The correlation and prediction of the solubility of compounds in water using an amended solvation energy relationship

Estimation of passive gastrointestinal absorption of new dual DNA gyrase and topoisomerase IV inhibitors using PAMPA and biopartitioning micellar chromatography and quantitative structure-retention relationship analysis

DNA gyrase and topoisomerase IV play significant role in maintaining the correct structure of DNA during replication and they have been identified as validated targets in antibacterial drug discovery. Inadequate pharmacokinetic properties are responsible for many failures during drug discovery and their estimation in the early phase of this process maximizes the chance of getting useful drug candidates. Passive gastrointestinal absorption of a selected group of thirteen dual DNA gyrase and topoisomerase IV inhibitors was estimated using two in vitro tests - parallel artificial membrane permeability assay (PAMPA) and biopartitioning micellar chromatography (BMC). Due to good correlation between obtained results, passive gastrointestinal absorption of remaining ten compounds was estimated using only BMC. With this experimental setup, it was possible to identify compounds with high values of retention factors (k) and highest expected passive gastrointestinal absorption, and compounds with low values of k for which low passive gastrointestinal absorption is predicted. Quantitative structure-retention relationship (QSRR) modelling was performed by creating multiple linear regression (MLR), partial least squares (PLS) and support vector machines (SVM) models. Descriptors with the highest influence on retention factor were identified and their interpretation can be used for the design of new compounds with improved passive gastrointestinal absorption.

Identifying uncertainty in physical-chemical property estimation with IFSQSAR

This study describes the development and evaluation of six new models for predicting physical-chemical (PC) properties that are highly relevant for chemical hazard, exposure, and risk estimation: solubility (in water SW and octanol SO), vapor pressure (VP), and the octanol-water (KOW), octanol-air (KOA), and air-water (KAW) partition ratios. The models are implemented in the Iterative Fragment Selection Quantitative Structure-Activity Relationship (IFSQSAR) python package, Version 1.1.0. These models are implemented as Poly-Parameter Linear Free Energy Relationship (PPLFER) equations which combine experimentally calibrated system parameters and solute descriptors predicted with QSPRs. Two other ancillary models have been developed and implemented, a QSPR for Molar Volume (MV) and a classifier for the physical state of chemicals at room temperature. The IFSQSAR methods for characterizing applicability domain (AD) and calculating uncertainty estimates expressed as 95% prediction intervals (PI) for predicted properties are described and tested on 9,000 measured partition ratios and 4,000 VP and SW values. The measured data are external to IFSQSAR training and validation datasets and are used to assess the predictivity of the models for "novel chemicals" in an unbiased manner. The 95% PI intervals calculated from validation datasets for partition ratios needed to be scaled by a factor of 1.25 to capture 95% of the external data. Predictions for VP and SW are more uncertain, primarily due to the challenges in differentiating their physical state (i.e., liquids or solids) at room temperature. The prediction accuracy of the models for log KOW, log KAW and log KOA of novel, data-poor chemicals is estimated to be in the range of 0.7 to 1.4 root mean squared error of prediction (RMSEP), with RMSEP in the range 1.7-1.8 for log VP and log SW. Scientific contributionNew partitioning models integrate empirical PPLFER equations and QSARs, allowing for seamless integration of experimental data and model predictions. This work tests the real predictivity of the models for novel chemicals which are not in the model training or external validation datasets.

Comparative Analysis of Chemical Descriptors by Machine Learning Reveals Atomistic Insights into Solute-Lipid Interactions

This study explores the research area of drug solubility in lipid excipients, an area persistently complex despite recent advancements in understanding and predicting solubility based on molecular structure. To this end, this research investigated novel descriptor sets, employing machine learning techniques to understand the determinants governing interactions between solutes and medium-chain triglycerides (MCTs). Quantitative structure-property relationships (QSPR) were constructed on an extended solubility data set comprising 182 experimental values of structurally diverse drug molecules, including both development and marketed drugs to extract meaningful property relationships. Four classes of molecular descriptors, ranging from traditional representations to complex geometrical descriptions, were assessed and compared in terms of their predictive accuracy and interpretability. These include two-dimensional (2D) and three-dimensional (3D) descriptors, Abraham solvation parameters, extended connectivity fingerprints (ECFPs), and the smooth overlap of atomic position (SOAP) descriptor. Through testing three distinct regularized regression algorithms alongside various preprocessing schemes, the SOAP descriptor enabled the construction of a superior performing model in terms of interpretability and accuracy. Its atom-centered characteristics allowed contributions to be estimated at the atomic level, thereby enabling the ranking of prevalent molecular motifs and their influence on drug solubility in MCTs. The performance on a separate test set demonstrated high predictive accuracy (RMSE = 0.50) for 2D and 3D, SOAP, and Abraham Solvation descriptors. The model trained on ECFP4 descriptors resulted in inferior predictive accuracy. Lastly, uncertainty estimations for each model were introduced to assess their applicability domains and provide information on where the models may extrapolate in chemical space and, thus, where more data may be necessary to refine a data-driven approach to predict solubility in MCTs. Overall, the presented approaches further enable computationally informed formulation development by introducing a novel in silico approach for rational drug development and prediction of dose loading in lipids.

