Is Experimental Data Quality the Limiting Factor in Predicting the Aqueous Solubility of Druglike Molecules?

Revisiting the Application of Machine Learning Approaches in Predicting Aqueous Solubility

The solubility of chemical substances in water is a critical parameter in pharmaceutical development, environmental chemistry, agrochemistry, and other fields; however, accurately predicting it remains a challenge. This study aims to evaluate and compare the effectiveness of some of the most popular machine learning modeling methods and molecular featurization techniques in predicting aqueous solubility. Although these methods were not implemented in a competitive environment, some of their performance surpassed previous benchmarks, offering gradual but significant improvements. Our results show that methods based on graph convolution and graph attention mechanisms demonstrated exceptional predictive abilities with high-quality data sets, albeit with a sensitivity to data noise and errors. In contrast, models leveraging molecular descriptors not only provided better interpretability but also showed more resilience when dealing with inherent noise and errors in data. Our analysis of over 4000 molecular descriptors used in various models identified that approximately 800 of these descriptors make a significant contribution to solubility prediction. These insights offer guidance and direction for future developments in solubility prediction.

Prediction of the First-Pass Metabolism of a Drug After Oral Intake Based on Structural Parameters and Physicochemical Properties

BACKGROUND AND OBJECTIVE

The oral first-pass metabolism is a crucial factor that plays a key role in a drug's pharmacokinetic profile. Prediction of the oral first-pass metabolism based on chemical structural parameters can be useful in the drug-design process. Developing an orally administered drug with an acceptable pharmacokinetic profile is necessary to reduce the cost and time associated with evaluating the extent of the first-pass metabolism of a candidate compound in preclinical studies. The aim of this study is to estimate the first-pass metabolism of an orally administered drug.

METHODS

A set of compounds with reported first-pass metabolism data were collected. Moreover, human intestinal absorption percentage and oral bioavailability data were extracted from the literature to propose a classification system that split the drugs up based on their first-pass metabolism extents. Various structural parameters were calculated for each compound. The relations of the structural and physicochemical values of each compound to the class the compound belongs to were obtained using logistic regression.

RESULTS

Initial analysis showed that compounds with logD7.4 > 1 or a rugosity factor of > 1.5 are more likely to have high first-pass metabolism. Four different models that can predict the oral first-pass metabolism with acceptable error were introduced. The overall accuracies of the models were in the range of 72% (for models with simple descriptors) to 78% (for models with complex descriptors). Although the models with simple descriptors have lower accuracies compared to complex models, they are more interpretable and easier for researchers to utilize.

CONCLUSION

A novel classification of drugs based on the extent of the oral first-pass metabolism was introduced, and mechanistic models were developed to assign candidate compounds to the appropriate proposed classes.

Outline and background for the EU-OS solubility prediction challenge

In June 2022, EU-OS came to the decision to make public a solubility data set of 100+K compounds obtained from several of the EU-OS proprietary screening compound collections. Leveraging on the interest of SLAS for screening scientific development it was decided to launch a joint EUOS-SLAS competition within the chemoinformatics and machine learning (ML) communities. The competition was open to real world computation experts, for the best, most predictive, classification model of compound solubility. The aim of the competition was multiple: from a practical side, the winning model should then serve as a cornerstone for future solubility predictions having used the largest training set so far publicly available. From a higher project perspective, the intent was to focus the energies and experiences, even if professionally not precisely coming from Pharma R&D; to address the issue of how to predict compound solubility. Here we report how the competition was ideated and the practical aspects of conducting it within the Kaggle framework, leveraging of the versatility and the open-source nature of this data science platform. Consideration on results and challenges encountered have been also examined.

Designing solvent systems using self-evolving solubility databases and graph neural networks

Designing solvent systems is key to achieving the facile synthesis and separation of desired products from chemical processes, so many machine learning models have been developed to predict solubilities. However, breakthroughs are needed to address deficiencies in the model's predictive accuracy and generalizability; this can be addressed by expanding and integrating experimental and computational solubility databases. To maximize predictive accuracy, these two databases should not be trained separately, and they should not be simply combined without reconciling the discrepancies from different magnitudes of errors and uncertainties. Here, we introduce self-evolving solubility databases and graph neural networks developed through semi-supervised self-training approaches. Solubilities from quantum-mechanical calculations are referred to during semi-supervised learning, but they are not directly added to the experimental database. Dataset augmentation is performed from 11 637 experimental solubilities to >900 000 data points in the integrated database, while correcting for the discrepancies between experiment and computation. Our model was successfully applied to study solvent selection in organic reactions and separation processes. The accuracy (mean absolute error around 0.2 kcal mol-1 for the test set) is quantitatively useful in exploring Linear Free Energy Relationships between reaction rates and solvation free energies for 11 organic reactions. Our model also accurately predicted the partition coefficients of lignin-derived monomers and drug-like molecules. While there is room for expanding solubility predictions to transition states, radicals, charged species, and organometallic complexes, this approach will be attractive to predictive chemistry areas where experimental, computational, and other heterogeneous data should be combined.

