- Email: [email protected]
Ultrasonic absorption and density studies of the aggregation in aqueous solutions of bile acid salts
Ultrasonic Absorption and Density Studies of the Aggregation in Aqueous Solutions of Bile Acid Salts A. D J A V A N B A K H T , K. M. K A L E , AND R. Z A N A 1 Centre National de la Recherche Sdentifique, Centre de Recherches sur les Macromolecules, Strasbourg Cedex, France
Received February 12, 1976; accepted May 17, 1976 The ultrasonic absorption of sodium cholate, deoxycholate and dehydrocholate has been measured as a function of concentration in water, H~O, 0.2 M NaC1, and methanol. The effect of pH has also been investigated. The results indicate that the observed excess absorption is due to the aggregation of the bile acid ions, the association being much stronger for deoxycholate than for cholate and negligible for dehydrocholate. The measurements of density confirm the ultrasonic absorption results. However, the excess ultrasonic absorption of bile salt solutions has features differing considerably from those found for solutions of classical detergents where a true micellization takes place. In particular the ultrasonic absorption relaxation spectra of bile salt solutions show evidence of a distribution of relaxation frequencies rather than a single relaxation frequency as found for ionic detergents. These results lead to the conclusion that the association takes place in the whole range of concentration and not at some critical micelle concentration, and that the distribution curve of aggregate sizes must be wide and shifting upward as the concentration is increased. INTRODUCTION AND THEORY Bile acids have been the subject of numerous investigations recently reviewed b y Small and Carey (1). From the recent studies of Fontell (2) and other workers (3), and from earlier work (4), it appears that the self-association of these compounds is very complex. The "micelles" formed in aqueous solutions of bile acids contain only a small number of bile acid ions [-two in some instances (1) 1 . Also, as the concentration is increased, peculiar concentrations are observed where the investigated physicochemical property shows a rapid change. This has been interpreted as indicating that association occurs in several steps, at least three in the case of sodium cholate (2, 4). However, a close look at the curve representing the variation of the measured physicochemical property as a function of aCorrespondence should be sent to: R. Zana, C.R.M., CNRS, 6, rue Boussingault, 67083, Strasbourg Cedex, France.
concentration shows that in m a n y instances a continuous line m a y be drawn through the experimental pointS. Of course, very different models would have to be used to describe the state of aggregation in bile salt solutions, depending on the type of variation which is found. I n the case of steep changes (micellization), the bile salt solutions would contain bile ions and aggregates with a fairly welldefined shape a n d / o r aggregation number, in a given concentration range. The aggregate shape a n d / o r size would change by step in going from one concentration range to another. I n case of a continuous change of the measured property, this change can be viewed as a continuous variation caused b y a progressive association of the bile salt under study, as the concentration is increased. Whichever the concentration, the solution would contain monomers, dimers, trimers, etc. The larger species would become predominant at higher concentration but the distribution curve of 139
Copyright ~ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and InterJace Science, Vol. 59, No. 1, March 15, 1977 ISSN 0021-9797
140
DJAVANBAKHT, KALE AND ZANA
the aggregate sizes would always be wide. Recently Mukerjee (5) emphasized the care that must be exercised when talking about micelle formation. He showed on classical examples that the change in the physicochemical property of a solution due to a dimerization of the solute may be mistakingly taken as indicating the existence of a critical micelle concentration (CMC). Likewise, a continous association could lead to the erroneous claim of the existence of several CMC's. On the other hand if we adopt Tanford's (6) definition for micelle one may wonder whether bile salt aggregates in salt-free solutions can be referred to as micelles owing to the small number of bile ion per aggregate. These above problems incited us to undertake an ultrasonic absorption study of bile acid salts. Ultrasonic absorption methods have proved extremely successful in the study of micelle formation in solutions of ionic detergents (7) as well as in the formation of stacks in solutions of aromatic compounds such as methyl purine (8) and N6,Ng-dimethyladenine (9). Stacking is a multistep association process while in micellar solution, micellization can be ideally thought of as occurring only at concentrations above the CMC. It has been found that ultrasonic waves in the megahertz range can perturb both processes (7-9). This interaction results in a relaxational excess ultrasonic absorption characterized by a single relaxation frequency fR and given by (10): a --
A =
+
B,
[1]
where c~ is the absorption coefficient, f the ultrasonic frequency, and B a constant, which is usually found equal to the c~/ff value for water, where the measurements are performed (7-9). A is a constant proportional to f~-i and AV02, where AV0 is the volume change for the association reaction. Thus if the association equilibrium is not characterized by a sizable volume change the amplitude A of the ultrasonic relaxation would be small.
AV0 is of course related to the change of hydration of the associating compounds. Very different shapes have been found for the curves a/ff versus concentration (c) in the case of micellization and stacking. For micellization a/ff differs from (c¢/ff)~c~,~r only at c > CMC and the curve a/ff versus c shows a maximum (7) while for stacking the results show a monotonous increase of c~/ff with c. Thus one may expect to obtain from ultrasonic studies of bile acid salts informations on the association behavior of these systems. The density of the investigated bile acid salts was also measured with great accuracy, as a function of the concentration of the solution. Indeed, many investigations of detergent solutions have shown (11) that density measurements can be used to obtain the CMC and the volume change AV0 upon micelle formation of the detergent under study. Since the excess absorption due to micelle formation is proportional to zXV02, we thought it worthwhile to directly measure this quantity and correlate it with the observed excess absorption of bile salt solutions. EXPERIMENTAL
METHODS
Materials. Cholic (C), deoxycholic (DOC) and dehydrocholic (DHC) acids were purchased from Fluka (Switzerland). The samples were of purissimum grade and used without further purification. The sodium or potassium salts of the three acids were prepared by weighing a certain amount of acid in a 50 ml volumetric flask and adding the stoichiometric amount of a carbonate free 1 N NaOH or KOH solution. The mixture was stirred until complete dissolution and water added to complete the volume of solution to the 50 ml mark. The molal concentration m of the solution was calculated from the weights of bile acid, hydroxyde and water used to make the solution. The molar concentration c was calculated after measuring the density of the solution (see below). Melhods. The ultrasonic absorption measurements were performed at 25°C using a two-crystal interferometer (12) at frequencies
Journal of Colloid and Interface Sdenee. VoL 59. No. 1. March 13, 1977
141
A G G R E G A T I O N IN BILE SALT SOLUTIONS
below 6 MHz and the standard pulse method (13) at frequencies between 3 and 250 MHz. The overlapping of the frequency ranges of the two methods was sufficient. The density measurements were performed at 25 4- 0.01°C using an improved automatic densimeter (14) (Anton Parr DMA 02), with an estimated accuracy of 4-5.10 .6 g/cm 3. The density of pure water was taken as do = 0.997047 (15). The apparent molal volumes 9~ were calculated by means of the equation: M =
- -
do
d - - do -
lo
.
,
doc
400500[ 1017e'/'f2(crn-lsec ' 2) '
1000
' x/
Na DOC//
./ ......// 300
,,'x
// •
,,7
""
or
NoCIo,.,,,"/ × .I/~N aC :,.~/x ,"
200
500
[2] 100
where M is the molecular weight of the bile acid salt and d the density of the solution of molar concentration c. RESULTS AND ASSIGNMENT OF THE EXCESS ULTRASONIC ABSORPTION OF BILE ACID SODIUM SALTS IN AQUEOUS SOLUTIONS
1. Effect of the concentration on the excess ultrasonic absorption. Figure 1 shows the curves c~/ff against concentration for aqueous solutions of sodium cholate (NaC), deoxycholate (NaDOC), and dehydrocholate (NaDHC) at around pH 8.4. The excess ultrasonic absorption of NaDHC solution with respect to water is seen to be very small in the whole concentration range investigated. On the contrary, the solutions of NaC and NaDOC show an excess absorption even at the lowest concentrations where the measurements were performed. This absorption becomes very large at higher concentrations, but shows no rapid change at the concentrations corresponding to Fontell's (2) limits 2 and 3. However, no conclusion could be reached about the change of the absorption at the concentration corresponding to Fontell's limit 1 (0.015 M for NaC and 0.004 M for NaDOC) because the excess absorption was then very small and of the same order as the error on tile measured ultrasonic absorption. Nevertheless, to illustrate the difference between the ultrasonic absorption behaviors of bile acid salts and typical ionic
0
,x..:, "
0,1
O.2
0.3
0.4
0.5
FIG. 1. Variation of a / f f with concentration, at 9.06 MHz, pI-I=8.4 and 25 ° for aqueous solutions NaDHC (A), NaC ( e ) , and NaDOC (M) and for solutions of NaC in H20, 0.2 M NaC1 (©). The curve in dotted line to which corresponds the right ordinate scale is for sodium decanoate (NaC10) at 25 ° and 5.04 MHz, from Ref. (7).
detergents we have shown in dotted line on Fig. 1 the curve a/ff versus c previously obtained for sodium decanoate (7). In the whole concentration range the excess absorption of the three bile salt solutions increases in the same sequence as their association (1) : Na DHC << NaC < Na DOC. This result is a first indication that the excess absorption of NaC and NaDOC solutions is mainly caused by the association of bile acid anions. Indeed, other processes such as proton transfer at the carboxyl group (16a), hydrogen bonding involving hydroxyl and/or carbonyl groups (16b) and conformational changes such as rotational isomerism (17) involving the-CH(CI-I3)CH2CH2CO~side chain, can be all readily dismissed. First, proton transfer processes should give rise to an excess absorption orders of magnitude smaller than actually found, at the pH where the measurements were performed (16, 18).
