J. Phys. Chem. B 2000, 104, 7745-7751
7745
Hydrophobic Self-Association of Sodium Taurochenodeoxycholate and Tauroursodeoxycholate Noriaki Funasaki,* Masao Nomura, Seiji Ishikawa, and Saburo Neya Kyoto Pharmaceutical UniVersity, Misasagi, Yamashina-ku, Kyoto 607-8414, Japan ReceiVed: March 30, 2000; In Final Form: May 31, 2000
The aggregation patterns of sodium taurochenodeoxycholate (TCDC) and tauroursodeoxycholate (TUDC) in an isotonic sodium chloride solution are investigated by frontal chromatography on Sephadex G-10 columns at 298.2 K and are quantitatively analyzed on the basis of stepwise aggregation models. The micellar aggregation numbers, critical micelle concentrations (cmc’s), stepwise aggregation constants, and micelle size distributions of TCDC and TUDC are determined and compared to those of sodium taurocholate and taurodeoxycholate. The logarithms of gel-water partition coefficients, dimerization constants, and reciprocal cmc values for the four bile salts exhibit linearity with their hydrophobic molecular surface areas, and the slopes are close to that of the logarithms of reciprocal cmc values against the hydrophobic molecular surface areas of lecithins. This fact shows that the gel adsorption, dimerization, and micellization of bile salts are driven mainly by hydrophobic interactions and that the Small model for the micellization of bile salts is better than models based on hydrophilic interactions. The micelle of TUDC grows less cooperatively than that of TCDC, an epimer of TUDC. This result suggests that the 7β-hydroxyl group of TUDC inhibits micellar growth because of increased intermolecular mismatching contact with the hydrophobic surface and decreased intermolecular hydrogen bonds in the micelle.
Introduction The micellization of bile salts plays a critical role in the digestion of lipids in animals. Many studies on this topic have been reported and reviewed in monographs1-4 and a review article.5 There are a number of controversies about the micellization of bile salts; e.g., the presence or absence of a critical micelle concentration (cmc), micellar aggregation numbers, the monodispersity or polydispersity of micelle size, critical or noncritical self-association, structures of micelles, the nature of driving forces of micellization (hydrogen bonding or hydrophobic interactions), the presence or absence of dimers, and the degree of micellar counterion binding.1-8 Sodium taurocholate (TC) and sodium taurodeoxycholate (TDC) are the two bile salts that have been most extensively studied.1-10 Much less is known about the micellization of sodium taurochenodeoxycholate (TCDC) and sodium tauroursodeoxycholate (TUDC), commonly occurring bile salts.1,3,11-14 As Figure 1 shows, TCDC and TUDC are epimers different in the stereochemistry of the 7-hydroxy group and are positional isomers of TDC. These three dihydroxyl bile salts will be more hydrophobic than TC, a trihydroxyl bile salt. Comparisons among the micellization behaviors of these bile salts are expected to resolve the above-mentioned controversies, in particular, those regarding the presence or absence of cmc’s, the monodispersity or polydispersity of micelle size, critical or noncritical self-association, the nature of driving forces of micellization, and the presence or absence of dimer. The cmc values of TCDC and TUDC were determined by the surface tension,13 dye titration,9 light scattering,11,12 and solubilization,1 and their micellar aggregation numbers were determined by equilibrium ultracentrifugation1 and light scattering.11,12 By gel filtration chromatography (GFC), we determined aggregation numbers, cmc’s, stepwise aggregation constants, micelle size distributions, and aggregation models for TC and TDC in a 154 mM sodium chloride solution at 298.2
K.4,6,7 This method has also been applied to the micellization of surfactants,15 a dye,16 and drugs.4,17,18
* Author to whom correspondence should be addressed. Fax: +81-75595-4762. E-mail:
[email protected].
In the present work, we determine cmc values, micellar aggregation numbers, and stepwise aggregation constants for
Figure 1. Chemical structures of TCDC, TUDC, TDC, and TC.
