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

Predictive computational models for assessing the impact of co-milling on drug dissolution

Co-milling is an effective technique for improving dissolution rate limited absorption characteristics of poorly water-soluble drugs. However, there is a scarcity of models available to forecast the magnitude of dissolution rate improvement caused by co-milling. Therefore, this study endeavoured to quantitatively predict the increase in dissolution by co-milling based on drug properties. Using a biorelevant dissolution setup, a series of 29 structurally diverse and crystalline drugs were screened in co-milled and physically blended mixtures with Polyvinylpyrrolidone K25. Co-Milling Dissolution Ratios after 15 min (COMDR15 min) and 60 min (COMDR60 min) drug release were predicted by variable selection in the framework of a partial least squares (PLS) regression. The model forecasts the COMDR15 min (R2 = 0.82 and Q2 = 0.77) and COMDR60 min (R2 = 0.87 and Q2 = 0.84) with small differences in root mean square errors of training and test sets by selecting four drug properties. Based on three of these selected variables, applicable multiple linear regression equations were developed with a high predictive power of R2 = 0.83 (COMDR15 min) and R2 = 0.84 (COMDR60 min). The most influential predictor variable was the median drug particle size before milling, followed by the calculated drug logD6.5 value, the calculated molecular descriptor Kappa 3 and the apparent solubility of drugs after 24 h dissolution. The study demonstrates the feasibility of forecasting the dissolution rate improvements of poorly water-solube drugs through co-milling. These models can be applied as computational tools to guide formulation in early stage development.

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.

Multivariate Analysis of Solubility Parameters for Drug-Polymer Miscibility Assessment in Preparing Raloxifene Hydrochloride Amorphous Solid Dispersions

The success of obtaining solid dispersions for solubility improvement invariably depends on the miscibility of the drug and polymeric carriers. This study aimed to categorize and select polymeric carriers via the classical group contribution method using the multivariate analysis of the calculated solubility parameter of RX-HCl. The total, partial, and derivate parameters for RX-HCl were calculated. The data were compared with the results of excipients (N = 36), and a hierarchical clustering analysis was further performed. Solid dispersions of selected polymers in different drug loads were produced using solvent casting and characterized via X-ray diffraction, infrared spectroscopy and scanning electron microscopy. RX-HCl presented a Hansen solubility parameter (HSP) of 23.52 MPa1/2. The exploratory analysis of HSP and relative energy difference (RED) elicited a classification for miscible (n = 11), partially miscible (n = 15), and immiscible (n = 10) combinations. The experimental validation followed by a principal component regression exhibited a significant correlation between the crystallinity reduction and calculated parameters, whereas the spectroscopic evaluation highlighted the hydrogen-bonding contribution towards amorphization. The systematic approach presented a high discrimination ability, contributing to optimal excipient selection for the obtention of solid solutions of RX-HCl.

Advancing algorithmic drug product development: Recommendations for machine learning approaches in drug formulation

Artificial intelligence is a rapidly expanding area of research, with the disruptive potential to transform traditional approaches in the pharmaceutical industry, from drug discovery and development to clinical practice. Machine learning, a subfield of artificial intelligence, has fundamentally transformed in silico modelling and has the capacity to streamline clinical translation. This paper reviews data-driven modelling methodologies with a focus on drug formulation development. Despite recent advances, there is limited modelling guidance specific to drug product development and a trend towards suboptimal modelling practices, resulting in models that may not give reliable predictions in practice. There is an overwhelming focus on benchtop experimental outcomes obtained for a specific modelling aim, leaving the capabilities of data scraping or the use of combined modelling approaches yet to be fully explored. Moreover, the preference for high accuracy can lead to a reliance on black box methods over interpretable models. This further limits the widespread adoption of machine learning as black boxes yield models that cannot be easily understood for the purposes of enhancing product performance. In this review, recommendations for conducting machine learning research for drug product development to ensure trustworthiness, transparency, and reliability of the models produced are presented. Finally, possible future directions on how research in this area might develop are discussed to aim for models that provide useful and robust guidance to formulators.

