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gibbs oct mem Note that pKa is the conceptual equivalent of pKa and pKa [(see Eq (51)] We should not be surprised that this is a conditional constant, depending on the value of the background salt
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Figure 65 Solubility tetrad equilibria [Avdeef, A, Curr Topics Med Chem, 1, 277 351 (2001) Reproduced with permission from Bentham Science Publishers, Ltd]
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At this point we bring in the now familiar tetrad diagram, Fig 65, and conclude that
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Figure 64 shows a hypothetical solubility pH pro le with sdiff 4, as typical as one nds with simple acids in the presence of 015 M Na or K [473] Compare Eq (612) with Eq (46) In principle, all the curves in Figs 61a, 62a, and 63a would be expected to have solubility limits imposed by the salt formation Under conditions of a constant counterion concentration, the effect would be indicated as a point of discontinuity gibbs (pKa ), followed by a horizontal line of constant solubility Si 62 COMPLICATIONS MAY THWART RELIABLE MEASUREMENT OF AQUEOUS SOLUBILITY There are numerous experimental complications in the measurement of solubility Solid phases, formed incipiently, are often metastable with respect to a
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thermodynamically more stable phase, especially with highly insoluble compounds An active form of a solid, a very ne crystalline precipitate with a disordered lattice, can drop out of a strongly oversaturated solution, which then ages only slowly into a more stable inactive form [465] Hence, if measurements are done following initial precipitation, higher solubilities are observed Amorphism [464] and polymorphism [466] can be troubling complications Various solvates of a solid (either water or cosolvent in the crystal lattice) have different solubilities [43] Certain surface-active compounds [499], when dissolved in water under conditions of saturation, form self-associated aggregates [39,486 488] or micelles [39,485], which can interfere with the determination of the true aqueous solubility and the pKa of the compound When the compounds are very sparingly soluble in water, additives can be used to enhance the rate of dissolution [494,495] One can consider DMSO used in this sense However, the presence of these solvents can in some cases interfere with the determination of the true aqueous solubility If measurements are done in the presence of simple surfactants [500], bile salts [501], complexing agents such as cyclodextrins [489 491,493], or ion-pair-forming counterions [492], extensive considerations need to be applied in attempting to extract the true aqueous solubility from the data Such corrective measures are described below
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Two sensibly priced commercial databases for solubility exist [366,507] An article in the journal Analytical Pro les of Drug Substances carries solubility data [496] Abraham and Le [508] published a list of intrinsic aqueous solubilities of 665 compounds, with many ionizable molecules It is dif cult to tell from published lists what the quality of the data for ionizable molecules is Sometimes, it is not clear what the listed number stands for For example, Sw , water solubility, can mean several different things: either intrinsic value, or value determined at a particular pH (using buffers), or value measured by saturating distilled water with excess compound In the most critical applications using ionizable molecules, it may be necessary to scour the original publications in order to be con dent of the quality of reported values
EXPERIMENTAL METHODS
Lipinski et al [12] and Pan et al [463] compared several commonly used methods of solubility measurement in early discovery, where samples are often introduced as 10 mM DMSO solutions Turbidity-based and UV plate scanner-based detections systems were found to be useful The methods most often used in discovery and in preformulation will be brie y summarized below
EXPERIMENTAL METHODS
Saturation Shake-Flask Methods
Solubility measurement at a single pH [37 39] under equilibrium conditions is largely a labor-intensive procedure, requiring long equilibration times (12 h 7 days) It s a simple procedure The drug is added to a standard buffer solution (in a ask) until saturation occurs, indicated by undissolved excess drug The thermostated saturated solution is shaken as equilibration between the two phases is established After micro ltration or centrifugation, the concentration of the substance in the supernatant solution is then determined using HPLC, usually with UV detection If a solubility pH pro le is required, then the measurement needs to be performed in parallel in several different pH buffers 642 Turbidimetric Ranking Assays
Turbidity-detection-based methods [12,459 463], popularized by Lipinski and others, in part have met some high-throughput needs of drug discovery research The approach, although not thermodynamically rigorous, is an attempt to rank molecules according to expected solubilities Usually, the measurements are done at one pH Various implementations of the basic method are practiced at several pharmaceutical companies, using custom-built equipment Detection systems based on 96-well microtiter plate nephelometers are well established An automated solubility analyzer incorporating such a detector usually requires the user to develop an appropriate chemistry procedure and to integrate a robotic uidic system in a customized way It is important that turbidity methods using an analate addition strategy be designed to keep the DMSO concentration in the buffer solution constant in the course of the additions The shortcomings of the turbidity methodology are (1) poor reproducibility for very sparingly water-soluble compounds, (2) use of excessive amounts ( 5% v/v) of DMSO in the analate addition step, and (3) lack of standardization of practice 643 HPLC-Based Assays
In an effort to increase throughput, several pharmaceutical companies have transferred the classical saturation shake- ask method to 96-well plate technology using a robotic liquid dispensing system [463] Analyses are performed with fast generic gradient reverse-phase HPLC In some companies, the DMSO is eliminated by a freeze-drying procedure before aqueous buffers are added This adds to the assay time and can be problematic with volatile samples (eg, coumarin) Still, the serial chromatographic detection systems are inherently slow Data handling and report generation are often the rate-limiting steps in the operations 644 Potentiometric Methods
Potentiometric methods for solubility measurement have been reported in the literature [467 471] A novel approach, called dissolution template titration (DTT), has been introduced [472 474] One publication called it the gold standard [509]