Ensemble Geometric Deep Learning of Aqueous Solubility

Geometric deep learning is one of the main workhorses for harnessing the power of big data to predict molecular properties such as aqueous solubility, which is key to the pharmacokinetic improvement of drug candidates. Two ensembles of graph neural network architectures were built, one based on spectral convolution and the other on spatial convolution. The pretrained models, denoted respectively as SolNet-GCN and SolNet-GAT, significantly outperformed the existing neural networks benchmarked on a validation set of 207 molecules. The SolNet-GCN model demonstrated the best performance on both the training and validation sets, with RMSE values of 0.53 and 0.72 log molar unit and Pearson r2 values of 0.95 and 0.75, respectively. Further, the ranking power of the SolNet models agreed well with a QM-based thermodynamic cycle approach at the PBE-vdW level of theory on a series of benzophenylurea derivatives and a series of benzodiazepine derivatives. Nevertheless, testing the resultant models on a set of inhibitors of the macrophage migration inhibitory factor (MIF) illustrated that the inclusion of atomic attributes to discriminate atoms with a higher tendency to form intermolecular hydrogen bonds in the crystalline state and to identify planar or nonplanar substructures can be beneficial for the prediction of aqueous solubility.

A new set of solute descriptors to calculate solubility of drugs in mono-solvents

A new set of solute parameters derived from a correlation model using Catalan parameters. The parameters represent the interaction of the solute with the mono-solvents at 298.15K. The computational procedure was adopted from Abraham's solvation model and the obtained results are promising. In this work, the calculated parameters were used to back-calculate the drugs solubility in various mono-solvents at different temperatures employing the van't Hoff's model as the skeleton on the derived model. The obtained mean percentage deviations (MPDs) were in the range of 3.1 to 88.5% with the overall MPD of 29.1%. (1) Derivation of a new set of solute parameters from a correlation model using Catalan parameters; (2) adoption of the calculation method of Abraham's solvation model with the skeleton of van't Hoff's equation; (3) using the achieved parameters for back-calculation of drugs solubility in various mono-solvents; (4) obtaining an overall acceptable mean percentage deviation of 29.1% from calculations.

Targeted Protein Degradation: Advances, Challenges, and Prospects for Computational Methods

The therapeutic approach of targeted protein degradation (TPD) is gaining momentum due to its potentially superior effects compared with protein inhibition. Recent advancements in the biotech and pharmaceutical sectors have led to the development of compounds that are currently in human trials, with some showing promising clinical results. However, the use of computational tools in TPD is still limited, as it has distinct characteristics compared with traditional computational drug design methods. TPD involves creating a ternary structure (protein-degrader-ligase) responsible for the biological function, such as ubiquitination and subsequent proteasomal degradation, which depends on the spatial orientation of the protein of interest (POI) relative to E2-loaded ubiquitin. Modeling this structure necessitates a unique blend of tools initially developed for small molecules (e.g., docking) and biologics (e.g., protein-protein interaction modeling). Additionally, degrader molecules, particularly heterobifunctional degraders, are generally larger than conventional small molecule drugs, leading to challenges in determining drug-like properties like solubility and permeability. Furthermore, the catalytic nature of TPD makes occupancy-based modeling insufficient. TPD consists of multiple interconnected yet distinct steps, such as POI binding, E3 ligase binding, ternary structure interactions, ubiquitination, and degradation, along with traditional small molecule properties. A comprehensive set of tools is needed to address the dynamic nature of the induced proximity ternary complex and its implications for ubiquitination. In this Perspective, we discuss the current state of computational tools for TPD. We start by describing the series of steps involved in the degradation process and the experimental methods used to characterize them. Then, we delve into a detailed analysis of the computational tools employed in TPD. We also present an integrative approach that has proven successful for degrader design and its impact on project decisions. Finally, we examine the future prospects of computational methods in TPD and the areas with the greatest potential for impact.

Machine-Learning-Enabled Ligand Screening for Cs/Sr Crystallizing Separation

The reprocessing of spent nuclear fuel is critical for the sustainability of the nuclear energy industry. However, several key separation processes present challenges in this regard, calling for continuous research into next-generation separation materials. Herein, we propose a high-throughput screening framework to improve efficiency in identifying potential ligands that selectively coordinate metal cations of interest in liquid wastes that considers multiple key chemical characteristics, including aqueous solubility, pKa, and coordination bond length. Machine-learning models were designed for the fast and accurate prediction of these characteristics by using graph convolution and transfer-learning techniques. Suitable ligands for Cs/Sr crystallizing separation were identified through the "computational funnel", and several top-ranking, nontoxic, low-cost ligands were selected for experimental verification.

Bridging the Gap between Differential Mobility, Log S, and Log P Using Machine Learning and SHAP Analysis

Aqueous solubility, log S, and the water-octanol partition coefficient, log P, are physicochemical properties that are used to screen the viability of drug candidates and to estimate mass transport in the environment. In this work, differential mobility spectrometry (DMS) experiments performed in microsolvating environments are used to train machine learning (ML) frameworks that predict the log S and log P of various molecule classes. In lieu of a consistent source of experimentally measured log S and log P values, the OPERA package was used to evaluate the aqueous solubility and hydrophobicity of 333 analytes. With ion mobility/DMS data (e.g., CCS, dispersion curves) as input, we used ML regressors and ensemble stacking to derive relationships with a high degree of explainability, as assessed via SHapley Additive exPlanations (SHAP) analysis. The DMS-based regression models returned scores of R² = 0.67 and RMSE = 1.03 ± 0.10 for log S predictions and R² = 0.67 and RMSE = 1.20 ± 0.10 for log P after 5-fold random cross-validation. SHAP analysis reveals that the regressors strongly weighted gas-phase clustering in log P correlations. The addition of structural descriptors (e.g., # of aromatic carbons) improved log S predictions to yield RMSE = 0.84 ± 0.07 and R² = 0.78. Similarly, log P predictions using the same data resulted in an RMSE of 0.83 ± 0.04 and R² = 0.84. The SHAP analysis of log P models highlights the need for additional experimental parameters describing hydrophobic interactions. These results were achieved with a smaller dataset (333 instances) and minimal structural correlation compared to purely structure-based models, underscoring the value of employing DMS data in predictive models.

