Langmuir 1997, 13, 4383-4390
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Dynamics of Resin-Bound Cholate Ions Studied by Deuterium NMR Spectroscopy C. T. Yim* Department of Chemistry, Dawson College, 3040 Sherbrooke Street West, Westmount, Que´ bec, Canada H3Z 1A4
G. R. Brown† and F. G. Morin Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montre´ al, Que´ bec, Canada H3A 2K6 Received February 28, 1997X
Deuterium NMR spectroscopy has been used to probe the dynamics of deuterated cholate (-2,2,4,4-d4) ions bound to two strong anion exchange resins: a poly(acrylamide)-based resin (-[CH2CH(CONH(CH2)12N+(CH3)3Cl-)-]n) and cholestyramine (Dowex 1X2-100). For the poly(acrylamide)-cholate system a nearly rigid Pake doublet with a horn splitting of 119 ( 1 kHz was observed between 0 and 20 °C, indicating that the bound ions experience a highly restricted environment. At higher temperatures, the spectra show an additional, relatively narrow and featureless peak superimposed onto the broader Pake doublet. An increase in temperature also causes the relative intensity of the narrow peak to grow at the expense of the broader signal, which disappears completely above 50 °C. Line-shape simulations show that, over the whole temperature range, the cholate ions execute slow reorientation motions with correlation times in the range of 10-4-10-6 rad/s. The spectra observed for the Dowex-cholate system display similar variations with temperature; however, a Pake doublet is only observed near 0 °C. These results suggest the presence of strong hydrophobic, possibly “cooperative”, interactions in the cholate-resin systems. To further probe the dynamics of bound ions in these systems the spin-lattice relaxation times were measured as a function of temperature. Analyses of the relaxation data with various motional models revealed small amplitude librations, with rates near the Larmor frequency. The difference observed between the poly(acrylamide) and Dowex systems is also discussed.
Introduction Cholic acid belongs to a group of physiologically important steroids, known as bile acids. Due to their amphiphilic nature, bile acids play a crucial role in lipid digestion, transportation, and absorption. The conversion of cholesterol to bile acids, which occurs in the human liver, represents the major pathway for the elimination of cholesterol. Anion-exchange resins, such as cholestyramine (i.e., Dowex 1X2-100) and colestipol, have been used widely to bind bile salts in the intestinal tract thereby effecting a reduction of serum cholesterol levels, especially the LDL levels.1 Other polymeric ion-exchange resins with various chemical structures, improved efficiency and specificity have been prepared and examined.2-4 Recent studies in this laboratory4 confirmed previous suggestions5 that in addition to ionic interactions hydrophobic interactions contribute significantly to the binding of bile salts by poly(acrylamide) based ion-exchange resins. Using deuterium NMR, we have also shown that the resin-bound cholate ions are capable of “solubilizing” nonpolar hydrocarbon molecules into the resin phase, suggesting the existence of strong hydrophobic interactions in these systems.6 These results support the view that bound * To whom correspondence should be addressed. † Present address: University of Northern British Columbia, Chemistry Programme, 3333 University Way, Prince George, British Columbia, Canada V2N 4Z9. X Abstract published in Advance ACS Abstracts, July 15, 1997. (1) Yalpani, M. Chem. Ind. 1996, 85-89. (2) Thomas, E. W.; Cudahy, M.; Spilman, C. H.; Dinh, D. M.; Watkins, T. L.; Vidmar, T. J. J. Med. Chem. 1992, 35, 1233. (3) Stredronsky, E. R. Biochim. Biophys. Acta 1994, 1210, 255. (4) Wu, G.; Brown, G. R.; St-Pierre, L. E. Langmuir 1996, 12, 466. (5) Johns, W. H.; Bates, T. R. J. Pharm. Sci. 1969, 58, 179; 1970, 59, 329; 1970, 59, 788. (6) Yim, C. T.; Brown, G. R. Langmuir 1994, 10, 4195.
S0743-7463(97)00223-0 CCC: $14.00
cholate ions participate in the formation of micellelike surface aggregates within the resin phase.7 NMR spectroscopy has been employed widely in studies of heterogeneous systems. Relevant information has been deduced from line splitting, chemical shielding anisotropy, relaxation rates, and self-diffusion measurements. Among the commonly accessible nuclei, the deuteron has become a particularly popular probe for the study of molecular dynamics and organization in solid and in other anisotropic systems, such as micellar solutions,6 lipid bilayers,9 polymers,10 liquid crystals,11,12 and interfacial regions.13 Interesting 2H NMR studies have been conducted on the dynamics of surface groups of alkyl-modified silica in the “dry” state and in the presence of wetting solvents, surfactants and mesogenic molecules.14-16 Recently, line splittings and spin relaxation behavior have been determined for deuterated surfactant molecules adsorbed onto nonporous silica gel,17 porous alumina,18,19 and polystyrene latex.20,21 In some systems the spectra of bound groups (7) Le´onard, D.; Clas, S.-D.; Brown, G. R. React. Polym. 1993, 20, 131. (8) Chachaty, C. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 183. (9) Seelig, J.; Macdonald; P. M. Acc. Chem. Res. 1987, 20, 221. (10) Spiess, H. W. Adv. Polym. Sci. 1985, 66, 23. (11) Hoatson, G. L.; Vold, R. L. In NMR Basic Principles and Progress; Diehl, P.; Fluck, E., Gu`nther, R., Kosfeld, R., Seelig, J., Eds.; Springer-Verlag: Berlin, Heidelberg, Germany, New York, 1994; Vol. 32, p 1. (12) Muller, K.; Meier, P.; Kothe, G. Prog. Nucl. Magn. Reson. Spectrosc. 1985, 17, 211. (13) Grandjean, J. Annu. Rep. NMR Spectrosc. 1992, 24, 181. (14) Gangoda, M. E.; Gilpin, R. K.; Figueirinhas J. J. Phys. Chem. 1989, 93, 4815. (15) Gangoda, M. E.; Gilpin, R. K. Langmuir 1990, 6, 941. (16) Zeigler, R. C.; Maciel, G. E. J. Am. Chem. Soc. 1991, 113, 6349. (17) So¨derlind, E.; Stilbs, P. Langmuir 1993, 9, 2024; 1994, 10, 890 (18) So¨derlind, E.; Blum, F. D. J. Colloid Interface Sci. 1993, 157, 172. (19) So¨derlind, E. Langmuir 1994, 10, 1122.
