First-Principles Calculation of the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules

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.

Predicting absolute aqueous solubility by applying a machine learning model for an artificially liquid-state as proxy for the solid-state

In this study, we use machine learning algorithms with QM-derived COSMO-RS descriptors, along with Morgan fingerprints, to predict the absolute solubility of drug-like compounds. The QM-derived descriptors account for the molecular properties of the solute, i.e., the solute-solute interactions in an artificial-liquid-state (super-cooled liquid), and the solute-solvent interactions in solution. We employ two main approaches to predict solubility: (i) a hypothetical pathway that involves melting the solute at room temperature T = T¯ ([Formula: see text]) and mixing the artificially liquid solute into the solvent ([Formula: see text]). In this approach [Formula: see text] is predicted using machine learning models, and the [Formula: see text] is obtained from COSMO-RS calculations; (ii) direct solubility prediction using machine learning algorithms. The models were trained on a large number of Bayer in-house compounds for which water solubility data is available at physiological pH of 6.5 and ambient temperature. We also evaluated our models using external datasets from a solubility challenge. Our models present great improvements compared to the absolute solubility prediction with the QSAR model for the artificial liquid state as implemented in the COSMOtherm software, for both in-house and external datasets. We are furthermore able to demonstrate the superiority of QM-derived descriptors compared to cheminformatics descriptors. We finally present low-cost alternative models using fragment-based COSMOquick calculations with only marginal reduction in the quality of predicted solubility.

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.

Multi-order graph attention network for water solubility prediction and interpretation

The water solubility of molecules is one of the most important properties in various chemical and medical research fields. Recently, machine learning-based methods for predicting molecular properties, including water solubility, have been extensively studied due to the advantage of effectively reducing computational costs. Although machine learning-based methods have made significant advances in predictive performance, the existing methods were still lacking in interpreting the predicted results. Therefore, we propose a novel multi-order graph attention network (MoGAT) for water solubility prediction to improve the predictive performance and interpret the predicted results. We extracted graph embeddings in every node embedding layer to consider the information of diverse neighboring orders and merged them by attention mechanism to generate a final graph embedding. MoGAT can provide the atomic-specific importance scores of a molecule that indicate which atoms significantly influence the prediction so that it can interpret the predicted results chemically. It also improves prediction performance because the graph representations of all neighboring orders, which contain diverse range of information, are employed for the final prediction. Through extensive experiments, we demonstrated that MoGAT showed better performance than the state-of-the-art methods, and the predicted results were consistent with well-known chemical knowledge.

EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules

Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.

Solvation entropy, enthalpy and free energy prediction using a multi-task deep learning functional in 1D-RISM

Simultaneous calculation of entropies, enthalpies and free energies has been a long-standing challenge in computational chemistry, partly because of the difficulty in obtaining estimates of all three properties from a single consistent simulation methodology. This has been particularly true for methods from the Integral Equation Theory of Molecular Liquids such as the Reference Interaction Site Model which have traditionally given large errors in solvation thermodynamics. Recently, we presented pyRISM-CNN, a combination of the 1 Dimensional Reference Interaction Site Model (1D-RISM) solver, pyRISM, with a deep learning based free energy functional, as a method of predicting solvation free energy (SFE). With this approach, a 40-fold improvement in prediction accuracy was delivered for a multi-solvent, multi-temperature dataset when compared to the standard 1D-RISM theory [Fowles et al., Digital Discovery, 2023, 2, 177-188]. Here, we report three further developments to the pyRISM-CNN methodology. Firstly, solvation free energies have been introduced for organic molecular ions in methanol or water solvent systems at 298 K, with errors below 4 kcal mol^-1 obtained without the need for corrections or additional descriptors. Secondly, the number of solvents in the training data has been expanded from carbon tetrachloride, water and chloroform to now also include methanol. For neutral solutes, prediction errors nearing or below 1 kcal mol^-1 are obtained for each organic solvent system at 298 K and water solvent systems at 273-373 K. Lastly, pyRISM-CNN was successfully applied to the simultaneous prediction of solvation enthalpy, entropy and free energy through a multi-task learning approach, with errors of 1.04, 0.98 and 0.47 kcal mol^-1, respectively, for water solvent systems at 298 K.

