J. Phys. Chem. 1994, 98, 11541- 11548
11541
Stepwise Self-Association of Sodium Taurocholate and Taurodeoxycholate As Revealed by Chromatography Noriaki Funasaki,* Ryota Ueshiba, Sakae Hada, and Saburo Neya Kyoto Pharmaceutical University, Misasagi, Yamashina-ku, Kyoto 607, Japan
Received: April 21, 1994; In Final Form: August 19, 1994@
From frontal chromatograms and derivatives of sodium taurocholate (TC) and taurodeoxycholate (TDC) on Sephadex G-10 columns in 0.154 M sodium chloride, monomer concentrations (Cl), weight and number average aggregation numbers excluding and including the monomer contribution, critical micelle concentrations (cmc's), and minimum multimerization concentrations have been determined as a function of the total concentration (C). Since the micellization of TC occurs rather noncritically, the cmc values obtained from the same centroid volume data depend on the data treatment. The definition of cmc, that cmc is the total concentration at the inflection on the C1 vs C curve, is applicable to TC and TDC as well as surfactants. The dimerization of TC and TDC has been proven by several pieces of chromatographic evidence, and their dimerization constants are determined independently from centroid volume and peak volume data. The stepwise aggregation constants are determined and are used to calculate micelle size distributions. Micelles of TC and TDC grow above the cmc more gradually than those of surfactants. This gradual growth is the main reason for inconsistencies in the literature of bile salt micellization. Since TDC is more hydrophobic than TC, the dimerization constant and aggregation numbers of TDC are larger than those of TC. This result supports the Small model for small micelles of bile salt.
Introduction Bile salts act as a powerful detergent. This helps the mixing movements of the intestine break the large fat globules of the food into small globules, thus allowing the lipases of the intestinal tract to attack larger surface areas of the fat and to digest it. Without this action of bile almost none of the fats in the food would be digested. At high concentrations, the bile salts form micelles (aggregates), which can solubilize or emulsify the water-insoluble fats. The concentration of bile salts in human hepatic bile is probably 20-50 mM. In many vertebrates, the concentration of bile salts in gallbladder bile is remarkably high, viz., 200-300 mM. Micelle formation permits the concentration of bile salts to increase to such high concentrations with retention of isotonicity.' As the concentration of a detergent (surfactant) is increased, it forms micelles at a small range of concentration, called a critical micelle concentration (cmc). The concept of the cmc is, however, fraught with definitional and interpretational problems for bile As a result, many values, depending upon the experimental techniques and, in many cases, arbitrary choices of values are quoted in the l i t e r a t ~ r e . ~Different .~ techniques are differently sensitive to different things. Since the bile salts self-associate less cooperatively than detergents, micellization occurs in a broad range of concentration. The average size of bile salt micelles and the distribution of micellar sizes around this mean value are important physical-chemical characteristics of a bile salt solution. Traditional methods for characterizing micellar size all suffer from some limitations. The most restrictive disadvantage is that most methods require measurements at several finite concentrations, followed by linear extrapolation of these values to the c ~ c Micelle . ~ sizes so derived are therefore only applicable to just above the cmc and depend, inter alia, on an accurate determination of the cmc. Thus, the more investigations that have been made, the more confusing the self-association picture has become. @Abstractpublished in Advance ACS Abstracts, October 1, 1994.