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data are further analyzed to yield detailed models for the motions involved. Experimental Section
Figure 1. Structure of the cholate (-2,2,4,4-d4) ion.
or adsorbed molecules showed well-defined powder patterns, while in others only broad, featureless peaks were observed. These studies further reveal the presence of both fast and slow motions in these restricted systems. Deuterium NMR is dominated by quadrupolar interactions and is almost exclusively governed by the motions and orientation of the deuteron-containing bond (e.g., the C-D bond) relative to the applied magnetic field. A “rigid” C-D bond in non-oriented samples produces a rigid lattice powder pattern with a horn splitting ∆νstatic given by
∆νstatic ) (3/4)(e2qQ/h)
(1)
where (e2qQ/h) is the deuterium quadrupole coupling constant, usually taken to be 170 and 185 kHz for aliphatic and aromatic C-D bonds, respectively. In writing eq 1 the small nonzero asymmetry parameter η of the electric field gradient tensor has been neglected. The reorientation motions of the C-D bonds modulate the quadrupolar interactions and thus affect the observed line shape and relaxation time. A Pake powder pattern with reduced splitting will be observed when the reorientation rate about a definite axis is much faster than the quadrupole coupling constant and the motional average asymmetry parameter η can be taken as zero. The reduced horn splitting ∆νeff is then given by
∆νeff ) (3/4)(e2qQ/h)S
(2)
where S is known as the generalized order parameter, which can be related to the spatial restriction of the relevant motion.22 Various motional models have been proposed for the evaluation of the magnitudes and rates of the fast internal motions from the observed spectra and relaxation times. On the other hand, motions having rates comparable to the observed line width, i.e., 250 kHz, strongly affect the intensity and shape of the signal. They can be evaluated by employing quadrupolar echo line shape simulations.23,24 In this paper we report the measurements of 2H NMR spectra of deuterated cholate (-2,2,4,4-d4), Figure 1, bound to two different bile acid binding resins. For both samples, deuterium NMR quadrupole echo line shapes and T1 values were acquired as a function of temperature. The results clearly indicate the presence of slower motions of relatively large-amplitude, as well as small-amplitude, librations that occur on a nanosecond time scale. The dynamics of the bound cholate ions are discussed, and the (20) Macdonald, P. M.; Yue, Y.; Rydall, J. R. Langmuir 1992, 8, 164. (21) Kuebler, S. C.; Macdonald, P. M. Langmuir 1992, 8, 397. (22) Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546; 1982, 104, 4559. (23) Greenfield. M. S.; Ronemus, A. D.; Vold, R. L.; Vold, R. R.; Ellis, P. D.; Raidy, T. R. J. Magn. Reson. 1987, 72, 89 (24) Wittebort, R. J.; Olejniczak, E. T.; Griffin, R. G. J. Chem. Phys. 1987, 86, 5441.