Leveraging the use of in vitro and computational methods to support the development of enabling oral drug products: An InPharma commentary

Due to the strong tendency towards poorly soluble drugs in modern development pipelines, enabling drug formulations such as amorphous solid dispersions, cyclodextrins, co-crystals and lipid-based formulations are frequently applied to solubilize or generate supersaturation in gastrointestinal fluids, thus enhancing oral drug absorption. Although many innovative in vitro and in silico tools have been introduced in recent years to aid development of enabling formulations, significant knowledge gaps still exist with respect to how best to implement them. As a result, the development strategy for enabling formulations varies considerably within the industry and many elements of empiricism remain. The InPharma network aims to advance a mechanistic, animal-free approach to the assessment of drug developability. This commentary focuses current status and next steps that will be taken in InPharma to identify and fully utilize 'best practice' in vitro and in silico tools for use in physiologically based biopharmaceutic models.

Can Pure Predictions of Activity Coefficients from PC-SAFT Assist Drug-Polymer Compatibility Screening?

The bioavailability of poorly water-soluble active pharmaceutical ingredients (APIs) can be improved via the formulation of an amorphous solid dispersion (ASD), where the API is incorporated into a suitable polymeric carrier. Optimal carriers that exhibit good compatibility (i.e., solubility and miscibility) with given APIs are typically identified through experimental means, which are routinely labor- and cost-inefficient. Therefore, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, a popular thermodynamic model in pharmaceutical applications, is examined in terms of its performance regarding the computational pure prediction of API-polymer compatibility based on activity coefficients (API fusion properties were taken from experiments) without any binary interaction parameters fitted to API-polymer experimental data (that is, kij = 0 in all cases). This kind of prediction does not need any experimental binary information and has been underreported in the literature so far, as the routine modeling strategy used in the majority of the existing PC-SAFT applications to ASDs comprised the use of nonzero kij values. The predictive performance of PC-SAFT was systematically and thoroughly evaluated against reliable experimental data for almost 40 API-polymer combinations. We also examined the effect of different sets of PC-SAFT parameters for APIs on compatibility predictions. Quantitatively, the total average error calculated over all systems was approximately 50% in the weight fraction solubility of APIs in polymers, regardless of the specific API parametrization. The magnitude of the error for individual systems was found to vary significantly from one system to another. Interestingly, the poorest results were obtained for systems with self-associating polymers such as poly(vinyl alcohol). Such polymers can form intramolecular hydrogen bonds, which are not accounted for in the PC-SAFT variant routinely applied to ASDs (i.e., that used in this work). However, the qualitative ranking of polymers with respect to their compatibility with a given API was reasonably predicted in many cases. It was also predicted correctly that some polymers always have better compatibility with the APIs than others. Finally, possible future routes to improve the cost-performance ratio of PC-SAFT in terms of parametrization are discussed.

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.

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.

Purely Predicting the Pharmaceutical Solubility: What to Expect from PC-SAFT and COSMO-RS?

A pair of popular thermodynamic models for pharmaceutical applications, namely, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state and the conductor-like screening model for real solvents (COSMO-RS) are thoroughly benchmarked for their performance in predicting the solubility of active pharmaceutical ingredients (APIs) in pure solvents. The ultimate goal is to provide an illustration of what to expect from these progressive frameworks when applied to the thermodynamic solubility of APIs based on activity coefficients in a purely predictive regime without specific experimental solubility data (the fusion properties of pure APIs were taken from experiments). While this kind of prediction represents the typical modus operandi of the first-principles-aided COSMO-RS, PC-SAFT is a relatively highly parametrized model that relies on experimental data, against which its pure-substance and binary interaction parameters (k_ij) are fitted. Therefore, to make this benchmark as fair as possible, we omitted any binary parameters of PC-SAFT (i.e., k_ij = 0 in all cases) and preferred pure-substance parameter sets for APIs not trained to experimental solubility data. This computational approach, together with a detailed assessment of the obtained solubility predictions against a large experimental data set, revealed that COSMO-RS convincingly outperformed PC-SAFT both qualitatively (i.e., COSMO-RS was better in solvent ranking) and quantitatively, even though the former is independent of both substance- and mixture-specific experimental data. Regarding quantitative comparison, COSMO-RS outperformed PC-SAFT for 9 of the 10 APIs and for 63% of the API-solvent systems, with root-mean-square deviations of the predicted data from the entire experimental data set being 0.82 and 1.44 log units, respectively. The results were further analyzed to expand the picture of the performance of both models with respect to the individual APIs and solvents. Interestingly, in many cases, both models were found to qualitatively incorrectly predict the direction of deviations from ideality. Furthermore, we examined how the solubility predictions from both models are sensitive to different API parametrizations.