Blinded Predictions and Post Hoc Analysis of the Second Solubility Challenge Data: Exploring Training Data and Feature Set Selection for Machine and Deep Learning Models

Accurate methods to predict solubility from molecular structure are highly sought after in the chemical sciences. To assess the state of the art, the American Chemical Society organized a "Second Solubility Challenge" in 2019, in which competitors were invited to submit blinded predictions of the solubilities of 132 drug-like molecules. In the first part of this article, we describe the development of two models that were submitted to the Blind Challenge in 2019 but which have not previously been reported. These models were based on computationally inexpensive molecular descriptors and traditional machine learning algorithms and were trained on a relatively small data set of 300 molecules. In the second part of the article, to test the hypothesis that predictions would improve with more advanced algorithms and higher volumes of training data, we compare these original predictions with those made after the deadline using deep learning models trained on larger solubility data sets consisting of 2999 and 5697 molecules. The results show that there are several algorithms that are able to obtain near state-of-the-art performance on the solubility challenge data sets, with the best model, a graph convolutional neural network, resulting in an RMSE of 0.86 log units. Critical analysis of the models reveals systematic differences between the performance of models using certain feature sets and training data sets. The results suggest that careful selection of high quality training data from relevant regions of chemical space is critical for prediction accuracy but that other methodological issues remain problematic for machine learning solubility models, such as the difficulty in modeling complex chemical spaces from sparse training data sets.

Attention-Based Graph Neural Network for Molecular Solubility Prediction

Drug discovery (DD) research is aimed at the discovery of new medications. Solubility is an important physicochemical property in drug development. Active pharmaceutical ingredients (APIs) are essential substances for high drug efficacy. During DD research, aqueous solubility (AS) is a key physicochemical attribute required for API characterization. High-precision in silico solubility prediction reduces the experimental cost and time of drug development. Several artificial tools have been employed for solubility prediction using machine learning and deep learning techniques. This study aims to create different deep learning models that can predict the solubility of a wide range of molecules using the largest currently available solubility data set. Simplified molecular-input line-entry system (SMILES) strings were used as molecular representation, models developed using simple graph convolution, graph isomorphism network, graph attention network, and AttentiveFP network. Based on the performance of the models, the AttentiveFP-based network model was finally selected. The model was trained and tested on 9943 compounds. The model outperformed on 62 anticancer compounds with metric Pearson correlation R ² and root-mean-square error values of 0.52 and 0.61, respectively. AS can be improved by graph algorithm improvement or more molecular properties addition.

Intrinsic Aqueous Solubility: Mechanistically Transparent Data-Driven Modeling of Drug Substances

Intrinsic aqueous solubility is a foundational property for understanding the chemical, technological, pharmaceutical, and environmental behavior of drug substances. Despite years of solubility research, molecular structure-based prediction of the intrinsic aqueous solubility of drug substances is still under active investigation. This paper describes the authors’ systematic data-driven modelling in which two fit-for-purpose training data sets for intrinsic aqueous solubility were collected and curated, and three quantitative structure–property relationships were derived to make predictions for the most recent solubility challenge. All three models perform well individually, while being mechanistically transparent and easy to understand. Molecular descriptors involved in the models are related to the following key steps in the solubility process: dissociation of the molecule from the crystal, formation of a cavity in the solvent, and insertion of the molecule into the solvent. A consensus modeling approach with these models remarkably improved prediction capability and reduced the number of strong outliers by more than two times. The performance and outliers of the second solubility challenge predictions were analyzed retrospectively. All developed models have been published in the QsarDB.org repository according to FAIR principles and can be used without restrictions for exploring, downloading, and making predictions.

Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization

Artificial intelligence and specifically machine learning applications are nowadays used in a variety of scientific applications and cutting-edge technologies, where they have a transformative impact. Such an assembly of statistical and linear algebra methods making use of large data sets is becoming more and more integrated into chemistry and crystallization research workflows. This review aims to present, for the first time, a holistic overview of machine learning and cheminformatics applications as a novel, powerful means to accelerate the discovery of new crystal structures, predict key properties of organic crystalline materials, simulate, understand, and control the dynamics of complex crystallization process systems, as well as contribute to high throughput automation of chemical process development involving crystalline materials. We critically review the advances in these new, rapidly emerging research areas, raising awareness in issues such as the bridging of machine learning models with first-principles mechanistic models, data set size, structure, and quality, as well as the selection of appropriate descriptors. At the same time, we propose future research at the interface of applied mathematics, chemistry, and crystallography. Overall, this review aims to increase the adoption of such methods and tools by chemists and scientists across industry and academia.

