Critical Compilation of pK_a Values for Pharmaceutical Substances

Publisher Summary

There are numerous compilations of pK_a values in the physical chemistry literature, including several for pharmaceutically relevant organic weak acids and bases. These are complemented by further compilations of pharmaceutically relevant physicochemical data, such as partition coefficients, solubilities, and reaction rate constants. At the same time, other pharmaceutically interesting phenomena have not yet received the attention they deserve, such as the detailed substrate specificity and the kinetics of endogenous enzyme systems (e.g., esterases and phosphatases), which are relevant to the rational design of prodrugs and the predictability of their bioconversion to active drug. Along with solubilities, partition coefficients, and reaction rates, pK_a values are the most important physicochemical properties of drugs and the excipients used to formulate them into useful medicines. The extent of ionization (overall state of charge) for a dissolved drug is a function of its intrinsic pK_a value(s) and the pH value of the solution. The extent of ionization for a drug can control its solubility, dissolution rate, reaction kinetics, complexation with drug carriers (e.g., cyclodextrins), absorption across biological membranes, distribution to the site of action, renal elimination, metabolism, protein binding, or receptor interactions.

Introduction

There are numerous compilations of pK_a values” in the physical chemistry literature, including several for pharmaceutically relevant organic weak acids and bases [[1], [2], [3], [4], [5], [6], [7], [8]]. These are complemented by further compilations of pharmaceutically relevant physicochemical data such as partition coefficients, solubilities, and reaction rate constants [6]. At the same time, other pharmaceutically interesting phenomena have not yet received the attention they deserve, such as the detailed substrate specificity and kinetics of endogenous enzyme systems (e.g., esterases and phosphatases), which are relevant to the rational design of prodrugs and the predictability of their bioconversion to active drug [13].

Along with solubilities, partition coefficients, and reaction rates, pK_a values are the most important physicochemical properties of drugs and the excipients used to formulate them into useful medicines. The determination of pK_a values is typically discussed either first or second (after solubility) in preformulation textbooks. The extent of ionization (overall state of charge) for a dissolved drug is a function of its intrinsic pK_a value(s) and the pH value of the solution [14]. The extent of ionization for a drug can control its solubility, dissolution rate, reaction kinetics, complexation with drug carriers (e.g., cyclodextrins), absorption across biological membranes, distribution to the site of action, renal elimination, metabolism, protein binding, or receptor interactions. Clearly, research in many aspects of the drug sciences requires knowledge and use of drug pK_a values. When an investigator chooses to make use of tabulated or compiled physicochemical constants, reliably assessed data is required to account best for physicochemical or biopharmaceutical results that are dependent on the relationship between pH and pK_a.

The critical assessment of data quality is one of the major features of the seminal group of pK_a compilations [[9], [10]] for weak organic acids and bases sponsored by the International Union of Pure and Applied Chemistry (IUPAC). These compilations feature assessment of data quality, based on aspects of pK_a measurement such as the mathematical definition chosen to calculate the value from the raw data, choice of the experimental method, and the degree to which technical refinements have been applied. The pK_a values are described in these compilations as “very reliable” (pK_a error < ±0.005), “reliable” (pK_a error ±0.005 to ±0.02), “approximate” (pK_a error ±0.02 to ±0.04), and “uncertain” (pK_a error > ±0.04). These error criteria may seem overly restrictive to some readers. However, it must always be remembered that pK_a values are logarithmic representations of the acid dissociation constant K_a. These error criteria, when applied to the dissociation constants that they represent, are substantially larger than first appears. For example, a decrease in pH of 0.3 unit (which many would regard as small) actually represents a twofold increase in hydronium ion activity. This increase in ${\text{a}}_{{\text{H}}^{+}}$ may double a reaction rate, and thereby halve the corresponding shelf life. A variation in assigned pK_a of 0.05 unit (trivial to many) represents a change in the extent of ionization for a weak acid or base of 10.9% at a fixed pH. The resulting change in polarity may influence solubility or partitioning properties to a similar extent, and which approaches comparison with the experimental errors in careful pharmacokinetic or biopharmaceutical work. Attention was drawn to this issue with respect to partitioning behavior [15] many years ago. The variation in pK_a of < ±0.005 which is required to qualify a result for status of “very reliable” corresponds to an uncertainty in the dissociation constant, K_a, of <1%, which seems reasonable for the most careful physicochemical work. It is most regrettable that very few authors in the pharmaceutical sciences [16] have ever seen fit to include comparisons of their data with the IUPAC reliability criteria.