0022-365419412098-11541$04.50/0
Carey pointed out the disadvantages of ultracentrifugation, static light scattering, tracer diffusion, osmometry, gel filtration chromatography (GFC), small-angle X-ray scattering, and electron microscopy. For instance, GFC has the following disadvantages: large dilution effects on the micellar concentrations, adhesion of bile salt monomers to the gel bed, equilibration of a column with bile salt concentrations higher than the cmc or intermicellar concentration, and charge effects between micelles and counter ion^.^ The hydrodynamic radii of the micelles of sodium taurocholate (TC) and sodium dodecyl sulfate were estimated by zonal analysis of GFC6 This is the small sample size method conventionally used, which has most of the disadvantages pointed out by Carey. Carey and his co-workers considered that dynamic light scattering is the best method for determining micelle size above the cmc4s7 One of the causes for confusion in aggregation numbers of bile salts is that different averages are reported in the literature. The number average aggregation number is determined by osmometry,8 and the weight average value is done so by static light scatteringg-'* and ultracentrifugation.* We can generally define four average aggregation numbers depending on the inclusion or exclusion of the monomer and on the weight average or number average. Different averages, at the cmc in most cases, are reported in the literature, and therefore any quantitative comparison among these averages is difficult. Furthermore, two weight fractions, w[ and wi,of i-mer depending on the inclusion or exclusion of the monomer are used in the l i t e r a t ~ r e .The ~ ~ ~corresponding number (or mole) fractions, x; and xI,seem not to have been reported in bile salt studies. The micelle size distribution or the relationship between wi and i has not yet been reported for any bile salt, since quantitative knowledge on the aggregation pattern is required. Recently we have developed a GFC method for determination of the monomer concentration, C1, as a function of total c~ncentration.'~-'~ The Sephadex G-10 gel has small pores, so that all aggregates including the dimer are excluded from there. The boundary of the chromatogram (frontal chromato0 1994 American Chemical Society
11542 J. Phys. Chem., Vol. 98, No. 44, 1994 HO
Funasaki et al.
Ay
Figure 1. Chemical structure of TC, TDC, CHAPSO, and CHAPS: TC, X = OH and Y = NHCHzCHzS03-; TDC, X = H and Y = NHCHZCHZSO~-; CHAPS, X = OH and Y = NHCH2CH2CH2NfX = OH and Y = NHCH2( C H ~ ) Z C H ~ C H ~ C H ~ SCHAPSO, O~-;
CHZCHZN+(CH~)~CH~CH(OH)CH~SO~-. TABLE 1: Chromatographic Data for TC and TDC on the Sephadex Columns compd Vt(mL) Vl(mL) Vm(mL) V1,"(mL) Vzpw(mL) N TC TDC
23.63 22.78
29.30 69.45
9.89 9.21
29.26 10.23
8.96 8.81
35 25
gram), obtained when a large volume of dilute sample is applied onto the Sephadex G-10 gel, is determined by the weight average of the monomer and all aggregates. Analysis of this boundary yields the monomer concentration. From further analysis of the concentration dependence of the monomer concentration, we can determine all aggregation numbers defined above as a function of total concentration. By using an appropriate aggregation model, we can calculate equilibrium aggregation constants and the weight fractions mentioned above. We have applied this approach to surfactant^,'^,'^.'^,^^ chlorpromazine hydrochloride (CPZ),18 and zwitterionic derivatives of cholic acid19s20and have shown that there is a close correlation between the chemical structure and the aggregation pattem of a chemical compound.15 In this work we investigate the aggregation pattems of sodium taurocholate (TC) and taurodeoxycholate (TDC), which have the chemical structures shown in Figure 1, and determine their cmc values, monomer concentrations, aggregation numbers, and equilibrium aggregation constants in 0.154 M sodium chloride. Some of the confusion in the literature, mentioned above, will be resolved, and the micelle size distribution will be reported for TC and TDC.
Experimental Section Materials. A specimen of TC (Calbio) was treated with charcoal in methanol three times and recrystallized from methanol. The crystals were freeze-dried several times and dried at 110 "C under reduced pressure. The purified sample of TC was 99.0% pure, as estimated by high-performance liquid chromatography (HPLC). Similarly to TC, TDC (Sigma) was purified, and the purity of the final product was 99.1%, as estimated by HPLC. Blue dextran and Sephadex G-10 were purchased from Pharmacia. Sephadex G-10 columns were prepared as suggested by the manufacturer. Solute molecules possessing molecular weights larger than 700 were excluded from the Sephadex G-10 gel pores. The double-distilled water was degassed just before the GFC experiments. Methods. All GFC experiments were carried out on two columns in 0.154 M sodium chloride solution under a flow rate of ca. 0.4 mL min-'. The columns were jacketed to maintain a constant temperature of 25.0 f 0.2 "C. The total volume of the columns are shown in Table 1. A large volume of dilute sample was applied so that the plateau region would appear on the chromatogram (frontal method). The elution process was monitored with both a Waters 4 10 differential refractometer and a Water 484 tunable absorbance detector (at a wavelength of 220 nm) and recorded with a data processor. The refractive index data were used for further analysis with a personal
V (mL)
Figure 2. Frontal chromatogram of its derivative of TC at CO= 4.003 mM and S = 61.38 mL in 0.154 M sodium chloride solution and definition of some characteristic parameters.
