International Journal of Pharmaceutics 540 (2018) 185–193

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International Journal of Pharmaceutics

journal homepage: www.elsevier.com/locate/ijpharm

Computational prediction of drug in water-based systems: T Qualitative and quantitative approaches used in the current drug discovery and development setting ⁎ Christel A.S. Bergström , Per Larsson

Department of Pharmacy, Uppsala University, Biomedical Centre P.O. Box 580, SE-751 23 Uppsala, Sweden

ARTICLE INFO ABSTRACT

Keywords: In this review we will discuss recent advances in computational prediction of solubility in water-based . Computational prediction Our focus is set on recent advances in predictions of biorelevant solubility in media mimicking the human Solubility intestinal fluids and on new methods to predict the thermodynamic cycle rather than prediction of solubility in Solid state pure water through quantitative structure property relationships (QSPR). While the literature is rich in QSPR Intestinal fluid models for both solubility and melting point, a physicochemical property strongly linked to the solubility, recent Quantitative structure property relationships advances in the modelling of these properties make use of theory and computational simulations to better predict Molecular dynamics simulations these properties or processes involved therein (e.g. solid state crystal lattice packing, dissociation of molecules from the lattice and ). This review serves to provide an update on these new approaches and how they can be used to more accurately predict solubility, and also importantly, inform us on molecular interactions and processes occurring during drug dissolution and solubilisation.

1. Background precipitation it is much more difficult to interpret the results. This may lead to false conclusions being drawn from the assay and the “false Poor drug solubility is one of the main obstacles in the drug dis- positives” of the assay pushing the compound forward in the discovery covery and development process and was recently identified to be process. In the worst case scenario, this could lead to a poor pharma- strongly related to the choice of target explored. (Bergstrom et al., cological and/or ADMET profile of the chosen compound. Indeed, 2016) Solubility is the driving force for absorption and acceptable so- based on Pfizer clinical trial data, Morgan and colleagues have identi- lubility in the intestinal fluid is a prerequisite for achieving sufficiently fied that, to a large extent, failure of drugs in clinical trials could be high drug blood to obtain a therapeutic effect when related to poor efficacy (Morgan et al., 2012). More importantly, the systemic effects are warranted. The solubility of a compound affects its authors questioned whether the target had been explored and validated absorption, distribution, metabolism, excretion and toxicity (ADMET) correctly during the drug discovery stage. As an example, promiscuous profile. Only when the ADMET properties of a drug-like compound are compounds may aggregate in in vitro buffers and by this mechanism of a sufficiently high quality, and when the target has been validated, then cause a non-competitive inhibition, whereas they are diluted in the can the compound be developed into a new medication (Cook et al., blood stream and the much lower of the free fraction 2014; Morgan et al., 2012). Since the molecular requirements of some does not result in target engagement. targets inevitably result in poor solubility of the ligands, early aware- Since solubility has a profound impact on all the factors that are ness of this fact by the medicinal chemistry team is crucial for them to important for decision making with respect to the fate of the compound, make the right decisions on which analyses and assays to perform. much effort has been directed to developing tools applicable to pre- Understanding the risk of poor solubility is also important for analysing dicting drug solubility (Delaney, 2005). Various in vitro assays have the results of ADMET assays, since there is potential to identify false been developed, ranging from high throughput assays based on titra- readouts as an effect of precipitation or aggregation of the drug com- tions of DMSO stock and identification of the precipitations as pound (Coan and Shoichet, 2008; Pohjala and Tammela, 2012). If the a qualitative screen providing yes/no answers to highly accurate small compound is precipitating, it is easy to identify why the in vitro screen scale thermodynamic measurements (Bergstrom et al., 2014). Typically has failed. However, if there is no visible sign of aggregation and/or these studies have focussed on solubility in pure water or in non-

⁎ Corresponding author. E-mail address: [email protected] (C.A.S. Bergström). https://doi.org/10.1016/j.ijpharm.2018.01.044 Received 10 November 2017; Received in revised form 20 January 2018; Accepted 22 January 2018 Available online 06 February 2018 0378-5173/ © 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/). C.A.S. Bergström, P. Larsson International Journal of Pharmaceutics 540 (2018) 185–193

