+
+
1180
Langmuir 1996, 12, 1180-1187
Structural Study of the Micellar Aggregates of Sodium and Rubidium Glyco- and Taurodeoxycholate G. Briganti Dipartimento di Fisica, Universita` di Roma “La Sapienza”, P.le A. Moro 5, 00185 Roma, Italy
A. A. D’Archivio, L. Galantini, and E. Giglio* Dipartimento di Chimica, Universita` di Roma “La Sapienza”, P.le A. Moro 5, 00185 Roma, Italy Received September 21, 1995. In Final Form: November 30, 1995X Some salts of bile acids increase the size of their micellar aggregates in aqueous solutions by varying parameters such as pH or ionic strength and give rise to transitions: aqueous micellar solution f gel f fiber f crystal. Helical fibers of sodium and rubidium salts of glycodeoxycholic and taurodeoxycholic acids (NaGDC, RbGDC, NaTDC, and RbTDC, respectively) were drawn from aqueous solutions and investigated by means of X-ray diffraction analysis to clarify the structure of their micellar aggregates and to verify whether the micellar structures of the sodium and rubidium salts were similar. In this case, the rubidium salts can be studied in place of the sodium ones by extended X-ray absorption fine structure spectroscopy. The X-ray patterns of the NaGDC, RbGDC, NaTDC, and RbTDC fibers showed a close resemblance and were interpreted by means of very similar unit cell parameters and helical structures, formed by trimers arranged in 7/1 helices. Calculations of interatomic distances provided a model of the 7/1 helix which satisfactorily packs into the unit cells of the fibers. Quasi-elastic light-scattering measurements carried out on aqueous micellar solutions up to a concentration of NaCl or RbCl of about 0.3 M supported the similarity among the structures of the NaGDC, RbGDC, NaTDC, and RbTDC micellar aggregates. Oligomers of small size were observed without NaCl or RbCl. The extent of micellar growth increased upon increasing NaCl or RbCl concentration. The micellar size, which seemed to be dependent on the peculiar cationanion Coulombic interaction starting from a NaCl or RbCl concentration of about 0.2 M, was in the following order: NaGDC > NaTDC ≈ RbTDC > RbGDC. Electromotive force measurements accomplished on NaTDC solutions at constant ionic medium provided the distribution of micellar sizes. Most of the aggregates have aggregation numbers that are a multiple of 3. The fraction of bound Na+ ions is high in accordance with an ordered structure like that of the 7/1 helix. Further support for the 7/1 helix came from the calculation of mean hydrodynamic radii using the helical model. The agreement with quasi-elastic light-scattering measurements at low bile salt concentration and within a wide range of ionic strength was satisfactory. The helical structure of the anions seems to be similar in the micellar aggregates of NaGDC, RbGDC, NaTDC, RbTDC, and tetramethylammonium taurodeoxycholate.
Introduction Some salts of dihydroxy bile acids form aqueous micellar solutions, gels, fibers, and crystals. The fibers can be drawn from aqueous solutions, and the crystals can be obtained from the solutions by slow evaporation or from the fibers by aging.1-5 These phases appear to be strictly related to each other, since their X-ray diffraction patterns show maxima of intensity at nearly equal Bragg angles. Thus, the structural units could be very similar in all these phases, and the determination of a crystal structure could provide a suitable model of the micellar aggregate. Models of the dihydroxy and trihydroxy bile acid salts were inferred from the determination of the crystal structure of sodium and rubidium deoxycholate1,6,7 (NaDC and RbDC, respectively) and taurodeoxycholate2,5 (NaTDC X Abstract published in Advance ACS Abstracts, February 15, 1996.
(1) Conte, G.; Di Blasi, R.; Giglio, E.; Parretta, A.; Pavel, N. V. J. Phys. Chem. 1984, 88, 5720. (2) Campanelli, A. R.; Candeloro, De Sanctis, S.; Giglio, E.; Scaramuzza, L. J. Lipid Res. 1987, 28, 483. (3) Campanelli, A. R.; Candeloro De Sanctis, S.; Chiessi, E.; D’Alagni, M.; Giglio, E.; Scaramuzza, L. J. Phys. Chem. 1989, 93, 1536. (4) Campanelli, A. R.; Candeloro De Sanctis, S.; Giglio, E.; Pavel, N. V.; Quagliata, C. J. Inclusion Phenom. Mol. Recognit. Chem. 1989, 7, 391. (5) D’Alagni, M.; D’Archivio, A. A.; Giglio, E.; Scaramuzza, L. J. Phys. Chem. 1994, 98, 343. (6) Campanelli, A. R.; Candeloro De Sanctis, S.; Giglio, E.; Petriconi, S. Acta Crystallogr., Sect. C 1984, C40, 631. (7) Coiro, V. M.; Giglio, E.; Morosetti, S.; Palleschi, A. Acta Crystallogr., Sect. B 1980, B36, 1478.
and RbTDC, respectively), and sodium glycodeoxycholate3 (NaGDC), glycocholate,8 and taurocholate.9,10 Moreover, the crystal structures of rubidium glycocholate and taurocholate and that of a monoclinic phase of NaTDC were solved but not yet published. Although the rubidium salts have no biological significance, they were taken into account because they can be studied in aqueous solution by means of extended X-ray absorption fine structure (EXAFS) spectroscopy, at variance with the sodium salts, owing to the low K-edge absorption of the sodium ions. EXAFS spectroscopy was used when the structural units of the sodium and rubidium salts in the crystals were very similar. The most recurrent structural units observed in the crystals of the dihydroxy and trihydroxy bile acid salts were helices with 6-fold,1,3 pseudo-6-fold,6 3-fold,2 or 2-fold screw axes,5,8,10 a structural unit with a 2-fold rotation axis,10 and a bilayer9 (see Figure 1 for some examples of structural units). The validity of some models was verified by studying aqueous solutions of the micellar aggregates and of their interaction complexes with probe molecules as, for example, bilirubin-IXR (BR) and a spin-labeled (8) Campanelli, A. R.; Candeloro De Sanctis, S.; Galantini, L.; Giglio, E.; Scaramuzza, L. J. Inclusion Phenom. Mol. Recognit. Chem. 1991, 10, 367. (9) Campanelli, A. R.; Candeloro De Sanctis, S.; D’Archivio, A. A.; Giglio, E.; Scaramuzza, L. J. Inclusion Phenom. Mol. Recognit. Chem. 1991, 11, 247. (10) D’Alagni, M.; Galantini, L.; Giglio, E.; Gavuzzo, E.; Scaramuzza, L. Trans. Faraday Soc. 1994, 90, 1523. (11) Esposito, G.; Giglio, E.; Pavel, N. V.; Zanobi, A. J. Phys. Chem. 1987, 91, 356.
