Aqueous Solubility: Measurement and Prediction Tools

Submitted by amolsmalpani on Mon, 10/05/2009 - 17:20

Abstract

Solubility of active pharmaceutical ingredients (API) has always been a concern for formulators, since poor aqueous solubility may hamper development of parenteral products and limit bioavailability of oral products. Aqueous solubility is a crucial molecular property for successful drug development as it is a key factor governing drug access to biological membranes. This article focus briefly on different methods of solubility measurement, challenges for predicting correct solubility, different models for predicting water solubility with emphasis on the accuracy of the various prediction methods and also discusses the potential and limitations of them.

keywords: Biopharmaceutical classification system, intrinsic solubility, kinetic solubility, thermodynamic solubility, general solubility equation.

1. Introduction

Solubility plays an essential role in drug disposition, since the maximum rate of passive drug transport across a biological membrane, the main pathway for drug absorption, is the product of permeability and solubility. The number of poorly water-soluble drug candidates has risen sharply, particularly with recent progress in combinatorial chemistry and high- throughput screening. Development of oral formulations for such compounds can put forward significant challenges at all stages of drug development ¹. Insufficient bioavailability of these compounds due to their low solubility may result in delays in development or cause them to be dropped from the pipeline.

Solubility may be defined as the amount of a substance that dissolves in a given volume of solvent at a specified temperature. More specifically, compound solubility can be defined as unbuffered, buffered, and intrinsic solubility. Unbuffered solubility, usually in water, means solubility of a saturated solution of the compound at the final pH of the solution (which may be far from pH 7 due to self-buffering). Buffered solubility also termed apparent solubility refers to solubility at a given pH, e.g. 2 or 6.8, measured in a defined pH-buffered system and usually neglects the influence of salt formation with counter-ions of the buffering system on the measured solubility value. Intrinsic solubility means the solubility of the neutral form of an ionizable compound.

2.Biopharmaceutics Classification System (BCS)

The Biopharmaceutics Classification System is guidance for predicting the intestinal drug absorption provided by the U.S. Food and Drug Administration. The fundamental basis for the BCS was established by Dr. Gordon Amidon. This system allows restricting the prediction using the parameters solubility and intestinal permeability. The solubility classification is based on a United States Pharmacopoeia (USP). The intestinal permeability classification is based on a comparison to the intravenous injection. All those factors are highly important, since 85% of the most sold drugs in the USA and Europe are orally administered.

The BCS group, poorly soluble compounds as class II (compounds is featured poorly solubility and high permeability) and class IV drugs (poor solubility and poor permeability) as shown in figure no. 1. Drugs substances are considered highly soluble when the largest dose of a compound is soluble in < 250 ml water over a range of pH from 1.0 to 7.5; highly permeable compounds are classified as those compounds that demonstrate > 90 percent absorption of the administered. According to the Biopharmaceutics Classification System (BCS), drug substances are classified as follows:

class I - high permeability, high solubility

Example: Metoprolol

Those compounds are well absorbed and their absorption rate is usually higher than excretion.

class II - high permeability, low solubility

Example: Glibenclamide

The bioavailability of those products is limited by their solvation rate. A correlation between the in vivo bioavailability and the in vitro solvation can be found.

class III - low permeability, high solubility

Example: Cimetidine

The absorption is limited by the permeation rate but the drug is solvated very fast. If the formulation does not change the permeability or gastro-intestinal duration time then class I criteria can be applied.

class IV - low permeability, low solubility

Example: Hydrochlorothiazide

Those compounds have a poor bioavailability. Usually they are not good absorbed over the intestinal mucosa and a high variability is expected ^{2, 3}.

Solubility is one of the components of the BCS and is particularly important for immediate release BCS class II drugs, for which absorption is limited by solubility (thermodynamic barrier) or dissolution rate (kinetic barrier). Further, if the solubility is incorrectly estimated, this can lead to wrong interpretation of results in a number of in-vitro assays and weaken structure activity relationship (SAR).

