A comparison of USP 2 and µDISS Profiler™ apparatus for studying dissolution phenomena of ibuprofen and its salts.

BACKGROUND: Pharmaceutical salts of poorly soluble drugs typically dissolve faster than their corresponding free acid or base, resulting in supersaturation under some circumstances. The key questions relevant to drug bioavailability "does the salt invoke the supersaturated state?" and, if so, "does precipitation occur?" remain. To answer these questions, different types of dissolution equipment are often used at different stages of the development process. AIM: To compare the dissolution behaviour of ibuprofen and its sodium and lysine salts in the USP 2 apparatus and the µDISS Profiler™ apparatus. The dissolution, supersaturation of the salt forms and precipitation to the free acid of ibuprofen were characterized along with the dissolution of the free acid form. METHODS: Media containing different concentrations of the salt-forming counterions - sodium and lysine - were used to investigate the influence of the type of dissolution apparatus used for the study on dissolution, supersaturation and precipitation behaviour. KEY RESULTS: Supersaturation was observed for both the sodium and lysinate salts of ibuprofen in all USP 2 apparatus and µDISS Profiler™ experiments. However, precipitation tended to be far greater in the µDISS Profiler™ than in the USP 2 apparatus. The difference was most pronounced in pH 4.5 acetate buffer, in which precipitation was observed exclusively in experiments with the µDISS Profiler™. CONCLUSION: Choice of dissolution apparatus can affect the dissolution/supersaturation/precipitation characteristics of pharmaceutical salts. This has to be carefully taken into account when investigating salts over different stages of pharmaceutical research and development.

Mechanistically transparent models for predicting aqueous solubility of rigid, slightly flexible, and very flexible drugs (MW<2000) Accuracy near that of random forest regression.

Yalkowsky's General Solubility Equation (GSE), with its three fixed constants, is popular and easy to apply, but is not very accurate for polar, zwitterionic, or flexible molecules. This review examines the findings of a series of studies, where we have sought to come up with a better prediction model, by comparing the performances of the GSE to Abraham's Solvation Equation (ABSOLV), and Random Forest regression (RFR) machine-learning (ML) method. Large, well-curated aqueous intrinsic solubility databases are available. However, drugs may be sparsely distributed in chemical space, concentrated in clusters. Even a large database might overlook some regions. Test compounds from under-represented portions of space may be poorly predicted, as might be the case with the 'loose' set of 32 drugs in the Second Solubility Challenge (2020). There appears to be still a need for better coverage of drug space. Increasingly, current trends in predictions of solubility use calculated input descriptors, which may be an advantage for exploring properties of molecules yet to be synthesized. The risk may be that overall prediction approaches might be based on accumulated uncertainty. The increasing use of ML/AI methods can lead to accurate predictions, but such predictions may not readily suggest the strategies to pursue in selecting yet-to-be-synthesized compounds. Based on our latest findings, we recommend predictions based on both 'grouped' ABSOLV(GRP) and 'Flexible Acceptor' GSE(Φ,B) models with the provided best-fit parameters, where Φ is the Kier molecular flexibility index and B is the Abraham H-bond acceptor strength. For molecules with Φ < 11, the prudent choice is to pick the Consensus Model, the average of ABSOLV(GRP) and GSE(Φ,B). For more flexible molecules, GSE(Φ,B) is recommended.

Anomalous salting-out, self-association and pKa effects in the practically-insoluble bromothymol blue.

