Anal. Chem. 1995, 67, 4077-4085
Interaction between Dihydroxy Bile Salts and Divalent Heavy Metal Ions Studied by Polarography G. Feroci, A. Fini, and G. Fazio lstituto di Scienze Chimiche, Universita di Bologna, Bologna, Italy
P. Zuman* Department of Chemistry, Clarkson Univetsify, Potsdam, New York 13699-5810
The interaction between anions of dihydroxy bile acids (BS-) (chenodeoxycholate,ursodeoxycholate, hyodeoxycholate, and deoxycholate)and divalent metal ions (Cu2+, Cd2', Pb2+,and Zn2+)was followed by polarography. For solutions containing 0.1 mM metal(I1) ions (M2+), invariability of the half-wavepotentials and limiting currents at [BSI below about 1 mM indicates the absence of interactions of M2+ with monomeric BS-. At [BS-I between about 1 and 7 mM, the shifts of the half-wave potentials indicate formation of soluble complexes. Simultaneously, the decrease of limiting current indicates formation of slightly soluble compounds of M2+with small aggregates of bile salts. Between about 7 and 10 mM BS-, the solutions are saturated with the compounds of M2+ with small aggregatesof BS-. The current of M2+ is a function of solubility of this product. At concentrations above about 10 mM B!-,increase of current indicates formation of large ("micelle-like") aggregates bearing free COOgroups, responsible for the increase in solubility. Exact concentrations corresponding to the limits of individual ranges depend on the natures of both BS- and M2+. Overall equilibrium constants for the reaction of M2+ with small aggregates of BS-, obtained from i/id = AB!-] plots and the solubility of these compounds, indicate dependence on the nature of the metal ion. The stabilities of the complexes increases and their solubilities decrease in the sequence Cu2+> Cd2+> Zn2+> Pb2+,characteristic for interactions of M2+ with carboxylate ions. Structure of the bile salt also affects the solubility of complexes formed, but the sequence or reactivity is different for each individual metal ion. The position and stereochemistry of individual hydroxy groups probably affects the stacking of bile anions in the small aggregates, yielding slightly soluble complexes. The formation of larger aggregates occurs at concentrations of BS- comparable with reported values of critical micelle concentration.
gallstones? Bodily fluids contain high concentrations of anions, such as hydrogen carbonate, dihydrogen phosphate, anions of htty acids, and others, which readily form slightly soluble salts with Ca2+and heavy metal ions. Precipitation of such compounds of limited solubility results in formation of deposits denoted as calculi. Alternatively,they can act as seeds for nucleation and crystallization of other substances. It has been postulated that bile salts (BS-) or their aggregates (often denoted as micelles) interact with calcium ions, lower the activity of free Ca2+aquo ions? and inhibit the precipitation of slightly soluble calcium salts of biliary anions, such as bilirubinates, lecithins, and anions of fatty acids.4 Similar interactions can be assumed to occur between bile salt and heavy metal ions, but the experimental evidence for such reactions has been rather limited. Thus, for Fez+ions, it has been postuiated,5s6on the basis of dialysis studies, that binding of Fez+ by taurocholate was stronger than that by its aggregates. To demonstrate that bile salts can act as metal ion buffers, preventing precipitation of heavy metal salts with other anions, the reactions of ~ h o l a t e ~and - ~ glycocholate8 with metal(II) ions were studied. Polarography was the method of choice since it offers information concerning the equilibria between BS- and M2+ ions. In solutions, where the reduction of M2+remains reversible, the shifts of half-wave potentials offer information about the presence of rapidly established equilibria between free M2+aquo ions and their labile complexes. Moreover, changes in the limiting current of M2+yield information on relatively slowly established heterogeneous equilibria between M2+ and their slightly soluble compounds. It is an advantage of polarography that measurements can be carried out directly in the reaction mixture, in the presence of colloidal and solid particles. Under such conditions, the use of spectrophotometry, HPLC,or ion-selective electrodes is more limited. In the case of potentiometric measurements, adsorption of colloidal and solid particles can affect the data obtained with a membrane electrode. To minimize the effects of (2) Hervey, R. C.; Taylor D.;Petrunka, C. N.; Murray, A D.; Strasberg, S. M.
