On the acid dissociation constants of bilirubin and biliverdin. pKa values from 13C NMR spectroscopy.

Biliverdin and bilirubin are naturally-occurring tetrapyrrolic bile pigments containing two propionic acid side chains. These side chains, and their propensity for ionization, are critical in the biological disposition of the pigments. Surprisingly, accurate dissociation constants for the propionic acid groups of biliverdin are unknown, and a wide range of values, extending over some 4 orders of magnitude, has been suggested for the Ka values of the propionic acid groups of bilirubin in aqueous solutions. Recently, pKa values of 6.7-9.3 have been reported for bilirubin-values much greater than the value of ∼5 typical of propionic acid groups. These curiously high values, currently being used to explain the biological transport and metabolism of bilirubin and related compounds, have been attributed to intramolecular hydrogen bonding. We have determined the pKa values of 99% 13C-enriched (13CO2>H) [83,123-13C2>]mesobilirubin-XIIIα, the corresponding biliverdin, and several monopropionic model compounds by 13C NMR spectroscopy. This technique allows direct observation and quantitative measurement of the carboxylic acid and carboxylate anion carbon signals. Analysis of the variation of carboxyl 13C NMR chemical shift with pH gave rubin pKa values of 4.2 and 4.9 and verdin pKa values of 3.9 and 5.3 in aqueous buffers containing only a very small quantity (0.086 mol fraction) of dimethyl sulfoxide. When extrapolated to water, the pKavalues are essentially unchanged. The data provide the first experimentally-determined pKa values for a biliverdin. They indicate that intramolecular hydrogen bonding has little effect on the acid dissociation of bilirubin and suggest that the equilibrium acidity of the bilirubin carboxylic acid groups is not abnormally high but similar to the thermodynamic acidity found in other carboxylic acids, as originally suggested by Overbeek et al. (Overbeek, J. T. G., Vink, C. L. J., and Deenstra, H. (1955) Recl. Trav. Chim. Pays-Bas 74, 81-84).

Bilirubin and biliverdin are blue-green and yellow-orange pigments formed from heme during normal metabolism in humans and other animals (1,2). Like heme, biliverdin and bilirubin have two propionic acid groups and low solubility in water (1)(2)(3). The acidity constants of bilirubin have been determined many times during the past 40 years (4 -13), but those of heme and biliverdin have not been measured (3). A mean pK a of ϳ5.3 has been predicted for porphyrin dicarboxylic acids (14), and pK a values of ϳ5.0 and ϳ7.2 have been estimated for biliverdin (3). A wide range of pK a values has been reported for bilirubin, with most investigators favoring a pK a of 6.2 to 6.5 (15), but recent determinations suggest that the true pK a values are even higher (6.8 to Ն 9.3) because of intramolecular hydrogen bonding (11,12). Since most carboxylic acid pK a values are ϳ5 and values Ͼ6 are seldom encountered (16 -18), these recent determinations imply a remarkable and unprecedented effect of intramolecular hydrogen bonding on proton dissociation. To investigate this effect, we have used 13 C NMR to study the dissociation of hydrogen-bonded and non-hydrogen-bonded pyrrolic acids and to determine the pK a values of mesobilirubin-XIII␣ (1) and mesobiliverdin-XIII␣ (2), two synthetic surrogates that differ from bilirubin and biliverdin, respectively, only by trivial differences in the nature, i.e. vinyl groups reduced to ethyl, and sequence of alkyl side chains on the lactam rings. Being remote from the propionic acid side chains, the alkyl substituents on the lactam rings are expected to have little influence on the dissociation constants of the carboxyl groups.