Fig. 1. The thermodynamics behind the solubility process. The drug molecule needs to dissociate from its solid form (step 1) and the tight structure of the water needs to form a cavity large enough to incorporate the drug molecule (step 2). Finally, the drug molecule is inserted into the water where it interacts with the surrounding water molecules (step 3). complex buffers. However, over the last two decades a large number of aqueous solubility. We will discuss how these findings can be applied in modified media have also been developed, with the aim of better pre- the drug discovery and development settings both as tools for pre- dicting the intestinal solubility of new compounds in vivo (Fuchs et al., dicting solubility and as indicators of whether the compound will make 2015; Galia et al., 1998; Jantratid et al., 2008). Recently also media it to the market after extensive formulation strategies are applied. The mimicking the interindividual variability of the composition of in- review will not focus on statistical approaches to solubility predictions; testinal fluids in fasted and fed state have been explored for their in- the interested reader is referred to several other reviews within this fluence on drug solubility (Khadra et al., 2015; Madsen et al., 2018; area, e.g. (Delaney, 2005; Johnson and Zheng, 2006; Norinder and Perrier et al., 2017). These more biorelevant solvents include additives Bergstrom, 2006; Skyner et al., 2015). Instead, we will discuss new such as bile salts, , cholesterol and to reflect fasted approaches recently presented for modelling properties of importance and fed intestinal states. Biorelevant dissolution media have so far for solubility. These include models revealing molecular features that mainly been used in the early phases of development and have not to indicate solid-state-limited versus solvation-limited solubility, models any major extent been investigated for their potential as a base for that include the current status of prediction of biorelevant solubility computational predictions. Instead, in silico models developed for pre- reflecting the intestinal environment, models for predicting crystal diction of solubility are based on the solubility of the neutral (non- structure and solid-state properties such as melting point (Tm) and ionised) compound in pure water (see e.g. examples provided in models that make use of the thermodynamic cycle theory. The extent to Norinder and Bergstrom (2006)). There are several reasons for taking which solubility and solubility changes can be calculated from first this approach, including the complexity of the solubility process, since principles is also addressed. both dissociation from the solid state and solvation of the molecule by the studied influence the final solubility (this is further dis- 2. Molecular properties resulting in poor aqueous solubility cussed in Section 2, and Fig. 1). This, together with the difficulty of predicting ionisation constants for complex protolytes, and the diffi- The thermodynamics behind solubility are shown in Fig. 1. In order culties associated with forecasting the influence of additives (such as for the molecule to dissolve in the aqueous solvent, it must be able to the bile salts, phospholipids and cholesterol included in simulated in- dissociate from its crystal lattice. This process is dependent on the in- testinal fluids) on the solubility, has made pure water adjusted to a pH termolecular interactions between the molecules in the crystal lattice. allowing the non-ionised species to be determined the first choice for Compounds with strong intermolecular bonds and/or complex inter- computational modelling. Unfortunately, several of the datasets used, action patterns with a large number of interaction points between the or large fractions thereof, do not reflect the drug-like chemical space. molecules in the crystal lattice often show a limited capacity to dis- These datasets are repeatedly used and it is not always possible to sociate from the solid form. These compounds are sometimes referred to evaluate the experimental quality of the data. For instance, one of the as ‘brick dust’ molecules, to demonstrate the poor solubility of a strong most repeatedly used datasets includes experimental data ranging from (stone-like) solid structure. Typically T is used to identify whether a -11.62 to 2.77 on a log molar scale, corresponding to 2 pM and 589 M m compound shows solid-state-limited solubility (i.e. is a brick dust (Kühne et al., 1995). The exact quality of these data can be questioned, compound). A T of 200 °C has been identified as the cut-off value; for since the pM concentrations need a very sensitive analytical method to m compounds that melt at higher temperatures, the crystal lattice will be trustworthy and the high end of the range corresponds to a solubility have a strong influence on the solubility (Bergstrom et al., 2016). For value greater than that of water in water (which is 55 M). Hence, if data these compounds, any formulation strategy that changes the solid like these are used in computational modelling, the accuracy of the crystal form (e.g. using salts, cocrystals or amorphous systems) will be predictions could be improved by weighting the influence of the ob- useful for increasing the dissolution rate and achieving a greater ap- servation by the accuracy of the experimental data, in order not to let parent solubility (Edueng et al., 2017; Elder et al., 2013; Kuminek et al., poor experimental data influence the final model. 2016; Taylor and Zhang, 2016). While the compound needs to dis- In this review we will discuss computational models and modelling sociate from its crystal lattice, the surrounding solvent also needs to approaches that have identified the molecular features resulting in poor prepare for incorporating a new molecule. The larger the cavity needs

