Aug 2026· European Journal of Pharmaceutical Sciences· Vol 225, pp.
107631
· 0 citations· 58 references
Medicine
TL;DR
The proposed CPC-TST model demonstrated good accuracy in predicting solubility parameter, particularly for strongly associating systems, while maintaining low computational complexity, and highlights the potential of the CPC-TST model as a robust and efficient alternative for modeling solubility behavior in pharmaceutical systems.
Abstract
Accurate prediction of drug solubility parameter is essential for understanding drug-solvent interactions and guiding formulation design. Experimental determination is often limited by low solubility and measurement complexity; thus, reliable predictive methods are required. In this work, the main objective is to estimate drug solubility parameter using a modified Cubic-Plus-Chain (CPC) equation of state (EoS). This work emphasizes that a simple cubic-based EoS can effectively model complex pharmaceutical systems and can be readily implemented in commercial simulation software. Accordingly, the CPC EoS was coupled with the Two-State Theory (TST) to enhance the description of complex molecular interactions, such as association in drug systems. The primary motivation for employing the TST instead of Wertheim's theory lies in the difficulty of defining the number and types of association sites in large and complex drug molecules. In contrast to Wertheim's approach, TST does not require explicit specification of association sites, which greatly simplifies the modeling of associating components. Moreover, the proposed CPC-TST model retains analytical solvability comparable to conventional cubic EoS, further enhancing its practicality for implementation in commercial simulation tools. The model parameters were determined using available experimental solubility data for selected drug-solvent systems. The solubility of drugs in various pure and mixed solvents was then estimated with the CPC-TST model. The analysis shows that accounting for a binary interaction parameter that varies with temperature leads to a notable improvement in the model's capability, yielding the average RMSD of 0.034 and AAD% of 0.168. The CPC-TST model was employed to predict the solubility parameter of several drug compounds. The predicted values were compared with those obtained from regression-based, group-contribution methods, and PC-SAFT EoS. The CPC-TST model demonstrated good accuracy in predicting solubility parameter, particularly for strongly associating systems, while maintaining low computational complexity. These results highlight the potential of the CPC-TST model as a robust and efficient alternative for modeling solubility behavior in pharmaceutical systems.
Solubility is a widely measured physicochemical property and a highly sought-after descriptor in the evaluation of molecules for drug design and development, medicinal chemistry, and agrochemical sciences. Consequently, a wide range of in silico models based on deductive and inductive reasoning have been developed. However, the General Solubility Equation (GSE) stands out as a simple, thermodynamically derived equation to predict intrinsic solubility (log S0, in mol/L) of molecules from their melting point and n-octanol/water partition coefficient (log PN). Despite its widespread use, the applicability of this equation has not been rigorously evaluated to establish when it can or cannot produce accurate predictions. Therefore, a large-scale evaluation of the GSE was conducted using an extensive database of fully experimental melting point and log PN data for 2740, mostly drug-like compounds. A systematic analysis based on cheminformatics descriptors was conducted to identify the primary factors that allow the GSE to achieve predictions within the experimental uncertainty range (±1 log S unit). This information has been used to create GSESolver: a supervised machine learning classification model that, based on the selected descriptors, can predict whether the GSE will perform accurately solely from its SMILES string. GSESolver tool can be used by anyone in the scientific community to quickly assess molecule solubility and it was developed under the FAIR principles (Findable, Accessible, Interoperable, and Reusable) in a Google Colab notebook to ensure ease of use. Finally, the utility of the GSESolver tool was exploited in medicinal chemistry applications for the in silico prediction of the Maximum Absorbable Dose (MAD) of potential drugs, and in a rational agrochemical design application where solubility is a key factor.
Esteban Bertsch-Aguilar, Nahomy Quirós, Frederick Schosinsky et al.· Journal of Chemical Informat...· 0 citations
Aqueous solubility is a critical parameter in drug design. Common methods to measure solubility are often too slow or too inaccurate to be routinely used. Measuring very low solubilities (10-6 M and below) represents additional challenges. In this paper, we first describe a fast and reliable method to measure aqueous solubility of drug-like molecules in a 96-well plate format using only conventional laboratory equipment and a UV absorbance plate reader. The method was validated against the gold-standard saturation shake-flask on a set of 31 drug molecules and represents a practical improvement over already described high-throughput solubility determination methods. We then use this method to explore the solubility of six poorly soluble molecules in water-organic solvent mixtures. We discuss the relationship between solvent fraction and logarithmic solubility (logS), conditions to make this relationship linear, and how to use it to extrapolate solubility to 0 % cosolvent. We demonstrate that the MDM mixture (1:1:1 methanol, acetonitrile and dioxane) provides linear logS - cosolvent relationship for all tested compounds, and excellent extrapolation abilities. Our method opens the way to the systematic determination of very low solubilities at the very first stages of drug design programs, a valuable input for structure-property relationship studies.
