Chemistry and Physics of Lipids, 57 (1991) 17--27 Elsevier Scientific Publishers Ireland Ltd.
17
Calcium binding to bile salts E. Baruch a, D. Lichtenberg a, P. Barakb, c a n d S. N i t ¢ adept, of Physiology and Pharmacology, Tel-Aviv University, Sackler School of Medicine, Tel-Aviv 69978 (Israel), bDept, of Soil Science, University of Minnesota, St Paul, MN 55108 (U. S. A. ) and cSeagram Centerfor Soil and Water Sciences, Faculty of Agriculture, Hebrew University of Jerusalem, Rehovot 76100 (Israel) (Received May 21st, 1990; revision received September 20th, 1990; accepted October 5th, 1990)
Calcium binding to bile salt monomers and micelles is an important issue with respect to the possible (but rare) precipitation of calcium bile salts in the gallbladder. In the present work the binding of Ca 2+ to six bile salts was measured in solutions containing 2 to 100 mM bile salts by means of a calcium-sensitive dye, murexide, which determines the ionic calcium concentration. In solutions containing bile salt at concentration higher than 20 mM most, if not all, of the bound Ca 2+ isassociated with micellar surfaces. The results were analyzed by employing a model which combines specific binding with electrostatic equations and accounts for the system being a closed one. The analysis of Ca 2+ binding data considered explicitly the presence of Na + ions and yielded intrinsic binding coefficients for Ca 2+ and Na + which were utilized to explain and predict binding results for v~irious concentrations of Ca 2+, Na + and bile salts. The calculations indicate that in saline solutions most of the surface sites were bound by Na +, whereas less than 10% were bound by Ca 2+ even in the presence of 8 mM Ca 2+. The binding of Ca 2+ to bile salt micelles increases with pH. An increase in temperature results in reduced binding affinity of Ca 2+ to the bile salt micelles.
Keywords: bile salts; bile salt micelles; calcium binding; calcium precipitation; murexide; gallstones.
Introduction Insoluble calcium salts (carbonate, phosphate, bilirubinate and salts of fatty acids) have long been recognized as constituents of gallstones [1--2]. The possible involvement of these salts in the pathogenesis of cholesterol gallstones has been considered by several authors, who proposed that microcrystals of insoluble calcium salts may act as nuclei on which cholesterol may be deposited [3--9],
Correspondence to: D. Lichtenberg, Department of Physiology and Pharmacology, Tel-Aviv University, Sackler School of Medicine, Tel-Aviv 69978, Israel. Abbreviations: B, bile acid; B', bile acid, ionized; BNa, bile acid, sodium salt; Kca, intrinsic binding constant of Ca 2+ to B'; kNa, intrinsic binding constant of Na + to B'; CT, total Ca 2+-concentration; Ca, bound Ca2+-concentration; CF, free (ionized) Ca2+-concentration, Ca2+-activity; cmc, critical miceilar concentration; DC, deoxycholate; GC, glycocholate; GDC, glycodeoxycholate; PC, phosphatidylcholine; PCS, photon correlation spectroscopy; PS, phosphatidylserine; TC, taurocholate; TDC, taurodeoxycholate.
thus forming gallstones. The potential to form calcium carbonate, phosphate and bilirubinate may be related to the activity of calcium ions rather than to the total calcium concentration [3]. On the other hand, formation of calcium salts of long chain fatty acids, e.g., palmitate, probably occurs within calcium-containing aggregates of mixed micelles composed of these fatty acids and bile salts [10,1 I]. Calcium binding to bile salt monomers, micelles and mixed micelles can therefore be expected to promote precipitation of calcium salts of free fatty acids while at the same time reducing the concentration of free calcium and thereby inhibiting the precipitation of calcium bilirubinate, carbonate and phosphate. The latter possibility has motivated studies of the binding of calcium to various bile salts using ultraffltration methods [4,12], calcium-specific electrode [3--5] and a calcium-binding dye [6]. However, in spite of the systematic nature of these studies, the results have thus far yielded much controversy. For example, while Moore [3] proposes that the "Ca2+ electrode is offering a powerful new
0009-3084/91/$03.50 © 1991 Elsevier Scientific Publishers Ireland Ltd. Published and Printed in Ireland
18 tool for studies of the physical chemistry of bile", Williamson and Percy-Robb [4] used the Ca 2÷ electrode only in solutions containing up to 3 mM bile salts since higher concentrations of bile salts affected the electrode, "making the Ca 2÷ activity measurements of subsequent standards surprisingly low". In the present communication, we have employed the dye murexide to re-investigate the binding of Ca 2+ to bile salts. This dye is suitable for studying Ca 2÷ binding which is characterized by binding constants within the range of 1 to 100 M -1 [13]. Murexide has been previously used by Lester et al. [6] to measure the binding constants of calcium to monomeric taurocholate and glycocholate [6] but the technique adopted for our studies [13] is quite different, as described in Materials and Methods. The data measured in previous studies on the binding of calcium to bile salts were analysed in terms of apparent binding coefficients. These values vary with the concentrations of other cations in the system, such as Na +. We have chosen to analyse the binding in terms of intrinsic binding coefficients. This approach requires taking into account the presence of sodium cations which are competing with Ca 2+ for binding. The analysis of binding data employed a model developed to explain and predict cation adsorption to charged surfaces [ 14,15]. The three main elements in this model are: (i) consideration of specific binding; it assumes that the total amount of cation adsorbed consists of (a) cations tightly bound to the surface and (b) cations residing in the double layer region; (ii) the electrostatic Gouy-Chapman equations are solved for a system containing several cations of various valencies, and particles whose surfaces are charged and partially neutralized by cation binding, and (iii) the concentration of surface sites is explicitly taken into account since it affects the concentration of cations in solution due to adsorption. The coupling of electrostatic and binding equations proved to be profitable in studies on membranes [15--22] and soil particles [14,23--25]. Application of this approach to micelles required an extension of the equation to non-planar geometries. The combination of experimental and theoretical methods enabled us to investigate the binding of Ca 2÷ to several bile salts and its dependence on Na +, pH, temperature and the presence of other bile salts.
Materials and Methods
All the bile salts used were of the highest purity produced by Sigma Chemical Co. (St. Louis, MO) and were used without further purificaton. Their concentrations were assayed by the enzymatic method of Turnberg and Anthony-Mote [26] using 3-/3-hydroxysteroid dehydrogenase and /3-NAD + (Sigma). Solutions were made of double distilled water using various NaC1 concentrations (150 mM unless stated otherwise) at various pH values (pH = 7.5, unless stated otherwise), using 45 mM imidazole, adjusted to the appropriate pH value by HC1, as a buffer. Experiments carried out using the techniques described below showed that imidazole had little effect on the binding of calcium to bile salts in the absence of added NaCI and no effect in the presence of NaC1. Preparation of mixed micellar systems (400 mM total bile salts concentration) was carried out either by dissolving a mixture of the solid (powder) bile salts or, in several experiments, by mixing stock solutions of the two bile salts. The latter procedure appears to lead to an apparent equilibrium value of calcium binding only after a prolonged incubation period (see below). Calcium determination Total calcium concentration was determined by atomic adsorption spectrophotometry using a Perkin Elmer model 2380 spectrophotometer. Calcium activity was measured either by a calciumselective electrode (in, solutions with low bile salt concentration [4]) or by a spectrophotometric technique using the metaUochromatic indicator ammonium purpurate (Murexide) [131. In our measurements we have used solutions containing 50 /~M murexide at 27"C unless stated otherwise. The difference spectrum between two murexidecontaining solutions, with and without calcium, is characterised by a minimum at 540 nm, a maximum at 470 nm and an isosbestic point at 507 nm. The difference between the absorbance at 540 nm and at 470 nm (A OD) is an increasing linear function of calcium activity [131. For any given solution (of a given pH, [Na +] and temperature) a calibration curve was made by measuring AOD as a function of [Ca 2+ ] in the absence of bile salts. Difference
19 spectra were measured between solutions containing 2---8 mM CaCI 2 and a solution containing no Ca 2+ but otherwise of the same composition. Free calcium concentrations in BS-containing media were evaluated from experiments carded out as follows. First, to correct for any possible effect of light scattering on the absorption difference spectrum, baseline correction was carded out: the difference spectrum between a sample containing the appropriate buffered medium, Ca 2+ and bile salt and a reference containing the same composition but no Ca 2+ was hulled by this correction. Subsequently, murexide was added to both the sample and reference and the difference spectrum was measured. OD was then used to evaluate calcium activity on the basis of the corresponding calibration curve, measured in the absence of BS. A calcium-selective electrode (Radiometer, F2112 Ca/940---249) was used to determine calcium activity in BS-containing media ([BS] < 3 mM), using a calomel electrode (K-401) as a reference electrode and a temperature compensator. A calibration curve was made before each experiment by plotting the potential (.mV) as function of pCa 2+ for samples with varying known [Ca2+]. Measurements were made in 20-ml stirred solutions after soaking the electrode for 6 min in the measured solution. The results obtained by this method differed significantly from those obtained by the use of the calcium-sensitive dye, the differences being larger when high bile salt concentrations were used. Based on the considerations which were previously raised by Williamson and Percy-Robb [4], we have chosen to disregard those data for bile salt concentrations in excess of 3 mM.