computer and were supported by the UV data. The chromatographic data at low concentrations were subjected to the smoothing treatment.21 The derivative chromatogram was approximated by the difference chromatogram. The height and position of the peak in the derivative chromatogram were evaluated by a polynomial approximation.22 Simulations of chromatograms were carried out by a plate theory (the continuous flow model) with an adequate aggregation model, and the number of the plate was regarded as an adjustable parameter. Further details on the simulation procedure have already been reported elsewhere.22
Results Evaluation of Aggregation Numbers and Cmc Values. Figure 2a shows the frontal chromatogram of TC at an applied concentration of CO= 4.003 mM in 0.154 M NaCl. Since an applied volume of S = 61.38 mL is larger than the total volume, V,, of the column bed, the plateau region with COappears on the chromatogram. The centroid volumes, V,' and V,, of this chromatogram at the leading and trailing boundaries can be calculated from23
hcoVd C (leading boundary) V, = hcoV dC + S (trailing boundary) V,' =
For these determinations the volume coordinate, V, is assigned a zero value when the leading boundary of the applied sample enters the column bed. Since the centroid volumes at the leading and trailing boundaries were equal to each other within experimental error, we took V, as the average of them. The centroid volume was determined at different TC concentrations, as shown in Figure 3a. Centroid volumes were also determined for TDC. As Figure 3a shows, V, decreases rather abruptly around a concentration. Therefore we can regard this concentration as a critical micelle concentration (cmc). This cmc value is shown in Table 2. When the same V , data as shown in Figure 3a are plotted against the reciprocal concentrations, we can find another rather critical concentration. This concentration is also included as a cmc in Table 2 . The difference between these cmc values for TDC is smaller than that for TC. This fact reflects that TDC is micellized more abruptly than TC. A typical surfactant, octaethylene glycol decyl ether (CloEg), is micellized more abruptly than TDC, as shown in Table 2.
Sodium Taurocholate and Taurodeoxycholate
J. Phys. Chem., Vol. 98, No. 44, 1994 11543 numbers mentioned above:24 m
m
n, = c i 2 [ A i ] / ~ i [ A i= ] d log(C - CJd log C,
(4)
i=2
i=2
n,' = xi2[Ai]/Zi[Ai] = d log C/d log C, i= 1 m
m
n, = x i [ A , ] / x [ A i ] = (C - C , ) / ( A- C,) j=2
(5)
i= 1
(6)
i=2
C (mM) Figure 3. (a) Centroid volumes and (b) monomer concentrations plotted against total concentrations for TC (closed circles) and TDC (open circles). The solid lines are calculated on the basis of model 11-10 for TC, and the dashed lines are based on model N-8 for TDC.
TABLE 2: Critical Micelle Concentrations, Minimum Multimerization Concentrations, and Dimerization Constants of TC and TDC compd
TC TDC CHAPS" CHAPSOb CPZ' Cl&Sd
cmc (mM) mmc (mM) V,vs C V,vs 1/C theory n, V, (dC/dV),
4.5 1.4 5.4 5.2 5.3 1.0
6.3 1.6 7.4 6.7 5.8 1.1
6.15 1.51 6.45 6.19 5.45 1.09
2.8 2.2 1.0 0.8 3.2 3.7 2.43.1 4.0 4.0 1.0 1 . 1
2.3 1.0 4.1 3.5 4.0 1.0
kz (M-') V, V, 6.11
7.0 17.3 4.63 4.7 4.93 5.1 124 118 7.7 7.3 16.09
Original data taken from ref 19. Original data taken from ref 20. Original data taken from refs 18 and 29. Original data taken from refs 16 and 29.
