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Unconjugated bilirubin (UCB) is an unstable substance with very low aqueous solubility. Its aqueous pKa values affect many of its interactions, particularly their pH-dependence. A companion paper shows that only our prior solvent partition studies, leading to pKa values of 8.12 and 8.44, met all essential requirements for valid pKa determinations. Other published values, generally lower, some below 5.0, were shown to be invalid. The present work was designed to derive suitable models for interpreting published data on the pH-dependent binding of UCB with four agents, mentioned below, chosen because they are not, themselves, sensitive to changes in the pH range 4-10, and the data, mainly spectrometric, were of reasonable quality.
These analyses indicated that the high pKa values, dianion dimerization constant and solubilities of UCB at various pH values, derived from our partition studies, along with literature-derived pH- and time-dependent supersaturation effects, were essential for constructing useful models that showed good qualitative, and sometimes quantitative, fits with the data. In contrast, published pKa values below 5.0 were highly incompatible with the data for all systems considered. The primary species of bound UCB in our models were: undissociated diacid for phosphatidylcholine, dianion for dodecyl maltoside micelles and cyclodextrins, and both monoanions and dianion for sodium taurocholate. The resulting binding versus pH profiles differed strikingly from each other.
The insights derived from these analyses should be helpful to explore and interpret UCB binding to more complex, pH-sensitive, physiological moieties, such as proteins or membranes, in order to understand its functions.
The true pKa values of unconjugated bilirubin (UCB) are an important determinant of the proportion of the three ionization species of UCB in present in solution, and of the overall aqueous solubility of UCB, at any given pH value . In a companion paper  we re-examined many published studies that assessed pKa values for UCB in simple solutions, determined by a wide variety of methods. We critically assessed the reliability of the methods used, in relationship to minimal criteria for validity, as well as other considerations. We summarized the deficiencies in the many reports which suggested that pKa values of UCB were below 7.0 and even below 5.0 (see Table eight in Boiadjiev et al. ). The only experiments which fulfilled all the validity criteria were our solvent partition data [4,5], which indicated that the two pKa values were much higher, 8.12 and 8.44.
pKa values of UCB are clearly of great importance in determining the effects of pH on the interactions of UCB with other molecules . In the present paper, we critically re-examine and reinterpret several reports dealing with the effects of varied pH on the interactions of UCB with phospholipid vesicles, cyclodextrins, and dodecylmaltoside and bile salt micelles. Some general approaches have been developed to deal with the binding equilibria involved. We show that these studies are incompatible with proposed low aqueous pKa values for UCB. In several cases, the reinterpretations, using high pKa's and incorporating the effects of binding ratios, self-association and pH-dependent supersaturation, lead to some interesting new models and findings.
Studies of UCB binding vs. pH should meet the same criteria of validity proposed in the companion paper that deals with UCB alone in simple systems : 1) The UCB is pure; 2) There should be no significant degradation of UCB; 3) Measurements are made after a rapidly achieved equilibrium; 4) Unbound UCB concentrations are below to minimally above aqueous saturation; 5) The pH range studied should encompass all suggested pKa values of UCB, and sufficient data points should be available to permit mathematical modeling.
In addition, for studies of the effects of pH on UCB binding: 6) The large molecule or components of the aggregate must also be purified; 7) Changes with pH in the ionization and/or conformation of constituent regions of the large molecule or aggregate must not affect its intrinsic affinity for each UCB species. This last criterion renders it difficult to perform detailed mathematical modeling of pH effects on interactions of UCB with proteins, natural membranes and other biologically-relevant systems, which are often impure and include molecules whose conformation and binding properties for UCB are affected by pH in incompletely known ways.
Further discussion is needed regarding criterion 4, above, including the thermodynamic solubility of UCB crystals , and the possibility of stable supersaturation [6,7]. Brodersen & Theilgaard , showed that, after extensive sedimentation at 100,000 xg, the UCB concentrations were 0.1 μM at pH 7.40, 0.5 μM at pH 7.83, 17 μM at pH 8.05, and 34 μM at pH 8.2. Solubility calculated from our partition data  was 0.062 μM at pH 7.40, in reasonable agreement with the data of Brodersen's & Theilgaard , but our parition-derived solubilities at the higher pH values were considerably lower than theirs: 0.084 μM at pH pH 7.83, 0.112 μM at pH 8.05, and 0.148 μM at pH 8.2. Thus, for reasons discussed previously [4,6,7], stable supersaturation with UCB, up to fairly high UCB concentrations, may be expected at pH values of 8.0 and above, particularly with the short time intervals between solution preparation and data gathering in most spectroscopic studies. At modestly high concentrations of UCB, such supersaturation may actually be promoted by amphipathic additives, for example bile salts [8,9]. In the reinterpretations attempted below, we have made comparisons of results expected in the presence and absence of supersaturation and assuming high vs. low pKa values for UCB.