Poor aqueous solubility is caused by two main factors:

·High lipophilicity and

·Strong intermolecular interactions which make the solubilization of the solid energetically costly. What is meant by good and poorly soluble depends partly on the expected therapeutic dose and potency. As a rule of thumb, a compound with an average potency of 1mg/kg should have a solubility of at least 0.1g/L to be adequately soluble. If a compound with the same potency has a solubility of less than 0.01g/L it can be considered poorly soluble.

3.Assays methods for determining aqueous solubility

Solubility can be measured as either a kinetic or thermodynamic value.

3.1.kinetic solubility measurement

In most cases, kinetic solubility measurements start from dissolved compound and represent the maximum (kinetic) solubility of the fastest precipitating species of a compound. The type of precipitating material is not determined and can be amorphous or crystalline, neutral or a salt, exist as a co-crystal or a combination of these possibilities. Kinetic solubility values are strongly time dependent and due to the degree of supersaturation that may occur, values are likely to over-predict the thermodynamic solubility and are not expected to be reproducible between different kinetic methods ⁴. Figure no. 2 give idea about some key elements of traditional kinetic and thermodynamic solubility assay in drug discovery and development.

Several high-throughput assays for kinetic solubility measurement have been described in the literature ^{1, 5, 6}. These assays typically involve scaling down to 96-well or 384-well microtiter plate format, and can be automated with a robotic liquid-handling system that significantly increases sample throughput. In these methods, a drug solution in dimethyl sulfoxide (DMSO) is diluted with aqueous media. When the drug in the aqueous solution reaches its solubility, excess drug precipitates, and the kinetic solubility is measured by turbidity, nephelometry, or UV absorption.

3.1.1. solubility by turbidimetric/nephelometric method

The high-throughput turbidimetric method for kinetic solubility measurement was introduced by Lipinski et al ¹. A drug solution in DMSO is titrated into a blank aqueous solution as shown in figure no. 3, and the precipitation point is determined turbidimetrically at 620–820 nm ranges. Similar approaches using nephelometers for solubility screening/measurement have been also reported ^5-7. Several microplate nephelometers are commercially available for rapid measurement of kinetic solubility using 96-well or 384-well plate formats.

Recently, a fully automated, laser-based nephelometry system has been developed for high-throughput measurement of kinetic aqueous solubility ⁸. The protocol integrates a robotic liquid/ plate handler with nephelometry detection. The fully automated measurement system is able to determine the kinetic solubility of 1800 compounds within 6 days.

Limitations of this method include any factors that result in turbidity or light scattering could interfere with data. For example, colored compounds may be misassigned as insoluble in determining the precipitation point when turbidimetric method is used, leading to lower solubility values. In nephelometry assays the imperfections including scratches on the wells in the plates or any foreign materials in the wells could scatter light and produce a false positive reading.

3.1.2. Solubility measurement by UV absorption

Kinetic solubility in high-throughput assays can be also quantitated by UV plate readers or HPLC- UV. In these methods, a drug solution in DMSO is diluted with aqueous media. After precipitation, the saturated solution is passed through a 96-well filter plate. The drug concentration in the filtrate is quantitated by UV absorption, and solubility is calculated using a calibration curve. In these assays, the amount of drug in each well of a 96- well plate can be sub-milligram quantities. The assays can be also automated with a robotic liquid dispensing system. An integrated protocol with software and hardware using a UV plate reader is commercially available for rapid measurement of kinetic solubility using 96-well or 384 -well plate formats (pION,

Woburn, MA ).

UV absorption methods can achieve a limit of detection down to 1 μM ⁶. They provide a more accurate determination of solubility because the value is determined based on absorption of drug molecules against a calibration curve. However, the methods cannot distinguish multiple chromophores that overlap in their absorption. False positive results can be generated if any impurities in the compounds or excipients absorb light in the wavelength region of interest.