On the Sephadex column, monomers retain longer than aggregates. As a result of rapid exchange between the monomers and the aggregates, the derivative chromatogram at the leading boundary becomes unimodal and that at the trailing boundary becomes bimodal. These results will be shown in Figures 8 and 9. Hereafter, we assume that the equilibria for solute partition between the stationary and mobile phases and for solute self-association are instantaneously established. The gel pores of Sephadex G-10 are small enough that compounds with molecular weights greater than 700 are excluded therefrom. For a self-associable compound whose monomeric molecular weight is between 350 and 700, the observed centroid volume can be written as the weight average of the centroid volumes of monomer ( V I )and all aggregates (Vm):14J9
v, = [ClV, + (C - C,)V,]/C
(3)
Here C1 denotes the monomer concentration. The centroid volumes, VI and V, of the monomer and the aggregate were estimated by extrapolation of the observed V, values (Figure 3a) to infinite dilution and concentration, respectively. These estimated centroid volumes are shown in Table 1. For the column used for TDC, the centroid volume of blue dextran was determined to be 9.15 mL by frontal analysis with 0.03% blue dextran. This value is close to the V, value for TDC, as expected. The estimation procedure of V, for micellar systems has been reported in detai1.13J4117J9 From eq 3 we can calculate the monomer concentration using the observed V, value, together with the estimated values of VI and V,. The monomer concentration thus calculated is shown as a function of the total concentration in Figure 3b. The concentration dependence of the monomer concentration reflects the aggregation pattem. From the concentration dependence of the monomer concentration we can estimate the aggregation
i= 1
i= 1
Here [Ai] stands for the molarity of the i-mer. The total molarity, A , can be calculated from
These equations hold true for self-associating systems, irrespective of the kind and concentration of aggregate. From the slopes of the curves of Figure 4a and b, we can evaluate the weight average aggregation numbers, nw and n,', excluding and including the monomer, respectively. Furthermore, using the total molarity calculated from the graphical integration of eq 8, we can evaluate the number average aggregation numbers, n, and n,,', from eqs 6 and 7 . Figure 5 shows the micellar weight and number average aggregation numbers, excluding the monomer, for TC and TDC. For both TC and TDC dimerization takes place at the lowest concentrations conducted experimentally, followed gradually by higher multimerizations. At the cmc, TDC is micellized more abruptly than TC. The solute weight and number average aggregation numbers including the monomer are depicted in Figure 6 for TC and TDC. Aggregation Patterns and Equilibrium Constants. When the i-mer is in equilibrium with the ( i - 1)-mer and monomer, we can define the stepwise aggregation constant, k,:
Al-l
k, + A, *A,
k, = [A,I/([A,-,lC,)
(9) (10)
When the i-mer is formed from i monomers, we can define the one-step (overall) aggregation constant, Ki: Ki
iA, == Ai
(11)
These equilibrium constants can be connected by
Ki = nki 2
Hereafter we will apply four aggregation models which take into consideration all aggregate species and give analytical expressions for the total concentration as a function of the monomer concentration. In model I we assume a series of equations, ki = ki+l = = k; that is, aggregation occurs isodesmically at large aggregation numbers. Then we can write the total concentration as
-
11544 J. Phys. Chem., Vol. 98, No. 44, 1994 ca
C = z i [ A i ] = C, i= 1
Funasaki et al.
+ 2k2CI2+ - + (i - 1)Ki-,Cli-' + Ki-,kCl'[i - (i - l)kC,]/(I - kCJ2 (14)
In model 11, we assume a marked attenuation (anticooperativity) of k; at large aggregation numbers; that is, iki = (i l)ki+l = = k. Then we can write C as
+
-
In model 111, we assume a mild attenuation of ki at large aggregation numbers; that is, when (i - I)k;/i = iki+l/(i 1) k, we can write C as
+
-...=
+ - + (i - 1)Ki-,Cli-' + Kj-,kC,'[i2 - (2i2 - 2i - I ) ~ c +,(i - I ) ~ ( ~ c , ) ~ I / +
C = C, 2k2C12
0
-0.5
0.5
1.0
log CI
Figure 4. Plots of monomer concentration data according to (a) eq 4 and (b) eq 5 for TC (closed circles) and TDC (open circles). The solid lines are drawn through observed data.
