From Quantum Chemistry to Prediction of Drug Solubility in Glycerides

Graph Neural Networks for Predicting Solubility in Diverse Solvents Using MolMerger Incorporating Solute-Solvent Interactions

The prediction of solubility is a complex and challenging physicochemical problem that has tremendous implications for the chemical and pharmaceutical industry. Recent advancements in machine learning methods have provided a great scope for predicting the reliable solubility of a large number of molecular systems. However, most of these methods rely on using physical properties obtained from experiments and expensive quantum chemical calculations. Here, we developed a method that utilizes a graphical representation of solute-solvent interactions using "MolMerger," which captures the strongest polar interactions between molecules using Gasteiger charges and creates a graph incorporating the true nature of the system. Using these graphs as input, a neural network learns the correlation between the structural properties of a molecule in the form of node embedding and its physicochemical properties as the output. This approach has been used to calculate molecular solubility by predicting the Log solubility values of various organic molecules and pharmaceuticals in diverse sets of solvents.

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.

Lipid based formulations as supersaturating oral delivery systems: From current to future industrial applications

Lipid-based formulations, in particular supersaturated lipid-based formulations, are important delivery approaches when formulating challenging compounds, as especially low water-soluble compounds profit from delivery in a pre-dissolved state. In this article, the classification of lipid-based formulation is described, followed by a detailed discussion of different supersaturated lipid-based formulations and the recent advances reported in the literature. The supersaturated lipid-based formulations discussed include both the in situ forming supersaturated systems as well as the thermally induced supersaturated lipid-based formulations. The in situ forming drug supersaturation by lipid-based formulations has been widely employed and numerous clinically available products are on the market. There are some scientific gaps in the field, but in general there is a good understanding of the mechanisms driving the success of these systems. For thermally induced supersaturation, the technology is not yet fully understood and developed, hence more research is required in this field to explore the formulations beyond preclinical studies and initial clinical trials.

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.

COSMO Models for the Pharmaceutical Development of Parenteral Drug Formulations

The aqueous solubility of active pharmaceutical ingredients is one of the most important features to be considered during the development of parenteral formulations in the pharmaceutical industry. Computational modelling has become in the last years an integral part of pharmaceutical development. In this context, ab initio computational models, such as COnductor-like Screening MOdel (COSMO), have been proposed as promising tools for the prediction of results without the effective use of resources. Nevertheless, despite the clear evaluation of computational resources, some authors had not achieved satisfying results and new calculations and algorithms have been proposed over the years to improve the outcomes. In the development and production of aqueous parenteral formulations, the solubility of Active Pharmaceutical Ingredients (APIs) in an aqueous and biocompatible vehicle is a decisive step. This work aims to study the hypothesis that COSMO models could be useful in the development of new parenteral formulations, mainly aqueous ones.

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.

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.

Molecular Dynamics Simulations and Experimental Results Provide Insight into Clinical Performance Differences between Sandimmune® and Neoral® Lipid-Based Formulations

OBJECTIVE

Molecular dynamics (MD) simulations provide an in silico method to study the structure of lipid-based formulations (LBFs) and the incorporation of poorly water-soluble drugs within such formulations. In order to validate the ability of MD to effectively model the properties of LBFs, this work investigates the well-known cyclosporine A formulations, Sandimmune® and Neoral®. Sandimmune® exhibits poor dispersibility and its absorption from the gastrointestinal tract is enhanced when administered after food, whereas Neoral® disperses comparatively well and shows no food effect.

METHODS

MD simulations were performed of both LBFs to investigate the differences observed in fasted and fed conditions. These conditions were also tested using an in vitro experimental model of dispersion and digestion.

RESULTS

These MD simulations were able to show that the food effect observed for Sandimmune® can be explained by large changes in drug solubilization on addition of bile. In contrast, Neoral® is well dispersed in water or in simulated fasted conditions, and this dispersion is relatively unchanged on moving to fed conditions. These differences were confirmed using dispersion and digestion in vitro experimental model.

CONCLUSIONS

The current data suggests that MD simulations are a potential method to model the fate of LBFs in the gastrointestinal tract, predict their dispersion and digestion, investigate behaviour of APIs within the formulations, and provide insights into the clinical performance of LBFs.