Multi-Stimuli-Responsive, Topology-Regulated, and Lignin-Based Nano/Microcapsules from Pickering Emulsion Templates for Bidirectional Delivery of Pesticides

The increasing demand for improving pesticide utilization efficiency has prompted the development of sustainable, targeted, and stimuli-responsive delivery systems. Herein, a multi-stimuli-responsive nano/microcapsule bidirectional delivery system loaded with pyraclostrobin (Pyr) is prepared through interfacial cross-linking from a lignin-based Pickering emulsion template. During this process, methacrylated alkali lignin nanoparticles (LNPs) are utilized as stabilizers for the tunable oil-water (O/W) Pickering emulsion. Subsequently, a thiol-ene radical reaction occurs with the acid-labile cross-linkers at the oil-water interface, leading to the formation of lignin nano/microcapsules (LNCs) with various topological shapes. Through the investigation of the polymerization process and the structure of LNC, it was found that the amphiphilicity-driven diffusion and distribution of cyclohexanone impact the topology of LNC. The obtained Pyr@LNC exhibits high encapsulation efficiency, tunable size, and excellent UV shielding to Pyr. Additionally, the flexible topology of the Pyr@LNC shell enhances the retention and adhesion of the foliar surface. Furthermore, Pyr@LNC exhibits pH/laccase-responsive targeting against Botrytis disease, enabling the intelligent release of Pyr. The in vivo fungicidal activity shows that efficacy of Pyr@LNC is 53% ± 2% at 14 days postspraying, whereas the effectiveness of Pyr suspension concentrate is only 29% ± 4%, and the acute toxicity of Pyr@LNC to zebrafish is reduced by more than 9-fold compared with that of Pyr technical. Moreover, confocal laser scanning microscopy shows that the LNCs can be bidirectionally translocated in plants. Therefore, the topology-regulated bidirectional delivery system LNC has great practical potential for sustainable agriculture.

Discovery of Rhodanine Inhibitors Targeting Of ChtI Based on the π-Stacking Effect and Aqueous Solubility

The application of some reported inhibitors against the chitinolytic enzyme Of ChtI was limited due to their unsatisfactory insecticidal activities. Hence, we first performed a synergetic design strategy combining the π-stacking effect with aqueous solubility to find novel rhodanine analogues with inhibitory activities against Of ChtI. Novel rhodanine compounds IAa-f and IBa-f have weak aqueous solubility, but they (IAd: Ki = 4.0 μM; IBd: Ki = 2.2 μM) showed better inhibitory activities against Of ChtI and comparable insecticidal efficiency toward Ostrinia furnacalis compared to the high aqueous solubility compounds IIAa-f and IIBa-f (IIAd: Ki = 21.6 μM; IIBd: Ki = 14.3 μM) without a large conjugate plane. Further optimized compounds IIIAa-j with a conjugate plane as well as a higher aqueous solubility exhibited similar good inhibitory activities against Of ChtI (IIIAe: Ki = 2.4 μM) and better insecticidal potency (IIIAe: mortality rate of 63.33%) compared to compounds IAa-f and IBa-f, respectively. Molecular docking studies indicated that the conjugate planarity with the π-stacking effect for rhodanine analogues is responsible for their enzyme inhibitory activity against Of ChtI. This study provides a new strategy for designing insect chitinolytic enzyme inhibitors as insect growth regulators for pest control.

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.

Revised descriptors for polycyclic aromatic and related hydrocarbons for the prediction of environmental properties using the solvation parameter model

Revised descriptors for twenty-five polycyclic aromatic and related hydrocarbons (PAHs) forming a component of the Wayne State University (WSU) descriptor database are provided for use with the solvation parameter model. The descriptors are determined by the Solver method using experimental data for calibrated gas-liquid and reversed-phase liquid chromatographic retention factors and liquid-liquid partition constants in totally organic biphasic systems. The characteristic solvation properties of the PAHs are accounted for mainly by the additional dispersion interactions (E descriptor) and dipole-type interactions (S descriptor) resulting from the availability of easily polarizable electrons that complement typical dispersion interactions for saturated hydrocarbons. The descriptors afford acceptable prediction of the water-air partition constant (average absolute deviation AAD = 0.17, n = 22), octanol-air partition constant (AAD = 0.12, n = 20), and water-octanol partition constant (AAD = 0.10, n = 23). A two-parameter model containing only the V and B descriptors provides an unbiased prediction of aqueous solubility for the PAHs with an AAD = 0.26 (n = 22). The descriptors estimated by convenient chromatographic and partition constant measurements are demonstrated to be a viable alternative to the experimental determination of environmental properties otherwise only available by tedious, expensive, and low data throughput experimental techniques.