Background and Purpose: The widely-used and practically insoluble diprotic acidic dye, bromothymol blue (BTB), is a neutral molecule in strongly acidic aqueous solutions. The Schill (1964) extensive solubility-pH measurement of bromothymol blue in 0.1 and 1.0 M NaCl solutions, with pH adjusted with HCl from 0.0 to 5.4, featured several unusual findings. The data suggest that the difference in solubility of the neutral-form molecule in 1M NaCl is more than 0.7 log unit lower than the solubility in pure water. This could be considered as uncharacteristically high for a salting-out effect. Also, the study reported two apparent values of pKa1, 1.48 and 1.00, in 0.1 M and 1.0 M NaCl solutions, respectively. The only other measured value found for pKa1 in the literature is -0.66 (Gupta and Cadwallader, 1968). Experimental Approach: It was reasoned that the there can be only a single pKa1 for BTB. Also, it was hypothesized that salting-out alone might not account for such a large difference in solubility observed at the two levels of salt. A generalized mass action approach incorporating activity corrections for charged species using the Stokes-Robinson hydration equation and for neutral species using the Setschenow equation, was selected to analyze the Schill solubility-pH data to seek a rationalization of these unusual results. Key Results: BTB reveals complex speciation chemistry in saturated aqueous solutions which had been poorly understood for many years. The appearance of two different values of pKa1 at different levels of NaCl and the anomalously high value of the empirical salting-out constant could be rationalized to normal values by invoking the formation of a very stable neutral dimer (log K2 = 10.0 ± 0.1 M-1). A 'normal' salting-out constant, 0.25 M-1 was then derived. It was also possible to estimate the 'self-interaction' constant. The data analysis in the present study critically depended on the pKa1 = -0.66 reported by Gupta and Cadwallader. Conclusion: A more reasonable salting-out constant and a consistent single value for pKa1 have been determined by considering a self-interacting (aggregation) model involving an uncharged form of the molecule, which is likely a zwitterion, as suggested by literature spectrophotometric studies.

Clofazimine pKa Determination by Potentiometry and Spectrophotometry: Reverse Cosolvent Dependence as an Indicator of the Presence of Dimers in Aqueous Solutions.

The weakly basic antibiotic and anti-inflammatory drug, clofazimine (CFZ), was first described in 1957. It has been used therapeutically, most notably in the treatment of leprosy. However, the compound is extremely insoluble in aqueous media, and, indeed, there is poor consensus about what its intrinsic solubility is since the reported values range from 0.04 to 11 ng/mL. To understand the speciation and solubilization of CFZ as a function of pH, it is of paramount importance to know the true aqueous pKa. However, there is also poor consensus about the value of the pKa (reported measured values range from 6.08 to 9.11). In the present study, we report the determination of the CFZ ionization constant using two independent techniques. A state-of-the-art potentiometric analysis was performed, drawing on titration data in methanol-water solutions (46-75 wt % MeOH) of CFZ, using the bias-reducing consensus of two different procedures of extrapolating the apparent psKa values to zero cosolvent to approximate the true aqueous pKa as 9.43 ± 0.12 (25 °C, I = 0.15 M reference ionic strength). In parallel, spectrophotometric UV/vis titration data were acquired (250-600 nm at different pH) in 10 mM HEPES buffer solutions containing up to 54 wt % MeOH. The alternating least squares (ALS) method was used in the analysis of the absorbance-pH spectra. Uncharacteristically, the cosolvent UV/vis data in our study showed reverse cosolvent dependence (apparent pKa values increased with increasing cosolvent) which could be explained by a dimerization of the free base. The analysis of UV/vis data obtained from 54 wt % MeOH-water solution containing 20 µM CFZ yielded the apparent pKa 9.51 ± 0.17 (I ≈ 0.005 M). To assess whether self-assembly of CFZ was energetically feasible, density functional theory (DFT) calculations were used to study the putative CFZ dimers in aqueous and methanol media. The DFT-optimized geometries and infrared spectra of CFZ dimers using water and methanol as solvents were calculated and analyzed. Based on the lack of negative frequencies in calculated infrared spectra, it was confirmed that optimized geometries correspond to the true energetic minima. Visual analysis of optimized structures indicates the presence of stacking interactions between two CFZ molecules. The protonation site (the imine nitrogen atom) was determined by 1H NMR spectroscopy.

Understanding the pH Dependence of Supersaturation State-A Case Study of Telmisartan.

Creating supersaturating drug delivery systems to overcome the poor aqueous solubility of active ingredients became a frequent choice for formulation scientists. Supersaturation as a solution phenomenon is, however, still challenging to understand, and therefore many recent publications focus on this topic. This work aimed to investigate and better understand the pH dependence of supersaturation of telmisartan (TEL) at a molecular level and find a connection between the physicochemical properties of the active pharmaceutical ingredient (API) and the ability to form supersaturated solutions of the API. Therefore, the main focus of the work was the pH-dependent thermodynamic and kinetic solubility of the model API, TEL. Based on kinetic solubility results, TEL was observed to form a supersaturated solution only in the pH range 3-8. The experimental thermodynamic solubility-pH profile shows a slight deviation from the theoretical Henderson-Hasselbalch curve, which indicates the presence of zwitterionic aggregates in the solution. Based on pKa values and the refined solubility constants and distribution of macrospecies, the pH range where high supersaturation-capacity is observed is the same where the zwitterionic form of TEL is present. The existence of zwitterionic aggregation was confirmed experimentally in the pH range of 3 to 8 by mass spectrometry.