Theoretical analysis The procedure is essentially as previously described [14,15]. The concentration of cations, near the negatively charged micellar surface, Xi(o), is given
by Xi(o) = S i exp(-e~b(o)Zi/kT)
(1)
The quantity S i is the solution concentration of a cation i far away from the surface, Z i is its valency, k is Boltzmann's factor and T is the absolute temperature. If a negatively charged bile acid
molecule is denoted by B-, its association to a sodium salt is described by B" + N a + ~ B N a
(2)
The intrinsic binding coefficient for this complex, KNa (M "l) is defined by KNa = [BNa]/([B-] x [Na+])
(3)
in which the concentration of the cation should be taken at the surface, as given by Eqn. 1. A similar expression can be written for the binding reaction of Ca 2+, in which case two types of complexes are possible, (B2-Ca)° and (B-Ca) +, with binding coefficients K2,ca and K l,Ca. The existence of the charged complex implies that charge reversal can occur. In our treatment we considered only the neutral complex, and thus we employed only one binding coefficient for Ca 2+, Kca. The programs for the analysis of Ca2+-binding described previously [14,15] assume a planar geometry. Approximate forms for a spherical geometry are given in Ref. 28. For this study we developed an accurate and efficient numerical procedure for a spherical geometry, which was originally described by Barak [29] for a cylindrical geometry. The main elements of this procedure are described in the Appendix. As will be shown, an analysis of Ca 2+ binding based upon the assumption of a planar geometry can be essentially adequate. The intrinsic binding coefficents, which were assumed to be independent of the concentrations of Ca 2+, Na + and bile salts, were determined by fitting the experimental results for the binding of Ca 2+ to the bile salts. These intrinsic binding constants were then employed for generating predicted values, i.e., concentrations of Ca 2+ bound for different concentrations of Ca 2+, Na + and bile salts, at a given pH and temperature. When fitting the binding data for a particular bile salt, e.g., TDC, at a given NaCl and bile salt concentration, we had to fix two parameters, KNa and Kca, in order to fit seven data points (i.e. the calcium activities measured at seven different calcium concentrations). Such a fit yielded many sets [e.g., (Kca = 0.2 M'i; KNa = 0.5 M'I); (Kca = I M'l; KNa = 2 M'l); (Kca = 1.5 M'l; KNa = 3 M'l)]. However, a comparison of the predictions for Ca 2+ binding to TDC in solutions
20 of other Na + concentrations could discriminate between these sets in favor of the last one. A similar trend was found for other bile salts. Consequently, we decided to f'LXKNa = 3 M "1 in all calculations. Since the murexide, which yields the concentrati6n of C F (Ca free) is also present in the double layer region we refer to
Ca=CT-CF
(4)
as the concentration of Ca bound to the bile, C T being the total calcium concentration. Apparent binding constants refer to K =
Ca/(CF[n']) These values were derived from the best fits of the dependence of C a on CF, assuming that [B-] *,C a. Results
Most of the binding measurements employed concentrated bile salt solutions (100 raM), to ensure that most of the bound calcium was associated with micvlles rather than with monomers. The results in Fig. 1 illustrate the dependence of the amount of
Ca 2+ bound to the bile salt micelles as a function of total Ca 2+ concentration for two bile salts. Table I summarizes the calcium binding affinities o f the various bile salts employed in terms of apparent and intrinsic binding coefficients. The intrinsic binding coefficients of the various bile salts varied within a relatively small range (1.3--2.8 M -1) and were all smaller than the intrinsic binding coefficient of Na + (fixed at 3 M "1 for all the bile salts). Noticeably, it appears that Ca 2+ has a somewhat greater binding affinity to micelles composed of dihydroxy bile salts than to the trihydroxy ones. In order to test the predictions of our theoretical model and to reduce the uncertainties in the deterruination o f the intrinsic binding coefficients, we have measured calcium activity at various concentrations of NaCI. The effect of variations in NaCI concentrations from 0 to 200 m M is illustrated for TDC in Fig. 2. The agreement between the experimental and predicted values of the concentrations of bound Ca 2+ is within experimental errors, supporting our model. Elevation of p H results in enhancement of Ca 2+ binding to bile salt micelles as illustrated for the case of chelate in Fig. 3. Noticeably, the intrinsic bin-
CBCmH) 5 []
~ o
mH Cholate
!
I
2
,
; Ct(mH)
Fig. 1. Dependenceof bound calciumconcentration on the total concentration of CaCI2 in 100 mM solutions of sodium chelate and sodium glycodeoxylatein saline (150 mM NaCI) at room temperature and pH = 7.5. Note that the lines give the calculated values (see text for details).
21 TABLEI Binding constants of Ca2+ to various bile salts (and bile salt mixtures). Both the apparent binding constant and the intrinsic binding constant (calculated as described in text), were determined from the spectra of murexide in solutions of 100 mM of the various bile salts in solutions at pH = 7.5, at room temperature, in the presence of 2--8 mM CaC12. Bile salt
Binding constants (M -I) Apparent in 150 mM NaCI
Intrinsic
Intrinsic, in h l mixture with C
GDC
C
5.8
1.38
--
2.15
TC GC DC TDC GDC
5.9 6.2 7.0 7.9
1.34 1.44 1.60 1.47
1.55 1.55 2.40 1.60
N.D. 2.25 3.20 N.D.
12.9
2.75
2.15
--
d i n g c o n s t a n t f o r c h o l a t e micelles i n c r e a s e s m o n o t o n i c a l l y a n d d o u b l e s w h e n the p H is raised f r o m 6 to 8.5, a l t h o u g h the a p p a r e n t b i n d i n g c o n s t a n t does n o t c h a n g e m o n o t o n i c a l l y . T h e t e m p e r a t u r e d e p e n d e n c e o f the b i n d i n g o f C a 2+ t o c h o l a t e m i c e l l e s s h o w n in F i g . 4
CB(mM) 6"
• n
o
d e m o n s t r a t e s t h a t c a l c i u m b i n d i n g is a d e c r e a s i n g function o f t e m p e r a t u r e within the r a n g e o f 5 ° to 51°C. T h e intrinsic b i n d i n g coefficients d e c r e a s e with t e m p e r a t u r e f r o m 2.6 M "i at 5 ° C to 0.7 M -1 at 51 °C. (Fig. 4). T h e effect o f t e m p e r a t u r e was explicitly c o n s i d e r e d in the c a l c u l a t i o n s t h r o u g h the
~
O l OmM TDC
5" 4 3
~
100mMTDC
2
200mMNaCI
l
•
0
0
I
0
= D
au
I
2
,,g I
4
o
r=
20mM
I
6
TDO =
8
10
Ct(mM) Fig. 2. Dependence of bound calcium on the total concentration of calcium in solutions of TDC (20 and 100 raM) in saline at room temperature and pH = 7.5.
22
K(Ca)( M" 1) 6apparent
5
4 3 2
intrinsic
1 0
!
!
5
!
8
7
6
9
pH Fig. 3. Effect of pH on the binding of calcium to cholate as measured in cholate solution (100 raM) in saline at room temperature.
Boltzmann factor in Eqn. 1, and through the value of the dielectric constant. Binding of Ca 2+ to binary mixed micellar systems depended upon the method used for mixing the two bile salts. Mixing of powders (see Materials and
Methods) always resulted in the formation of solutions in which calcium activity was independent of the time of incubation. In contrast, mixing of solutions of the individual bile salts resulted in slightly higher calcium activities (apparently lower binding
K(Ca)( M" 1) ]2 10
8 6 4 e~.,,,,,,.~,....,...~~
intrinsic
2 0
I
o
10
I
l
20
30
I
I
!
40
50
6O
T e m p e r a t u r e (Oc) Fig. 4. Effect of temperature on the binding of calcium to cholate in cholate solution (100 mM) in saline at pH = 7.5.
