Thermodynamic Characterization of Bile Salt Aggregation as a

as a Function of Temperature and Ionic Strength Using. Isothermal ... For comparison with other systems, the thermodynamic parameters ΔGdemic and ΔS...
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Langmuir 2000, 16, 5267-5275

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Thermodynamic Characterization of Bile Salt Aggregation as a Function of Temperature and Ionic Strength Using Isothermal Titration Calorimetry P. Garidel,† A. Hildebrand,‡ R. Neubert,‡ and A. Blume*,† Martin-Luther-Universita¨ t Halle-Wittenberg, Institute of Physical Chemistry, Muehlpforte 1, D-06108 Halle/Saale, Germany and Martin-Luther-Universita¨ t Halle-Wittenberg, Department of Pharmacy, Wolfgang-Langenbeck-Str. 4, D-06120 Halle/Saale, Germany Received September 17, 1999. In Final Form: March 3, 2000 The critical micellar concentration (cmc) and the demicellization enthalpy ∆Hdemic of the primary aggregates of sodium cholate (NaC) and sodium deoxycholate (NaDC) in water and 0.1 M NaCl at pH 7.5 were determined by isothermal titration calorimetry (ITC). The cmc of NaC and NaDC in water and 0.1 M NaCl at pH 7.5 shows a minimum between 295 and 300 K. With increasing ionic strength, the cmc of the bile salts decreases. ∆Hdemic is strongly temperature-dependent but shows almost no dependence on the ionic strength. For comparison with other systems, the thermodynamic parameters ∆Gdemic and ∆Sdemic associated with the demicellization process were calculated using the pseudo-phase-separation model. From the temperature dependence of ∆Hdemic, the change in heat capacity ∆Cpdemic for the demicellization process was determined. The data obtained for ∆Cpdemic are positive and at 298 K have values of 250 J‚mol-1‚K-1 for NaC and 350 J‚mol-1‚K-1 for NaDC. These values correspond to changes in the exposed hydrophobic surface area of 1.1-1.5 nm2 per molecule. For NaDC, ∆Cpdemic decreases at 343 K to ∼250 J‚mol-1‚K-1, whereas ∆Cpdemic for NaC remains essentially unchanged. The calorimetric titration curves were simulated using a mass action model including counterion condensation for the aggregation process. The simulation of the titration curves yielded values for the aggregation number n. In the concentration region of the cmc, n is approximately 4-6 for NaC in water or 0.1 M NaCl and independent of temperature. For NaDC in water values of n of 7 and 12 were obtained at low temperature (284 K) in water and 0.1 M NaCl, respectively. For NaDC in water and 0.1 M NaCl, the aggregation number n decreases to 5 and 7, respectively, at 328 K.

Introduction Amphiphilic molecules are constituted of a hydrophobic group, usually a hydrocarbon chain, and an ionic or nonionic hydrophilic polar headgroup. Dispersed in water, these amphiphiles form different types of aggregates in which the hydrophobic moieties are shielded from water, the solvated hydrophilic groups being located at the surface of the aggregate.1 The state of aggregation of amphiphiles in an aqueous solution is a complex function of their structure, the charge of the molecules, and the aqueous solvent properties (concentration of the detergent, ionic strength, pH, temperature, etc.). Surfactants with aliphatic chains generally aggregate to micelles with aggregation numbers between 40 and 200, depending on the particular molecular structure of the amphiphile.2 The behavior of bile salts (Figure 1A) is more complex. Bile salts are physiological detergents in mammals and important cholesterol end products. In addition, they play a major role in intestinal lipid absorption. The bile salts are removed from the blood by the liver and secreted into the bile, and their physiological concentrations are of interest with respect to the interaction of these detergents with plasma membranes.3 The concentration of bile salts in the gall bladder is about 10-50 mM, in gall capillaries * Corresponding author: Institut fu¨r Physikalische Chemie, Martin-Luther-Universita¨t Halle-Wittenberg, Mu¨hlpforte 1, D-06108 Halle/Saale, Germany. E-mail: [email protected] † Institute of Physical Chemistry. ‡ Department of Pharmacy. (1) Tanford, C. The Hydrophobic Effect. Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980. (2) Moroi, A. Micelles. Theoretical and Applied Aspects; Plenum Press: New York, 1992. (3) Lasch, J. Biochim. Biophys. Acta 1995, 1241, 269.