+
Micellar Aggregates
+
Langmuir, Vol. 12, No. 5, 1996 1181
Figure 1. Projection along (a) the 65 axis of the NaGDC helix, (b) the 31 axis of the NaTDC helix, (c) the 21 axis of one RbTDC helix, (d) the 2-fold rotation axis of one NaTC structural unit, and (e) a direction parallel to the plane in which the NaTC bilayer extends. A thicker line represents an anion nearer to the observer. Full or broken lines indicate ion-ion and ion-dipole or hydrogen-bonding interactions.
cholestane. Small-angle X-ray scattering,11 nuclear magnetic resonance,1,12-14 electron spin resonance,11 EXAFS,15-17 and circular dichroism3,5,10,14,18,19 (CD) measurements together with energy calculations3,10,12,16 were performed. The type of helical structure found in the NaDC and RbDC crystals satisfactorily explains the experimental data of the micellar aggregates.1,4,6,11,12,14-16 This structure is similar to that of the NaGDC crystal (Figure 1a). Unfortunately, a less clear picture emerged from the NaTDC and RbTDC crystals.2,5 Therefore, the NaTDC and RbTDC fibers were studied because their structural units are more reliable models of the micellar aggregates than are the crystal structural units. In fact, the fiber is a system nearer to the aqueous micellar (12) Esposito, G.; Zanobi, A.; Giglio, E.; Pavel, N. V.; Campbell, I. D. J. Phys. Chem. 1987, 91, 83. (13) Chiessi, E.; D’Alagni, M.; Esposito, G.; Giglio, E. J. Inclusion Phenom. Mol. Recognit. Chem. 1991, 10, 453. (14) D’Alagni, M.; Delfini, M.; Galantini, L.; Giglio, E. J. Phys. Chem. 1992, 96, 10520. (15) Giglio, E.; Loreti, S.; Pavel, N. V. J. Phys. Chem. 1988, 92, 2858. (16) Burattini, E.; D’Angelo, P.; Giglio, E.; Pavel, N. V. J. Phys. Chem. 1991, 95, 7880. (17) Ascone, I.; D’Angelo, P.; Pavel, N. V. J. Phys. Chem. 1994, 98, 2982. (18) D’Alagni, M.; Forcellese, M. L.; Giglio, E. Colloid Polym. Sci. 1985, 263, 160. (19) D’Alagni, M.; Giglio, E.; Petriconi, S. Colloid Polym. Sci. 1987, 265, 517.
solutions than is the crystal. The NaTDC and RbTDC fiber structures were nearly equal and adequately described by 7/1 helices formed by trimers. Moreover, the similarity between the CD spectra of their interaction complexes with BR supported the hypothesis of similar micellar structures.5 On the other hand, preliminary X-ray fiber patterns5 and CD spectra3 of NaGDC seemed to point out a close resemblance between the NaGDC and NaTDC micellar structures. In this paper we present the X-ray analysis of the NaGDC, RbGDC, NaTDC, and RbTDC fibers, together with quasi-elastic light-scattering (QELS) and electromotive force (emf) measurements carried out on aqueous micellar solutions, in order to get information on the structure of the micellar aggregates. Experimental Section Materials. NaGDC and NaTDC (Sigma) were twice crystallized from water and acetone. RbGDC was obtained by adding a little less than the equivalent amount of RbOH (Aldrich, about 99.9%) to glycodeoxycholic acid (Sigma) and filtering the resulting aqueous suspension. Subsequently, acetone was added until the solution became cloudy. RbTDC was obtained from NaTDC by using Ba(NO3)2 and Rb2SO4 (Merck, Suprapur). Ba(NO3)2 was added to an aqueous solution of NaTDC. Barium taurodeoxycholate was filtered and recrystallized. RbTDC was prepared by adding a little more than the equivalent amount of Rb2SO4
+
+
1182
Langmuir, Vol. 12, No. 5, 1996
to an aqueous suspension of barium taurodeoxycholate and filtering BaSO4. The crystals of RbTDC and RbGDC were twice crystallized by diffusion of acetone in the aqueous solution of RbTDC or RbGDC. NaCl and RbCl (Merck, Suprapur) were used. Fibers of NaGDC, RbGDC, NaTDC, and RbTDC were prepared from 0.4-0.5 M aqueous solutions containing 0.2-0.3 M NaCl or RbCl. These solutions gradually increased their viscosity and the size of their micellar aggregates until gels were obtained after the solutions were allowed to stand about 24 h. These gels were drawn out into long glassy and brittle fibers. Fibers of NaTDC and RbTDC were also drawn from about 0.8 M aqueous solutions without NaCl or RbCl. Sometimes HI was used instead of NaCl or RbCl in order to prevent the presence of these salts in the fibers, when density and thermogravimetric measurements were performed. I- ions were oxidized to I2 and removed from the solution by flushing oxygen. All the compounds used in the emf and polarographic measurements were prepared and analyzed as previously described.20,21 X-ray Measurements. Fibers