10.1021/jp001205x CCC: $19.00 © 2000 American Chemical Society Published on Web 07/14/2000
7746 J. Phys. Chem. B, Vol. 104, No. 32, 2000
Funasaki et al.
TABLE 1: Chromatographic Data for Taurine-Conjugated Bile Salts on Sephadex G-10 Columns bile TCDC TUDC TDCb TCb a
Vt (mL) 17.90 16.57 22.78 23.63
V1 (mL) 52.80 42.65 69.45 29.30
Vm (mL) 7.49 6.25 9.21 9.89
V1/Vt 2.95 2.57 3.05 1.24
kava 0.639 0.547 0.647 0.150
log kav 4.352 3.527 4.439 1.413
N 13 16 25 35
kav ) (V1 - Vm)/(Vt - Vm). b Taken from ref 6.
TCDC and TUDC on the basis of GFC data and relate these aggregation properties with the chemical structures of bile salts. Experimental Section Materials. TCDC was synthesized from chenodeoxycholic acid (Sigma) and taurine by means of a peptide-coupling reagent, 2-ethoxy-1-ethyloxycarbonyl-1,2-dihydroquinoline.19 This specimen of TCDC was treated with charcoal in methanol three times and recrystallized from methanol. The crystals were freeze-dried from water several times and dried at 383 K under reduced pressure. Similarly to TCDC, TUDC was synthesized from ursodeoxycholic acid (Sigma) and purified. The purified samples of TCDC and TUDC were both 99.0% pure or better, as estimated by reverse-phase high-performance liquid chromatography (HPLC).20 Sephadex G-10 (Pharmacia) columns were treated as suggested by the manufacturer. The double-distilled water was degassed just before each GFC experiment. Methods. All GFC experiments were carried out in a 154 mM sodium chloride solution under a flow rate of ca. 0.4 mL min-1. Different columns were used for TCDC and TUDC. The characteristic data on the columns are shown in Table 1. The columns were water-jacketed in order to maintain them at a constant temperature of 298.2 ( 0.2 K. The concentration of bile salt in the eluate was monitored continuously with a differential refractometer and an absorbance detector at 220 nm. The flow rate was also monitored with an electrobalance. The refractive index data were mainly used for further analysis with a personal computer and were supported by the UV data. The chromatographic data were subjected to baseline correction and a smoothing treatment. The GFC experiments were carried out at a number of concentrations; the number, n, of data points is 11 for TCDC and 14 for TUDC. The derivative chromatogram was approximated by the difference chromatogram. Simulations of chromatograms were carried out by a plate theory (continuous flow model).21 The number of the plates (N) and the void volume (Vm) of the column are shown in Table 1. Further details on experiments and calculations were reported elsewhere.6,21 Results Frontal Chromatograms. Figure 2a shows the frontal chromatogram of TCDC at an applied concentration of C0 ) 4.5 mM in a 154 mM sodium chloride solution on the Sephadex G-10 column. Because a large volume S ) 84.74 mL of a dilute TCDC solution was applied to the column, a plateau region appeared on the chromatogram. This chromatogram is termed the frontal chromatogram. Because the concentration C of TCDC in the plateau is the same as that applied, this chromatogram affords us with quantitative information about the self-association of TCDC.4,18,22 We can assume that the equivalent sharp boundary for the leading or trailing edge of the solute zone on the chromatogram is approximately the beginning or termination of the plateau region (centroid) of the elution profile and satisfies the relationships4,18,22
Figure 2. (a) Frontal chromatogram and (b) derivative chromatogram of 4.5 mM TCDC, together with definitions of chromatographic parameters.