Aqueous solutions were prepared by adding 50 l of a 6-8 ϫ 10 Ϫ3 M stock solution of acid or its salt dissolved in deionized H 2 O to 500 l of buffer. Aqueous dimethyl sulfoxide solutions were prepared by adding a 50-l aliquot of a 6 -8 ϫ 10 Ϫ3 M stock solution of acid or its salt in (CD 3 ) 2 SO to an aliquot of buffer. Final sample concentrations typically ranged from 8 ϫ 10 Ϫ4 M to 2 ϫ 10 Ϫ5 M, with the chemical shift (␦ obs ) for the carboxyl group being independent of concentration in this range. Only a single, well-demarcated line appears in the carboxyl region of the 13 C NMR spectrum: that of the labeled carbon. Only trivial UVvisible spectral changes, 0 -2 nm bathochromic shifts, were detected in the pigment solutions with added (CD 3 ) 2 SO, from 1.8 to 27 volume %, in pH 7.4 Tris buffer, and solutions were usually optically clear. At 64 volume % (CD 3 ) 2 SO, the mesobilirubin absorption band half-width decreases slightly, causing a 20% increase in molar absorptivity and a 10-nm bathochromic shift of the absorption maximum. Mesobilirubin-XIII␣ (1) and mesobiliverdin-XIII␣ (2) were less soluble than dipyrrole 3 and monopyrrole 6 at low pH. Their solutions were prepared and analyzed 1 or 2 orders of magnitude more dilute, and the 13 C NMR spectra were run in 10-mm tubes with overnight scanning. Occasionally at low pH, some turbidity developed; however, this did not interfere with obtaining useful ␦ obs values for the dissolved pigment.
NMR measurements of ␦ obs for carboxyl groups were obtained with 60°pulse widths and duty cycles approximately 5 times T 1 on a Varian Unity Plus 500-MHz spectrometer. Three separate determinations were carried out for each acid; uncertainties in the measured pK a values were Ϯ 0.05. The NMR instrument settings and parameters specific to the Varian Unity Plus were as follows: frequency, 125.706 MHz; spectral width, 28,368.8 Hz; acquisition time, 2.000 s; relaxation time, 0.000 s; pulse width, 5.0 s; decouple, 1 H; high power, 40; decoupler continuously, on; Waltz 16 modulated software; double precision acquisition; line broadening, 1.8 Hz; and temperature, 25°C. The number of acquisitions varied depending on sample concentration. A sealed melting point capillary insert filled with 50 l of (CD 3 ) 2 SO was used as the lock and external reference to standardize all samples to an independent of environment reference.
Carboxylic acid pK a values were determined either graphically or by nonlinear regression analysis. In the first method, titration curves were constructed by plotting ␦ obs versus pH (19,23). The pK a values for monocarboxylic acids were read directly as the pH when ␦ obs ϭ 0.5 (␦ CO 2 H Ϫ ␦ CO -2 ). For a dicarboxylic acid, the pK a values were interpolated from the titration curves and literature (16) pK a values of the known dicarboxylic acid adipic acid, as described below. Alternatively, a modified Hill equation (24) was solved by nonlinear regression techniques. Solving the Hill equation for compounds 3 and 6 gave best fits for 0.86 Ͻ n Ͻ 0.93 and pK a values within 0.03 units of those found by the graphical method.

13
C NMR titration curves were determined for the following 99% 13 CO 2 H-enriched compounds: mesobilirubin-XIII␣ (1) and mesobiliverdin-XIII␣ (2); their tetrapyrrole counterparts bearing only one propionic acid (compounds 4 and 5, respectively); and di-and monopyrrole calibration compounds, 3 and 6, which cannot form intramolecular hydrogen bonds of the type seen in bilirubin. The titration curves of all of these compounds showed two plateaux, at low and high pH respectively, separated by ϳ5 ppm. These plateaux clearly represent the un-ionized and the fully ionized species, respectively, and the chemical shift dif-ference corresponds to the titration shift, ⌬ ϭ ␦ CO -2 Ϫ ␦ CO 2 H , where ␦ CO -2 is the chemical shift of the carboxylate anion and ␦ CO 2 H is the chemical shift of the carboxylic acid. The titration shifts observed (Table I) are consistent with those reported for a variety of carboxylic acids (20,21) and were found to be independent of the number of carboxylic acid groups and almost unaffected by added dimethyl sulfoxide, up to about 30 volume %.