23 constants) which decreased with time. Thus, the results obtained from mixtures made by the two different methods after 1 h of incubation were very different, whereas 24 h after preparation the results were independent of the method of preparation. A summary of the results obtained with mixtures made from mixed powders is given in Table I in terms of intrinsic binding coefficients. We note that mixtures of DC with either cholate or GDC have higher affinity for calcium than either of the pure components, whereas the binding constants of the other mixtures are close to those of the pure mixed micelles. Discussion Our calculations of Ca 2+ binding have employed intrinsic binding coefficients, which are independent of the concentrations of Ca 2+, bile salt and Na +. Table I illustrates that the intrinsic binding coefficients are several-fold smaller than the apparent binding constants. This difference (for a given Na + concentration) is due to the fact that the calculations based on Eqn. 1 take explicitly into account the enhancement in Ca 2+ concentrations close to the micellar surface. This difference would have been much larger in the absence of Na + ions which compete with Ca 2+ for binding to the surface sites and reduce the magnitude of the surface potential. Figure 2 illustrates the significance of the effect of Na + concentrations on the amount of Ca 2+ bound to the micelles. When 2 mM CaC12 was added to 100 mM sodium-TDC in the absence of NaCI, only 2.4% of the surface sites were occupied by Ca 2+ and 74.8% by Na +. For [CT] = 8 mM the corresponding values are 9.2% and 67.5%. This situation is significantly different from the case of phosphatidylserine (PS) vesicles where, under similar conditions, the majority of surface sites are bound by Ca 2+ [15,16]. A comparison between bile acids and PS shows that KNa for PS (0.6--1.0 M -l) is three- to four-fold smaller than for bile acid micelles, whereas Kca (30--70 M -l) is about an order of magnitude larger. Furthermore, for vesicles which are induced to fuse by Ca 2+, measurements showed a dramatic increase in the binding affinity of Ca 2+ to PS [15], which is accompanied by a transformation to a dehydrated Ca(PS)2 phase
[30,31]. The rate of these transformations depends upon concentrations of PS, Ca 2+ and Na +. For 1 mMPS in the presence of 100 mM NaCI and about 1 mM of Ca 2+, such transformations occur within minutes [15]. Similar transformations occur upon addition of Ca 2+ to bile salt micelles, but much larger Ca 2+ and bile acid concentrations are required to induce BS-Ca precipitation, which is also much slower [10,11]. This comparison illustrates the lower binding affinity of Ca 2+ to bile acid micelles than to PS vesicles. The relative affinity of Ca 2+ to bile salt monomers versus micelles has been an issue: Williamson and Percy-Robb havre reported that the activity of Ca 2+ in monomeric solutions of sodium giycocholate is independent of the bile salt concentration, suggesting that binding of Ca 2+ to the bile salt monomers is insignificant [4]. This conclusion appears to be consistent with the results of Rajagopalan and Lindenbaum [5] and forms the basis for the interpretation used by Jones et al. [7] in their studies of the solubility products of the calcium salts of glycine-conjugated bile acids. In contrast, the work of Moore and his colleagues concluded, on the basis of their calcium selective electrode measurements, that the affinity of pre-micellar glycocholate to calcium ions is much higher than that of the micellar bile salt [3,8]. The high affinity of calcium to monomeric bile acids has been attributed by these authors to "interposition of Ca 2+ ions between the side chain ion and hydroxyl substituent of the cholanic acid ring to form a reversible Ca 2+ ion exchange site". However, it is not clear whether comparison of dihydroxy-bile salts with trihydroxy bile salts is consistent with this interpretation. Figure 2 demonstrates the dependence of Ca2+-binding on bile salt concentration. We have also measured Ca 2+ binding to 2 mM of TDC. As it turned out, the amount of Ca 2+ bound was negligibly small, below the experimental resolution. Thus our results cannot yield binding coefficients of Ca 2+ to bile salt monomers. On the other hand we were justified in neglecting the binding of Ca 2+ to monomers in bile salt solutions of concentrations of 20 mM and above. Most of our studies employed 100 mM bile salts. The calculations based on the binding coefficients measured at this high bile salt
24 concentration yielded reasonable predictions for the amounts of Ca 2+ bound to 50 mM bile salts (results not shown) or to 20 mM bile salts where Ca 2+ binding to monomers could have made a contribution. In the latter case our predictions for the measured quantity (ionized Ca 2+) were within the experimental uncertainty of 5%, although the calculated values o f b o u n d calcium appear to be slightly underestimated. However, our finding of a small CB value for a 2 mM solution of TDC whose cmc = 2 mM [21] rules out a large contribution to CB from TDC monomers at 20 mM TDC. ~Unfortunately, the accuracy of our calcium activity measurements (both carried out by a CaX+-selective electrode and those which employed murexide) appears to be inadequate to allow for a comparision between binding of calcium to bile salt monomers and to micelles. We favor the conclusion that the polyvalent micellar surface is more attractive for calcium ions than the bile salt ions. The apparent contradiction between this conclusion [4,5] and that of Moore and his collaborators [3,8] may be attributed to the extreme sensitivity of the calculated apparent binding constants of monomers to small experimental errors in the determination of the ionized calcium concentration. To demonstrate this sensitivity, note the following example: a bile salt has a cmc value of 2 raM; suppose that CaC12 (2 mM) is added to a 2 mM solution of this bile salt and the ionized calcium concentration (CF) is measured. The apparent binding constant is given by K = Cn/(CF x B) × 103, where CB, C F and B are the concentrations (in mM) of bound Ca 2+, free Ca 2+ and free monomeric bile salt, respectively, and C B = CT - C E. If the measured value of C F is 2.0 raM, it must mean that no calcium binds to monomers. On the other hand, a measured value of C F = 1.9 mM would mean that K = 100/(1.9 x 1.9) = 28 M "1, namely that the Ca2+-binding affinity of monomers is greater than that of the micelles. In our experimental systems (and probably in other studies as well), the accuracy of the results can hardly differentiate between those two extremes; other cases are not likely to yield reliable binding coefficients to monomers by the techniques available to us. The results in Fig. 4 indicate that more Ca 2+ is bound to cholate micelles as the temperature is
lowered. This variation is due to changes in the intrinsic binding coefficient of calcium to the micelles. This conclusion is based on the following considerations: (1) Temperature appears explicitly in the calculations of binding through the Boltzmann distribution factor (Eqn. 1) and implicitly through the dielectric constant, ~, (e.g., ~(5 °C) = 86; e(25 °C) = 78.5, etc.). Both these effects were accounted for by the calculations. (2) The area per site can be expected to affect C B only slightly. This is illustrated in Table II, which shows that a 10% increase in the area per site yields less than 3% decrease in CB. The observed variation of the binding affinity with temperature probably reflects a dependence on temperature of the arrangement of bile salt ions within the micelles. Interestingly, Ca 2+ binding to PS vesicles, in which temperature-induced molecular rearrangement is less likely, appears to be independent of temperature [32]. The calculations presented in Table II also illustrate that the size of the mixed micelles should affect the binding of calcium to the surface only slightly. For a given binding constant per site, an increased number of sites per micelle, which of course is a function of the aggregation number, enhances calcium binding by up to 10% as the micelle grows from 3 nm to infinity. For particles of smaller sizes, the size may have a more pronounced effect on calcium binding but analysing this effect quantitatively may be inadequate because the macroscopic treatment is limited to cases where the radius of the particles is sufficiently larger than the width of the double layer. Recently we have studied the sizes of CJC, TC, DC and TDC micelles (100 mM) by photon correlation spectroscopy (PCS) (A. Bor and D. Lichtenberg, unpublished results). All these micelles were .found to have average diameters within the range of 2.7--2.9 nm (in saline) at pH 8.0 and within the range of 3.0--3.9 nm at pH 5.5. In the presence of Ca 2+ (5 raM), the size of the micelles increases only slightly (if at all) and the sizes of the various bile salt micelles remain very similar. Noticeably, however, the precision of our PCS measurements is not very high. The distribution mean for any given bile salt in any given solution varies by as much as 40%. Thus, these data do not contribute much to the confusing state of our knowledge of the size of
25 TABLE II Effect of particle (Micelle) radius on Ca 2+ bindinga,
NaCl (raM)
R (rim)
Area per site (rim2)
Ce (raM)
- ~o(mV)
0 0 0 0 0 0 200 200 200 200
3 5 15 Planar Planar Planar 3 5 15 Planar
0.6 0.6 0.6 0.6 0.66 0.54 0.6 0.6 0.6 0.6
2.95 2.97 2.98 3.03 2.95 3.11 1.04 1.07 1.11 1.15
75 79 80 86 83 88 40 41 42 43
aCalculations presented are for a system containing 4 mM CaC12 and 100 mM "sites" at 25 °, employing the values Kca = 1.5 M -l KNa = 3 M -l (as in the case for TDC). The presence of another non-binding monovalent cation (imizadole; at a concentration of 45 raM) was considered in the calculations.
bile salt micelles [27]. Nevertheless, the general trend is clear: the dihydroxy bile salt micelles appear to be slightly larger than those of the trihydroxy bile salts and the reduction of pH results in a size increase of all the bile salt micelles. In fact, the experimentally observed small differences in radius can amount to several-fold differences in the aggregation number, which is proportional to the volume of the mixed micelles. In any event, the pH-induced changes in calcium binding cannot be explained by changes in micellar size; at low pH values, the mixed miceUes are larger while the affinity of the micelles for calcium is lower, in contrast with the tendency pointed out by Fig. 3. The alternative explanation is that at low pH values, protons compete with calcium in binding to the bile salt micelles, thus reducing calcium binding. On the other hand, we think that differences in micellar sizes can explain some of the differences in calcium binding between the different bile salts. In fact, the differences between the binding of calcium to the various bile salts micelles and mixed micelles are rather small and the only micelles that appear to have significantly higher intrinsic binding constants than the other bile salt micelles are GDC and mixtures of GDC with other bile salts. We have no satisfactory explanation for this finding as we
are unaware of any other difference between GDC and all other bile salts studied. Micellar size may be responsible for the finding that any of the trihydroxy bile salts binds less calcium than corresponding dihydroxy bile salts (DC > cholate; TDC > TC; GDC > GC), as previously suggested by Rajogapalan and Lindenbaum [5]. The conjugation of the "head group" of either cholate or deoxycholate by either taurine or glycine appears to affect calcium binding, such that the taurine reduces calcium binding, while glycine has the opposite effect. The results are, again, in agreement with the latter previous report [5] in which these effects were attributed to differences in hydration of the conjugated group. In conclusion, it appears that in solutions containing more than 20 mM bile salts, calcium binding involves predominantly, if not exclusively, bile salt micelles rather than monomers. The intrinsic binding coefficients are within the range of 1 to 3 M -l, with the species of bile salt, the pH and the temperature having only small effects on the bincling affinity of the micelles for calcium. Sodium binding, which is characterized by a binding coefficient of the same order of magnitude, is an important factor in determining calcium binding. It should, however, be noted that the rather low
26
(A6)
binding affinity of calcium to the bile salt micelles at calcium concentrations of up to 8mM increases dramatically at the range where Ca2+-induced precipitation occurs, leading to crystalline structures.