186 C.A.S. Bergström, P. Larsson International Journal of Pharmaceutics 540 (2018) 185–193 to be, the larger the energy penalty for the formation. Hence, molecular (Eq. (1)) and the knowledge that compounds with a logP of 2 or less will weight can be used as a simple physicochemical descriptor to reflect the tend to have solid-state-dependent solubility, then compounds with volume required of the cavity. In order to decrease the energy penalty extraordinarily high melting points (of about 325 °C) would be esti- associated with cavity formation, additives which loosen up the tight mated to have a solubility of about 30 µM. Secondly, we believe that water structure can be included in the solvent, resulting in an im- compounds which are solely solubility-limited because of their solid provement in the solubility of the molecules. Typically, such compo- state are terminated relatively early in the drug development process. nents are cosolvents (e.g. ethanol and polyethylenglycol 400). Finally, The lack of truly poorly soluble compounds with a lipophilicity value to be soluble, the dissociated free molecule needs to be inserted in the of < 2 is also shown in Fig. 3. This plot shows the general relationship solvent cavity. Hydrophobic compounds have a limited capacity to in- between the lipophilicity and solubility of 292 drugs. At a logP ≤ 2, teract with the water phase, in accordance with similia similibus sol- there were only a few compounds with solubility values < 100 µM. vuntur (like dissolves like), and these compounds are solubility-limited Hence, the possibility of analysing which molecular features drive poor by poor hydration. Poorly soluble compounds restricted in solubility by solubility truly originating from the synthesis of crystal structures that poor hydration are described in the popular scientific jargon as ‘grea- are too stable is currently limited, since relevant data are only sparsely seball’ molecules, due to their high hydrophobicity and lack of inter- publicly available. action with water. The molecular descriptor commonly used to describe the role of hydration is the partition coefficient between octanol and 3. Prediction of the solid state water (P), often presented as the log10 value (logP). LogP values of 2–3 have been recommended as the cut-off point for hydration becoming a One property that has been explored for its potential to be com- significant limitation for solubility; the higher the value the poorer the putationally predicted is the melting point, since such models would hydration (Bergstrom et al., 2016; Wassvik et al., 2008). It should be facilitate predictions of many other properties including the solubility noted that, for ionisable compounds, it is the corresponding logD value as described in Section 2 and presented in Eq. (1). The first model that (at the pH of interest) that should be greater than the logP cut-off value was built on a larger series of drug-like compounds (n = 277) was (Fagerberg and Bergstrom, 2015). Formulation strategies successful for published in 2003 and approached the problem by establishing quan- delivery of the solvation-limited compounds are -based formula- titative structure-property relationships (QSPRs) between calculated tions that are composed of lipids, and/or cosolvents (Feeney molecular descriptors and the melting point reported in Merck Index et al., 2016). Unfortunately, compounds that display both solid-state- (Bergstrom et al., 2003). Only the stable polymorph was predicted. and solvation-limited solubility also exist. These are compounds with These efforts resulted in RMSE-value of 35.1 °C when a consensus model high melting points and high logP values, and these compounds can be was established that made use of both 2D and 3D descriptors to cal- viewed as ‘anything’-phobic. These compounds typically aggregate or culate the Tm. In this particular study, PLS was used to establish the precipitate out of . Such compounds are truly difficult to ma- relationship. The same dataset has since then been used for further nipulate, even by altering the formulation, and are likely to produce development, however, the RMSE is still in the same ball park regard- concentrations in vivo that are too low to allow therapeutic effects. less of the molecular descriptors and the statistical methodology used The modified general solubility equation (GSE) established by Jain (McDonagh et al., 2015; Tetko et al., 2016). and Yalkowsky in 2001 allows the roles of logP and Tm in solubility to Recently, computational crystal structure prediction (CSP), i.e. be clarified (Jain and Yalkowsky, 2001). The GSE states that prediction of crystal lattice structure, has significantly advanced. These predictions have their basis in experimental data, usually obtained from logS=−0.5 0.01( Tm −− 25) logP (1) 0 measurements of single crystals but recently also proven to be possible where S0 is the intrinsic solubility, i.e. the solubility of the non-ionised to obtain from powders (Baias et al., 2013). CSP has also proven fea- (neutral) species. Making use of the GSE and hypothetical values for the sible to apply on larger and drug-like molecules (Jones et al., 2011; lipophilicity (logP of 2, 4 and 6) and melting point (Tm of 50, 150 and Kazantsev et al., 2011; Reilly et al., 2016; Santos et al., 2013). One 250 °C) can help identify which properties dominate the solubility means to arrive at computational predictions of crystal structure using (Wassvik et al., 2008). By this means, it was established that the solu- ab initio calculations is to perform Monte Carlo simulations with a bility of compounds with a logP < 2 is mainly dependent on the solid number of simulations are run starting from a random configuration of state. molecules in the simulation box. The ranking of the resulting packing is Multivariate data analysis making use of principal component thereafter performed by some sort of energy-based metric (Reilly et al., analysis (PCA) and projection to latent structures (PLS) of a number of 2016). However, all types of ab initio calculations are very time con- datasets enabled the identification of the molecular features resulting in suming, and especially so for drug-like compounds with higher mole- solid-state- versus solvation-limited solubility (Bergstrom et al., 2007; cular flexibility than typical model compounds used for the metho- Fagerberg et al., 2010; Wassvik et al., 2008; Zaki et al., 2010). Solva- dology development. Therefore other techniques have been explored. tion-limited compounds are lipophilic, relatively large molecules, and One approach that has shown promise is the solid state perturbation lack conjugated systems (Fig. 2). Many of these have been developed as where only the 2D structure of the drug is needed as input data in the oral dosage forms, however, dosage forms typically include several solid state prediction (Briggner et al., 2014). different excipients that may improve dissolution (disintegration and dispersion) and solubilisation (Bergstrom et al., 2007). This indicates 4. In silico models that include biorelevant solubility that an extensive drug development process would be required to bring these compounds to the market. In contrast, solid-state-limited com- Over the last two decades great efforts have been put into research pounds are often flat, typically with an extended ring structure, and on computational models for predicting aqueous solubility. This can be display high aromaticity. These molecular features are important for seen in the increased number of publications on the computational forming a more stable crystal lattice (Wassvik et al., 2008). prediction of solubility (Fig. 4). We will not go through all the strategies It should be noted, however, that while compounds described as used in detail with regard to algorithms and descriptors; instead the solvation-limited often display intrinsic solubility values in the lower reader is guided to other reviews where datasets, methodologies and nanomolar scale, none of the compounds included in the solid-state- descriptors are discussed (Delaney, 2005; Johnson and Zheng, 2006; limited dataset published by Wassvik et al. had solubility values in this Norinder and Bergstrom, 2006; Skyner et al., 2015). Herein we will range (Wassvik et al., 2008). The least soluble compound in that dataset present a few recent studies where in silico modelling has been used to was griseofulvin, which has a solubility of approximately 15 µM. There predict solubility in more biorelevant solvents. It should be noted that are two explanations for why this is the case. Firstly, if we use the GSE the response value (i.e. solubility) is commonly presented as the log10

