J. Phys. Chem. 1981, 85, 3715-3720
3715
Self-Association of Cholesterol in Nonaqueous Solutionst Bruce W. Foster, Julle Robeson, Nobuo Tagata, John M. Beckerdite, Robert L. Hugglns, and E. T. Adams, Jr." Chemistry Department, Texas A&M University, College Statlon, Texas 77843 (Receive& May 19, 1981; In Final Form: August 3, 198 1)
The state of aggregation of cholesterol at various temperatures in CHCl, and in CCl, solutions has been determined by vapor pressure osmometry (VPO). There is hydrogen bonding by the CHC1, to the cholesterol, so the self-associationof cholesterol is weaker in CHC1, than in CCl,, where no solvent hydrogen bonding occurs. With both solvents the self-associationincreased as the temperature decreased. In CHC1, the self-associationis described by two models-an indefinite self-association with all odd species beyond monomer absent, or a monomer-dimer association. In CC14the self-association was best described by a monomer-trimer-hexamer model. Values of the thermodynamic functions for these self-associations are reported. Proton nuclear magnetic resonance studies on these solutions at 33.0 "C parallel the VPO studies. The chemical shift of the hydroxyl proton showed linear concentration dependence in CHCl,, whereas a parabolic concentration dependence was observed in CC4. These downfield chemical shifts indicated that hydrogen bonding was involved in the self-association. Introduction Cholesterol is one of the most ubiquitous lipids found in mammalian organisms. I t is a constituent of bile, lipoproteins, and membranes and is implicated in hardening of the arteries and in some types of gall stones. It is a precursor of bile acids. Dietary cholesterol is solubilized in the intestine by a combination of bile salts and lecithins. A study of the interaction of cholesterol with bile salts in aqueous solutions would be difficult since bile salts by themselves solubilize relatively little cholesterol; therefore, lecithin (natural lecithins are heterogeneous), supporting electrolytes such as KC1 or NaCl, and buffer components to control pH would be needed. In addition, Haberland and Reynolds2 reported that the solubility of cholesterol in water is extremely small, being 1.8 pg/mL or 4.7 pM, this concentration is below the sensitivity of commercial vapor pressure osmometers. A simpler approach to understanding the interaction of cholesterol with bile salts is to study the interaction with esters of bile acids in nonaqueous media. In this three-component system, one can see how changes in the number and/or stereochemical position of the hydroxyl groups affects the interaction with cholesterol. Before these studies can be performed, it is necessary to know the state of aggregation (or type of self-association) of the individual solutes in the desired solvents. In a previous publication we have reported on the state of aggregation of some bile acid methyl esters; these studies were carried out by vapor pressure osmometry (VPO). Additional experiments were carried out by using lH NMR and 13C NMR studies. Here we report on similar studies with cholesterol in CHCl,, a hydrogenbonding solvent, and in CC14, a non-hydrogen-bonding solvent. Cholesterol has been studied by a variety of experimental methods; very elegant studies using IR and lH NMR spectroscopic studies on the association of cholesterol and other related 3P-hydroxysteroidsin nonaqueous solvents have been reported by Feher, Wright, and McC~rmick.~They used IR studies in CHC13 and CC14 solutions as a qualitative guide. The interaction of cholesterol with CHCl, and the self-association were obtained from a series of 'H NMR experiments. Surprisingly, little 'Presented in part at the 71st Annual Meeting of the American Society of Biological Chemists and the 24th Annual Meeting of the Biophysical Society, New Orleans, LA, June 1-5, 1980. 0022-3654/81/2085-3715$01.25/0
or no experimental data are available on the state of aggregation (self-association) of cholesterol in nonaqueous solvents by VPOa5 This technique, which is based on vapor pressure lowering, can be used to test for the presence or absence of a wide variety of self-associationsunder ideal or nonideal conditions. If a self-association is present, one can usually find an approriate model to describe it and evaluate the equilibrium constant(s) and nonideal term for the model. Some VPO experiments on various dihydroxy and trihydroxy cholane derivatives in CC14at 28 "C have been reported by Kovac and Eglintod and by Bennett, Eglinton, and KovacS7 These studies were used in a qualitative sense; they did not report which type of association was present, nor were values of equilibrium constants or nonideal terms reported from their VPO data. They did attempt to order their association data on the basis of monomer-dimer association constants estimated from their IR data, but it is evident from their VPO data that some of the self-associations were more complex. Here we report on the temperature-dependent self-association of cholesterol in CHC1, and CCl, as determined by VPO. Some of these data will be used in the study of the interaction of cholesterol with various bile acid methyl esters. The concentration dependence of the chemical shifts, determined by 'H NMR spectroscopy, of the hydroxyl protons in the two solvents are reported also.