∼5 mM, in the gut ∼4 mM, and much lower in the peripheral blood (∼0.02 mM).3 Cholesterol/lecithin microvillar-like vesicles are exocytosed into the gall capillaries, where they are solubilized by the bile salts in the form of mixed micelles. In contrast to classical detergents, where the hydrophilic headgroup and the lipophilic flexible aliphatic chains are clearly separated, bile salt molecules have a lipophilic surface, which is the convex side of the rigid steroid ring system, and a hydrophilic surface, which is the polyhydroxylated concave side of the molecule (Figure 1B). Because of their particular structure and the rigidity of the molecules, the aggregation properties are completely different from surfactants with aliphatic chains. Bile salt micelles have much smaller aggregation numbers.4-6 Furthermore, the aggregation process seems to proceed stepwise over a broad concentration range.7 Small et al.8-10 suggested a two-step model for the aggregation of bile salts. Initially, small aggregates with an aggregation number of less than 10 are formed where the hydrophobic surface of the molecules is shielded toward water. In a second step at higher concentration, secondary aggregates are formed by the interaction of the primary aggregates via formation of hydrogen bonds. This se(4) Jover, A.; Meijide, F.; Nu´n˜ez, E. R.; Tato, J. V. Langmuir 1997, 13, 161. (5) Jover, A.; Meijide, F.; Nu´n˜ez, E. R.; Tato, J. V.; Mosquera, M. Langmuir 1997, 13, 3590. (6) Janich, M.; Lange, J.; Graener, H.; Neubert, R. J. Phys. Chem. 1998, 102, 5957. (7) Mukerjee, P. J. J. Pharm. Sci. 1974, 63, 972. (8) Small, D. M.; Penkett, S. A.; Chapman, D. Biochim. Biophys. Acta 1969, 176, 178. (9) Carey, M. C.; Small, D. M. J. Colloid Interface Sci. 1969, 31, 381. (10) Small, D. M. Adv. Chem. Ser. 1968, 84, 31.

10.1021/la9912390 CCC: $19.00 © 2000 American Chemical Society Published on Web 05/03/2000

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Figure 1. A, Chemical structure of the bile salts sodium cholate (NaC) and sodium deoxycholate (NaDC), and B, structural formula of NaC, indicating the hydrophobic and hydrophilic parts of the molecule, respectively.

quential model was extended by Kawamura et al.11 who suggested a back-to-back association of bile salt molecules with alternating up and down orientation of the molecules, the hydrophobic surfaces thus shielded from water. An alternative model was suggested by Giglio and coworkers.12,13 In this model, the association of the molecules proceeds by polar interactions leading to a helical association of the monomers in the aggregate with their hydrophobic surfaces exposed to water. A whole range of different experimental methods have been applied to decide which of these models is correct9-20 but a definite consensus on the structure of the aggregates still does not exist. First, it is still not clear whether the primary aggregates are monodisperse.18,19 The consensus is that the aggregation number increases with concentration. The secondary aggregates observed at higher concentrations have aggregation numbers between 10 and (11) Kawamura, H.; Murata, Y.; Yamagushi, T.; Igimi, H.; Tanaka, M.; Sugihara, G.; Kratohvil, J. P. J. Phys. Chem. 1989, 93, 3321. (12) Campanelli, A. R.; De Sanctic, S. C.; Giglio, E.; Pavel, N. V.; Quagliata, C. J. Inclusion Phenom. Mol Recognit. Chem. 1989, 7, 391. (13) D′Alagni, M.; D′Archivo, A. A.; Galanti, L.; Giglio, E. Langmuir 1997, 13, 5811. (14) Gouin, S.; Zhu, X. X. Langmuir 1998, 14, 4025. (15) Zana, R.; Gu¨veli, D. E. J. Phys. Chem. 1985, 89, 1687. (16) Gu¨veli, D. E. J. Phys. Chem. 1986, 83, 123. (17) Lopez, F.; Samseth, J.; Mortensen, K.; Rosenqvist, E.; Rouch, J. Langmuir 1996, 12, 6188. (18) Coello, A.; Meijide, F.; Nu´n˜ez, E. R.; Va´zque Tato, J. J. Phys. Chem. 1993, 97, 10186. (19) Coello, A.; Meijide, E.; Nu´n˜ez, E. R.; Va´zque Tato, J. J. Pharm. Sci. 1996, 85, 9. (20) Hao, L.; Lu, R.; Leaist, D. G.; Poulin, P. R. J. Solution Chem. 1997, 26, 113.