187 C.A.S. Bergström, P. Larsson International Journal of Pharmaceutics 540 (2018) 185–193

Grease balls

Brick dust

Fig. 2. Typical greaseball and brick dust molecules. Solvation-limited compounds (‘greaseball molecules’) are large, show a high degree of flexibility and are highly lipophilic (Bergstrom et al., 2007). Solid-state-limited compounds (‘brick dust molecules’) are small in their structure, and quite large portions of the molecule are often flat and rigid (Wassvik et al., 2008).

2 20 R =0.54 18 0 16

14

12

-5 10

log S (M) 8

6

Number of publications 4

-10 2 -5 0 5 10 0 1997 2002 2007 2012 2017 log P Year Fig. 3. Relationship between lipophilicity and intrinsic solubility for 292 drugs. Data Fig. 4. Number of publications on computational prediction of solubility. The search was taken from Bergstrom et al. (2004). performed Oct 9, 2017 on PubMed, using a search string of “theoretical OR prediction OR in silico OR comput* AND aqueous solubility”. Thus the number of publications reflects value when developing in silico models. scientificefforts where computational methods have been used to different extents to The relationship between lipophilicity and the solubilization ratio understand processes, mechanisms and the impact of e.g. additives on solubility as well as (SR) in water-based solvents including surfactants is well-known and producing in silico models enabling quantitative predictions of solubility values. was first shown for the natural taurocholate by Mithani et al. (1996). This work showed a strong relationship between logP and the lipophilicity (logDpH6.5 and logDpH5.0) should be used instead of logP; SR (R2 of 0.99). The SR is described as: R2 increased from 0.32 to 0.74 when logD was used instead of logP. Lipophilicity has also been related to dissolution kinetics in FeSSIF SC SR = bs version 2 in a more qualitative manner (Gamsiz et al., 2010). When SCaq (2) logP < 1 (low lipophilicity), logP 1–4 (intermediate lipohilicity) and logP > 4 (high lipophilicity) were separated out, it was found that where SCbs is the solubilisation capacity of the bile salt (here taur- solubility and dissolution kinetics were greatly enhanced for highly li- ocholate) and SCaq is the solubilisation capacity of the water. This re- pophilic compounds (logP > 4), for which a dissolution rate up to 6- lationship was further explored by Fagerberg et al., who made use of fold higher was measured. However, it was also noted that improve- the measurements of ten structurally diverse compounds in the more ment in solubility was not always related to similarly strong improve- complex systems of fasted and fed state simulated intestinal fluids ments in dissolution kinetics. (FaSSIF and FeSSIF, respectively) (Fagerberg et al., 2010). These media The dataset studied for the dissolution rate mentioned above was differ from a pure bile salt system in that they also contain phospho- part of the dataset used by SimulationsPlus to establish their in silico lipids. FeSSIF has 5-fold higher concentrations of these additives than models for predicting solubility in biorelevant media (fasted-state si- does FaSSIF (Galia et al., 1998). Further, the pH differs between the two mulated gastric fluid (FaSSGF), FaSSIF and FeSSIF version 2). These media, with the pH of FaSSIF being 6.5 and that of FeSSIF 5.0. Based on models and datasets have not been fully published, but the models are these measured values it was suggested that the pH-dependent

188 C.A.S. Bergström, P. Larsson International Journal of Pharmaceutics 540 (2018) 185–193

Fig. 5. The thermodynamic cycle. The following abbreviations are used: ΔGsub = Gibbs free energy of sublimation; ΔGsolv = Gibbs free energy of solvation; ΔGhyd = Gibbs free energy of hydration; ΔGtr = Gibbs free energy of transfer.