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
142
DJAVANBAKHT, KALE AND ZANA
600I
40C
20[ ~ ~ / i / c ~ / L ) OA
0.2
0.3
0.4
0.5
FIG. 2. Variation of tile excess ultrasonic absorption of N a D O C at 9.06 MItz, 25 ° and p H = 8 . 4 as a function of concentration in water (©), H20, 0.2 M
NaC1 (O), and methanol ()<). The crosses (+) refer to results in pure water at pH = 7.46. Moreover, this contribution should be almost independent of the nature of the bile acid, since the carboxyl group has about the same pK= for the three bile acids. Hydrogen bonding does not seem likely either, because the excess ultrasonic absorption of NaDOC which contains two OH groups is larger than that of NaC which contains three OH groups. Finally conformational changes should show with a linear increase of c~/ff with c, and with almost equal contributions for the three compounds. Neither of these predictions is verified.
2. Ultrasonic relaxation spectra of solutions of bile acid sodium salts. The results are shown
IO17~/F2 (crn-lsec2) o
o
50
40
4 x_.__,
,
,
5 7 10
t"( MH z~ 20 30 50 70 iO0 200 ,
Therefore, the association of bile acid anions remains as the process most likely responsible for the excess ultrasonic absorption of NaC and NaDOC. Additional experiments, based on the known influence of pH, added NaC1 and methanol on the association behavior of NaC and NaDOC were performed as further checks on this assignment. First, it is known that in dilute solution the association of NaC and N a D O C is more extensive in H20, 0.2 M NaC1 than in pure H~O (1). The results of Figs. 1 and 2 show that in the whole concentration range the excess absorption is larger in H20, 0.2 M NaC1 than in H~O. Moreover, the effect of NaC1 is more pronounced for NaDOC than for NaC, and for the former, more pronounced in dilute solutions than in concentrated ones. Second, it can be seen on Fig. 2 that the curve a/ff versus c at p H = 7.46 is above that at p H = 8.4. This again parallels the association behavior of NaDOC (1). Finally, Fig. 2 shows that the excess absorption of NaDOC in methanol, where association is greatly reduced with respect to water (1), is much smaller than in water. Having thus clearly shown that the excess ultrasonic absorption of NaDOC and NaC is essentially due to association, we undertook the study of their ultrasonic relaxation behavior. NaDI-IC was also investigated as a reference compound where the association is very small.
±
~
,
,
FIG. 3. Ultrasonic relaxation spectrum of a 0.35 M
solution of NaDHC at 25° and pH = 8.4.
on Figs. 3 to 5. In the whole frequency range the excess absorption of the N a D H C is very small compared to that of the two other salts. The sequence found at 9.06 M H z is seen to hold in the whole frequency range. the difference between the curves for N a D O C and NaC vanishes at high frequency, but these two curves remain well above that for NaDHC. Also the addition of NaC1 results in an increase of absorption, whichever the frequency (see Fig. 4). The main feature of Figs. 3 to 5 is that the ultrasonic relaxation
Journal of Colloid and Interface Science, Vol. 5% No. 1, March 15, 1977
AGGREGATION IN BILE SALT SOLUTIONS
143
600 • 1017a/F 2 ( c m - l s e c 2) 500
s001~ " , ,
400 300
~ 500 200
~x
0
---n 2
- -,- - - r'H20-, - ---'n---,-3 5 10 20 30
-n .... 50
001 .~
"x
100 x .... r-- - ~ _ _ 100 200 F ( M H z )
~
,,
t~~ o
x~-x~ x ~ ~'x~ x ~ ~x~
,
200
FIG. 4. Ultrasonic relaxation spectra of solutions of NaC and NaDHC at pI-I = 8.4 and 25°: (@) 0.35 M NaDHC in water; (X) 0.5 M NaC in water; (O) 0.5 M NaC in H20, 0.2 M NaC1; (A) 0.25 M NaC in water. spectra are much wider than those obeying Eq. [-1] for a single relaxation process. This is illustrated on Fig. 5 where the curve in dotted line obeys Eq. [-1] and has about the same inflexion frequency and amplitude as the curve for N a D O C . The examination of the results of Figs. 3 to 5 reveals that the curve relative to N a D O C is closer to a curve characterized by a single relaxation frequency than those for N a D H C and NaC.
3. Ej~ect of concentration on the apparent molal volumes of bile acid salts in aqueous solutions. The results are shown on Fig. 6 and the numerical values listed in the Appendix. The quantity ~ -- 1.868 c½ has been plotted against c, because bile acid salts are 1-1 electrolytes (19). The curves for potassium cholate (KC) and N a D O C show a large increase of ~, with c, at concentration below 0.05 M, but the results relative to K D H C fall on a straight line, with a very small positive slope. This difference of behavior obviously stems from the much larger association occurring in the first two systems, than in the third one. The curves of Fig. 6 also show that the association starts at lower concentration in N a D O C than in K C solutions, indicating a larger association constant for the first system, in agreement with the above ultrasonic absorption results and with results from other studies (1, 2). The results indicate that the volume changes upon association are of about 4-4.5
0 [1
T 2
T
3
x
~ H20 7- T 10 20 30
, 5
~
, 100
50
q r(b4Hz)
FIG. 5. Ultrasonic relaxation spectra of 0.5 M aqueous solutions of NaC (X) and NaDOC (@) at 25° and pH = 8.4. The curve in dotted line obeys Eq. [-1] with 1017.A = t080 cm-I sec2, fn = 9 MHz. cm3/mole and 8 cm3/mole for K C and N a D O C , respectively. Thus, deoxycholate salts are more tightly associated than cholates, as to be expected from their stronger hydrophobic character. I n fact the curve qv, versus c for N a D O C resembles very much those found with ionic detergents (1t). This is an agreement with the observation made on the basis of ultrasonic relaxation spectra, namely, that the deoxycholate is the bile acid ion whose association most resembles micellization. Finally the self Consistency of the values of the apparent molal volumes at infinite . . . . i . ~v-1.868 c 1 / 2 ( c m 3 / r n o l e )
331
.
.
.
i
.
.
_,+I +_+__-----+- - + - - + ~ -
329
+4/
327 -~÷~ 323
Na DOC
×/x______-~
- - - x ~ ~ x -
321 / 319 ~ / x 317
KDHC
/~
315
c(M/L) ,
0
,
,
,
I
,
0.1
,
,
,
I
L
,
0.2
FIG. 6. Plot of e0_ 1.868c{ against concentration :[or potassium cholate (-t-), potassium dehydrocho]ate (O), and sodium deoxycholate (X) in aqueous solutions at 25°.
Journal of Colloid and Interface Science,
Vol. 59, No. 1, March 15,
1977
144
DJAVANBAKHT, KALE AND ZANA
dilution, ~0, of the three bile acid ions must be emphasized. The extrapolation to zero concentration of the results of Fig. 6 yields the following values 9~0(NaDOC) = 315.8 4- 1 cm3/mole 9~°(KC) = 327.6 4- 1 cm3/mole 9~0(KDHC) = 320.0 4- 0.5 cm3/mole. Using the values ~,~°(K+) -- 3.6 cm3/mole and 9 ~ ° ( N a + ) = - 6 . 6 cm~/mole (19), one obtains ~0(DOC-) = 322.4 4- 1 cm~/mole f,°(C-) = 324.0 4- 1 cm3/mole 9~0(DHC-) = 316.4 4- 0.5 cm3/mole. The difference of 1.6 cm3/mole between the ~0 of the cholate and deoxycholate ions is in agreement with the value which can be obtained from various data reported in the literature for the substitution of a hydrogen atom by a hydroxyl group (20) as in going from the deoxycholate ion to the cholate ion. On the other hand, the difference between ~°(C-) and ~ ° ( D H C - ) is also consistent with the volume increment for the substitution of a ) C H O H group by a ) C
= 0 group.