Monocarboxylic Acids-All of the monocarboxylic compounds gave typical sigmoidal (␦ obs ) versus pH plots with one plateau corresponding to no ionization and the other to complete ionization as exemplified in Fig. 1. The pK a values (Table II) were determined by reading the pH at which ␦ obs ϭ 0.5 (␦ CO 2 H ϩ ␦ CO -2 ). Analysis of the data by the Hill equation (24) gave essentially identical results.
As noted previously for compound 6 and other carboxylic acids (19), the presence of (CD 3 ) 2 SO cosolvent influences the titration curves by displacing them slightly downward with increasing % (CD 3 ) 2 SO. Yet their shapes and the corresponding pK a values vary only modestly over the range of H 2 O/(CD 3 ) 2 SO solvent mixtures used. For example, for dipyrrinone acid 3 ( Fig.  1), the pK a values varied by only 0.13 pK units over the range 9 -64 volume % (2.5-31 mol %) (CD 3 ) 2 SO (Table II). This surprisingly small variation is probably due to the fact that in aqueous solutions containing as much as 64 volume % dimethyl sulfoxide, water is still the principle solvent (and base) on a molar scale. In fact, equimolar solutions are not reached until the volume % (CD 3 ) 2 SO reaches ϳ80%. Thus, when the solvent is mainly water, especially when the volume % of (CD 3 ) 2 SO Յ 27 (Ն91 mol % H 2 O), aqueous dimethyl sulfoxide solutions can be used for estimating the pK a values of water-insoluble carboxylic acids.
Previously, we noted that pK a values determined in aqueous dimethyl sulfoxide solutions could be extrapolated accurately to known pK a values in water (19). For compound 6, the small correction to 100% water was based on the excellent linear correlation between the pK a values and the logarithm of the volume % (CD 3 ) 2 SO. Similar empirical correlations have been noted previously (19). The extrapolated pK a thus obtained (pK a ϭ 4.7) is in perfect agreement with that measured directly in water (pK a ϭ 4.7). For xanthobilirubic acid (3), the linear correlation ( Fig. 1) led to a corrected value of 4.6 for the apparent pK a in water. Similarly, from the titration curves of the tetrapyrrole acids 4 and 5 ( Fig. 2), which are monopropionic acid analogs of biliverdin and bilirubin, the apparent pK a values were found to be 4.5 and 4.8, respectively, in aqueous dimethyl sulfoxide (31 mol %), which extrapolated to 4.3 and 4.5, respectively, for water (Table II).
Dicarboxylic Acids-Exact determinations of the two individual pK a values of a dicarboxylic acid are usually difficult (25) unless the titration curve exhibits an inflection lying between the plateaux; i.e. unless pK a2 Ӎ 3 ϩ pK a1 (or K a1 Ն ϳ10 3 K a2 ), a condition that applies to few dicarboxylic acids (16). For mesobilirubin-XIII␣ (1) and mesobiliverdin-XIII␣ (2), inflection points were not detected, as expected. However, limits on the apparent pK a values can readily be set from plots of ␦ obs versus pH. Thus, it is evident from the titration curves of pigments 1 and 2 (Fig. 2), which are similar to those of their monocarboxylic acid analogs, that the pK a value of each propionic acid lies between ϳ3.5 and 5.5. Fig. 2 also indicates that, despite the differing polarity and solubility properties of 1 and 2, their actual pK a values are similar to the intrinsic acidity constant of propionic acid, pK a ϭ 4.88 (16), as found for analogs 3-6 ( Table II).