To find papers for possible review, we electronically searched PubMed (1967-date), and ISI and Chemical Abstracts databases back to 1950, using the keywords "bilirubin, bile pigments, binding, hydrogen-ion concentration, pH, pKa, ionization", as well as the reference lists in papers thus discovered. To locate papers published earlier than 1968, we manually searched T.K. With's two comprehensive compendia of studies related to bilirubin [10,11]. After eliminating papers that dealt only with bile pigments other than biladienes, or with bilirubin ester conjugates, papers were then eliminated that failed to meet the majority of the criteria of validity summarized above. In line with validity criterion 7, above, we then focused on studies of interactions of UCB with host systems not expected to be sensitive to pH in the range of 5.5 to 10. These 12 papers and one abstract are summarized in Additional files 1, 2 and 3 (Tables S1, S2 & S3), which specify experimental deficiencies for each study. Finally, we confined our detailed analyses to the four best studies; binding of UCB to phosphatidylcholine (PC) , dodecylmaltoside micelles , β-cyclodextrins , and sodium taurocholate .
The equilibria governing the binding of unconjugated bilirubin (UCB) involve its three unbound species, the protonated diacid (H2B), the monoanions (HB-) and the dianion (B=), one or more of which binds independently to a larger host system , such as phospholipid vesicles, cyclodextrins, or micelles. For each UCB species, this binding can then be described in terms of a distribution ratio, K = mols bound/mols unbound (free).
The ionization equilibria of the unbound species apply whether or not a binder is present. Thus, with a binder present, at any pH, the relative fraction (f) of each unbound monomeric species of UCB (fH2B, fHB-, and fB=) will be equal to f for that species, at the same pH, in an aqueous phase containing only monomeric UCB species . Therefore, as described in the appendix in Hahm et al. , these unbound fractions are determined solely by the pH and the assumed pKa values of the monomeric species. The total concentration of unbound, monomeric UCB species (Bm) is given by Bm = [H2B] + [HB-] + [B=] = [H2B] × (1 + K1/[H+] + K1.K2/[H+]2). Note that these illustrative calculations and simulations (Figures (Figures1,1, ,22 and and33 and Table Table1)1) deal only with pH effects on monomeric UCB species, so that fH2B + fHB- + fB= = 1.00. Additional effects of the formation of B= dimers  and supersaturation [7,9,16] have been considered below in the actual fitting of experimental data on UCB binding to phospholipid vesicles, cyclodextrins and micelles (Figures (Figures4,4, ,55 and and66 and Table Table22).
Figure Figure11 shows the fractions of UCB species over the pH range of 4 to 10, using the high pKa values of 8.12 and 8.44 . Table Table11 shows the fractions derived by applying the low pKa values of 4.2 and 4.9, advocated in recent papers [3,17-20]. For such low pKa values, B= is the dominant fraction at pH values above 7.0 (fB= ≥ 0.992, close to unity), with fH2B < 0.001 at pH values above 6.0 and fHB- < 0.001 at pH values above 8.0. In stark contrast, for pKa values above 8.0 , the f values of H2B, HB- and B= are moderately high over wide ranges of pH and are of comparable magnitude at most pH values between 6 and 10 (Figure (Figure1).1). At pH ≤ 6.0, only fH2B is above 0.99 and, over the pH range of 6.5 to 10.0, significant roles can be played by any of the three UCB species, each of which will show significant dependence on pH (Figure (Figure1).1). The inescapable qualitative conclusion from these considerations is that numerous studies which show UCB interactions increasing with pH in range of 6.5-10.0 are far more compatible with the high pKa values of UCB (> 8.0) than the low ones (< 5.0).
The values of pKa affect some characteristic features of the uptake and binding curves of UCB as a function of pH. As the pH increases, the equilibrium among the unbound species of UCB will shift to the more ionized forms (Figure (Figure1,1, Table Table1).1). The binding of UCB will, therefore, increase with pH if the preferentially bound species is B= (as proposed for sodium taurocholate micelles [1,21]), but will decrease with pH if H2B is preferentially bound (as proposed for PC vesicles [4,12]).
The mid-point pH values of plots of binding vs. pH may shift significantly from the pKa of the unbound UCB ligand according to its affinity for the large molecule or aggregate, especially if the binding affinity for one of the three UCB species, H2B, HB- and B=, is strongly dominant. This effect is easily modeled by assuming that only one of the three species is bound and that the unbound UCB concentrations are low enough for self-association of the unbound UCB species to be negligible. The proportions of the unbound species, H2B, HB- and B=, are determined by the pKa values and the pH and calculated from the relevant terms in the model equation , as described above. If the relevant UCB species is not the only one bound, but is the predominant bound species, these analyses still apply qualitatively and the plots will closely resemble those derived by assuming that only a single UCB species binds.