Garidel et al.

60 and are formed by the association of the primary aggregates via hydrogen bonding between hydroxyl groups.8 For NaDC, it was also found that the addition of electrolyte induces the formation of larger aggregates.19 Isothermal titration calorimetry (ITC) has been used before to determine the critical micelle concentration (cmc) and the demicellization enthalpy (∆Hdemic) of a variety of surfactants, including bile salts, as a function of temperature.21-23 ITC has the advantage that the cmc and the thermodynamic parameter ∆Hdemic can be determined directly from the same experiment, whereas with other techniques ∆Hdemic has to be calculated from the temperature dependence of the cmc using the van’t Hoff reaction isobar. Therefore, these other methods require a high precision for the determination of cmc data, particularly when the heat of demicellization itself is not constant but temperature-dependent.1,2,21,24 In addition, the experimentally observed quantity, the reaction heat, is already a differential quantity, because changes in enthalpy caused by changes in concentration are measured. This improves the precision of the cmc determination as long as ∆Hdemic is sufficiently large. ∆Hdemic, the cmc, and the thermodynamic parameters ∆Gdemic (change in Gibbs energy) and ∆Sdemic (change in entropy) are usually calculated using the pseudo-phaseseparation model (first approach). This facilitates the comparison between different detergents and with reported data. The experimental data show that ∆Hdemic is clearly temperature-dependent.21 The heat capacity change, ∆Cpdemic, obtained from the temperature dependence of ∆Hdemic, contains information on changes in exposed hydrophobic surface area when the aggregates dissociate. This finding can be used for making suggestions about the structure of the micelles in terms of waterexposed hydrophobic surface area in the aggregates.21,25-27 For the low aggregation numbers found for bile salt micelles the pseudo-phase-separation model is a crude approximation. The aggregation process can be described better using a mass action model.2,18,19,21,28 To derive the thermodynamic parameters for the aggregation process, the ITC titration curves have to be simulated (second approach) with the aggregation number n as one of the variable parameters. We will show that with this model additional information on the aggregation number n as a function of salt concentration and temperature can be obtained. Materials and Methods Chemicals and Sample Preparation. The bile salts sodium cholate (NaC) and sodium deoxycholate (NaDC) were obtained from Sigma and were used without further purification. Sodium chloride of p.A. grade was purchased from E. Merck, Darmstadt (Germany). Surfactant solutions of a definite concentration were freshly prepared by weighing a certain amount of surfactant and dissolving it in deionized water or in 0.1 M NaCl. The pH of the solutions was measured with a pH-meter equipped with a glass electrode and adjusted to 7.5 with dilute NaOH. (21) Paula, S.; Su¨s, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742. (22) Keller, M.; Kerth, A.; Blume, A. Biochim. Biophys. Acta 1997, 1326, 178. (23) Majhi, P. R.; Moulik, S. P. Langmuir 1998, 14, 3986. (24) Blokzijl, W.; Engberts, J. B. F. N. Angew. Chem. 1993, 195, 1610. (25) Garidel, P. Ph.D. Thesis, University of Kaiserslautern, Germany, 1997. (26) Blume, A. In Biocalorimetry: Applications of Calorimetry in the Biological Sciences; Ladbury, J. E., Chowdhry, B. Z., Eds.; John Wiley and Sons Ltd.: New York, 1998; p 77. (27) Garidel, P.; Blume, A. Langmuir 1999, 15, 5526.