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, log10 S 0, 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 S 0 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-pS 0 database (nearly 400 added log10 S 0 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.

Integration of In Silico, In Vitro and In Situ Tools for the Preformulation and Characterization of a Novel Cardio-Neuroprotective Compound during the Early Stages of Drug Development.

The main aim of this work is the biopharmaceutical characterization of a new hybrid benzodiazepine-dihydropyridine derivative, JM-20, derived with potent anti-ischemic and neuroprotective effects. In this study, the pKa and the pH-solubility profile were experimentally determined. Additionally, effective intestinal permeability was measured using three in vitro epithelial cell lines (MDCK, MDCK-MDR1 and Caco-2) and an in situ closed-loop intestinal perfusion technique. The results indicate that JM-20 is more soluble at acidic pH (9.18 ± 0.16); however, the Dose number (Do) was greater than 1, suggesting that it is a low-solubility compound. The permeability values obtained with in vitro cell lines as well as with the in situ perfusion method show that JM-20 is a highly permeable compound (Caco-2 value 3.8 × 10-5). The presence of an absorption carrier-mediated transport mechanism was also demonstrated, as well as the efflux effect of P-glycoprotein on the permeability values. Finally, JM-20 was provisionally classified as class 2 according to the biopharmaceutical classification system (BCS) due to its high intestinal permeability and low solubility. The potential good oral absorption of this compound could be limited by its solubility.

Nortriptyline Hydrochloride Solubility-pH Profiles in a Saline Phosphate Buffer: Drug-Phosphate Complexes and Multiple pHmax Domains with a Gibbs Phase Rule "Soft" Constraints.

The solubility of a model basic drug, nortriptyline (Nor), was investigated as a function of pH in phosphate and/or a chloride-containing aqueous suspension using experimental practices recommended in the previously published "white paper" (Avdeef et al., 2016). The pH-Ramp Shake-Flask (pH-RSF) method, introduced in our earlier work (Markovic et al., 2019), was applied. An improved and more detailed experimental design of the Nor solubility measurement allowed us to exploit the full capacity of the pH-RSF method. Complex equilibria in the aqueous phase (cationic and anionic complex formation between Nor and the phosphate) and solid-phase transformations (Nor free base, 1:1 Nor hydrochloride salt, 1:1 and 1:2 Nor phosphate salts) were characterized by a detailed analysis of the solubility measurements using the computer program pDISOL-X. The solid phases were characterized by thermogravimetric analysis, differential scanning calorimetry, powder X-ray diffraction, and elemental analyses. The results of the present investigation illustrate the influence of competing counterions, such as buffering agents, complexing agents, salt coformers, tonicity adjusters, and so forth, on the aqueous solubility of drugs and interconversion of salts. Careful attention given to these factors can be helpful in the formulation of drug products.

Salt Solubility and Disproportionation - Uses and Limitations of Equations for pHmax and the In-silico Prediction of pHmax.

A multiphasic mass action equilibrium model was used to study the phase properties near the critical pH ('pHmax') in an acid-base transformation of a solid drug salt into its corresponding solid free base form in pure water slurries. The goal of this study was to better define the characteristics of disproportionation of pharmaceutical salts, objectively (i) to classify salts as µ-type (microclimate stable) or δ-type (disproportionation prone) based on the relationship between the calculated pHmax and the calculated pH of the saturated salt solution, (ii) to compare the distribution of µ/δ-type salts to predictions from the disproportionation potential equation introduced by Merritt et al.,20 (iii) to determine if the intrinsic solubility of the free base, S0, can be predicted from the measured µ-type salt solubility as a means of estimating the value of pHmax, (iv) to determine S0 directly from the measured δ-type salt solubility, and (v) to address some of the limitations of the equations commonly used to calculate pHmax. When the salt solubility is measured for a basic API (pKa of which is known), but the experimental value of S0 is unavailable, a potentially useful simple screen for disproportionation is still possible, since pHmax can be estimated from a 'µ-predicted' (objective iii) or 'δ-measured' S0 (objective iv). Twelve model weak base API were selected in the study. For each API, 2-17 different salt forms with reported salt solubilities in distilled water were sourced from the literature. In all, 73 salt solubility values based on 29 different salt-forming acids comprise the studied set. All the corresponding free base solubility values were available. The pKa values for all the acids and bases studied are generally well known. For each API salt, an acid-base titration simulation was performed, anchored to the measured salt solubility value, using the general mass action analysis program pDISOL-X. The log S-pH profiles were drawn out by analytic continuity from pH 0 to 13, as described in detail previously.24 Potentially useful in-silico models were developed that correlate pS0 to linear functions of the salt solubility in water, pSw, the partition coefficient of the salt-forming acid (log POCTacid) and the melting point (mp) of the drug salt, thereby enabling the derivation of the approximate pHmax value from the predicted pS0.