Figures Figures22 and and33 show some simple representations of such modeling, using the high pKa values of 8.12 and 8.44 ; the fraction F = [UCB]bound/[UCB]total is plotted against pH. For Figure Figure2,2, it is assumed that only H2B binds, e.g. to a phospholipid vesicle . The fraction F is calculated for values of the partition ratio K = [H2B]bound/[H2B]free, increasing from 0.2 to 104. As expected (Figure (Figure2),2), with increasing pH, F decreases sigmoidally due to the decreasing fraction (fH2B) of the unbound UCB diacid (Figure (Figure1).1). For each curve, its mid-point pH, where the binding of H2B is 50% of the maximum, is represented in Figure Figure22 by a shaded star. These mid-point pH values increase from 8.255 for K = 1, to 8.780 for K = 10, 9.251 for K = 102 and 9.778 for K = 103; for very low K values <<1 (e.g. for K = 0.2), the limiting mid-point pH is 7.994. This increase in the mid-point pH of the binding curves of H2B with increasing K is a general result that applies to binding to any large molecule and to any pKa values that are chosen. An example is binding of UCB to PC (Figure (Figure4,4, curve A)
When the UCB dianion, B=, is the only interacting species, the uptake or binding is expected to increase with pH (Figure (Figure3),3), due to the increasing fraction (fB=) of the unbound UCB dianion (Figure (Figure1).1). Figure Figure33 plots F vs. pH at values of K' (= [B=]bound/[B=]free) of 0.2, 1, 10, 102, 103 and 104, assuming the pKa values are 8.12 and 8.44. The mid-point pH values of these sigmoidal curves (shaded stars), where binding of B= is 50% of the maximum, decrease from 8.348 for K' = 1, to 7.863 for K' = 10, 7.315 for K' = 102, 6.794 for K' = 103 and 6.287 for K' = 104. The limiting value of the mid-point pH, when K' values are <<1 (e.g. K = 0.2), is 8.574. This trend of decreasing mid-point pH values with increasing K' is also a general result for binding of B= to any large molecule for any pKa values chosen.
Many curves of UCB interactions as a function of pH show binding increasing with increasing pH (Figure (Figure5;5; Additional files 1, 2 and 3, Tables S1, S2 & S3), indicating a primary role for the binding of B= and dictating that the mid-point pH values must be lower than the true pKa values of unbound UCB (Figure (Figure3).3). Therefore, the large number of these titration curves with mid-point pH values between 6 and 8 are compatible with high pKa values of 8.12 and 8.44 , and quite incompatible with pKa values below 5.0. If pKa values were low, e.g. 4.2 and 4.9 [3,17-20], curves showing increasing binding of UCB with increasing pH and, therefore, binding of B=, would yield mid-point pH values lower than about 5.0.
The mid-point pH values of sigmoidal titration curves, like those in Figures Figures22 & 3, are sometimes misinterpreted as average pKa values. This is clearly wrong, since all of the curves in Figures Figures22 &3 assume the pKa values of unbound monomeric UCB to be 8.12 and 8.44.
Unilamellar vesicles of phosphatidylcholine (PC) are bilayers with a hydrophobic core of the fatty acid polymethylene chains, and hydrophilic exterior and interior surfaces composed of phosphryl-choline sidechains whose terminal -N+(CH3)3 groups are on the surfaces . In the pH range 4 to 10, PC's are zwitterions, with both the amine and phosphoric acid groups fully ionized [23,24]; thus, changes in UCB binding to PC may be attributed to altered proportions of the three ionization states of unbound UCB in this pH range. Depending upon the molar ratios and experimental conditions under which the UCB and PC are mixed, either H2B or B= may be the UCB species that is preferentially bound .
pH effects on the interactions of UCB with PC vesicles have been reported in a number of studies [12,16,22,25-27]. Many of them involve time-dependent processes in non-equilibrium situations. Some used PC systems containing fluorescent probes, which are difficult to interpret due to uncertainties regarding the localization of the probes and the nature of their interactions with UCB.
The report by Tipping et al. , which assessed binding of UCB to egg PC vesicles from the effects of binding on the spectrum of UCB, most fulfills the above criteria of an acceptable study (Additional file 1, Table S1), although neither the UCB (10 μM) nor the PC (100 μM) were purified. We have, therefore, amplified our previous analysis  of this study.
The data points in Figure Figure44 (black squares) show values of ñ (moles of UCB bound per mole of total PC) vs. pH over the pH range of 6.54 to 9.54, obtained from Figure 10 in the paper of Tipping et al. . ñ decreases from a maximum of 0.049 as pH increases, indicating (see Figure Figure2)2) that the binding of H2B is the predominant interaction. The concentration of bound UCB (Bb = ñ × 100 μM) is then used to calculate the concentration of unbound UCB (Bf = 10 μM - Bb). Bf ranges from 5.1 μM at pH 6.54 to 9.5 μM at pH 9.54.
At each pH, the fraction of unbound H2B (= [H2B]f/Bt) in the presence of 100 μM PC , is assumed to be equal to the fraction of H2B ([H2B]/Bw) in the aqueous phase in the absence of PC, calculated using Equation four in Hahm et al. ) and applying the high pKa values of 8.12 and 8.44 and the dimerization constant for the B= dianion of 0.26 μM-1.
Assuming that unbound UCB is in a solution state and that H2B is the only species that binds to the PC yields a simple model of distribution of H2B between the free and vesicle-bound state, ñ = K" [H2B]f. Applying this equation to the 9 data points of Tipping et al. , yields a mean K" = 0.00932 ± 0.00053 μM-1) and curve A in Figure Figure4).4). The fit of curve A with the experimental ñ values (black squares) is quite good (r = 0.953), and suggests that our assumptions are valid and that the H2B partition model is reasonable. The deviation of the data points from Curve A at the highest two pH values possibly reflects weak binding of the B= dianion [16,22,27], which constitutes over 80% of the UCB species above pH 9.0.