ITC Determination of Bile Salt Aggregation Isothermal Titration Calorimetry. ITC measurements were performed with a MicroCal Omega titration calorimeter and an MCS ITC unit (MicroCal, Inc., Northhampton, MA). The reaction cell (V ) 1.34 mL) was filled with water or 0.1 M NaCl solution (pH 7.5, degassed). The removable integrated injectionstirrer syringe (250 µL) was loaded with the surfactant and the two solutions were mixed by injecting 5- to 10-µL aliquots into the cell. The injection-stirrer syringe was rotated at constant speed (∼400 rpm) throughout the experiment. Determination of Heats of Demicellization. Aliquots (25 × 10 µL or 50 × 5 µL) of micellar surfactant solution (200 mM NaC, 100 mM NaDC) were injected into the reaction cell. A high enough concentration of the surfactant in the syringe was chosen so that with increasing surfactant concentration in the reaction cell, ct, the cmc was reached during the experiment. The injection duration was 7 s, and the equilibration time between two consecutive injections was 6-10 min. The ITC experiments were performed in the temperature range between 10 and 80 °C. Three to five individual measurements at each temperature (( 0.1 K) were executed. Integration of the peaks gave the reaction enthalpy as a function of total surfactant concentration in the cell. The values for ∆Hdemic were determined as described before21 and as shown below. The precision in ∆Hdemic determination is approximately (5%. Determination of Heats of Dilution. The injection syringe was loaded with a monomeric surfactant solution (concentration well below the cmc) and injected into water or 0.1 M NaCl (degassed, pH 7.5). Six to eight injections (25-µL aliquots per injection) were performed, and the reaction heats were averaged. Simulation of Titration Curves. The simulation of the calorimetric titration curves on the basis of the mass action model (see below) was performed by converting the equations of the mass action model to appropriate equation files for the computer software SCIENTIST, Version 2.02 (MicroMath, Inc., Salt Lake City, Utah). The calorimetric titration curves were fitted using five adjustable parameters as described below with the nonlinear least-squares fitting routine of the program.

Results and Discussion Figure 2A shows an experimental ITC titration curve of NaC in 0.1 M NaCl (pH 7.5) at 284.3 K. A micellar solution of NaC (200 mM, in 0.1 M NaCl, pH 7.5) was titrated in 10-µL steps (25 injections) into 0.1 M NaCl at pH 7.5. Each injection produces an exothermic heat effect, which gradually decreases with the number of injections. By integration of the peaks (Figure 2B) the reaction enthalpy as a function of total detergent concentration in the cell, ct, was obtained. The enthalpogram (Figure 2B) can be subdivided into two concentration ranges at low and high concentration, where the reaction enthalpies are almost constant, and an intermediate regime, where the reaction enthalpy changes drastically. The large exothermic peaks observed for the first injections are caused by two or three processes, depending on the hypothetical dilution scheme. In the first scheme, the aggregates are diluted to the final concentration in the cell and the dissociation occurs at this concentration. In the second hypothetical scheme, a dilution of the aggregates to the cmc is postulated, then the aggregates disintegrate, and the resulting monomer solution is diluted to the final concentration. In these hypothetical schemes, the following processes can give rise to heat effects: (1) dilution of aggregates, (2) dissociation of the aggregates and release of bound counterions, and (3) dilution of monomers. The major contribution to the observed heat of reaction will be the heat of dissociation of the aggregates, including the release of bound counterions. The latter process cannot be separated but we will show that its enthalpic contribution will be small (see below). During the experiment, the reaction heat will diminish in the concentration region of the cmc (intermediate concentration range); and at the end of the titration experiment, at

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Figure 2. Titration of 25 × 10 µL aliquots of 200 mM NaC in 0.1 M NaCl (pH 7.5) into 1.34 mL 0.1 M NaCl (pH 7.5) at 284.3 K. A, calorimetric traces (heat flow vs time); B, reaction enthalpy versus the total detergent concentration ct in the reaction cell; C, first derivative of curve B calculated numerically from interpolated values.