of NaGDC, RbGDC, NaTDC, and RbTDC are preferentially oriented microcrystalline specimens. Their X-ray diffraction photographs were recorded on flat and cylindrical films by means of Weissenberg, DebyeScherrer, and Buerger precession cameras, using Ni-filtered Cu KR radiation (λ ) 1.5418 Å). Some measurements were made on a MAR Research imaging plate mounted on a 12 kW rotating anode generator with graphite-monochromated Cu KR radiation. Density measurements were accomplished by flotation using a chloroform/chlorobenzene mixture, the density of which was determined by means of an Anton Paar DMA 02C densimeter. Thermogravimetric analyses were carried out by means of a Perkin-Elmer Model TGA7 apparatus equipped with a FT-IR Perkin-Elmer 1760X spectrometer. QELS Measurements. A Brookhaven instrument constituted by a BI-2030AT digital correlator with 136 channels and a BI-200SM goniometer was used. The light source was an argon ion laser model 85 from the Lexel Corporation operating at 514.5 nm. Dust elimination was achieved by a Brookhaven ultrafiltration unit (BIUU1) for flow-through cells, the volume of the flow cell being about 1.0 cm3. Nuclepore filters with pore size of 0.1 µm were used. The sample temperature was maintained constant within 0.5 °C by a circulating water bath. The samples were placed in the cell for at least 15 min prior to measurement to allow for thermal equilibration. Since the observed apparent diffusion coefficients did not depend on the exchanged wave vector in the range 30-150° in our experimental conditions, the timedependent light-scattering correlation function was analyzed only at the 90° scattering angle. The scattering decays were analyzed by means of cumulant expansion up to second order, because higher order contributions did not improve the statistic. The results are reported in term of the apparent hydrodynamic radius (Rh), obtained by the Stokes-Einstein relationship. emf and Polarographic Measurements. Radiometers, models pHM4 and pHM64, and potentiometers, Metrohm models 654 and 605, were used for emf measurements. Polarographic measurements were accomplished by means of Metrohm model 646 VA Processor connected with a Stand model 647. A DP50 differential pulse polarograph was used. Solutions at pH g 8.5 were protected against the absorption of CO2 from the atmosphere. The measurements were carried out in a thermostated room at 25 ( 1 °C.
Results and Discussion X-ray Analysis of NaGDC, NaTDC, RbGDC, and RbTDC Fibers. Very similar X-ray diffraction patterns of air-dried fibers of NaGDC, NaTDC, RbGDC, and RbTDC were recorded photographically. The most intense NaCl and RbCl interplanar spacings, known with great precision, were employed to calculate those of the four salts. The X-ray photographs of the NaTDC and RbTDC fibers (see Figure 8 of ref 5) were previously interpreted by means of nearly equal unit cells and helical structures.5 Lately we were able to get oriented specimens with a higher degree of ordering and to record X-ray photographs (20) Bottari, E.; Festa, M. R. Ann. Chim. (Rome) 1986, 76, 405. (21) Bottari, E.; Festa, M. R. Analyst 1994, 119, 469.
Briganti et al.
Figure 2. Two-dimensional hexagonal packing of alternate rows of nonequivalent helices (open and dotted circles): unit cell of the NaTDC or NaGDC crystal (broken lines), unit cell of the NaTDC fiber in the previous work5 (a ) 35.4, b ) 20.4 Å), and unit cell of the fibers in this work (full lines). Table 1. Observed (do) and Calculated (dc) Spacings (Å) of Layer Lines for NaTDC (c ) 45.0 Å), RbTDC (c ) 45.0 Å), NaGDC (c ) 45.1 Å), and RbGDC (c ) 45.1 Å) NaGDC
RgGDC
layer line
do
NaTDC dc
do
RbTDC dc
do
dc
do
dc
1 2 3 4 5 6 7 8 9 13 14 15 20 21
45.0 22.5 15.0 11.3 9.0 7.5 6.4 5.6 5.0 3.5 3.2 3.0 2.3 2.1
45.0 22.5 15.0 11.3 9.0 7.5 6.4 5.6 5.0 3.5 3.2 3.0 2.3 2.1
45.0 22.6 15.0 11.2 9.0 7.5 6.4 5.6 5.0 3.5
45.0 22.5 15.0 11.3 9.0 7.5 6.4 5.6 5.0 3.5
45.1 22.5 15.0 11.3 9.0 7.5 6.5 5.6 5.0 3.5
45.1 22.6 15.0 11.3 9.0 7.5 6.4 5.6 5.0 3.5
45.1 22.6 15.0 11.3 9.0 7.5 6.5 5.6 5.0 3.5
45.1 22.6 15.0 11.3 9.0 7.5 6.4 5.6 5.0 3.5