The data do not permit an accurate determination of pK a1 and pK a2 for 1 and 2. However, the values can be estimated from the titration curve of a calibration standard, adipic acid. From the known acidity constants, pK a1 ϭ 4.44 and pK a2 ϭ 5.44 (16), and the measured ␦ obs versus pH titration curve, we found that pK a1 for adipic acid corresponds to the value of ␦ obs when ␦ obs ϭ ␦ (CO 2 H) 2 ϩ 0.354⌬, and pK a2 corresponds to the value of ␦ obs when ␦ obs ϭ ␦ (CO 2 H) 2 2 , viz., the difference between the chemical shift of the dianion and the chemical shift of the diacid (see Table I). Use of these correction factors gave pK a1 ϭ 4.2 and pK a2 ϭ 4.9 for rubin (1), and pK a1 ϭ 3.9 and pK a2 ϭ 5.3 for verdin (2) in 100% water (Table II). More accurate estimates of the pK a values would require knowledge of the exact carboxyl chemical shifts of the individual verdin and rubin monoanions, which would be difficult to measure (25). DISCUSSION Biliverdin and bilirubin are water-insoluble pigments that occur widely in nature (1). Although similar in constitution, they have markedly different physicochemical properties largely because of their different three-dimensional structures and modes of hydrogen bonding. Biliverdins tend to assume helical, "lock-washer," conformations in solution that are sta-bilized by intramolecular hydrogen bonding between NH groups and the unprotonated nitrogen atom (26,27); whereas, bilirubin adopts enantiomeric conformations that are shaped like ridge tiles and are stabilized by intramolecular hydrogen bonds between the pyrrole/lactam functions and the propionic carboxyl (or carboxylate) groups (26,28) (Fig. 3). In solution, enantiomeric conformers of bilirubin interconvert via nonplanar intermediates in which the hydrogen bonding network is never completely broken (28, 29) (not via flat non-hydrogenbonded conformers as proposed recently by Ostrow et al. (30)), and their chirality depends on their backbone shape (not on the unsymmetrical methyl-vinyl substitution pattern as erroneously stated by the same authors (30,48)). The ridge tile conformation is the only one that has been observed in crystals of bilirubin and its carboxylate salts (31)(32)(33), and spectroscopic, particularly NMR, studies supported by energy calculations strongly indicate that similar conformers prevail in solution, even in the dipolar protophilic solvent dimethyl sulfoxide (22,28,34,35). The preferred conformation of bilirubin in proteinfree aqueous solutions is not known, but calculations and the absorption spectra of freshly-made dilute solutions indicate that it is similar to that in dimethyl sulfoxide (29,36). The acid-base properties of biliverdin and bilirubin are undoubtedly important determinants of their transport, metabolism, and distribution within organisms, and the pK a values of the carboxyl groups of bilirubin are thought to be a key factor in its hepatic transport and neurotoxicity and in the formation of pigment gallstones (30,37,38). In view of the extensive literature on bile pigments and related compounds, it is surprising that there are no reliable measurements of the pK a values of biliverdin and that the pK a values of the carboxyl groups of bilirubin are controversial. There are several probable reasons for this dearth of definitive data. First, until recently there has been no persuasive reason to suppose that the carboxyl pK a values are anomalous or substantially different from the expected values of ϳ4. 5-5.5. Second, commercial preparations of bilirubin and biliverdin are generally impure, making them unsuitable for accurate pK a measurements, and difficult to purify (1). Third, bilirubin is prone to photoisomerization, even in dim light (39), and unstable in alkaline aqueous solutions in the dark, undergoing rapid radical reactions (1) that have often been neglected in pK a studies. Fourth, ionization of the carboxyl groups has little effect on the chromophores of biliverdin and bilirubin, making spectrophotometric methods of pK a determination insensitive and unreliable. Last, but probably the main reason, is the low solubility of the pigments in water (1, 3), particularly at pH Ͻ 7, which can cause precipitation and phase separation during pK a determinations.
There appear to be only two reports in the literature concerning the pK a values of biliverdin. Carey and Spivak (3) estimated pK a1 and pK a2 to be ϳ5.0 and 7.2, respectively, but precipitation of pigment at ϳpH 6.6 during acidimetric titration banjaxed accurate measurements (3). Gray et al. (5) were similarly unsuccessful. Many more measurements of the pK a values of bilirubin have been published (Table III). Several groups have used potentiometric or spectrophotometric backtitrations in water, methanol/water, or water/detergent (5,7,9,11). However, precipitation of pigment, causing breaks or inflections in the titration curves, is a major problem with these methods, and spectrophotometric titrations are further complicated by autoxidation and aggregation of bilirubin and by the requirement for accurate extinction coefficients for the unionized and ionized forms of the pigment in water, which are not available. Using the spectrophotometric method, Gray et al. (5) were unable to obtain accurate pK a values for bilirubin, but Moroi et al. (11) found values of 6.1-6.5 for pK a1 and 7.3-7.6 for pK a2 , ascribing these remarkably high values, without explanation, to intramolecular hydrogen bonding (11). In contrast, using similar methods, Kolosov and Shapovalenko (9) estimated pK a1 and pK a2 for bilirubin to be 4.5 and 5.9, respectively.