C-H···π interactions disrupt electrostatic interactions between non-aqueous electrolytes to increase solubility

Grid-scale energy storage applications, such as redox flow batteries, rely on the solubility of redox-active organic molecules. Although redox-active pyridiniums exhibit exceptional persistence in multiple redox states at low potentials (desirable properties for energy storage applications), their solubility in non-aqueous media remains low, and few practical molecular design strategies exist to improve solubility. Here we convey the extent to which discrete, attractive interactions between C-H groups and π electrons of an aromatic ring (C-H···π interactions) can describe the solubility of N-substituted pyridinium salts in a non-aqueous solvent. We find a direct correlation between the number of C-H···π interactions for each pyridinium salt and its solubility in acetonitrile. The correlation presented in this work highlights a consequence of disrupting strong electrostatic interactions with weak dispersion interactions, showing how minimal structural change can dramatically impact pyridinium solubility.

Those That Remain: Sorption/Desorption Behaviour and Kinetics of the Neonicotinoids Still in Use

In January 2023, the derogation loophole was closed on “emergency authorisations” for the use of three out of five neonicotinoids in all EU states. In this study, we analysed the sorption/desorption behaviour and kinetic parameters of acetamiprid and thiacloprid, the two neonicotinoids that are still approved for use, either regularly or under emergency authorisations in the EU, and widely used worldwide. Sorption and desorption curves in four soils with different organic matter content were analysed using four kinetic models, namely, Lagergren’s pseudo first-order model, two-site model (TSM), Weber–Morris intraparticle diffusion model and Elovich’s model. Kinetic parameters were correlated to soil physico-chemical characteristics. To determine the mutual influence of soil characteristics and sorption/desorption parameters in the analysed soils, a factor analysis based on principal component analysis (PCA) was performed. Even though the two insecticides are very similar in size and chemical structure, the results showed different sorption/desorption kinetics. The model that best fits the experimental data was TSM. Thiacloprid showed a more rapid sorption compared to acetamiprid, and, in all soils, a higher proportion sorbed at equilibrium. Intra-particle diffusion seemed to be a relevant process in acetamiprid sorption, but not for thiacloprid. Desorption results showed that acetamiprid is more easily and more thoroughly desorbed than thiacloprid, in all soils. The kinetic behaviour differences stem from variations in molecular structure, causing disparate water solubility, lipophilicity, and acid–base properties.

Trends in oral small-molecule drug discovery and product development based on product launches before and after the Rule of Five

In 1997, the 'Rule of Five' (Ro5) suggested physicochemical limitations for orally administered drugs, based on the analysis of chemical libraries from the early 1990s. In this review, we report on the trends in oral drug product development by analyzing products launched between 1994 and 1997 and between 2013 and 2019. Our analysis confirmed that most new oral drugs are within the Ro5 descriptors; however, the number of new drug products of drugs with molecular weight (MW) and calculated partition coefficient (clogP) beyond the Ro5 has slightly increased. Analysis revealed that there is no single scientific or technological reason for this trend, but that it likely results from incremental advances are being made in molecular biology, target diversity, drug design, medicinal chemistry, predictive modeling, drug metabolism and pharmacokinetics, and drug delivery.

Recent advances for estimating environmental properties for small molecules from chromatographic measurements and the solvation parameter model

The transfer of neutral compounds between immiscible phases in chromatographic or environmental systems can be described by six solute properties (solute descriptors) using the solvation parameter model. The solute descriptors are size (McGowan's characteristic volume), V, excess molar refraction, E, dipolarity/polarizability, S, hydrogen-bond acidity and basicity, A and B, and the gas-liquid partition constant on n-hexadecane at 298.15 K, L. V and E for liquids are accessible by calculation but the other descriptors and E for solids are determined experimentally by chromatographic, liquid-liquid partition, and solubility measurements. These solute descriptors are available for several thousand compounds in the Abraham solute descriptor databases and for several hundred compounds in the WSU experimental solute descriptor database. In the first part of this review, we highlight features important in defining each descriptor, their experimental determination, compare descriptor quality for the two organized descriptor databases, and methods for estimating Abraham solute descriptors. In the second part we focus on recent applications of the solvation parameter model to characterize environmental systems and its use for the identification of surrogate chromatographic models for estimating environmental properties.

In silico package models for deriving values of solute parameters in linear solvation energy relationships

Environmental partitioning influences fate, exposure and ecological risks of chemicals. Linear solvation energy relationship (LSER) models may serve as efficient tools for estimating environmental partitioning parameter values that are commonly deficient for many chemicals. Nonetheless, scarcities of empirical solute parameter values of LSER models restricted the application. This study developed and evaluated in silico methods and models to derive the values, in which excess molar refraction, molar volume and logarithm of hexadecane/air partition coefficient were computed from density functional theory; dipolarity/polarizability parameter, solute H-bond acidity and basicity parameters were predicted by quantitative structure-activity relationship models developed with theoretical molecular descriptors. New LSER models on four physicochemical properties relevant with environmental partitioning (n-octanol/water partition coefficients, n-octanol/air partition coefficients, water solubilities, sub-cooled liquid vapour pressures) were constructed using the in silico solute parameter values, which exhibited comparable performance with conventional LSER models using the empirical solute parameter values. The package models for deriving the LSER solute parameter values, with advantages that they are free of instrumental determinations, may lay the foundation for high-throughput estimating environmental partition parameter values of diverse organic chemicals.