Multi-channel GCN ensembled machine learning model for molecular aqueous solubility prediction on a clean dataset

This study constructed a new aqueous solubility dataset and a solubility regression model which was ensembled by GCN and machine learning models. Aqueous solubility is a key physiochemical property of small molecules in drug discovery. In the past few decades, there have been many studies about solubility prediction. However, many of these studies have high root mean squared error (RMSE). Meanwhile, their dataset always contains salt compounds and solubility data obtained from different experimental conditions. In this paper, we constructed a clean dataset with 2609 compounds, which was small but contains only solubility records without salts at the same temperatures (25 °C). Here, we applied graph convolutional neural network (GCN) to construct an aqueous solubility prediction model. To enhance the performance of the model, the molecular MACCS key fingerprints and physiochemical descriptors were also combined with the GCN model to build a multi-channel model. Additionally, the authors also built two machine learning models (support vector regression and gradient boost decision tree) and assembled them to the GCN model to improve the root mean squared error (RMSE = 0.665). Finally, comparative experiments have shown that our framework achieved the best performance on ESOL dataset (RMSE_val = 0.56, RMSE_test = 0.44) and surpassed four established software on aqueous solubility prediction of new compounds.

Simulation Models for Prediction of Bioavailability of Medicinal Drugs-the Interface Between Experiment and Computation

The oral drug bioavailability (BA) problems have remained inevitable over the years, impairing drug efficacy and indirectly leading to eventual human morbidity and mortality. However, some conventional lab-based methods improve drug absorption leading to enhanced BA, and the recent experimental techniques are up-and-coming. Nevertheless, some have inherent drawbacks in improving the efficacy of poorly insoluble and low impermeable drugs. Drug BA and strategies to overcome these challenges were briefly highlighted. This review has significantly unravelled the different computational models for studying and predicting drug bioavailability. Several computational approaches provide mechanistic insights into the oral drug delivery system simulation of descriptors like solubility, permeability, transport protein-ligand interactions, and molecular structures. The in silico techniques have long been known still are just being applied to unravel drug bioavailability issues. Many publications have reported novel applications of the computational models towards achieving improved drug BA, including predicting gastrointestinal tract (GIT) drug absorption properties and passive intestinal membrane permeability, thus maximizing time and resources. Also, the classical molecular simulation models for free solvation energies of soluble-related processes such as solubilization, dissolutions, supersaturation, and precipitation have been used in virtual screening studies. A few of the tools are GastroPlus^TM that supports biowaiver for drugs, mainly BCS class III and predicts drug compounds' absorption and pharmacokinetic process; SimCyp® simulator for mechanistic modelling and simulation of drug formulation processes; pharmacodynamics analysis on non-linear mixed-effects modelling; and mathematical models, predicting absorption potential/maximum absorption dose. This review provides in silico-experiment annexation in the drug bioavailability enhancement, possible insights that lead to critical opinion on the applications and reliability of the various in silico models as a growing tool for drug development and discovery, thus accelerating drug development processes.

Predicting the Drug Clearance Pathway with Structural Descriptors

BACKGROUND AND OBJECTIVE

The clearance, by renal elimination or hepatic metabolism, is one of the most important pharmacokinetic parameters of a drug. It allows the half-life, bioavailability, and drug-drug interactions to be predicted, and it can also affect the dose regimen of a drug. Predicting the clearance pathways of new chemical candidates during drug development is vital in order to minimize the risks of possible side effects and drug interactions. Many in vivo methods have been established to predict drug clearance in humans, and these mainly rely on data from in vivo studies in preclinical species-mainly rats, dogs, and monkeys. They are also time consuming and expensive. The aim of this study was to find the relationship between structural parameters of drugs and their clearance pathways.

METHODS

The clearance pathway of each drug was obtained from the literature. Various structural descriptors [Abraham solvation parameters, topological polar surface area, numbers of hydrogen-bond donors and acceptors, number of rotatable bonds, molecular weight, logarithm of the partition coefficient (logP), and logarithm of the distribution coefficient at pH 7.4 (logD_7.4)] were applied to develop a mechanistic model for predicting clearance pathways.

RESULTS

The results of this study indicate that compounds with logD_7.4 > 1 or with zero or one hydrogen-bond donor undergo hepatic metabolism, whereas the clearance pathway for chemicals with logD_7.4 < - 2 is renal elimination. Furthermore, models established using logistic regression based on five structural parameters for compounds with - 2 < logD_7.4 < 1 could be used in a clearance pathway prediction tool. The overall prediction accuracies of the first and second models were 84.8% and 84.4%, respectively.

CONCLUSION

The developed model can be used to find the clearance pathways of new drug candidates with acceptable accuracy. The main descriptors that are used to evaluate this parameter are the hydrophobicity and the number of hydrogen-bonding functional groups of the compound.