Two strong anion exchange resins, Dowex 1X2-100 (cholestyramine, 2% cross-linked, 50-100 mesh, 3.3 mequiv/g) and a poly(acrylamide)-based resin (-[CH2CH(CONH(CH2)12N+(CH3)3Cl-)-]n, 4% cross-linked, 20-40 mesh, 3.4 mequiv/g), designated as PAA12, were used in this study. The former was obtained from Aldrich Co. and was further treated according to procedures described previously.25 The poly(acrylamide)-based resin was synthesized in this laboratory.4 Both were kept under vacuum at room temperature for 24 h prior to use. The deuterated cholic acid (-2,2,4,4-d4) was obtained from MSD Isotopes and was used without further purification. A sodium cholate (NaC) solution of ca. 6.0 mM was prepared by dissolving cholic acid-d4 in an equivalent amount of NaOH solution with subsequent dilution. Appropriate amounts of resin were added to 50 mL of NaC solution. These samples were left at room temperature, with occasional agitation for at least 1 week. The wet resin, which contained 2 mmol of NaC/g of resin, was transferred into either a 10- or 5-mm NMR tube and washed several times with small aliquots of deuterium-depleted water to reduce the intensity of the narrow peak from residual deuterium nuclei in natural water. This also decreased the concentration of free Cl- ions, thus minimizing possible effects due to chloride-cholate exchange. The sample tube was then sealed with a Teflon cap and epoxy resin. No noticeable change was observed in the spectra during the course of the investigation. Isotherms were determined for the sorption of nondeuterated sodium cholate (NaC) by resin PAA12. The NaC solutions of various initial concentrations, prepared with the addition of solid NaCl to maintain a constant sodium ion concentration of 6.0 mM, were mixed with appropriate amounts of resin. The equilibrium NaC concentrations were determined by HPLC using a Waters autosampler and a C-18 reverse phase column, following procedures described elsewhere.26 Most of the 2H NMR spectra were acquired with a Chemagnetics CMX-300 spectrometer operating at 45.99 MHz using the phase-alternating quadrupolar echo sequence ((π/2)x-τ1-(π/2)-xτ1-acquisition-(π/2)y-τ1-(π/2)-y-τ1-acquisition). The acquisition conditions and parameters were as follows: number of acquisitions, 5000-40000; π/2 pulse length, 3.5-4.0 µs; acquisition recycle time, 200 ms; dwell time, 1.5 µs; pulse delay time τ1, 22-100 µs. After Fourier transformation, the resulting spectra were further symmetrized. The spin-lattice relaxation times were measured using a saturation-recovery pulse sequence, consisting of a comb of closespaced π/2 pulses followed, after a suitable recovery period, by a quadrupolar echo sequence. Unless stated otherwise, the recovered magnetization was determined from the height of the echo maximum, resulting in a “powder-average” 〈T1〉 value. All T1 values were evaluated using a nonlinear three-parameter least-squares fitting procedure.27 For the Dowex-cholate sample at higher temperatures, the collection of spectra and measurements of relaxation times were performed with a Varian XL-300 spectrometer operating at 45.98 MHz and using the phase alternating quadrupolar echo sequence. The π/2 pulse length was 9.5 µs, and the pulse delay time was 20 to 100 µs. Simulations of deuterium powder line shapes were performed with a PC using a modified Wittebort program.24,28 All calculated line shapes were corrected for finite pulse length and convoluted with a Lorentzian broadening of 1.5 kHz.
Results Figure 2 shows the quadrupole echo spectra, recorded with τ1 ) 22 µs, for PAA12-cholate-d4 as a function of (25) Zhu, X. X.; Brown, G. R.; St-Pierre, L. E. J. Pharm. Sci. 1992, 81, 65. (26) (a) Zhu, X. X.; Brown, G. R. Anal. Lett. 1990, 23, 2011. (b) Snyder, L. R.; Glajch, J. L.; Kirkland, J. J. Practical HPLC Method Development; John Wiley & Sons: New York, 1988. (27) Sass, M.; Ziessow, D. J. Magn. Reson. 1977, 25, 263. (28) Yim, C. T.; Gilson, D. F. R.; Budgell, D. R.; Gray, D. G. Liq. Cryst. 1989, 14, 1445.
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Figure 4. Isotherms for the sorption of sodium cholate by PAA12 in 6.0 mM NaCl, at 22 °C (3) and at 60 °C (O).
Figure 2. 2H NMR spectra of cholate-d4 bound onto PAA12 resin at various temperatures, recorded with pulse spacing τ ) 22 µs. Note that the spectra at different temperatures are not plotted on the same vertical scale.
Figure 3. 2H NMR spectrum of solid sodium cholate-d4 at room temperature, recorded with pulse spacing τ ) 22 µs.
temperature. Between 0 and 20 °C, a nearly rigid Pake doublet with a horn splitting of 118-120 kHz was observed. These spectra also contain a small and narrow liquidlike central peak which can be attributed to the residual deuterium nuclei in water. The measured horn splitting is slightly smaller than the corresponding value of 124 kHz observed in the 2H spectrum of solid sodium cholate-d4 (NaC, Figure 3). The spectrum of solid NaC can be simulated as a rigid lattice spectrum with e2qQ/h ) 168 kHz and η ) 0, i.e., using the standard values for an aliphatic C-H bond. On the other hand the spectra of adsorbed cholate show distinct nonrigid characteristics, especially the horns which are considerably broader with a much slower falling off from the horns toward the center of the doublet. Due to these nonrigid features, the spectrum cannot be simulated by merely varying the quadrupole coupling constant and asymmetry parameter. At higher temperatures, an additional narrow featureless peak appears, with a line width of 15-30 kHz superimposed on the broader signal. The relative intensity of the broader signal decreases with temperature, and it disappears completely above 50 °C. However, the doublet
Figure 5. 2H NMR spectra of cholate-d4 bound by Dowex resin at several temperatures, recorded with pulse spacing τ ) 22 µs.