[(i - 1)(1 - kC,)3] (16) In model IV, we assume a modification of the Tanford theory of micellization of surfactant^.'^^^^ The standard Gibbs free energy, A@, of i-mer formation from i monomers can be written as
= -ai
iAG:/RT
+ bi2I3+ ct'I3
(17)
The term a corresponds to the driving force of micellization due to the transfer of the hydrophobic group from water to the micelle. The term b expresses the reduction of hydrophobic surface area due to spherical micelle formation. The term c denotes the repulsion between the hydrophilic groups at the micellar surface. The molarity of the i-mer may be calculated from
"0
20
10 C(mM)
Figure 5. Micellar weight (circles) and number (triangles) average aggregation numbers excluding monomers for TC (closed symbols) and TDC (open symbols). The solid lines are calculated on the basis of model 11-10 for TC, and the dashed lines are based on model IV-8 for TDC. 20 -
If eq 18 holds for the formation of large micelles, then the total concentration can be written as
c = C,+ 2k,c12 +
-+
15C
+
(i - I ) K ~ - , C ~ ~ - '
10-
m
x i C l i exp(-iAG:/RT)
(19)
~, -A*
5
1
The observed V, data were fitted by using one of the above aggregation models and eq 3. That is, the SS value for V, is minimized:
c(vc,calc n
ss =
- Vc,obsd)
2
(20)
1
Here n denotes the number of V, data (n = 13 for TC and n = 19 for TDC). The fitting procedure has already been reported e l ~ e w h e r e . ~ ~Table J ~ . ~3~ summarizes the best fit stepwise aggregation constants based on models 1-111, and Table 4 is based on model IV. The Arabic numeral for each model indicates the number of adjustable parameters. Further increases in this number did not improve fitting. The standard deviation for each parameter is also shown in these tables. Judging from the SS value, model 11-10 is best for TC and model IV-8 is best for TDC. The stepwise aggregation constants, calculated from model 11-10 for TC and model IV-8 for TDC, are shown
15 20 C (mM) Figure 6. Solute weight (circles) and number (triangles) average aggregation numbers including monomers for TC (closed symbols) and TDC (open symbols). The solid lines are calculated on the basis of model 11-10 for TC, and the dashed lines are based on model IV-8 for TDC.
0'
5
10
as a function of the aggregation number in Figure 7. At small aggregation numbers, stepwise aggregation constants with even numbers are larger than those with the nearest odd numbers. This odd-even alternation in ki is also observed for 3-[(3cholamidopropyl)dimethyla"onio]- 1-propanesulfonate (CHAPS) and 3-[(3-cholamidopropyl)dimethylammonio]-2-hydroxy-1propanesulfonate (CHAPSO) and indicates that micelles with even aggregation numbers are more stable than those with odd aggregation numbers.19,20 Derivative Chromatograms. Figures 8 and 9 depict some derivative chromatograms at the leading and trailing boundaries
J. Phys. Chem., Vol. 98, No. 44, 1994 11545
Sodium Taurocholate and Taurodeoxycholate
TABLE 3: Best Fit Stepwise Aggregation Constants Based on Models 1-111 model SS (mL2) kz (M-I) k3 (M-I) k4 (M-l) ks (M-I) k (M-I) k7 (M-I) TC 1-9 0.020 94 6.17 1.08 423 191 3100 19 f0.72" f0.90 f79 f90 f180 f85 11-9 0.02045 6.13 1.13 430 198 3180 8 f0.66 f0.96 f140 f 71 f8lO f13 11-10 0.02040 6.11 1.2 420 200 3180 6 f0.69 f3.9 f600 f900 f910 f68 111-9 0.020 87 6.17 1.01 460 192 3060 18 f0.48 f0.69 1120 f77 f120 f26 TDC 1-9 0.636 6 16.1 2.6 1420 700 1200 1200 f1.2 12.2 f660 f760 f4200 f3400 11-8 0.463 9 17.3 0.30 1400 700 1200 1200 f1.2 f0.24 f1400 f800 f1900 f1200 16.3 0.35 1400 1450 2000 1800 111-9 0.485 0 fl.1 f0.53 13800 f840 11900 f3300
ks (M-I)
kg (M-I)
100 1150 130 1140 150 f950 110 f120
100 f210 150 f130 130 f780 90 f150
1790 f750 1790 f940 1500 f3200
600 fllOO
kio (M-l)
150 f2100
k (M-')
85 f39 1100 f300 1100 f490 79 f23 531.7 18.4 9670 f390 495 f14
1100 f3400
Standard deviation.