X = xr
Acknowledgments
I S = rSiZi2/2
This work was partially supported by the Basic Research Foundation administered by the Israel Academy of Sciences and Humanities, the Ministry of Science and Technology of Israel, the Commission of the European Communities (Grant 3946), and the S.A. Schonbrunn Research Endowment Fund of the Hebrew University of Jerusalem.
in which N A is Avogadro's number and S i is molar concentration of ion species i. With this notation and the use of Eqns. A4 to A8, Eqn. (A1) becomes
where x = ((8*re2NA(IS))/(IO00
e
kT)) 1/2
c~" + 2¢~'/X = (F,ZiS.o, zi)/(2IS)
(A7)
(A8)
(A9)
and Eqn. A3 yields
~/~1S2+)/
$'(a) = (4a" aoe/(~kTr)) x [(1 - y(a) 2 (1 + y(a) ~, KiSi + + y(a) 2 X;/~Sj2+)] (A10)
Appendix The electrical potential ~b around a spherical particle satisfies the equation
~l'" + 2 ~ ' / r = - 4wp/E
(A1)
in which p(r) is the charge density in solution and e is the bulk dielectric constant. The boundary conditions are
~b (o,) = ~b' (oo) = 0
(A2)
¢'
(A3)
( a ) = - 4 T a/E
in which a is the radius of a spherical particle and a is the surface charge density. The volume charge density is given by p(r) = ~,eZiNiyZi(r)
(A4)
where e is the absolute magnitude of an electronic charge, Z i is the valence of an ion, being positive for a cation and negative for an anion, and y(r) = exp[ck(r)] = exp [-e~b(r)/kT]
(A5)
where k is the Boltzmann constant and T is the absolute temperature. A s in Ref. 29 we have employed the dimensionless potential $, and dimensionless distance, X, given by
where a 0 is charge density in absence of binding. Usually only Ci, the total concentration of cation i in the system, which consists of the concentration of the cation in solution, in the double layer region, and as surface complexes is known a priori. The solution of Eqn. A9 satisfying Eqns. A2 and A10 starts from an initial guess of ~#(a) which can be obtained from a solution of either the planar equation or the Debye-Huckel approximation of Eqn. Ag. Substitution of ok(a) in Eqn. A10 yields '(a) and Eqn. A9 yields ~ "(a). The solution of Eqn. A9 is numerical with intervals of size 1/25 divided into smaller steps solved by a fifth-order series and extrapolated to infinitesimal stepsize using Richardson's deferred approach to the limit with rational function extrapolation [ 33 ]. For a given 4)(a), numerical integration was terminated when either ~(X) had a sign different than that of 6(a) or when ¢~'(X) had a sign different than that of ¢~'(a). As an exact solution of Eqn. A9 would begin with a value of q~(a) that would allow integration to continue to an infinite distance without changing signs of either ok(X) or 6'(X), iterating between values of ~(a) that lead to the two types of sign reversals leads to maximization of distance of calculation and approaches a true solution. Iteration of ¢~(a) was continued until convergence to a preset tolerance. Best values of ¢ffX) were utilized to recalculate the concentrations of ca-
27
tions in the double layer and bound to the surface. Eqn. A9 was then recalculated iteratively as described elsewhere [ 14] until convergence of all components of the system was reached. Mass balance and equality of the right- and left-hand sides of Eqn. A9 were checked. The calculated values in Table II illustrate the effect of micelle (or vesicle) radius on the surface potential and on CB, the concentration of Ca 2+ bound, for two extreme cases of 0 and 200 mM NaCI. The values of l~bolare about 10--15% smaller for R = 3 nm than in the planar case, whereas the corresponding CB values are 3 - - 10% smaller. The relatively smaller effect of radius on CB values is due to the presence of competing monovalent cations. In general, the term specifically reflecting the spherical geometry, 2 ~k'/r, is relatively small compared to the term ~b#, which is common to planar, cylindrical and spherical geometries. These results also demonstrate that a knowledge of the details of the micellar shape and dimension, which desirable, is not essential for the analysis and prediction of Ca 2+ binding to bile salt miceUes. References 1 D.J. Sutor and S.E. Wooley (1971) Gut 12, 55----64. 2 C.S. Pitehumoni, K.V. Viswanathan and E.W. Moore (1987) Gastroenterology 92, 1764 (Abstract). 3 E.W. Moore (1984) Hepatology 4, 228--243s. 4 B.W.A. Williamson and I.W. Perey-Robb (1979) Biochem. J. 181, 61-----66. 5 N. Rajagopalan and S. Lindenbaum (1982) Biochim. Biophys. Acta 711, 66--74. 6 D.G. Oelberg, W.P. Dubinsky, E.W. Adeock and R. Lester (1984) Am. J. Physiol. 247, G112---43115. 7 C.A. Jones, A.F. Hofmann, K.A. Mysels and A. Roda (1986) J. Coll. Inter. Sei. 114, 452----470. 8 E.W. Moore (1985) Gastroenterology 83, 1079---1089. 9 D.M. Small (1980) N. Engl. J. Med. 302, 1305--1307. 10 D. Lichtenberg, N. Younis, A. Bor, T. Kushnir, M. Shefi,
11 12 13 14 15 16 17 18
19 20 21
22 23 24 25 26 27 28 29
30 31 32 33
S. Almog and S. Nir (1988) Chem. Phys. Lipids 46, 279---291. D. Lichtenberg, E. Werker, A. Bor, S. Almog and S. Nir (1988) Chem. Phys. Lipids 48, 231--243. B.W.A. Williamson and I.W. Percy-Robb (1980) Gastroenterology 78, 696----702. A. Scarpa (1972) Methods Enzymol. 24, 343--351. S. Nit (1986) Soil Sci. Soc. Am. J. 50, 52--57. S. Nit (1984) J. Colloid Interface Sci. 102, 313--321. S. Nit, C. Newton and D. Papahadjopoulos (1978) Biolectrochem. Bioenerg. 5, 116--133. M. Eisenbcrg, T. Gresalfi, T. Riccio and S. McLaughlin (1979) Biochemistry 18, 5213--5223. M. Duzgunes, S. Nit, J. Wilschut, J. Bentz, C. Newton, A. Portis and D. Papahadjopoulos (1981) J. Membr. Biol. 59, 115---125. S. McLaughlin, N. Mulrine, T. Gresaifi, G. Vaio and A. McLaughlin (1981) J. Gen. Physiol. 77, 445-----473. S.G.A. McLaughlin (1977) Curt. Top. Membr. Transp. 9, 71--144. A.P. Winiski, A.C. McLaughlin, R.V. McDaniel, M. Eisenberg and S. McLaughlin (1986) Biochemistry 25, 8206--8214. J. Bentz, D. Alford, J. Cohen and N. Duzgunes (1988) Biophys. J. 53, 593---607. S. Nir, D. Hirsch, J. Navrot and A. Banin (1986) Soil Sci. Soc. Am. J. 50, 40-----45. L. Margulies, H. Rozen and S. Nir (1988) Clays Clay Miner. 36, 270--276. D. Hirsch, S. Nir and A. Banin (1989) Soil Sci. Soc. Am. J. 53, 716--721. L.A. Turnberg and A. Anthony-Mote (1969) Clin. Chim. Acta 24, 253--259. J. Kratohvil (1984) Hepatology 4, 85--97S. J. Bentz (1982) J. Colloid Interface Sci. 90, 164--182. P. Barak (1987) The Interaction of Anions with Humic Substances, Ph.D. Thesis, Hebrew University of Jerusalem, Israel. A. Portis, C. Newton, W. Pangborn and D. Papahadjopoulos (1979) Biochemistry 18, 780--790. G.W. Feigenson (1986) Biochemistry 25, 5819--5825. C. Newton, W. Pangborn, S. Nir and J. Papahadjopoulos (1978) Biochim. Biophys. Acta 506, 281--287. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling (1986) Numerical Recipes. Cambridge Univ. Press, Cambridge, 818 pp.