separation varies only slightly with temperature, from 120 ( 1 kHz at 1 °C to 113 ( 1 kHz at 50 °C. To determine whether the observed spectral change reflects a change in adsorption, isotherms were determined for the sorption of NaC by PAA12, both at 22 and at 60 °C. The isotherms as plotted in Figure 4 show only a small, insignificant decrease in the amount adsorbed at 60 °C. In addition, examination under a microscope revealed no changes in bead shape and size with temperature variation. These results indicate that there is minimal, if any, variation in the amount of “free” cholate ions, nor are there any significant structural changes in the resin gel phase. Therefore, these factors cannot be held responsible for the appearance of narrow spectral component at higher temperatures. A significant variation in spectral intensity with temperature accompanied the appearance of this narrow featureless peak. The signal intensity at 40 °C is less than one-quarter of that observed at 1 or 60 °C. This loss in NMR signal at the intermediate temperatures reflects a reduction of the magnetization at the time of the refocusing echo. Furthermore, over the whole temperature range from 1 to 60 °C, there are significant variations in line shape and spectral intensity with pulse delay time τ1 in the quadrupolar echo sequence. All these observations can be attributed to slow motions having correlation times in the range 10-4-10-6 s, that occur during the formation of the quadrupolar echo. The spectra of the Dowex-cholate system, in Figure 5, show similar variations with temperature. However, the broad doublet with horn separation of about 120 kHz was only observed at the two lowest temperatures studied, i.e., at 1 and 10 °C. The “powder average” spin-lattice relaxation times for the two systems were determined as a function of
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Figure 6. Temperature dependence of the spin-lattice relaxation times for cholate ions bound by ion exchange resins, PAA12 (O) and Dowex (4).
temperature. Although the four deuterons in the cholate ions are presumably nonequivalent, within the experimental error only a single exponential decay of echo amplitude was observed. The T1 values, shown in Figure 6, decrease with increasing temperature. The small T1 values suggest that the motions responsible for the spinlattice relaxation occur at rates approximating the Larmor frequency. It is of interest to note that, for the PAA12cholate system, no large change in T1 values was observed with the onset of the appearance of the narrow component, indicating that the two components have similar T1 values. Attempts were made to deconvolute the total intensity observed for this system at 30 and 40 °C into broad and narrow signals and to determine the T1 value of each component. At the two corresponding temperatures, values of 26 and 17 ms were obtained for the broad doublet and values of 17 and 12 ms for the narrow component. Although considerable uncertainty may be associated with these values, they indicate, at least qualitatively, that the narrow component has somewhat shorter relaxation times. Discussion The experimental data given above dictate the presence of two distinct types of motions, one having correlation times τc in the range 10-4-10-6 s which exert a strong effect on the line shape and signal intensity and the other with τc < 10-8 s, which determines the relaxation behavior. Several simple and physically meaningful motional models will be considered for their effects on the NMR spectra and 2H relaxation rates. Since the systems studied are highly heterogeneous and disordered, motions with complicated trajectories and broad distributions in both rates and amplitude are expected. Therefore, our aim is not to achieve an exact fit to the observed data but to evaluate simple models so as to determine whether they can account for the important spectral features and trends. By adopting this approach, we expect to reveal the essential attributes of the dynamic processes involved. The following discussion is focused primarily on the PAA12cholate system. Analysis of Line Shape. In Figure 7 the 2H spectra of cholate ions bound by PAA12 resin, at 1 °C, are shown as a function of pulse delay time τ1. The number adjacent to each line shape is the echo intensity (i.e., the signal intensity) normalized to the intensity at τ1 ) 22 µs. Both the line shape and signal intensity display strong dependence on τ1. As stated above, these features can be attributed to the presence of motions having correlation times τc in the range 10-4-10-6 s. One possible model for these motions involves the reorientation of the bound ion around its long molecular axis. Specifically, if the angles
Figure 7. Experimental and simulated 2H NMR spectra of cholate-d4 bound by PAA12 resin, at 1 °C with τ ) 22, 40, 70, and 100 µs. The number adjacent to each line shape is the corresponding echo intensity normalized to the τ ) 22 µs intensity.
β between individual C-D bonds and the reorientation axis are close to 54.7°, i.e., the magic angle value, fast reorientation would lead to the appearance of a featureless narrow peak as observed in the higher temperature spectra. At first glance it would appear that all of the spectral features at different temperatures can be understood in terms of this reorientational motion, provided that it has a wide distribution of rates. It can be shown that the intermediate-rate line shapes are effectively unobservable because of their extremely low intensities.29 Thus, for a broad distribution (standard deviation g3 decades) the observed line shapes will appear to be given by the simple sum of slow and fast motion limit line shapes; i.e., the spectrum is expected to consist of a relatively narrow center peak superimposed on the broad doublet, similar to those shown in Figure 2. However, more detailed line shape simulations based on this model failed to accurately reproduce the experimental spectra. Furthermore, the four deuterons of the cholate ion are attached to the rigid cyclopentaphenanthrene unit so that the four C-D bonds are expected to have different orientations with respect to the long molecular axis. Therefore, it is hard to justify the assumption that the angles between the individual C-D bond and reorientation axis are all close to the magic angle. A conformational search, using a commercial molecular modeling program (Hyperchem from Hypercube Inc.), yielded about 25 low-energy conformations. The angles β between individual C-D bond and the long molecular axis varied between 10 and 83°, with most falling in the range 25-75°. Therefore, we decided to simulate the broad components using a distribution of β values within the range 25-75°. Simulated spectra were calculated for β values of 25, 35, 45, 55, 65 and 75°, assuming a two-site rotation jump about the long molecular axis with jumping angles (∆φ) of 40, 45, 50, and 55°. The parameters used (29) Schadt, R. J.; Cain, E. J.; English, A. D. J. Phys. Chem. 1993, 97, 8387.