Role of Crystal Disorder and Mechanoactivation in Solid-State Stability of Pharmaceuticals

Common energy-intensive processes applied in oral solid dosage development, such as milling, sieving, blending, compaction, etc. generate particles with surface and bulk crystal disorder. An intriguing aspect of the generated crystal disorder is its evolution and repercussion on the physical- and chemical stabilities of drugs. In this review, we firstly examine the existing literature on crystal disorder and its implications on solid-state stability of pharmaceuticals. Secondly, we discuss the key aspects related to the generation and evolution of crystal disorder, dynamics of the disordered/amorphous phase, analytical techniques to measure/quantify them, and approaches to model the disordering propensity from first principles. The main objective of this compilation is to provide special impetus to predict or model the chemical degradation(s) resulting from processing-induced manifestation in bulk solid manufacturing. Finally, a generic workflow is proposed that can be useful to investigate the relevance of crystal disorder on the degradation of pharmaceuticals during stability studies. The present review will cater to the requirements for developing physically- and chemically stable drugs, thereby enabling early and rational decision-making during candidate screening and in assessing degradation risks associated with formulations and processing.

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.

Predicting the Solubility of Organic Energy Storage Materials Based on Functional Group Identity and Substitution Pattern

Organic electrode materials (OEMs) provide sustainable alternatives to conventional electrode materials based on transition metals. However, the application of OEMs in lithium-ion and redox flow batteries requires either low or high solubility. Currently, the identification of new OEM candidates relies on chemical intuition and trial-and-error experimental testing, which is costly and time intensive. Herein, we develop a simple empirical model that predicts the solubility of anthraquinones based on functional group identity and substitution pattern. Within this statistical scaffold, a training set of 18 anthraquinone derivatives allows us to predict the solubility of 808 quinones. Internal and external validations show that our model can predict the solubility of anthraquinones in battery electrolytes within log S ± 0.7, which is a much higher accuracy than existing solubility models. As a demonstration of the utility of our approach, we identified several new anthraquinones with low solubilities and successfully demonstrated their utility experimentally in Li-organic cells.

A benchmark for non-covalent interactions in organometallic crystals

Organometallic complexes are the basis for homogeneous catalysis, have applications in materials science and are also active pharmaceutical ingredients. The interaction between transition metal complexes in the solid state is determining their thermodynamics and bio-availability. Non-covalent interactions such as hydrogen bonding and van der Waals are stabilizing crystals of transition metal complexes. The variation of ligand field, central metal atoms and their oxidation and spin states are determinants of the magnitude of their inter-molecular interactions. A comparison of a set of 43 manually curated experimental heats of sublimation (the new XTMC43 set) and results from periodic DFT calculations shows that an agreement to within 9% can be achieved using GGA or mGGA functionals with atom-centred Gaussian-type basis functions. The need for careful assessments of consistency, calibration and reproducibility of experimental and computational data is discussed. Results regarding the new XTMC43 benchmark set are suggested to serve as a starting point for further method development, systematic screening and crystal engineering.

Boosting the predictive performance with aqueous solubility dataset curation

Intrinsic solubility is a critical property in pharmaceutical industry that impacts in-vivo bioavailability of small molecule drugs. However, solubility prediction with Artificial Intelligence(AI) are facing insufficient data, poor data quality, and no unified measurements for AI and physics-based approaches. We collect 7 aqueous solubility datasets, and present a dataset curation workflow. Evaluating the curated data with two expanded deep learning methods, improved RMSE scores on all curated thermodynamic datasets are observed. We also compare expanded Chemprop enhanced with curated data and state-of-art physics-based approach using pearson and spearman correlation coefficients. A similar performance on pearson with 0.930 and spearman with 0.947 from expanded Chemprop is achieved. A steadily improved pearson and spearman values with increasing data points are also illustrated. Besides that, the computation advantage of AI models enables quick evaluation of a large set of molecules during the hit identification or lead optimization stages, which helps further decision making within the time cycle at drug discovery stage.