Is equilibrium slurry pH a good surrogate for solid surface pH during drug dissolution?

The purpose of the present study was to investigate the suitability of equilibrium slurry pH (pHeq) as a surrogate of solid surface pH during drug dissolution (pH0). A comprehensive calculation scheme for pHeq and pH0 was formalized based on the principle of charge neutrality (equilibrium charge neutrality for pHeq and charge flux neutrality for pH0). The formalized scheme was then used to investigate the validity of pH0 ≈ pHeq approximation. The approximation of pH0 ≈ pHeq was suggested to be accurate for small molecules (ca. MW = 150) in high concentration buffer media (ca. buffer capacity = 30 mM/ΔpH). In addition, it is valid provided no precipitation of its free form for salts (vice versa for free forms) in both the slurry pH measurement and at the dissolving drug surface. The formalized calculation scheme is simple and applicable to free and salt form drugs in unbuffered and buffered media including bicarbonate buffer. The computational expense is very small so that it is applicable to various computer simulations such as biopharmaceutics modeling and simulation.

Disproportionation of Pharmaceutical Salts: pHmax and Phase-Solubility/pH Variance.

A multiphasic mass action equilibrium model is used to show that the critical pH in the acid-base disproportionation of a solid salt into its corresponding solid free-base form in aqueous suspensions, widely known as "pHmax", is incompletely interpreted. It is shown that the traditional thermodynamic model does not predict the invariance of pH and solubility during the salt-to-free-base conversion process in an alkalimetric titration. Rather, the conversion entails a range of pH and solubility values, depending on the amount of added excess salt above that needed to form a saturated solution. A more precise definition is proposed for pHmax (pH at the maximum solubility of a eutectic mixture), and three new terms are introduced: pHmin (pH at the minimum solubility of the eutectic mixture), pHδ (disproportionation invariant pH within the eutectic, i.e., the equilibrium pH of a spontaneously disproportionating salt slurry), and pHγ (Gibbs pH at which disproportionation yields equimolar amounts of excess salt and excess free-base solids within the eutectic). Two test compounds with reported multiple salts and the free-base solubility values were selected to illustrate the expanded concepts, the bases WR-122455 and RPR-127963. Also, dibasic calcium phosphate was selected as an ionizable test excipient. The salts are designated in the study as µ-type, when they are thermodynamically stable with respect to spontaneous disproportionation in pure water (e.g., WR-122455 salts), and δ-type, when they are predicted to spontaneously disproportionate in pure water (e.g., RPR-127963 salts). In an alkalimetric titration, when an acidified suspension of a salt of a basic molecule is titrated with a strong base (e.g., NaOH), the passage across the eutectic domain (bounded by pHmax and pHmin) is often characterized by (a) minimum in ionic strength either at pHmax (µ-type salt) or pHδ (δ-type salt) and (b) maximum buffer capacity at pHγ. When the alkalimetric titration is performed with a large excess of added salt, a wide eutectic domain forms: pHmax and pHδ remain invariant, but pHmin and pHγ shift substantially in pH. The acid-base mass action model described here can be useful in predicting the stability of salt formulations in mixtures with excipients that can act as pH modifiers.

Ionizable Drug Self-Associations and the Solubility Dependence on pH: Detection of Aggregates in Saturated Solutions Using Mass Spectrometry (ESI-Q-TOF-MS/MS).