of better quality. Some additional low-angle equatorial reflections of weak intensity were detected for each of the four salts. Their spacings could not be indexed in the unit cell proposed for NaTDC and RbTDC, namely a ) 35.4 Å, b ) 20.4 Å, c ) 44.8 Å, R ) β ) γ ) 90°, c being the fiber axis.5 Since a ) b/tan 30°, the corresponding two-dimensional lattice can be derived from the trigonal or hexagonal one of the NaTDC2 or NaGDC3 crystal (Figure 2) which has a ) b ) 18.4 or 20.0 Å, respectively. Unit cells nearly equal to that of NaTDC, derived by doubling the a and b axes previously reported,5 were assigned to RbTDC, NaGDC, and RbGDC. The ratio b/a was kept equal to tan 30° (Figure 2). The unit cell parameters, the observed and calculated spacings of the layer lines and equatorial reflections, and their possible Miller indices are reported in Tables 1 and 2. Each unit cell contains eight helices with an identity period along the helical axis of about 45 Å and with a radius of about 10 Å, assuming that the helices can be described by closely packed cylinders. The spacings of the first 13 layer lines can be considered practically equal for NaTDC, RbTDC, NaGDC, and RbGDC (see Table 1). The seventh layer line (spacing of about 6.4-6.5 Å) is always the most intense and, hence, could represent the pitch of a helix with seven turns in the identity period. Thermogravimetric analyses of the NaTDC and RbTDC fibers pointed out that there are 3-5 water molecules for each salt molecule. This result and density measurements indicated that 20-22 salt molecules are present within the identity period along the helical axis. If 21 molecules are assumed, one turn contains 3 salt molecules (a trimer),
+
+
Micellar Aggregates
Langmuir, Vol. 12, No. 5, 1996 1183
Table 2. Observed (do) and Calculated (dc) Spacings (Å) and Miller Indices (hk0) in Parentheses of Equatorial Reflections for NaTDC (a ) 70.8, b ) 40.8 Å), RbTDC (a ) 71.2, b ) 41.2 Å), NaGDC (a ) 70.0, b ) 40.4 Å), and RbGDC (a ) 74.0, b ) 42.6 Å) NaTDC
RbTDC
do
dc (h,k)
dc (h,k)
35.6 26.8 23.5 20.4 17.7 13.6 11.6 10.1 9.8 8.8 8.0
35.4 (2,0) 26.7 (2,1) 23.6 (3,0) 20.4 (0,2) 17.7 (2,2) 13.6 (0,3) 11.6 (5,2) 10.1 (1,4) 9.8 (2,4) 8.8 (4,4) 8.0 (2,5)
35.4 (1,1)
dc (h,k)
do
dc (h,k)
dc (h,k)
34.9 26.5 19.3 17.5 13.5 11.5 10.1 9.7 9.0 8.0
35.0 (2,0) 26.5 (2,1) 19.4 (1,2) 17.5 (4,0) 13.5 (0,3) 11.5 (5,2) 10.1 (0,4) 9.7 (2,4) 9.0 (7,2) 8.0 (1,5)
35.0 (1,1)
20.4 (3,1) 17.7 (4,0) 10.2 (0,4) 9.8 (5,3) 8.9 (6,3)
10.2 (6,2)
do
dc (h,k)
dc (h,k)
35.6 26.9 20.6 17.8 13.5 11.9 10.3 9.9 9.0 7.8
35.6 (2,0) 26.9 (2,1) 20.6 (0,2) 17.8 (2,2) 13.5 (4,2) 11.9 (6,0) 10.3 (0,4) 9.9 (2,4) 9.0 (6,3) 7.8 (6,4)
35.7 (1,1)
do
dc (h,k)
dc (h,k)
37.0 24.7 21.3 18.6 14.2 10.7 10.3 9.4 8.5 6.1 5.8
37.0 (2,0) 24.7 (3,0) 21.3 (0,2) 18.5 (4,0) 14.2 (0,3) 10.7 (0,4) 10.3 (7,1) 9.5 (7,2) 8.5 (0,5) 6.1 (0,7) 5.8 (4,7)
36.9 (1,1)
NaGDC
13.5 (5,1) 10.2 (1,4)
RbGDC dc (h,k)
17.5 (2,2) 10.1 (6,2) 9.7 (5,3)
9.7 (7,1)
8.0 (8,2)
8.0 (7,3)
Table 3. Comparison of Estimated Average Intensity (EAI) of the Layer Line (Index) with Orders n of Bessel Functions for 20/7, 7/1, and 22/7 Helices n 0 1 2 3 4 5 6 7 8 9 10 11 12 13
20.6 (3,1) 17.8 (4,0) 13.5 (1,3) 11.9 (3,3) 10.3 (6,2) 9.9 (5,3) 8.9 (4,4) 7.8 (3,5)
dc (h,k)
EAI
20/7
7/1
22/7
very strong strong medium medium weak medium weak medium weak strong very strong medium strong medium weak very weak very weak weak medium
-20;0;20 -17;3 -14;6 -11;9 -8;12 -5;15 -2;18 -19;1 -16;4 -13;7 -10;10 -7;13 -4;16 -1;19
-7;0;7 -6;1 -5;2 -4;3 -3;4 -2;5 -1;6 -7;0;7 -6;1 -5;2 -4;3 -3;4 -2;5 -1;6
-22;0;22 -3;19 -6;16 -9;13 -12;10 -15;7 -18;4 -21;1 -2;20 -5;17 -8;14 -11;11 -14;8 -17;5
which very probably are related by a 3, 31, or 32 symmetry axis. In this case the resulting 7/1 helix has the trimer as the repetitive unit and could be generated by a rotation of 360°/7 ) 51.43°, 240°/7 ) 34.29°, or 120°/7 ) 17.14° and a translation of 6.4-6.5 Å. The helical transform theory,22 which allows discrimination between alternative models, supports this helix.5 A comparison of the permitted smaller orders n of Bessel functions for each layer line corresponding to the 20/7, 7/1, and 22/7 helices with the observed integral intensities of the same layer line is reported in Table 3. The 7/1 helix presents the best agreement (appreciable intensity observed only for layer lines characterized by zero or near-zero values of n). Thus, only the structural units shown in Figure 1a-b can be considered formed by trimers and, therefore, can be accepted as models of the micellar aggregates, whereas those of Figure 1c,d,e do not satisfy the intensity distribution and must be rejected. The hypothesis that the trimer could be the building unit of the helix was strongly supported by emf measure(22) Cochran, W.; Crick, F. H. C.; Vand, V. Acta Crystallogr. 1952, 5, 581.