Prediction of small-molecule compound solubility in organic solvents by machine learning algorithms

Rapid solvent selection is of great significance in chemistry. However, solubility prediction remains a crucial challenge. This study aimed to develop machine learning models that can accurately predict compound solubility in organic solvents. A dataset containing 5081 experimental temperature and solubility data of compounds in organic solvents was extracted and standardized. Molecular fingerprints were selected to characterize structural features. lightGBM was compared with deep learning and traditional machine learning (PLS, Ridge regression, kNN, DT, ET, RF, SVM) to develop models for predicting solubility in organic solvents at different temperatures. Compared to other models, lightGBM exhibited significantly better overall generalization (logS  ± 0.20). For unseen solutes, our model gave a prediction accuracy (logS  ± 0.59) close to the expected noise level of experimental solubility data. lightGBM revealed the physicochemical relationship between solubility and structural features. Our method enables rapid solvent screening in chemistry and may be applied to solubility prediction in other solvents.

UNGAP best practice for improving solubility data quality of orally administered drugs

An important goal of the European Cooperation in Science and Technology (COST) Action UNGAP (UNderstanding Gastrointestinal Absorption-related Processes, www.ungap.eu) is to improve standardization of methods relating to the study of oral drug absorption. Solubility is a general term that refers to the maximum achievable concentration of a compound dissolved in a liquid medium. For orally administered drugs, relevant information on drug properties is crucial during drug (product) development and at the regulatory level. Collection of reliable and reproducible solubility data requires careful application and understanding of the limitations of the selected experimental method. In addition, the purity of a compound and its solid state form, as well as experimental parameters such as temperature of experimentation, media related factors, and sample handling procedures can affect data quality. In this paper, an international consensus developed by the COST UNGAP network on recommendations for collecting high quality solubility data for the development of orally administered drugs is proposed.

Application of Artificial Neural Networks to Predict the Intrinsic Solubility of Drug-Like Molecules

Machine learning (ML) approaches are receiving increasing attention from pharmaceutical companies and regulatory agencies, given their ability to mine knowledge from available data. In drug discovery, for example, they are employed in quantitative structure-property relationship (QSPR) models to predict biological properties from the chemical structure of a drug molecule. In this paper, following the Second Solubility Challenge (SC-2), a QSPR model based on artificial neural networks (ANNs) was built to predict the intrinsic solubility (logS0) of the 100-compound low-variance tight set and the 32-compound high-variance loose set provided by SC-2 as test datasets. First, a training dataset of 270 drug-like molecules with logS0 value experimentally determined was gathered from the literature. Then, a standard three-layer feed-forward neural network was defined by using 10 ChemGPS physico-chemical descriptors as input features. The developed ANN showed adequate predictive performances on both of the SC-2 test datasets. Benefits and limitations of ML approaches have been highlighted and discussed, starting from this case-study. The main findings confirmed that ML approaches are an attractive and promising tool to predict logS0; however, many aspects, such as data quality, molecular descriptor computation and selection, and assessment of applicability domain, are crucial but often neglected, and should be carefully considered to improve predictions based on ML.

ADME prediction with KNIME: A retrospective contribution to the second "Solubility Challenge"

Computational models for predicting aqueous solubility from the molecular structure represent a promising strategy from the perspective of drug design and discovery. Since the first "Solubility Challenge", these initiatives have marked the state-of-art of the modelling algorithms used to predict drug solubility. In this regard, the quality of the input experimental data and its influence on model performance has been frequently discussed. In our previous study, we developed a computational model for aqueous solubility based on recursive random forest approaches. The aim of the current commentary is to analyse the performance of this already trained predictive model on the molecules of the second "Solubility Challenge". Even when our training set has inconsistencies related to the pH, solid form and temperature conditions of the solubility measurements, the model was able to predict the two sets from the second "Solubility Challenge" with statistics comparable to those of the top ranked models. Finally, we provided a KNIME automated workflow to predict aqueous solubility of new drug candidates, during the early stages of drug discovery and development, for ensuring the applicability and reproducibility of our model.

Toward Physics-Based Solubility Computation for Pharmaceuticals to Rival Informatics

We demonstrate that physics-based calculations of intrinsic aqueous solubility can rival cheminformatics-based machine learning predictions. A proof-of-concept was developed for a physics-based approach via a sublimation thermodynamic cycle, building upon previous work that relied upon several thermodynamic approximations, notably the 2RT approximation, and limited conformational sampling. Here, we apply improvements to our sublimation free-energy model with the use of crystal phonon mode calculations to capture the contributions of the vibrational modes of the crystal. Including these improvements with lattice energies computed using the model-potential-based Ψ_mol method leads to accurate estimates of sublimation free energy. Combining these with hydration free energies obtained from either molecular dynamics free-energy perturbation simulations or density functional theory calculations, solubilities comparable to both experiment and informatics predictions are obtained. The application to coronene, succinic acid, and the pharmaceutical desloratadine shows how the methods must be adapted for the adoption of different conformations in different phases. The approach has the flexibility to extend to applications that cannot be covered by informatics methods.

Synergistic Computational Modeling Approaches as Team Players in the Game of Solubility Predictions

Several approaches to predict and model drug solubility have been used in the drug discovery and development processes during the last decades. Each of these approaches have their own benefits and place, and are typically used as standalone approaches rather than in concert. The synergistic effects of these are often overlooked, partly due to the need of computational experts to perform the modeling and simulations as well as analyzing the data obtained. Here we provide our views on how these different approaches can be used to retrieve more information on drug solubility, ranging from multivariate data analysis over thermodynamic cycle modeling to molecular dynamics simulations. We are discussing aqueous solubility as well as solubility in more complex mixed solvents and media with colloidal structures present. We conclude that the field of computational pharmaceutics is in its early days but with a bright future ahead. However, education of computational formulators with broad knowledge of modeling and simulation approaches is imperative if computational pharmaceutics is to reach its full potential.