Experimental Section Materials. Cholesterol used was Sigma-grade 99+ % chromatographically pure A5-cholesten-3-01as received from Sigma Chemical Co. All solvents were of the highest spectral quality available and were used as received from (1) Small, D. M. In "The Bile Acids, Chemistry, Physiology, and Metabolism"; Nair, D. P., Kutchevsky, D., Eds.; Plenum Press: New York, 1971; Vol. 1, pp 249-356. (2) Haberland, M. E.;Reynolds, J. A. R o c . Natl. Acad. Sci. U.S.A. 1973, 70, 2313. (3) Robeson, J.; Foster, B.;Rosenthal, S. N.;Adams, E. T., Jr.; Fender, E. J. J. Phys. Chem. 1981, 85,1254. (4) Feher, J. J.;Wright, L. D.; McCormick, D. B. J. Phys. Chem. 1974, 78., 250. (5) A computer search of Chemical Abstracts indexes from 1967 through 1980 supports this contention. VPO measurements on cholesterol in CHCIS were reported by: Brezinski, J.; Glowala, H KornasCalka, A. Eur. Polym. J . 1973,9, 1251. However, they were concerned only with its use as a calibration standard and did not consider the association behavior. (6) Kovac, S.;Eglinton, G.Tetrahedron 1969,25, 3609. (7)Bennet, W. S.; Eglinton, G.; Kovac, S. Nature (London) 1967,214, 776.
0 1981 American Chemical Society
3776
The Journal of Physical Chemistry, Vol. 85, No. 24, 1981
Fisher Scientific Co. and/or MCB Manufacturing Chemists, Inc. Benzil used for calibration of the VPO was purchased from Eastment Kodak Co., recrystallized from methanol, and dried under a high vacuum at 40 OC for ca. 4 h. Vapor Pressure Osmometry (VPO). The VPO experiments were carried out on a Knauer vapor pressure osmometer equipped with a Knauer universal temperature measuring apparatus (essentially a Wheatstone bridge) and a chart recorder. The experimental procedure followed is described in earlier work^.^^^ Benzil was used as a primary external calibration standard. Because the monomer molecular weight of cholesterol is known, it was used as an internal standard. The results were comparable in all cases. N M R Spectroscopy. All NMR data were obtained at 100 MHz on a modified Varian Associates HA-100 spectrometer equipped with a Hewlett-Packard 200 ABR audio oscillator and digital frequency counter. Each spectrum was recorded after equilibration to an ambient probe temperature of 33.0 f 0.5 “C. For experiments in CHCl,, the spectrometer was locked onto the proton of the solvent and the chemical shift of the 3-hydroxy group measured relative to the lock frequency. CC14solutions were run with an internal coaxial capillary containing spectral-quality benzene for use as an external reference. The instrument was locked onto the benzene signal and the chemical shift of the 3-hydroxyl group was measured relative to benzene. Reproducibility measurements indicate that all values are accurate to ca. 0.005 ppm. Results were converted to 6 (ppm) from Me4Siby using the literature value of 7.27 ppm for the shift of both reference compounds.1°
Results Results from VPO Experiments. Quantities Needed for the Analysis of the Self-Association. The vertical deflections on the chart recorder were converted to AE values, where PE is the microvolts imbalance on the Wheatstone bridge circuit of the VPO apparatus. The plots of AE vs. c at various temperatures were smoothed as described p r e v i o ~ s l y .Values ~ ~ ~ of the osmotic coeffi, calculated from the relation cient, g (g = M l / M n a )were AE = Kvpc/Mna (1) where c is the total solute concentration in g/L, Kvpis an operational constant whose value depends on the temperature and on the solvent used, and M , is the apparent number average molecular weight. The quantity K w is determined from the calibration experiment. The osmotic coefficient, g is defined by (2) g = M l / M , , = M1/Mnc + B M l c / 2 where M 1 is the molecular weight of the monomer, MnCis the number average molecular weight, and BMl is the nonideal term. These quantities have their usual definitions: (3) M , = c / C ( c i / M i )= c M l / C ( c i / i ) Mi = iMl (i = 1, 2, ...) (4)
ci = kicli ( i = 2 , 3, ...) c = c1 + CkiCl”
(5)
(6)
(8) Lo, F. Y.-F.; Escott, B. M.; Fendler, E. J.; Adams, E. T., Jr.; Larsen, R. D.; Smith P. W. J. Phys. Chern. 1975, 79,2609. (9) Adams, E. T.,Jr.; Wan, P. J.; Crawford, E. F. Methods Enzyrnol.