dc (h,k)
21.4 (3,1) 18.5 (2,2) 10.7 (6,2) 10.3 (5,3) 8.5 (8,2) 6.1 (1,7)
10.2 (2,4) 8.5 (7,3)
ments of galvanic cells containing electrodes reversible to hydrogen, sodium, deoxycholate, glycodeoxycholate, and taurodeoxycholate ions carried out on aqueous micellar solutions of NaDC,23 NaGDC,24 and NaTDC25 as a function of pH, ionic strength, and bile salt concentration. Significant concentrations of trimeric species were found in the bile salts up to high ionic strengths in the following order: NaTDC > NaGDC > NaDC. The case of NaTDC is striking; most aggregates have a number of anions that is a multiple of three. This suggests that the trimer is a stable unit within the range of pH investigated (7-10) and that the trimers associate to form micellar aggregates. The arrangement of the anions in the 7/1 helix and the packing of the helices in the unit cell are very similar for the four salts (see Tables 1 and 2). The main variations among the four structures are the coordination of the cations and the location of the side chains. The two most promising starting models of the fiber structure are the 31 helix of the NaTDC crystal (Figure 1b) and the 65 helix of the NaGDC crystal (Figure 1a). The repeat of the trimer along the helical axis is flattened in the fibers (6.4 Å) as compared with that of the NaTDC crystal (7.1 Å), whereas the area of one helix in the ab plane of a fiber is greater than that in the NaTDC crystal.2 The radius of the 31 helix is about 16 Å, much more than half of 18.4 Å, the distance between the axes of two adjacent helices in the crystal. Nevertheless, the packing is made possible since adjacent helices are embedded one inside the other as cogwheels (see Figure 3 of ref 2). On the contrary, the empty space in the helix is partially filled when the trimers are rotated 51.43°, 34.29°, or 17.14°, and the fitting is forbidden. Calculations of interatomic distances were performed in order to ascertain whether 7/1 helices suitably pack into the unit cells of the fibers. The analysis was accomplished in the unit cell of the NaGDC fiber, assuming the geometry of the NaGDC anion observed in the crystal.3 (23) Bottari, E.; Festa, M. R.; Jasionowska, R. J. Inclusion Phenom. Mol. Recognit. Chem. 1989, 7, 443. (24) Bottari, E.; Festa, M. R. Monatsh. Chem. 1993, 124, 1119. (25) Bottari, E.; Festa, M. R. Langmuir, in press.
+
1184
+
Langmuir, Vol. 12, No. 5, 1996
Briganti et al.
Figure 4. Rh of 0.05 and 0.10 M NaTDC and RbTDC aqueous micellar solutions as a function of NaCl or RbCl concentration.
Figure 3. Projection of the anions of a trimer along the helical axis (top) and an axis perpendicular to the helical axis (bottom). The thicker line represents an anion nearer to the observer.
The hydrogen atoms were generated at the expected positions with C-H and N-H bond lengths of 1.08 and 1.00 Å, respectively. Since the NaGDC unit cell has the smallest volume, a satisfactory packing obtained in this cell is acceptable also for those of RbGDC, NaTDC, and RbTDC. The anion was moved as a rigid body in a righthanded rectangular framework OXYZ by rotations and translations. The conformation of the side chain was changed by rotating around its seven bonds. The three helices at a ) b ) 0, a ) b ) 1/4, and a ) 0, b ) 1/2 constituted the asymmetric unit (see Figure 2). The calculations pointed out that trimers similar to that of the NaTDC crystal structure with a 3, 31, or 32 symmetry axis cannot pack into the unit cell of the NaGDC fiber, even though the arrangement of the molecules in the trimer (Figure 1b) is modified. On the other hand, the distance between the helical axes of two adjacent helices range from 20.2 (NaGDC) to 21.3 Å (RbGDC) (see Table 2). Therefore, a reasonable value of the helical radius is about 10 Å, as in the case of the helices observed in the NaDC, RbDC, and NaGDC crystals.1,3,6 For this reason the 65 helix of NaGDC was proved as starting model. The loss of the 65 axis in the helix of the fiber did not allow the fitting of the helices, and the packing was more difficult when the trimer had a 31 or 32 symmetry axis. The anions were distributed in a more homogeneous mode on the lateral surface of the helix, thus hindering the approach of the helices. A good packing was obtained when a trimer with a 3-fold rotation axis (Figure 3) was rotated clockwise by 34.29° and translated 6.45 Å. The resultant 7/1 helix is stabilized by some hydrogen bonds involving N28, O25, O27, O31, and O32. A listing of the atomic coordinates of one anion of the trimer is available as Supporting Information. Assuming as reference the helix at a ) b ) 0, the one at a ) b
) 1/4 was rotated around and translated along the helical axis -2° and -0.3 Å, and that at a ) 0, b ) 1/2, 4° and -0.3 Å. The anticlockwise rotation was taken as positive. The distances of the atoms from the helical axis were about 1 Å less than those of the corresponding atoms in the 65 helix of the NaGDC crystal. The sodium ions and the water molecules were omitted in the calculations, but inspection of the 7/1 helix showed that there is enough room for them. Of course, since the parametric space was not thoroughly explored, other 7/1 helices could give rise to satisfactory packings, even though their structures should not differ much from that shown in Figure 3. The 7/1 clockwise helix is in agreement with the enantioselective complexation of the left-handed conformer of BR to the micellar aggregates of NaGDC,3 NaTDC,3,5 and RbTDC.5 The two wings of the butterflyshaped BR molecule have opposite screw sense in the leftand right-handed enantiomers. The left-handed screw sense coincides with that of the NaDC, RbDC,1,3,6,14 and 7/1 clockwise helices. Thus, the left-handed conformer fits these helices better than the right-handed one. Moreover, NMR data and potential energy calculations indicate that the C18 and C19 methyl groups, which are the most protruding in the 7/1 helix, are mainly involved in some interaction complexes of NaDC, NaGDC, and NaTDC micellar aggregates with probe molecules as, for example, BR,3,14 a spin-labeled cholestane,12 acridine orange,13 and aromatic hydrocarbons.1 These molecules interact with sites of the bile salts located at the boundary between the micellar aggregates and the bulk aqueous phase. Hence, the 7/1 helix provides an approximate structure of the fibers and is a promising model which could adequately represent the micellar aggregates in aqueous solution. QELS and emf Study of Aqueous Micellar Solutions. The apparent hydrodynamic radii Rh of 0.05 and 0.10 M NaTDC or RbTDC aqueous solutions are reported as a function of NaCl or RbCl concentration, respectively, in Figure 4. Our results agree with previous data obtained under similar conditions of concentration and ionic strength26,27 but extend to lower ionic strengths. The values of Rh, at a fixed NaTDC or RbTDC concentration and up to a 0.7 M NaCl or RbCl concentration, do not differ by more than 5% by exchanging Na+ with Rb+. Thus, the salt aggregation and/or the cation-anion interactions are similar. The Rh values almost coincide within 5% also changing the concentration of the bile acid salt with NaCl or RbCl less than 0.4 M. This behavior was already observed within a wider range of concentration with 0.15 M NaCl.26 (26) Mazer, N. A.; Carey, M. C.; Kwasnick, R. F.; Benedek, G. B. Biochemistry 1979, 18, 3064. (27) Schurtenberger, P.; Mazer, N.; Ka¨nzig, W. J. Phys. Chem. 1983, 87, 308.