Machine learning with physicochemical relationships: solubility prediction in organic solvents and water

Solubility prediction remains a critical challenge in drug development, synthetic route and chemical process design, extraction and crystallisation. Here we report a successful approach to solubility prediction in organic solvents and water using a combination of machine learning (ANN, SVM, RF, ExtraTrees, Bagging and GP) and computational chemistry. Rational interpretation of dissolution process into a numerical problem led to a small set of selected descriptors and subsequent predictions which are independent of the applied machine learning method. These models gave significantly more accurate predictions compared to benchmarked open-access and commercial tools, achieving accuracy close to the expected level of noise in training data (LogS ± 0.7). Finally, they reproduced physicochemical relationship between solubility and molecular properties in different solvents, which led to rational approaches to improve the accuracy of each models.

Accurate predictions of aqueous solubility of drug molecules via the multilevel graph convolutional network (MGCN) and SchNet architectures

Deep learning based methods have been widely applied to predict various kinds of molecular properties in the pharmaceutical industry with increasingly more success. In this study, we propose two novel models for aqueous solubility predictions, based on the Multilevel Graph Convolutional Network (MGCN) and SchNet architectures, respectively. The advantage of the MGCN lies in the fact that it could extract the graph features of the target molecules directly from the (3D) structural information; therefore, it doesn't need to rely on a lot of intra-molecular descriptors to learn the features, which are of significance for accurate predictions of the molecular properties. The SchNet performs well in modelling the interatomic interactions inside a molecule, and such a deep learning architecture is also capable of extracting structural information and further predicting the related properties. The actual accuracy of these two novel approaches was systematically benchmarked with four different independent datasets. We found that both the MGCN and SchNet models performed well for aqueous solubility predictions. In the future, we believe such promising predictive models will be applicable to enhancing the efficiency of the screening, crystallization and delivery of drug molecules, essentially as a useful tool to promote the development of molecular pharmaceutics.

ADME prediction with KNIME: In silico aqueous solubility consensus model based on supervised recursive random forest approaches

In-silico prediction of aqueous solubility plays an important role during the drug discovery and development processes. For many years, the limited performance of in-silico solubility models has been attributed to the lack of high-quality solubility data for pharmaceutical molecules. However, some studies suggest that the poor accuracy of solubility prediction is not related to the quality of the experimental data and that more precise methodologies (algorithms and/or set of descriptors) are required for predicting aqueous solubility for pharmaceutical molecules. In this study a large and diverse database was generated with aqueous solubility values collected from two public sources; two new recursive machine-learning approaches were developed for data cleaning and variable selection, and a consensus model based on regression and classification algorithms was created. The modeling protocol, which includes the curation of chemical and experimental data, was implemented in KNIME, with the aim of obtaining an automated workflow for the prediction of new databases. Finally, we compared several methods or models available in the literature with our consensus model, showing results comparable or even outperforming previous published models.

Fundamental aspects of DMPK optimization of targeted protein degraders

Targeted protein degraders are an emerging modality. Their properties fall outside the traditional small-molecule property space and are in the 'beyond rule of 5' space. Consequently, drug discovery programs focused on developing orally bioavailable degraders are expected to face complex drug metabolism and pharmacokinetics (DMPK) challenges compared with traditional small molecules. Nevertheless, little information is available on the DMPK optimization of oral degraders. Therefore, in this review, we discuss our experience of these DMPK optimization challenges and present methodologies and strategies to overcome the hurdles dealing with this new small-molecule modality, specifically in developing oral degraders to treat cancer.

Improved Prediction of Aqueous Solubility of Novel Compounds by Going Deeper With Deep Learning

Aqueous solubility is an important physicochemical property of compounds in anti-cancer drug discovery. Artificial intelligence solubility prediction tools have scored impressive performances by employing regression, machine learning, and deep learning methods. The reported performances vary significantly partly because of the different datasets used. Solubility prediction on novel compounds needs to be improved, which may be achieved by going deeper with deep learning. We constructed deeper-net models of ~20-layer modified ResNet convolutional neural network architecture, which were trained and tested with 9,943 compounds encoded by molecular fingerprints. Retrospectively tested by 62 recently-published novel compounds, one deeper-net model outperformed four established tools, shallow-net models, and four human experts. Deeper-net models also outperformed others in predicting the solubility values of a series of novel compounds newly-synthesized for anti-cancer drug discovery. Solubility prediction may be improved by going deeper with deep learning. Our deeper-net models are accessible at http://www.npbdb.net/solubility/index.jsp.

Building attention and edge message passing neural networks for bioactivity and physical-chemical property prediction

Neural Message Passing for graphs is a promising and relatively recent approach for applying Machine Learning to networked data. As molecules can be described intrinsically as a molecular graph, it makes sense to apply these techniques to improve molecular property prediction in the field of cheminformatics. We introduce Attention and Edge Memory schemes to the existing message passing neural network framework, and benchmark our approaches against eight different physical–chemical and bioactivity datasets from the literature. We remove the need to introduce a priori knowledge of the task and chemical descriptor calculation by using only fundamental graph-derived properties. Our results consistently perform on-par with other state-of-the-art machine learning approaches, and set a new standard on sparse multi-task virtual screening targets. We also investigate model performance as a function of dataset preprocessing, and make some suggestions regarding hyperparameter selection.