Differences large enough to correspond to the “uncertain” classification may substantially alter aqueous solubilities or partition coefficients, and certainly can lead to gross errors in derived thermodynamic quantities where pK_a data are measured as a function of temperature. In one example, pK_a errors of 0.05 at most led to the derivation of ΔH° and ΔS° values for ionization of 5, 5‐diethylbarbituric acid [17] that varied with temperature in the wrong direction, compared to the best data [18] in the literature. In other words, the temperature dependences of these quantities were shown [19] to have the wrong sign, because of apparently quite small errors in the pK_a values. In the present compilation, the criterion for “uncertain” has been widened to a pK_a error > ±0.06. This is equivalent to variability in the dissociation constant of about 15%.

The IUPAC dissociation constant compilations [[9], [10], [11], [12]] are not focused on drug substances, although they do include some pharmaceuticals, such as morphine and other opiates, acetanilide, some barbiturates, vitamins, antibiotics, and alkaloids. In a sense, this is a limitation of these compilations. A set of cross‐referencing indexes to these compilations would be a useful tool.

The IUPAC compilations are entirely confined to pK_a values of weak organic acids and bases measured in aqueous solutions only. As those compilations predated the Yasuda‐Shedlovsky [[20], [21]] extrapolation procedure, any pK_a values derived from simple extrapolation of organic cosolvent composition to 100% water would have to be assigned “uncertain” reliability. The world of drug sciences has not been able to avoid the use of aqueous‐organic cosolvent mixtures for pK_a determination, as well as numerous other purposes. This is due to the low aqueous solubilities often seen for drug‐like molecules, which are often a function of the lipophilicity range needed to ensure adequate passive transfer across biological membranes. The apparent pK_a values that result from measurements in aqueous‐organic solvent mixtures are generally not able to be precisely converted to the values that would result in water alone, due to: (a) the nonlinearity of direct relationships between apparent pK_a and solvent composition, especially for bases at low organic cosolvent content; and (b) the lack of values obtained in solvent mixtures with a sufficient number of different compositions (however, see Section 2.2.4). Wider application (and possible further refinement) of the Yasuda‐Shedlovsky extrapolation for correlating apparent pK_a values with solvent composition [[20], [21]] may go some way toward solving this problem, although the method at present does not consistently lead to precisely the same results for compounds with sufficient water solubility to be used as validation controls. Hence, a compilation of drug pK_a values must, at the least, draw attention to the use of different cosolvent combinations, where this has occurred.

It has also been noted [22] that the use of pK_a values measured in aqueous media (or extrapolated to the same through the Yasuda‐Shedlovsky procedure) are not ideal in accounting for enzyme‐substrate interactions, where binding to an active site involves ionizable functional groups. The active sites of enzymes and receptors, along with biological membranes, tend to be less polar in nature than water, and thus the relevant pK_a value is more likely to be one that pertains to a partially aqueous solvent. Theoretical treatments for this situation were described [23] long ago by Bjerrum, Wynne‐Jones, and Kirkwood and Westheimer, and further applied in the exceedingly careful physicochemical work of Ives and his school [[24], [25], [26]]. Hence, the use of partially aqueous cosolvent mixtures has a physicochemical–pharmacological legitimacy, although one that has so far received very little theoretical attention in the pharmaceutical literature compared to the mere convenience of keeping acidic or basic solutes in solution for the purpose of pK_a measurement. It must be noted, however, that pH meter calibration for use in partially aqueous solutions is more complex [20] than for purely aqueous solutions.