Machine learning methods for prediction of food effects on bioavailability: A comparison of support vector machines and artificial neural networks

Despite countless advances in recent decades across various in vitro, in vivo and in silico tools, anticipation of whether a drug will show a human food effect (FE) remains challenging. One means to predict potential FE involves probing any dependence between FE and drug properties. Accordingly, this study explored the potential for two machine learning (ML) algorithms to predict likely FE. Using a collated database of drugs licensed from 2016-2020, drugs were classified into three groups; positive, negative or no FE. Greater than 250 drug properties were predicted for each drug which were used to train predictive models using Support Vector Machine (SVM) and Artificial Neural Network (ANN) algorithms. When compared, ANN outperformed SVM for FE classification upon training (82%, 72%) and testing (72%, 69%). Both models demonstrated higher FE prediction accuracy than the Biopharmaceutics Classification System (BCS) (46%). This exploratory work provided new insights into the connection between FE and drug properties as the Octanol Water Partition Coefficient (S+logP), Number of Hydrogen Bond Donors (HBD), Topological Polar Surface Area (T_PSA) and Dose (mg) were all significant for prediction. Overall, this study demonstrated the utility of ML to facilitate early anticipation of likely FE in pre-clinical development using four well-known drug properties.

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.

In Silico, In Vitro, and In Vivo Evaluation of Precipitation Inhibitors in Supersaturated Lipid-Based Formulations of Venetoclax

The concept of using precipitation inhibitors (PIs) to sustain supersaturation is well established for amorphous formulations but less in the case of lipid-based formulations (LBF). This study applied a systematic in silico–in vitro–in vivo approach to assess the merits of incorporating PIs in supersaturated LBFs (sLBF) using the model drug venetoclax. sLBFs containing hydroxypropyl methylcellulose (HPMC), hydroxypropyl methylcellulose acetate succinate (HPMCAS), polyvinylpyrrolidone (PVP), PVP-co-vinyl acetate (PVP/VA), Pluronic F108, and Eudragit EPO were assessed in silico calculating a drug–excipient mixing enthalpy, in vitro using a PI solvent shift test, and finally, bioavailability was assessed in vivo in landrace pigs. The estimation of pure interaction enthalpies of the drug and the excipient was deemed useful in determining the most promising PIs for venetoclax. The sLBF alone (i.e., no PI present) displayed a high initial drug concentration in the aqueous phase during in vitro screening. sLBF with Pluronic F108 displayed the highest venetoclax concentration in the aqueous phase and sLBF with Eudragit EPO the lowest. In vivo, the sLBF alone showed the highest bioavailability of 26.3 ± 14.2%. Interestingly, a trend toward a decreasing bioavailability was observed for sLBF containing PIs, with PVP/VA being significantly lower compared to sLBF alone. In conclusion, the ability of a sLBF to generate supersaturated concentrations of venetoclax in vitro was translated into increased absorption in vivo. While in silico and in vitro PI screening suggested benefits in terms of prolonged supersaturation, the addition of a PI did not increase in vivo bioavailability. The findings of this study are of particular relevance to pre-clinical drug development, where the high in vivo exposure of venetoclax was achieved using a sLBF approach, and despite the perceived risk of drug precipitation from a sLBF, including a PI may not be merited in all cases.

In-Silico Screening of Lipid-Based Drug Delivery Systems

PURPOSE

This work proposes an in-silico screening method for identifying promising formulation candidates in complex lipid-based drug delivery systems (LBDDS).

METHOD

The approach is based on a minimum amount of experimental data for API solubilites in single excipients. Intermolecular interactions between APIs and excipients as well as between different excipients were accounted for by the Perturbed-Chain Statistical Associating Fluid Theory. The approach was applied to the in-silico screening of lipid-based formulations for ten model APIs (fenofibrate, ibuprofen, praziquantel, carbamazepine, cinnarizine, felodipine, naproxen, indomethacin, griseofulvin and glibenclamide) in mixtures of up to three out of nine excipients (tricaprylin, Capmul MCM, caprylic acid, Capryol™ 90, Lauroglycol™ FCC, Kolliphor TPGS, polyethylene glycol, carbitol and ethanol).

RESULTS

For eight out of the ten investigated model APIs, the solubilities in the final formulations could be enhanced by up to 100 times compared to the solubility in pure tricaprylin. Fenofibrate, ibuprofen, praziquantel, carbamazepine are recommended as type I formulations, whereas cinnarizine and felodipine showed a distinctive solubility gain in type II formulations. Increased solubility was found for naproxen and indomethacin in type IIIb and type IV formulations. The solubility of griseofulvin and glibenclamide could be slightly enhanced in type IIIb formulations. The experimental validation agreed very well with the screening results.

CONCLUSION

The API solubility individually depends on the choice of excipients. The proposed in-silico-screening approach allows formulators to quickly determine most-appropriate types of lipid-based formulations for a given API with low experimental effort. Graphical abstract.

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.

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

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