Indeed a volume decrease of 2 to 4 cm3/mole ts expected for such a process (i) on the basis of Van der Waals volume calculations performed as part of this work, using Bondi's Van der Waals radii (21) and (ii) when comparing the ~0 values for cyclohexanol: 103.5 cm3/mole (20a) and cyclohexanone: 99.6 cm3/mole (this value has been determined as part of this work). There has been several reports of specific volumes of bile salts (22-24). In particular, Tanford el el. (22) have found that the partial specific volume of NaDOC is 0.778 cm~/g below and above the reported CMC of this compound. This result corresponds to an apparent molal volume of 322.5 cm~/mole, i.e., a value in agreement with that found in this work at c > 0.05 M. However, at c < 0.02 M the difference between Tanford et el. value
and those found in this work appears to be well above the experimental accuracy (see error bars on Fig. 6). One of the referees who examined this paper suggested that the compound used in our study might have contained some surface active impurities. This suggestion cannot be discarded although a very large amount of such impurities would be required to explain the shape of the 9~ versus c curves of NaDOC and NaC. Moreover, the following two facts should be emphasized: (1) a constant 9~ for bile salts in the whole range of concentration would imply that there is a negligible volume change upoI1 association of these compounds. This in turn would result in no excess ultrasonic absorption upon association. In the case of NaC and NaDOC our results amply show that bile ion association is indeed responsible for the observed excess absorption, (2) If one assumes a constant ~v(NaDOC) the same assumption is likely to hold for ~ ( K C ) . Using for ev°(NaDOC) and ~°(KC) the high concentration values (at c > 0.05 M) of Fig. 6 and the above 9~°(NaDHC) value would result in a set of data which are not selfconsistent. Indeed, the difference between any two of these three values differs from that which can be calculated from results on model compounds (see the above comparison of the , 0 of the three bile ions) by an amount much larger than the experimental accuracy. In any case, the divergence between the results in Ref. (22) and those reported here about the concentration dependence of ~ clearly emphasizes the need for additional studies. DISCUSSION From the results of Figs. I and 2 the association process in bile acid salts looks more like a continuous association, similar to stacking, than to micelle formation. Indeed the curves ~ / f f versus c do not show the
absorption maximum which has been found for solutions of alkali metal salts of alkylcarboxylates (7) and alkylsulfates (25). The curves of Figs. 1 and 2 only show a curvature
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
AGGREGATION IN BILE SALT SOLUTIONS towards the axis of the ordinates. A monotonous increase was also observed in the case of stacking (8, 9) with a curvature of the a/ff versus c curves towards the c-axis. This result is in agreement with the prediction which can be made using the theoretical expression of the excess absorption derived by Porschke and Eggers (9), for a series of consecutive association reactions with equal equilibrium association constant. Indeed the derivative of this expression with respect to solute concentration retains the same sign in the whole concentration range. Thus the excess absorption must vary monotonically. A second difference between aggregation in solutions of bile acid salts and micellization lies in the ultrasonic relaxation spectra for the two processes. The latter is always characterized by discrete relaxation frequencies: a single one for dilute micellar solutions, and two well-separated relaxation frequencies, for more concentrated solutions (7, 25). In contrast, Figs. 4 and 5 show that the relaxation spectra of bile salt solutions are very wide and likely to be characterized by a distribution of relaxation frequencies. As already pointed out the relaxation spectrum of NaDOC appears to be more narrow than that of NaC. It thus looks as if the width of the distribution of relaxation frequencies is in relation with the extend of association. In the case of stacking, both single relaxation frequency spectra (9) and spectra with a fairly narrow distribution of relaxation frequencies (8) have been reported. Finally, it must be mentioned that preliminary T-jump investigations have been conducted on NaDOC and NaC solutions (26). No relaxation processes were observed in these studies. These results establish an additional clear difference between bile salts and classical ionic detergents where a slow process is usually observed in T-jump and pressure jump studies (27, 28). In view of our results we are led to propose for bile acid ions an association behavior which has similarities both with stacking, and micellization. Bile acid aggregates would be
145
formed by the series of bimolecular reactions (27-29) : k2 +
B + B ~ Bk2-~ ks +
B2 + B ~- B3 le3-
ki +
B~ + t3 ~ B~-+I ki-
[3]
kn4"
Bn_I+ B~.~--B,~ kn-
where B refers to the monomer and B~ to an aggregate containing i monomers. Reactions between two aggregates such as
Bi -{- B~,~- Bi+i
[4]
which are considered in case of stacking are eliminated in the case of bile acid ions be, cause they involve very complex reorganizations of the reacting aggregates, which render their probability very small. Reactions [4] are also discarded in the process of micellization (29). A requirement for the system of reactions [-3] to be characterized by a distribution of relaxation frequencies is that the successive equilibrium constants J¢2i=[-Bi]/ [B~_I].[-B] are n o t equal. The attenuated association constant model proposed by Garland and Christian (30) may, in our mind, constitue a good approximation of the association behavior in bile salt solutions. The aggregate distribution curve, [-B~] versus i, will then show a monotonous change from the monomer to the larger aggregates, rather than going through a minimum of very small amplitude, as for classical detergents (29). In such a case, an extension of Aniansson and Wall (29) theoretical treatment of the kinetics of micellar solutions, would probably lead to predict a distribution of relaxation frequencies. From the kinetic point of view, it is likely that, as in the case of the self association of n-alcohols in organic solvents (31) and micellization (28), the association rate constants k~+ are practically independent of the aggregate size (diffusion controlled asso-
Journal of Colloid and Interface Science, Vol. 59, No. 1, M a r c h 15, 1977
146
DJAVANBAKHT, KALE AND ZANA
ciation, see below). On the contrary the dissociation rate constants k~- are in the case of bile acid aggregates very likely to be sizedependent. Indeed, these aggregates are always fairly small [in aqueous solutions, the aggregation numbers for cholate and deoxycholate are less than 10 (1)] and it is always in the first steps of aggregation that the amount of hydrophobic free energy gained per monomer depends the most on the aggregation number. From the ultrasonic absorption results reported in this work it is not possible to deduce any meaningful rate constant or intrinsic equilibrium constant pertinent to the reaction scheme [-3]. This was possible in the case of micellar solutions of classical ionic detergents (28) because: (i) a single relaxation time (and not a distribution of relaxation time) is associated with the association/dissociation equilibrium of a detergent ion to/from a stable micelle and (ii) the CMC and micellar number are known with fairly good accuracy. However, the value of the average relaxation frequency for NaC and NaDOC indicates that the association of one bile ion to a bile ion aggregate is close to diffusion controlled. Indeed, a calculation of the order of magnitude of k + = k-/EDOC-] (28) based on the expression of the relaxation time r = (2~'fR)-1 derived by Kresheck et el. (32) and assuming an aggregation number of 10, an average relaxation frequency fR = 10 MHz for the 0.5 M solution of NaDOC and a concentration of 0.004 M for the free deoxycholate ions (2) yields