17
Calcium binding to bile salts E. Baruch a, D. Lichtenberg a, P. Barakb, c a n d S. N i t ¢ adept, of Physiology and Pharmacology, Tel-Aviv University, Sackler School of Medicine, Tel-Aviv 69978 (Israel), bDept, of Soil Science, University of Minnesota, St Paul, MN 55108 (U. S. A. ) and cSeagram Centerfor Soil and Water Sciences, Faculty of Agriculture, Hebrew University of Jerusalem, Rehovot 76100 (Israel) (Received May 21st, 1990; revision received September 20th, 1990; accepted October 5th, 1990)
Calcium binding to bile salt monomers and micelles is an important issue with respect to the possible (but rare) precipitation of calcium bile salts in the gallbladder. In the present work the binding of Ca 2+ to six bile salts was measured in solutions containing 2 to 100 mM bile salts by means of a calcium-sensitive dye, murexide, which determines the ionic calcium concentration. In solutions containing bile salt at concentration higher than 20 mM most, if not all, of the bound Ca 2+ isassociated with micellar surfaces. The results were analyzed by employing a model which combines specific binding with electrostatic equations and accounts for the system being a closed one. The analysis of Ca 2+ binding data considered explicitly the presence of Na + ions and yielded intrinsic binding coefficients for Ca 2+ and Na + which were utilized to explain and predict binding results for v~irious concentrations of Ca 2+, Na + and bile salts. The calculations indicate that in saline solutions most of the surface sites were bound by Na +, whereas less than 10% were bound by Ca 2+ even in the presence of 8 mM Ca 2+. The binding of Ca 2+ to bile salt micelles increases with pH. An increase in temperature results in reduced binding affinity of Ca 2+ to the bile salt micelles.
Keywords: bile salts; bile salt micelles; calcium binding; calcium precipitation; murexide; gallstones.
Introduction Insoluble calcium salts (carbonate, phosphate, bilirubinate and salts of fatty acids) have long been recognized as constituents of gallstones [1--2]. The possible involvement of these salts in the pathogenesis of cholesterol gallstones has been considered by several authors, who proposed that microcrystals of insoluble calcium salts may act as nuclei on which cholesterol may be deposited [3--9],
Correspondence to: D. Lichtenberg, Department of Physiology and Pharmacology, Tel-Aviv University, Sackler School of Medicine, Tel-Aviv 69978, Israel. Abbreviations: B, bile acid; B', bile acid, ionized; BNa, bile acid, sodium salt; Kca, intrinsic binding constant of Ca 2+ to B'; kNa, intrinsic binding constant of Na + to B'; CT, total Ca 2+-concentration; Ca, bound Ca2+-concentration; CF, free (ionized) Ca2+-concentration, Ca2+-activity; cmc, critical miceilar concentration; DC, deoxycholate; GC, glycocholate; GDC, glycodeoxycholate; PC, phosphatidylcholine; PCS, photon correlation spectroscopy; PS, phosphatidylserine; TC, taurocholate; TDC, taurodeoxycholate.
thus forming gallstones. The potential to form calcium carbonate, phosphate and bilirubinate may be related to the activity of calcium ions rather than to the total calcium concentration [3]. On the other hand, formation of calcium salts of long chain fatty acids, e.g., palmitate, probably occurs within calcium-containing aggregates of mixed micelles composed of these fatty acids and bile salts [10,1 I]. Calcium binding to bile salt monomers, micelles and mixed micelles can therefore be expected to promote precipitation of calcium salts of free fatty acids while at the same time reducing the concentration of free calcium and thereby inhibiting the precipitation of calcium bilirubinate, carbonate and phosphate. The latter possibility has motivated studies of the binding of calcium to various bile salts using ultraffltration methods [4,12], calcium-specific electrode [3--5] and a calcium-binding dye [6]. However, in spite of the systematic nature of these studies, the results have thus far yielded much controversy. For example, while Moore [3] proposes that the "Ca2+ electrode is offering a powerful new
0009-3084/91/$03.50 © 1991 Elsevier Scientific Publishers Ireland Ltd. Published and Printed in Ireland
18 tool for studies of the physical chemistry of bile", Williamson and Percy-Robb [4] used the Ca 2÷ electrode only in solutions containing up to 3 mM bile salts since higher concentrations of bile salts affected the electrode, "making the Ca 2÷ activity measurements of subsequent standards surprisingly low". In the present communication, we have employed the dye murexide to re-investigate the binding of Ca 2+ to bile salts. This dye is suitable for studying Ca 2÷ binding which is characterized by binding constants within the range of 1 to 100 M -1 [13]. Murexide has been previously used by Lester et al. [6] to measure the binding constants of calcium to monomeric taurocholate and glycocholate [6] but the technique adopted for our studies [13] is quite different, as described in Materials and Methods. The data measured in previous studies on the binding of calcium to bile salts were analysed in terms of apparent binding coefficients. These values vary with the concentrations of other cations in the system, such as Na +. We have chosen to analyse the binding in terms of intrinsic binding coefficients. This approach requires taking into account the presence of sodium cations which are competing with Ca 2+ for binding. The analysis of binding data employed a model developed to explain and predict cation adsorption to charged surfaces [ 14,15]. The three main elements in this model are: (i) consideration of specific binding; it assumes that the total amount of cation adsorbed consists of (a) cations tightly bound to the surface and (b) cations residing in the double layer region; (ii) the electrostatic Gouy-Chapman equations are solved for a system containing several cations of various valencies, and particles whose surfaces are charged and partially neutralized by cation binding, and (iii) the concentration of surface sites is explicitly taken into account since it affects the concentration of cations in solution due to adsorption. The coupling of electrostatic and binding equations proved to be profitable in studies on membranes [15--22] and soil particles [14,23--25]. Application of this approach to micelles required an extension of the equation to non-planar geometries. The combination of experimental and theoretical methods enabled us to investigate the binding of Ca 2÷ to several bile salts and its dependence on Na +, pH, temperature and the presence of other bile salts.
Materials and Methods
All the bile salts used were of the highest purity produced by Sigma Chemical Co. (St. Louis, MO) and were used without further purificaton. Their concentrations were assayed by the enzymatic method of Turnberg and Anthony-Mote [26] using 3-/3-hydroxysteroid dehydrogenase and /3-NAD + (Sigma). Solutions were made of double distilled water using various NaC1 concentrations (150 mM unless stated otherwise) at various pH values (pH = 7.5, unless stated otherwise), using 45 mM imidazole, adjusted to the appropriate pH value by HC1, as a buffer. Experiments carried out using the techniques described below showed that imidazole had little effect on the binding of calcium to bile salts in the absence of added NaCI and no effect in the presence of NaC1. Preparation of mixed micellar systems (400 mM total bile salts concentration) was carried out either by dissolving a mixture of the solid (powder) bile salts or, in several experiments, by mixing stock solutions of the two bile salts. The latter procedure appears to lead to an apparent equilibrium value of calcium binding only after a prolonged incubation period (see below). Calcium determination Total calcium concentration was determined by atomic adsorption spectrophotometry using a Perkin Elmer model 2380 spectrophotometer. Calcium activity was measured either by a calciumselective electrode (in, solutions with low bile salt concentration [4]) or by a spectrophotometric technique using the metaUochromatic indicator ammonium purpurate (Murexide) [131. In our measurements we have used solutions containing 50 /~M murexide at 27"C unless stated otherwise. The difference spectrum between two murexidecontaining solutions, with and without calcium, is characterised by a minimum at 540 nm, a maximum at 470 nm and an isosbestic point at 507 nm. The difference between the absorbance at 540 nm and at 470 nm (A OD) is an increasing linear function of calcium activity [131. For any given solution (of a given pH, [Na +] and temperature) a calibration curve was made by measuring AOD as a function of [Ca 2+ ] in the absence of bile salts. Difference
19 spectra were measured between solutions containing 2---8 mM CaCI 2 and a solution containing no Ca 2+ but otherwise of the same composition. Free calcium concentrations in BS-containing media were evaluated from experiments carded out as follows. First, to correct for any possible effect of light scattering on the absorption difference spectrum, baseline correction was carded out: the difference spectrum between a sample containing the appropriate buffered medium, Ca 2+ and bile salt and a reference containing the same composition but no Ca 2+ was hulled by this correction. Subsequently, murexide was added to both the sample and reference and the difference spectrum was measured. OD was then used to evaluate calcium activity on the basis of the corresponding calibration curve, measured in the absence of BS. A calcium-selective electrode (Radiometer, F2112 Ca/940---249) was used to determine calcium activity in BS-containing media ([BS] < 3 mM), using a calomel electrode (K-401) as a reference electrode and a temperature compensator. A calibration curve was made before each experiment by plotting the potential (.mV) as function of pCa 2+ for samples with varying known [Ca2+]. Measurements were made in 20-ml stirred solutions after soaking the electrode for 6 min in the measured solution. The results obtained by this method differed significantly from those obtained by the use of the calcium-sensitive dye, the differences being larger when high bile salt concentrations were used. Based on the considerations which were previously raised by Williamson and Percy-Robb [4], we have chosen to disregard those data for bile salt concentrations in excess of 3 mM.