A major limitation of all current compilations of pharmaceutically relevant pK_a values is their incomplete coverage of the literature. First, there is a large number of new drugs (about 330) that has been commercialized since the early 1980s. Few of these have had pK_a values reported. Most compilations deal with older drugs, many of them no longer in therapeutic use. Rarely do any of the current compilations in the drug literature cite more than one value for each compound. For example, for glibenclamide, a secondary source cited only one of the three values reported in the original paper [27], without acknowledging the existence of the other two values. All three values were substantially different to each other, yet there was no apparent reason for citing one value over the others. Later work [28] suggested that one of the uncited values was the more accurate. Needless to say, it is recognized that a compilation goes out of date the moment that the first new piece of relevant data is entered into the literature.

A second limitation of existing compilations is overreliance on requoting the secondary literature, so that experimenters are unable to ascertain the quality of pK_a data that they wish to use. Also, there is the risk of errors creeping into data sets when they are copied and recopied. In the course of finding raw data for this compilation, it was often necessary to track sequentially through two or three secondary literature citations to find the original source, from which experimental validation information might be obtained. In one compilation, no literature references were given at all. Frequently, important details had been omitted in the transmission. For example, a pK_a value = 5.93 cited for atropine looked more like a pK_b value, until discovery of the primary reference [29] showed that the original data had been obtained from titrations in glacial acetic acid as solvent, rather than water. This vital fact was omitted in the secondary source. Occasionally, the pharmacology literature uses the symbol “pK_a” to mean the negative log of the affinity of a drug for a receptor, which is not at all the same as the acid–base behavior of the compound. The secondary pK_a compilations have sometimes quoted these affinity values as if they referred to acid–base equilibria. For procaine, three different pK_a values for the tertiary amine were found in seven secondary sources [[5], [6], [8], [30], [31], [32], [33]], none of which had cited a primary reference. In a few cases, different values from the same primary source were cited by two separate secondary sources. One reason for the omission of key details such as temperature is that some data was originally published in hard‐to‐access foreign language journals and any information at all is only readily available through Chemical Abstracts.

It was disappointing to find a few extremely old and inaccurate data quoted in very recent secondary compilations, for example, one textbook cited a value for 5,5‐dimethylbarbituric acid that had been first published [34] over 100 years ago, but which has also been requoted in other secondary literature [35]. The value given (pK_a = 7.1) is highly inaccurate and was superseded by a more reliable value (pK_a = 8.51) [36] over 25 years ago. Most compilations continue to list pK_a values for numerous other barbituric acid derivatives from a large study [37] published in 1940. That study had a flawed experimental design which resulted in low values for most compounds, when compared to validated, more recent studies [[36], [38]]. One published secondary compilation was acknowledged to be the result of a library data collection exercise given to undergraduate pharmacy students. The collected references were later checked randomly, but not exhaustively, by a graduate student. While that compilation is quite extensive (more than 700 total citations), ∼68% were from the secondary literature. The compilation of the present database has as one of its objectives the citation of original sources wherever possible. Only one secondary source is regarded as sufficiently careful in its handling of the original data, and that is the series of compilations prepared under the auspices of IUPAC [[9], [10], [11], [12]]. Even so, virtually all citations from the IUPAC compilations have been rechecked with the original literature, with one or two revisions necessary (e.g., see no. 1988 in the database).

A third limitation of all previous compilations is the failure to critically review data quality. It was regrettable to note a number of examples where the pK_b values for bases had been misquoted as if they were pK_a values due to failure to compare the numerical values with those expected for the functional groups to which they had been assigned. A further problem with reported pK_b values is that when secondary compilers did convert them to pK_a values (using pK_a + pK_b = pK_w) the value for pK_w at 25 °C (14.008) was always used, even when the temperature for the pK_b measurement (≠ 25 °C) was available. This avoidable error led to discrepancies of several tenths of a pK_a unit over the commonly employed temperature range (15–37 °C) for single measurements.