Computational and experimental investigation of the effect of cation structure on the solubility of anionic flow battery active-materials

Recent advances in clean, sustainable energy sources such as wind and solar have enabled significant cost improvements, yet their inherent intermittency remains a considerable challenge for year-round reliability demanding the need for grid-scale energy storage. Nonaqueous redox flow batteries (NRFBs) have the potential to address this need, with attractive attributes such as flexibility to accommodate long- and short-duration storage, separately scalable energy and power ratings, and improved safety profile over integrated systems such as lithium-ion batteries. Currently, the low-solubility of NRFB electrolytes fundamentally limits their energy density. However, synthetically exploring the large chemical and parameter space of NRFB active materials is not only costly but also intractable. Here, we report a computational framework, coupled with experimental validation, designed to predict the solubility trends of electrolytes, incorporating both the lattice and solvation free energies. We reveal that lattice free energy, which has previously been neglected, has a significant role in tuning electrolyte solubility, and that solvation free energies alone is insufficient. The desymmetrization of the alkylammonium cation leading to short-chain, asymmetric cations demonstrated a modest increase in solubility, which can be further explored for NRFB electrolyte development and optimization. The resulting synergistic computational-experimental approach provides a cost-effective strategy in the development of high-solubility active materials for high energy density NRFB systems.

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.

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.

A Comparative Review of Metal-Based Charge Carriers in Nonaqueous Flow Batteries

Energy storage is becoming the chief barrier to the utilization of more renewable energy sources on the grid. With independent service operators aiming to acquire gigawatts in the next 10-20 years, there is a large need to develop a suite of new storage technologies. Redox flow batteries (RFB) may be part of the solution if certain key barriers are overcome. This Review focuses on a particular kind of RFB based on nonaqueous media that promises to meet the challenge through higher voltages than the organic and aqueous variants. This class of RFB is divided into three groups: molecular, macromolecular, and redox-targeted systems. The growing field of theoretical modeling is also reviewed and discussed.

Novel Physics-Based Ensemble Modeling Approach That Utilizes 3D Molecular Conformation and Packing to Access Aqueous Thermodynamic Solubility: A Case Study of Orally Available Bromodomain and Extraterminal Domain Inhibitor Lead Optimization Series

Drug design with patient centricity for ease of administration and pill burden requires robust understanding of the impact of chemical modifications on relevant physicochemical properties early in lead optimization. To this end, we have developed a physics-based ensemble approach to predict aqueous thermodynamic crystalline solubility, with a 2D chemical structure as the input. Predictions for the bromodomain and extraterminal domain (BET) inhibitor series show very close match (0.5 log unit) with measured thermodynamic solubility for cases with low crystal anisotropy and good match (1 log unit) for high anisotropy structures. The importance of thermodynamic solubility is clearly demonstrated by up to a 4 log unit drop in solubility compared to kinetic (amorphous) solubility in some cases and implications thereof, for instance on human dose. We have also demonstrated that incorporating predicted crystal structures in thermodynamic solubility prediction is necessary to differentiate (up to 4 log unit) between solubility of molecules within the series. Finally, our physics-based ensemble approach provides valuable structural insights into the origins of 3-D conformational landscapes, crystal polymorphism, and anisotropy that can be leveraged for both drug design and development.

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.

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.

Effect of residual solvent on performance of acrylamide-containing dental materials

OBJECTIVE

Methacrylamide-based monomers are being pursued as novel, hydrolytically stable materials for use in dental adhesives. The impact of residual solvents, due to the chemical synthesis procedures or the need for solvated adhesives systems, on the kinetics of polymerization and mechanical properties was the aim of the present investigation.

METHODS

Two base monomers (70wt% BisGMA or HEMAM-BDI - newly synthesized secondary methacrylamide) were combined with 30wt% N,N-dimethylacrylamide. Eethyl acetate (EtOAc), or 75vol% ethanol/25vol% water (EtOH/H2O) were added as solvents in concentrations of 2, 5, 15 and 20wt%. The resins were made polymerizable by the addition of 0.2wt% 2,2-dimethoxy-2-phenyl acetophenone (DMPA) and 0.4wt% diphenyliodonium hexafluorophosphate (DPI-PF6). Specimens (n=3) were photoactivated with a mercury arc lamp (Acticure 4000, 320-500nm, 250mW/cm2) for 5min. Degree of conversion (DC, %) was tracked in near-IR spectroscopy in real time and yield strength and modulus of elasticity were measured in three-point bending after dry and wet storage (n=6). The data was subject to one-way ANOVA/Tukey's Test (p≤0.05), or Student's t-test (p≤0.001).

RESULTS

In all groups for both BisGMA and HEMAM-BDI-based materials, DC and DC at Rpmax increased and maximum rate of polymerization decreased as solvent concentration increased. Despite the increased DC, BisGMA mixtures showed a decrease in FS starting at 5wt% EtOAc or 15wt% EtOH/H2O. Yield strength for the HEMAM-BDI groups was overall lower than that of the BisGMA groups, but the modulus of elasticity was significantly higher.