available in the ADMET Predictor software. The manual for this soft- logSE=−×−×+×−×0.0678 0.1857 E 0.3963 S 0.5571 A 0.9423 B0 ware states that these models are based on 160 diverse drug-like +×1.1600 V (3) compounds. The models were developed using neural network metho- dology based on 2D molecular descriptors. Approximately 10% of the where E is the excess molar refractivity, S is the dipolarity/polarisa- compounds were used as a test set for each model developed bility, A is the hydrogen-bonding acidity, B0 is the hydrogen-bond ba- (n = 16–21, dependent on the media studied). The R2 of the training sicity and V is the McGowan characteristic volume. The model gave 2 sets was in the range of 0.71–0.76 and the root mean square error good results (R of 0.81 and mean absolute error (MAE) of 0.299) but (RMSE) was 0.47–0.50 logS (mg/mL) units. There are only two pub- was not challenged by application of external test sets. A similar ap- lished papers that make use of a similar approach, both by Fagerberg proach was also used by Fagerberg et al. who used calculated de- et al. (2012, 2015) who explored the PLS methodology combined with scriptors from the Dragon package and PLS methodology to predict the 2 DragonX descriptors for their usefulness in predicting solubility in si- SE in FaSSIF (Fagerberg et al., 2012). This resulted in an R of 0.88 and mulated (FaSSIF) and aspirated fasted-state human intestinal fluid RMSE of 0.17 log units but, although promising, the dataset only con- (FaHIF) (Fagerberg et al., 2012, 2015). In the first study, the capability sisted of 22 compounds and therefore was not challenged with test sets. 2 of PLS and molecular descriptors to predict solubility was investigated The model was instead validated using permutation tests and Q ; both in FaSSIF for only 22 compounds, resulting in R2 of 0.82 and RMSE of of which showed that the model did not show signs of being over-fitted 0.32 log (M) units. In the follow-up study, 112 compounds were studied to the training set used. in FaSSIF and 74 compounds in FaHIF. The results of these modelling studies are similar to those described for the neural network models, 5. Prediction of solubility by modelling the thermodynamic cycle with R2 of 0.69 (RMSE of 0.48) and R2 of 0.85 (RMSE of 0.34) for FaSSIF and FaHIF, respectively. It should be noted that the number of A common feature of the QSPR-based models is that it has been compounds examined for solubility in different simulated and aspirated proven difficult to obtain solubility predictions with an external vali- intestinal fluids has increased in recent years and compilations have dation of accuracy better than an RMSE of 0.7–1.0 log units, i.e. the been made (see, for example, (Augustijns et al., 2014; Fagerberg and predicted solubility value can be up to 10 times higher or lower than Bergstrom, 2015)). Hence, this experimental database is now available the actual experimental value, irrespective of the statistical metho- for studies using computational modelling and advanced modelling and dology and descriptor space used (Bergstrom et al., 2004; McDonagh simulation approaches that demand larger datasets. et al., 2014). In reality, the predictions are likely to be even more in- Recently, the solubility of drugs in FaSSIF was modelled making use accurate when they are used to predict new chemical entities, since of the linear solvation energy relationship (LFER) based on the these can be quite structurally different from the training set used in the Abraham descriptors (Niederquell and Kuentz, 2017). Abraham de- model. The lack of an accurate model has been attributed to variations scriptors have previously been used to predict drug solubility in water in the accuracy of the experimental data extracted from the literature, of polychloronaphtalenes as well as the partitioning into of since the model cannot be more accurate than the input data. However, sodium dodecyl sulphate (SDS) (Abraham and al-Hussaini, 2001; this has been challenged by Palmer and Mitchell, who studied datasets Sprunger et al., 2007). In the work by Niederquell and Kuentz, the carefully determined in-house versus datasets extracted from the lit- modelled solubility data were given as the ratio of the solubility in erature (Palmer and Mitchell, 2014). They found that the poor accuracy FaSSIF to that in the corresponding blank buffer, defined as the solu- was more dependent on deficiencies in the algorithms and the de- bility enhancement (SE) (Niederquell and Kuentz, 2017). The following scriptors than deficiencies in the experimental values. Hence more ef- equation was developed from results obtained based on 40 compounds: fort is required for investigation of descriptors and models that will