Dynamics of Resin-Bound Cholate Ions
for simulations were as follows: (e2qQ/h)eff ) 164 kHz and ηeff ) 0. It was found that simulations with ∆φ values outside the range 40-55° failed to reproduce the experimental line shapes shown in Figure 7. This restricted reorientation motion with relatively large jumping angles (∆φ) of 40-55° is also consistent with the proposed smallamplitude fast libration model based on the relaxation data (see below). The resulting spectra, obtained by simple addition of individual spectra calculated for a given reorientation rate assuming an equal probability distribution for both β and ∆φ values, were then compared with the experimental spectra. The reorientation rates were varied until the best fits were obtained. The simulated line shapes and relative intensities (the number adjacent to the corresponding line shape) are also presented in Figure 7. Although the line shapes are in reasonable agreement with the experimental spectra, the simulated signal intensity shows a weaker τ1 dependence. It should be pointed out that these simulations did not include the additional intensity decay arising from 1H2 H dipolar couplings. The echo intensity decay due to dipolar interactions is usually assumed to be an exponential function of pulse delay τ1 with a time constant T2d.30,31 Since relevant data are not available for this system, a rough estimate can be obtained from results for other polymeric systems; T2d values of 200-300 µs have been used to simulate the 2H NMR spectra of DNA oligonucleotides and of Nylon 66.30-32a It has also been found that these values remain more or less constant with change in temperature. Thus, a T2d value of 250 µs was chosen to calculate the additional echo intensity decay for our system.32b The calculated intensities, normalized to the τ1 ) 22 µs intensity and presented in parentheses in Figure 7, show better agreement with experimental values, but discernible differences remain. These small and systematic intensity differences between simulated and experimental spectra were also observed at other temperatures (see below). Simulations with rate distributions were performed, but they did not remedy these problems. Calculations performed using three-site and four-site rotation jumping models but with the same ∆φ values yielded line shapes similar to those of two-site jumping, but they produced a faster echo intensity decay than the experimental spectra. Although it is possible to reproduce the observed echo intensity decay using a model consisting of a combination of two- and three-site jumps, this approach was rejected because it seems more likely that the discrepancy reflects the fact that the slow reorientation cannot be treated as completely uniaxial, and deviation from uniaxial reorientation could accelerate the intensity decay. Since we wanted to keep our model simple and since the two-site jump model yields line shapes in reasonable agreement with the experiment, we will utilize this simple model for spectral simulation with the full awareness of its limitations. The echo intensity decay due to dipolar interactions will be calculated using a fixed T2d value of 250 µs. The bound cholate ions, situated inside the resin matrix and confined by the available space, may adopt a “stretched-out” conformation, as shown in Figure 1. Due (30) Hirschinger, J.; Miura, H.; Gardner, K. H.; English, A. D. Macromolecules 1990, 23, 2153. (31) Miura, H.; Hirschinger, J.; English, A. D. Macromolecules 1990, 23, 2169. (32) (a) Kintanar, A.; Huang, W. C.; Schindele, D. C.; Wemmer, D. E. Dorbny, G. Biochemistry, 1989, 28, 282. (b) A better fit results when a T2d value of 300 µs or higher is used. However, for spectra at 10 °C (not shown) and 20 °C, a value of 200 µs gives better fits.
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to the rigidity of the cyclopentaphenanthrene unit, the hydrophilic part of the bound ions tends to form hydrogen bonds with the surrounding water molecules.33 The hydrophobic regions of the bound ions can interact with each other or, in the case of PAA12, with the dodecyl group in the resin side chain, thereby leading to the formation of aggregates. The reorientation processes proposed above would interchange the hydrophobic and hydrophilic sides of the bound species and, thus, could disrupt the aggregates. The relatively low reorientation rates and the observation of almost rigid powder pattern testify to the presence of strong hydrophobic interactions in the aggregates. Because of the strong hydrophobic interactions, motions of neighboring groups tend to become cooperative and they can accelerate one another. The cholate ions, firmly attached to the resin pendent groups by ionic interaction, can be considered as part of the extended side chain. Motions involving any part of this extended chain, including the motions of the pendent groups, will affect the orientation of the C-D bonds and thus the observed deuterium spectra. With increasing temperature and motional rates, more intervening bonds become involved, and the deuterons situated at the end of the extended chain will execute large-amplitude and multiaxis reorientation motions. The combined effect of these motions is nearly isotropic, as is evident by the appearance of the featureless center peak. Due to the inhomogeneity of the system only some of the deuterons, those in the “free” domain, undergo the nearly isotropic motion; the deuterons in the “constrained” domain continue to execute the restricted jumping motion. Thus, the spectral pattern observed for the temperature range 20-50 °C can be viewed as the sum of the contributions from two different domains. As expected, the fraction of the line shape represented by the narrow middle peak and attributable to the deuterons in the free domain increases with increasing temperature. At 60 °C all deuterons execute a nearly isotropic motion. It is very difficult to propose a realistic model for the analysis and simulation of the featureless narrow peak. However, since the nearly isotropic motion is considered as originating from the restricted reorientation motion about the long molecular axis, a uniaxial 12-site (over 360°) reorientation model was employed, with β, the angle between C-D bonds and the reorientation axis, set to equal or nearly equal to 54.7°. Furthermore, a log Gaussian distribution of reorientation rates with low cutoff rate of 105 rad/s was assumed.34 Thus, the proposed model for the simulation of spectra at and above room temperature depended on four parameters: the fraction of constrained and free domains, the rate of the restricted motion in the constrained domain, the center rate, and the standard deviation for the log-Gaussian distribution of reorientation rates of the free domain. In Figures 8-10 the simulated spectra based on this model are compared with experimental spectra for temperatures of 20, 30, and 40 °C, respectively. Again, there is reasonable agreement in line shapes but discernible differences in relative intensities. The parameters used in the simulation are reported in Table 1. An increase in temperature greatly increases the fraction of deuterons in the free domain, but it does not significantly accelerate the average reorientation rates. The observed fast decay of the featureless peak with increasing τ requires a relatively narrow rate distribution (e1 decade) for the nearly isotropic motion. In the simulations presented above the effects of the (33) Carey, M. C.; Small, D. M. Arch. Intern. Med. 1972, 130, 506. (34) Connor, T. M. Trans. Faraday Soc. 1964, 60, 1574; Pschorn, U.; Ro¨ssler, E.; Sillescu, H.; Kaufmann, S.; Schaefer, D.; Spiess, H. W. Marcromolecules 1991, 24, 398.