SIGNIFICANCE

The presence of residual solvent, from manufacturing or from practitioner's handling, affects polymerization kinetics and mechanical properties of resins. Methacrylates appear to be more strongly influenced than methacrylamides.

Predictive models of aqueous solubility of organic compounds built on A large dataset of high integrity

Aqueous solubility is one of the most important properties in drug discovery, as it has profound impact on various drug properties, including biological activity, pharmacokinetics (PK), toxicity, and in vivo efficacy. Both kinetic and thermodynamic solubilities are determined during different stages of drug discovery and development. Since kinetic solubility is more relevant in preclinical drug discovery research, especially during the structure optimization process, we have developed predictive models for kinetic solubility with in-house data generated from 11,780 compounds collected from over 200 NCATS intramural research projects. This represents one of the largest kinetic solubility datasets of high quality and integrity. Based on the customized atom type descriptors, the support vector classification (SVC) models were trained on 80% of the whole dataset, and exhibited high predictive performance for estimating the solubility of the remaining 20% compounds within the test set. The values of the area under the receiver operating characteristic curve (AUC-ROC) for the compounds in the test sets reached 0.93 and 0.91, when the threshold for insoluble compounds was set to 10 and 50 μg/mL respectively. The predictive models of aqueous solubility can be used to identify insoluble compounds in drug discovery pipeline, provide design ideas for improving solubility by analyzing the atom types associated with poor solubility and prioritize compound libraries to be purchased or synthesized.

Solubility of paracetamol in ethanol by molecular dynamics using the extended Einstein crystal method and experiments

Li and co-workers [Li et al., J. Chem. Phys. 146, 214110 (2017)] have recently proposed a methodology to compute the solubility of molecular compounds from first principles, using molecular dynamics simulations. We revise and further explore their methodology that was originally applied to naphthalene in water at low concentration. In particular, we compute the solubility of paracetamol in an ethanol solution at ambient conditions. For the simulations, we used a force field that we previously reparameterized to reproduce certain thermodynamic properties of paracetamol but not explicitly its solubility in ethanol. In addition, we have determined the experimental solubility by performing turbidity measurements using a Crystal16 over a range of temperatures. Our work serves a dual purpose: (i) methodologically, we clarify how to compute, with a relatively straightforward procedure, the solubility of molecular compounds and (ii) applying this procedure, we show that the solubility predicted by our force field (0.085 ± 0.014 in mole ratio) is in good agreement with the experimental value obtained from our experiments and those reported in the literature (average 0.0585 ± 0.004), considering typical deviations for predictions from first principle methods. The good agreement between the experimental and the calculated solubility also suggests that the method used to reparameterize the force field can be used as a general strategy to optimize force fields for simulations in solution.

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.

Computational methodology for solubility prediction: Application to sparingly soluble organic/inorganic materials

The solubility of a crystalline material can be estimated from the absolute free energy of the solid and the excess solvation free energy. In the earlier work, we presented a general-purpose molecular-dynamics-based methodology enabling solubility predictions of crystalline compounds, yielding accurate estimates of the aqueous solubilities of naphthalene at various pressures and temperatures. In the present work, we investigate a number of prototypical complex materials, including phenanthrene, calcite, and aragonite over a range of temperatures and pressures. Our results provide stronger evidence for the power of the methodology for universal solubility predictions.

Computational methodology for solubility prediction: Application to the sparingly soluble solutes

The solubility of a crystalline substance in the solution can be estimated from its absolute solid free energy and excess solvation free energy. Here, we present a numerical method, which enables convenient solubility estimation of general molecular crystals at arbitrary thermodynamic conditions where solid and solution can coexist. The methodology is based on standard alchemical free energy methods, such as thermodynamic integration and free energy perturbation, and consists of two parts: (1) systematic extension of the Einstein crystal method to calculate the absolute solid free energies of molecular crystals at arbitrary temperatures and pressures and (2) a flexible cavity method that can yield accurate estimates of the excess solvation free energies. As an illustration, via classical Molecular Dynamic simulations, we show that our approach can predict the solubility of OPLS-AA-based (Optimized Potentials for Liquid Simulations All Atomic) naphthalene in SPC (Simple Point Charge) water in good agreement with experimental data at various temperatures and pressures. Because the procedure is simple and general and only makes use of readily available open-source software, the methodology should provide a powerful tool for universal solubility prediction.