final bile salt concentrations in the reaction cell ct above the cmc, only the heat caused by the dilution of aggregates is measured. The reaction heat of this process is very low, as seen from Figures 2A and 2B. According to the pseudophase-separation model, the cmc corresponds by definition to the concentration at which the first derivative of the reaction heat with respect to the final detergent concentration in the cell displays an extreme value2 (see Figure 2C). The concentration region for the dissociation of bile salts aggregates is very broad and is not characterized by a sharp decrease in the reaction enthalpy as observed for surfactants with aliphatic chains. This is caused by the much smaller aggregation number of bile salt molecules as mentioned above. Changing the temperature leads to a change in sign of the demicellization enthalpy. ∆Hdemic becomes positive above room temperature and increases further with increasing temperature as already observed.21 This is illustrated in Figure 3 for the system NaC in 0.1 M NaCl. Similar titration experiments as shown in Figures 2 and 3 were performed for NaC and NaDC in water and 0.1 M NaCl (pH 7.5) in a temperature range from 284 to 343 K. We determined the cmc as a function of temperature from the first derivatives of the titration curves. The data for the demicellization of NaC and NaDC in 0.1 M NaCl are listed in Table 1 and the complete data sets are shown in a van’t Hoff plot of ln cmc vs 1/T (Figure 4). As expected and observed previously,19,21 the cmc of NaC is larger than that of NaDC because of its higher hydrophilicity. Increasing the salt concentration reduces the electrostatic repulsion between the charged groups and therefore favors the aggregation process inducing a decrease of the cmc.

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Table 1. Thermodynamic Parameters for Demicellization of NaC and NaDC as a Function of Temperature, Calculated on the Basis of the Pseudo-Phase Separation Model compound NaC (0.1 M NaCl)

NaDC (0.1 M NaCl)

T (K)

cmc (mM)

∆Hdemic (kJ‚mol-1)

∆Gdemic (kJ‚mol-1)

T‚∆Sdemic (kJ‚mol-1)

284.3 288.7 297.3 308.6 317.6 327.9 338.1 342.8 283.1 287.4 297.9 307.6 317.8 327.8 331.1 337.8 342.6

12.5 12 10 14 14.5 14 14.5 15.5 4.2 4.0 4.0 3.8 4.0 4.0 4.1 4.2 4.8

-4.6 -3.3 -1.6 1.6 4.4 6.2 8.4 9.7 -3.8 -2.7 1.4 4.8 7.3 11.0 12.3 13.5 15.0

19.9 20.3 21.0 21.6 22.1 22.6 23.2 23.3 22.3 22.8 23.6 24.5 25.2 26.0 26.3 26.7 26.7

-24.4 -23.6 -22.5 -20.0 -17.7 -16.4 -14.8 -13.6 -26.1 -25.5 -22.2 -19.7 -17.9 -15.0 -14.0 -13.1 -11.7

Figure 3. Reaction enthalpy versus total detergent concentration ct in the cell for the titration of 200 mM NaC (0.1 M NaCl, pH 7.5) into 1.34 mL 0.1 M NaCl (pH 7.5) at different temperatures.

The minimum of the cmc is difficult to observe from the data of the cmc alone because its temperature dependence is not very pronounced. The minimum occurs around room temperature for demicellization in water. This is in accordance with previously published data.1,18,19,21 The determination of the demicellization enthalpy as a function of temperature will give more exact data for the temperature of the minimum (see below). The data obtained here for the demicellization of NaC and NaDC in water are slightly higher than those reported earlier21 but deviate less than 10% in most cases. Because the titration was performed to higher bile salt concentrations in cell, the determination of the cmc and the demicellization enthalpy was easier than in previous experiments, and we therefore believe that the values reported here are more precise (see below). From Figure 4 it is also evident that the determination of the demicellization enthalpy ∆Hdemic from the slope of the van’t Hoff plots is very difficult, because the slope changes with temperature and the cmc data have to be very precise to get reliable results. However, because of the low aggregation number of bile salt micelles, this precision cannot be obtained regardless of the method used. Therefore, the direct determination of the heat of demicellization is of great advantage. With use of the pseudo-phase separation model (see below), ∆H for the reaction is obtained as the difference between the two extrapolated lines in Figure 2B. ∆Hdemic is then calculated taking into account that the solution in the syringe