Bile contains-in addition to alkali and alkaline earth metal ions-ions of iron, manganese, copper, molybdenum, and zinc at levels ranging from 5 to 20 pg per gram of the solid content.' These levels can be even higher in lithiasic biles, as indicated by the amounts of these metals found in pigment or cholesterol (1) Fini, A; Roda, A In A c i d Bilian': Ricerca e Applicazioni Terapeutiche; Roda, A, Pellicciari. R., Eds.: Momento Medico: Bologna, Italy, 1991; p 88ff. 0003-2700/95/0367-4077$9.00/0 0 1995 American Chemical Society
Hepatology 1985,5 , 129-132. (3) Moore, E. W.; Celic, L.; Ostrow,J. D. Gastroenterology 1982,83, 10791089. (4) Ostrow, J. D.; Celic, L.;Moore, E. W. Gastroenterology, 1984,86,A1335. (5) Sanyal, A J.: Hirsch, J. I.; Moore E. W.J. Lab. Clin. 1990,116,76-86. (6) Sanyal, A J.; Hirsch, J. I.; Moore, E. W. Gastroenterology 1991,100,A792. (7) Feroci, G.; Fini, A; Zuman, P. Bioelectrochem. Bioenerg. 1992,29, 91102. (8) Feroci, G.;Fazio, G.; Fini, A; Zuman,P.J. Pharm. Sci. 1995,84, 119-125. (9) Feroci, G.; Fini, A; Fazio, G.; Zuman, P. J. Colloid Inte?face Sci. 1994,166, 180-190.
Analytical Chemistty, Vol. 67, No. 22, November 15, 1995 4077
adsorption, dc polarography is preferred over differential pulse polarography. Studies on trihydroxy bile salts indicated that monomeric bile salts practically do not interact with Cu2+,Cd2+,Zn2+,and Pb 2t (refs 7-9), nor with Fez+ (ref 10). T a u r o ~ h o l a t e ~does - ~ ~not react either in the monomeric form or in aggregates. Unconjugated bile salts, as well as glycocholate bearing a carboxylate group, react with all M2+ions studied at “premicellar” concentrations of BS-. Observed reactions are attributed to an interaction of M2+ with small aggregates of BS-. These reactions yield both soluble and slightly soluble species. At concentration of BS- above the critical micelle concentration (cmc) ,formation of larger aggregates takes place, which show much higher solubility due to an excess of free COO- groups. Turbidimetric results paralleled polarographic results. Diametrically opposite conclusions of our studies,7-1°as compared to those reached by Moore’s g 1 - 0 ~ ~ 5in~ 6their studies on the reaction of Fez+, are probably due to their use of dialysis, which is not suitable for study of equilibria between metal ions and labile complexes. In the course of dialysis, such equilibria are perturbed. In this study, reactions of Cu2+, Cd2+, Zn2+, and Pb2+ are reported. Cu2+ and ZnZf are present in biological systems, whereas Cd2+and Pb2+ are xenobiotic, toxic species. It was of interest to show how bile salts might be involved in a detoxification of these ions. The reduction of Cu2+, Cd2+, and Pb2+ at the dropping mercury electrode in the absence of BS- is reversible, while that of Zn2+ is irreversible. Reactions of these ions with the following dihydroxy bile acids were studied, which differ in the position and orientation of the hydroxy groups in the steroid moiety: chenodeoxycholateO (CDC), ursodeoxycholate0 W C ) , deoxycholate (I10 @C), and hyodeoxycholate 0(HDC).
eR1
#
R*
R3
R‘
I
uOH H
aOH H
I1
aOH H
POH H
I11
aOH H
H
IV
aOH aOH H
aOH H
EXPERIMENTAL SECTION Apparatus. Polarographic current-voltage curves were recorded using an Amel Mark 472 polarograph using an electrolytic cell with a saturated calomel electrode. The dropping mercury electrode used had the following characteristics: m = 1.9 mg ssl at h = 50 cm, tl = 4.2 s, controlled drop time t = 2.0 s. The cyclic voltammetry (CV) curves (Figure 1)were obtained with a hanging mercury drop electrode (A = 3 “2) using the Model 433-A trace analyzer (Amel Instruments, Milano, Italy). Chemicals and Solutions. Sodium salts of chenodeoxycholic and deoxycholic as well as hyodeoxycholic acids were obtained from Sigma (St. Louis, MO); ursodeoxycholic acid was a gift from Alfa-Wasserman (Bologna, Italy). All compounds were used as delivered. CopperOD, lead (ID, cadmium(ID, and zincOI) nitrates were analytical grade from Carlo Erba (Milano, Italy). Stock solutions of bile salts were prepared freshly, usually less than 24 h before the experiment, using oxygen-free distilled water, either by dissolution of a sodium salt or by dissolution of an (10) Fini, A; Feroci, G.; Fazio, G.; Zuman, P. Eur. 1.Pharm. Sci., submitted for
publication.