bonding as in reaction (4). This possibility is not in contradiction with the model presented above. It simply extends it to higher concentrations. Indeed reactions between aggregates of maximum size cannot be excluded if interactions other than those leading to the formation of the small aggregates become operative at above a certain concentration range (H-bonding rather than hydrophobic interactions). CONCLUSIONS The excess ultrasonic absorption found in solutions of sodium cholate and deoxycholate is due to the aggregation of the bile acid ions. The results indicate that the deoxycholate association is stronger than of cholate. The measurements of density confirm this result. However, the ultrasonic absorption behavior of bite salts show considerable differences from that of classical ionic detergents. From these results, it is concluded that the association in bile salt solutions occurs in a continuous manner at concentration above 10.2 M leading to a wide distribution of aggregate size. APPENDIX: MOLAR CONCENTRATIONS, DENSITIES, AN~D APPARENT MOLAL VOLLWIES OF BILE SALT AQUEOUS SOLUTIONS AT 25°C
k+ ,~ 10~ M-1 sec-1. The value of k+ is of the same order as those found for classical ionic detergents with a linear alkyl chain containing 8 to 16 carbon atoms (28). A last remark must be made about the model for the aggregation in solutions of bile salts presented by Small (1). This author postulates that superaggregates may be formed once the regular aggregates have reached a maximum aggregation number (10 or less), by subsequent association through hydrogen Journal of Colloid and Interface Science, Vol. 59, No. 1, M a r c h 15, 1977
Potassium dehydrocholate (M/l) 0.01021 0.01959 0.04008 0.06080 0.07937 0.10042 0.14846 0.20061 0.25031
0.00981 0.01233 0.01493 0.02054 0.02826 0.02964
lO3
(d -do)
(g/cma) 1.233 2.367 4.854 7.378 9.618 12.139 17.927 24.170 30.210
Potassium cholate 1.173 1.488 1.778 2.458 3.370 3.527
~
(cma/mole) 320.83 320.75 320.48 320.22 320.40 320.70 320.82 321.10 320.89
328.10 326.99 328.53 327.99 328.41 328.64
AGGREGATION IN BILE SALT SOLUTIONS APPENDIX--Continued
0.03943 0.04940 0.06000 0.07941 0.08942 0.11946 0.13824 0.15964
4.659 5.826 7.049 9.306 10.476 13.941 16.078 18.569
329.50 329.72 330.18 330.46 330.49 330.95 33i.35 331.33
Sodium deoxycholate 0.00489 0.00824 0.01188 0.01273 0.01524 0.02000 0.05022 O.10096 O.15199 0.22472
0.478 0.822 1.160 1.246 1.458 1.912 4.706 9.378 14.049 20.662
317.61 315.69 317.92 317.63 319.82 319.89 321.81 322.64 323.09 323.58
ACKNOWLEDGMENT The authors are pleased to thank Dr. J. Francois for the use of the densimeter. REFERENCES 1. SMALL, D. M., in "The Bile Acids" (P. Nair and D. Kritschewsky, Eds.), Vol. I, Chap. 8. Plenum Press, New York, 1971; CARRY, M. C. AND SMALL, D., Amer. J. Med. 49, 590 (1970). 2. FONT~LL, K., Kolloid Z. Z. Polym. 244, 246 (1972); 244, 253 (1972); 246, 614 (1972); 246, 710 (1972). 3. LINDMAN, B., BRUN, B., AND KAMENKA, N., to appear; GUSTAVSSON, H. AND LINDMAN, B., Y. Amer. Chem. Soc. 97, 3929 (1975). 4. EXWALL, P. et al., Acta Chem. Scan& 10, 327, 681 (1956); 11, 190, 568, 590 (1957); 12, 1622
(1958). 5. MVXERJEE, P., J. Pharmac. Sd. 63, 972 (1974). 6. TAN~O~D, C., "The Hydrophobic Effect," Wiley, New York, 1973. 7. ZANA, R. AZ~mLANO, J., C. R. Acad. Sci. (Paris) Set. C 266, 893, 1347 (1966); GP.ABER, E., LANO, J., ArrD ZANA, R., Kolloid Z. Z. Polym. 237, 470, 479 (1970). 8. GARLAND,F. AND PATEL, R., .T. Phys. Chem. 78, 848 (1974). 9. PORSCHKE,D. AND EGGERS, F., Europ. ]. Biochem. 26, 490 (1972). i0. LINEN, M. AND DE~EYER, L., in "Techniques of Organic Chemistry" (S. Friess, E. Lewis, and A. Weissberger, Eds.), Vol. VIII, Part II, p. 95. Interscience, New York, 1963.
147
11. SItINODA, K. AND SODA, T., Y. Phys. Chem. 67, 2072 (1963); MUSBALLY, G., PERRON, G., AND DESNOYERS, ~., Y. Colloid Interface Sci. 48, 494 (1974); CORKILL, J., GOODMAN, J., AND WALKER, T., Trains. Faraday Soc. 63, 768 (1967). 12. MUSA, R., Y. Acoust. Soc. Amer. 30, 215 (1958), 13. ANDREAE, ~r., BASS, R., HEASELL, E., AND LAMB, J., Acustica 8, 131 (1958). 14. F~ANCOIS, J., CLEMENT, R., AND FRANTA, E., C. R. Acad. Sci. (Paris) Ser. C 273, 1577 (1973). 15. KELL, G. S., J. Chem. Eng. Data. 12, 66 (1967). 16. MICHELS, B. AND ZANA, R. (a) J. Chim Phys. Physicochim. Biol. 66, 240 (1969); "Proceedings 7th Int. Cong. Acoustics," Vol. 2, p. 41. Akademiai Kiado, Budapest 1971; (b) Kolloid Z. Z. Polym. 234, 1008 (1969). 17. WYN-~orms, E. A~n)ORVILLE-THOMAS,W., Advan. Molec. Relax. Proc. 2, 201 (1972). 18. APPLEGATE, K., SLUTSKY, L., AND PARKER, R . J. Amer. Chem. Soc. 90, 6909 (1968); ZANA,R. AND LANG, J., J. Phys. Chem. 74, 2734 (1970). 19. MILLERO, F., Chem. Rev. 71, 147 (1971); ZANA, R. ANDYEAGER,E., J. Phys. Chem. 71, 521 (1967). 20. The average value of the difference between the g, 0 for cyclopentanol, cyclohexanol and cycloheptanol (a) and for cyclopentane, cyclohexane, and cycloheptane, respectively, is 1.8 cm3/mole. The 9~° values for the three cyclic alkanes were estimated from their molal volumes (b) assuming the same excess volume as for cyclic amines (c) with an equal number of carbon atoms. Note that the average value of the difference between the ~v° for methanol, ethanol and propanol (d), and for methane, ethane and propane (e) respectively is 2.8 cm3/mole. (a) CABANI, S., CONTI, G., AND LEPORI, L:, J. _Phys. Chem. 78, 1030 (1974); (b) JOLICOEUR, C., BOILEAU, J., BAZINET, S., AND PICKER, P., Can. Y. Chem. 53, 716 (1975); (c) CABANI, S., CONTI, G., AND LEPORI, L., J. Phys. Chem. 76, 1338 (1972); (d) Average values from NAI~AJIMA, T., KOMATSU, T., AND NAKAGAWA,T., Bull. Chem. Soc. Jpn. 48, 783 (1975) ; KODA, M., MANABE, M., Bull. Chem. Soc. Ypn. 48, 2376 (1975); TE~SAWA, S., ITSrJKI, H., AND ARAr:AWA, S., J. Phys. Chem. 79, 2345 (1975); (e) MASTERTON, W., J. Chem. Phys. 54, 1830
(1954). 21. BONa)I, A., J. Phys. Chem" 68, 441 (1964). 22. TANrOm), C., NOZAKI, Y., REYNOLDS, A., AND MAXINO, S., Biochemistry 13, 2369 (1974). 23. LAURENT, T. C. AND PERSSON, H., Biochem. Biophys. Acta 106, 616 (1965). 24. KRATO~WL, :[. P . AND DELLICOLLI, H. T., Fed. Proc. Fed. Amer. Soc. Exp. Biol. 29, 1335 (1970).
Journal of Colloid and Interface~Sdence.Voh 59. No. 1, March 15, 1977
148
Dj'AVANBAKHT, KALE AND ZANA
25. RASSING, J'. AND WYN-JONES, E., Chem. Phys. Lett. 21, 93 (1973) ; I¢.ASSING,J., SAMS,P. J., AhrD WYN-JO~mS, E., J. C. S. Faraday Trans. I I 69, 180 (1973). 26. LA~,*G,J. AND ZANA, R., unpublished results. 27. LAN`G, J., TONDRE, C., ZANA, R., BAUER, R., HOFFMANN', H., AND ULBRICHT, W.~ ft. Phys. Chem. 79, 276 (1975). 28. ANIANSSON,E., WALL, S., ALMGREN, M., HOFF:MANN~H.~ KIEL:t~IANN~J'., ULBRICHT~~¢V.~ZANA~
29.
30. 31. 32.
R., LANG, ~., AND TONI)RE, C., .f. Phys. Chem. 80, 905 (1976). A~TANSSON,E. AND WALL, S., Y. Phys. Chem. 78, 1024 (1974); 79, 857 (1975). GARLAND,F. AND CHRISTIAN,S., J. Phys. Chem. 79, 1247 (1975). ZANA, R. AND LANO, ~[., Advan. Molec. Relax. Proc. 7, 21 (1975). KRESI~ECI~, G. C., HAMORI, E., DAVENPORT, G., ar,m SCrlERAOA,H. A., Y. Amer. Chem. Soc. 88, 246 (1966).