High-performance liquid chromatography evaluation of lipophilicity and QSRR modeling of a series of dual DNA gyrase and topoisomerase IV inhibitors

Bacterial DNA gyrase and topoisomerase IV control the topological state of DNA during replication and represent important antibacterial drug targets. To be successful as drug candidates, newly synthesized compounds must possess optimal lipophilicity, which enables efficient delivery to the site of action. In this study, retention behavior of twenty-three previously synthesized dual DNA gyrase and topoisomerase IV inhibitors was tested in RP-HPLC system, consisting of C8 column and acetonitrile/phosphate buffer (pH 5.5 and pH 7.4) mobile phase. logD was calculated at both pH values and the best correlation with logD was obtained for retention parameter φ0, indicating that this RP-HPLC system could be used as an alternative to the shake-flask determination of lipophilicity. Subsequent QSRR analysis revealed that intrinsic lipophilicity (logP) and molecular weight (bcutm13) have a positive, while solubility (bcutp3) has a negative influence on this retention parameter.

Novel Solubility Prediction Models: Molecular Fingerprints and Physicochemical Features vs Graph Convolutional Neural Networks

Predicting both accurate and reliable solubility values has long been a crucial but challenging task. In this work, surrogated model-based methods were developed to accurately predict the solubility of two molecules (solute and solvent) through machine learning and deep learning. The current study employed two methods: (1) converting molecules into molecular fingerprints and adding optimal physicochemical properties as descriptors and (2) using graph convolutional network (GCN) models to convert molecules into a graph representation and deal with prediction tasks. Then, two prediction tasks were conducted with each method: (1) the solubility value (regression) and (2) the solubility class (classification). The fingerprint-based method clearly demonstrates that high performance is possible by adding simple but significant physicochemical descriptors to molecular fingerprints, while the GCN method shows that it is possible to predict various properties of chemical compounds with relatively simplified features from the graph representation. The developed methodologies provide a comprehensive understanding of constructing a proper model for predicting solubility and can be employed to find suitable solutes and solvents.

Predicting Solubility of Newly-Approved Drugs (2016–2020) with a Simple ABSOLV and GSE(Flexible-Acceptor) Consensus Model Outperforming Random Forest Regression

This study applies the ‘Flexible-Acceptor’ variant of the General Solubility Equation, GSE(Φ,B), to the prediction of the aqueous intrinsic solubility, log₁₀S₀, of FDA recently-approved (2016–2020) ‘small-molecule’ new molecular entities (NMEs). The novel equation had been shown to predict the solubility of drugs beyond Lipinski’s ‘Rule of 5’ chemical space (bRo5) to a precision nearly matching that of the Random Forest Regression (RFR) machine learning method. Since then, it was found that the GSE(Φ,B) appears to work well not only for bRo5 NMEs, but also for Ro5 drugs. To put context to GSE(Φ,B), Yalkowsky’s GSE(classic), Abraham’s ABSOLV, and Breiman’s RFR models were also applied to predict log₁₀ S₀ of 72 newly-approve NMEs, for which useable reported solubility values could be accessed (nearly 60% from FDA New Drug Application published reports). Except for GSE (classic), the prediction models were retrained with an enlarged version of the Wiki-pS₀ database (nearly 400 added log₁₀ S₀ entries since our recent previous study). Thus, these four models were further validated by the additional independent solubility measurements which the newly-approved drugs introduced. The prediction methods ranked RFR ~ GSE (Φ,B) > ABSOLV > GSE (classic) in performance. It was further demonstrated that the biases generated in the four separate models could be nearly eliminated in a consensus model based on the average of just two of the methods: GSE (Φ,B) and ABSOLV. The resulting consensus prediction equation is simple in form and can be easily incorporated into spreadsheet calculations. Even more significant, it slightly outperformed the RFR method.

Evaluating pediatric and adult simulated fluids solubility: Abraham solvation parameters and multivariate analysis

PURPOSE

To understand drug solubilization as a function of age and identify drugs at risk of altered drug solubility in pediatric patients. To assess the discrimination ability of the Abraham solvation parameters and age-related changes in simulated media composition to predict in vitro drug solubility differences between pediatric and adult gastrointestinal conditions by multivariate data analysis.

METHODS

Differences between drug solubility in pediatric and adult biorelevant media were expressed as a % pediatric-to-adult ratio [Sp/Sa (%)]. Solubility ratios of fourteen poorly water-soluble drugs (2 amphoteric; 4 weak acids; 4 weak bases; 4 neutral compounds) were used in the analysis. Partial Least Squares Regression was based on Abraham solvation parameters and age-related changes in simulated gastrointestinal fluids, as well as their interactions, to predict the pediatric-to-adult solubility ratio.