Tipping et al.  reported that "The spectral differences developed within the time required to mix the solutions and start recording and were the same whether multilamellar or unilamellar vesicles were used". This rapid analysis and establishment of equilibrium are necessary conditions for our detailed interpretation of the data. With the total concentrations of UCB = 10 μM and PC = 100 μM (molar ratio of UCB/PC, 0.1) used in the pH-variation study, the unbound UCB concentrations (Bf) at equilibrium were modestly above the aqueous solubility of UCB at all pH values ≤ 9.0 . If supersaturation were absent, the concentration of H2B would be at its saturation value over the entire pH range, and ñ should maintain its value of 0.049 at pH 6.54 (the horizontal dashed line B, in Figure Figure4).4). The experimental data indicate, therefore, that stable supersaturation was indeed likely present in these short term experiments.
If, by contrast, the low pKa values of 4.2 and 4.9 [3,17-20], are used to fit the ñ value at pH 6.54, a much higher value of K", 94 μM-1, is needed to yield the calculated [H2B]. Using this constant and [H2B], determined from Bf and the low pKa values, yields curve C in Figure Figure4.4. As pH increases from 6.5 to 7, ñ decreases steeply, and is below 0.01 at a pH of 6.9 or higher. The low pKa values are, thus, not compatible with ñ vs. pH data determined for the binding of UCB by neutral PC vesicles . Since, in this study, K ≈ 1 , the mid-point pH value of 8.1 (shaded star, Figure Figure4,4, curve A) would be close to the mid-point value of the curve for K = 1 in Figure Figure2,2, and thus compatible with our proposed high pKa values in the absence of a UCB binder .
Comments are warranted on an often-cited study, by Eriksen, et al., of the binding of UCB to egg PC vesicles . The concentrations were 12.8 μM UCB and 130 μM PC. Figure two in that paper plots the changes with pH of the quenching by bound UCB of the fluorescence of diphenyl-hexatriene incorporated into the lipid bilayer, measured 3 hours after adding the UCB in an aqueous alkaline solution (pH 11). The sigmoidal curve exhibits decreasing fluorescence (increasing quenching by bound UCB) as pH increases, with a mid-point near pH 7.8. This evidence for increased affinity of UCB binding to PC as pH increases would indicate a primary role of binding of the dianion, B=. Since the dianion fraction for low pKa values is already 0.992 at pH 7.0 (Table (Table1),1), any significant increase in binding at higher pH values is incompatible with low pH values (see above). The increasing affinity of UCB for PC with increasing pH is in stark contrast to Tipping's data  and to our model based on uptake of H2B (above). However, examination of data in Table one of the Eriksen paper, reveals that results obtained "immediately" after adding the UCB at pH 7.4 and 8.3 are just the reverse of those obtained three hours later (as in their Figure two).
Eriksen's Figure one  indicates complex, pH-dependent time effects. Using the percent decrease in fluorescence, P, as a rough measure of the extent of binding of UCB, the data show a high value of P = 79% at pH 7.43 "immediately" after addition of UCB. Within one minute, there is rapid reversal of binding and P is decreased to 28%, followed by a far less rapid decrease in P to 23% after 3 hours. Results at pH 6.79 are similar. In contrast, at the highest pH in their Figure one, 8.34, the "immediate" value of P = 57% remains about the same for three hours. At the intermediate pH of 7.90, the "immediate" value of P = 73% increases a little over the first minute, remains about the same for four more minutes, and then decreases gently over the next two hours or so to a plateau of P = 22%. These complex time effects yield very different sequences of P values decreasing with pH: 7.43>7.90>8.34 for "immediate" measurements; the irregular sequence 7.90>8.34>7.43 between 1 and 20 minutes; 8.43>7.90>7.43 at 60 minutes; and 8.34>7.90 ≈ 7.43 at 3 hours. Some discrepancies among data in Eriksen's Table one, Figure one and Figure two , suggest irreproducible time effects.
These observations can be rationalized roughly on the basis of the progressive formation of aggregates of UCB, after the initial rapid binding of UCB. Cestaro et al.  have made a similar proposal, and Eriksen et al.  themselves warn that, as the pH falls, supersaturation of the aqueous medium with UCB must be avoided to prevent progressive formation of H2B aggregates. Their gradient ultracentrifugation data of 3 hour incubations (Figures three-d&e of Eriksen et al.)  showed large aggregates of UCB, with or without phospholipids, at pH 7.0 and smaller aggregates at pH 8.2. The dependence on pH, of the rates of formation of colloids and precipitates from supersaturated solutions of UCB itself, is clearly relevant. As discussed earlier, after extensive sedimentation at 100,000 xg, the measured supernatant concentrations of UCB at pH values of 7.40, 7.83, 8.05 and 8.2 were 0.1 μM, 0.5 μM, 17 μM and 34 μM respectively . These are much higher than the calculated solubilities of UCB at the same pH values , which were low (0.062 μM, 0.084 μM, 0.112 μM and 0.148 μM) and increased only a little as pH increased. This indicates that the egg PC-UCB systems of Eriksen et al.  were highly supersaturated when first prepared, and that aggregates of UCB formed to relieve the supersaturation. This occurred to a much greater extent and much more rapidly at pH 7.43 than at pH 8.34, with intermediate behavior at pH 7.90. Any micro-precipitation of UCB, which may contain small proportions of PC, will reduce Bf and its interactions with PC vesicles. Vazquez et al.  have also reported significant reversal of UCB interaction with phospholipid membranes with time.