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.

Solvation of diclofenac in water from atomistic molecular dynamics simulations - interplay between solute-solute and solute-solvent interactions

The solubility-permeability relationship of active pharmaceutical ingredients determines the efficacy of their usage. Diclofenac (DCL), which is a widely used nonsteroidal anti-inflammatory drug, is characterized by extremely good membrane permeability, but low water solubility limiting drug effectiveness. The present research focuses on the fundamental explanation of this limitation using the combination of ab initio and classical molecular dynamics simulations of different ionic forms of DCL in water, namely, ionized, un-ionized and the mixture of them both. The analysis of diclofenac solvation in an aqueous environment is used to understand the origin of drug precipitation, especially in gastric pH. The used computational approach reveals the formation of micelle-like self-associated aggregates of diclofenac in water as the result of intermolecular π-π interactions and C-Hπ hydrogen bonds. The DCL aggregation in water is shown to depend mostly on drug concentration, protonation and temperature of the aqueous environment. The detected self-association properties of the drug in water are likely to be of great importance during the development of new drug formulations and fabrication of drug adsorbents for wastewater.

Can human experts predict solubility better than computers?

In this study, we design and carry out a survey, asking human experts to predict the aqueous solubility of druglike organic compounds. We investigate whether these experts, drawn largely from the pharmaceutical industry and academia, can match or exceed the predictive power of algorithms. Alongside this, we implement 10 typical machine learning algorithms on the same dataset. The best algorithm, a variety of neural network known as a multi-layer perceptron, gave an RMSE of 0.985 log S units and an R² of 0.706. We would not have predicted the relative success of this particular algorithm in advance. We found that the best individual human predictor generated an almost identical prediction quality with an RMSE of 0.942 log S units and an R² of 0.723. The collection of algorithms contained a higher proportion of reasonably good predictors, nine out of ten compared with around half of the humans. We found that, for either humans or algorithms, combining individual predictions into a consensus predictor by taking their median generated excellent predictivity. While our consensus human predictor achieved very slightly better headline figures on various statistical measures, the difference between it and the consensus machine learning predictor was both small and statistically insignificant. We conclude that human experts can predict the aqueous solubility of druglike molecules essentially equally well as machine learning algorithms. We find that, for either humans or algorithms, combining individual predictions into a consensus predictor by taking their median is a powerful way of benefitting from the wisdom of crowds.

Estimations of the thermodynamic properties of halogenated benzenes as they relate to their environment mobility

In this work, several simple new equations for predicting important environmental mobility properties, at T = 298.15 K, were derived for halogenated benzenes: standard Gibbs energy of hydration, aqueous solubility, octanol-water partition coefficients, and Henry's law constants. A discussion on our previous estimates of other related properties (standard Gibbs energy and vapor pressure of sublimation and of vaporization) and their relation with entropy of fusion is also presented. As we aimed to estimate these properties for any of the ca. 1500 halogenated benzenes that may exist theoretically, an equation for estimating the temperature of fusion was also derived, since some of the proposed predictive equations (solubility of solids and Gibbs energy of sublimation) require its knowledge. For the other estimated properties just the number of each halogen that replaces hydrogen atoms in the halogenated benzene is needed. It was found that the coefficients that multiply the number of halogen atoms in the predictive equations vary linearly with the volume of the halogen atom.

Are the Sublimation Thermodynamics of Organic Molecules Predictable?

We compare a range of computational methods for the prediction of sublimation thermodynamics (enthalpy, entropy, and free energy of sublimation). These include a model from theoretical chemistry that utilizes crystal lattice energy minimization (with the DMACRYS program) and quantitative structure property relationship (QSPR) models generated by both machine learning (random forest and support vector machines) and regression (partial least squares) methods. Using these methods we investigate the predictability of the enthalpy, entropy and free energy of sublimation, with consideration of whether such a method may be able to improve solubility prediction schemes. Previous work has suggested that the major source of error in solubility prediction schemes involving a thermodynamic cycle via the solid state is in the modeling of the free energy change away from the solid state. Yet contrary to this conclusion other work has found that the inclusion of terms such as the enthalpy of sublimation in QSPR methods does not improve the predictions of solubility. We suggest the use of theoretical chemistry terms, detailed explicitly in the Methods section, as descriptors for the prediction of the enthalpy and free energy of sublimation. A data set of 158 molecules with experimental sublimation thermodynamics values and some CSD refcodes has been collected from the literature and is provided with their original source references.

