Findings and their relation to thermodynamic theory
Supersaturated aqueous systems of UCB, that are optically clear before centrifugation, may exhibit considerable variation in the extent of sedimentation [12–14, 18]. Although sedimentation is often extensive, it is generally incomplete and may not be observed at all. Our data in DMSO-water show the same features, which are expected from the complex kinetics of nucleation and growth of insoluble aggregates of UCB diacid (H2B), leading to the formation of a new solid phase [19, 20]. Our centrifugation, 5 min at 14,000 g, was quite mild, and the short 20-minute period between preparation of UCB-DMSO-water systems and centrifugation severely limited the time-dependent growth to large aggregates. Lack of sedimentation of the UCB-HSA complex (mol. wt. 68,000) indicates that fine colloids composed of 100 UCB molecules would be too small to sediment. Thus, supersaturated systems lacking coarse, insoluble aggregates may not show sedimentation, but any sedimentation observed indicates their presence.
To evaluate the important effect of pH on sedimentation efficiency, we calculated S in water using chloroform-water partition data on UCB and the best measure of So in chloroform, 0.88 mM [2]. S at any pH, e.g. 62 nM at pH 7.4 and 0.32 μM at pH 8.5, can be calculated from the fitted partition data, or, equivalently, from Eq. 1, using the partition-derived So in water of 51 nM and pK
a
values of 8.12 and 8.44 [2]. In aqueous systems [12], the lowest [UCB] in water, below which no sedimentation was observed at 100,000 × g for a few hours, was 100 nM at pH 7.4, modestly higher than our partition-derived S of 62 nM [2]. Even under such vigorous centrifugation, the lowest [UCB] increased rapidly with increasing pH, to 17 μM (150 times S) at pH 8.05 and 34 μM (230 times S) at pH 8.2 [12]. This indicates increasing charge-stabilization of fine, non-sedimenting colloids of H2B by adsorbed UCB anions [12, 19, 20]. In contrast, below pH 6.7, sedimentation of 10 μM UCB was nearly complete [13]. This is compatible with a dearth of stabilizing UCB anions at this pH, as expected from the high pK
a
values of 8.12 and 8.44 [2].
Our present data on residual [UCB] in DMSO-water systems likewise show decreased sedimentation with increasing pH (Fig. 1A,1B,1C). At each NDMSO, the lowest [UCB] were at the lowest pH values: 0.1 μM (N = 0.025, pH 4.15); 0.3 μM (N = 0.086, pH 4.5); and 2.8 μM (N = 0.31, pH 5.9). As in water, these are likely to be closest to the So values at each N. Indeed, they are only moderately higher than the corresponding So values of 0.07 μM, 0.15 μM and 2.2 μM, respectively, calculated from Equation 2 using So values of 51 nM in water [2] and 10 mM in DMSO [10].
log So,mixed = log So,water + (log So,DMSO - log So,water) × N (Eq. 2)
Equation 2 is a thermodynamic relationship based on assumptions of complete ideality of mixing [21]. In general, a roughly linear variation of log So with N at low N is expected. For example, data from 1-naphthoic acid in DMSO-water [22] show that log So is a linear function of N up to N = 0.35. Such a relationship leads to a relatively small effect of low N values on So. Thus, according to Equation 2, So increases by a factor of only 1.4 at N = 0.025 and 2.9 at N = 0.086, but by a relatively larger factor of 44 at N = 0.31. This would markedly reduce the supersaturation factor ([UCB]/ So), which is a measure of the tendency of UCB to come out of solution at N = 0.31. This explains in part the relatively high [UCB] at high pH at N = 0.31 (Fig. 1A).
The pH effects on [UCB] at each NDMSO are of interest also. The lowest [UCB] at each pH registered relatively small increases with significant increases in pH: for example from 0.1 μM (pH 4.14) to 0.2 μM (pH 7.0) at N = 0.025; from 0.3 μM (pH 4.5) to 1.4 μM (pH 7.1) at N = 0.086; and from 111 μM (pH 7.1) to 166 μM (pH 8.4) at N = 0.31. These increases are probably caused mainly by increasing charge-stabilization of colloidal aggregates, as in aqueous media [12, 19, 20]. If, instead, the relatively small increases are ascribed entirely to increases in true solubility (S) at the high pH (Eq. 1), the required pK
a
values are about 7 at N = 0.025 and 0.086, and 8.5 at N = 0.31. The true pK
a
s of UCB in DMSO-water are thus probably significantly higher.
We note that some variability in sedimentation results from our short-term experiments, most evident at the low residual [UCB] in Figs. 1B and 1C, in part magnified by the log-log scale used. Some variability is expected, however, because of the complexity of the kinetic processes of nucleation, growth and flocculation that precede sedimentation. In Fig. 1A, the difference between acetate and Tris buffers is quite small (note the linear scale), compatible with the 58% higher [H+] in the acetate buffer. In Fig. 1B, the markedly lower sedimentation from phosphate buffers at pH 7.6–7.7, as compared to Tris buffer at pH 7.1, can be ascribed mainly to the much higher pH values and ionic strength of the phosphate systems. Another significant factor may be the difference in charge between the buffer salts; phosphate is anionic whereas Tris is cationic and zwitterionic. The cationic species of Tris can, in principle, reduce the negative charges on the surface of the colloidal H2B sufficiently to facilitate the formation of coarser particles and, thus, increase sedimentation.