Journal of Colloid and Interface Science, Vol. 59, No. I, March 15, 1977
Received February 12, 1976; accepted May 17, 1976 The ultrasonic absorption of sodium cholate, deoxycholate and dehydrocholate has been measured as a function of concentration in water, H~O, 0.2 M NaC1, and methanol. The effect of pH has also been investigated. The results indicate that the observed excess absorption is due to the aggregation of the bile acid ions, the association being much stronger for deoxycholate than for cholate and negligible for dehydrocholate. The measurements of density confirm the ultrasonic absorption results. However, the excess ultrasonic absorption of bile salt solutions has features differing considerably from those found for solutions of classical detergents where a true micellization takes place. In particular the ultrasonic absorption relaxation spectra of bile salt solutions show evidence of a distribution of relaxation frequencies rather than a single relaxation frequency as found for ionic detergents. These results lead to the conclusion that the association takes place in the whole range of concentration and not at some critical micelle concentration, and that the distribution curve of aggregate sizes must be wide and shifting upward as the concentration is increased. INTRODUCTION AND THEORY Bile acids have been the subject of numerous investigations recently reviewed b y Small and Carey (1). From the recent studies of Fontell (2) and other workers (3), and from earlier work (4), it appears that the self-association of these compounds is very complex. The "micelles" formed in aqueous solutions of bile acids contain only a small number of bile acid ions [-two in some instances (1) 1 . Also, as the concentration is increased, peculiar concentrations are observed where the investigated physicochemical property shows a rapid change. This has been interpreted as indicating that association occurs in several steps, at least three in the case of sodium cholate (2, 4). However, a close look at the curve representing the variation of the measured physicochemical property as a function of aCorrespondence should be sent to: R. Zana, C.R.M., CNRS, 6, rue Boussingault, 67083, Strasbourg Cedex, France.
concentration shows that in m a n y instances a continuous line m a y be drawn through the experimental pointS. Of course, very different models would have to be used to describe the state of aggregation in bile salt solutions, depending on the type of variation which is found. I n the case of steep changes (micellization), the bile salt solutions would contain bile ions and aggregates with a fairly welldefined shape a n d / o r aggregation number, in a given concentration range. The aggregate shape a n d / o r size would change by step in going from one concentration range to another. I n case of a continuous change of the measured property, this change can be viewed as a continuous variation caused b y a progressive association of the bile salt under study, as the concentration is increased. Whichever the concentration, the solution would contain monomers, dimers, trimers, etc. The larger species would become predominant at higher concentration but the distribution curve of 139
Copyright ~ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and InterJace Science, Vol. 59, No. 1, March 15, 1977 ISSN 0021-9797
140
DJAVANBAKHT, KALE AND ZANA
the aggregate sizes would always be wide. Recently Mukerjee (5) emphasized the care that must be exercised when talking about micelle formation. He showed on classical examples that the change in the physicochemical property of a solution due to a dimerization of the solute may be mistakingly taken as indicating the existence of a critical micelle concentration (CMC). Likewise, a continous association could lead to the erroneous claim of the existence of several CMC's. On the other hand if we adopt Tanford's (6) definition for micelle one may wonder whether bile salt aggregates in salt-free solutions can be referred to as micelles owing to the small number of bile ion per aggregate. These above problems incited us to undertake an ultrasonic absorption study of bile acid salts. Ultrasonic absorption methods have proved extremely successful in the study of micelle formation in solutions of ionic detergents (7) as well as in the formation of stacks in solutions of aromatic compounds such as methyl purine (8) and N6,Ng-dimethyladenine (9). Stacking is a multistep association process while in micellar solution, micellization can be ideally thought of as occurring only at concentrations above the CMC. It has been found that ultrasonic waves in the megahertz range can perturb both processes (7-9). This interaction results in a relaxational excess ultrasonic absorption characterized by a single relaxation frequency fR and given by (10): a --
A =
+
B,
[1]
where c~ is the absorption coefficient, f the ultrasonic frequency, and B a constant, which is usually found equal to the c~/ff value for water, where the measurements are performed (7-9). A is a constant proportional to f~-i and AV02, where AV0 is the volume change for the association reaction. Thus if the association equilibrium is not characterized by a sizable volume change the amplitude A of the ultrasonic relaxation would be small.
AV0 is of course related to the change of hydration of the associating compounds. Very different shapes have been found for the curves a/ff versus concentration (c) in the case of micellization and stacking. For micellization a/ff differs from (c¢/ff)~c~,~r only at c > CMC and the curve a/ff versus c shows a maximum (7) while for stacking the results show a monotonous increase of c~/ff with c. Thus one may expect to obtain from ultrasonic studies of bile acid salts informations on the association behavior of these systems. The density of the investigated bile acid salts was also measured with great accuracy, as a function of the concentration of the solution. Indeed, many investigations of detergent solutions have shown (11) that density measurements can be used to obtain the CMC and the volume change AV0 upon micelle formation of the detergent under study. Since the excess absorption due to micelle formation is proportional to zXV02, we thought it worthwhile to directly measure this quantity and correlate it with the observed excess absorption of bile salt solutions. EXPERIMENTAL
METHODS
Materials. Cholic (C), deoxycholic (DOC) and dehydrocholic (DHC) acids were purchased from Fluka (Switzerland). The samples were of purissimum grade and used without further purification. The sodium or potassium salts of the three acids were prepared by weighing a certain amount of acid in a 50 ml volumetric flask and adding the stoichiometric amount of a carbonate free 1 N NaOH or KOH solution. The mixture was stirred until complete dissolution and water added to complete the volume of solution to the 50 ml mark. The molal concentration m of the solution was calculated from the weights of bile acid, hydroxyde and water used to make the solution. The molar concentration c was calculated after measuring the density of the solution (see below). Melhods. The ultrasonic absorption measurements were performed at 25°C using a two-crystal interferometer (12) at frequencies
Journal of Colloid and Interface Sdenee. VoL 59. No. 1. March 13, 1977
141
A G G R E G A T I O N IN BILE SALT SOLUTIONS
below 6 MHz and the standard pulse method (13) at frequencies between 3 and 250 MHz. The overlapping of the frequency ranges of the two methods was sufficient. The density measurements were performed at 25 4- 0.01°C using an improved automatic densimeter (14) (Anton Parr DMA 02), with an estimated accuracy of 4-5.10 .6 g/cm 3. The density of pure water was taken as do = 0.997047 (15). The apparent molal volumes 9~ were calculated by means of the equation: M =
- -
do
d - - do -
lo
.
,
doc
400500[ 1017e'/'f2(crn-lsec ' 2) '
1000
' x/
Na DOC//
./ ......// 300
,,'x
// •
,,7
""
or
NoCIo,.,,,"/ × .I/~N aC :,.~/x ,"
200
500
[2] 100
where M is the molecular weight of the bile acid salt and d the density of the solution of molar concentration c. RESULTS AND ASSIGNMENT OF THE EXCESS ULTRASONIC ABSORPTION OF BILE ACID SODIUM SALTS IN AQUEOUS SOLUTIONS
1. Effect of the concentration on the excess ultrasonic absorption. Figure 1 shows the curves c~/ff against concentration for aqueous solutions of sodium cholate (NaC), deoxycholate (NaDOC), and dehydrocholate (NaDHC) at around pH 8.4. The excess ultrasonic absorption of NaDHC solution with respect to water is seen to be very small in the whole concentration range investigated. On the contrary, the solutions of NaC and NaDOC show an excess absorption even at the lowest concentrations where the measurements were performed. This absorption becomes very large at higher concentrations, but shows no rapid change at the concentrations corresponding to Fontell's (2) limits 2 and 3. However, no conclusion could be reached about the change of the absorption at the concentration corresponding to Fontell's limit 1 (0.015 M for NaC and 0.004 M for NaDOC) because the excess absorption was then very small and of the same order as the error on tile measured ultrasonic absorption. Nevertheless, to illustrate the difference between the ultrasonic absorption behaviors of bile acid salts and typical ionic
0
,x..:, "
0,1
O.2
0.3
0.4
0.5
FIG. 1. Variation of a / f f with concentration, at 9.06 MHz, pI-I=8.4 and 25 ° for aqueous solutions NaDHC (A), NaC ( e ) , and NaDOC (M) and for solutions of NaC in H20, 0.2 M NaC1 (©). The curve in dotted line to which corresponds the right ordinate scale is for sodium decanoate (NaC10) at 25 ° and 5.04 MHz, from Ref. (7).
detergents we have shown in dotted line on Fig. 1 the curve a/ff versus c previously obtained for sodium decanoate (7). In the whole concentration range the excess absorption of the three bile salt solutions increases in the same sequence as their association (1) : Na DHC << NaC < Na DOC. This result is a first indication that the excess absorption of NaC and NaDOC solutions is mainly caused by the association of bile acid anions. Indeed, other processes such as proton transfer at the carboxyl group (16a), hydrogen bonding involving hydroxyl and/or carbonyl groups (16b) and conformational changes such as rotational isomerism (17) involving the-CH(CI-I3)CH2CH2CO~side chain, can be all readily dismissed. First, proton transfer processes should give rise to an excess absorption orders of magnitude smaller than actually found, at the pH where the measurements were performed (16, 18).