Inverse-QSPR for de novo Design: A Review

The use of computer tools to solve chemistry-related problems has given rise to a large and increasing number of publications these last decades. This new field of science is now well recognized and labelled Chemoinformatics. Among all chemoinformatics techniques, the use of statistical based approaches for property predictions has been the subject of numerous research reflecting both new developments and many cases of applications. The so obtained predictive models relating a property to molecular features - descriptors - are gathered under the acronym QSPR, for Quantitative Structure Property Relationships. Apart from the obvious use of such models to predict property values for new compounds, their use to virtually synthesize new molecules - de novo design - is currently a high-interest subject. Inverse-QSPR (i-QSPR) methods have hence been developed to accelerate the discovery of new materials that meet a set of specifications. In the proposed manuscript, we review existing i-QSPR methodologies published in the open literature in a way to highlight developments, applications, improvements and limitations of each.

Concepts of Artificial Intelligence for Computer-Assisted Drug Discovery

Artificial intelligence (AI), and, in particular, deep learning as a subcategory of AI, provides opportunities for the discovery and development of innovative drugs. Various machine learning approaches have recently (re)emerged, some of which may be considered instances of domain-specific AI which have been successfully employed for drug discovery and design. This review provides a comprehensive portrayal of these machine learning techniques and of their applications in medicinal chemistry. After introducing the basic principles, alongside some application notes, of the various machine learning algorithms, the current state-of-the art of AI-assisted pharmaceutical discovery is discussed, including applications in structure- and ligand-based virtual screening, de novo drug design, physicochemical and pharmacokinetic property prediction, drug repurposing, and related aspects. Finally, several challenges and limitations of the current methods are summarized, with a view to potential future directions for AI-assisted drug discovery and design.

Aqueous Drug Solubility: What Do We Measure, Calculate and QSPR Predict?

Detailed critical analysis of publications devoted to QSPR of aqueous solubility is presented in the review with discussion of four types of aqueous solubility (three different thermodynamic solubilities with unknown solute structure, intrinsic solubility, solubility in physiological media at pH=7.4 and kinetic solubility), variety of molecular descriptors (from topological to quantum chemical), traditional statistical and machine learning methods as well as original QSPR models.

Challenges in the use of atomistic simulations to predict solubilities of drug-like molecules

Background: Solubility is a physical property of high importance to the pharmaceutical industry, the prediction of which for potential drugs has so far been a hard task. We attempted to predict the solubility of acetylsalicylic acid (ASA) by estimating the absolute chemical potentials of its most stable polymorph and of solutions with different concentrations of the drug molecule. Methods: Chemical potentials were estimated from all-atom molecular dynamics simulations.  We used the Einstein molecule method (EMM) to predict the absolute chemical potential of the solid and solvation free energy calculations to predict the excess chemical potentials of the liquid-phase systems. Results: Reliable estimations of the chemical potentials for the solid and for a single ASA molecule using the EMM required an extremely large number of intermediate states for the free energy calculations, meaning that the calculations were extremely demanding computationally. Despite the computational cost, however, the computed value did not agree well with the experimental value, potentially due to limitations with the underlying energy model. Perhaps better values could be obtained with a better energy model; however, it seems likely computational cost may remain a limiting factor for use of this particular approach to solubility estimation.    Conclusions: Solubility prediction of drug-like solids remains computationally challenging, and it appears that both the underlying energy model and the computational approach applied may need improvement before the approach is suitable for routine use.

Improved understanding of aqueous solubility modeling through topological data analysis

Topological data analysis is a family of recent mathematical techniques seeking to understand the 'shape' of data, and has been used to understand the structure of the descriptor space produced from a standard chemical informatics software from the point of view of solubility. We have used the mapper algorithm, a TDA method that creates low-dimensional representations of data, to create a network visualization of the solubility space. While descriptors with clear chemical implications are prominent features in this space, reflecting their importance to the chemical properties, an unexpected and interesting correlation between chlorine content and rings and their implication for solubility prediction is revealed. A parallel representation of the chemical space was generated using persistent homology applied to molecular graphs. Links between this chemical space and the descriptor space were shown to be in agreement with chemical heuristics. The use of persistent homology on molecular graphs, extended by the use of norms on the associated persistence landscapes allow the conversion of discrete shape descriptors to continuous ones, and a perspective of the application of these descriptors to quantitative structure property relations is presented.