189 C.A.S. Bergström, P. Larsson International Journal of Pharmaceutics 540 (2018) 185–193 describe the solubility better than those typically used in QSPR models. calculation extremely important. Instead of applying only QM, the au- Steps have, in fact, been taken in this direction over the last decade. thors also included molecular descriptors with the QM-calculated New principles have been investigated in more detail, with the purpose properties in a multilinear regression. Hence, several different compu- of modelling the fundamental underlying mechanisms of solubility and tational methodologies were combined in the final equation (QM and increasing understanding of this property. One such approach is to molecular descriptor calculations partly dependent on secondary QSPR model solubility using the thermodynamic cycle (Fig. 5). The re- models to allow prediction of logP). The final proposed model included lationship between the intrinsic solubility and the change in Gibbs free a QM-calculated term, a flexibility descriptor (fraction of energy is rotatable bonds) and the calculated lipophilicity value, and resulted in an RMSE of 0.71 for the test set. This accuracy is comparable to that in ΔGΔGΔGRTlnSV(sol)=+ (sub) (hydr) =−0 m (4) previously published computational models based on molecular de- where ΔG(sol) is the Gibbs free energy for solution, ΔG(sub) is the Gibbs scriptors. In a second study, the authors attempted to predict aqueous fi free energy for sublimation, ΔG(hydr) is the Gibbs free energy for hy- solubility from rst principles (Palmer et al., 2012). For details around fi dration, R is the molar gas constant, T is the temperature (in Kelvin), S0 rst principles, see Section 6 below. Information about the crystal lat- is the intrinsic solubility (M) and Vm is the molar volume of the crystal. tice was again obtained from experiments and used as input crystal An organic solvent, typically octanol, can be used as an intermediate structures for the sublimation calculations. Model potential-based between the gaseous and hydrated states in the experimental assess- crystal lattice simulations to calculate ΔG(sub) were combined with ment of the hydration process and, in such cases, Eq. (4) will be statistical mechanics to calculate ΔG(hyd). This method is not yet as transformed to accurate as the empirical methods – i.e. the QSPR methods where re- lationships are sought between structural features and solubility – and ΔGΔGΔGΔGRTlnSV(sol)=++=− (sub) (solv) (tr) 0 m (5) the best model for the dataset explored showed an RMSE of 1.45. where ΔG(solv) is the Gibbs free energy for solvation in octanol and However, this approach offers full computational characterization of ΔG(tr) is the Gibbs free energy for the transfer of the molecule from the thermodynamic cycle. When these models become optimized, e.g. octanol to water. If the logP value of the molecule is determined, ΔG(tr) by using force fields that better describe the drug molecule as well as can be replaced by the solvent (water), they may represent a new approach for exploring the impact of the solid-state versus hydration effects on the resulting ΔG(tr) = 2.303RTlogP (6) solubility. In theory it would be possible to calculate the Gibbs free energy of all three steps of the thermodynamic cycle. ΔG(sub) can be calculated by 6. First principles for prediction of solubility changes modelling the potential-based lattice energy and by lattice dynamics simulations, ΔG(hydr) and ΔG(solv) can be calculated by quantum me- In addition to methods for calculating solubility that rely on em- chanics (provided an appropriate model for the solvent is available) and pirical or semi-empirical corrections and/or different kinds of mole-

ΔG(tr) can be estimated from the calculated logP. In fact, several of these cular descriptors as input, as discussed above, solubility can also be steps have lately been subjects for computational modelling. A series of predicted using only the underlying physical principles. One advantage papers has been published by Lüder and coworkers, in which they used of this approach is that the input data that are needed for the non- stepwise methods to model the free energy of hydration (Westergren physics-based methods to work might not be readily available (e.g. for a et al., 2007), the free energy of solvation in pure melts (Luder et al., novel compound), and a significant amount of work would be required 2007b), and the free energy of solvation in pure amorphous matter to produce these data. An example of such an approach was provided in (Luder et al., 2007a). By producing models for both pure melts and pure Section 5 above, although that model used the crystal structure as amorphous matter, the hypothesis was that it should be possible to input. In this section we will focus primarily on relative solubility cal- predict the difference in solubility between the crystalline and amor- culations (e.g. change in solubility as the result of other components phous states using a computer. In their studies, 46 to 48 drug molecules being present) rather than absolute predictions of aqueous solubility. were investigated. They concluded that the electrostatic interactions It makes sense, however, to start with a description of the use of are much larger than the Lennard-Jones interactions in the hydration physical principles to determine solubility with the Hansen-Hildebrand process, whereas the opposite is true for the pure melt. Among the solubility parameters. These were first introduced in 1936 by different free energy calculations needed to cover the thermodynamic Hildebrand and Scott (1936) and later extended by Hansen to include cycle, the free energy of hydration is the most studied process; small systems with polar and hydrogen-bonding characters (Hansen, 1967). organic molecules, drug-like molecules and proteins have been com- Briefly, the Hansen-Hildebrand parameters describe the miscibility of putationally studied for this property (see e.g. (Michielan et al., 2008; solvents, and are defined as the square root of the “cohesive energy Palmer et al., 2011; Tjong and Zhou, 2008)). density”; the heat of vaporization divided by the molar volume. The The first attempt to predict drug solubility using a computational original Hildebrand parameter is a single number, and solvents with approach to solve the complete thermodynamic cycle was published in similar Hildebrand parameters are generally considered to be miscible. 2008 (Palmer et al., 2008). This work included a dataset of 34 drugs The later extension by Hansen splits the solubility parameter into three and drug precursors, and only compounds with experimental crystal components, representing polar, dispersion and hydrogen-bonding structures available in the Cambridge Structural Database were se- contributions to the solubility. A thorough description on how to use lected. The mean solubility of the dataset was 1 mM, so focus in this physics-based methods to calculate these parameters for a particular study was not on particularly poorly soluble compounds, and all the solute is given by Belmares et al. (2004) However, regardless of the molecules were quite small with a maximum molecular weight of method used to calculate these solubility parameters (group contribu- 339 Da. Crystal lattice energies, the entropy change for sublimation and tions or physics-based methods), they are based on regular solution gas, the vibrational entropy occurring in the crystal and the free en- theory assumptions and do not, for example, take into account entropy ergies of hydration and solvation were calculated from energy-mini- and free-volume changes, making them inaccurate in some circum- mised crystal structures using quantum mechanics (QM). Calculated stances. Nor do they account for changes in solubility with different molecular descriptors were also explored. Unfortunately the ab initio solute concentrations or conformations, or the fact that individual approach using QM-calculated thermodynamics failed to predict the molecules might interact with each other in very specific ways, which experimental result. This was probably because the prediction of ΔG(sol) may also affect their solubility (Hancock and Zografi, 1997). −1 was not accurate enough. The error of 5.7 kJ mole in ΔG(sol) results in The Flory-Huggins (FH) theory is closely related to the Hildebrand- a 10-fold shift (1 log unit) in the predicted solubility value, making this Hansen solubility parameter theory (Flory, 1941; Huggins, 1941). In