Because of the problems in working with aqueous solutions, Lee et al. (8) used dimethylformamide, in which bilirubin is soluble, as cosolvent for spectrophotometric titrations (8). They estimated pK a1 and pK a2 values for bilirubin in water to be 4.3 and 5.3, respectively. Hansen et al. (10) followed the ionization of bilirubin in dimethyl sulfoxide by natural abundance 13 C NMR and estimated the mean pK a of the two carboxyl groups, by extrapolation, to be 4.4 in water (10). These values are close to those expected for aliphatic carboxyl groups (16). More recently, Harman et al. (40) attempted to measure pK a values for bilirubin by micellar electrokinetic capillary chromatography but obtained inconclusive results.
Moroi et al. (11) and Ostrow et al. (12) used solubility methods to determine the pK a values for bilirubin (11,12). In general, the solubility method is less accurate than potentiometric, spectrophotometric, or conductimetric methods and is particularly prone to error if the acid contains impurities, especially impurities that are more soluble than the acid itself. Moroi et al. (11) used analytically pure bilirubin and estimated solubilities spectrophotometrically, whereas Ostrow et al. (12) used poorly characterized bilirubin preparations derived from unpurified commercial material and estimated bilirubin solubilities spectrophotometrically and by the nonspecific and rather insensitive diazo reaction. Both groups were unable to accurately measure the intrinsic solubility of un-ionized bilirubin and had to use estimates in calculating pK a values. Moroi et al. (11) FIG. 2. Upper panel, 13 C NMR titration curves of tetrapyrrole monopropionic acids 4 and 5 in aqueous (CD 3 ) 2 SO (0.31 mol fraction). The dashed lines connect the midpoint of the titration curve at ␦ obs ϭ 0.5 (␦ CO 2 H ϩ ␦ CO -2 ) to pH (pK a of the acid). Lower panel, 13 C NMR titration curves showing variation of carboxyl carbon 13 C NMR chemical shift (␦ obs ) with changes in pH for 99% 13 CO 2 H-enriched rubin 1 and verdin 2. The dashed line connects the midpoint of the titration curve of compound 1 in H 2 O Ϫ 27% vol (CD 3 ) 2 SO at ␦ obs ϭ 0.5 (␦ CO 2 H ϩ ␦ CO -2 ) to pH, which should be close to the average of the two pK a values, pK a1 and pK a2 . estimated pK a1 to be 6.0 -6.5 and pK a2 to be 7.3-7.7, whereas Ostrow et al. (12) found pK a1 to be 5.6 -6.8 and pK a2 to be Ͼ9.2. The latter incredibly high and widely separated pK a values were attributed to retarded proton dissociation caused by intramolecular hydrogen bonding. Recognizing the methodological deficiencies (13,30,41) of their earlier determinations, Ostrow and co-workers (13) subsequently remeasured dissociation constants for bilirubin using a complicated solvent partitioning technique involving extraction of chloroform solutions with aqueous buffer, back-extraction of aqueous extracts with chloroform, evaporation of the extracts, and diazo assay of the residues in dimethyl sulfoxide containing sodium taurocholate and sodium EDTA (13). They concluded that the two pK a values of bilirubin are not widely separated, as they had reported previously, but are similar, with values of pK a1 ϭ 8.12 and pK a2 ϭ 8.44. Derivation of these values was based on questionable assumptions regarding the solubilities, aggregation, and phase-transfer properties of bilirubin species. Again intramolecular hydrogen bonding was invoked as the cause of such remarkably high values.