4078
Analytical Chemisty, Vol. 67, No. 22, November 15, 1995
0.8
J
a
b
C
appropriate quantity of the acid in sodium hydroxide solution to maintain a small fraction of the acid in the free form, in order to control the final pH of the solution. The final pH of all solutions, after being filtered through a 0.45 pm Millipore disk, was 7.80. Procedures. Solutions containing 1 x 10-4-1 x 10-l M bile salt and l.10-4 M divalent metal ion, in which the ionic strength was adjusted by addition of sodium nitrate to p = 0.15, were equilibrated by shaking for 24 h. These solutions were then deoxygenated with a stream of nitrogen, and polarographic current-voltage were curves recorded. For evaluation of the free metal ion concentration, the ratio of the limiting current (2) in the presence of bile salt to the limiting current governed by diffusion (id), recorded in the absence of bile salt, was used. Unbuffered solutions were investigated in this study to avoid introduction of additional ligands; pH values of these solutions were adjusted (when necessary) to 7.8. At this pH, all the acids are in their ionized forms, and the metal(I0 ions do not precipitate as hydroxides. This follows for solutions of Cd2+and Zn 2+ from reported” pH limits at which precipitation of hydroxide in unbuffered solution occurs @H 7.9 for Cd2+and 7.8 for Zn2+at 1 x M M2+). For Cu2+(PH 6.5) and Pb2+ (PH 7.2), the onset of precipitation is evidently shifted to higher pH in the presence of bile salts acting as surfactant. This has been proved by identical wave heights of Cu2+and W2+ions in the presence of 0.1 mM bile salts at pH 7.8 and in solutions at pH 3 in the absence of bile salts. Reversibility of the reduction process has been confirmed by CV (Figure 1). The reported values of half-wave potentials, measured relative to that of Tl+ ions as internal standard, are accurate to 0.005 V and are reported vs SCE. The limiting currents were measured with an accuracy of 5%. The values of overall equilibrium constants K, and 4 are reproducible to 0.2 pKunits (from triplicate sets of experiments). The estimates of concentrations corresponding to the edges of individual concentration ranges have an uncertainty of 0.2 pBS (where pBS = -log [BS-). RESULTS Polarographic limiting currents of reductions of m e t a l 0 ions in the presence of bile salts (BS-) are proportional to the concentration of free M2+ aquo ions. Denoting the current at a given [BS-] as i and the diffusion current in the absence of BS(or at [BS-I 0.1 mM) as id, the ratio i / i d can be plotted as a (11) Kolthoff, I. M.,Elving, P. J., Eds. Treatise on Analytical Chemisty, 2nd ed.; J. Wiley: New York, 1983; Part I, Vol. 3, pp 384 and 385.
A
YI
YI
-a
B
mmw
Cdw
.-50
a5.
-0
0-
I
,
-4
CdH
mV
I
-2
-3
-1
.
Ahla mV -50
L -50
.
0.5-
-0
0-
OJ
,
-2
-3
-4
Log
I
-1
-0
-4
-2
-3
[=I
-1
Log [OCI
Figure 2. Dependence of the relative limiting current ( l i d ) (0,left-hand scale) and half-wave potential changes (&) ( 0 ,right-hand scale) in M Cd2+and 0.15 M NaN03 on the concentration of the bile salt: (A) for hyodeoxycholate, (B) for ursodeoxycholate, (C) for solution of 1 x chenodeoxycholate, and (D) for deoxycholate at 25 "C.
B Ahfa mV
AEl, mV -1 00
t 00
-4
.
-3
-2
5
1
-1 , I 0
-0
~
-4
-3 Log
-4
-i
-2
-1
-2
-1
c m 1
I
I
-2
-1
Loo [Q)CI
-4
-3 Loo [OCI
Figure 3. Dependence of the relative limiting current (lid) (0,left-hand scale) and half-wave potential changes ( f l / 2 ) (0,right-hand scale) in M Cu2+and 0.15 M NaN03 on the concentration of the bile salt: (A) for hyodeoxycholate, (B) for ursodeoxycholate, (C) for solution of 1 x chenodeoxycholate, and (D) for deoxycholate at 25 "C.
function of log [BS-I (Figures 2-5). On these plots, it is possible to distinguish up to four ranges (Figure 2A). For some combinations of bile salts and M2+,all four ranges I-IV can be observed. In other combinations, range I or I11 can be rather narrow, and in
some, range IV cannot be reached within the accessible range of [BS-I (Figure 4D). In Figures 2-4, only the half-wave potentials of waves corre sponding to electrolysis resulting in a rapidly established equiAnalyticai Chemistty, Vol. 67, No. 22, November 15, 1995
4079
A \
0.5 *
c -70
Ai
A 0.5-
- -100
-50
0-
%¶
mV
-0
0 -4
-5
n
-2 Log
u
-1
[=I
1.0-
il
/id
ZnH
.