The influence of solid state information and descriptor selection on statistical models of temperature dependent aqueous solubility

Predicting the equilibrium solubility of organic, crystalline materials at all relevant temperatures is crucial to the digital design of manufacturing unit operations in the chemical industries. The work reported in our current publication builds upon the limited number of recently published quantitative structure-property relationship studies which modelled the temperature dependence of aqueous solubility. One set of models was built to directly predict temperature dependent solubility, including for materials with no solubility data at any temperature. We propose that a modified cross-validation protocol is required to evaluate these models. Another set of models was built to predict the related enthalpy of solution term, which can be used to estimate solubility at one temperature based upon solubility data for the same material at another temperature. We investigated whether various kinds of solid state descriptors improved the models obtained with a variety of molecular descriptor combinations: lattice energies or 3D descriptors calculated from crystal structures or melting point data. We found that none of these greatly improved the best direct predictions of temperature dependent solubility or the related enthalpy of solution endpoint. This finding is surprising because the importance of the solid state contribution to both endpoints is clear. We suggest our findings may, in part, reflect limitations in the descriptors calculated from crystal structures and, more generally, the limited availability of polymorph specific data. We present curated temperature dependent solubility and enthalpy of solution datasets, integrated with molecular and crystal structures, for future investigations.

Brief overview of solubility methods: Recent trends in equilibrium solubility measurement and predictive models

Solubility is a crucial physicochemical parameter affecting the whole process of drug discovery and development. Thus, understanding of the methods and concepts to measure and predict this propensity are of utmost importance for the pharmaceutical scientist. Despite their inherent limitations, kinetic solubility screening methods became routine assays by mimicking bioassay conditions and guiding the lead optimization process. In contrast, thermodynamic solubility methods show a clear evolution: miniaturized high throughput assays coupled to analytical techniques such as solid-state characterization, ultra performance liquid chromatography, or polychromatic turbidimetry, have been developed, thereby enabling a more complex physicochemical profiling at the early discovery stage. Solubility prediction still poses a significant challenge at the industrial level. Classification and critical evaluation of recent in silico models are provided. Discussion of experimental and computational methods: was based on relevant industrial references.

The current limits in virtual screening and property prediction

Beyond finding inhibitors that show high binding affinity to the respective target, there is the challenge of optimizing their properties with respect to metabolic and toxicological issues, as well as further off-target effects. To reduce the experimental effort of synthesizing and testing actual substances in corresponding assays, virtual screening has become an indispensable toolbox in preclinical development. The scope of application covers the prediction of molecular properties including solubility, metabolic liability and binding to antitargets, such as the hERG channel. Furthermore, prediction of binding sites and drugable targets are emerging aspects of virtual screening. Issues involved with the currently applied computational models including machine learning algorithms are outlined, such as limitations to the accuracy of prediction and overfitting.

Intermolecular interaction as a direct measure of water solubility advantage of meloxicam cocrystalized with carboxylic acids

The solubility advantage (SA) of meloxicam cocrystalized with mono- and dicarboxylic acids was expressed in terms of equilibrium constants involving active pharmaceutical ingredient and coformer in aqueous solutions. It is argued that SA can be quantified by concentration of pairs formed in water. The pH and concentration of dissolved components is included explicitly in the model. The alternative behavior of mono- and dicarboxylic acids was emphasized and addressed to different structural motifs. The structural and energetic properties of meloxicam and its complexes with carboxylic acids were characterized, including tautmerism and dissociation in aqueous media. In particular, performed in silico modeling confirmed experimental observation that meloxicam dissolved in water or modest acidic solutions is expected to be a mixture of anionic form in equilibrium with at least five neutral isomers. Tautomer-related diversity of pairs formation and the possibility of salt formation is also discussed. Graphical abstract Two types of motifs found in meloxicam cocrystals reveal two sources of solubility advantage.

Computational prediction of drug solubility in water-based systems: Qualitative and quantitative approaches used in the current drug discovery and development setting

In this review we will discuss recent advances in computational prediction of solubility in water-based solvents. Our focus is set on recent advances in predictions of biorelevant solubility in media mimicking the human intestinal fluids and on new methods to predict the thermodynamic cycle rather than prediction of solubility in pure water through quantitative structure property relationships (QSPR). While the literature is rich in QSPR models for both solubility and melting point, a physicochemical property strongly linked to the solubility, recent advances in the modelling of these properties make use of theory and computational simulations to better predict these properties or processes involved therein (e.g. solid state crystal lattice packing, dissociation of molecules from the lattice and solvation). This review serves to provide an update on these new approaches and how they can be used to more accurately predict solubility, and also importantly, inform us on molecular interactions and processes occurring during drug dissolution and solubilisation.

Physico-chemical properties of aqueous drug solutions: From the basic thermodynamics to the advanced experimental and simulation results

The physical chemical properties of aqueous solutions of model compounds are illustrated in relation to hydration and solubility issues by using three perspectives: thermodynamic, spectroscopic and molecular dynamics simulations. The thermodynamic survey of the fundamental backgrounds of concentration dependence and experimental solubility results show some peculiar behavior of aqueous solutions with several types of similar solutes. Secondly, the use of a variety of experimental spectroscopic devices, operating under different experimental conditions of dimension and frequency, has produced a large amount of structural and dynamic data on aqueous solutions showing the richness of the information produced, depending on where and how the experiment is carried out. Finally, the use of molecular dynamics computational work is presented to highlight how the different types of solute functional groups and surface topologies organize adjacent water molecules differently. The highly valuable contribution of computer simulation studies in providing molecular explanations for experimental deductions, either of a thermodynamic or spectroscopic nature, is shown to have changed the current knowledge of many aqueous solution processes. While this paper is intended to provide a collective view on the latest literature results, still the presentation aims at a tutorial explanation of the potentials of the three methodologies in the field of aqueous solutions of pharmaceutical molecules.