Figure 4. van’t Hoff plot of the temperature dependence of the cmc of bile salts at pH 7.5: (9) NaC, H2O; (0) NaC, 0.1 M NaCl; (b) NaDC, H2O; (O) NaDC, 0.1 M NaCl; solid lines, obtained using eq 5; dotted lines, obtained using a secondorder polynominal fit.

contains molecules in monomeric as well as micellar form. In the framework of the phase-separation model, the monomer concentration in the syringe equals the cmc. The concentration of molecules in micellar form in the syringe cmic is the difference between the total concentration in the syringe csyringe and the cmc (i.e., cmic ) csyringe - cmc). The demicellization enthalpies obtained from the titration experiment were therefore calculated based on cmic and using the cmc values determined from the same experiment. This is an approximation for bile salts, but the only way to obtain comparable data. The exact concentration of molecules in the syringe in micellar form can only be calculated using the mass action model (see below). Taking into account that the monomer concentration in the syringe is in reality higher than the cmc determined by using the pseudo-phase-separation model, the ∆Hdemic data listed in Table 1 would have to be corrected to slightly higher values.

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In the framework of the pseudo-phase-separation model, the thermodynamic quantities and ∆Gdemic ) - R‚T‚ln cmc′, with cmc′ being the cmc in mole fraction units, and T∆Sdemic ) ∆Hdemic - ∆Gdemic were calculated. The resulting data for both bile salts are shown in Figure 5. It is clear that for bile salts aggregates the pseudo-phase-separation model is a crude approximation and only justified for comparison with reported data. It is evident that in ITC experiments a difficulty for the cmc determination arises in the temperature range where ∆Hdemic becomes very small or even zero. However, the cmc and ∆Hdemic in this range can be interpolated from the temperature dependence of ∆Hdemic measured over a wider temperature range. The ∆Hdemic data can then be interpolated using a second-order polynomial fit ∆Hdemic(T) ) ∆Hdemic(0) + aT + bT2 of the experimental points (see Figure 5). In this way, the temperature of the cmc minimum was determined to 303 K for NaC and to 295 K for NaDC. No salt dependence in the concentration range was observed. The cmc values can also be calculated and compared with experimental data using the van′t Hoff equation with a temperature-dependent ∆Hdemic(T):

(∂ ln cmc′/∂ T)p ) ∆Hdemic(T)/R‚T2

(1)

Integration of eq 1 gives:

ln cmc′(T) ) 1/R(-∆Hdemic(0)/T + a‚ln T + b‚T) + constant (2) The solid lines in Figure 4 were obtained using this equation with a variable constant as fitting parameter and constants a and b determined from the second-order polynomial fits shown in Figure 5. Although the fits for the ln cmc values of NaC are quite satisfactory, significant deviations are apparent for the fits of ln cmc of NaDC. The reasons for these discrepancies are unclear. One can speculate that for NaDC the change in aggregation number with temperature and concentration is more pronounced leading to larger deviations from the pseudo-phaseseparation model with which the data were analyzed. We will show below that this may indeed be the case. The ∆Gdemic data (Table 1, Figure 5) are large, positive, and vary only slightly with the temperature in accordance with previous measurements.21 The T∆Sdemic term is always negative (see Table 1) and increases with higher temperatures (Figure 5). The extrapolation to T∆Sdemic ) 0 yields a temperature between 380 and 410 K. At this temperature the aggregation process is driven solely by enthalpy. Because ∂∆Gdemic/∂T ) -∆Sdemic ) 0, this is also the temperature at which the maximum of ∆Gdemic occurs. The almost parallel lines for temperature dependence of ∆Hdemic and T∆Sdemic with the only slightly temperaturedependent ∆Gdemic term are a manifestation of the hydrophobic effect with its enthalpy-entropy compensation, which has been described in detail.1,2,21,24 The association of amphiphiles at low temperatures is entropy driven, but at elevated temperatures (T > 350 K) the enthalpy becomes the major driving force for aggregation (Figure 5). The observed temperature dependence of ∆Hdemic clearly shows that changes in hydrophobic hydration are involved in the aggregation process. However, the absolute values of ∆Hdemic can also contain contributions from changes in hydration of the polar parts of the molecules. Assuming an aggregation model with the polar groups pointing outward,11 the contributions are probably small, because the environment of the polar groups does not change when the aggregates fall apart. But even within this model some changes in hydration can occur caused by changes in counterion binding.