Theoretical analysis The procedure is essentially as previously described [14,15]. The concentration of cations, near the negatively charged micellar surface, Xi(o), is given
by Xi(o) = S i exp(-e~b(o)Zi/kT)
(1)
The quantity S i is the solution concentration of a cation i far away from the surface, Z i is its valency, k is Boltzmann's factor and T is the absolute temperature. If a negatively charged bile acid
molecule is denoted by B-, its association to a sodium salt is described by B" + N a + ~ B N a
(2)
The intrinsic binding coefficient for this complex, KNa (M "l) is defined by KNa = [BNa]/([B-] x [Na+])
(3)
in which the concentration of the cation should be taken at the surface, as given by Eqn. 1. A similar expression can be written for the binding reaction of Ca 2+, in which case two types of complexes are possible, (B2-Ca)° and (B-Ca) +, with binding coefficients K2,ca and K l,Ca. The existence of the charged complex implies that charge reversal can occur. In our treatment we considered only the neutral complex, and thus we employed only one binding coefficient for Ca 2+, Kca. The programs for the analysis of Ca2+-binding described previously [14,15] assume a planar geometry. Approximate forms for a spherical geometry are given in Ref. 28. For this study we developed an accurate and efficient numerical procedure for a spherical geometry, which was originally described by Barak [29] for a cylindrical geometry. The main elements of this procedure are described in the Appendix. As will be shown, an analysis of Ca 2+ binding based upon the assumption of a planar geometry can be essentially adequate. The intrinsic binding coefficents, which were assumed to be independent of the concentrations of Ca 2+, Na + and bile salts, were determined by fitting the experimental results for the binding of Ca 2+ to the bile salts. These intrinsic binding constants were then employed for generating predicted values, i.e., concentrations of Ca 2+ bound for different concentrations of Ca 2+, Na + and bile salts, at a given pH and temperature. When fitting the binding data for a particular bile salt, e.g., TDC, at a given NaCl and bile salt concentration, we had to fix two parameters, KNa and Kca, in order to fit seven data points (i.e. the calcium activities measured at seven different calcium concentrations). Such a fit yielded many sets [e.g., (Kca = 0.2 M'i; KNa = 0.5 M'I); (Kca = I M'l; KNa = 2 M'l); (Kca = 1.5 M'l; KNa = 3 M'l)]. However, a comparison of the predictions for Ca 2+ binding to TDC in solutions
20 of other Na + concentrations could discriminate between these sets in favor of the last one. A similar trend was found for other bile salts. Consequently, we decided to f'LXKNa = 3 M "1 in all calculations. Since the murexide, which yields the concentrati6n of C F (Ca free) is also present in the double layer region we refer to
Ca=CT-CF
(4)
as the concentration of Ca bound to the bile, C T being the total calcium concentration. Apparent binding constants refer to K =
Ca/(CF[n']) These values were derived from the best fits of the dependence of C a on CF, assuming that [B-] *,C a. Results
Most of the binding measurements employed concentrated bile salt solutions (100 raM), to ensure that most of the bound calcium was associated with micvlles rather than with monomers. The results in Fig. 1 illustrate the dependence of the amount of
Ca 2+ bound to the bile salt micelles as a function of total Ca 2+ concentration for two bile salts. Table I summarizes the calcium binding affinities o f the various bile salts employed in terms of apparent and intrinsic binding coefficients. The intrinsic binding coefficients of the various bile salts varied within a relatively small range (1.3--2.8 M -1) and were all smaller than the intrinsic binding coefficient of Na + (fixed at 3 M "1 for all the bile salts). Noticeably, it appears that Ca 2+ has a somewhat greater binding affinity to micelles composed of dihydroxy bile salts than to the trihydroxy ones. In order to test the predictions of our theoretical model and to reduce the uncertainties in the deterruination o f the intrinsic binding coefficients, we have measured calcium activity at various concentrations of NaCI. The effect of variations in NaCI concentrations from 0 to 200 m M is illustrated for TDC in Fig. 2. The agreement between the experimental and predicted values of the concentrations of bound Ca 2+ is within experimental errors, supporting our model. Elevation of p H results in enhancement of Ca 2+ binding to bile salt micelles as illustrated for the case of chelate in Fig. 3. Noticeably, the intrinsic bin-
CBCmH) 5 []
~ o
mH Cholate
!
I
2
,
; Ct(mH)
Fig. 1. Dependenceof bound calciumconcentration on the total concentration of CaCI2 in 100 mM solutions of sodium chelate and sodium glycodeoxylatein saline (150 mM NaCI) at room temperature and pH = 7.5. Note that the lines give the calculated values (see text for details).
21 TABLEI Binding constants of Ca2+ to various bile salts (and bile salt mixtures). Both the apparent binding constant and the intrinsic binding constant (calculated as described in text), were determined from the spectra of murexide in solutions of 100 mM of the various bile salts in solutions at pH = 7.5, at room temperature, in the presence of 2--8 mM CaC12. Bile salt
Binding constants (M -I) Apparent in 150 mM NaCI
Intrinsic
Intrinsic, in h l mixture with C
GDC
C
5.8
1.38
--
2.15
TC GC DC TDC GDC
5.9 6.2 7.0 7.9
1.34 1.44 1.60 1.47
1.55 1.55 2.40 1.60
N.D. 2.25 3.20 N.D.
12.9
2.75
2.15
--
d i n g c o n s t a n t f o r c h o l a t e micelles i n c r e a s e s m o n o t o n i c a l l y a n d d o u b l e s w h e n the p H is raised f r o m 6 to 8.5, a l t h o u g h the a p p a r e n t b i n d i n g c o n s t a n t does n o t c h a n g e m o n o t o n i c a l l y . T h e t e m p e r a t u r e d e p e n d e n c e o f the b i n d i n g o f C a 2+ t o c h o l a t e m i c e l l e s s h o w n in F i g . 4
CB(mM) 6"
• n
o
d e m o n s t r a t e s t h a t c a l c i u m b i n d i n g is a d e c r e a s i n g function o f t e m p e r a t u r e within the r a n g e o f 5 ° to 51°C. T h e intrinsic b i n d i n g coefficients d e c r e a s e with t e m p e r a t u r e f r o m 2.6 M "i at 5 ° C to 0.7 M -1 at 51 °C. (Fig. 4). T h e effect o f t e m p e r a t u r e was explicitly c o n s i d e r e d in the c a l c u l a t i o n s t h r o u g h the
~
O l OmM TDC
5" 4 3
~
100mMTDC
2
200mMNaCI
l
•
0
0
I
0
= D
au
I
2
,,g I
4
o
r=
20mM
I
6
TDO =
8
10
Ct(mM) Fig. 2. Dependence of bound calcium on the total concentration of calcium in solutions of TDC (20 and 100 raM) in saline at room temperature and pH = 7.5.
22
K(Ca)( M" 1) 6apparent
5
4 3 2
intrinsic
1 0
!
!
5
!
8
7
6
9
pH Fig. 3. Effect of pH on the binding of calcium to cholate as measured in cholate solution (100 raM) in saline at room temperature.
Boltzmann factor in Eqn. 1, and through the value of the dielectric constant. Binding of Ca 2+ to binary mixed micellar systems depended upon the method used for mixing the two bile salts. Mixing of powders (see Materials and
Methods) always resulted in the formation of solutions in which calcium activity was independent of the time of incubation. In contrast, mixing of solutions of the individual bile salts resulted in slightly higher calcium activities (apparently lower binding
K(Ca)( M" 1) ]2 10
8 6 4 e~.,,,,,,.~,....,...~~
intrinsic
2 0
I
o
10
I
l
20
30
I
I
!
40
50
6O
T e m p e r a t u r e (Oc) Fig. 4. Effect of temperature on the binding of calcium to cholate in cholate solution (100 mM) in saline at pH = 7.5.