TABLE 4: Best Fit Stepwise Aggregation Constants for Model IV model SS (mL2) k2 (M-I) k3 (M-I) k4 (M-') k5 (M-') TC N-6 0.020 49 6.01 2 220 f0.59" f12 f310 TDC 600 IV-8 0.348 4 16.1 1.8 4700 f1500 f1.4 f4.6 f2000 a Standard deviation.
k6
(M-')
3200 f2900
a
b
C
-0.12 f0.13
2.15 f0.25
0.598 f0.075
5.47 f0.76
9.26 f0.99
1.05 f0.15
30.2 E
fE w
Y
90.1
V
0
i
Figure 7. Logarithms of stepwise aggregation constants, calculated on the basis of model 11-10 for TC (closed circles) and model IV-8 for TDC (open circles), as a function of the aggregation number.
V (mL)
Figure 8. (a) Observed and (b) simulated derivative chromatograms of TC (mode1 11-10) at the leading (open symbols) and trailing (closed symbols) boundaries. Concentrations (mM) of TC: 0 and 0, 3.983; A and A, 6.006; 0 and B, 10.027; V and v, 15.025. for TC and TDC. For the sake of direct comparison, the chromatograms for the trailing boundary are shown against the volume coordinate of elution volume V minus applied volume S (compare Figures 2b and 8a). For the self-associating
0'
20
LO
60
80
.,
0 20 V (mL)
40
60
80 100
Figure 9. (a) Observed and (b) simulated derivative chromatograms of TDC (model N-8) at the leading (open symbols) and trailing (closed symbols) boundaries. Concentrations (mM) of TDC: 0 and 0,0.498; A and A, 1.004; 0 and 2.008; V and V, 4.003. systems,15 generally, the trailing boundary spreads more than its leading counterpart. As these figures show, the selfassociation of TC and TDC occurs at much lower concentrations than the cmc. A plate theory, based on the continuous flow model,** was used for simulations of derivative chromatograms. This theory requires some chromatographic and aggregation parameters. The number, N , of the plate was regarded as an adjustable parameter (Table 1). The observed values of VI and V, were used to calculate the partition coefficients of the monomer and the micelles between the mobile and stationary phases: (VI - VO)/ VOand 0. Here VOdenotes the void volume of the column. The relationship between the monomer concentration and the total concentration in the mobile phase can be calculated from any of eqs 14-16 and 19, to obtain the concentrations of the monomer and the micelle in the gel phase. According to the asymptotic theory for chromatography, generally, the trailing peak splits into two peaks for selfassociating systems.27 In fact, the trailing peaks for TC and
11546 J. Phys. Chem., Vol. 98, No. 44, 1994
Funasaki et al.
c
,,C
(mM)
Figure 10. Plots of trailing peak volume data for TC (closed circles) and TDC (open circles) according to eq 21. i
Figure 12. Micelle size distributions calculated on the basis of (a) model 11-10 of TC and (b) model IV-8 of TDC at the following concentrations (m).TC: 0,4.998; A, 8.021; 0, 20.004. TDC: 0, 2.008; A, 3.019; 0, 20.010.