Predicting Solubility Limits of Organic Solutes for a Wide Range of Solvents and Temperatures

The solubility of organic molecules is crucial in organic synthesis and industrial chemistry; it is important in the design of many phase separation and purification units, and it controls the migration of many species into the environment. To decide which solvents and temperatures can be used in the design of new processes, trial and error is often used, as the choice is restricted by unknown solid solubility limits. Here, we present a fast and convenient computational method for estimating the solubility of solid neutral organic molecules in water and many organic solvents for a broad range of temperatures. The model is developed by combining fundamental thermodynamic equations with machine learning models for solvation free energy, solvation enthalpy, Abraham solute parameters, and aqueous solid solubility at 298 K. We provide free open-source and online tools for the prediction of solid solubility limits and a curated data collection (SolProp) that includes more than 5000 experimental solid solubility values for validation of the model. The model predictions are accurate for aqueous systems and for a huge range of organic solvents up to 550 K or higher. Methods to further improve solid solubility predictions by providing experimental data on the solute of interest in another solvent, or on the solute's sublimation enthalpy, are also presented.

Designing Soluble PROTACs: Strategies and Preliminary Guidelines

Solubility optimization is a crucial step to obtaining oral PROTACs. Here we measured the thermodynamic solubilities (log S) of 21 commercial PROTACs. Next, we measured BRlogD and log k_w^IAM (lipophilicity), EPSA, and Δ log k_w^IAM (polarity) and showed that lipophilicity plays a major role in governing log S, but a contribution of polarity cannot be neglected. Two-/three-dimensional descriptors calculated on conformers arising from conformational sampling and steered molecular dynamics failed in modeling solubility. Infographic tools were used to identify a privileged region of soluble PROTACs in a chemical space defined by BRlogD, log k_w^IAM and topological polar surface area, while machine learning provided a log S classification model. Finally, for three pairs of PROTACs we measured the solubility, lipophilicity, and polarity of the building blocks and identified the limits of estimating PROTAC solubility from the synthetic components. Overall, this paper provides promising guidelines for optimizing PROTAC solubility in early drug discovery programs.

Hydroxypropyl Cellulose for Drug Precipitation Inhibition: From the Potential of Molecular Interactions to Performance Considering Microrheology

There has been recent interest in using hydroxypropyl cellulose (HPC) for supersaturating drug formulations. This study investigated the potential for molecular HPC interactions with the model drug celecoxib by integrating novel approaches in the field of drug supersaturation analysis. Following an initial polymer characterization study, quantum-chemical calculations and molecular dynamics simulations were complemented with results of inverse gas chromatography and broadband diffusing wave spectroscopy. HPC performance was studied regarding drug solubilization and kinetics of desupersaturation using different grades (i.e., HPC-UL, SSL, SL, and L). The results suggested that the potential contribution of dispersive interactions and hydrogen bonding depended strongly on the absence or presence of the aqueous phase. It was proposed that aggregation of HPC polymer chains provided a complex heterogeneity of molecular environments with more or less excluded water for drug interaction. In precipitation experiments at a low aqueous polymer concentration (i.e., 0.01%, w/w), grades L and SL appeared to sustain drug supersaturation better than SSL and UL. However, UL was particularly effective in drug solubilization at pH 6.8. Thus, a better understanding of drug-polymer interactions is important for formulation development, and polymer blends may be used to harness the combined advantages of individual polymer grades.