23 constants) which decreased with time. Thus, the results obtained from mixtures made by the two different methods after 1 h of incubation were very different, whereas 24 h after preparation the results were independent of the method of preparation. A summary of the results obtained with mixtures made from mixed powders is given in Table I in terms of intrinsic binding coefficients. We note that mixtures of DC with either cholate or GDC have higher affinity for calcium than either of the pure components, whereas the binding constants of the other mixtures are close to those of the pure mixed micelles. Discussion Our calculations of Ca 2+ binding have employed intrinsic binding coefficients, which are independent of the concentrations of Ca 2+, bile salt and Na +. Table I illustrates that the intrinsic binding coefficients are several-fold smaller than the apparent binding constants. This difference (for a given Na + concentration) is due to the fact that the calculations based on Eqn. 1 take explicitly into account the enhancement in Ca 2+ concentrations close to the micellar surface. This difference would have been much larger in the absence of Na + ions which compete with Ca 2+ for binding to the surface sites and reduce the magnitude of the surface potential. Figure 2 illustrates the significance of the effect of Na + concentrations on the amount of Ca 2+ bound to the micelles. When 2 mM CaC12 was added to 100 mM sodium-TDC in the absence of NaCI, only 2.4% of the surface sites were occupied by Ca 2+ and 74.8% by Na +. For [CT] = 8 mM the corresponding values are 9.2% and 67.5%. This situation is significantly different from the case of phosphatidylserine (PS) vesicles where, under similar conditions, the majority of surface sites are bound by Ca 2+ [15,16]. A comparison between bile acids and PS shows that KNa for PS (0.6--1.0 M -l) is three- to four-fold smaller than for bile acid micelles, whereas Kca (30--70 M -l) is about an order of magnitude larger. Furthermore, for vesicles which are induced to fuse by Ca 2+, measurements showed a dramatic increase in the binding affinity of Ca 2+ to PS [15], which is accompanied by a transformation to a dehydrated Ca(PS)2 phase
[30,31]. The rate of these transformations depends upon concentrations of PS, Ca 2+ and Na +. For 1 mMPS in the presence of 100 mM NaCI and about 1 mM of Ca 2+, such transformations occur within minutes [15]. Similar transformations occur upon addition of Ca 2+ to bile salt micelles, but much larger Ca 2+ and bile acid concentrations are required to induce BS-Ca precipitation, which is also much slower [10,11]. This comparison illustrates the lower binding affinity of Ca 2+ to bile acid micelles than to PS vesicles. The relative affinity of Ca 2+ to bile salt monomers versus micelles has been an issue: Williamson and Percy-Robb havre reported that the activity of Ca 2+ in monomeric solutions of sodium giycocholate is independent of the bile salt concentration, suggesting that binding of Ca 2+ to the bile salt monomers is insignificant [4]. This conclusion appears to be consistent with the results of Rajagopalan and Lindenbaum [5] and forms the basis for the interpretation used by Jones et al. [7] in their studies of the solubility products of the calcium salts of glycine-conjugated bile acids. In contrast, the work of Moore and his colleagues concluded, on the basis of their calcium selective electrode measurements, that the affinity of pre-micellar glycocholate to calcium ions is much higher than that of the micellar bile salt [3,8]. The high affinity of calcium to monomeric bile acids has been attributed by these authors to "interposition of Ca 2+ ions between the side chain ion and hydroxyl substituent of the cholanic acid ring to form a reversible Ca 2+ ion exchange site". However, it is not clear whether comparison of dihydroxy-bile salts with trihydroxy bile salts is consistent with this interpretation. Figure 2 demonstrates the dependence of Ca2+-binding on bile salt concentration. We have also measured Ca 2+ binding to 2 mM of TDC. As it turned out, the amount of Ca 2+ bound was negligibly small, below the experimental resolution. Thus our results cannot yield binding coefficients of Ca 2+ to bile salt monomers. On the other hand we were justified in neglecting the binding of Ca 2+ to monomers in bile salt solutions of concentrations of 20 mM and above. Most of our studies employed 100 mM bile salts. The calculations based on the binding coefficients measured at this high bile salt
24 concentration yielded reasonable predictions for the amounts of Ca 2+ bound to 50 mM bile salts (results not shown) or to 20 mM bile salts where Ca 2+ binding to monomers could have made a contribution. In the latter case our predictions for the measured quantity (ionized Ca 2+) were within the experimental uncertainty of 5%, although the calculated values o f b o u n d calcium appear to be slightly underestimated. However, our finding of a small CB value for a 2 mM solution of TDC whose cmc = 2 mM [21] rules out a large contribution to CB from TDC monomers at 20 mM TDC. ~Unfortunately, the accuracy of our calcium activity measurements (both carried out by a CaX+-selective electrode and those which employed murexide) appears to be inadequate to allow for a comparision between binding of calcium to bile salt monomers and to micelles. We favor the conclusion that the polyvalent micellar surface is more attractive for calcium ions than the bile salt ions. The apparent contradiction between this conclusion [4,5] and that of Moore and his collaborators [3,8] may be attributed to the extreme sensitivity of the calculated apparent binding constants of monomers to small experimental errors in the determination of the ionized calcium concentration. To demonstrate this sensitivity, note the following example: a bile salt has a cmc value of 2 raM; suppose that CaC12 (2 mM) is added to a 2 mM solution of this bile salt and the ionized calcium concentration (CF) is measured. The apparent binding constant is given by K = Cn/(CF x B) × 103, where CB, C F and B are the concentrations (in mM) of bound Ca 2+, free Ca 2+ and free monomeric bile salt, respectively, and C B = CT - C E. If the measured value of C F is 2.0 raM, it must mean that no calcium binds to monomers. On the other hand, a measured value of C F = 1.9 mM would mean that K = 100/(1.9 x 1.9) = 28 M "1, namely that the Ca2+-binding affinity of monomers is greater than that of the micelles. In our experimental systems (and probably in other studies as well), the accuracy of the results can hardly differentiate between those two extremes; other cases are not likely to yield reliable binding coefficients to monomers by the techniques available to us. The results in Fig. 4 indicate that more Ca 2+ is bound to cholate micelles as the temperature is
lowered. This variation is due to changes in the intrinsic binding coefficient of calcium to the micelles. This conclusion is based on the following considerations: (1) Temperature appears explicitly in the calculations of binding through the Boltzmann distribution factor (Eqn. 1) and implicitly through the dielectric constant, ~, (e.g., ~(5 °C) = 86; e(25 °C) = 78.5, etc.). Both these effects were accounted for by the calculations. (2) The area per site can be expected to affect C B only slightly. This is illustrated in Table II, which shows that a 10% increase in the area per site yields less than 3% decrease in CB. The observed variation of the binding affinity with temperature probably reflects a dependence on temperature of the arrangement of bile salt ions within the micelles. Interestingly, Ca 2+ binding to PS vesicles, in which temperature-induced molecular rearrangement is less likely, appears to be independent of temperature [32]. The calculations presented in Table II also illustrate that the size of the mixed micelles should affect the binding of calcium to the surface only slightly. For a given binding constant per site, an increased number of sites per micelle, which of course is a function of the aggregation number, enhances calcium binding by up to 10% as the micelle grows from 3 nm to infinity. For particles of smaller sizes, the size may have a more pronounced effect on calcium binding but analysing this effect quantitatively may be inadequate because the macroscopic treatment is limited to cases where the radius of the particles is sufficiently larger than the width of the double layer. Recently we have studied the sizes of CJC, TC, DC and TDC micelles (100 mM) by photon correlation spectroscopy (PCS) (A. Bor and D. Lichtenberg, unpublished results). All these micelles were .found to have average diameters within the range of 2.7--2.9 nm (in saline) at pH 8.0 and within the range of 3.0--3.9 nm at pH 5.5. In the presence of Ca 2+ (5 raM), the size of the micelles increases only slightly (if at all) and the sizes of the various bile salt micelles remain very similar. Noticeably, however, the precision of our PCS measurements is not very high. The distribution mean for any given bile salt in any given solution varies by as much as 40%. Thus, these data do not contribute much to the confusing state of our knowledge of the size of
25 TABLE II Effect of particle (Micelle) radius on Ca 2+ bindinga,
NaCl (raM)
R (rim)
Area per site (rim2)
Ce (raM)
- ~o(mV)
0 0 0 0 0 0 200 200 200 200
3 5 15 Planar Planar Planar 3 5 15 Planar
0.6 0.6 0.6 0.6 0.66 0.54 0.6 0.6 0.6 0.6
2.95 2.97 2.98 3.03 2.95 3.11 1.04 1.07 1.11 1.15
75 79 80 86 83 88 40 41 42 43
aCalculations presented are for a system containing 4 mM CaC12 and 100 mM "sites" at 25 °, employing the values Kca = 1.5 M -l KNa = 3 M -l (as in the case for TDC). The presence of another non-binding monovalent cation (imizadole; at a concentration of 45 raM) was considered in the calculations.
bile salt micelles [27]. Nevertheless, the general trend is clear: the dihydroxy bile salt micelles appear to be slightly larger than those of the trihydroxy bile salts and the reduction of pH results in a size increase of all the bile salt micelles. In fact, the experimentally observed small differences in radius can amount to several-fold differences in the aggregation number, which is proportional to the volume of the mixed micelles. In any event, the pH-induced changes in calcium binding cannot be explained by changes in micellar size; at low pH values, the mixed miceUes are larger while the affinity of the micelles for calcium is lower, in contrast with the tendency pointed out by Fig. 3. The alternative explanation is that at low pH values, protons compete with calcium in binding to the bile salt micelles, thus reducing calcium binding. On the other hand, we think that differences in micellar sizes can explain some of the differences in calcium binding between the different bile salts. In fact, the differences between the binding of calcium to the various bile salts micelles and mixed micelles are rather small and the only micelles that appear to have significantly higher intrinsic binding constants than the other bile salt micelles are GDC and mixtures of GDC with other bile salts. We have no satisfactory explanation for this finding as we
are unaware of any other difference between GDC and all other bile salts studied. Micellar size may be responsible for the finding that any of the trihydroxy bile salts binds less calcium than corresponding dihydroxy bile salts (DC > cholate; TDC > TC; GDC > GC), as previously suggested by Rajogapalan and Lindenbaum [5]. The conjugation of the "head group" of either cholate or deoxycholate by either taurine or glycine appears to affect calcium binding, such that the taurine reduces calcium binding, while glycine has the opposite effect. The results are, again, in agreement with the latter previous report [5] in which these effects were attributed to differences in hydration of the conjugated group. In conclusion, it appears that in solutions containing more than 20 mM bile salts, calcium binding involves predominantly, if not exclusively, bile salt micelles rather than monomers. The intrinsic binding coefficients are within the range of 1 to 3 M -l, with the species of bile salt, the pH and the temperature having only small effects on the bincling affinity of the micelles for calcium. Sodium binding, which is characterized by a binding coefficient of the same order of magnitude, is an important factor in determining calcium binding. It should, however, be noted that the rather low
26
(A6)
binding affinity of calcium to the bile salt micelles at calcium concentrations of up to 8mM increases dramatically at the range where Ca2+-induced precipitation occurs, leading to crystalline structures.