1978, 48, 69. (10) Lambert, J. B.; Shurvell, H. F.; Verbit, L.; Cooks, R. G.; Stout, G. H. “Organic Structural Analysis”; Macmillan: New York, 1976; Chapter 3.
Foster et el.
.IO
6
30
20
lo
40
C(B/I)
Flgure 1. Plots of the osmotic coefficient g (EM,/&,) vs. concentration (g/L) for cholesterol in CHCl3 at 27 (N),32 (A),and 37 (0)OC. The solld lines represent the regenerated flt of the type I1 SEK model based on the equilibrium constants and nonideal terms given in Table I. The M,MWacurve (dotted line) for the 27 O C data is also shown.
Figure 2. Plots of osmotic coefficient vs. concentration (g/L) for cholesterol in CCI, at 27 (W), 32 (A),and 37 (0)O C . The solld lines were regenerated based on the 1-3-6 association model from equllibrium constants and nonldeal terms given in Table 11. The M1/M, curve (dotted line) is shown for the 27 O C data.
Here it is assumed that the natural logarithm of the activity coefficient far self-associating species i (i = I, 2, ...) is defined by In y i = B.Mlc (7) where B, is a constant whose value depends on the temperature and the solute-solvent combination. Note that B = B* + IJ/(1000M1) (8) where IJ is the partial specific volume of the associating solute. For simplicity it is assumed that all IJi values are equal. Figure 1 shows plots of g vs. c for cholesterol in CHC13 at various temperatures; it is evident from these plots that a temperature-dependent self-association is present, with the association increasing as the temperature decreases. Plots of g vs. c for cholesterol in CCll are shown in Figure 2. It is evident from this figure that a nonideal, temperature-dependent self-association is present; the extent of self-association seems to increase as the temperature decreases. Is is quite evident from a comparison of the two figures that the mode of self-association of cholesterol is different in the two solvents. In order to analyze the self-associations, it is useful to have available the apparent values of the weight average molecular weight, Mwa,and the natural logarithm of the weight fraction of monomer, In f a . These quantities are available from the experimental data. One notes that (9) Ml/Mwa = (d/dc)(cMl/Mna) = MI/Mwc + BM1c In f a =
Jc[(M1/Mna) -
11 d c / c
= In fl
+ [(Ml/Mna)- 11
+ BMlc
(10)
The Journal of Physical Chemlstty, Vol. 85, No. 24, 1981 3717
Self-Assoclatlon of Cholesterol
TABLE I: Self-Association of Cholesterol in CHCl, monomer-dimer association BMi, L/g
t, "C k , , L/g 27 (5.3c 0.1)x 32 (3.8f 0.1)x lo-' 37 (1.4f 0.05)x lo-'
T,K 300 305 310
type I1 SEK indefinite association k , L/g BMl, L/g variance
variance
(6.5 0.05)x 2.04 X lo-' (3.2c 0.1)x lo-' (1.3+ 0.05)X lo-' 2.26 x lo-' (6.1 0.05)x 1.16 x lo-' (2.4c 0.1)x lo-' (1.1+ 0.05)x lo-' 7.42x low6 (4.7c 0.03)x 10.' 1.9 x lo-' (8.2f 0.05)x lo-' (6.1 0.03)x lo-' 8.36 x 10" AH" = -24.4 f 7.3 kcal/mol AH" = -25.0 c 8.6 kcal/mol A Go,kcal/mol AS", cal/(mol deg) AGO, kcal/mol AS",cal/(mol deg) -1.4 k 0.05 -86c 26 -1.5 0.02 -88 + 32 -1.4 f 0.02 -87 30 -1.2 0.05 -84 25 -81 t 25 -0.71 f 0.002 -83 29 -0.61 * 0.03 +_