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Figure 8. Experimental and simulated 2H NMR spectra of cholate-d4 bound by PAA12 resin, at 20 °C, with τ ) 22, 40, 60, and 80 µs. The number adjacent to each line shape is the corresponding echo intensity normalized to the τ ) 22 µs intensity.
Yim et al.
Figure 10. Experimental and simulated 2H NMR spectra of cholate-d4 bound by PAA12 resin, at 40 °C with τ ) 22, 40, 60, and 80 µs. The number adjacent to each line shape is the corresponding echo intensity normalized to the τ ) 22 µs intensity. Table 1. Spectral Simulation Parameters for the PAA12-Cholate System
temp (°C) 1 10 20 30 40
Figure 9. Experimental and simulated 2H NMR spectra of cholate-d4 bound by PAA12 resin, at 30 °C with τ ) 22, 40, 60, and 80 µs. The number adjacent to each line shape is the corresponding echo intensity normalized to the τ ) 22 µs intensity.
fast small-amplitude motions were not explicitly considered. Since these motions are expected to have the correlation times τc < 10-8 s, the so-called sequential method35 was employed, and their effect has been taken into account by using the average rather than rigid lattice parameters as input data for the simulation calculations. (35) Wemmer, D. E.; Ruben, D. J.; Pine, A. J. J. Am. Chem. Soc. 1981, 103, 28.
broad component (“constrained” domain) rate fraction (rad/s) 1.0 1.0 0.65 0.33 0.08
2.5 × 104 3.0 × 104 3.5 × 104 4.0 × 104 5.0 × 104
narrow component (“free” domain) center rate (rad/s)
std dev of log-Gaussian distribution of rates
n.a. n.a. 6 × 105 9 × 105 1.3 × 106
n.a. n.a. 1 decade 1 decade 1 decade
Spin-Lattice Relaxation. For PAA12-cholate-d4 the observed spectra in the temperature range 1-20 °C, shown in Figure 2, can be considered as axially symmetric powder patterns with a measured quadrupole splitting ∆νeff ) 119 ( 1 kHz and ηeff ≈ 0. As indicated above, this horn splitting is only slightly smaller than the corresponding value of 124 kHz, observed for solid sodium cholate-d4 (NaC). Preliminary measurements of the 2H spin-lattice relaxation time for solid NaC at 20 °C yielded values of 1.2 and 9 s, presumably corresponding to the nonequivalent deuterons in NaC crystals. A T1 value of several seconds indicates there remains some small librational motion in the solid state; thus we consider 125 kHz to be a reasonable approximation for the static ∆ν value, ∆νstatic in eq 1. When this value was combined with the observed ∆νeff obtained from the spectra of the bound cholate ions at different temperatures, eq 2 yielded values for the order parameter S in the range 0.90-0.96. These values are shown in Table 2 with the corresponding values for ∆νeff. Various motional models have been proposed to relate the amplitude and rate of the librational motion to the observed order parameter and relaxation rates. Below two different models are considered: (1) diffusion in a cone and (2) restricted diffusion about a discrete axis. These models have been applied to systems where molecular reorientation is expected to occur in a less-well defined manner, such as lipid bilayers, synthetic and biological polymers, and adsorbed species.36
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Table 2. Rate and Amplitude of Librational Motion for the PAA12-Cholate System diffusion in a cone
restricted diffusion
temp (°C)
∆νeff (kHz)
T1 (ms)
S
θo (deg)
τc (ns/rad)
∆ (deg)
τc (ns/rad)
1.0 10.0 23.0 30.0 40.0 50.0
120 119 118 118 114 113
54 ( 4 37 ( 4 31 ( 4 24 ( 3 16 ( 2 9.3 ( 1.5
0.960 ( 0.01 0.952 ( 0.01 0.944 ( 0.01 0.944 ( 0.01 0.912 ( 0.01 0.904 ( 0.01
13.4 ( 1.6 14.6 ( 1.5 15.8 ( 1.4 15.8 ( 1.4 19.9 ( 1.1 20.8 ( 1.1
7.8 ( 2.4 5.9 ( 2.0 5.7 ( 1.8 3.5 ( 1.9 1.2 ( 1.0
11.0 ( 1.2 12.1 ( 1.2 13.1 ( 1.2 13.1 ( 1.2 16.6 ( 1.0 17.4 ( 1.0
7.7 ( 2.4 5.9 ( 1.9 5.6 ( 1.9 3.4 ( 1.9 1.3 ( 1.0
In the “diffusion in a cone” model the C-D bond is assumed to wobble freely in a cone of semiangle θo with diffusion constant Dw.37 The generalized order parameter S is then given by
S ) (1/2) cos θo (1 + cos θo)
(3)
Since the motion is symmetric with respect to the cone axis, the model presupposes a zero value for ηeff. The 2H spin-lattice relaxation rate is given by 2
ωQ 1 ) [J (ω) + 4J2(2ω)] T1 3 1
(4)
where ωQ ) (3π/2)(e2qQ/h). For this model, highly accurate spectral density functions Jm(ω), expressed in terms of three correlation times (τo, τ(1 and τ(2), have been derived by Lipari and Szabo.38 The three correlation times are functions of the diffusion constant Dw. However, for small θo, the powder-average T1 value can be more conveniently expressed as a function of a single “effective” correlation time τc39