D. Fayolle, Emilie M F Mwakondet, Marianne Carpentier et al.· International journal of pha...· 0 citations
Accurate prediction of solubility is crucial in various fields, including pharmaceuticals, environmental chemistry, and materials science. In this study, we demonstrate the application of Adaptive Force Matching (AFM) to predict the solubility of molecular liquids in water. By developing high-quality force fields using AFM, we accurately compute the free energy of vaporization and hydration, which are essential components for predicting solubility. Our results show that AFM models can reliably predict the solvation free energy of selected small molecules, exhibiting a deviation of <1.3 kJ/mol from experimental references for cyclohexene, isopentane, and n-butanol. Although a slightly larger error is observed for n-octanol, which was developed by borrowing AFM parameters from other molecules, the deviation remains comparable to commonly accepted chemical accuracy. This study highlights the potential of AFM as a powerful tool for predicting solubility, enabling the design and development of new materials and molecules with tailored properties.
Unknown authors· Journal of Chemical Physics· 0 citations
ABSTRACT Apparent permeability (Papp) of a drug molecule serves as a principal indicator of drug absorption for pharmacokinetic modeling, and accurate prediction of Papp values using machine learning would avoid time‐consuming and expensive In Vitro experiments. In this study, four different feature representations were compared for predicting logPapp values, with each representation serving as input to three subsequent regression models. The best predictive model achieved an R2 value of 0.68 and RMSE of 0.42 on the test data. Furthermore, the SHAP values corresponding to individual molecular descriptors were analyzed to interpret the influence of these descriptors on the model prediction. Some key properties like octanol–water partition coefficient and number of basic atoms were found to have a strong influence on the Papp value. Additionally, some specific molecular substructures were identified that contribute either positively or negatively to the model output, thereby inferring effects on drug permeability. Finally, the uncertainty in the predictions was quantified through a distribution‐free and model‐agnostic method, jackknife+, used for the estimation of confidence intervals. At the optimal experimental setting, the confidence intervals derived using the overall best performing model covered 96.12% and 86.73% of the original logPapp values with more than 95% confidence for test and independent data, respectively. With the same confidence, the confidence intervals contained 99.87% and 100% of the predicted logPapp values for the test and independent data, respectively, underscoring the reliability of the model. Overall, the presented ML provides the most robust informed Papp prediction among compared models presented to date.
Rajdeep Mondal, Rajith K. R. Rajoli, Andrew Owen et al.· CPT: Pharmacometrics & Syste...· 0 citations
Drug crystallization is a fundamental approach to extending release through enhanced solid‑state stability and tunable particle size. Drug-release kinetics can be further modulated through co-crystallization, which alters drug-molecule-to-drug-molecule interactions, and can be used to simultaneously deliver agents with synergistic potency. However, co-formulating physicochemically diverse drugs into a common system can be challenging. Here, we investigate solvent/anti‑solvent crystallization as a simple and versatile method for producing single‑drug as well as co‑formulated crystalline depots using curcumin and piperine as a model system. We evaluate the effects of drug concentration, drug ratio, and solvent/anti‑solvent ratio on crystal formation, structure, and release behavior. Our results demonstrate that the solvent/anti-solvent ratio strongly modulates crystal properties and accelerated release kinetics for single‑drug formulations. In co‑formulated systems, the interaction between drug ratio and solvent/anti-solvent ratio mediates actual (as opposed to theoretical) curcumin or piperine loading within the crystals and solids yield. In vivo, all formulations exhibited low and extended curcumin release, consistent with solubility‑limited kinetics, while piperine release was more sensitive to formulation composition. Additionally, most crystals remained within bead explants after 14 days, suggesting the potential for longer release of curcumin. These findings illustrate the tunability of solvent/anti‑solvent crystallization for engineering single‑ and multi‑drug crystalline depots and provide insight into how crystallization parameters influence release from co‑formulated small‑molecule systems.
Jamie L. Hernandez, Neeti R. Prasad, J. Daniel et al.· International journal of pha...· 0 citations
Quantification of drug-cell interactions and subsequent cellular responses by using experimental data together with mathematical models of assumed binding and signalling schematics is vital to many research programmes; data fitting provides estimates for important pharmacological parameters including kinetic parameters controlling drug affinity and efficacy. Ordinary differential equation (ODE) models are a key component of many receptor theory studies used for this purpose. In using ODE simulations to fit experimental data and estimate these parameters, the theory of the identifiability properties of the system is often overlooked. Indeed, structural identifiability analysis (SIA) is often overlooked in many fields of bio-modelling. Building on recent SIA for linear ligand binding models in receptor theory, we present a new analysis of identifiability properties of nonlinear receptor theory models. We include models of ligand depletion in binding assays and ligand-induced dimerisation (LID). The classical SIA approaches of Taylor Series and similarity transformation are applied, using detailed step-by-step calculations to illustrate the complexity of the implementations. New results are obtained which show that the nonlinear ligand-depletion counterpart models of non-identifiable linear ligand excess models are globally identifiable from a single timecourse. Also, the LID model is shown to be globally identifiable if an experimental aparatus-dependent parameter is obtained. The analysis highlights issues of tractability of the methods for similar and higher-dimensional nonlinear models in receptor theory.
C. White, Vivi Rottschäfer, L. Bridge· Journal of Pharmacokinetics...· 0 citations
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