+_
+_
+_
+_
These quantities can be used to analyze self-associations as described previ~usly.~,~ The dashed-lineplots in Figures 1 and 2 show values of Ml/Mwa vs. c for the 27 "C data. VPO Experiments in CHC13. The plots of g vs. c (and also of Ml/Mwavs. c) in Figure 1 indicate that cholesterol undergoes a weak self-associationin CHCl3 The simplest self-association to analyze is a monomer-n-mer association. This model can be represented by
nP1 e P,
( n = 2, 3, ...) (11) where P represents the self-associating solute. For these associations the following relations a p p l ~ : ~ > ~ 5 = (2M1/Mna) - (Ml/Mwa) = (2M,/Md - M,/Mwc (12) fl
= [n/4(n - 1)][([
+ 2 - 2/n)
- ((5
I
' ' IISEK
.................... - - - - - - - - -& - - - - - - - - -C2c - - - - - - - - -165%-
+ 2 - 2/n)2 -
18wO
(8/n)(@- 1))1'21 (13) Here f l = cl/c is the weight fraction of monomer. The equilibrium constant, k,, is obtained from a plot based on (1 - f 1 ) /f," = k,cn-l
( n = 2, 3, ...)
calculated from eq 12; note that these values of 5 are independent of the model for the self-association. Values of fi were calculated for various monomer-n-mer models ( n = 2,3, and 4) by using eq 13, and plots based on eq 14 were constructed for these choices of n. These plots are shown in Figure 3 for the 27 "C data, and it is evident that the plot based on n = 2 gives a straight line with an intercept close to the origin, as required by eq 14. The curvature in the plots for n = 3 and n = 4 indicates-that these models fail. The nonideal term BM, was calculated from eq 2 by using the appropriate form of Ml/Mn,; for a monomer-dimer association (15)
The values of k2 and BM, at the various temperatures are listed in Table I. Although the monomer-dimer model gave a fair description of the observed data, we were not quite satisfied with the diagnostic plot based on eq 14. We believed that the intercept should be closer to zero. Thus, other models were investigated. Testing for various monomer-n-merj-mer models (e.g., 1-2-3, 1-2-4, 1-2-6, 1-3-6) yielded negative results. The next models examined were the various indefinite self-associations. These models are represented by
nP, e QPZ + mP3 + hP4 + ...
- - - - - -- -
~ ~ a m
c3
Flgure 3. Results of the analysis of the cholesterol/CHC13 system at 32 "C based on eq 14 and 20 for the monomer-n-mer models and the type I1 SEK model, respectively. All three temperatures gave similar results.
(14)
At various solute concentrations, c (g/L), values of 5 were
(Mi/Md = (1 + f1)/2
J
(16)
By making some simplifying assumptions, one can divide these indefinite self-associations into two general classes: (1) sequential, equal equilibrium constant (SEK) models and (2) attenuated equilibrium constant (AK) models.
Analysis of the cholesterol in CHCl:, data was attempted on the basis of four types of SEK and four AK-type models using previously described methods."J2 The best model found was a type I1 SEK; this association is described by
nP1 F?
QPg
+ hP, + LP, + ...