C (mM)
Figure 11. Peak height data at the leading (open circles) and trailing (closed circles) boundaries for (a) TC and (b) TDC. The solid lines are calculated on the basis of model 11-10 of TC, and the dashed lines are based on model IV-8 of TDC. TDC at high concentrations exhibit bimodality (Figures 8 and 9). However, the trailing peak is expected to be unimodal only for the dimerizing system,27and the volume, V,, of the peak obeys the following equation:22 [(VI," - V2,")/(V, - V2pca)]2 =1
+ 9.6k2C,,
(21)
where C, denotes the concentration at V,, as shown in Figure 2. This is a modification of the equation developed by Ackers and Thompson2' and may also hold true for systems including the dimer and higher multimers at so low concentrations that the multimers are negligible. The monomer peak volume, VI,", can be estimated by extrapolation of the observed V, values to infinite dilution. For the Sephadex G-10 gel whose pores are smaller than dimers, the dimer peak volume, V2,", may be obtained by extrapolation of the observed micellar peak volume, V,,, to infinite concentration or it may be set as the peak volume of a large molecule, such as blue dextran. The extrapolated values of VlPo and V2,- are shown in Table 1. Figure 10 shows the plots for TC and TDC according to eq 21. From the slope of the straight line, we can evaluate the dimerization constant, which is shown in the column labeled V, in Table 2. The concentration above which the linearity of eq 21 does not hold may be regarded as a minimum multimerization concentration (mmc) (Table 2). In Figure 11 the trailing and leading peak heights at rather low concentrations are plotted against the total concentration for TC and TDC. The gap between the leading and trailing heights reflects the extent of self-association. The trailing height is proportional to the total concentration at very low concentrations. This linearity seems to hold for the dimerizing system only. Therefore the concentration above which this linearity does not hold may be regarded as a mmc. This mmc value is shown in the column labeled (dC/dV), in Table 2. hedictions of Some Aggregation Properties. The observed data of monomer concentration and centroid volume shown in
Figure 3 are in excellent agreement with those based on model 11-10 of TC and model IV-8 of TDC, as expected. The observed aggregation numbers shown in Figures 5 and 6 are well predicted by these models. The solid and dashed lines in Figure 11, obtained from simulations based on model 11-10 of TC and model IV-8 of TDC, reproduce well the tendencies of the experimental results. Thus, these are very good aggregation models for TC and TDC. There is a controversy whether or not cmc values are present for bile salts,*s5 and uncritical or noncritical micellization concentration has been proposed, instead of cmc3 Furthermore, a few theoretical definitions of cmc are used for surfactants. For surfactants we have shown that the cmc is the total concentration at which the third derivative of the monomer concentration with respect to the total concentration is null: l6 d3C,ldC3= 0
(22)
The utility of this definition of cmc for TC and TDC is shown in Table 2, where model 11-10 of TC and model IV-8 of TDC are used for the relationship between the monomer concentration and the total concentration. For a surfactant its monomer concentration is often assumed to be equal to the cmc. This, however, is a rough approximation for TC (though better for TDC), as is evident from a comparison between the cmc (Table 2) and the monomer concentration (Figure 3b). Micellar size distributions at several concentrations are predicted by model 11-10 of TC and model IV-8 of TDC, as shown in Figure 12. Here the weight fraction of the i-mer, wi, is defined as ca
wi = i [ A i ] / ~ i [ A i= ] i[A,]/(C - C,)
(23)
i=2
The weight fraction of the i-mer including the monomer species and the number fractions of the i-mer including and excluding the monomer species are also calculabie (data not shown).
Discussion Retention Mechanism of TC and TDC on the Sephadex Gels. In general, the molecular size plays a major role in the retention of most substances on Sephadex gels. According to this mechanism, the elution volume should be smaller than the total volume, V,, of the column. Since some self-associable compounds have hydrophobic groups, their monomers can be
Sodium Taurocholate and Taurodeoxycholate adsorbed on Sephadex gels by hydrophobic interactions. The micelles have hydrophilic surfaces, albeit hydrophobic interiors, so that they are not adsorbed and are eluted according to their sizes.28 As Table 1 shows, the monomer elution volumes, V1, of TC and TDC are larger than the total volumes of the columns. This is ascribed to adsorption of the monomers of TC and TDC on the gels. The difference between VI and V, is larger for TDC than for TC. Since TDC has less hydroxy groups than TC, the monomer of the former is adsorbed more strongly than that of the latter. For both TDC and TC, the micellar elution volume, V,, is essentially equal to the elution volume of blue dextran, suggesting that all micelles of TDC and TC are excluded from the Sephadex gels. Dimerization and Its Equilibrium Constants. The micellar aggregation numbers of n, and n, of TC and TDC are 2 at low concentrations (Figure 5 ) . The peak height at the trailing boundary is directly proportional to the total concentration at concentrations lower than