+
+
Micellar Aggregates
Langmuir, Vol. 12, No. 5, 1996 1185 Table 4. NaTDC Micellar Solutions (0.01 M) at pH 9.5 Containing Different Molar Concentrations of N(CH3)4Cl: Experimental Rh (Å), 〈Rh〉 (Å), and Na+,a TDCAggregation Number and Percentages in Parentheses N(CH3)4Cl 0.09 0.19 0.29 0.39
Figure 5. Rh of 0.10 M NaTDC, RbTDC, NaGDC, and RbGDC aqueous micellar solutions as a function of NaCl or RbCl concentration.
0.49
Rh
〈Rh〉
Na+, TDC- aggregation number (percentage)
15.8 16.2 0, 1 (19.6); 1, 1 (9.7); 3, 3 (29.3); 3, 6 (23.7); 5, 6 (15.9); 12, 15 (1.7) 17.6 17.7 0, 1 (26.0); 3, 3 (25.3); 5, 6 (17.5); 7, 12 (21.2); 9, 12 (3.7); 12, 15 (5.1); 14, 18 (1.1) 19.9 18.8 0, 1 (17.5); 3, 3 (19.5); 7, 12 (35.2); 12, 15 (16.2); 20, 24 (0.9); 24, 27 (1.8); 27, 32 (2.2); 28, 36 (6.7) 21.4 22.1 0, 1 (16.7); 3, 3 (21.4); 13, 15 (18.6); 24, 27 (6.2); 30, 36 (21.3); 44, 50 (0.7); 49, 60 (15.2) 22.6 23.0 0, 1 (11.1); 3, 3 (13.0); 12, 15 (27.9); 22, 27 (9.8); 35, 39 (22.1); 53, 60 (8.3); 62, 72 (3.1); 71, 90 (4.7) 23.2 25.8 0, 1 (3.6); 3, 3 (15.1); 12, 15 (17.7); 22, 27 (19.4); 38, 45 (20.2); 57, 66 (11.7); 71, 81 (5.8); 72, 99 (6.6) 24.1 27.3 0, 1 (2.7); 3, 3 (6.4); 12, 15 (21.3); 22, 27 (27.7); 56, 69 (26.5); 70, 85 (9.7); 80, 105 (5.7)
The same plots are reported in Figure 5 for 0.10 M NaGDC and RbGDC together with those of NaTDC and RbTDC of Figure 4 for comparison. In this case the Rh experimental points are practically equal up to 0.2 M NaCl or RbCl. NaGDC shows a faster increase of Rh than does RbGDC, whereas the data of NaTDC and RbTDC fall in between. The Rh values of the Na+ salts, generally larger than those of the Rb+ salts, suggest a greater affinity of the Na+ ions for the taurodeoxycholate and glycodeoxycholate micellar aggregates. The different behavior of NaTDC and NaGDC, observed at NaCl concentration greater than 0.2 M, could be mainly ascribed to the charge density of the SO3- group, lower than that of the CO2- group, because it is distributed on a greater volume. Thus, the Coulombic interactions of the cations with CO2- are stronger than those with SO3-. If the cations are actively involved in stabilizing the micellar structure, the increase of the aggregate size passing from NaTDC to NaGDC is accounted for. However, the situation is reversed for RbGDC and RbTDC. A possible explanation is provided by the results of EXAFS measurements carried out on RbGDC and RbTDC aqueous micellar solution.28 Since the Rb+ ions show a disordered coordination, practically equal to that in water, they weakly stabilize the micellar aggregates. The apparent hydrodynamic radii of NaGDC, RbGDC, NaTDC, and RbTDC have values varying from 5.3 to 9.1 Å and very similar linear trends within the concentration range 0.05-0.50 M and without added NaCl or RbCl. Even if the low Rh values obtained for the four salts are affected by polar and apolar interactions among aggregates, the observed data point out that micellar aggregates of small size are present. The cations and anions of a small aggregate can be more exposed to the water molecules than those of the stable helical structure, and therefore, the Coulombic interactions of the four cation-anion pairs tend to be leveled. The distribution of micellar aggregation numbers was obtained for a 0.01 M NaTDC aqueous solution, containing N(CH3)4Cl,25 resorting to emf measurements by means of the method of the constant ionic medium.23-25,29 The distribution is independent of pH within the range 8.310.0. Protonated species were observed at pH lower than 8.3.25 The minimum number of micellar species necessary to satisfactorily fit the emf data was determined. These species, together with their percentages expressed as a function of the monomer (taurodeoxycholate anion) concentration, are reported in Table 4. Only a few aggregates have aggregation numbers of the anions that are not a
multiple of 3, and generally they are present at low percentages. The mean hydrodynamic radius 〈Rh〉 depends on the aggregation number, the mole fraction, and the calculated Rh of each micellar aggregate (the lightscattering form factor is in the limit where approximates unity).26,27 It can be computed from the actual distribution of micellar aggregates with the following assumptions. The length of a NaTDC anion was 19 Å (distance between an oxygen of the SO3- group and O25 when the molecule is approximately in the fully extended conformation). Its cross-sectional radius was 3.3 Å on the basis of a partial specific volume30 of 0.76 cm3 g-1 (monomer volume 659 Å3). The trimer (no dimers were detected by emf measurements25 at variance with NaDC23 and NaGDC24) has a 3-fold rotation axis and was represented by a disk with a thickness of 6.6 Å (diameter of the molecular cross section) and with a radius of 22 Å (sum of 19 Å, length of a NaTDC anion, and 3 Å, distance from the 