The continuing disagreement over the pK a values of bilirubin (41,42), the increasing use of high values in the biomedical  (26,27,31,33) and by molecular dynamics calculations (28). literature (30), and the unprecedented effects being ascribed to intramolecular hydrogen bonding led us to reinvestigate the problem using 13 C NMR. This method is rapid and sensitive, allows direct observation of the carboxyl groups undergoing deprotonation (43), and, unlike partitioning and solubility methods, is insensitive to traces of polar impurities in the acid and does not require extensive manipulation or extraction of solutions. Although the technique has not been used extensively, its utility for measuring dissociation constants accurately is well established (44,45). It is particularly useful for bile pigments, because it focuses specifically on the carboxyl group. Ionization of pyrrole or lactam groups, which may occur at extreme pH values and can complicate spectrophotometric titrations, is not detected (21). Natural abundance 13 C NMR (10) has already been used to estimate pK a values for bilirubin, but the results have been dismissed because of the use of dimethyl sulfoxide as solvent (12,13,30). In our studies, we used highly labeled compounds and high field NMR to increase sensitivity and allow accurate measurements on dilute solutions. Since 13 COOH-labeled bilirubin and biliverdin are not easy to synthesize, we used the corresponding available meso-XIII␣ analogs as surrogates. The symmetrical side chain substitution pattern of these compounds simplifies the NMR spectra and amplifies the 13 C signals but is expected to have negligible effect on the intramolecular hydrogen bonding or pK a values compared with the natural analogs. We also measured the pK a values of a dipyrrolic pigment that cannot undergo intramolecular hydrogen bonding, of tetrapyrrole analogs with only one propionic acid side chain, and of the dicarboxylic acid standard adipic acid. Use of this interrelated set of compounds allowed us to examine specifically the effects of intramolecular hydrogen bonding and electrostatic interactions on pK a values. We used perdeuterated (CD 3 ) 2 SO as a cosolvent to facilitate the rapid preparation of solutions and to ensure that solutions remained homogeneous over a wide pH range, and we kept the concentration of cosolvent in the final solutions to Յ31 mol %. Solutions were optically clear and devoid of colloidal or particulate material, except at low pH, where there was sometimes some turbidity. However, any insoluble pigment present is not detected by the NMR under the conditions used, nor does it seem to interfere with the determination of the carboxyl chemical shift of the dissolved pigment. Although pK a values determined by 13 C NMR chemical shifts in (CD 3 ) 2 SO may differ markedly from those determined in water, pK a values of aryl and pyrrolic carboxylic acids derived by NMR in aqueous solutions containing up to 31 mol % (CD 3 ) 2 SO differ little from values determined in the absence of the organic cosolvent (28). Thus, the caveat that pK a values measured in aqueous organic solvents cannot be extrapolated to give reliable pK a values for water (46) does not apply to the present 13 C NMR method when aqueous dimethyl sulfoxide solutions containing excess water are used. As found previously (21) (Table II), values for the pK a of the monopyrrolic model compound 6 in aqueous (CD 3 ) 2 SO solutions were within about 0.1 pK a unit of the value measured in water, and extrapolation from the aqueous (CD 3 ) 2 SO data gave a value for water that was identical within the experimental error to the measured value of 4.7. Similarly, the water-insoluble dipyrrinone xanthobilirubic acid 3 showed typical sigmoid pH versus chemical shift curves in aqueous (CD 3 ) 2 SO solutions (Fig. 1). Apparent pK a values, determined from the midpoints of these curves varied by only 0.13 pK a units over the range 2.5-31 mol % (CD 3 ) 2 SO and were similar to the corresponding values for monopyrrolic acid 6. In addition, the slopes of the pK a versus log volume % (CD 3 ) 2 SO lines were similar for compounds 3 and 6, allowing an extrapolated value of 4.6 to be determined for the apparent pK a of xanthobilirubic acid in water.