Figure 5. Thermodynamic parameters of demicellization of bile salts as a function of temperature calculated using the pseudo-phase-separation model. Filled symbols, experimental values in H2O; open symbols, experimental value in 0.1 M NaCl; lines were obtained using eq 3.

For NaC, values for the fraction of bound counterions β of < 0.2 were reported, whereas for NaDC β was 0.3.18,19 The enthalpic effects arising from changes in counterion binding can be estimated from data reported by Marcus.29 For Na+ the hydration enthalpy ∆Hhyd is - 415 J mol-1 at 298 K with a ∆Cp value of - 42 J mol-1 K-1. For a value of β ) 0.3 (NaDC), a contribution of ∼ - 125 J mol-1 to the total value of ∆Hdemic would then be expected at 298 K and of - 690 J mol-1 at 343 K. Even for this high value of β, the calculated values are only a small fraction of the observed experimental ∆Hdemic values. Therefore, contributions to ∆Hdemic from changes in counterion binding are negligible at all temperatures except those close to the temperature at which ∆Hdemic becomes zero. This contribution is even lower for NaC with β values less than 0.1. Therefore, one can conclude that the major enthalpic effects arise from changes in hydration of hydrophobic surfaces. The structure of the bile salt molecules is a crucial factor for the aggregation process and some controversies exist regarding the structure of bile salt aggregates (see above). Bile salt molecules (Figure 1) are characterized by their rigid ring structure and by the hydrophobic and the hydrophilic surface, the latter giving rise to possibilities of specific hydrogen bonding.12-14,30 A scheme involving (28) Birdi, K. S., Ed. Handbook of Surface and Colloid Chemistry; CRC Press LLC: Boca Raton, FL, 1997. (29) Marcus, Y. Biophys. Chem. 1994, 51, 111.

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the orientation of the hydrophobic plane pointing inward with the hydrophilic parts pointing outward, forming a sheet structure was proposed by Small and Carey8-10 and was extended by other authors.11,15,16,31 This model is actually not accepted by all researchers, using arguments that the hydrophobic interactions are too weak to be responsible for the stability of bile salt micelles.32,33 For instance, Roda et al.34 have shown that the amphipathicity of bile salts does not arise entirely from the structure of the molecules but is imposed by the stereochemical possibilities, and this has great implications for the formation of different aggregates.35 Giglio and co-workers12,13 proposed a radically different model with a helical arrangement of monomers with specific hydrogen bonding between the monomers and with the hydrophobic surfaces of the bile salts molecules pointing outward. The determination of the temperature dependence of ∆Hdemic actually helps to decide whether more hydrophobic surface is exposed to water when the aggregates dissociate into monomers. The most reliable thermodynamic quantity for the extent of hydrophobic hydration is the change in heat capacity ∆Cp obtained from the slope of the ∆Hdemic vs temperature plot. When hydrophobic molecules are transferred from a nonpolar medium to water ∆Cp is always positive, and the absolute value of ∆Cp is a linear function of the hydrophobic surface area that gets exposed to water during this process.36-38 The calculated ∆Cpdemic for the four systems at pH 7.5 and 298 K are: ∆Cpdemic (NaC, H2O) ) 240 J‚mol-1‚K-1, ∆Cpdemic (NaC, 0.1 M NaCl) ) 260 J‚mol-1‚K-1, ∆Cpdemic (NaDC, H2O) ) 360 J‚mol-1‚K-1, and ∆Cpdemic (NaDC, 0.1 M NaCl) ) 340 J‚mol-1‚K-1. ∆Cpdemic is positive and one can conclude that the dissociation of the aggregates leads to the exposure of additional hydrophobic surface area. The ∆Cpdemic data obtained for NaC are somewhat smaller than those obtained for NaDC. Increasing the ionic strength to 0.1 M NaCl has negligible effects. For NaDC, ∆Cpdemic decreases to ∼250 J mol-1 K-1 at T ) 343 K. Again, as elaborated for the heat of dimicellization ∆Hdemic, ∆Cpdemic can also be interpreted as the sum of changes of the heat capacities arising changes in hydration of the hydrophilic and hydrophobic parts of the molecule.