3-fold rotation axis of the nearest oxygen atom of the SO3- group). The aggregates were formed by adding a disk of this size for each trimer. Those up to the dodecamer were considered oblate ellipsoids. The 7/1 helix geometry was used for the aggregates greater than the dodecamer (prolate ellipsoids), since it was supposed that the cooperative effect in the formation of the helix arises starting from the pentadecamer. In fact, a trimer i has the strongest interactions with trimers i ( 1 and i ( 2 in the 7/1 helix. In the pentadecamer, for the first time, there is a trimer (the third one) which gives rise to four of such interactions (3-2 and 3-4 of the type i ( 1 and 3-1 and 3-5 of the type i ( 2) with considerable energy gain in the helix formation. The radius of the helix was 10.7 Å (from the area of one helix in the ab plane of the unit cell of the NaTDC fiber). The contribution of each trimer to the height of the aggregate was 6.45 Å, except that of the first one, which is 12 Å on the basis of a model similar to that of NaGDC (Figure 3). For all the aggregates a water shell with 2 Å thickness was added. The hydrodynamic radii were computed assuming that the aggregates are oblate ellipsoids31 (flat cylinders) and prolate ellipsoids32 (elongated cylinders). The shape of the micellar aggregates is
(28) D’Angelo, P.; Di Nola, A.; Giglio, E.; Mangoni, M.; Pavel, N. V. J. Phys. Chem. 1995, 99, 5471. (29) Biedermann, G.; Sille´n, L. G. Ark. Kemi 1953, 5, 425.
(30) Matsuoka, H.; Kratohvil, J. P.; Ise, N. J. Colloid Interface Sci. 1987, 118, 387. (31) Perrin, F. J. Phys. Radium 1936, 7, 1.
0.59 0.74
a
Apparent number of bound counterions.
+
1186
+
Langmuir, Vol. 12, No. 5, 1996
Figure 6. Rh of 0.01 M NaTDC aqueous micellar solutions at pH 9.5 as a function of N(CH3)4Cl molar concentration (open circles). The black circles and squares represent the calculated values of 〈Rh〉 for the helical and KK models, respectively. The size of the open circles corresponds to the average standard deviation ((0.6 Å).
mainly disklike and globular within the 0.09-0.29 M range of N(CH3)4Cl concentration, whereas at higher ionic strength it becomes rodlike (Table 4). The low NaTDC concentration (0.01 M) allows a decrease of the effect of the intermicellar interactions and a better comparison of the calculated 〈Rh〉 with the QELS data. The 〈Rh〉 values of the polydisperse solutions (Table 4) are in good agreement with the experimental data up to 0.49 M N(CH3)4Cl (Figure 6). The small difference between calculated and experimental values, observed at 0.59 and 0.74 M N(CH3)4Cl, can be explained by the increase of the dressed excluded volume interaction, due to micellar growth, neglecting the preferential interaction effects between micellar aggregates and solvent components (water and N(CH3)4Cl). The agreement within the range 0.09-0.49 M suggests that the interparticle correlation effects due to charge interactions are small, and therefore, the micellar aggregates have a low charge density on their outer surfaces. A comparison with other models can be accomplished. The model of Small33,34 involves the formation of globular primary micelles with aggregation numbers of approximately 10 or less and rodlike secondary micelles from the polymerization of the primary micelles. The polymerization was supposed to occur in a linear fashion in order to account for QELS data.26,27 It could be consistent with the aggregation numbers of the micellar aggregates found by emf measurements only if the primary micelle is a trimer or has an aggregation number that is a multiple of 3. The disklike micellar model, proposed by Kawamura et al.35 (KK) for the dihydroxy and the trihydroxy bile salts on the basis of an electron spin resonance study, involves bile salt monomers oriented with their molecular long axes parallel or approximately parallel (probably 50% “up-pointing” and 50% “down-pointing” anions). The 〈Rh〉 values for the KK model were calculated, assuming that the disks have a thickness of 19 Å, the length of a NaTDC anion, and a radius inferred from the volume of each aggregate, computed by multiplying its aggregation number by the volume of one anion. This volume was increased from 659 to 774 Å3 (volume of one NaTDC and about four water molecules in the fiber) in order to improve the fitting with the experimental data. As for the helical model, a water shell with 2 Å thickness was added. The results (Figure 6) are in poor agreement with the QELS (32) Chu, B. In Laser Light Scattering; Academic Press: New York, 1974; p 212. (33) Small, D. M. Adv. Chem. Ser. 1968, No. 84, 31. (34) Small, D. M.; Penkett, S. A.; Chapman, D. Biochim. Biophys. Acta 1969, 176, 178. (35) Kawamura, H.; Murata, Y.; Yamaguchi, T.; Igimi, H.; Tanaka, M.; Sugihara, G.; Kratohvil, J. P. J. Phys. Chem. 1989, 93, 3321.
Briganti et al.