RESULTS

The use of Abraham solvation parameters was useful as a theory-informed set of molecular predictors of drug solubility changes between pediatric and adult simulated gastrointestinal fluids. Our findings suggest that the molecular solvation environment in the fasted gastric state was similar in the pediatric age-groups studied, which led to fewer differences in the pediatric-to-adult solubility ratio. In the intestinal fasted and fed state, there was a high relative contribution of the physiologically relevant surfactants to the alteration of drug solubility in the pediatric simulated conditions compared to the adult ones, which confirms the importance of an age-appropriate composition in biorelevant media.

CONCLUSION

Statistical models based on Abraham solvation parameters were applied mostly to better understand drug solubility differences in adult and pediatric biorelevant media.

Molecular docking and pharmacophore models to probe binding hypothesis of inhibitors of hypoxia inducible factor-1

Hypoxia inducible factor-1 is a heterodimeric transcription factor that regulates cellular responses to hypoxia and is involved in tumor progression and resistance to chemotherapy. Dimerization between HIF-1α and β subunits has been recognized crucial for DNA binding and transcriptional activity of HIF-1. Therefore, inhibitors of α and β dimerization subunits of HIF-1 may potentially evade HIF-1-mediated chemotherapy resistance. In the current study, ligand-based pharmacophore model was developed to determine 3 D binding features of HIF-1 inhibitors. The selected pharmacophore model comprises of one hydrogen bond donor, one hydrogen bond acceptor and one hydrophobic feature. The selected model was used for virtual screening of publically available data base by ChemBridge Corporation. Overall, six potential hits against HIF-1α and β dimerization have been identified. These include, Hit 1 (4-(4-chlorophenyl)-2,6-dimethyl-3,5-pyridinedicarboxylic acid), 3 (2-[2-(2-hydroxybenzoyl)carbonohydrazonoyl]benzoic acid) and 5 (3-(4-methoxyphenyl)-2,4-quinolinedicarboxylic acid) nicotonic acid derivatives, Hit 2 (3-[(1-adamantylamino)sulfonyl]benzoic acid), 4 (5-{[(2-fluorophenyl)amino]sulfonyl}-2-methylbenzoic acid), and 6 (4-({[2-(trifluoromethyl)phenyl]sulfonyl}amino)benzoic acid) sulfonamide derivatives. Additionally, adamantyl moiety of compound 2 shows interactions with the experimentally known hydrophobic amino acid residues (V336, C334, E245) of HIF-1α and β dimerization site. The identified hits showed lower to higher µM biological activity (IC₅₀) values and thus, after further structure optimization may serve as potential inhibitor of HIF-1 dimerization in cancer chemotherapy.Communicated by Ramaswamy H. Sarma.

Guest Encapsulation within Surface-Adsorbed Self-Assembled Cages

Coordination cages encapsulate a wide variety of guests in the solution state. This ability renders them useful for applications such as catalysis and the sequestration of precious materials. A simple and general method for the immobilization of coordination cages on alumina is reported. Cage loadings are quantified via adsorption isotherms and guest displacement assays demonstrate that the adsorbed cages retain the ability to encapsulate and separate guest and non-guest molecules. Finally, a system of two cages, adsorbed on to different regions of alumina, stabilizes and separates a pair of Diels-Alder reagents. The addition of a single competitive guest results in the controlled release of the reagents, thus triggering their reaction. This method of coordination cage immobilization on solid phases is envisaged to be applicable to the extensive library of reported cages, enabling new applications based upon selective solid-phase molecular encapsulation.

"Flexible-Acceptor" General Solubility Equation for beyond Rule of 5 Drugs

This study describes a novel nonlinear variant of the well-known Yalkowsky general solubility equation (GSE). The modified equation can be trained with small molecules, mostly from the Lipinski Rule of 5 (Ro5) chemical space, to predict the intrinsic aqueous solubility, S₀, of large molecules (MW > 800 Da) from beyond the rule of 5 (bRo5) space, to an accuracy almost equal to that of a recently described random forest regression (RFR) machine learning analysis. The new approach replaces the GSE constant factors in the intercept (0.5), the octanol-water log P (-1.0), and melting point, mp (-0.01) terms with simple exponential functions incorporating the sum descriptor, Φ+B (Kier Φ molecular flexibility and Abraham H-bond acceptor potential). The constants in the modified three-variable (log P, mp, Φ+B) equation were determined by partial least-squares (PLS) refinement using a small-molecule log S₀ training set (n = 6541) of mostly druglike molecules. In this "flexible-acceptor" GSE(Φ,B) model, the coefficient of log P (normally fixed at -1.0) varies smoothly from -1.1 for rigid nonionizable molecules (Φ+B = 0) to -0.39 for typically flexible (Φ ∼ 20, B ∼ 6) large molecules. The intercept (traditionally fixed at +0.5) varies smoothly from +1.9 for completely inflexible small molecules to -2.2 for typically flexible large molecules. The mp coefficient (-0.007) remains practically constant, near the traditional value (-0.01) for most molecules, which suggests that the small-to-large molecule continuum is mainly solvation responsive, apparently with only minor changes in the crystal lattice contributions. For a test set of 32 large molecules (e.g., cyclosporine A, gramicidin A, leuprolide, nafarelin, oxytocin, vancomycin, and mostly natural-product-derived therapeutics used in infectious/viral diseases, in immunosuppression, and in oncology) the modified equation predicted the intrinsic solubility with a root-mean-square error of 1.10 log unit, compared to 3.0 by the traditional GSE, and 1.07 by RFR.

