common solvents for nucleophiles in the Mayr's reactivity parameter database (R² = 0.93 and 81.6% of predictions within ±2.0 of the experimental values with Extra Trees algorithm). A Causal Structure Property Relationship (CSPR) approach was utilized, with focus on the physicochemical relationships between the descriptors and the predicted parameters, and on rational improvements of the prediction models. The nucleophiles were represented with a series of electronic and steric descriptors and the solvents were represented with principal component analysis (PCA) descriptors based on the ACS Solvent Tool. The models indicated that steric factors do not contribute significantly, because of bias in the experimental database. The most important descriptors are solvent-dependent HOMO energy and Hirshfeld charge of the nucleophilic atom. Replacing DFT descriptors with Parameterization Method 6 (PM6) descriptors for the nucleophiles led to an 8.7-fold decrease in computational time, and an ∼10% decrease in the percentage of predictions within ±2.0 and ±1.0 of the experimental values.

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.

Graph-Based Approaches for Predicting Solvation Energy in Multiple Solvents: Open Datasets and Machine Learning Models

The solvation properties of molecules, often estimated using quantum chemical simulations, are important in the synthesis of energy storage materials, drugs, and industrial chemicals. Here, we develop machine learning models of solvation energies to replace expensive quantum chemistry calculations with inexpensive-to-compute message-passing neural network models that require only the molecular graph as inputs. Our models are trained on a new database of solvation energies for 130,258 molecules taken from the QM9 dataset computed in five solvents (acetone, ethanol, acetonitrile, dimethyl sulfoxide, and water) via an implicit solvent model. Our best model achieves a mean absolute error of 0.5 kcal/mol for molecules with nine or fewer non-hydrogen atoms and 1 kcal/mol for molecules with between 10 and 14 non-hydrogen atoms. We make the entire dataset of 651,290 computed entries openly available and provide simple web and programmatic interfaces to enable others to run our solvation energy model on new molecules. This model calculates the solvation energies for molecules using only the SMILES string and also provides an estimate of whether each molecule is within the domain of applicability of our model. We envision that the dataset and models will provide the functionality needed for the rapid screening of large chemical spaces to discover improved molecules for many applications.

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.

Accurate theoretical evaluation of solvation free energy is challenging. Here the authors introduce a machine-learning based polarizable continuum solvation approach to improve the accuracy of widely accepted continuum solvation models by almost one order of magnitude without additional computational costs.

Biomolecular modeling thrives in the age of technology

The biomolecular modeling field has flourished since its early days in the 1970s due to the rapid adaptation and tailoring of state-of-the-art technology. The resulting dramatic increase in size and timespan of biomolecular simulations has outpaced Moore's law. Here, we discuss the role of knowledge-based versus physics-based methods and hardware versus software advances in propelling the field forward. This rapid adaptation and outreach suggests a bright future for modeling, where theory, experimentation and simulation define three pillars needed to address future scientific and biomedical challenges.

Experimental and Artificial Intelligence Modelling Study of Oil Palm Trunk Sap Fermentation

Five major operations for the conversion of lignocellulosic biomasses into bioethanol are pre-treatment, detoxification, hydrolysis, fermentation, and distillation. The fermentation process is a significant biological step to transform lignocellulose into biofuel. The interactions of biochemical networks and their uncertainty and nonlinearity that occur during fermentation processes are major problems for experts developing accurate bioprocess models. In this study, mechanical processing and pre-treatment on the palm trunk were done before fermentation. Analysis was performed on the fresh palm sap and the fermented sap to determine the composition. The analysis for total sugar content was done using high-performance liquid chromatography (HPLC) and the percentage of alcohols by volume was determined using gas chromatography (GC). A model was also developed for the fermentation process based on the Adaptive-Network-Fuzzy Inference System (ANFIS) combined with particle swarm optimization (PSO) to predict bioethanol production in biomass fermentation of oil palm trunk sap. The model was used to find the best experimental conditions to achieve the maximum bioethanol concentration. Graphical sensitivity analysis techniques were also used to identify the most effective parameters in the bioethanol process.

Machine learning of free energies in chemical compound space using ensemble representations: Reaching experimental uncertainty for solvation

Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes, or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 490 molecules (80% of FreeSolv). Corresponding FML model errors are on par with state-of-the art physics based approaches. To generate the input representation for a new query compound, FML requires approximate and short molecular dynamics runs. We showcase its usefulness through analysis of solvation free energies for 116k organic molecules (all force-field compatible molecules in the QM9 database), identifying the most and least solvated systems and rediscovering quasi-linear structure-property relationships in terms of simple descriptors such as hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms. FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges rapidly with respect to the prediction error.

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.

Artificial neural networks for the prediction of solvation energies based on experimental and computational data

The knowledge of thermodynamic properties for novel electrolyte formulations is of fundamental interest for industrial applications as well as academic research. Herewith, we present an artificial neural networks (ANN) approach for the prediction of solvation energies and entropies for distinct ion pairs in various protic and aprotic solvents. The considered feed-forward ANN is trained either by experimental data or computational results from conceptual density functional theory calculations. The proposed concept of mapping computed values to experimental data lowers the amount of time-consuming and costly experiments and helps to overcome certain limitations. Our findings reveal high correlation coefficients between predicted and experimental values which demonstrate the validity of our approach.

A LSER-based model to predict the solubilizing effect of drugs by inclusion with cucurbit[7]uril

A large number of traditional drugs and the development of new drugs often encounter the problem of poor water solubility. Cucurbit[7]uril, a novel macrocyclic host, has attracted great interest in this field. Investigating the solubilizing effect of drugs by inclusion with cucurbit[7]uril could provide guidance for drug solubilization. In this work, the interactions of drugs with cucurbit[7]uril, drugs with water and the inclusion complexes with water, and the properties of drugs and inclusion complexes, are considered to establish a linear solvation energy relationships (LSER)-based model. This model could be applied to predicting the solubility of drugs with cucurbit[7]uril in water. Density functional theory (DFT) is employed to obtain the properties and interaction parameters. The multi-parameter solubility model obtained by stepwise regression shows good fitting and predicting results. And the surface area of inclusion complexes (A 3), the LUMO energy of inclusion complexes (E 3LUMO), the polarity index of inclusion complexes (I 3), the electronegativity of drugs (χ 1), and the oil-water partition coefficient of drugs (log p 1w) are effective parameters related to the solubilization of drugs with cucurbit[7]uril. Futhermore, the model could be extended to calculate the solubilizing effect of other macrocycles.

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.