It is widely accepted that solubility-pH profiles of ionizable compounds follow the Henderson-Hasselbalch equation. However, several studies point out that compounds often undergo additional processes in saturated solutions, such as sub-micellar oligomerization, micellar aggregation, or drug-buffer complexation among others, which make the experimental profiles deviate from the behavior predicted by the Henderson-Hasselbalch equation. Often, the presence of additional processes is supported by the analysis of experimental data through solubility computer programs. However, the purpose of this work is to experimentally prove the aggregation phenomena for a series of bases for which deviations from the theoretical profile have been observed. To this end, five monoprotic bases (lidocaine, maprotiline, cyproheptadine, bupivacaine, and mifepristone) susceptible to form ionic aggregates in solution have been selected, and mass spectrometry has been the technique of choice to prove the presence of aggregation. High declustering potentials have been applied to prevent aggregates from forming in the ionization source of the mass spectrometer. In addition, haloperidol has been used as a negative control since according to its profile, it is not suspected to form ionic aggregates. In all instances, except for haloperidol, the analysis of the saturated solutions revealed the presence of mixed-charged dimers (aggregates formed by a neutral molecule and a charged one) and even trimers in the case of mifepristone and bupivacaine. For lidocaine, the most soluble of the compounds, the presence of neutral aggregates was also detected. These experiments support the hypothesis that the simple Henderson-Hasselbalch equation may explain the solubility-pH behavior of certain compounds, but it can be somewhat inaccurate in describing the behavior of many other substances.

Do you know your r2?

The prediction of solubility of drugs usually calls on the use of several open-source/commercially-available computer programs in the various calculation steps. Popular statistics to indicate the strength of the prediction model include the coefficient of determination (r2), Pearson's linear correlation coefficient (rPearson), and the root-mean-square error (RMSE), among many others. When a program calculates these statistics, slightly different definitions may be used. This commentary briefly reviews the definitions of three types of r2 and RMSE statistics (model validation, bias compensation, and Pearson) and how systematic errors due to shortcomings in solubility prediction models can be differently indicated by the choice of statistical indices. The indices we have employed in recently published papers on the prediction of solubility of druglike molecules were unclear, especially in cases of drugs from 'beyond the Rule of 5' chemical space, as simple prediction models showed distinctive 'bias-tilt' systematic type scatter.

"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 âˆ¼ 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.

The Critical Role of Passive Permeability in Designing Successful Drugs.

Passive permeability is a key property in drug disposition and delivery. It is critical for gastrointestinal absorption, brain penetration, renal reabsorption, defining clearance mechanisms and drug-drug interactions. Passive diffusion rate is translatable across tissues and animal species, while the extent of absorption is dependent on drug properties, as well as in vivo physiology/pathophysiology. Design principles have been developed to guide medicinal chemistry to enhance absorption, which combine the balance of aqueous solubility, permeability and the sometimes unfavorable compound characteristic demanded by the target. Permeability assays have been implemented that enable rapid development of structure-permeability relationships for absorption improvement. Future advances in assay development to reduce nonspecific binding and improve mass balance will enable more accurately measurement of passive permeability. Design principles that integrate potency, selectivity, passive permeability and other ADMET properties facilitate rapid advancement of successful drug candidates to patients.

Findings of the Second Challenge to Predict Aqueous Solubility.

Ten years ago, we issued an open prediction challenge to the cheminformatics community: would participants be able to predict the equilibrium intrinsic solubilities of 32 druglike molecules using only a high-precision (CheqSol instrument, performed in one laboratory) set of 100 compounds as a training set? The "solubility challenge" was a widely recognized success and spurred many discussions about the prediction methods and quality of data. We revisited the competition a second time recently and challenged the community to a different challenge, not a blind test this time but using a larger test set of molecules, gathered and curated from published sources (mostly "gold standard" saturation shake-flask measurements), where the average interlaboratory reproducibility for the molecules was estimated to be ∼0.17 log unit. Also, a second test set was included, comprising "contentious" molecules, the reported (mostly shake-flask) solubility of which had higher average uncertainty, ∼0.62 log unit. In the second competition, the participants were invited to use their own training sets, provided that the training sets did not contain any of the test set molecules. We were motivated to revisit the competition to (1) examine to what extent computational methods had improved in 10 years, (2) verify that data quality may not be the main limiting factor in the accuracy of the prediction method, and (3) attempt to seek a relationship between the makeup of the training set data and the prediction outcome.