3.2.Estimation of Thermodynamic Solubility

Although kinetic measurements have proven useful in the early discovery stage, kinetic data cannot serve as a substitute for thermodynamic solubility to predict the drug properties during lead optimization. Recently, several new methods that aim to measure or estimate thermodynamic solubility at smaller scales have been described in the literature ^9-12.They increase the sample throughput, reduce sample amount, and integrate solubility measurements with determination of other drug properties. These methods are scaled down shake-flask method and a solvent evaporation method.

3.2.1.Scaled down shake-flask method

This approach is to scale down conventional shake -flask assay with automation for rapid solubility screening or measurement using small quantities o f compounds ^{9, 11}. In these automated assays, a solid dispenser deposits small quantity of drug powders to each well of a 96-well plate, while the solubility medium is dispensed to the well by a robotic liquid-handling system. Following a sufficiently long incubation with the medium, the drug slurry at equilibrium is passed through a filter plate and the thermodynamic aqueous solubility of drug candidates is determined by a UV plate reader ⁹, HPLC-UV ¹⁰ or chemiluminescent nitrogen detection ¹¹.These methods are usually fully integrated systems with automation in 96-well plate formats, and are capable of rapid assay sample preparation and processing in high-throughput workflow. For example, one of the integrated measurement systems requires only 5 mg of an API and measures thermodynamic solubility values in the range of 0.001-3 mg/ mL with a throughput of ∼100 compounds a week.

Some thermodynamic solubility assays have included additional features, such as rapid pH measurement and crystallinity assessment in order to increase sample throughput and reducing compound consumption ⁹.

3.2.2.Solvent evaporation method

Another approach in measuring or estimating thermodynamic solubility at smaller scales is to use a solvent evaporation method in combination with integrated robotic liquid handling, centrifugal separation, and HPLC-UV quantification. In the method the drug candidate is first dissolved in organic solvent and then dispensed into a 96-well plate. Following removal of solvents, an aqueous medium is added to the drug solid for incubation. After the saturated solution reaches equilibrium, the solution is filtered through a 96-well filter plate, and solubility is determined by HPLC analysis. Using 1 mg of solid compound, the automated assay determines the solubility of compound in three media in the range of 1–200 μg/ml, and the sample throughput can be up to 192 compounds a week ¹².

Limitations of thermodynamic solubility assays include HPLC-UV techniques are limited by requiring the compound to have a UV chromophore for quantitative determination, and usually also require a chromatographic separation of compounds from impurities or excipients that would interfere with compound signal. A chemiluminescent nitrogen detection technique has been used to increase analysis throughput over HPLC-UV ¹¹. This technique is only suited for analysis of nitrogen containing compounds in non nitrogen containing solvents. In addition, this is expensive and resource dependent.

4.Challenges for experimental determinations

Despite the availability of a number of methods to measure solubility, it remains a challenge to collect homogenous, high quality data in an appropriate format. The lack of high quality solubility datasets in turn, has a large impact on our ability to create predictive models for solubility. Common issues encountered can be divided into two categories.

improper expression of “solubility” term

It is very important to define the experimental conditions well. Analogous to log P and log D, one needs to distinguish the intrinsic solubility, S, from the solubility measured at a given pH value in a defined medium. Artursson et al ¹³ has shown that this parameter is relatively independent of the nature of the medium used. In contrast, solubility measured at a fixed pH value may be highly dependent on the nature and concentration of the counter-ions present in the medium. This is especially critical for poorly soluble compounds which are strongly ionized at the pH of the measurement. Finally, it is important to note that single pH measurements (using the shake flask method, for example) cannot distinguish between soluble monomers and soluble aggregates of the drug molecules (which may range from dimers to micelles), unless more sophisticated experiments are performed.

problems in data due to assay limitations

There are a number of issues which can affect the quality of the data. If the traditional shake-flask method is used, adsorption to the vial or to the filter, incomplete phase separation, compound instability and slow dissolution can affect the result.