In view of the above considerations, and evidence that the uptake of UCB by PC vesicles is almost instantaneous (t1/2 = 2 msec) , we conclude that the "immediate" effects on P after addition of UCB to PC are least susceptible to time-dependent effects arising from the thermodynamic drive to decrease supersaturation. Indeed, even the "immediate" values of P may still be subject to some aggregation effects, particularly at pH 7.43. The qualitative trend in the "immediate" decrease of P with increasing pH is consistent with the results of Tipping et al.  and with our model, based on the binding of H2B and high pKa values for UCB. The conclusions are opposite to those given by Eriksen et al. , which were based on assumptions of binding of the dianion, B=, and low pKa values.
Other systems studied by Eriksen et al.  (their Table one and Figure one-b) also show exceptionally large and rapid decreases in binding of UCB with time at pH 7.4, intermediate behavior at pH 7.90, and minor effects at pH 8.34. These systems all contained 12.8 μM UCB, mixed with various types of phospholipids ± cholesterol, at varied concentrations: egg PC, 150 μM + cholesterol 15 μM; phosphatidlyethanolamine, 106 μM; phosphatidlyethanolamine, 102 μM + cholesterol 10 μM; sphingomyelin, 32 μM; and phosphatidylserine, 55 μM. The qualitative interpretations above apply to all of them. The data points are limited, and some of these systems involve charge effects, which introduce further uncertainties. In all systems, after 3 hours, UCB binding is greater at pH 8.3 than at pH 7.4. The "immediate" results, however, show a stronger reverse effect of pH, P = 82% at pH 7.4 vs. 25% at pH 8.3, for the egg PC-cholesterol system as compared to the egg PC system. They also show lower binding to sphingomyelin at the higher pH, indicating predominant binding of H2B. This common pattern leads us to conclude that the complex pH-dependence of precipitation of UCB from supersaturated solutions can lead to highly anomalous pH-dependence of UCB interactions with phospholipids.
The study of UCB binding to gangliosides by Vazquez et al. , reported little change in UCB binding going to pH 7.4 to 8.0, but a small increase in going from pH 7.0 to 7.4, suggesting an important role for UCB anions. Assuming low pKa values, the unbound dianion fraction changes only from 0.992 at pH 7.0 to 0.999 at pH 8.0, whereas the monoanion fraction decreases by a factor of 10 (Table (Table1).1). Therefore, these observations are incompatible with low pKa values, whereas with high pKa values, both the mono- and dianon fractions increase significantly over this pH range (Figure (Figure1).1). Other problems with this study (Additional file 1, Table S1) are that: the systems were highly supersaturated with UCB, the UCB was neither purified nor protected against degradation, equilibrium was not attained rapidly, and the pH range studied was insufficiently broad to derive pKa values.
Zucker and Gössling used stop-flow kinetics to examine the rates of uptake of BSA-bound UCB by cultured HepG2 cells . They found an inverse correlation between pH and the rate of UCB flip-flop, which they showed to be due to pH effects on the rates of dissociation of UCB from albumin and from the membrane bilayer. They concluded that "the identification of an inflection point at pH 8.1 is indicative of a pKa value for bilirubin in this range". Although this seemingly supports our contention that the pKa's of UCB are above 8.0 , these are kinetic and not equilibrium data, involve BSA (which is pH-sensitive in this range), and measure diffusion across a complex hepatocyte membrane. Studies of binding of UCB to whole cells , or natural membranes (e.g. red cell ghosts, mitochondria, synaptosomes) [28,32-35], likewise cannot be used to evaluate unequivocally the role of pKa values for UCB. These heterogeneous structures contain a mix of phospholipids, as well as proteins and other components, which may ionize and change conformation in the pH range studied and have unknown effects on membrane structure.
Non-ionic long-chain alkyl-saccharides, such as octylglucoside (C8G) or dodecylmaltoside (C12M), are readily purified and form micellar systems that are suitable for studies of the influence of pH on the uptake of UCB. Binding probably involves interactions of the -OH groups of the saccharide with the ionized -COO- groups of UCB, and induces marked changes in the ellipticity of the bound UCB .
Kano et al.  showed that solubilization of UCB (20 μM) in 1 mM C12M micelles (their Figure five) generated no circular dichroism effects from pH 4.5 to 6.2. (Note that their legend for Figure five misidentifies the saccharide as C8M, octylmaltoside; the text indicates it is C12M that was studied.) Kano's Figure three shows that UCB does not interact with C8G below the c.m.c. of 22 mM. The same would be expected of C8M, whose c.m.c. value should be similarly high, but the concentration of the alkyl-saccharide used in their Figure five is 1 mM, well below the presumed c.m.c. of C8M.) Above pH 6.2, the observed ellipiticity increased steeply with rising pH up to about pH 8.5, and leveled off to a constant value from pH 8.8 to 10. Since the conformation of the non-ionic C12M is unaffected by pH, their titration curve reflects increased binding of UCB dianion (B=) as the proportion of unbound dianion, fB=, increases with increasing pH.