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
142
DJAVANBAKHT, KALE AND ZANA
600I
40C
20[ ~ ~ / i / c ~ / L ) OA
0.2
0.3
0.4
0.5
FIG. 2. Variation of tile excess ultrasonic absorption of N a D O C at 9.06 MItz, 25 ° and p H = 8 . 4 as a function of concentration in water (©), H20, 0.2 M
NaC1 (O), and methanol ()<). The crosses (+) refer to results in pure water at pH = 7.46. Moreover, this contribution should be almost independent of the nature of the bile acid, since the carboxyl group has about the same pK= for the three bile acids. Hydrogen bonding does not seem likely either, because the excess ultrasonic absorption of NaDOC which contains two OH groups is larger than that of NaC which contains three OH groups. Finally conformational changes should show with a linear increase of c~/ff with c, and with almost equal contributions for the three compounds. Neither of these predictions is verified.
2. Ultrasonic relaxation spectra of solutions of bile acid sodium salts. The results are shown
IO17~/F2 (crn-lsec2) o
o
50
40
4 x_.__,
,
,
5 7 10
t"( MH z~ 20 30 50 70 iO0 200 ,
Therefore, the association of bile acid anions remains as the process most likely responsible for the excess ultrasonic absorption of NaC and NaDOC. Additional experiments, based on the known influence of pH, added NaC1 and methanol on the association behavior of NaC and NaDOC were performed as further checks on this assignment. First, it is known that in dilute solution the association of NaC and N a D O C is more extensive in H20, 0.2 M NaC1 than in pure H~O (1). The results of Figs. 1 and 2 show that in the whole concentration range the excess absorption is larger in H20, 0.2 M NaC1 than in H~O. Moreover, the effect of NaC1 is more pronounced for NaDOC than for NaC, and for the former, more pronounced in dilute solutions than in concentrated ones. Second, it can be seen on Fig. 2 that the curve a/ff versus c at p H = 7.46 is above that at p H = 8.4. This again parallels the association behavior of NaDOC (1). Finally, Fig. 2 shows that the excess absorption of NaDOC in methanol, where association is greatly reduced with respect to water (1), is much smaller than in water. Having thus clearly shown that the excess ultrasonic absorption of NaDOC and NaC is essentially due to association, we undertook the study of their ultrasonic relaxation behavior. NaDI-IC was also investigated as a reference compound where the association is very small.
±
~
,
,
FIG. 3. Ultrasonic relaxation spectrum of a 0.35 M
solution of NaDHC at 25° and pH = 8.4.
on Figs. 3 to 5. In the whole frequency range the excess absorption of the N a D H C is very small compared to that of the two other salts. The sequence found at 9.06 M H z is seen to hold in the whole frequency range. the difference between the curves for N a D O C and NaC vanishes at high frequency, but these two curves remain well above that for NaDHC. Also the addition of NaC1 results in an increase of absorption, whichever the frequency (see Fig. 4). The main feature of Figs. 3 to 5 is that the ultrasonic relaxation
Journal of Colloid and Interface Science, Vol. 5% No. 1, March 15, 1977
AGGREGATION IN BILE SALT SOLUTIONS
143
600 • 1017a/F 2 ( c m - l s e c 2) 500
s001~ " , ,
400 300
~ 500 200
~x
0
---n 2
- -,- - - r'H20-, - ---'n---,-3 5 10 20 30
-n .... 50
001 .~
"x
100 x .... r-- - ~ _ _ 100 200 F ( M H z )
~
,,
t~~ o
x~-x~ x ~ ~'x~ x ~ ~x~
,
200
FIG. 4. Ultrasonic relaxation spectra of solutions of NaC and NaDHC at pI-I = 8.4 and 25°: (@) 0.35 M NaDHC in water; (X) 0.5 M NaC in water; (O) 0.5 M NaC in H20, 0.2 M NaC1; (A) 0.25 M NaC in water. spectra are much wider than those obeying Eq. [-1] for a single relaxation process. This is illustrated on Fig. 5 where the curve in dotted line obeys Eq. [-1] and has about the same inflexion frequency and amplitude as the curve for N a D O C . The examination of the results of Figs. 3 to 5 reveals that the curve relative to N a D O C is closer to a curve characterized by a single relaxation frequency than those for N a D H C and NaC.
3. Ej~ect of concentration on the apparent molal volumes of bile acid salts in aqueous solutions. The results are shown on Fig. 6 and the numerical values listed in the Appendix. The quantity ~ -- 1.868 c½ has been plotted against c, because bile acid salts are 1-1 electrolytes (19). The curves for potassium cholate (KC) and N a D O C show a large increase of ~, with c, at concentration below 0.05 M, but the results relative to K D H C fall on a straight line, with a very small positive slope. This difference of behavior obviously stems from the much larger association occurring in the first two systems, than in the third one. The curves of Fig. 6 also show that the association starts at lower concentration in N a D O C than in K C solutions, indicating a larger association constant for the first system, in agreement with the above ultrasonic absorption results and with results from other studies (1, 2). The results indicate that the volume changes upon association are of about 4-4.5
0 [1
T 2
T
3
x
~ H20 7- T 10 20 30
, 5
~
, 100
50
q r(b4Hz)
FIG. 5. Ultrasonic relaxation spectra of 0.5 M aqueous solutions of NaC (X) and NaDOC (@) at 25° and pH = 8.4. The curve in dotted line obeys Eq. [-1] with 1017.A = t080 cm-I sec2, fn = 9 MHz. cm3/mole and 8 cm3/mole for K C and N a D O C , respectively. Thus, deoxycholate salts are more tightly associated than cholates, as to be expected from their stronger hydrophobic character. I n fact the curve qv, versus c for N a D O C resembles very much those found with ionic detergents (1t). This is an agreement with the observation made on the basis of ultrasonic relaxation spectra, namely, that the deoxycholate is the bile acid ion whose association most resembles micellization. Finally the self Consistency of the values of the apparent molal volumes at infinite . . . . i . ~v-1.868 c 1 / 2 ( c m 3 / r n o l e )
331
.
.
.
i
.
.
_,+I +_+__-----+- - + - - + ~ -
329
+4/
327 -~÷~ 323
Na DOC
×/x______-~
- - - x ~ ~ x -
321 / 319 ~ / x 317
KDHC
/~
315
c(M/L) ,
0
,
,
,
I
,
0.1
,
,
,
I
L
,
0.2
FIG. 6. Plot of e0_ 1.868c{ against concentration :[or potassium cholate (-t-), potassium dehydrocho]ate (O), and sodium deoxycholate (X) in aqueous solutions at 25°.
Journal of Colloid and Interface Science,
Vol. 59, No. 1, March 15,
1977
144
DJAVANBAKHT, KALE AND ZANA
dilution, ~0, of the three bile acid ions must be emphasized. The extrapolation to zero concentration of the results of Fig. 6 yields the following values 9~0(NaDOC) = 315.8 4- 1 cm3/mole 9~°(KC) = 327.6 4- 1 cm3/mole 9~0(KDHC) = 320.0 4- 0.5 cm3/mole. Using the values ~,~°(K+) -- 3.6 cm3/mole and 9 ~ ° ( N a + ) = - 6 . 6 cm~/mole (19), one obtains ~0(DOC-) = 322.4 4- 1 cm~/mole f,°(C-) = 324.0 4- 1 cm3/mole 9~0(DHC-) = 316.4 4- 0.5 cm3/mole. The difference of 1.6 cm3/mole between the ~0 of the cholate and deoxycholate ions is in agreement with the value which can be obtained from various data reported in the literature for the substitution of a hydrogen atom by a hydroxyl group (20) as in going from the deoxycholate ion to the cholate ion. On the other hand, the difference between ~°(C-) and ~ ° ( D H C - ) is also consistent with the volume increment for the substitution of a ) C H O H group by a ) C
= 0 group.