Crystal structure prediction of rigid molecules

A non-polarizable force field based on atomic multipoles fit to reproduce experimental crystal properties andab initiogas-phase dimers is described. The Ewald method is used to calculate both long-range electrostatic and 1/r6dispersion energies of crystals. The dispersion energy of a crystal calculated by a cutoff method is shown to converge slowly to the exact Ewald result. A method for constraining space-group symmetry during unit-cell optimization is derived. Results for locally optimizing 4427 unit cells including volume, cell parameters, unit-cell r.m.s.d. and CPU timings are given for both flexible and rigid molecule optimization. An algorithm for randomly generating rigid molecule crystals is described. Using the correct experimentally determined space group, the average and maximum number of random crystals needed to find the correct experimental structure is given for 2440 rigid single component crystals. The force field energy rank of the correct experimental structure is presented for the same set of 2440 rigid single component crystals assuming the correct space group. A complete crystal prediction is performed for two rigid molecules by searching over the 32 most probable space groups.

An optimized intermolecular force field for hydrogen-bonded organic molecular crystals using atomic multipole electrostatics

We present a re-parameterization of a popular intermolecular force field for describing intermolecular interactions in the organic solid state. Specifically we optimize the performance of the exp-6 force field when used in conjunction with atomic multipole electrostatics. We also parameterize force fields that are optimized for use with multipoles derived from polarized molecular electron densities, to account for induction effects in molecular crystals. Parameterization is performed against a set of 186 experimentally determined, low-temperature crystal structures and 53 measured sublimation enthalpies of hydrogen-bonding organic molecules. The resulting force fields are tested on a validation set of 129 crystal structures and show improved reproduction of the structures and lattice energies of a range of organic molecular crystals compared with the original force field with atomic partial charge electrostatics. Unit-cell dimensions of the validation set are typically reproduced to within 3% with the re-parameterized force fields. Lattice energies, which were all included during parameterization, are systematically underestimated when compared with measured sublimation enthalpies, with mean absolute errors of between 7.4 and 9.0%.

Transferable force field for crystal structure predictions, investigation of performance and exploration of different rescoring strategies using DFT-D methods

A new force field, here called AZ-FF, aimed at being used for crystal structure predictions, has been developed. The force field is transferable to a new type of chemistry without additional training or modifications. This makes the force field very useful in the prediction of crystal structures of new drug molecules since the time-consuming step of developing a new force field for each new molecule is circumvented. The accuracy of the force field was tested on a set of 40 drug-like molecules and found to be very good where observed crystal structures are found at the top of the ranked list of tentative crystal structures. Re-ranking with dispersion-corrected density functional theory (DFT-D) methods further improves the scoring. After DFT-D geometry optimization the observed crystal structure is found at the leading top of the ranking list. DFT-D methods and force field methods have been evaluated for use in predicting properties such as phase transitions upon heating, mechanical properties or intrinsic crystalline solubility. The utility of using crystal structure predictions and the associated material properties in risk assessment in connection with form selection in the drug development process is discussed.

Using MD Simulations To Calculate How Solvents Modulate Solubility

Here, our interest is in predicting solubility in general, and we focus particularly on predicting how the solubility of particular solutes is modulated by the solvent environment. Solubility in general is extremely important, both for theoretical reasons - it provides an important probe of the balance between solute-solute and solute-solvent interactions - and for more practical reasons, such as how to control the solubility of a given solute via modulation of its environment, as in process chemistry and separations. Here, we study how the change of solvent affects the solubility of a given compound. That is, we calculate relative solubilities. We use MD simulations to calculate relative solubility and compare our calculated values with experiment as well as with results from several other methods, SMD and UNIFAC, the latter of which is commonly used in chemical engineering design. We find that straightforward solubility calculations based on molecular simulations using a general small-molecule force field outperform SMD and UNIFAC both in terms of accuracy and coverage of the relevant chemical space.

A review of methods for the calculation of solution free energies and the modelling of systems in solution

Over the past decade, pharmaceutical companies have seen a decline in the number of drug candidates successfully passing through clinical trials, though billions are still spent on drug development. Poor aqueous solubility leads to low bio-availability, reducing pharmaceutical effectiveness. The human cost of inefficient drug candidate testing is of great medical concern, with fewer drugs making it to the production line, slowing the development of new treatments. In biochemistry and biophysics, water mediated reactions and interactions within active sites and protein pockets are an active area of research, in which methods for modelling solvated systems are continually pushed to their limits. Here, we discuss a multitude of methods aimed towards solvent modelling and solubility prediction, aiming to inform the reader of the options available, and outlining the various advantages and disadvantages of each approach.