The rise in ellipticity with pH has a mid-point of about pH 7.5. Reference to our Figure Figure33 shows that this is compatible with high pKa values of 8.12 and 8.44 and a UCB distribution ratio K (bound/free) between 10 and 100. If the low pKa values of 4.2 and 4.9 are invoked, the midpoint pH value would have to be lower than about 5, as discussed above. Moreover, at pH 6.5, the fraction of UCB dianion, fB=, would already be 97.5%, yet the observed ellipticity is near zero at that pH. In addition, the steep rise in ellipticity observed above pH 6.5 would not be expected. Thus, only the higher pKa values are compatible with the observed data.
Kano et al.  and Lightner et al.  studied CD of UCB in solutions of β-cyclodextrin (β-CDx) as a function of pH. Both studies used purified UCB and were conducted within minutes of mixing UCB with the cyclodextrins; Kano's studies also took precautions to minimize oxidation and photo-oxidation of the pigment. In each study, the molar circular dichroism absorption coefficient (Δε) was minimal at pH 6.0 and increased steeply as pH increased above pH 7.0, indicating that UCB dianions are the primary interacting species. Lightner's systems  were even more supersaturated than Kano's and measurements were provided only at integral pH values from 6 to 10, rendering Kano's data  preferable for analysis.
In the study by Kano et al. of UCB binding to β-CDx , no ellipticity was observed at pH 5.5, but Δε increased sigmoidally as pH increased from 5.5 to 9.5, with a steep slope between pH 7.0 and 8.5, and no further change between pH 9.5 and 10.8 (their Figure Figure3).3). Chiral recognition effects, registered at several pH values with the protonated 1-amino-β-cyclodextrin as the host molecule, (their Figure three ), support the conclusion that predominantly UCB dianion was bound.
At pH 10.8, an affinity constant of 23 L/mol was reported for UCB binding to β-CDx, indicating that 4.67 μM, or 18.7% of the total [UCB] (25 μM), was bound to 10 mM β-CDx at that pH. Assuming that the UCB binding is confined to B=, and that binding of UCB is proportional to the concentration of unbound, monomeric B=, the amount of UCB bound at lower pH values can be calculated using Δε values relative to Δε at pH 10.8. It is then possible to calculate Bf and, akin to modeling the data on binding of UCB to PC as described above, to apply Equation four of Hahm et al.  to calculate the unbound, monomeric dianion concentration, [B=], at each pH, assuming different pKa values.
Assuming the high pKa values of 8.12 and 8.44 and the dianion dimerization constant of 0.26 μM-1  in calculating [B=]f from Bf, the four data points at pH values of 10.8, 9.5, 8.65 and 8.2 showed an excellent proportionality between Δε and [B=] using the equation Δε = Q × [B=]f, where the constant, Q = 1.099 ± 0.018 (n = 4, r = 0.974, S.D. = 0.17). Curve A in Figure Figure55 shows the results of fitting all the data to the above equation, Δε = 1.099 × [B=]. Curve A gives a reasonable fit for the experimental Δε at the five highest pH values (7.83 and above) and, of course, the very low pH of 5.5, where Δε = 0. Bf was below calculated solubilities at both pH 10.8 and 9.5, but there was likely stable supersaturation of the unbound UCB phase at the three lower pH values, based on previous observations , as discussed earlier. The rapid decrease in Δε below pH 8.65 is primarily due to the rapid decrease in the fraction of unbound monomeric UCB that exists as the dianion (fB=). The systematic discrepancies between the data and Curve A in the pH range of 7.3 to 6.9 (Figure (Figure5)5) can be ascribed to many factors that are difficult to evaluate, including self-aggregation of the more highly supersaturated phase of unbound UCB (e.g. R = 369 at pH 7.0).
In comparison to the reasonable representation of the Δε data using pKa values above 8.0, the results obtained are very different (Figure (Figure5,5, Curve B) if the lower pKa values of 4.2 and 4.9 [3,17-20], are used to calculate [B=] from Bf. The proportionality constant K, relating Δε to [B=] was determined by fitting the data at the pH values of 9.5 and 10.8, where the solutions are undersaturated with unbound UCB. K was then used to calculate Δε from the estimated [B=] at other pH values. Since the dianion fraction (fB=) of unbound UCB would be close to unity at pH 7.0 or above, and have the value of 0.79 even at pH 5.5, little variation is expected in [B=] and, therefore, in Δε over the alkaline pH range. This is shown by Curve B in Figure Figure5,5, which does not fit Kano's Δε vs. pH data . This indicates that the low pKa values are highly incompatible with the experimental observations. The same conclusions apply to the data of Lightner et al. , which show similar pH dependence of binding at alkaline pH.