Indeed a volume decrease of 2 to 4 cm3/mole ts expected for such a process (i) on the basis of Van der Waals volume calculations performed as part of this work, using Bondi's Van der Waals radii (21) and (ii) when comparing the ~0 values for cyclohexanol: 103.5 cm3/mole (20a) and cyclohexanone: 99.6 cm3/mole (this value has been determined as part of this work). There has been several reports of specific volumes of bile salts (22-24). In particular, Tanford el el. (22) have found that the partial specific volume of NaDOC is 0.778 cm~/g below and above the reported CMC of this compound. This result corresponds to an apparent molal volume of 322.5 cm~/mole, i.e., a value in agreement with that found in this work at c > 0.05 M. However, at c < 0.02 M the difference between Tanford et el. value
and those found in this work appears to be well above the experimental accuracy (see error bars on Fig. 6). One of the referees who examined this paper suggested that the compound used in our study might have contained some surface active impurities. This suggestion cannot be discarded although a very large amount of such impurities would be required to explain the shape of the 9~ versus c curves of NaDOC and NaC. Moreover, the following two facts should be emphasized: (1) a constant 9~ for bile salts in the whole range of concentration would imply that there is a negligible volume change upoI1 association of these compounds. This in turn would result in no excess ultrasonic absorption upon association. In the case of NaC and NaDOC our results amply show that bile ion association is indeed responsible for the observed excess absorption, (2) If one assumes a constant ~v(NaDOC) the same assumption is likely to hold for ~ ( K C ) . Using for ev°(NaDOC) and ~°(KC) the high concentration values (at c > 0.05 M) of Fig. 6 and the above 9~°(NaDHC) value would result in a set of data which are not selfconsistent. Indeed, the difference between any two of these three values differs from that which can be calculated from results on model compounds (see the above comparison of the , 0 of the three bile ions) by an amount much larger than the experimental accuracy. In any case, the divergence between the results in Ref. (22) and those reported here about the concentration dependence of ~ clearly emphasizes the need for additional studies. DISCUSSION From the results of Figs. I and 2 the association process in bile acid salts looks more like a continuous association, similar to stacking, than to micelle formation. Indeed the curves ~ / f f versus c do not show the
absorption maximum which has been found for solutions of alkali metal salts of alkylcarboxylates (7) and alkylsulfates (25). The curves of Figs. 1 and 2 only show a curvature
Journal of Colloid and Interface Science, Vol. 59, No. 1, March 15, 1977
AGGREGATION IN BILE SALT SOLUTIONS towards the axis of the ordinates. A monotonous increase was also observed in the case of stacking (8, 9) with a curvature of the a/ff versus c curves towards the c-axis. This result is in agreement with the prediction which can be made using the theoretical expression of the excess absorption derived by Porschke and Eggers (9), for a series of consecutive association reactions with equal equilibrium association constant. Indeed the derivative of this expression with respect to solute concentration retains the same sign in the whole concentration range. Thus the excess absorption must vary monotonically. A second difference between aggregation in solutions of bile acid salts and micellization lies in the ultrasonic relaxation spectra for the two processes. The latter is always characterized by discrete relaxation frequencies: a single one for dilute micellar solutions, and two well-separated relaxation frequencies, for more concentrated solutions (7, 25). In contrast, Figs. 4 and 5 show that the relaxation spectra of bile salt solutions are very wide and likely to be characterized by a distribution of relaxation frequencies. As already pointed out the relaxation spectrum of NaDOC appears to be more narrow than that of NaC. It thus looks as if the width of the distribution of relaxation frequencies is in relation with the extend of association. In the case of stacking, both single relaxation frequency spectra (9) and spectra with a fairly narrow distribution of relaxation frequencies (8) have been reported. Finally, it must be mentioned that preliminary T-jump investigations have been conducted on NaDOC and NaC solutions (26). No relaxation processes were observed in these studies. These results establish an additional clear difference between bile salts and classical ionic detergents where a slow process is usually observed in T-jump and pressure jump studies (27, 28). In view of our results we are led to propose for bile acid ions an association behavior which has similarities both with stacking, and micellization. Bile acid aggregates would be
145
formed by the series of bimolecular reactions (27-29) : k2 +
B + B ~ Bk2-~ ks +
B2 + B ~- B3 le3-
ki +
B~ + t3 ~ B~-+I ki-
[3]
kn4"
Bn_I+ B~.~--B,~ kn-
where B refers to the monomer and B~ to an aggregate containing i monomers. Reactions between two aggregates such as
Bi -{- B~,~- Bi+i
[4]
which are considered in case of stacking are eliminated in the case of bile acid ions be, cause they involve very complex reorganizations of the reacting aggregates, which render their probability very small. Reactions [4] are also discarded in the process of micellization (29). A requirement for the system of reactions [-3] to be characterized by a distribution of relaxation frequencies is that the successive equilibrium constants J¢2i=[-Bi]/ [B~_I].[-B] are n o t equal. The attenuated association constant model proposed by Garland and Christian (30) may, in our mind, constitue a good approximation of the association behavior in bile salt solutions. The aggregate distribution curve, [-B~] versus i, will then show a monotonous change from the monomer to the larger aggregates, rather than going through a minimum of very small amplitude, as for classical detergents (29). In such a case, an extension of Aniansson and Wall (29) theoretical treatment of the kinetics of micellar solutions, would probably lead to predict a distribution of relaxation frequencies. From the kinetic point of view, it is likely that, as in the case of the self association of n-alcohols in organic solvents (31) and micellization (28), the association rate constants k~+ are practically independent of the aggregate size (diffusion controlled asso-
Journal of Colloid and Interface Science, Vol. 59, No. 1, M a r c h 15, 1977
146
DJAVANBAKHT, KALE AND ZANA
ciation, see below). On the contrary the dissociation rate constants k~- are in the case of bile acid aggregates very likely to be sizedependent. Indeed, these aggregates are always fairly small [in aqueous solutions, the aggregation numbers for cholate and deoxycholate are less than 10 (1)] and it is always in the first steps of aggregation that the amount of hydrophobic free energy gained per monomer depends the most on the aggregation number. From the ultrasonic absorption results reported in this work it is not possible to deduce any meaningful rate constant or intrinsic equilibrium constant pertinent to the reaction scheme [-3]. This was possible in the case of micellar solutions of classical ionic detergents (28) because: (i) a single relaxation time (and not a distribution of relaxation time) is associated with the association/dissociation equilibrium of a detergent ion to/from a stable micelle and (ii) the CMC and micellar number are known with fairly good accuracy. However, the value of the average relaxation frequency for NaC and NaDOC indicates that the association of one bile ion to a bile ion aggregate is close to diffusion controlled. Indeed, a calculation of the order of magnitude of k + = k-/EDOC-] (28) based on the expression of the relaxation time r = (2~'fR)-1 derived by Kresheck et el. (32) and assuming an aggregation number of 10, an average relaxation frequency fR = 10 MHz for the 0.5 M solution of NaDOC and a concentration of 0.004 M for the free deoxycholate ions (2) yields