In silico ADME/T modelling for rational drug design

In recent decades, in silico absorption, distribution, metabolism, excretion (ADME), and toxicity (T) modelling as a tool for rational drug design has received considerable attention from pharmaceutical scientists, and various ADME/T-related prediction models have been reported. The high-throughput and low-cost nature of these models permits a more streamlined drug development process in which the identification of hits or their structural optimization can be guided based on a parallel investigation of bioavailability and safety, along with activity. However, the effectiveness of these tools is highly dependent on their capacity to cope with needs at different stages, e.g. their use in candidate selection has been limited due to their lack of the required predictability. For some events or endpoints involving more complex mechanisms, the current in silico approaches still need further improvement. In this review, we will briefly introduce the development of in silico models for some physicochemical parameters, ADME properties and toxicity evaluation, with an emphasis on the modelling approaches thereof, their application in drug discovery, and the potential merits or deficiencies of these models. Finally, the outlook for future ADME/T modelling based on big data analysis and systems sciences will be discussed.

Fast and General Method To Predict the Physicochemical Properties of Druglike Molecules Using the Integral Equation Theory of Molecular Liquids

We report a method to predict physicochemical properties of druglike molecules using a classical statistical mechanics based solvent model combined with machine learning. The RISM-MOL-INF method introduced here provides an accurate technique to characterize solvation and desolvation processes based on solute-solvent correlation functions computed by the 1D reference interaction site model of the integral equation theory of molecular liquids. These functions can be obtained in a matter of minutes for most small organic and druglike molecules using existing software (RISM-MOL) (Sergiievskyi, V. P.; Hackbusch, W.; Fedorov, M. V. J. Comput. Chem. 2011, 32, 1982-1992). Predictions of caco-2 cell permeability and hydration free energy obtained using the RISM-MOL-INF method are shown to be more accurate than the state-of-the-art tools for benchmark data sets. Due to the importance of solvation and desolvation effects in biological systems, it is anticipated that the RISM-MOL-INF approach will find many applications in biophysical and biomedical property prediction.

Predicting Melting Points of Organic Molecules: Applications to Aqueous Solubility Prediction Using the General Solubility Equation

In this work we make predictions of several important molecular properties of academic and industrial importance to seek answers to two questions: 1) Can we apply efficient machine learning techniques, using inexpensive descriptors, to predict melting points to a reasonable level of accuracy? 2) Can values of this level of accuracy be usefully applied to predicting aqueous solubility? We present predictions of melting points made by several novel machine learning models, previously applied to solubility prediction. Additionally, we make predictions of solubility via the General Solubility Equation (GSE) and monitor the impact of varying the logP prediction model (AlogP and XlogP) on the GSE. We note that the machine learning models presented, using a modest number of 2D descriptors, can make melting point predictions in line with the current state of the art prediction methods (RMSE≥40 °C). We also find that predicted melting points, with an RMSE of tens of degrees Celsius, can be usefully applied to the GSE to yield accurate solubility predictions (log10 S RMSE<1) over a small dataset of drug-like molecules.

Low solubility in drug development: de-convoluting the relative importance of solvation and crystal packing

OBJECTIVES

An increasing trend towards low solubility is a major issue for drug development as formulation of low solubility compounds can be problematic. This paper presents a model which de-convolutes the solubility of pharmaceutical compounds into solvation and packing properties with the intention to understand the solubility limiting features.

METHODS

The Cambridge Crystallographic Database was the source of structural information. Lattice energies were calculated via force-field based approaches using Materials Studio. The solvation energies were calculated applying quantum chemistry models using Cosmotherm software.

KEY FINDINGS

The solubilities of 54 drug-like compounds were mapped onto a solvation energy/crystal packing grid. Four quadrants were identified were different balances of solvation and packing were defining the solubility. A version of the model was developed which allows for the calculation of the two features even in absence of crystal structure.

CONCLUSION

Although there are significant number of in-silico models, it has been proven very difficult to predict aqueous solubility accurately. Therefore, we have taken a different approach where the solubility is not predicted directly but is de-convoluted into two constituent features.