The biliverdin analog 4 with one propionic acid showed a typical sigmoid titration curve in 31 mol % (CD 3 ) 2 SO (Fig. 2), qualitatively similar to those obtained with the mono and dipyrrolic acids 3 and 6. This curve undoubtedly corresponds to ionization of the lone carboxyl group. The apparent pK a for 4 in 31 mol % (CD 3 ) 2 SO was 4.5-close to, but slightly lower than the corresponding values for 3 and 6. Assuming that the slope of the pK a versus log volume % (CD 3 ) 2 SO plot for 4 would be similar to that for xanthobilirubic acid, we estimated the pK a for 4 in water to be ϳ4.3. Thus, the measured and extrapolated pK a values for the three monocarboxylic model compounds, 3, 4, and 6, for which intramolecular hydrogen bonding of the type seen in bilirubin is impossible, were similar and within the range expected for propionic acid groups. These results indicate that the presence of mono-, di-, or tetrapyrrole components has no unusual effect on propanoic side chain acidity, and they lend further support to the reliability and utility of 13 C NMR for determining the pK a values of bile pigments.
In contrast to the propionic acid group in verdin 4, the single propionic acid group in rubin 5 can participate in intramolecular hydrogen bonding of the type seen in the ridge tile conformation of bilirubin. Nevertheless, in 31 mol % (CD 3 ) 2 SO, 5 displayed a sigmoid titration curve (Fig. 2) that resembled the titration curve for the corresponding verdin 4 and yielded an apparent pK a of 4.8. Extrapolation to zero mol % (CD 3 ) 2 SO, as for the verdin 4, gave an estimated pK a of 4.5 for 5 in water. Comparison of the pK a values of 4 and 5 indicates that intramolecular hydrogen bonding within a ridge-tile conformation has little effect, if any, on the pK a . Hydrogen bonding may retard the dissociation of the COOH proton slightly, but it does not reduce the dissociation constant by orders of magnitude, as suggested previously (11-13, 30, 41).
The titration curves of the biliverdin analog 2 and the bilirubin analog 1 in aqueous (CD 3 ) 2 SO solutions were qualitatively similar and showed unambiguously that the pK a values for both compounds are below 5.5. The pK a values for the first and second ionizations, estimated using adipic acid as a standard and extrapolated to zero mol % (CD 3 ) 2 SO, were 3.9 and 5.3 for the verdin 2 and 4.2 and 4.9 for the rubin 1. From the measured pK a of the monopropionic verdin 5, pK a1 and pK a2 for the biliverdin analog 2 would be expected to be 4.0 and 4.6, respectively, taking into account the statistical factor but assuming negligible electrostatic repulsion between the carboxylate groups in the dianion. Thus, the measured pK a1 was close to the calculated value, but the measured pK a2 was greater than expected. The difference between the measured and calculated pK a2 values and the rather large difference of 1.4 pK a units between pK a1 and pK a2 suggests that the monoanion of verdin 2 may be stabilized by intramolecular hydrogen bonding (Fig. 3) and that there may be significant electrostatic repulsion between the propionate groups in 2, which is reasonable for a helical conformation. In contrast, the experimental values for both pK a1 and pK a2 for the rubin 1 were close to the values (4.2 and 4.0) calculated from the measured pK a of the monopropionic rubin 4. This excellent agreement indicates that electrostatic interactions between the carboxylate groups in bilirubins are unimportant with respect to pK a values, as expected for ridge-tile conformers. Again, comparison of the pK a values of the verdin 2 with those of the rubin 1 indicates that intramolecular hydrogen bonding of the carboxyl groups has no significant effect on either pK a1 or pK a2 .