A b
%/I
0.5-
0.
mV
mV
- -50
L -50
-0
-0
-4
-5
-2
-1
Figure 4. Dependence of the relative limiting current (i/id) (0,left-hand scale) and half-wave potential changes (€I/$ (e, right-hand scale) in M Zn2+and 0.15 M NaN03 on the concentration of the bile salt: (A) for hyodeoxycholate, (B) for ursodeoxycholate, (C) for solution of 1 x chenodeoxycholate, and (D) for deoxycholate at 25 "C.
B
A
mV
03
*
0
-4
-3
-2
-1
-100
0
-4
-3
-i
-1
-4
-5
-2
-1
LoO[HDCl
C
1.0 1
AEl/I mV
c -50
-4
-3
-2
-1
Log l a 1 Loci [Wl Figure 5. Dependence of the relative limiting current (i/id) (0,left-hand scale) and half-wave potential changes (€1/2) (e,right-hand scale) in solution of 1 x M Pb2+and 0.15 M NaN03 on the concentration of the bile salt: (A) for hyodeoxycholate, (B) for ursodeoxycholate, (C)for chenodeoxycholate, and (D) for deoxycholate at 25 "C.
librium between the oxidized and reduced forms of the metal (called "reversible") are given for Cu2+,Cd2+,and Pb2+. Only for such reversible systems is it possible to obtain information 4080 Analytical Chemistry, Vol. 67, No. 22, November 15, 1995
about thermodynamic quantities from variations of half-wave potentials. The values of half-wave potentials at higher [BS-1, where the reduction is irreversible, were not included. Such
values have no simple physical meaning. Since the reduction of Zn2+ions is only quasireversible,half-wave potentials in Figure 5 indicate only trends in the ease of reduction. Information obtained from limiting currents is independent of the rate of the electrode process. The limiting current changes offer information about chemical reactions occuning in the studied solutions independent of the electrode process being reversible or irreversible. The changes of limiting currents and half-wave potentials in individual ranges can be described as follows: Range I. The limiting current does not change with increasing concentration of the bile salt, and the half-wave potential of the reduction of the metal ion remains unchanged. Range 11. A decrease of the limiting current with increasing concentration of the bile salt is observed. Simultaneously, in the majority of cases, a shift of the half-wave potential to more negative values with increasing concentration of the bile salt occurs. In this range, solutions become turbid, indicating formation of slightly soluble compounds, formed by the interaction of bile salts and metal ions, which are in equilibrium with soluble species. Range 111. Limiting currents attain the smallest value and remain independent of concentration of the bile salt. The intensity of the current in this range is directly proportional to the solubility of the compound formed by the interaction of the bile salt and the m e t a l 0 ion. In some instances, where the solubility is very low, the intensity of the current in this range of concentration of the bile salt limits to zero. In this range, the reduction of the metal ion becomes irreversible, probably due to a surface coverage of the electrode by slightly soluble species; hence, the half-wave potentials measured do not have a simple physical meaning. In this range, solutions also remain turbid. Range IV. The limiting currents of metalGI) ions increase with increasing concentration of the bile salt. Simultaneously, the turbidity of the solution decreases, and in some instances the solution becomes translucent The half-wave potentials are shifted to more negative values with increasing concentration of the bile salt, but the reduction remains irreversible, preventing simple correlation between these shifts and the complex formation. Based on experimental results, the interactions of metalGI) ions with studied dihydroxy bile salts can be described by the following equations: M2+(solution) nBS- (solution) (BS),"-(solution)
-
+ 2e == M(0) (Hg)
(BS)nn- (solution)
fast
(2)
+ M2+(solution) == M(BS),'n-2)-(solution)
pBS- (solution) * ( B S ) t - (solution) (BS);-(solution)
(1)
fast (3)
fast
(4)
+ M2+(solution) == M(BS)p@-2)-(solution)
M(BS)p@-2'-(solution)
M(BS)pNa@-2)(solid)
+ rBS-(solution)
*
@SI(p+r)
-
@++
(BS)
@+')-
(solution)
+ M2+(solution)
@+r-2)M (BS)@+r)
(solution) (9)
(solution) (10)