Vc′ ) Vc )
∫0C
∫0C
0
0
V dC/C0
V dC/C0 - S
(leading boundary) (trailing boundary)
(1) (2)
Here, S denotes the applied volume of the sample. For these determinations, the volume coordinate, V, is assigned a zero value when the leading boundary of the applied sample enters the column bed. According to this approximation (called asymptotic theory), the elution curve for a nonassociable solute is expected to fall within a rectangle of height C0 and width S.18,21,22 Because the centroid volumes, Vc′ and Vc, at the leading and trailing boundaries were equal to one another within experimental errors, we took the average of their values as Vc. Frontal derivative chromatograms (Figure 2b) reflect aggregation patterns.4,21,22 As Figure 3a shows, Vc decreases with increasing concentrations of TCDC and TUDC. The centroid volume of monomer, V1, can be obtained by extrapolation of Vc to infinite dilution. The concentration at which Vc begins to decrease abruptly can be regarded as a critical micelle concentration (cmc). Another cmc can be obtained from the intersection of two straight lines in the plot of Vc against the reciprocal concentration. The centroid volume of micelles, Vm, can be obtained by extrapolation of Vc to infinite concentration in this plot. Thus, we can determine two cmc values from a set of Vc data. These cmc values are shown in Table 2. Because pore sizes of Sephadex G-10 are smaller than homodimers of TCDC and TUDC, the Vm value can be regarded as the elution volume of all aggregates. It is identical to the void volume, if the chromatogram gives a completely symmetric peak.4,18 For small molecules, one can assume that equilibria of self-association and partitioning between the gel and aqueous phase are established rapidly on a chromatographic time scale. Under these conditions, the observed centroid volume is the sum of contributions of the
Hydrophobic Self-Association of TCDC and TUDC
J. Phys. Chem. B, Vol. 104, No. 32, 2000 7747
Figure 4. Plots of log(C - C1) versus log C1 according to eq 4, on the basis of monomer concentration data obtained for TCDC (solid circles) and TUDC (open circles).
Figure 3. (a) Centroid volume and (b) monomer concentration as a function of the total concentration for TCDC (solid circles) and TUDC (open circles). The solid lines are calculated from eq 10 with stepwise aggregation constants shown in Table 3.
TABLE 2: Critical Micelle Concentrations and Dimerization Constants for Taurine-Conjugated Bile Salts in a 154 mM Sodium Chloride Solution at 298.2 K bile
k2 (M-1)
cmc (mM) Vc vs Vc vs C 1/C DTa CLSa
TCDC TUDC TDC TC
1.7 2.6 1.4f 4.5f
2.0 3.7 1.6f 6.3f
1.8e
2.5e
1.6e 3.8e 0.9g 3.4g -
GFC 9.77 15.4 16.1f 6.11f
nw
molecular area (nm2)
GFCb averagec Sod
Swd
18 ( 2 15 ( 2 22 ( 3 5(3
1.85 1.93 1.87 2.15
20 14 23f 8f
4.34 4.29 4.36 4.09
aDT ) dye titration and CLS ) classical light scattering. b This work at 20 mM. c Average of the values determined by equilibrium ultracentrifugation, classical and quasi-elastic light scattering, ionic selfdiffusion, and gel filtration at 293.2 or 298.2 K; taken from ref 3. d Hydrophobic (So) and hydrophilic (Sw) molecular surface areas at a water radius of 0.14 nm for unconjugated cholanate ions; taken from ref 31. e Taken from ref 12. f Value at 20 mM, taken from ref 6. g Taken from ref 9.
Figure 5. Micellar weight-average aggregation number as a function of the total concentration for TCDC (solid circles), TUDC (open circles), TDC (open triangles),6 and TC (open squares).6 The solid lines are calculated from eq 10 with stepwise aggregation constants shown in Table 3.