X = xr
Acknowledgments
I S = rSiZi2/2
This work was partially supported by the Basic Research Foundation administered by the Israel Academy of Sciences and Humanities, the Ministry of Science and Technology of Israel, the Commission of the European Communities (Grant 3946), and the S.A. Schonbrunn Research Endowment Fund of the Hebrew University of Jerusalem.
in which N A is Avogadro's number and S i is molar concentration of ion species i. With this notation and the use of Eqns. A4 to A8, Eqn. (A1) becomes
where x = ((8*re2NA(IS))/(IO00
e
kT)) 1/2
c~" + 2¢~'/X = (F,ZiS.o, zi)/(2IS)
(A7)
(A8)
(A9)
and Eqn. A3 yields
~/~1S2+)/
$'(a) = (4a" aoe/(~kTr)) x [(1 - y(a) 2 (1 + y(a) ~, KiSi + + y(a) 2 X;/~Sj2+)] (A10)
Appendix The electrical potential ~b around a spherical particle satisfies the equation
~l'" + 2 ~ ' / r = - 4wp/E
(A1)
in which p(r) is the charge density in solution and e is the bulk dielectric constant. The boundary conditions are
~b (o,) = ~b' (oo) = 0
(A2)
¢'
(A3)
( a ) = - 4 T a/E
in which a is the radius of a spherical particle and a is the surface charge density. The volume charge density is given by p(r) = ~,eZiNiyZi(r)
(A4)
where e is the absolute magnitude of an electronic charge, Z i is the valence of an ion, being positive for a cation and negative for an anion, and y(r) = exp[ck(r)] = exp [-e~b(r)/kT]
(A5)
where k is the Boltzmann constant and T is the absolute temperature. A s in Ref. 29 we have employed the dimensionless potential $, and dimensionless distance, X, given by
where a 0 is charge density in absence of binding. Usually only Ci, the total concentration of cation i in the system, which consists of the concentration of the cation in solution, in the double layer region, and as surface complexes is known a priori. The solution of Eqn. A9 satisfying Eqns. A2 and A10 starts from an initial guess of ~#(a) which can be obtained from a solution of either the planar equation or the Debye-Huckel approximation of Eqn. Ag. Substitution of ok(a) in Eqn. A10 yields '(a) and Eqn. A9 yields ~ "(a). The solution of Eqn. A9 is numerical with intervals of size 1/25 divided into smaller steps solved by a fifth-order series and extrapolated to infinitesimal stepsize using Richardson's deferred approach to the limit with rational function extrapolation [ 33 ]. For a given 4)(a), numerical integration was terminated when either ~(X) had a sign different than that of 6(a) or when ¢~'(X) had a sign different than that of ¢~'(a). As an exact solution of Eqn. A9 would begin with a value of q~(a) that would allow integration to continue to an infinite distance without changing signs of either ok(X) or 6'(X), iterating between values of ~(a) that lead to the two types of sign reversals leads to maximization of distance of calculation and approaches a true solution. Iteration of ¢~(a) was continued until convergence to a preset tolerance. Best values of ¢ffX) were utilized to recalculate the concentrations of ca-
27
tions in the double layer and bound to the surface. Eqn. A9 was then recalculated iteratively as described elsewhere [ 14] until convergence of all components of the system was reached. Mass balance and equality of the right- and left-hand sides of Eqn. A9 were checked. The calculated values in Table II illustrate the effect of micelle (or vesicle) radius on the surface potential and on CB, the concentration of Ca 2+ bound, for two extreme cases of 0 and 200 mM NaCI. The values of l~bolare about 10--15% smaller for R = 3 nm than in the planar case, whereas the corresponding CB values are 3 - - 10% smaller. The relatively smaller effect of radius on CB values is due to the presence of competing monovalent cations. In general, the term specifically reflecting the spherical geometry, 2 ~k'/r, is relatively small compared to the term ~b#, which is common to planar, cylindrical and spherical geometries. These results also demonstrate that a knowledge of the details of the micellar shape and dimension, which desirable, is not essential for the analysis and prediction of Ca 2+ binding to bile salt miceUes. References 1 D.J. Sutor and S.E. Wooley (1971) Gut 12, 55----64. 2 C.S. Pitehumoni, K.V. Viswanathan and E.W. Moore (1987) Gastroenterology 92, 1764 (Abstract). 3 E.W. Moore (1984) Hepatology 4, 228--243s. 4 B.W.A. Williamson and I.W. Perey-Robb (1979) Biochem. J. 181, 61-----66. 5 N. Rajagopalan and S. Lindenbaum (1982) Biochim. Biophys. Acta 711, 66--74. 6 D.G. Oelberg, W.P. Dubinsky, E.W. Adeock and R. Lester (1984) Am. J. Physiol. 247, G112---43115. 7 C.A. Jones, A.F. Hofmann, K.A. Mysels and A. Roda (1986) J. Coll. Inter. Sei. 114, 452----470. 8 E.W. Moore (1985) Gastroenterology 83, 1079---1089. 9 D.M. Small (1980) N. Engl. J. Med. 302, 1305--1307. 10 D. Lichtenberg, N. Younis, A. Bor, T. Kushnir, M. Shefi,
11 12 13 14 15 16 17 18
19 20 21
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30 31 32 33
S. Almog and S. Nir (1988) Chem. Phys. Lipids 46, 279---291. D. Lichtenberg, E. Werker, A. Bor, S. Almog and S. Nir (1988) Chem. Phys. Lipids 48, 231--243. B.W.A. Williamson and I.W. Percy-Robb (1980) Gastroenterology 78, 696----702. A. Scarpa (1972) Methods Enzymol. 24, 343--351. S. Nit (1986) Soil Sci. Soc. Am. J. 50, 52--57. S. Nit (1984) J. Colloid Interface Sci. 102, 313--321. S. Nit, C. Newton and D. Papahadjopoulos (1978) Biolectrochem. Bioenerg. 5, 116--133. M. Eisenbcrg, T. Gresalfi, T. Riccio and S. McLaughlin (1979) Biochemistry 18, 5213--5223. M. Duzgunes, S. Nit, J. Wilschut, J. Bentz, C. Newton, A. Portis and D. Papahadjopoulos (1981) J. Membr. Biol. 59, 115---125. S. McLaughlin, N. Mulrine, T. Gresaifi, G. Vaio and A. McLaughlin (1981) J. Gen. Physiol. 77, 445-----473. S.G.A. McLaughlin (1977) Curt. Top. Membr. Transp. 9, 71--144. A.P. Winiski, A.C. McLaughlin, R.V. McDaniel, M. Eisenberg and S. McLaughlin (1986) Biochemistry 25, 8206--8214. J. Bentz, D. Alford, J. Cohen and N. Duzgunes (1988) Biophys. J. 53, 593---607. S. Nir, D. Hirsch, J. Navrot and A. Banin (1986) Soil Sci. Soc. Am. J. 50, 40-----45. L. Margulies, H. Rozen and S. Nir (1988) Clays Clay Miner. 36, 270--276. D. Hirsch, S. Nir and A. Banin (1989) Soil Sci. Soc. Am. J. 53, 716--721. L.A. Turnberg and A. Anthony-Mote (1969) Clin. Chim. Acta 24, 253--259. J. Kratohvil (1984) Hepatology 4, 85--97S. J. Bentz (1982) J. Colloid Interface Sci. 90, 164--182. P. Barak (1987) The Interaction of Anions with Humic Substances, Ph.D. Thesis, Hebrew University of Jerusalem, Israel. A. Portis, C. Newton, W. Pangborn and D. Papahadjopoulos (1979) Biochemistry 18, 780--790. G.W. Feigenson (1986) Biochemistry 25, 5819--5825. C. Newton, W. Pangborn, S. Nir and J. Papahadjopoulos (1978) Biochim. Biophys. Acta 506, 281--287. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling (1986) Numerical Recipes. Cambridge Univ. Press, Cambridge, 818 pp.