bonding as in reaction (4). This possibility is not in contradiction with the model presented above. It simply extends it to higher concentrations. Indeed reactions between aggregates of maximum size cannot be excluded if interactions other than those leading to the formation of the small aggregates become operative at above a certain concentration range (H-bonding rather than hydrophobic interactions). CONCLUSIONS The excess ultrasonic absorption found in solutions of sodium cholate and deoxycholate is due to the aggregation of the bile acid ions. The results indicate that the deoxycholate association is stronger than of cholate. The measurements of density confirm this result. However, the ultrasonic absorption behavior of bite salts show considerable differences from that of classical ionic detergents. From these results, it is concluded that the association in bile salt solutions occurs in a continuous manner at concentration above 10.2 M leading to a wide distribution of aggregate size. APPENDIX: MOLAR CONCENTRATIONS, DENSITIES, AN~D APPARENT MOLAL VOLLWIES OF BILE SALT AQUEOUS SOLUTIONS AT 25°C
k+ ,~ 10~ M-1 sec-1. The value of k+ is of the same order as those found for classical ionic detergents with a linear alkyl chain containing 8 to 16 carbon atoms (28). A last remark must be made about the model for the aggregation in solutions of bile salts presented by Small (1). This author postulates that superaggregates may be formed once the regular aggregates have reached a maximum aggregation number (10 or less), by subsequent association through hydrogen Journal of Colloid and Interface Science, Vol. 59, No. 1, M a r c h 15, 1977
Potassium dehydrocholate (M/l) 0.01021 0.01959 0.04008 0.06080 0.07937 0.10042 0.14846 0.20061 0.25031
0.00981 0.01233 0.01493 0.02054 0.02826 0.02964
lO3
(d -do)
(g/cma) 1.233 2.367 4.854 7.378 9.618 12.139 17.927 24.170 30.210
Potassium cholate 1.173 1.488 1.778 2.458 3.370 3.527
~
(cma/mole) 320.83 320.75 320.48 320.22 320.40 320.70 320.82 321.10 320.89
328.10 326.99 328.53 327.99 328.41 328.64
AGGREGATION IN BILE SALT SOLUTIONS APPENDIX--Continued
0.03943 0.04940 0.06000 0.07941 0.08942 0.11946 0.13824 0.15964
4.659 5.826 7.049 9.306 10.476 13.941 16.078 18.569
329.50 329.72 330.18 330.46 330.49 330.95 33i.35 331.33
Sodium deoxycholate 0.00489 0.00824 0.01188 0.01273 0.01524 0.02000 0.05022 O.10096 O.15199 0.22472
0.478 0.822 1.160 1.246 1.458 1.912 4.706 9.378 14.049 20.662
317.61 315.69 317.92 317.63 319.82 319.89 321.81 322.64 323.09 323.58
ACKNOWLEDGMENT The authors are pleased to thank Dr. J. Francois for the use of the densimeter. REFERENCES 1. SMALL, D. M., in "The Bile Acids" (P. Nair and D. Kritschewsky, Eds.), Vol. I, Chap. 8. Plenum Press, New York, 1971; CARRY, M. C. AND SMALL, D., Amer. J. Med. 49, 590 (1970). 2. FONT~LL, K., Kolloid Z. Z. Polym. 244, 246 (1972); 244, 253 (1972); 246, 614 (1972); 246, 710 (1972). 3. LINDMAN, B., BRUN, B., AND KAMENKA, N., to appear; GUSTAVSSON, H. AND LINDMAN, B., Y. Amer. Chem. Soc. 97, 3929 (1975). 4. EXWALL, P. et al., Acta Chem. Scan& 10, 327, 681 (1956); 11, 190, 568, 590 (1957); 12, 1622
(1958). 5. MVXERJEE, P., J. Pharmac. Sd. 63, 972 (1974). 6. TAN~O~D, C., "The Hydrophobic Effect," Wiley, New York, 1973. 7. ZANA, R. AZ~mLANO, J., C. R. Acad. Sci. (Paris) Set. C 266, 893, 1347 (1966); GP.ABER, E., LANO, J., ArrD ZANA, R., Kolloid Z. Z. Polym. 237, 470, 479 (1970). 8. GARLAND,F. AND PATEL, R., .T. Phys. Chem. 78, 848 (1974). 9. PORSCHKE,D. AND EGGERS, F., Europ. ]. Biochem. 26, 490 (1972). i0. LINEN, M. AND DE~EYER, L., in "Techniques of Organic Chemistry" (S. Friess, E. Lewis, and A. Weissberger, Eds.), Vol. VIII, Part II, p. 95. Interscience, New York, 1963.
147
11. SItINODA, K. AND SODA, T., Y. Phys. Chem. 67, 2072 (1963); MUSBALLY, G., PERRON, G., AND DESNOYERS, ~., Y. Colloid Interface Sci. 48, 494 (1974); CORKILL, J., GOODMAN, J., AND WALKER, T., Trains. Faraday Soc. 63, 768 (1967). 12. MUSA, R., Y. Acoust. Soc. Amer. 30, 215 (1958), 13. ANDREAE, ~r., BASS, R., HEASELL, E., AND LAMB, J., Acustica 8, 131 (1958). 14. F~ANCOIS, J., CLEMENT, R., AND FRANTA, E., C. R. Acad. Sci. (Paris) Ser. C 273, 1577 (1973). 15. KELL, G. S., J. Chem. Eng. Data. 12, 66 (1967). 16. MICHELS, B. AND ZANA, R. (a) J. Chim Phys. Physicochim. Biol. 66, 240 (1969); "Proceedings 7th Int. Cong. Acoustics," Vol. 2, p. 41. Akademiai Kiado, Budapest 1971; (b) Kolloid Z. Z. Polym. 234, 1008 (1969). 17. WYN-~orms, E. A~n)ORVILLE-THOMAS,W., Advan. Molec. Relax. Proc. 2, 201 (1972). 18. APPLEGATE, K., SLUTSKY, L., AND PARKER, R . J. Amer. Chem. Soc. 90, 6909 (1968); ZANA,R. AND LANG, J., J. Phys. Chem. 74, 2734 (1970). 19. MILLERO, F., Chem. Rev. 71, 147 (1971); ZANA, R. ANDYEAGER,E., J. Phys. Chem. 71, 521 (1967). 20. The average value of the difference between the g, 0 for cyclopentanol, cyclohexanol and cycloheptanol (a) and for cyclopentane, cyclohexane, and cycloheptane, respectively, is 1.8 cm3/mole. The 9~° values for the three cyclic alkanes were estimated from their molal volumes (b) assuming the same excess volume as for cyclic amines (c) with an equal number of carbon atoms. Note that the average value of the difference between the ~v° for methanol, ethanol and propanol (d), and for methane, ethane and propane (e) respectively is 2.8 cm3/mole. (a) CABANI, S., CONTI, G., AND LEPORI, L:, J. _Phys. Chem. 78, 1030 (1974); (b) JOLICOEUR, C., BOILEAU, J., BAZINET, S., AND PICKER, P., Can. Y. Chem. 53, 716 (1975); (c) CABANI, S., CONTI, G., AND LEPORI, L., J. Phys. Chem. 76, 1338 (1972); (d) Average values from NAI~AJIMA, T., KOMATSU, T., AND NAKAGAWA,T., Bull. Chem. Soc. Jpn. 48, 783 (1975) ; KODA, M., MANABE, M., Bull. Chem. Soc. Ypn. 48, 2376 (1975); TE~SAWA, S., ITSrJKI, H., AND ARAr:AWA, S., J. Phys. Chem. 79, 2345 (1975); (e) MASTERTON, W., J. Chem. Phys. 54, 1830
(1954). 21. BONa)I, A., J. Phys. Chem" 68, 441 (1964). 22. TANrOm), C., NOZAKI, Y., REYNOLDS, A., AND MAXINO, S., Biochemistry 13, 2369 (1974). 23. LAURENT, T. C. AND PERSSON, H., Biochem. Biophys. Acta 106, 616 (1965). 24. KRATO~WL, :[. P . AND DELLICOLLI, H. T., Fed. Proc. Fed. Amer. Soc. Exp. Biol. 29, 1335 (1970).
Journal of Colloid and Interface~Sdence.Voh 59. No. 1, March 15, 1977
148
Dj'AVANBAKHT, KALE AND ZANA
25. RASSING, J'. AND WYN-JONES, E., Chem. Phys. Lett. 21, 93 (1973) ; I¢.ASSING,J., SAMS,P. J., AhrD WYN-JO~mS, E., J. C. S. Faraday Trans. I I 69, 180 (1973). 26. LA~,*G,J. AND ZANA, R., unpublished results. 27. LAN`G, J., TONDRE, C., ZANA, R., BAUER, R., HOFFMANN', H., AND ULBRICHT, W.~ ft. Phys. Chem. 79, 276 (1975). 28. ANIANSSON,E., WALL, S., ALMGREN, M., HOFF:MANN~H.~ KIEL:t~IANN~J'., ULBRICHT~~¢V.~ZANA~
29.
30. 31. 32.
R., LANG, ~., AND TONI)RE, C., .f. Phys. Chem. 80, 905 (1976). A~TANSSON,E. AND WALL, S., Y. Phys. Chem. 78, 1024 (1974); 79, 857 (1975). GARLAND,F. AND CHRISTIAN,S., J. Phys. Chem. 79, 1247 (1975). ZANA, R. AND LANO, ~[., Advan. Molec. Relax. Proc. 7, 21 (1975). KRESI~ECI~, G. C., HAMORI, E., DAVENPORT, G., ar,m SCrlERAOA,H. A., Y. Amer. Chem. Soc. 88, 246 (1966).
Journal of Colloid and Interface Science, Vol. 59, No. I, March 15, 1977