(17)
where all odd species beyond monomer are absent. It is assumed for this association that AGO is the same for any step. For this model, it has been shown that
5
= (2M,/Mna) - (Ml/Mwa) =
+
1 2x/(1 - x2)2 2[1 + (x/(l - 3c2))1 (18) 1 + 2 ~ / ( l- x ' ) ~ 1 + 4 ~ ( 1 x2)/(1 - x ' ) ~
+
provided 0 I x C 1. Here x = kc,
(19)
x/f, = kc
(20)
The plot of x / f l vs. c for the 32 "C data is also shown in Figure 3. A comparison of this plot to the ana_lagous monomer-dimer plot (also in Figure 3) reveals that both models give linear results, as required by eq 14 and 20, but the type I1 SEK plot comes closer to the origin. A comparison of the variances computed for the fit of the type I1 SEK model vs. the monomer-dimer model indicates that the type I1 SEK is the better model to describe the 32 and 37 "C data, whereas the 27 "C data appear to be equally ~
~~~~
(11) Beckerdite, J. M.; Wan. C. C.:Adams. E.T..Jr. B ~ .O D-~ Chem. YS. 1980, 22, 199. (12) Garland, F.; Christian, S. D.J. Phys. Chem. 1975, 79,1247.
9718
The Journal of Physical Chemistry, Voi. 65,No. 24, 1881
Foster et ai. fq/flq
I
10
30
c IWII
4Q
Flguro 4. Plots of percent deviation of the regenerated curves from the experimentally observed data for the monomer-dimer (broken line) and the type I1 SEK (solid line) models.
well described by both models (see Table I). The variance is defined by n
variance
E
1/(N - p) C :6
(21)
i=l
where 6i = [(M1/Mna),,M - (Ml/Mm)ddli, N is the number of data points, and p is the number of parameters. The values of Ml/M, (or g) calculated from the values of k and BMl reported in Table I were used to generate the g vs. c curves shown as the solid lines in Figure 1. The differences in the accuracy of the two models would be indistinguishable on the graph in Figure 1, so a deviation plot for the 32 "C data is presented in Figure 4. VPO Experiments in CCl& The plot of g vs. c (and also Ml/M, vs. c at 27 "C) shown in Figure 2 are characteristic of a nonideal self-association in which dimer is absent. Note that the limiting slope of a plot of g vs. c is lim (d/dc)(Mi/Mna) = c-.o if dimer is present (-k2 + BMi)/2 BM1/2 if dimer is absent (22) Also note that plots of g vs. c for nonideal monomer-n-mer associations with n = 3 or for monomer-n-mer-j-mer (1n-j) associations with n = 3 and j > n can show a maximum with the values of g > 1 in the vicinity of infinite dilution. It is possible to have a very small amount of dimer, provided k 2 < BM1 and still get a maximum, but this would imply a very strong nonideal term. Attempts to analyze the self-association of cholesterol in CC14as a monomer-n-mer association using values of n = 2, 3, 4, and 6 were unsuccessful. Also, attempts to analyze the data by various indefinite SEK and AK models proved fruitless. Thus, we tried to analyze the association with the monomer-n-mer-j-mer (1-n-j) model; these equilibria are represented by nP1 F? qP, + lPJ (23) n = 2, 3, ... j = 3, 4, ... j > n Since these associations involve two equilibrium constants and a nonideal term, one must use the quantities 4 and q in order to analyze the self-association. The quantity 4 is defined by eq 12 and the quantity q is defined by 7 = (Ml/Mwa) - In fa = (Mi/MWJ - In f i (24) Following previous procedures, one notes that the following relations apply: E = 2[n + nho' - 1) + f,o' - n)l/nj - (7+ In f1) (25)
f,, = li- 0' - 1)fl- 1/h + In fJl/o'
-
n)
(26)
= Afi)
fJ =
- fl - ffl
(27)
= k,,cq-l
(q
= n or j)