〈〉 ( )
ωQ2 1 ) sin2 2θrms [J(τc,ω) + 4J(τc,2ω)] T1 10
(5)
where 〈 〉 indicates the average over all orientations of the field relative to the molecular fixed axis system, and J(τc,ω) is the usual spectral density function:
J(τc,ω) )
τc 1 + (τcω)2
(6)
The root mean square fluctuation in θ, θrms, is equal to (θo2/2)1/2. Using eq 3, θo can be calculated from the corresponding S value. Inserting the measured values of 〈1/T1〉, e2qQ/h ()170 kHz), ω/2π ()45.99 MHz), and θo into eqs 5 and 6 results in two τc values for each temperature. Only one of these is consistent with the observation that T1 decreases with increasing temperature. The derived values of θo and τc are listed with the measured T1 values in Table 2. For the uniaxial restricted diffusion model, the Gaussian distribution of libration angles proposed by English and colleagues was assumed;30 in further discussion this model is referred to as the Gaussian restricted diffusion model. In accordance with this model, and also with the model presented above for line shape analysis, the C-D bonds are assumed to execute fast small angle librational motion about a unique axis, the long molecular axis. The angle between the C-D bonds and the reorientation axis is fixed at a value β, and the librations relative to its equilibrium position φ ) 0 are described by a Gaussian azimuthal distribution P(φ) of standard deviation ∆. (36) Vold, R. R.; Vold, R. L; Adv. Magn. Opt. Reson. 1991, 16, 85. (37) Lipari, G.; Szabo, A. Biophys. J. 1980, 30, 489. (38) Lipari, G.; Szabo, A. J. Chem. Phys. 1981, 75, 2971. (39) Torchia, D. A.; Szabo, A. J. Magn. Reson. 1982, 49, 107.
P(φ) )
1
x2π∆
( )
exp
-φ2 2∆2
(7)
Simple calculations show the motionally averaged electric field gradient tensor usually does not have axial symmetry, i.e., ηeff > 0 and Vxx - Vyy > 0.40 However, since the experimental spectra show axially symmetric patterns with relatively broad horns, for small amplitude librations, it seems justifiable to relate the horn separation to the average of two tensor elements, Vxx and Vyy. The order parameter S is then given by
1 S ) (3 cos2 β - 1 + 3 sin2 β exp(-2∆2) + 8 [9(3 cos2 β - sin2 β exp(-2∆2) - 1)2 + 36 sin2 2β exp(-∆2)]1/2) (8) For the line shape analysis β values in the range 2575° were used. In this calculation an average value of 60° was employed. Equation 8 relates S values shown in Table 2 to the Gaussian standard deviation ∆, which can be considered as the amplitude of the motion. The powder average spin-lattice relaxation rate can be expressed as30
〈〉 ( )
ωQ2 1 ) {sin4 β [1 - exp(-4∆2)] + sin2 2β [1 T1 10 exp(-∆2)]}[J(τc,ω) + 4J(τc,2ω)] (9)
Using the values given above for β (60°), ωQ, and ω, the correlation time τc and standard deviation ∆ can be extracted by fitting eqs 8 and 9 to the experimentally determined values for S and 〈1/T1〉. The results are also listed in Table 2. Again, one of the two possible τc values was selected on the basis of the observed temperature dependence of T1. Detailed calculations show variation in β values leads to slightly different ∆ values but very similar τc values. The tabulated results show that the diffusion in a cone model and Gaussian restricted diffusion model yield identical effective correlation times τc. As pointed out by Vold and Vold,36 in the fast motion limit the spectral intensity is rather insensitive to motional details. Physically different models often yield quantitatively similar estimates of correlation times, as is observed in this case. Furthermore, the libration amplitudes obtained from these two models are also reasonably close although a strict comparison of two quantities, θo and ∆, is unwarranted because of their model specific meanings. Thus, these models indicate that the bound cholate ions execute fast librational motions of rates of 108-109 rad/s and of amplitudes of 10-20°. These motions are responsible for the observed fast relaxation rates. The reduction in T1 with temperature can be attributed to the increase in both the rate and the amplitude of the librational motion. In the above analysis we have assumed that the librational motion is the only motion contributing to the (40) Hirschinger, J.; English, A. D. J. Magn. Reson. 1989, 85, 542.