Potentiometric CheqSol and standardized shake-flask solubility methods are complimentary tools in physicochemical profiling.

The solubility of three drugs (glimepiride, pioglitazone, sibutramine) with different acid/base properties and expected supersaturation behavior was examined in detail using the shake-flask (SF) and potentiometric (CheqSol) methods. Both uncharged (free) species and hydrochloride salts were used as starting materials. On the one hand, the SF method provided information about the thermodynamic solubility at any pH value, including the counterion-dependent solubility of ionic species. Additionally, this method easily allowed the identification of the solid phase in equilibrated solutions by powder X-ray diffraction, and the detection and quantification of aggregation and complexation reactions. On the other hand, CheqSol method permitted the measurement of the equilibrium solubility of neutral species, the observation of changes in solid forms, and the extent and duration of supersaturation (kinetic solubility) for "chaser" compounds. The combined information from both methods gave an accurate picture of the solubility behavior of the studied drugs.

Prediction of aqueous intrinsic solubility of druglike molecules using Random Forest regression trained with Wiki-pS0 database.

The accurate prediction of solubility of drugs is still problematic. It was thought for a long time that shortfalls had been due the lack of high-quality solubility data from the chemical space of drugs. This study considers the quality of solubility data, particularly of ionizable drugs. A database is described, comprising 6355 entries of intrinsic solubility for 3014 different molecules, drawing on 1325 citations. In an earlier publication, many factors affecting the quality of the measurement had been discussed, and suggestions were offered to improve ways of extracting more reliable information from legacy data. Many of the suggestions have been implemented in this study. By correcting solubility for ionization (i.e., deriving intrinsic solubility, S0) and by normalizing temperature (by transforming measurements performed in the range 10-50 °C to 25 °C), it can now be estimated that the average interlaboratory reproducibility is 0.17 log unit. Empirical methods to predict solubility at best have hovered around the root mean square error (RMSE) of 0.6 log unit. Three prediction methods are compared here: (a) Yalkowsky's general solubility equation (GSE), (b) Abraham solvation equation (ABSOLV), and (c) Random Forest regression (RFR) statistical machine learning. The latter two methods were trained using the new database. The RFR method outperforms the other two models, as anticipated. However, the ability to predict the solubility of drugs to the level of the quality of data is still out of reach. The data quality is not the limiting factor in prediction. The statistical machine learning methodologies are probably up to the task. Possibly what's missing are solubility data from a few sparsely-covered chemical space of drugs (particularly of research compounds). Also, new descriptors which can better differentiate the factors affecting solubility between molecules could be critical for narrowing the gap between the accuracy of the prediction models and that of the experimental data.

Can small drugs predict the intrinsic aqueous solubility of 'beyond Rule of 5' big drugs?

The aim of the study was to explore to what extent small molecules (mostly from the Rule of 5 chemical space) can be used to predict the intrinsic aqueous solubility, S0, of big molecules from beyond the Rule of 5 (bRo5) space. It was demonstrated that the General Solubility Equation (GSE) and the Abraham Solvation Equation (ABSOLV) underpredict solubility in systematic but slightly ways. The Random Forest regression (RFR) method predicts solubility more accurately, albeit in the manner of a 'black box.' It was discovered that the GSE improves considerably in the case of big molecules when the coefficient of the log P term (octanol-water partition coefficient) in the equation is set to -0.4 instead of the traditional -1 value. The traditional GSE underpredicts solubility for molecules with experimental S0 < 50 µM. In contrast, the ABSOLV equation (trained with small molecules) underpredicts the solubility of big molecules in all cases tested. It was found that the errors in the ABSOLV-predicted solubilities of big molecules correlate linearly with the number of rotatable bonds, which suggests that flexibility may be an important factor in differentiating solubility of small from big molecules. Notably, most of the 31 big molecules considered have negative enthalpy of solution: these big molecules become less soluble with increasing temperature, which is compatible with 'molecular chameleon' behavior associated with intramolecular hydrogen bonding. The X-ray structures of many of these molecules reveal void spaces in their crystal lattices large enough to accommodate many water molecules when such solids are in contact with aqueous media. The water sorbed into crystals suspended in aqueous solution may enhance solubility by way of intra-lattice solute-water interactions involving the numerous H-bond acceptors in the big molecules studied. A 'Solubility Enhancement-Big Molecules' index was defined, which embodies many of the above findings.