(28)
The substitution of eq 26 into eq 25 leads to one equation in one unknown, f i , which can be solved by successive approximations of fl, since 0 I f l I 1. Once fl is known, so is f,, (f, = cn/(kncln)),the weight fraction of n-mer from eq 26. Then the weight fraction of j-mer is obtained from eq 27. The values of the equilibrium constants can be obtained from eq 28. We analyzed for various 1-n-j models-1-2-3, 1-2-4, 1-2-6, 1-3-6, and 1-3-9. The model which gave a satisfactory solution was the monomer-trimer-hexamer (the 1-3-6) model. The plots based on eq 28 are shown in Figure 5 for the 27 OC data. the 1-3-6 model gave the best description, as judged by the variance (see eq 21) of any model tested for the self-association of cholesterol in CC14at all temperatures. The values of k3, k6, and BM1 are shown in Table 11. Thermodynamic Potentials. Before calculating the molar thermodynamic functions, A G O , AH", and AS", it was necessary to know the molar equilibrium constants ( K ) from the following relations: monomer-dimer K2 = k2(M1/2)
(29)
K = kM1
(30)
= kdM1)~/3
(31)
type I1 SEK 1-3-6 K3
Ke = k&M1)'/6 (32) The values of AGO, the standard Gibbs free energy change, were obtained from (33) AGO = -RT In K These values were used in the van't Hoff equation (34) to obtain the standard enthalpy change, AH". The van't Hoff plota for the CHC1, data and the CCll data are shown in Figure 6, A and B, respectively. The standard entropy change, AS", was obtained from AS" = (AH" - AG")/T (35) The values of the thermodynamic functions are shown in Table I and 11. Results From NMR Experiments. Plots of the chemical shift, 6 (ppm downfield from Me4Si), of the 3-hydroxyl proton as a function of cholesterol concentration are shown in Figure 7. Note that, although there is an obvious difference in the behavior of this group in the two solvents, the plots do converge as c 0, in agreement with theoretical prediction. These data were analyzed for possible monomer-n-mer associations by using the Lippert equation: l3 (AS/Cn-l)l/n = [(SM - 6,)nK]1/n - [(6M - 6m)i-nnK]1/"A6 (36)
-
where A6 is the observed shift at concentration C (molarity) minus SM, the shift extrapolated to C = 0 (Le., chemical shift of the monomer), ,6 is the micellar chemical shift, n is the aggregation number, and K is the molar equilibrium constant for the association. A plot of the left-hand side of eq 36 vs. AS should be linear if the system (13) Lippert, E.Ber. Bunsenges. Phys. Chern. 1963,67, 267.
The Journal of Physical Chemistty, Voi. 85, No. 24, 1981 3719
Self-Association of Cholesterol
TABLE 11: Self-Association of Cholesterol in CCI, trimerization kcal/ mol
A G O ,
t , "C
k , , (L/g)Z
(4.1 i 0.4) x (2.8 i (4.0 i 0.9) x (8.3 c (5.9 i 0.6) x loe4 (6.1 i (4.4 i 1 . 3 ) x (2.4 f (1.0 i (5.2 i 0 . 8 ) x (1.0 i (6.4 i 0.7) x AH" from van't Hoff plots
27 30 32 37 41 45
'0
t
BM,, L k
k , , (L/gY 0.3) x 1.3) x 0.6)x 0.6) x 0.1) x 0.1) x
low8 lo-'
(6.0 c (1.0 i (1.1i (1.8 c (1.5 i (1.6 i
0.1) X 0.01)X 0.01) X 0.02) X 0.01) X 0.01) X
-1.8 f 0 . 2 13.0 c 6.7 -1.8 i 0.4 12.8 r 7.0 -2.0 i 0.2 13.6 i 6.9 -1.9 i 0.6 12.9 i 7.6 -2.0 i 0.3 13.1 i 6.8 -2.2 i 0.2 13.5 i 6.9 +3.8 i 1.9 kcal/mol
lo-* lo-' lo-*
3T
A/'rimer
hexamerization
AS", cal/ (mol deg)
kcal/ mol
AS", cal/ (mol deg)
AGO,
-6.3 e 0.7 45.2 i 29 -7.0 i 1.1 47.1 c 30 -6.9 i 0.7 46.6 i 29 -7.9 i 1 . 9 48.7 i 32 -7.4 i 0.7 46.6 * 29 -7.5 i 0.8 46.4 f 29 +12.2 i 7.6 kcal/mol
A
2..