There is also the important issue of data consistency. Many drugs and excipients have had their pK_a values measured by different methods with very good agreement, provided that all experimental conditions were maintained constant. Examples included atenolol [9.60 ± 0.04; potentiometric, partitioning ,and capillary electrophoresis (CE) studies in different laboratories], barbital (5,5‐diethylbarbituric acid) (7.98 ± 0.01; electrometric, potentiometric, and spectrophotometric studies in different laboratories), benzoic acid (4.205 ± 0.015; electrometric, potentiometric, spectrophotometric, and conductance measurements in many separate studies), ephedrine (9.63 ± 0.05; five potentiometric or spectrophotometric studies in different laboratories), isonicotinic acid (pK₁ = 1.77 ± 0.07, pK₂ = 4.90 ± 0.06; five potentiometric or spectrophotometric studies in different laboratories), nicotinic acid (pK₁ = 2.07 ± 0.07, pK₂ = 4.79 ± 0.04; six potentiometric, spectrophotometric, or capillary zone electrophoresis studies in different laboratories), phenobarbital (5‐ethyl‐5‐phenylbarbituric acid) (7.48 ± 0.02; potentiometric and spectrophotometric studies from several workers in multiple laboratories), nimesulide (6.51 ± 0.05; potentiometric and spectrophotometric studies in multiple laboratories), and chlorthalidone (9.35, potentiometric; 9.36, spectrophotometric/solubility‐pH). The recent comparative studies of Takacs‐Novak, Avdeef, and collaborators [[20], [21], [39], [40]] have gone some way toward increasing the stock of drug substances where agreement of replicated pK_a values to <0.05 has been found. Existing compilations of drug pK_a values almost invariably list only a single value for each compound. They do not comment on the conditions under which the value was obtained, or the quality of the data.

Conversely, there are many other drugs that have had their pK_a values reported more than once (in a few cases, eight or more times, e.g., ibuprofen, propranolol, and quinine), frequently by the same method, but often with discordant results. Examples include lidocaine (7.89 ± 0.07, from 6 independent potentiometric studies as long ago as 1948; but 7.18 from a recent conductance study), propranolol (11 studies giving values in the range 9.23–9.72), clofazimine (3 studies in the range 8.37–9.11), famotidine (6.76 by spectrophotometry, 6.89 by partitioning, and 6.98 by solubility–pH dependence), ibuprofen (8 studies giving values in the range 4.1–5.3), phenylbutazone (6 studies reporting values from 4.33 to 5.47), glibenclamide (5.3 by potentiometry, 6.3 by partitioning, and 6.8 by solubility–pH dependence), and also some of the fluoroquinolones. Some of these differences are due to differences in conditions, such as ionic strength or temperature, but others are experimental error. These variations are very rarely reported in previous secondary compilations.

Failure to take into account the effects of temperature, solvent composition, or ionic strength is usually responsible for differences between repeated measures of a drug pK_a value. This point was clearly made in a thorough report [41] on the pK_a values of numerous macrolide antibiotics. However, the large difference quoted above for lidocaine may be due to the failure of assumptions involved in an otherwise careful conductance study (pK_a = 7.18), the result of which is seriously at variance with six earlier potentiometric studies (pK_a = 7.89 ± 0.07, I = 0.00–0.15 M). It has been expressly stated [42] that the normal conductance method is unsuitable for acids with K_a < 10⁻⁵ (i.e., pK_a > 5).

Many of the drug pK_a values recorded in earlier volumes of the monograph series entitled Analytical Profiles of Drug Substances (now titled Analytical Profiles of Drugs and Excipients) were reported with little or no experimental detail. As well, there may be no primary references, an unsupported reference to secondary literature, or only a personal communication to identify the source of the data. Experimental details such as temperature, ionic strength, or solvent composition are critical for the assessment of data quality. These omissions are a matter of regret, especially where the pK_a value has been reported only once. Fortunately, more recent volumes in this series have begun to address these deficiencies. The same reservations regarding lack of experimental information also apply to the values listed in other earlier compilations.

The overriding aim of the present database is an attempt to make available as many as possible of the original sources, conditions, and methods for pK_a values of pharmaceutical interest that are in the literature. Then the users of such data can judge for themselves, as much as is possible, the reliability of these numbers, without having to search out original publications, many of which are becoming increasingly difficult to access. It is surprising how many drug pK_a values rest on unconvincing experimental work. The present emphasis on high‐throughput screening for potential therapeutic candidates means that there is an increasing demand for fundamental physicochemical quantities. These quantities are needed for the optimization of drug‐like properties in lead compounds. This demand is presently being filled at least partly by computerized (in silico) predictions. As the quality of the outputs from such predictive programs depend on the quality of the input data used for algorithm development or neural network training purposes, it is best to use input data that is as reliable as possible.