In range I, the equilibrium 3 is shifted to the left, most probably because the equilibrium 2 is also shifted to the left. Hence, the reduction of metal ions M2+following reaction 1 is not affected by the presence of the bile salt, and consequently, the half-wave potential and the limiting current are both independent of [BS-I. In range II,equilibria 2-5 are shifted to the right. As equilibria 2 and 3 are rapidly established, the half-wave potential of reduction of reaction 1is shifted to more negative potentials with increasing concentration of the bile salt. As long as the reduction occurs reversibly, the shift of the half-wave potential ( E I ~ follows z) eq 11:
where ( E I / z )is~ ~the potential of the reduction of M2+ in the absence of the bile salt and Ki is the equilibrium constant corresponding to reaction 3, defined as
At [BS-I >> Ki, eq 11 simplifies to
El,2 = const - 0.029n log [BS-1
(12)
Thus, the plot of Ell2 = f(log [BS-I) consists of two linear segments with an intersection at -log [BS-I = pKi. In range 111, equilibrium 6 is partly shifted to the right. Because the equilibrium between M(BS),Na@-2, in the precipitate and the oligomer OS)#- in the solution is established slowly relative to the time window of the measurement (typically 3 s), the decrease in current in this range is a measure of the concentration of the free M2+aquo ions in these solutions. For a slowly established heterogeneous equilibrium, it is possible to derive for the current i (relative to the current id observed in the absence of the bile salt or the current measured in range I) expression 13,
i/i, = K,/(K, + [BS-Iq
fast (5)
+ (p - 2)Na'(solution) M(BS),Na@-,, (solid)
(BS);p-(solution)
(13)
where slow (6)
+ rBS-(solution) +
rNa+ (solution) * M(BS) (p+r)Na(p+r-2) (solid) (7)
Therefore, the plot of i/id as a function of log [BS-I has a dissociation curve with an inflexion point at -log [BS-I = p q . Analytical Chemistty, Vol. 67, No. 22, November 75, 7995
4081
The steepness of this dissociation curve depends on the number of participating bile salt anions, p. Available experimental data indicate that in some cases pK, = pK, and n = p. In such cases, the complex which is predominant in the solution is also the least soluble one. In other instances, pK, f p& and n f p, indicating that a complex other than the least soluble one predominates in the solution. In range 111, all equilibria 2-6 are shifted to the right. Under these conditions, concentrations of M2+, M(BS)n("2)-, and M(BS),@-2)- are all low. The concentration of the free metal ion MZt, and hence the limiting current of M2+,are governed by the solubility product, Ksp = [M2+][BS-]P. The transport to the electrode involves both free ions M2+and soluble complex anions, M(BS)n(n-2)-and M(ES)P@-2)-. For n andp in the expected range between 1 and 4,the differences in the diffusion coefficients do not affect substantially the ratio i/i&partly because the ratio of diffusion coefficients is a small value, and partly because the relationship involves the diffusion coefficients in a square root. In range IV, a solubilization of the precipitate takes place. This can be achieved, in principle, in two ways: (a) Anions of the bile salt can add to the slightly soluble compound M(BS)@Na@-2) in reaction 7. This is followed by a shift of equilibrium 8 to the right. (b) Alternatively, a larger aggregate (BS)@tr)@tr)-is formed in the solution in reaction 9, which can form a larger complex species in reaction 10. As the species M(BS)cptr)@+'-2)has a more negative charge due to a larger number of free carboxylic groups not bound bound to the metal than M (BS)P@-2)-, the larger species is more soluble. Dissolved complex M(BS)(p+r)@+r-2)is in a rapidly established equilibrium-reversed reaction 10-with the reducible ions M2+. Changes in the polarographic limiting current are paralleled by changes in the turbidity of the reaction mixture. In range I, solutions remain translucent. Turbidity increases in range 11, reaches its maximum in range 111, and decreases in range IV, where at sufficiently high concentration of BS-, solutions become translucent. Investigated systems can be characterized by several quantities: (a) The value of log [BS-I at which the two linear segments of the E1/2 =f(log [BS-I) plots intersect (if accessible). This value corresponds according to eq 11 to the value of pK,. (b) The slope of the E112 = fOog [BS-I) plot (dE~is/dpBS= 0.029~). At pBS > pK,, this offers information about the number of BS- bound to a M2+ion, provided that the electrode process is reversible and effects of adsorption can be neglected. (c) The value of pBS at which the dependence of i/id on log [BS-1 shows an inflection point of the dissociation curve. At this pBS, i/id = 0.5, and the value of -log [BS-] = pK,. (d) The slope of a tangent to the plot of i/id =foog [BS-I) at the intlection point. This offers information about the number (p) of bile salt anions bound to the metal ion in the slightly soluble compound M(BS)pNacp-2). All the data in a-d can be obtained in range 11. (e) The limiting current in range 111, which is proportional to the concentration of the free metal M2+. This enables determination of the solubility of M(BS)PNa(p-2)and solubility product Ksp (if the value of p is known). Apart from these quantitative data, two semiquantitative types can be obtained: 4082 Analytical Chemistry, Vol. 67, No. 22,November 15, 7995