the mmc (Figure 11). This proportionality seems to be characteristic of dimerization. The trailing derivative chromatogram for the dimerizing system exhibits unimodality, in contrast with the bimodality of those of the other multimerizing systems.27 Therefore it is likely that the peak height of the dimerizing system at the trailing boundary is proportional to the total concentration. As Table 2 shows, the derivation from this proportionality occurs at the mmc. The dimerization constants of TC and TDC were determined by two methods, and they are close to each other. The centroid volume data generally provide more accurate k2 values than the peak volume data.29 Structure-AssociationRelationship. For C&g the stepwise aggregation constant exhibits a maximum at ca. 30, which is half of the aggregation number of C ~ O E S .For ’ ~ TC and TDC, however, the aggregation number at the maximum stepwise aggregation constant is smaller (Figure 7). This is the main reason for less critical micellization of TC and TDC than that of CloE8 and for inconsistencies in the bile salt literature of cmc and aggregation number^.^^^ As Table 2 shows, TDC selfassociates more critically than TC. The reason for this is that the aggregation number of TDC around the cmc is larger and increases more abruptly than that of TC (Figure 5 ) . The oddeven alternation in stepwise aggregation constant at small aggregation numbers (Figure 7) has also been observed for CHAPS19 and CHAPS0.20 The steroid nucleus of bile salts constitutes the rigid and convex hydrophobic side (back) and has a few hydroxy groups at the concave side (face). Small proposed that small micelles (i < 11) of bile salts are formed by hydrophobic interactions between the convex backs and that large micelles are formed by intermolecular hydrogen bonds between the hydroxy groups of these small micelles.30 Oakenfull and Fisher postulated that dimerization was due to hydrogen bonds of two bile molecules and that larger micelles could then be formed by ‘back to back’ hydrophobic interaction^.^^ As Table 2 shows, however, the dimerization constant of TC is smaller than that of TDC. This result supports the Small model for the dimer. Giglio et al. suggested that helical micelles, as observed in the crystalline state, of sodium deoxycholate3*and TDC33are formed in water and 0.2 M Tris buffer and NaCl by intermolecular hydrogen bonds. TDC in the crystalline state forms helices of trimers and hexamers, which both have a lateral surface covered by polar and nonpolar groups, at variance with the deoxycholate micelle.34 This structure of the TDC micelles seems to be unstable in aqueous media, and the trimer of TDC is unstable in 0.154 M NaCl solution (Figures 7 and 12b). The increase in concentration of bile salt or electrolyte generally results in
J. Phys. Chem., Vol. 98, No. 44, 1994 11547 an increase in micelle size of the bile ~ a l t . ~ It .was ~ suggested that helical micelles are present at high bile salt concentrations, such as 0.132and 0.3 The self-association of alcohols in water is not driven by the hydrogen bond formation between the alcoholic hydroxy groups.3s However, this does not exclude intermolecular hydrogen bonds in large micelles of bile salts. Since large micelles are chiral o b j e ~ t s , Small’s ~ ~ , ~ ~random model for such large micelles must be modified. Since we are mainly concerned with small micelles, we will consider the present results on the basis of Small’s model. The selfassociation of most amphiphilic compounds is governed by two opposing forces. The driving force is caused mainly by hydrophobic interactions, and the opposing force is electrostatic repulsion or steric hindrance between the head groups at the micellar surface.25 Mazer et al. suggested that this viewpoint is also applicable to the micellization of bile salts.7 As Table 2 shows, the dimerization constant of CPZ is large. This is due to stacking interactions between the rather planar rings. TC, TDC, and CHAPS, as well as CloEg, dimerize by hydrophobic interactions between aliphatic groups. CloE8 micellizes in a highly cooperative manner, owing to abrupt decreases of hydrophobic area.17,25 Since TC, TDC, and CHAPS have the rigid steroid nucleus, they can oligomerize rather cooperatively. According to Small’s model for small bile micelles, even multimers are more stable than odd ones. This is consistent with the odd-even altemation of stepwise aggregation constants shown in Figure 7. Since TDC is more hydrophobic than TC, TDC exhibits a larger dimerization constant than TC. Biological Implications of the Present Results. In addition to digestion of our results are useful for understanding the phase diagram of the bile salt-phospholipid-water system.37 Depending on the composition, bile salt and phospholipid form mixed micelles and liposomes. These aggregates, formed in bile, are in equilibrium with the monomer of bile salt.38,39 Roughly, the cmc of a surfactant is similar to its monomer concentration, but this approximation is very rough, particularly for TC (Figure 3b and Table 2 ) . Bile salts and CHAPS are excellent solubilizers of proteins in biological m e m b r a n e ~ . ~ O - ~ ~ Removal of bile salt from such solubilized solutions is carried out by dialysis and GFC. Then, the monomer concentration and micelle size of bile salt are important data for choosing experimental conditions.
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