A review of methods for solubility determination in biopharmaceutical drug characterization

The significance of thermodynamic solubility in biopharmaceutical compound or drug characterization as well as the importance of having methods that accurately establish it have been extensively addressed. Nonetheless, its precise determination continues to remain a challenging task to accomplish. Even more so when the number of compounds to evaluate is high and the available amount of each compound is low, both of which are inevitable for the compound characterization during the drug development process. Except for the shake-flask method which is still considered as the 'gold standard' in obtaining thermodynamic data, it is currently difficult to say that another satisfactory model which is routinely used to determine thermodynamic solubility is being applied. Therefore, this review summarizes the various experimental approaches which are based on the classical shake flask method but have yet attempted to speed up the experimental process of obtaining such data more conveniently. The most important experimental features of these approaches are provided to the reader. Some advantages and disadvantages associated with each approach are also highlighted, consequently offering a resource to those looking for the most appropriate of the approaches that have already fared well at determining the biopharmaceutically relevant drug solubility.

AqSolDB, a curated reference set of aqueous solubility and 2D descriptors for a diverse set of compounds

Water is a ubiquitous solvent in chemistry and life. It is therefore no surprise that the aqueous solubility of compounds has a key role in various domains, including but not limited to drug discovery, paint, coating, and battery materials design. Measurement and prediction of aqueous solubility is a complex and prevailing challenge in chemistry. For the latter, different data-driven prediction models have recently been developed to augment the physics-based modeling approaches. To construct accurate data-driven estimation models, it is essential that the underlying experimental calibration data used by these models is of high fidelity and quality. Existing solubility datasets show variance in the chemical space of compounds covered, measurement methods, experimental conditions, but also in the non-standard representations, size, and accessibility of data. To address this problem, we generated a new database of compounds, AqSolDB, by merging a total of nine different aqueous solubility datasets, curating the merged data, standardizing and validating the compound representation formats, marking with reliability labels, and providing 2D descriptors of compounds as a Supplementary Resource.

The Design, Synthesis, and Characterization of Resveratrol Derivatives Modified by Different γ-Aminobutyric Acid Esters

A novel series of resveratrol modified by γ-aminobutyric acid esters were designed and synthesized. Then, the products were characterized by 1H-NMR, 13C-NMR, and MS, and the melting point was determined. Molecular water solubility, polar surface area, and octanol-water partition were calculated, which correlated well with molecular transport through membranes and, therefore, enabled prediction of transport properties of drugs.

A review of the predictive models estimating association of neutral and ionizable organic chemicals with dissolved organic carbon

Dissolved organic carbon (DOC) plays a key role in environmental transport, fate and bioavailability of organic chemicals in terrestrial and aquatic ecosystems. Predicting the association of contaminants to DOC is therefore crucial in modelling chemical exposure and risk assessment. The models proposed so far to describe interaction mechanisms between chemicals and DOC and the most influential variables have been reviewed. The single-parameter linear free energy relationships (sp-LFERs) and the poly-parameter linear free energy relationships (pp-LFERs) in the form of linear solvation energy relationships (LSERs) currently available in literature for estimating dissolved organic carbon/water partition (K_DOC) and distribution (D_DOC) coefficients for organic chemicals were discussed, and limits of the existing approaches explored. For neutral chemicals many predictive equations are currently available in literature, but the quality of the input data on which they are based is often questionable, due to the lack of an unequivocal definition of DOC among different references and to the different and often unreliable K_DOC measurement method. For ionizable chemicals instead there is a substantial lack of predictive approaches that need to be fulfilled since just few models are nowadays available to predict D_DOC of ionized species. This paper reviews the current approaches for neutral and ionizable chemicals proposing guidelines to select conditions for obtaining reliable data and predictive equations for an improved estimation of K_DOC and D_DOC.

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.

Predicting dissolved organic carbon partition and distribution coefficients of neutral and ionizable organic chemicals

Estimating K_DOC (dissolved organic carbon/water partition coefficient) and D_DOC (dissolved organic carbon/water distribution coefficient) of neutral and ionizable organic chemicals is a crucial task for assessing mobility, modelling transport, environmental fate of a variety of chemicals and for evaluating their bioavailability in terrestrial and aquatic environments. A critical literature search of reliability-selected K_DOC and D_DOC values was performed to setup novel predictive relationships for K_DOC and D_DOC of neutral and ionizable organic chemicals. This goal was pursued by using: 1) LSER (linear solvation energy relationship) models to predict K_DOC for neutral chemicals using Abraham solute parameters calculated for different DOC sources (all DOC sources together, soil porewater, surface water, wastewater and Aldrich humic acid (HA)); 2) linear regressions for predicting D_DOC of organic acids from the octanol/water partition coefficient (Log K_OW or Log P) and the dissociation constant (pKa), accounting separately for the contribution of the neutral and ionic fraction. The proposed models predicted Log K_DOC and D_DOC values within a root mean square deviation (RMSD) generally smaller than 0.3 log units.