Figure 7. Fraction of bound Na+ to the micellar aggregates (black circles) and monomer percentage (open circles) at different N(CH3)4Cl concentrations.
data, especially at low ionic strength where the emf data are more reliable. An important point is the fractional binding of Na+, β, to the micellar aggregates. β was computed from the data of Table 4 as a function of N(CH3)4Cl concentration (Figure 7). It decreases from 0.65 to 0.55 within the range 0.090.29 M, suddenly increases to 0.74 at 0.39 M, and reaches a value of about 0.8 at 0.59 and 0.74 M. These high values suggest an ordered structure of the aggregates with Na+ ions firmly interacting with the anions. The consequent low charge density justifies the small interparticle correlation effects due to charge interactions, as it was supposed owing to the agreement between experimental Rh and calculated 〈Rh〉 within the 0.09-0.49 M N(CH3)4Cl range. The decrease of β within the 0.09-0.29 M N(CH3)4Cl range can be ascribed to the increase of the N(CH3)4+ ions. These progressively substitute the Na+ ions in the smaller aggregates (for examples, trimers, hexamers, and dodecamers) where the counterions are more exposed to the solvent than in the larger ones. The sudden increase of β at about 0.39 M N(CH3)4Cl agrees with the structural change of the aggregates (Table 4). They pass from a shape mainly disklike and globular to one rodlike as that of the 7/1 helix, in which the Na+ ions, possibly, are more strongly bound to the anions. The increase of the micellar size with the N(CH3)4Cl concentration favors the binding of the Na+ ions. At the same time the monomer concentration decreases, as it is expected, from about 3.0 to 0.3 mM within the range 0.090.74 M N(CH3)4Cl (Figure 7). The role of the N(CH3)4+ ions deserves some attention. Although there is a swamping excess of N(CH3)4+ ions, the β values show that, even though the micellar aggregates reach electroneutrality, the Na+ ions associated with the micellar aggregates are much more than the N(CH3)4+ ions (Table 4). Since only a few N(CH3)4+ ions are bound, very probably, to the smaller oligomers and to the ends of the helices, the free energy gain associated with the transfer of a Na+ ion from the bulk solution to the micellar aggregate is greater than in the case of the N(CH3)4+ ion. QELS measurements show that the Rh values of the NaTDC or tetramethylammonium taurodeoxycholate (N(CH3)4TDC) aggregates are nearly equal within the range of the investigated N(CH3)4Cl concentration, whereas NaTDC with NaCl differs only at 0.59 and 0.74 M, giving rise to higher Rh values (Figure 8). Again, the Na+ ions seem to have a greater affinity than do the N(CH3)4+ ions for the taurodeoxycholate aggregates at high ionic strength, as it was observed for the Na+ and Rb+ ions in the case of NaTDC and RbTDC. In conclusion, the results support that the helical structure of the anions is similar for NaTDC, RbTDC, N(CH3)4TDC, NaGDC, and RbGDC.
+
+
Micellar Aggregates
Figure 8. Rh of 0.01 M NaTDC aqueous micellar solutions at pH 9.5 as a function of N(CH3)4Cl (open circles) and NaCl (open triangles) molar concentrations. The open squares refer to 0.01 M N(CH3)4TDC aqueous micellar solutions at pH 9.5 as a function of N(CH3)4Cl molar concentration. The size of the symbols corresponds to the average standard deviation ((0.6 Å).
Conclusions The most important results of this study can be summarized as follows: (i) The NaGDC, RbGDC, NaTDC, and RbTDC fibers give rise to very similar X-ray patterns which can be interpreted by means of approximately equal unit cells and helical structures. These structures have been proposed to represent the corresponding micellar aggregates. The intensity distribution, thermogravimetric analyses, and density measurements agree with the presence of 7/1 helices formed by trimers. (ii) A packing analysis has been performed by means of distance calculations in order to check the reliability of the 7/1 helix, built up using as the repetitive unit a trimer having a 3-fold rotation axis. The 7/1 helices have been packed in the unit cell of the NaGDC fiber. (iii) emf measurements have been accomplished as a function of pH and ionic strength on aqueous micellar
Langmuir, Vol. 12, No. 5, 1996 1187
solutions of 0.01 M NaTDC, following the method of the constant ionic medium. They show that a trimer constitutes the building unit of the micellar aggregates in agreement with the X-ray results. The emf data have provided the distribution of micellar sizes (the aggregation numbers are almost always a multiple of 3) and the values of β, which indicate that the micellar aggregates have a low charge density. (iv) QELS measurements support that the NaGDC, RbGDC, NaTDC, and RbTDC micellar aggregates have similar structures. Small aggregates of equivalent size are formed without added salt. The sizes of the NaGDC, RbGDC, NaTDC, and RbTDC aggregates increase in a different way upon increasing the ionic strength, starting from a 0.2 M NaCl or RbCl concentration. The observed differences can be explained invoking the specificity of the cation-anion Coulombic interactions. Other measurements carried out on the same aqueous micellar solutions of NaTDC mentioned in iii have allowed the calculation of 〈Rh〉 using the 7/1 helix and KK models. The agreement is satisfactory for the helical model and poor for the KK model. The Na+ ions seem to have a greater affinity for the micellar aggregates than do the Rb+ and N(CH3)4+ ions. The X-ray and QELS data suggest a similar helical structure of the anions for the NaTDC, RbTDC, N(CH3)4TDC, NaGDC, and RbGDC micellar aggregates. Acknowledgment. This work was sponsored by the Italian Consiglio Nazionale delle Ricerche, Progetto Finalizzato Chimica Fine e Secondaria, and by the Italian Ministero per l’Universita` e per la Ricerca Scientifica e Tecnologica. Professor Emilio Bottari is gratefully acknowledged for having made available unpublished emf data and for helpful discussions. Supporting Information Available: Listing of the atomic coordinates (Å) of the NaGDC anion of the trimer used in the packing analysis (1 page). Ordering information is given on any current masthead page. LA950787K