monomer and micelles weighted by their weight fractions.4,18,22
Vc ) [V1C1 + Vm(C - C1)]/C
(3)
Because V1 and Vm have been estimated (Table 1), we can determine the monomer or intermicellar concentration C1 from eq 3. Figure 3b displays the observed monomer concentrations of TCDC (solid circles) and TUDC (open circles) as a function of the total concentration. According to multiple equilibrium theory for self-association,4,18,23 the weight-average micellar aggregation number, nw, can be calculated from
nw ) d log(C - C1)/d log C1
(4)
Figure 4 shows this log-log plot for TCDC and TUDC. From the tangent to this curve, we can determine weight-average
micellar aggregation numbers as a function of the total concentration. Figure 5 shows that TCDC and TUDC form dimers at low concentrations and larger multimers at higher concentrations. In this figure, the data for TC and TDC are also included.6 Self-Association Patterns. According to the multiple equilibrium model, the stepwise aggregation constant for the formation of an i-mer from an (i - 1)-mer and monomer is written as
Ai-1 + A1 ) ki Ai
(i ) 2, 3, 4, ..., 8)
ki ) [Ai]/[Ai-1]C1
(5) (6)
When the i-mer is formed from i monomers, we can define the one-step (overall) aggregation constant, Ki, as
7748 J. Phys. Chem. B, Vol. 104, No. 32, 2000
iA1 ) Ki Ai
(i ) 2, 3, 4, ..., 8)
Ki ) [Ai]/C1i
Funasaki et al.
(7) (8)
These equilibrium constants can be connected by i
Ki )
ki ∏ 2
(9)
Model II is best fit to the present results among several aggregation models.6,18 In model II, we assumed a marked attenuation (anticooperativity) of ki at large aggregation numbers; that is, ki ) k/i. The total concentration of TCDC can be written as
C ) C1 + 2k2C12 + ... + (i - 1)Ki-1C1i-1 + (i - 1)!Ki-1C1/ki-2[exp(kC1) - 1 - kC1 - (kC1)2/2! ... - (kC1)i-2/(i - 2)!] (10)
monomer and dimer. Therefore, it is proportional to the total concentration for the dimerization system.18,21,25 A negative deviation from this linearity indicates the appearance of trimer or larger aggregates, and this concentration is termed the minimum multimerization concentration. The values obtained were 1.3 mM (TCDC), 1.7 mM (TUDC), 2.3 mM (TC),6 and 1.0 mM (TDC).6 At higher concentrations, the height approaches a constant, indicating that the sum of the concentrations of monomer and dimer becomes almost a constant. The solid line in Figure 9 shows that the peak height obtained by simulations with a number of plates (Table 1) and stepwise aggregation constants (Table 3) is very close to the observed value. This agreement indicates the validity of the aggregation model used; in particular, the dimerization constant estimated from the centroid volume is appropriate for reproducing the monomer peak height. Micelle Size Distributions. Micellar size distributions for TCDC and TUDC at several concentrations are shown in Figure 10. The micellar weight fraction of i-mer, excluding monomer, was calculated from ∞
Once k2, K3, ..., Ki-1, and k are given, one can calculate a monomer concentration for a total concentration from eq 10 and then a theoretical centroid volume from eq 3. These aggregation constants were determined by minimizing the sum of the squares of the differences in Vc between theory and experiment, SS. n
SS )
∑1 (Vc,calcd - Vc,obsd)2
(11)
Here, n stands for the number of data points. Table 3 and Figure 6 show these constants as a function of aggregation number. The solid lines in Figures 3 and 5 are calculated by using these aggregation constants. Derivative Chromatograms. Derivative chromatograms at the trailing boundary reflect the aggregation pattern. The derivative chromatogram of the dimerizing system uniquely has a single peak, whereas those of the other multimerizations exhibit bimodality.4,16,18,24 This characteristic feature of dimerization can be used for detecting dimers in the presence of other multimers.7,25 Figure 7 shows the derivative chromatograms of TCDC, TUDC, TDC, and TC at ∼C ) 2 mM. TUDC has a single peak near the monomer centroid volume (V1 in Table 1), because the cmc of TUDC is larger than 2 mM. This unimodality, however, does not exclude the formation of dimers. A similar behavior is observed for TC. The main difference