190 C.A.S. Bergström, P. Larsson International Journal of Pharmaceutics 540 (2018) 185–193 brief, the FH theory involves determination of an interaction parameter

(χFH), which is a dimensionless quantity that represents the mixing behaviour (chiefly enthalpy) of a solute (originally considered by Flory and Huggins to be a polymer) and a solvent. These components are said to be miscible when χFH < 0.5 or, conversely, to be phase-separated when χFH > 0.5. This interaction parameter can also be calculated from physics-based simulation methods using the individual cohesive energy density of each component in the as well as the molar volume of the solute (Case and Honeycutt, 1994). This approach has been used, for example, by Huynh et al. to predict the solubility of docetaxel (an anti-cancer agent) in different excipients (Huynh et al., 2007), and by Pajula et al. to predict the miscibility of small molecules in binary (Pajula et al., 2010). This section has so far described methods primarily used to de- termine whether two components are miscible. In general, these methods do not inform on the underlying mechanisms behind solubi- lity. To that end, molecular dynamics (MD) or Monte Carlo (MC)-based simulations can be used, and these also allow prediction of the actual solubility of a particular compound, even in the complete absence of experimental data. Broadly, MD (as well as MC) schemes can be im- plicit, continuum-based methods that treat the surrounding solvent as an isotropic continuous medium, or methods that incorporate any sol- vent molecules explicitly. One example of an implicit method which has Fig. 6. Molecular dynamics simulation snapshot showing a felodipine molecule sur- been shown to yield accurate results for predicted solubility values is rounded by water and hexadecane. Felodipine is shown in red, water is shown as a the so-called conductor-like screening model (COSMO) (Klamt, 1995). transparent, blue surface and hexadecane molecules are shown as sticks. This setup could With COSMO, the solution-phase part of solubility is calculated ab initio potentially be used to run a free energy calculation to predict the excess or relative so- while the solid-phase contribution is estimated empirically using ex- lubility of a drug (felodipine in this case) in more complex systems using the framework perimental data. There is also an extension to and further development of Paluch et al. (2015). of COSMO, called COSMO-RS (RS for realistic solvent) (Klamt et al., 2002). One of the main drawbacks of implicit simulation methods is a particular solute, on the other hand, is readily measured. Mobley and that they do not provide details of the solvation process at an atomic co-workers have shown that MD simulations can be used to calculate level. With explicit solvation methods, on the other hand, solvent-spe- both relative and excess solubility directly for a number of compounds cificeffects and solute-solvent interactions are explicitly considered. (Paluch et al., 2015). Relative solubility is the ratio of the solubility of These should therefore, at least theoretically, be more accurate and two different compounds in the same solvent, while excess solubility is provide better information about solvation than the implicit models the solubility of a compound in the actual solution relative to that in an (Levy and Gallicchio, 1998). The main issue with explicit models is that (Ellegaard et al., 2010; O’Connell and Prausnitz, 1964). they require extensive sampling of a high-dimensional phase-space, i.e. The main advantage of these methods is that the properties of the solid they take a very long time to run, especially for some processes, even form of the solute do not have to be calculated. Obviously, knowledge with modern computers. This is primarily because of the high degree of of the relative or excess solubility of compound A and/or B, together freedom from the explicit solvent molecules. The interested reader is with an experimental measurement of the absolute solubility of e.g. directed to papers by Bernardi et al., Páll et al. and Ganesan et al. to compound A immediately leads to knowledge of the solubility of read more about explicit MD simulations and ways of enhancing sam- compound B. pling in general (Bernardi et al., 2015; Ganesan et al., 2017; Páll et al., All of the examples above have involved relatively simple mixtures, 2014). Here we highlight the use of explicit MD simulations to predict such as binary octanol-water systems with a single solute molecule. In solubility, of which relatively few attempts have been made to date the intestinal fluids of the gastrointestinal tract, however, lipophilic (Ferrario et al., 2002; Paluch et al., 2010; Sanz and Vega, 2007; molecules are solubilized in mixed lipid aggregates. In the fasted state, Schnieders et al., 2012). these are composed of bile salts and phospholipids. The aggregates Essentially, calculating solubility from explicit MD simulations interact with the drug molecules, and the composition of these ag- amounts to determining when the chemical potential of the solute in gregates will have a significant effect on the partitioning of the drug solution is equal to the chemical potential of the solute in its solid, molecules into them. This will then have an impact on both solubili- crystalline form (Paluch et al., 2015). This can most readily be achieved zation and bioavailability. To further complicate the picture, lipids in by running a series of free-energy calculations, but the chemical po- the intestinal tract are digested over time, adding another element of tential of the solid is still quite complicated to calculate, since it re- unpredictability. By matching experiments with MD simulations, Birru quires calculation of the fugacity of the solid (Liu et al., 2016). Re- et al. recently investigated the fate of danazol in different kinds of in- cently, Mobley and co-workers have shown how to use molecular testinal colloidal structures (Birru et al., 2017b). They concluded that dynamics free energy calculations to calculate both relative and excess the solubility of danazol increases with the concentration of digested directly, thus circumventing the need to determine the fu- triglycerides. In two related papers, the same team of researchers also gacity (Paluch et al., 2015). These calculations are done in the limit of studied how the digestion of lipids alters the phase behaviour in the infinite for small compounds (see Fig. 6). This is of particular intestinal fluid, as well as how cholesterol and pH impact the ag- interest since most of the published work related to free energy calcu- gregation behaviour of intestinal lipids (Birru et al., 2017a; Suys et al., lations and MD simulations focuses on calculations of solvation free 2017). Similarly, Benson and Pless found that, in a mixture of tri-, di-, energies and octanol-water partition coefficients (for example through and monoglycerides, the addition of extra monoglycerides leads to re- SAMPL challenges) (Marenich et al., 2009; Ribeiro et al., 2010). While orientation of cyclosporin to the core region of triglyceride moieties useful, corresponding direct measurements of solvation free energies (Benson and Pleiss, 2017). A related study by Larsson et al. showed that are challenging at best, and it is thus difficult to find or determine ex- the different phases of lipids that occur with water dispersion (as perimental values with which to compare calculations. The solubility of