In K2
Flgure 5. Results of the analysis of the 27 "C data for the cholesterol/CCI, system as a nonideal monomer-trimer-hexamer association, based on eq 27 and 28.
associates with aggregation number n. N M R Experiments in CHC13. As indicated in Figure 7, the chemical shift of the hydroxyl proton changes gradually and linearly with respect to cholesterol concentration. The downfield shift with increasing concentration is characteristic of hydrogen-bonding solutes. Figure 8A shows the Lippert plots for n = 2 , 3 , and 4. The obvious indication is the presence of a monomer-dimer association. NMR Experiments in CC14. Figure 7 illustrates the strong, curvilinear downfield shift observed with increasing concentration of cholesterol in CClb The indication is that the degree of hydrogen bonding or other deshielding interaction(s) is much stronger in the nonpolar solvent. The Lippert plots (Figure 8B) for n = 2-6 might suggest that a monomer-trimer association exists, since the plot for n = 3 appears to be linear, while others show slight curvature.
Discussion It is very evident from Figures 1 and 2, and also from Figure 7, that the solvent significantly influences the self-association of cholesterol. In CHC13hydrogen bonding occurs between the solute and the solvent, and the data are best described as a type I1 SEK indefinite association at 32 and 37 "C and by either the monomer-dimer or the type I1 SEK model at 27 "C (see Table I). It is not surprising that the monomer-dimer model closely approximates the type I1 SEK association in this case, since the association is a weak one and, in the limit as c 0, the two models are virtually indistinguishable. With weak self-associations it is possible to find two models with the same number of parameters that describe the observed association equally we11.12 No solute-solvent hydrogen bonding occurs in CC14,and the observed self-association is stronger (Figure 2). The association in this solvent is best described with the nonideal monomer-trimer-hexamer model. The values of the molar association constants obtained from the analysis of the cholesterol/CHC13 system are comparable to those obtained by Feher, Wright, and
*
I
3:2
3.3
IB
t
l4
N
4A
In K3
A A
A
A
2-
Figure 6. (A) van't Hoff plots for the cholesteroKHCI:, system, based on the molar equilibrium constants reported in Table I11 (see eq 34). (B) van't Hoff plots for the association of cholesterol in CCI,. The equilibrium constants reported in Table I1 were converted to molar equilibrium constants by using eq 31 and 32.
TABLE 111: Molar Association Constants for Cholesterol in CHClSa
-
T.K
a
K,ll-2)
K,K(I1 SEK) (Feher et. al)
300 10.3 i 0.2 12.4 i 0 . 4 9.7 9 . 3 i: 0 . 4 7.4 30 5 7.4 i 0.2 310 2.7 i 0.1 3.2 i: 1 5.6 The units for equilibrium constants are L/mol.
McCormick at the same temperatures (see Table III).4 From the slope of the van't Hoff plot (Figure 6A), we obtained AH" of -25.0 kcal/mol; the AH" reported by Feher, Wright, and McCormick should have been -10.2 kcal/mol (see their eq 14). The difference might be explained in part by the fact that their van't Hoff plot was
3720
Foster et al.
The Journal of Physical Chemktty, Vol. 85,No. 24, 1981
'T
0.1
0.5
0.3 [choleslerol], M
Figure 7. The chemical shifts, 6 (ppm from Me,Se), as a function of concentraton of cholesterol (molarity) in CHCI, (0)and CCI, (0).