between the frontal derivative chromatograms of TC and TUDC comes from the difference in their monomer centroid volumes (Table 1). TCDC has a small peak around 20 mL and a large peak around 53 mL. The former peak indicates the appearance of a small quantity of micelles at 2 mM, which is the cmc. The area ratio of the micellar peak to the “monomer” peak for TDC is larger than that for TCDC, as the cmc of TDC is smaller than that of TCDC. Here, it is particularly noted that the monomer peak is actually composed of monomer and dimer.4,16,18 These interpretations have been confirmed in Figure 8, which shows the derivative chromatograms simulated by appropriate aggregation constants (Table 3). The number of plates, N, (Table 1) was best fit to the observed chromatograms (Figure 7). The agreement between these derivative chromatograms is excellent. This indicates the validity of the present approach and analysis. Figure 9 shows the height of the monomer peak. This height should be proportional to the sum of the concentrations of
wi ) i[Ai]/
i[Ai] ) i[Ai]/(C - C1) ∑ i)2
(12)
At 2 mM, the micelles of TUDC consist of 92% dimer, 8% hexamer, and negligible amounts of larger aggregates in addition to monomer, and those of TCDC consist of 26% dimer and 74% larger aggregates centered at the tetradecamer. This difference is reflected in the derivative chromatograms shown in Figure 7. At higher concentrations, TUDC forms hexamers and larger aggregates. These size distributions of TUDC are similar to those of TC, whereas the size distributions of TCDC are close to those of TDC.6 Structure-Association Relationship. In GFC, solute molecules too large to penetrate the gel particle are confined to the external solvent space between the particles and thus are eluted rapidly, appearing in the earlier elution volume. Solute molecules small enough to penetrate freely into the interior of the particle are repeatedly delayed in their migration down the column and appear later in the elution volume. On the basis of this molecular sieving mechanism, one can expect that the elution volumes of all solutes are smaller than the total volume of the column. Nevertheless, as Table 1 shows, the monomer elution volumes of bile salts exceed the total column volumes. This anomaly is ascribed to the adsorption of solute on the gel particle. Selfassociable solute molecules tend to be adsorbed on the Sephadex G-10 gel by hydrophobic interactions.26 A partition coefficient of monomer between the gel phase and the aqueous phase is calculated from18,27
kav ) (V1 - Vm)/(Vt - Vm)
(13)
From the values of kav shown in Table 1, the hydrophobicity of monomers of bile salts is large and in the order TDC > TCDC > TUDC > TC. In general, the hydrophobicity of a molecule is linearly correlated to the hydrophobic (oleophilic) molecular surface area28-30
log(hydrophobic property) ) RSo - β
(14)
where R stands for the surface tension and β depends on the hydrophilic group. The reciprocal of the cmc is a hydrophobic property of surfactants. For cmc values of lecithins having different acyl chains, the coefficient R is estimated to be 1.7
Hydrophobic Self-Association of TCDC and TUDC
J. Phys. Chem. B, Vol. 104, No. 32, 2000 7749
TABLE 3: Best-Fit Stepwise Aggregation Constants for Taurine-Conjugated Bile Salts in a 154 mM Sodium Chloride Solution at 298.2 K bile TCDC TUDC TDCa TCa a
model II-7 II-7 II-10 IV-8
SS (mL2) 0.07456 0.1747 0.3484 0.00204
k2 (M-1) 9.77 15.4 16.1 6.11
k3 (M-1) 0.12 1.2 1.8 1.2
k4 (M-1) 1700 640 4700 420
k5 (M-1) 1260 270 600 200
k6 (M-1) 1700 10200 3200 3180
k7 (M-1) 1300 3.1 6
k8 (M-1)
k9 (M-1)
k10 (M-1)
k (M-1) 7690 2850
150
130
150
1100
a
b
c
5.47
9.26
1.05
All data are taken from ref 6.
Figure 6. Logarithms of stepwise aggregation constants as a function of aggregation number for TCDC (solid circles), TUDC (open circles), TDC (open triangles), and TC (open squares). Figure 8. Simulated derivative chromatograms of TCDC (solid circles), TUDC (open circles), TDC (open triangles), and TC (open squares) at C ) 2 mM. For the simulations, the elution volumes of the monomers and the micelle, the number of plates (Table 1), and the stepwise aggregation constants (Table 3) were used.