(0 The concentration of bile salt at which the first decrease in limiting current is observed. This can be considered as the lower edge of range 11. This value offers semiquantitative information about equilibria 4-6. (g) The concentration of bile salt where, at concentration higher than that corresponding to range 111, the current of reduction of M2+shows the first increase. This concentration can be considered as the lower edge of range IV and offers semiquantitative information about equilibria 7 and 8 or 9 and 10, respectively. Values of p& obtained from shifts of half-wave potentials and offering information about reactions 2 and 3 are, in most instances, practically equal to values of pK, obtained from the decrease in limiting currents, corresponding to reactions 4-6. As discussed in more detail below, that means that at n = p , the same complex predominates in the bulk of the solution and in the precipitate, and the sequence of reactions corresponding to processes in ranges I1 and I11 simplifies to reactions 1, and 4-6. The shapes of the i/id = foog [BS-1) plots indicate that, in some instances, a single complex with a given p predominates, while in others several complexes are present simultaneously. In a complex system like the one involved, which might be further complicated by mixed complexes involving hydroxo ligands, qualitative agreement of experimental data with the predicted shape of i/id =f(log [BS-1) plots is the best that can be expected. Similarly, eqs 7-10 qualitatively describe the increase in current in range IV and are in accordance with conversion of a slightly soluble species into a well soluble species. No information is available to decide whether formation of larger, soluble aggregates results from additions of BS-anions to the precipitate following reactions 7 and 8 or whether formation of larger aggregates (reaction 9), observed in the absence of bile salts, is followed by their reaction with M2f ions (reaction 10). The proposed interpretation is supported by formation of soluble large aggregates in solutions containing only Naf ions.I2 Data available for dihydroxy bile acid anions are summarized in Table 1. DISCUSSION Comparison of Figures 2-5 and data for individual systems (Table 1) indicates that, for all systems, principally four situations occur. At sufficiently low concentration of the bile salt, where monomers predominate, there is little interaction between the metal ion and the bile acid anions. In range 11, roughly between 0.1 and 10 mM bile salt, both soluble complexes and slightly soluble species are formed. It is assumed that, in this range, small aggregates (dimers to tetramers, premicellar species) are formed which interact with divalent metal ions. For these aggregates, where the two carboxylate groups are located close to each other, the interaction with metal ion results in a slightly soluble precipitate. In the majority of cases studied, the values of pK, obtained from the decrease in current (Table 1)and characterizing the slowly established equilibrium between metal ions in the solution and metal ions bound in a precipitate are similar to the values of pKi obtained from shifts of half-wave potentials, reflecting the rapidly established equilibrium between aquo ions of metals and labile complexes. This indicates that the soluble labile complexes which predominate in the solution have practically the (12) Reference 1, pp 52-54.
Table 1. Quantities Characterizing interactions of Bile Acids Anlons with Yetai(i1) ions'
range I1 slope: concn,bmM pIi;" pK;d mV HDC CDC UDC DC
-0.05 -0.05 0.1 0.1
HDC CDC UDC DC
0.3 0.5
HDC CDC UDC DC
-0.05
HDC CDC UDC DC
0.4 0.4
1.0 0.3
-0.05
-0.05 -0.05
0.9 -0.05
solubilityf range IV mM concn,gmM
Compounds with Cu2+ 3.5 3.5 -0.02 3.9 3.4 0.18 3.0 3.0 0.08 0.01 3.6