These studies provide the first dissociation constants for the carboxyl groups of a synthetic biliverdin closely resembling the naturally occurring biliverdin IX␣, and they strongly suggest that the pK a values for the two carboxyl groups of monomeric bilirubin in water are close to 4.2 and 4.9, respectively. These values are consistent with the observed solubility properties of bilirubin (4). Our results are in good agreement with previous measurements by Lucassen (6), Hansen et al. (10), and by Lee et al. (8), and with the values originally assumed by Overbeek et al. (4) some 40 years ago. The much higher values that have been reported recently have been rationalized by invoking intramolecular hydrogen bonding (11-13, 30, 41). However, these rationalizations appear to be based on misconceptions concerning the effects of ionization and solvent on the structure of bilirubin in solution and erroneous ideas concerning the effects of hydrogen bonding on acidity. Some misconceptions are that the hydrogen-bonded structure of bilirubin in solution is rigid (30,47), that intramolecular hydrogen bonding is not maintained in dimethyl sulfoxide (12,13,30,48), that flat (nonhydrogen-bonded) conformations of bilirubin occur in solution (12,30), that intramolecular hydrogen bonding in the free acid suppresses ionization of the carboxyl groups (11-13, 30, 41, 49, 50), and that the carboxyl groups no longer undergo intramolecular hydrogen bonding after they are ionized (12,49). Such misconceptions have fueled the view that the acid dissociation constants of bilirubin are abnormally low because of hydrogen bonding. In addition, the focus on deprotonation or dissociation has neglected the potential stabilization of the carboxylate anion by intramolecular hydrogen bonding. In general, the effect of intramolecular hydrogen bonding on the pK a values of dicarboxylic acids is small except for instances in which intramolecular hydrogen bonding between carboxyl and carboxylate groups occurs in the monoanion (17,51,52), which is sterically unlikely for bilirubin, though possible for biliverdin. In such acids, for example maleic or phthalic acid, hydrogen bonding invariably lowers pK a1 rather than increases it, as claimed for bilirubin (30). In bilirubin, proton dissociation might be facilitated somewhat by stabilization of the resulting carboxylate anion by intramolecular hydrogen bonding to a dipyrrinone, but this stabilization would be offset by electrostatic repulsion between carboxylate and lactam oxygens. When large effects of intramolecular hydrogen bonding occur in dicarboxylic acids, they are manifested by abnormally large values of K a1 /K a2 (17,51,52), which is clearly not the case for bilirubin.
The biochemical relevance of the earlier measurements by Hansen et al. (10) and by Lee et al. (8) has been cursorily disregarded on the unfounded basis that intramolecular hydrogen bonding within the ridge-tile structure of bilirubin is not maintained in dimethylformamide and dimethyl sulfoxide (12,13,30), the solvents in which the measurements were made. For dimethylformamide, there is little evidence to show whether this is true or not, but for dimethyl sulfoxide there is extensive NMR and spectroscopic evidence that intramolecular hydrogen bonding is maintained, albeit slightly altered (34,35,53). This evidence indicates that the ridge tile structure prevails, although somewhat flattened, and that, at high sulfoxide concentrations in organic solvents or in pure anhydrous dimethyl sulfoxide, a sulfoxide group intercalates between each propionic carboxyl and its apposite dipyrrinone NH groups (35,54,55). Although such solvation might influence proton dissociation, it is not likely to increase it by several orders of magnitude. In the present studies, where all measurements were done in solutions containing excess water, solvation or putative hydrogen bond breaking by dimethyl sulfoxide is evidently irrelevant (56), as shown by the weak effects of dimethyl sulfoxide concentration on the carboxyl chemical shifts and the measured pK a values. This conclusion is supported by measurements of the second ionization constants for adipic, malonic, and maleic acids by the same technique, which gave values identical to those measured in water. 1 Thus, there is no plausible reason to expect that intramolecular hydrogen bonding would decrease the acidity of bilirubin, and arguments invoking hydrogen bonding to explain improbably large measured pK a values are specious.
We conclude that the acid dissociation constants of natural bilirubin and biliverdin are likely to be almost the same and within the normal range for aliphatic propionic acids. Consequently, when unbound bilirubin and biliverdin occur in the aqueous phase of living tissues at physiologic pH, the predominant species present will be the dianions, not the monoanions or un-ionized acids, and current theories of bilirubin distribution, toxicity, and gallstone formation that assume otherwise are implausible and need reevaluating. We detected no major effects of intramolecular hydrogen bonding on acid dissociation of the bilirubin analog mesobilirubin-XIII␣ and only a weak effect on the second ionization of the biliverdin analog mesobiliverdin-XIII␣, confounding the prevalent notion that such bonding inhibits proton dissociation from bilirubin. Intramolecular hydrogen bonding is undoubtedly important in the biological chemistry of bilirubin-not because it retards carboxyl dissociation, but because it engenders lipophilicity (57).