Figure 7. Observed derivative chromatograms of TCDC (solid circles), TUDC (open circles), TDC (open triangles),6 and TC (open squares)6 at C ) 2 mM.
molecule nm-2.29 A very close R value is estimated for octanol/ water partition coefficients.28 In Figure 11, the values of kav, k2, and 1/cmc are plotted against the hydrophobic surface areas of bile salts. These areas are shown in Table 2, together with the hydrophilic molecular surface areas, Sw.31 The cmc values obtained from the Vc vs 1/C plot are shown in Figure 11, because they are more accurate than those from the Vc vs C plot.6 Roughly speaking, the slopes of eq 14 shown in Table 4 are
Figure 9. Observed and calculated peak heights at the trailing boundary for TCDC (solid circles), TUDC (open circles), TDC (open triangles), and TC (open squares). The solid lines are calculated on the basis of models shown in Table 3.
close to 1.7 molecule nm-2.29 This agreement suggests that gel adsorption, dimerization, and micellization of bile salts all take place mainly by hydrophobic interactions.
7750 J. Phys. Chem. B, Vol. 104, No. 32, 2000
Funasaki et al. TABLE 4: Linear Correlation (eq 14) of Three Properties with Hydrophobic Molecular Surface Areas for Taurine-Conjugated Bile Salts
Figure 10. Weight micelle size distributions of (a) TCDC at 2.00 (open circles), 3.00 (open triangles), 4.50 (open squares), 20.00 (solid triangles) mM, and (b) TUDC at 1.98 (open circles), 4.03 (open triangles), 9.06 (open squares), 20.31 (solid circles) mM, calculated from eq 12 with stepwise aggregation constants shown in Table 3.
property
R (molecule nm-2)
β
correlation coefficient
kav 1/cmc k2
1.901 2.032 1.291
7.621 9.146 4.481
0.9979 0.9329 0.8512
This order is slightly different from ours. The discrepancy can be resolved, when the water contents in the eluent are increased. The hydrophobicities of the bile salts estimated by thin-layer chromatography are in the order TCDC ≈ TUDC > TDC > TC,3 which is in line with our result. With respect to sodium salts of unconjugated bile acids, the order of hydrophobicity depends on the properties. It is DC > CDC > C > UDC for reverse-phase HPLC,32 DC > CDC > UDC > C for cholesterol adsorption,33 and CDC > DC > UDC > C for graphite adsorption.34 The reciprocal of the cmc is a measure of hydrophobicity, but one must pay attention to the charge effect on the cmc values of ionic surfactants. The R value for sodium alkyl sulfates in the absence of salt is smaller than that for nonionic surfactants, but in the presence of a swamping electrolyte, these values are in excellent agreement with one another.35 Because our experiments were performed in a 0.154 M sodium chloride solution, we can determine the hydrophobic effect of the bile salts alone. When surfactants having flexible alkyl chains form micelles, with almost all of the chains located in the hydrophobic cores of the micelles. However, part of the hydrophobic surface of the bile salt must contact water and part of the hydrophilic surface of the hydroxyl groups must be incorporated within the micelle. Then, one should use the decrease in hydrophobic surface area with micellization, ∆Soo, instead of So, and both the mismatching contact with the hydrophobic surface of a molecule and the hydrophilic surface of another molecule in the micelle can be taken into account. The importance of these effects has been demonstrated recently for cyclodextrin inclusion of hydrophobic guests.30 This is the reason for a rather poor correlation between log(1/cmc) and So (Figure 11). A worse correlation is observed between log k2 and So; again, the reason is the same as in the case of the cmc. For instance, eq 15, which takes into consideration the contribution of the hydrophilic surface area, should exhibit a better correlation than eq 14.
log(1/cmc) ) RSo - βSw + γ
Figure 11. Correlation of kav (open squares), 1/cmc (open circles), and k2 (open triangles) with hydrophobic molecular surface area for four taurine-conjugated bile salts. The slopes and intercepts of the straight lines are shown in Table 4.
Discussion The correlation between log kav and So is very good, and the slope is close to that of the cmc values of lecithins (Figure 11 and Table 4). The reason for the good correlation is that these are the properties of monomers of bile salts. As estimated from the elution volume (or retention time) of reverse-phase HPLC on an ODS column using 75% methanol-25% water14 and 70% methanol-30% water32 as eluents, the ordering of the hydrophobicity of the bile salts is TDC > TCDC > TC > TUDC.