191 C.A.S. Bergström, P. Larsson International Journal of Pharmaceutics 540 (2018) 185–193 typically happens when a drug formulated with lipids passes through formulation strategies for beyond-rule-of-5 compounds. Adv. Drug Deliv. Rev. the intestinal tract) can be reproduced also using coarse-grained mo- Bergstrom, C.A., Holm, R., Jorgensen, S.A., Andersson, S.B., Artursson, P., Beato, S., Borde, A., Box, K., Brewster, M., Dressman, J., Feng, K.I., Halbert, G., Kostewicz, E., lecular dynamics (Larsson et al., 2017), allowing studies of solubiliza- McAllister, M., Muenster, U., Thinnes, J., Taylor, R., Mullertz, A., 2014. Early tion of drug molecules under physiologically relevant conditions and pharmaceutical profiling to predict oral drug absorption: current status and unmet concentrations of lipids. Relative solubilization, or partitioning, of a needs. Eur. J. Pharm. Sci. 57, 173–199. Bergstrom, C.A., Norinder, U., Luthman, K., Artursson, P., 2003. Molecular descriptors number of drugs (danazol, felodipine, carbamazepine) as well as influencing melting point and their role in classification of solid drugs. J. Chem. Inf. ethanol and water into lipid bilayers consisting of a mixture of phos- Comput. Sci. 43, 1177–1185. pholipids (including ) and taurocholate was also studied using Bergstrom, C.A., Wassvik, C.M., Johansson, K., Hubatsch, I., 2007. Poorly soluble mar- – MD simulations by Holmboe and colleagues (Holmboe et al., 2016). keted drugs display solvation limited solubility. J. Med. Chem. 50, 5858 5862. Bergstrom, C.A., Wassvik, C.M., Norinder, U., Luthman, K., Artursson, P., 2004. Global They concluded that partitioning, and thereby solubilization, is strongly and local computational models for aqueous solubility prediction of drug-like mo- influenced by hydrogen bonding between drug molecules and taur- lecules. J. Chem. Inf. Comput. Sci. 44, 1477–1488. ocholate, again highlighting the importance of detailed knowledge at Bernardi, R.C., Melo, M.C.R., Schulten, K., 2015. Enhanced sampling techniques in mo- lecular dynamics simulations of biological systems. BBA 1850, 872–877. an atomic level for understanding drug solubilization in physiologically Birru, W.A., Warren, D.B., Han, S., Benameur, H., Porter, C.J., Pouton, C.W., Chalmers, relevant fluids. D.K., 2017a. Computational models of the gastrointestinal environment. 2. Phase behavior and drug solubilization capacity of a type I lipid-based drug formulation after digestion. Mol. Pharm. 14, 580–592. 7. Conclusion Birru, W.A., Warren, D.B., Headey, S.J., Benameur, H., Porter, C.J., Pouton, C.W., Chalmers, D.K., 2017b. Computational models of the gastrointestinal environment. 1. Significant advances have recently been made in computational The effect of digestion on the phase behavior of intestinal fluids. Mol. 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