5.Different models for predicting Intrinsic solubility

Poor aqueous solubility can often be overcome by appropriate formulation work. However, this approach is expensive and without guarantee of success. It is much better to improve solubility by chemistry means through adequate changes in the molecule itself. To this end, it is desirable to determine the aqueous solubility of candidates as early as possible in the discovery process. Even though higher throughput assays have recently become available, the generation of high quality solubility data remains a relatively expensive and time consuming activity. Therefore, the development of models to predict the aqueous solubility of drug candidates from their chemical structure has attracted considerable attention. Predictive models based on molecular forms also help understanding what feature(s) limits solubility and can thus provide useful information to medicinal chemists.

5.1.fragment-based models

Fragment-based models try to predict solubility as a sum of substructure contributions such as contributions of atoms, bonds or larger substructures. This approach is based on a general assumption that molecule properties are determined completely by molecule structure, and may be approximated by contributions of fragments in the molecule. Fragment-based methods work very well for purely additional molecule properties (such as log P or molar refractivity) where substructures have rather constant contributions to the studied property. This is, however, not the case for solubility, where effects like electron donating/accepting contributions of substituents, and intramolecular hydrogen bonding can play an important role. Such complex effects cannot be properly described solely by fragment contributions. On the other hand, the fragment contributions approach offers the possibility of describing, at least partially, the effect of crystal packing ¹⁴, which would otherwise be accessible only via expensive computations ¹⁵. When applying fragment contribution methods for prediction of solubility, one needs to use quite a large number of fragments to get reasonable performance (usually over 100) and this sets also high requirements on the number of data points needed to develop the model (the rule of thumb is to use minimally 5 to 6 data points per parameter/ fragment). This precludes the development of “local” fragment based models for smaller data sets. Numerous methods for solubility prediction based on fragment contributions exist; some of the more popular approaches include models of Huuskonen ¹⁶, Klopman ¹⁷ or Tetko et al ¹⁸.

5.2.models based on log p

The inverse relation between solubility and lipophilicity has been recognized for a long time and empirical relationships between log S and log P have been reported.

Log S = 0.978-1.339 log P with

n =1.56; r² =0.874 for liquid solutes ¹⁹

Log S =1.17-1.38 log P with

n = 300; r² = 0.931 for crystalline solutes ²⁰

However, when more complex, drug-like molecules were added to the set, the relation deteriorated and it became obvious that additional parameters are required. The octanol–water partition coefficient (log P), characterizing molecule hydrophobicity, is probably the single most important parameter influencing solubility. Hansch, who introduced log P in QSAR studies, formulated the first correlation between log P and solubility ¹⁹. Yalkowsky and coworkers proposed a general solubility equation (GSE) ²¹, in which the correlation with log P is improved by the addition of an experimental melting point (MP). This equation is physically reasonable because it covers the effect of hydrophobicity (log P) as well as the effect of crystal packing (approximated by MP). The GSE has the form

log S = 0.5 - 0.01 (MP- 25)- log P

The disadvantage of the method is the necessity to know the experimental melting point. When MP is not available, it was suggested to use a median value of 125°C instead ²².

5.3.models based on solvation properties

Abraham and Le ²³ proposed an elegant method to predict solubility by considering solute–solvent interactions. The equation has the form

log S₀= 0.52 –1.00R₂+0.77π^H+2.17∑α^H– 4.24∑β^H–3.36∑α^H ∑β^H–3.99V_x

where,

R₂ is excess molar refraction, π^H is dipolarity/polarizability, α^H and β^H are hydrogen-bond acidity and basicity, respectively, and finally V_x is the McGowan's molecular volume (which also characterizes the hydrophobicity of the solute).

The inclusion of additional hydrogen-bonding cross-correlation terms (which describe intramolecular hydrogen bonding and may account for solid state effects) improves the correlation with solubility. The advantage of the Abraham equations is the fact that each parameter used has a clear physical meaning and therefore the equation is easy to interpret. Most of the coefficients used in the Abraham's equation were derived from experimental measurements on relatively simple small molecules. To obtain reliable values of Abraham parameters for complex multifunctional drug-like structures is not an easy task, limiting to some extent the applicability of this elegant equation.