(15)
However, we did not actually use this equation, as Sw shown in Table 2 is the hydrophilic surface area for the unconjugated cholanate ion. To explain the quantitative correlations for the cmc and k2, one must calculate the change in surface area with dimerization and micellization. For this calculation, one must determine their structures at the atomic level. As Figure 1 shows, the steroid nucleus of bile salts consists of a rigid and convex hydrophobic side (back) with a few hydroxyl groups at the concave side (face). Small proposed that small micelles (i < 11) are formed by hydrophobic interactions among the convex backs of the nuclei and that large micelles are formed by intermolecular hydrogen bonds among the hydroxyl groups of these small micelles.1 This model is supported by H NMR data,36-38 molecular mechanics calculations,10 and crystallographic data.39 On the other hand, the opposite viewpoint is proposed, namely, that the micellization of bile salts is driven mainly by hydrogen bonds and polar interactions among headgroups and the hydrophobic groups form the outer surface to be exposed to water.40-42
Hydrophobic Self-Association of TCDC and TUDC The slopes for the plots of the logarithms of the hydrophobic properties against the hydrophobic surface area (Figure 11) are close to that for the logarithm of the reciprocal cmc of lecithin. This result shows that the hydrophobic interaction is the main driving force of the micellization of bile salts; thus, the Small model is better than the hydrogen-bonding and ionic interaction models. The odd-even alternation observed in the stepwise aggregation constant at small aggregation numbers (Figure 6 and Table 3) is consistent with the Small model.1 The micellization behavior of TUDC is remarkably different from that of TCDC, although their chemical structures are very similar. The magnitudes of their So values, however, are rather different from one another (Table 2), and this is the first reason for their different aggregation behaviors. The second reason is the orientation of the 7-hydroxyl group. The 7-hydroxyl group of TUDC is on the side of the β plane, whereas all hydroxyl groups of the four bile salts except for this 7-hydroxyl group of TUDC are on the side of the R plane (Figure 1). This 7βhydroxyl group of TUDC would inhibit micellar growth because of increased contact with hydrophobic surfaces and decreased hydrogen bonds in the micelles. This will account for less cooperative growth of the TUDC micellization (Figure 5). In general, the cmc value measured depends on the method, experimental conditions (temperature, kinds and concentrations of added salts), and data treatments, as well as the kind of compound.43 For instance, dye titration generally gives very small cmc values, and light scattering gives very large values (Table 1) because the former and latter methods are sensitive to small and large micelles, respectively. The Vc vs C plot of the GFC data gives a small cmc value, and the Vc vs 1/C plot gives a large value. The gap between these cmc values is a measure of the cooperativity of micellization. Cooperative selfassociation is strong in the order TDC > TCDC > TUDC > TC (Table 2). This behavior is consistent with the results of aggregation numbers (Figure 5) and stepwise aggregation numbers (Figure 6 and Table 3). Acknowledgment. Thanks are due to the late Dr. Sakae Hada, Ms. Miho Ikawa, Ms. Kazumi Kawamoto, Mr. Teruyoshi Matsushima, and Mr. Ryo Imaizumi for preliminary experiments and calculations. This work was supported by grants-in-aid for the Scientific Research Program (No. 11672153) and the Frontier Research Program from the Ministry of Education, Science, Culture, and Sports of Japan. References and Notes (1) Small, D. M. The Physical Chemistry of Cholanic Acids. In Chemistry; The Bile Acids; Nair, P. P., Kritchevsky, D., Eds.; Plenum Press: New York, 1971; Vol. 1, Chapter 8. (2) Carey, M. C. Measurement of the Physical-Chemical Properties of Bile Salt Solutions. In Sterols and Bile Acids in Gastroenterology; Barbara, L., Dowling, R. H., Hofmann, A. F., Roda, E., Eds.; MTP Press: Boston, MA, 1983; Chapter 2.
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