Partial Solvation Parameters of Drugs as a New Thermodynamic Tool for Pharmaceutics

Partial solvation parameters (PSP) have much in common with the Hansen solubility parameter or with a linear solvation energy relationship (LSER), but there are advantages based on the sound thermodynamic basis. It is, therefore, surprising that PSP has so far not been harnessed in pharmaceutics for the selection of excipients or property estimation of formulations and their components. This work introduces PSP calculation for drugs, where the raw data were obtained from inverse gas chromatography. It was shown that only a few probe gases were needed to get reasonable estimates of the drug PSPs. Interestingly, an alternative calculation of LSER parameters in silico did not reflect the experimentally obtained activity coefficients for all probe gases as well, which was attributed to the complexity of the drug structures. The experimental PSPs were proven to be helpful in predicting drug solubility in various solvents and the PSP framework allowed calculation of the different surface energy contributions. A specific benefit of PSP is that parameters can be readily converted to either classical solubility or LSER parameters. Therefore, PSP is not just about a new definition of solvatochromic parameters, but the underlying thermodynamics provides a unified approach, which holds much promise for broad applications in pharmaceutics.

Calculation of the water-octanol partition coefficient of cholesterol for SPC, TIP3P, and TIP4P water

We present a numerical study of the relative solubility of cholesterol in octanol and water. Our calculations allow us to compare the accuracy of the computed values of the excess chemical potential of cholesterol for several widely used water models (SPC, TIP3P, and TIP4P). We compute the excess solvation free energies by means of a cavity-based method [L. Li et al., J. Chem. Phys. 146(21), 214110 (2017)] which allows for the calculation of the excess chemical potential of a large molecule in a dense solvent phase. For the calculation of the relative solubility ("partition coefficient," log₁₀ P o / w ) of cholesterol between octanol and water, we use the OPLS/AA force field in combination with the SPC, TIP3P, and TIP4P water models. For all water models studied, our results reproduce the experimental observation that cholesterol is less soluble in water than in octanol. While the experimental value for the partition coefficient is log₁₀ P o / w = 3.7, SPC, TIP3P, and TIP4P give us a value of log₁₀ P o / w = 4.5, 4.6, and 2.9, respectively. Therefore, although the results for the studied water models in combination with the OPLS/AA force field are acceptable, further work to improve the accuracy of current force fields is needed.

Lipophilicity and hydrophobicity considerations in bio-enabling oral formulations approaches – a PEARRL review

Objectives

This review highlights aspects of drug hydrophobicity and lipophilicity as determinants of different oral formulation approaches with specific focus on enabling formulation technologies. An overview is provided on appropriate formulation selection by focussing on the physicochemical properties of the drug.

Key findings

Crystal lattice energy and the octanol–water partitioning behaviour of a poorly soluble drug are conventionally viewed as characteristics of hydrophobicity and lipophilicity, which matter particularly for any dissolution process during manufacturing and regarding drug release in the gastrointestinal tract. Different oral formulation strategies are discussed in the present review, including lipid-based delivery, amorphous solid dispersions, mesoporous silica, nanosuspensions and cyclodextrin formulations.

Summary

Current literature suggests that selection of formulation approaches in pharmaceutics is still highly dependent on the availability of technological expertise in a company or research group. Encouraging is that, recent advancements point to more structured and scientifically based development approaches. More research is still needed to better link physicochemical drug properties to pharmaceutical formulation design.

Addressing hysteresis and slow equilibration issues in cavity-based calculation of chemical potentials

In this paper, we explore the strengths and weaknesses of a cavity-based method to calculate the excess chemical potential of a large molecular solute in a dense liquid solvent. Use of the cavity alleviates some technical problems associated with the appearance of (integrable) divergences in the integrand during alchemical particle growth. The excess chemical potential calculated using the cavity-based method should be independent of the cavity attributes. However, the performance of the method (equilibration time and the robustness) does depend on the cavity attributes. To illustrate the importance of a suitable choice of the cavity attributes, we calculate the partition coefficient of pyrene in toluene and heptane using a coarse-grained model. We find that a poor choice for the functional form of the cavity may lead to hysteresis between growth and shrinkage of the cavity. Somewhat unexpectedly, we find that, by allowing the cavity to move as a pseudo-particle within the simulation box, the decay time of fluctuations in the integrand of the thermodynamic integration can be reduced by an order of magnitude, thereby increasing the statistical accuracy of the calculation.

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.