Study and Computational Modeling of Fatty Acid Effects on Drug Solubility in Lipid-Based Systems

Lipid-based systems have many advantages in formulation of poorly water-soluble drugs but issues of a limited solvent capacity are often encountered in development. One of the possible solubilization approaches of especially basic drugs could be the addition of fatty acids to oils but currently, a systematic study is lacking. Therefore, the present work investigated apparently neutral and basic drugs in medium chain triglycerides (MCT) alone and with added either caproic acid (C6), caprylic acid (C8), capric acid (C10) or oleic acid (C18:1) at different levels (5 - 20%, w/w). A miniaturized solubility assay was used together with X-ray diffraction to analyze the residual solid and finally, solubility data were modeled using the conductor-like screening model for real solvents (COSMO-RS). Some drug bases had an MCT solubility of only a few mg/ml or less but addition of fatty acids provided in some formulations exceptional drug loading of up to about 20% (w/w). The solubility changes were in general more pronounced the shorter the chain length was and the longest oleic acid even displayed a negative effect in mixtures of celecoxib and fenofibrate. The COSMO-RS prediction accuracy was highly specific for the given compounds with root mean square errors (RMSE) ranging from an excellent 0.07 to a highest value of 1.12. The latter was obtained with the strongest model base pimozide for which a new solid form was found in some samples. In conclusion, targeting specific molecular interactions with the solute combined with mechanistic modeling provides new tools to advance lipid-based drug delivery.

Artificial Neural Networks to Predict the Apparent Degree of Supersaturation in Supersaturated Lipid-Based Formulations: A Pilot Study

In response to the increasing application of machine learning (ML) across many facets of pharmaceutical development, this pilot study investigated if ML, using artificial neural networks (ANNs), could predict the apparent degree of supersaturation (aDS) from two supersaturated LBFs (sLBFs). Accuracy was compared to partial least squares (PLS) regression models. Equilibrium solubility in Capmul MCM and Maisine CC was obtained for 21 poorly water-soluble drugs at ambient temperature and 60 °C to calculate the aDS ratio. These aDS ratios and drug descriptors were used to train the ML models. When compared, the ANNs outperformed PLS for both sLBF_Capmul^MC (r² 0.90 vs. 0.56) and sLBF_Maisine^LC (r² 0.83 vs. 0.62), displaying smaller root mean square errors (RMSEs) and residuals upon training and testing. Across all the models, the descriptors involving reactivity and electron density were most important for prediction. This pilot study showed that ML can be employed to predict the propensity for supersaturation in LBFs, but even larger datasets need to be evaluated to draw final conclusions.

Rational Selection of Bio-Enabling Oral Drug Formulations - A PEARRL Commentary

New drug candidates often require bio-enabling formation technologies such as lipid-based formulations, solid dispersions, or nanosized drug formulations. Development of such more sophisticated delivery systems generally requires higher resource investment compared to a conventional oral dosage form, which might slow down clinical development. To achieve the biopharmaceutical objectives while enabling rapid cost effective development, it is imperative to identify a suitable formulation technique for a given drug candidate as early as possible. Hence many companies have developed internal decision trees based mostly on prior organizational experience, though they also contain some arbitrary elements. As part of the EU funded PEARRL project, a number of new decision trees are here proposed that reflect both the current scientific state of the art and a consensus among the industrial project partners. This commentary presents and discusses these, while also going beyond this classical expert approach with a pilot study using emerging machine learning, where the computer suggests formulation strategy based on the physicochemical and biopharmaceutical properties of a molecule. Current limitations are discussed and an outlook is provided for likely future developments in this emerging field of pharmaceutics.