From the mean fit of the Δε data at pH 9.5 and 10.8 to the concentrations of [B=] calculated using pKa values of 8.12 and 8.44 and the dianion dimerization constant of 0.26 μM-1, it is possible to calculate Δε from [B=] at lower pH values, where total solution concentrations are above solubility, by assuming that all solutions are at true saturation, with the excess [B=] forming a suspension. For such systems, [B=] = 0.051 × 10(2pH-16.56). Here, 0.051 μM is the solubility of H2B and 16.56 = pKa1 + pKa2 [4,6]. The calculated curve C (Figure (Figure5)5) shows a steep drop in Δε below pH 9.3. Curve C has little resemblance to the experimental data, suggesting that, at most pH values, a stable supersaturation was probably important in these relatively short-term experiments.
Taurine-amidates of bile salts, which have pKa values near 1.0, are the only bile salts which are fully ionized throughout the pH range from 4 to 10 , and are thus most suitable to assess the roles of pH and pKa values on UCB binding. Rapid solvent partition of purified UCB from undersaturated chloroform solutions into buffered aqueous solutions of 50 mM taurocholate (TC) (at least 80% in micelles), at ionic strength = 0.15, was performed over the pH range of 6.0 to 9.5 [1,21]. The data were fitted to the equation log P = log Po + [1 + 10(pH-A) + 10(2pH-B)], where Po is the partition ratio for H2B, and the values for A and B were 7.36 ± 0.5 and 14.08 ± 0.05 respectively.
Solubilities of UCB in 50 mM TC  and in water  were calculated from the fitted P data and an estimated solubility of UCB in chloroform of 1.14 mM . (As argued before [4,6], a better estimate of the solubility of UCB in chloroform is 0.88 mM, which will decrease the estimated UCB solubilities in 50 mM TC and water by 23%, but not affect the shape of the titration curves.) Using the high aqueous pKa values of 8.12 and 8.44, the total and unbound concentrations of each UCB species in 50 mM TC was calculated from the solubilities in 50 mM TC/chloroform  and water/chloroform  respectively; their difference equaled the concentration of the bound species. From these, the distribution ratios (bound/free) of the three UCB species were calculated to be 1.41 for H2B, 12.9 for HB-, and 730 for B=, indicating predominant binding of B= , as concluded previously by Kano et al. . From the relative contributions of bound B=, HB- and H2B, the apparent pKa values of UCB associated with the TC were estimated: 7.16 ± 0.5 for pKa1, 6.69 ± 0.5 for pKa2 and 13.85 ± 0.05 for the sum of pKa1 and pKa2, which is derived with somewhat greater precision.
The relationship of these pKa values, lower than the aqueous values of 8.12 and 8.44, to micelle-water distribution ratios for H2B, HB- and B=, has been discussed in our companion paper . pKa values in the bile salt systems in the range of 6 to 7 have also been reported from studies using micellar electrokinetic capillary chromatography [39,40]. Since these authors did not determine micelle-water distributions, these were average values for the whole system, but appear to be compatible with Hahm's pKa values in 50 mM TC derived by solvent partition . Utilizing essentially the same equations [1,40] relating changes in pKa values resulting from uptake in micelles and micelle-water distribution ratios for H2B, HB- and B= mentioned above , the pKa values of 6 to 7 in 50 mM TC are thus compatible with the high pKa values in water .
CD studies have been performed with unpurified UCB in 50 mM solutions of various bile salts [15,41,42]. In many cases, the UCB concentrations used appear to be above saturation. For 50 mM sodium taurocholate (TC), calculated Bf was above aqueous phase saturation at pH below 7.5 when total UCB was 4.6 μM and at pH below 8.3 when total UCB was 34 μM. Bile salts, however, have been shown to promote extensive, stable supersaturation of UCB [8,9]. In systems of UCB in 50 mM TC , the observed ellipticities were reasonably proportional to the two UCB concentrations, even though the calculated solubility in 50 mM TC was exceeded at several pH values. Similar proportionalities are seen over higher ranges of concentration of sodium glycocholate  and sodium deoxycholate  at pH values of 7.0 and above.
Since background information is available for 50 mM TC  and TC is expected to show no dependence upon pH, we have attempted a semi-quantitative interpretation of the pH effects for the ellipticity study of 4.6 μM and 34 μM UCB in 50 mM TC . We assumed stable supersaturation in these short-term experiments (30 min or less) at pH values of 7.23 and higher. Table Table22 presents ellipiticity values at 458 nm, estimated from their published graphs. The three measurements at 4.6 μM UCB have been multiplied by the factor, 34/4.6 to render them comparable to measurements at 34 μM UCB. The ellipticities are large and negative at the two lowest pH values of 7.23 and 7.35, become positive at pH about 8.1, and then show higher positive values as pH increases to 9.1 and above. This general trend was exhibited by all the bile salts studied [15,41,42].