3.0
I \
almost athermal reaction. The resulting T ASo terms are positive, which might suggest a dominant entropy of mixing effect. Note that the resulting AGO values have a different temperature dependence than those for the solutions in CHC13.14 In the analysis of the 1-3-6 association (eq 23-28), the weight fractions of monomer (fJ and trimer (f3) are determined first, and the weight fraction of hexamer (f6) is obtained from f6 = 1 - fi - f 3 (eq 27). Thus, values for f6 tend to be less precise, especially if the association is weak, and one might expect more scatter in the (and their logarithms). This effect was observed. The concentration dependence of the chemical shifts of the hydroxyl proton (6oH) also reflects the solvent effect. In CHC1, the plot of aOHvs. c is linear with a very small slope; in CC14 the plot is parabolic (Figure 7). This behavior also mimics the IR behavior of cholesterol in both solvents (see Figure 1and 2 of ref 4). In both solvents the self-associationis attributed to hydrogen bonding involving the 3-OH group. A comparison of the self-association behavior, obtained by VPO, of cholesterol and some related compounds (methyl lithocholate and methyl deo~ycholate)~ indicates that in CHC1, the degree of self-association of cholesterol is in between that of the two bile acid esters. At 37 "C in CHC13 methyl lithocholate does not associate; methyl deoxycholate undergoes a monomer-dimer association that is stronger than that observed for cholesterol. In C C 4 cholesterol and the bile acid methyl esters all self-associate. The bile acid esters do not have a double bond between carbons 5 and 6. Feher, Wright, and McCormick, who also studied cholestanol," found that the IR spectra of cholesterol and cholestanol were virtually indistinguishable in both solvents, so that the presence or absence of a double bond in this instance did not seem to affect the self-association. Analysis of the 60H data using the Lippert equation (eq 36) indicated the presence of dimer in CHC13 (see Figure 8A), which parallels the momoner-dimer and the limiting case (c 0) of the type I1 SEK model obtained from the VPO data. Application of the Lippert equation to the cholesterol/CCl, solutions data (see Figure 8B) suggests the presence of a monomer-trimer association, but analysis of the VPO data suggests that the best model is a nonideal monomer-trimer-hexamer. The spectroscopic data do indeed point out that hydrogen bonding is present and that the 3-OH group is involved in the hydrogen bonds. This information is not available from the VPO experiments. However, the VPO technique allows one to test for and analyze a large variety of self-associations under ideal or nonideal conditions.
-
I 2.0
-!=%dL
3
1.0
2.0
3.0
Abpm
Figure 8. (A) Results of the analysis of the cholesterol/CHCI:, 'H NMR data (shown in Figure 7) based on the Lippert equation (eq 36) for n = 2, 3, and 4. (B) Lippert equation plots of the cholesterol/CCI, 'H NMR data (Figure 7) for n = 2, 3, 4, 5, and 6. The plots for n = 5 and n = 6 were indistinguishable on the scale shown.
for a temperature range of -25 to +50 "C, whereas ours ranges only from 27 to 37 "C. In calculating their K2values and doing the van't Hoff plot, Feher et al. corrected the hydroxyl proton chemical shifts for the hydrogen-bonding interaction between CHC1, and cholesterol. Our values of K (or of K2) were obtained from VPO data in which nonideal effects were considered. For the CHC1, system, the negative AS" values reflect in part an increasing order in the system with self-association and hydrogen bonding to the solvent. At each temperature, the T AS" term is slightly smaller in magnitude than the AH" term, giving rise to a small, negative AGO which becomes less negative as temperature increases. This is consistent with the temperature dependence of the association illustrated in Figure 1. With the CC14experiments, the van't Hoff plots (Figure 6B) had a very slight, negative slope, indicating a small, positive AHo(AH",,N 3.8 kcal/mol, m " 1 - 6 = 12.2 kcal/mol); Le., the net effect of the interaction is an
Acknowledgment. This work was supported by grants from the National Institute of General Medical Sciences (GM 23877) and the Robert A. Welch Foundation (A485). Dr. Nobuo Tagata was a Robert A. Welch Foundation Postdoctoral Fellow from August 1, 1978, to July 31,1979; his present address is Research Laboratories, Japan Synthetic Rubber Co., Ltd., Yokkaichi Development Laboratory, 100 Kawajiri, Yokkaichi, Mie, 510 Japan. Bruce W. Foster was a Robert A. Welch Foundation Undergraduate Scholar from June 1979 to May 1980. We are very grateful to Dr. Daniel H. OBrien and Mr. David L. Breeden of the Chemistry Department, Texan A&M University, for their assistance with the NMR experiments. (14)I t is interesting to note that hydrophobic bonding in proteins shows an increase in AGO with an increase in temperature (see: Scheraga, H. A. In "The Proteins", 2nd ed.; Neurath, H., Ed.; Academic Press: New York, 1963; Vol. I, pp 527-8.