Matched Molecular Pair Analysis on Large Melting Point Datasets: A Big Data Perspective

A matched molecular pair (MMP) analysis was used to examine the change in melting point (MP) between pairs of similar molecules in a set of ∼275k compounds. We found many cases in which the change in MP (ΔMP) of compounds correlates with changes in functional groups. In line with the results of a previous study, correlations between ΔMP and simple molecular descriptors, such as the number of hydrogen bond donors, were identified. In using a larger dataset, covering a wider chemical space and range of melting points, we observed that this method remains stable and scales well with larger datasets. This MMP-based method could find use as a simple privacy-preserving technique to analyze large proprietary databases and share findings between participating research groups.

Estimating the Aqueous Solubility of Pharmaceutical Hydrates

Estimation of crystalline solute solubility is well documented throughout the literature. However, the anhydrous crystal form is typically considered with these models, which is not always the most stable crystal form in water. In this study, an equation which predicts the aqueous solubility of a hydrate is presented. This research attempts to extend the utility of the ideal solubility equation by incorporating desolvation energetics of the hydrated crystal. Similar to the ideal solubility equation, which accounts for the energetics of melting, this model approximates the energy of dehydration to the entropy of vaporization for water. Aqueous solubilities, dehydration and melting temperatures, and log P values were collected experimentally and from the literature. The data set includes different hydrate types and a range of log P values. Three models are evaluated, the most accurate model approximates the entropy of dehydration (ΔSd) by the entropy of vaporization (ΔSvap) for water, and utilizes onset dehydration and melting temperatures in combination with log P. With this model, the average absolute error for the prediction of solubility of 14 compounds was 0.32 log units.

Calculation of Five Thermodynamic Molecular Descriptors by Means of a General Computer Algorithm Based on the Group-Additivity Method: Standard Enthalpies of Vaporization, Sublimation and Solvation, and Entropy of Fusion of Ordinary Organic Molecules and Total Phase-Change Entropy of Liquid Crystals

The calculation of the standard enthalpies of vaporization, sublimation and solvation of organic molecules is presented using a common computer algorithm on the basis of a group-additivity method. The same algorithm is also shown to enable the calculation of their entropy of fusion as well as the total phase-change entropy of liquid crystals. The present method is based on the complete breakdown of the molecules into their constituting atoms and their immediate neighbourhood; the respective calculations of the contribution of the atomic groups by means of the Gauss-Seidel fitting method is based on experimental data collected from literature. The feasibility of the calculations for each of the mentioned descriptors was verified by means of a 10-fold cross-validation procedure proving the good to high quality of the predicted values for the three mentioned enthalpies and for the entropy of fusion, whereas the predictive quality for the total phase-change entropy of liquid crystals was poor. The goodness of fit (Q²) and the standard deviation (σ) of the cross-validation calculations for the five descriptors was as follows: 0.9641 and 4.56 kJ/mol (N = 3386 test molecules) for the enthalpy of vaporization, 0.8657 and 11.39 kJ/mol (N = 1791) for the enthalpy of sublimation, 0.9546 and 4.34 kJ/mol (N = 373) for the enthalpy of solvation, 0.8727 and 17.93 J/mol/K (N = 2637) for the entropy of fusion and 0.5804 and 32.79 J/mol/K (N = 2643) for the total phase-change entropy of liquid crystals. The large discrepancy between the results of the two closely related entropies is discussed in detail. Molecules for which both the standard enthalpies of vaporization and sublimation were calculable, enabled the estimation of their standard enthalpy of fusion by simple subtraction of the former from the latter enthalpy. For 990 of them the experimental enthalpy-of-fusion values are also known, allowing their comparison with predictions, yielding a correlation coefficient R² of 0.6066.

Retention of 14C-labeled multiwall carbon nanotubes by humic acid and polymers: Roles of macromolecule properties

Developing methods to measure interactions of carbon nanotubes (CNTs) with soils and sediments and understanding the impact of soil and sediment properties on CNT deposition are essential for assessing CNT environmental risks. In this study, we utilized functionalized carbon-14 labeled nanotubes to systematically investigate retention of multiwall CNTs (MWCNTs) by 3 humic acids, 3 natural biopolymers, and 10 model solid-phase polymers, collectively termed macromolecules. Surface properties, rather than bulk properties of macromolecules, greatly influenced MWCNT retention. As shown via multiple linear regression analysis and path analysis, aromaticity and surface polarity were the two most positive factors for retention, suggesting retention was regulated by π-π stacking and hydrogen bonding interactions. Moreover, MWCNT deposition was irreversible. These observations may explain the high retention of MWCNT in natural soils. Moreover, our findings on the relative contribution of each macromolecule property on CNT retention provide information on macromolecule selection for removal of MWCNTs from wastewater and provide a method for measuring CNT interactions with organic macromolecules.

Predictions of the physicochemical properties of amino acid side chain analogs using molecular simulation

A candidate drug compound is released for clinical trails (in vivo activity) only if its physicochemical properties meet desirable bioavailability and partitioning criteria.