As noted earlier, equations relating partition coefficients to pH for 50 mM TC  and water  allow the calculation of the fractions of total UCB solubilized by the TC as H2B, HB- and B=. The pH-dependence of the ellipticity values at 458 nm suggest strongly that the interactions with TC aggregates of the solubilized HB- cause negative ellipticities whereas interactions of the solubilized B= cause positive ellipticities. Table Table22 shows the estimated fractions of total UCB (34 μM) that are bound to TC as HB- and B=. As expected, as pH increases, the fraction of total UCB that is bound to TC as HB- (fsHB-) decreases and the fraction bound as B= (fsB=) increases. In order to test our model, we use the equation below in which the constants A* and B* are measures of the effectiveness of (fsHB-) and (fsB=) in determining the value of 103θ:
The experimental ellipticity values in Table Table22 are well described by this equation: n = 7, r = 0.992, SD = 1.1, A* = -98.7 ± 5.6, B* = 5.24 ± 0.54. Figure Figure66 shows that, at total UCB concentrations of 4.6 and 34 μM, the experimental ellipticities are in reasonable concordance with calculated ellipticities. Note that the two most positive ellipticity values for 4.6 μM UCB, at pH 8.13 and 9.12, and for 34 μM UCB at 9.35 and 11.60 were measured in unsaturated solutions. The significant changes in ellipticity at these high pH values are clearly due to significant changes in (fsHB-) and (fsB=) over this alkaline pH range. Remarkably, the measured ellipticity increased significantly, by about 2%, between pH 9.35 and 11.60, which is matched by a calculated increase in ellipticity of about 4%. Since, if low pKa values are assumed (Table (Table1),1), fB= is already close to unity at pH 8.5 (0.9997), and the changes in ellipticity at pH values above 9.0 are qualitatively incompatible with the low pKa values for UCB proposed by others [3,17-20]. The model proposed here for representing the circular dichroism values of UCB in 50 mM TC appears to be new and is likely to be useful also for other bile salt systems.
The analyses and interpretations presented above show that the high pKa values of 8.12 and 8.44 [1,4-6] are far superior to low pKa values of 4.2 and 4.9 [3,17-20] in rationalizing experimental data for the effects of pH on interactions of UCB with PC vesicles, cyclodextrins, and micelles of dodecyl maltoside and bile salts. The approaches outlined also demonstrate and take into account the possibly important roles of self-association of B= and pH-dependent supersaturation effects. They support further the conclusions of our companion paper  that analyzes the effects of pH on various properties of UCB alone in aqueous and organic solvent systems. That paper demonstrated that only our solvent partition studies [4,5] met all the requirements for valid experiments when using a poorly-soluble, unstable compound, such as UCB. Together, the two present papers clearly indicate that the pKa values of UCB are well above the pKa values of simple carboxylic acids (usually about 4.5). Theoretically these remarkably high values may result from the combined interactions of three factors that result from the unique, complex internal hydrogen-bonding of UCB, as presented elsewhere .
We do not claim that the high pKa values of 8.12 and 8.44, derived from our solvent partition study of UCB , are exact. The accuracy of these model-derived high pKa values of UCB is given on page 1131 of that paper. These values (mean ± S.D.) are: pK'1 = 8.12 ± 0.23; pK'1 + pK'2 = 16.56 ± 0.10; pK'2 = 8.44 ± 0.33. That paper also notes that "the analysis yields a less accurate estimate of the individual pKa values than of their sum, pK1 + pK2". The errors in these pKa values are insignificant when compared with the difference of 7.5 pH units between the sum (pK1 + pK2) of these high pKa values, and the sum (9.1) of the low pKa values of 4.2 and 4.9 proposed by others [3,17-20], with which our high pKa values were compared.
It should thus now be clear that such high pKa values not only acceptably explain the experimental findings on the effects of pH on the properties and interactions of UCB, but that the often quoted low pKa values [3,17-20], are incompatible with the experimental data. The implications are not trivial, since they invalidate older, but still widely held, interpretations and modeling of the binding and cytotoxicity of UCB [43-47] that were based on the assumptions that pKa values were below 5.0 and that B= was, therefore the dominant species of unbound UCB in the physiological pH range (Table (Table1).1). More recent reviews are available [1,48,49] that are based on the realistic pKa values above 8.0, and the consequent predominance of H2B among the unbound UCB species at physiological pH values (Figure (Figure11).
UCB: unconjugated bilirubin; H2B: UCB diacid; HB-: UCB monoanions; B=: UCB dianion; fH2B: fHB-, and fB=, relative fractions of the unbound monomeric UCB species; F: [UCB]bound/[UCB]total; Bf: unbound (free) UCB concentration; R: the UCB saturation ratio = Bf/estimated solubility of UCB at a given pH; K: distribution ratio = mols bound/mols unbound (free); PC: phosphatidylcholine; c.m.c., critical micellar concentration; C12M: dodecylmaltoside; C8M: octylmaltoside; C8G: octylglucoside; β-CDx: β-cyclodextrin.
Both authors were equally involved in the conceptualization and writing of this paper, and both have read and approved the final manuscript. JDO performed the literature search and PM developed the mathematical models.
Studies of interactions of UCB with phospholipids. Details of the three publications that were considered, including the degrees of supersaturation with UCB, the analytical methods used, the charateristics of the binding curve, the experimental problems, and the citation.
Studies of interactions of UCB with alkyl saccharides and cyclodextrins. Details of the three publications that were considered, including the degrees of supersaturation with UCB, the analytical methods used, the charateristics of the binding curve, the experimental problems, and the citation.
Studies of interactions of UCB with bile salts. Details of the seven publications that were considered, including the degrees of supersaturation with UCB, the analytical methods used, the charateristics of the binding curve, the experimental problems, and the citation.