4390 Langmuir, Vol. 13, No. 16, 1997
relaxation. It was further assumed that, for all cholate ions, the librational amplitude can be characterized by a single variable (θo or ∆) and its rate by a single correlation time. For the cholate-PAA12 system at the three lowest temperatures, these can be considered as acceptable approximations. However, for temperatures at 30 °C and higher the narrow component becomes substantial. The powder average T1 values listed in Table 1 are averages over both the narrow and broad components. In the line shape analysis the narrow components were attributed to cholate ions located in the free domain and undergoing nearly isotropic motion of rates in the order of 106 rad/s. Detailed calculations indicate that T1 values of about 500 ms may be expected for such motions. Thus, the nearly isotropic motion does not contribute significantly to the relaxation rates, and on the basis of the observed magnitude of T1, it is reasonable to assume that the cholate ions in the free domain execute similar librational motion of rates in the range of 109 rad/s. It should be pointed out that the S, θo or ∆ values were computed from the observed horn separation in the broad component and that τc values were, therefore, obtained with the assumption of the librational amplitude being the same for both the broad and narrow components. Of course it is not possible to substantiate the latter assumption since the corresponding doublet splitting was not observed. In fact, the observed decrease in the horn separation with increasing temperature suggests that the amplitude would be larger for molecules in the free domain. Therefore, the τc values listed in Table 2 for 30 and 40 °C, can only be regarded as rough estimations. The same reasoning also explains why a correlation time could not be obtained for 50 °C. Both models, the diffusion in a cone model with θo ) 20.8 and the Gaussian restricted diffusion model with ∆ ) 19.8 predict a T1 minimum of 13 ms, i.e., higher than the experimental T1 value at 50 °C. As stated above, both models are capable of reproducing the observed T1 value and its temperature dependence and lead to consistent values for libration rates and amplitudes. Other treatments of librational motion involve potential wells of various characteristics. For example, it has been shown that Gaussian distribution of libration angles is a good approximation for librational motions in a harmonic potential well.30 Thus, we can now consider the fast motion as librational motion in a potential well and the slow motion affecting line shape as jumps from one potential well to another. The T1 modeling yields a librational amplitude of about 15°, and spectral simulation results require a rotation jump of about 50° around the long molecular axis. At the present time we fail to understand the implication of this particular jump angle, i.e., 50°. It can be speculated that the relatively large angle attests to the cooperative nature of the jumping motion. The relatively long τc values (in the nanosecond range) indicate that the librational motion experiences a soft potential, as is expected for this system and other amorphous materials. Dowex-Cholate-d4. For the Dowex-cholate system only the spectra at the two lowest temperatures (at 1 and 10 °C; see Figure 5) show a narrow featureless peak superimposed on the broad doublet. At room temperature and above only the featureless narrow peak remains. The
Yim et al.
line shapes observed at 1 and 10 °C for the Dowex-cholate system are very similar to those of PAA12-cholate system at 30 and 40 °C. In addition, the T1 values also show corresponding similarities. We assume the same motional models can be applied for the analysis of 2H NMR data of the Dowex-cholate system. In the absence of the dodecyl chain in the pendent groups of the Dowex resin the hydrophobic interactions are expected to be weaker in the Dowex-cholate system. Consequently, the cholate ions experience less resistance to their motion, and the transition from nearly rigid spectra to a featureless peak should occur at lower temperatures. Conclusions We have described simple and plausible motional models which can account for the important spectral features and trends. The models have furnished a useful, although somewhat simplified picture which allows more quantitative discussion concerning the dynamics and the environment of the bound cholate ions. Of course, this does not offer assurance that some other models will not fit the experimental data equally well or better. We are of the opinion that the chosen models have yielded quantities that reflect the fundamental characteristics of the motions involved, specifically their amplitudes and their correlation times. We have demonstrated that, at lower temperatures, the cholate ions bound by PAA12 resin undergo slow restricted reorientational motions with relatively large jumping angles and with rates of 104-105 rad/s. At higher temperatures, with increasing rate and amplitude the reorientational motions in the less “constrained” domain become essentially isotropic, leading to the appearance of a narrow featureless peak. The fraction of cholate ions undergoing the near-isotropic motion increases gradually with temperature, reflecting the heterogeneous nature of the systems. We have shown that, in addition to the slow motion, the bound cholate ions execute fast librational motions. The spin-lattice relaxation rates are almost exclusively determined by the amplitude and the rate of these librations. Detailed analysis yields motional correlation times in the nanosecond range and a librational angle of about 15° at room temperature. The amplitude of the motion increases with temperature and leads to faster relaxation rates. The observations of rigid powder pattern and the relatively low reorientation rates suggest the presence of strong hydrophobic interactions which severely curtail the motional freedom of the bound cholate ions. The results also show that the hydrophobic interactions are stronger in the PAA12 resin than in the Dowex, a clear indication that PAA12 is a better binding agent for bile salts. The stronger interactions can be attributed to interactions with the dodecyl groups in the PAA12 side chain. Acknowledgment. Financial support in the form of operating grants from the Quebec Government (Fonds FCAR) is gratefully acknowledged. LA970223B