5.4.Hybrid models

Numerous other approaches to calculated aqueous solubility have been proposed. The list of molecular forms used in this endeavor is nearly unlimited. One of the most useful forms for correlating with solubility is the polar surface area (PSA), which characterizes molecule polarity and hydrogen bonding features. PSA, defined as a sum of surfaces of polar atoms ²⁴, is conceptually easy to understand and seems to encode in an optimal way a combination of hydrogen bonding features and molecular polarity. Forms calculated by quantum chemical methods (COSMO-RS approach) ²⁵ have also been shown to provide good correlation with experimental solubility values of drugs and pesticides. The method can be used to predict solubility in almost any arbitrary solvent. A drawback lies in the demands on computational time (about 2h of computational time per molecule), although this has been considerably improved by the COSMO frag approach ²⁶. Clark ²⁷ used a set of quantum chemically calculated parameters to obtain correlations with solubility. Unlike simple 2D forms, forms which require 3D molecule structure are not so commonly used for solubility prediction. Although this description of molecules is closer to physical reality, the necessity to handle conformational problems and transform forms to an alignment-free form adds complexity to the calculations. Moreover, reported results of 3D approaches do not provide any considerable improvement in comparison with 2D approaches.

In addition to the various forms used, a broad range of statistical and data-mining techniques have been applied in the field of solubility prediction. Besides classical linear regression and partial least square (PLS) approaches also neural networks ¹⁸, cellular automata ²⁸, genetic algorithms ²⁹, support vector machines ³⁰ or Monte Carlo simulations ³¹.

6. Future Prospects

Solubility of a compound is one of the most important factors for drug development. So that, accurate measurement and prediction of solubility in any media is become a crucial task but, accurate solubility prediction is rather more challenging thing. There were many models had been designed by scientists using different approaches, but most of models observed lacunae in it. Among them some finds good result that models were discussed in above section. Still in this area we have lot of scope for designing very precise and accurate models that help to get rid of that hurdle.

References

1. Lipinski CA, Lombardo F, Dominy BW, Feeney PJ. Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings. Adv. Drug Deliv. Rev. 1997, 23, 3-25.

2. Amidon GL, Lennernaes H, Shah VP, Crison JR. A theoretical basis for a biopharmaceutic drug classification: the correlation of in vitro drug product dissolution and in vivo bioavailability. Pharm. Res. 1995, 12, 413-420.

3. The Biopharmaceutics Classification System (BCS) Guidance, accessed on 25 may 2009, http://www.fda.gov/AboutFDA/CentersOffices/CDER/ucm128219.htm

4. Stuart M, Box K. Chasing equilibrium: measuring the intrinsic solubility of weak acids and bases. Anal. Chem. 2005, 77, 983 -990.

5. Bevan CD, Lloyd RS. A high-throughput screening method for the determination of aqueous drug solubility using laser nephelometry in microtiter plates. Anal. Chem. 2000, 72, 1781-1787.

6. Pan L, Ho Q, Tsutsui K, Takahashi L. Comparison of chromatographic and spectroscopic methods used to rank compounds for aqueous solubility, J. Pharm. Sci. 2001, 90, 521-529.

7. Fligge TA, Schuler A. Integration of a rapid automated solubility classification into early validation of hits obtained by high throughput screening. J. Pharm. Biomed. Anal. 2006, 42, 449-454.

8. Dehring KA, Workman HL, Miller KD, Mandagere A, Poole SK. Automated robotic liquid handling/laser-based nephelometry system for high throughput measurement of kinetic aqueous solubility. J. Pharm. Biomed. Anal. 2004, 36, 447-456.

9. Seadeek C, Ando H, Bhattachar SN, Heimbach T, Sonnenberg JL, Blackburn AC. Automated approach to couple solubility with final pH and crystallinity for pharmaceutical discovery compounds. J. Pharm. Biomed. Anal. 2007, 43, 1660-1666.

10.Sugano K, Kato T, Suzuki K, Keiko K, Sujaku T, Mano T. High throughput solubility measurement with automated polarized light microscopy analysis. J. Pharm. Sci. 2006, 95, 2115-2122.