Implications for pK
a
values of mesobilirubin-XIIIα (MBR)
In the recent 13C-NMR studies of the ionization of the 13C-COOH groups of MBR [3–6], it was assumed that the relevant physical properties of UCB and MBR, and of (CH3)2SO (DMSO) and (C2H3)2SO, are similar. Actually, as expected from the replacement of two vinyl groups in UCB with two ethyl groups in MBR, MBR is slightly more soluble in organic solvents [23] and has a higher Rf on silica gel t.l.c. [24]; MBR is thus more hydrophobic and should be less soluble in water than is UCB. Our low [UCB] in DMSO-water systems at comparable N, therefore, indicate that many of the (C2H3)2SO/buffer systems used in the 13C-NMR studies [3–6] were likely supersaturated with MBR. In those studies, the MBR concentrations used were stated to be 1 to 100 μM at N = 0.086 [3], compared to our lowest [UCB] of 0.3 μM at pH 4.5 and 1.4 μM at pH 7.05. At this N, 9 of 11 MBR data points were obtained at pH below 7.05 and 5 below pH 4.5 [4], so that even 1 μM MBR was likely to be supersaturated. At N = 0.31, our lowest [UCB], 2.8 μM at pH 5.9, was close to the lower limit of the 2 to 800 μM range of [MBR] used [4, 5]. Thus, many data points, obtained at pH values down to 2 [4, 5], were probably from supersaturated systems, despite being optically clear. As noted here and elsewhere [12–16, 18], optical clarity gives no assurance of the absence of supersaturation.
Actually, turbidity was reported in some of the 13C-NMR samples [4], indicating that coarse, insoluble aggregates of MBR were present. The claim that such turbidity did not affect 13C-NMR measurements [3, 5, 6] contrasts with evidence that even small multimers can change NMR chemical shifts [25, 26]. It should be noted also that, at high concentrations of B=, extensive, reversible self-association of B= can lead to apparently stable supersaturation with no separation of an insoluble phase [2]. For example, at pH 8.5 and a UCB concentration of 20 μM (63 times S), the weight-average aggregation number of UCB has been found to be 7.17 [18], corresponding to a molecular weight of 4,195. The aggregation number remained fairly high, 4.2, in 60% (w/v) ethanol [18]. The successful application of equilibrium ultracentrifugation for that study [18] suggests a complete absence of even small colloidal species of UCB. Self-association of MBR dianions in (C2H3)2SO-water mixtures cannot be ruled out on a priori grounds. It has been shown that neglect of self-association of B= leads to an artefactually low estimate of pK
a
values for UCB [2].
In addition to the problems of insolubility, supersaturation and self-aggregation of the MBR systems in (C2H3)2SO-water [3–6], we had shown previously that inaccuracies in the pH measurements affected both the magnitude of ΔpK
a
(the change in pK
a
on adding (C2H3)2SO to water), as well as the degree of the variation of ΔpK
a
with N [8]. This is important for extrapolating pK
a
values in (C2H3)2SO-water to pure water (N = 0). Indeed, remeasurement of one soluble acid raised its pK
a
by as much as 3 units at N = 0.31 [9]. Thus, the inaccuracies in pH measurement produced serious errors in reported pK
a
values of more than fifteen soluble acids used as models for MBR, as well as for MBR itself [3–7].
Many methods, using appropriate pH measurements, have been applied in the past to determine thermodynamic pK
a
values of soluble acids in non-aqueous or partially aqueous media, including DMSO-water systems [27, 28]. Many other relevant references were given in our prior paper [8]. In that paper, our pK
a
measurements on acetic acid in DMSO-water systems were based on the potentiometric method, using properly calibrated glass electrodes, which determine the activity of H+, and on estimates of the activity coefficients of the acetate ion. This method, which is well established for aqueous solutions, yielded results in good agreement with data from the literature that was based on a very different method, measurements of electrical conductivity [28]. In the 13C-NMR papers, therefore, it was not justified, to assume that pH values do not change on adding DMSO [3–7], or to use uncalibrated pH measurements for determination of the pK
a
values of soluble acids [9].
Our sedimentation data and their interpretation indicate that significant additional uncertainties, not important for the soluble acids investigated, exist for the reported pK
a
values of the relatively insoluble MBR in (CD3)2SO-water (4.2 and 4.9 at N = 0.086 and 4.3 and 5.0 at N = 0.31), as well as their extrapolation to obtain pK
a
values of 4.2 and 4.9 in water [9]. Indeed, if these low aqueous pK
a
values, along with the experimental S values at pH 8.5 of 0.32 μM [2], or 0.6 μM [17], are applied to Eq. 1, the calculated extremely low So values of UCB diacid of 4 or 8 × 10-15 M are seven orders of magnitude lower than the experimental So, 5.1 × 10–8 M [2]. Applying the So of 4 or 8 × 10-15 M to Eq. 2, moreover, would indicate massive supersaturation (up to 8 to 10 orders of magnitude) of MBR at the concentrations (1–800 μM) used in the 13C-NMR studies [3–6].