11.Bhattachar SN, Wesley JA, Seadeek C. Evaluation of the chemiluminescent nitrogen detector for solubility determinations to support drug discovery, J. Pharm. Biomed. Anal. 2006, 41, 152-157.

12. Tan H, Semin D, Wacker M, Cheetham J. An automated screening assay for determination of aqueous equilibrium solubility enabling SPR study during drug lead optimization. Jala. 10, 2005, 364-373.

13.Bergstrom CAS, Luthman K, Artursson P. Accuracy of calculated pH dependent aqueous drug solubility. Eur. J. Pharm. Sci. 2004, 22, 387-398.

14.Chickos JS, Braton CM, Hesse DG, Liebman JF. Estimating entropies and enthalpies of fusion of organic compounds. J. Org. Chem. 1991, 56, 927-938.

15.Lipinski CA, Lombardo F, Dominy BW, Feeney PJ. Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings. Adv. Drug Deliv. Rev. 2001, 46, 3-26.

16.Huuskonen J. Estimation of aqueous solubility for a diverse set of organic compounds based on molecular topology. J. Chem. Inf. Comput. Sci. 2000, 40, 773-777.

17.Klopman G, Zhu H. Estimation of aqueous solubility of organic molecules by the group contribution approach. J. Chem. Inf. Comput. Sci. 2001, 41, 439-445.

18. Tetko IV, Tanchuk VY, Kasheva TN, Villa AEP. Estimation of aqueous solubility of chemical compounds using E-State indices. J. Chem. Inf. Comput. Sci. 2001, 41, 1488-1493.

19. Hansch C, Quinlan JE, Lawrence GL. Linear free-energy relationship between partition coefficients and the aqueous solubility of organic liquids. J. Org. Chem. 1968, 33, 347-350.

20.Isnard P, Lambert S. Aqueous solubility and n-octanol/water partition coefficient correlations. Chemosphere. 1989, 18, 1837-1853.

21.Ran Y, Jain N, Yalkowski SH. Prediction of aqueous solubility of organic compounds by the General Solubility Equation (GSE). J. Chem. Inf. Model. 2001, 41, 1208-1217.

22.Delaney JS. Predicting aqueous solubility from structure. Drug Discov. Today. 2005, 10, 289-295.

23.Abraham MH, Le J. The correlation and prediction of the solubility of compounds in water using an amended solvation energy relationship. J. Pharm. Sci. 1999, 88, 868-880.

24.Ertl P, Rohde B, Selzer P. Fast calculation of molecular polar surface area as a sum of fragment-based contributions and its application to the prediction of drug transport properties. J. Med. Chem. 2000, 43, 3714-3717.

25.Klamt A, Eckert F, Hornig M, Beck ME, Burge T. Prediction of aqueous solubility of drugs and pesticides with COSMO-RS. J. Comput. Chem. 2001, 23, 275-281.

26.Hornig M, KLamt A. COSMO frag: a novel tool for high-throughput ADME property prediction and similarity screening based on quantum chemistry. J. Chem. Inf. Comput. Sci. 2005, 45, 1169-1177.

27. Clark T.Quantum cheminformatics: an oxymoron? in: Hicks MG (Ed.), Chemical Data Analysis in the Large. The Challenge of the Automation Age. 2000.

28. Kier LB, Cheng CK. A cellular automata model of an aqueous solution. J. Chem. Inf. Comput. Sci. 1994, 34, 1334-1337.

29.Wegner K, Zell A. Prediction of aqueous solubility and partition coefficient optimized by a genetic algorithm based descriptor selection method. J. Chem. Inf. Comput. Sci. 2003, 43, 1077-1084.

30.Lind P, Maltseva T. Support vector machines for the estimation of aqueous solubility. J. Chem. Inf. Comput. Sci. 2003, 43, 1855-1859.

31.Jorgensen WL, Duffy EM. Prediction of drug solubility from Monte Carlo simulations. Bioorg. Med. Chem. Lett. 2000, 10, 1155-1158.