∆Cpdemic ) ∆Cpdemic(hydrophilic) + ∆Cpdemic(hydrophobic) (3) The term ∆Cpdemic(hydrophilic) considers all differences in heat capacity arising from changes in headgroup interactions, that is, interactions of headgroups between adjacent molecules in the aggregates, interactions caused by changes in counterion binding, and changes in hydration during the dissociation process of the aggregates. The second term ∆Cpdemic(hydrophobic) takes into account all changes in hydration of hydrophobic surfaces of the molecules. The hydration of the polar parts of the bile salt molecules probably does not change to a large extent. Therefore, (30) Lamcharfi, C.; Cohen-Solal, C.; Parquet, M.; Lutton, C.; Dupre´, J.; Meyer, C. Eur. Biophys. J. 1997, 25, 285. (31) Vadnere, M.; Natarajan, R.; Lindenbaum, S. J. Phys. Chem. 1980, 84, 1900. (32) Gymesi, J.; Barcza, L. J. Inclusion Phenom. 1993, 15, 153. (33) Campedron, M.; Quiroa, V.; Therand, A.; Allouche, A.; Pouzard, G. Magn. Reson. Chem. 1986, 24, 624. (34) Roda, A.; Hofmann, A. F.; Mysels, K. J. J. Biol. Chem. 1983, 258, 6362. (35) Jones, M. N.; Chapman, D., Eds. Micelles, Monolayers, and Biomembranes; Wiley-Liss: New York, 1994. (36) Joliceur, C.; Philip, R. R. Can. J. Chem. 1974, 52, 1834. (37) Gill, S. J.; Wadso¨, I. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 2955. (38) Costas, M.; Kronberg, B.; Silveston, R. J. Chem. Soc., Faraday Trans. 1994, 90, 1513.

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∆Cpdemic(hydrophilic) should be determined mainly by changes in counterion binding. Counterion binding to the aggregates reduces the number of water molecules in the solvation shell because the ions can share hydration water. Upon demicellization additional water molecules are necessary for complete hydration of the sodium ions and the polar surface of the monomers. This solvation process is associated with a negative ∆Cp, and Marcus29 has shown that this contribution can be quite large for some ions. However, the reported ∆Cp value is only - 42 J mol-1 K-1 for Na+. Considering a maximum change in degree of counterion binding of 0.3, the contribution to the total ∆Cpdemic would be -13 J mol-1 K-1 and therefore a negligible correction to the experimental one, because these are much larger (see above). Therefore, the total change in heat capacity ∆Cpdemic originates almost exclusively from the change in hydrophobic hydration ∆Cpdemic(hydrophobic). Compared with molecules in the aggregates, the total surface area of the monomers is fully exposed to the solvent molecules. ∆Cpdemic is higher for NaDC, which indicates that the hydrophobic surface being exposed to water upon demicellization is larger for this molecule. This agrees with the fact that NaDC has one hydroxyl group less than cholate. The ∆Cpdemic values found for the two surfactants correspond to changes in exposed hydrophobic surface of 1.1 nm2 (NaC) and 1.6 nm2 (NaDC) per molecule using a value of ∆Cp for hydrophobic hydration of 370 J m-2 K-1 as reported by Costas et al.38 The two bile salts have a total surface area of approximately 11.5 nm2 per molecule, the hydrophobic surface being about 50-70% of the total surface. The total change in exposed hydrophobic surface is rather small, indicating that the molecules in the aggregates are only loosely associated and that only 1015% of the total surface or 20-40% of the hydrophobic surface is on the average not accessible to water. The finding that in bile salt aggregates only a small percentage of the total hydrophobic surface is not accessible to water seems to contradict results obtained by other groups that the interior of a bile salt aggregate is more hydrophobic than that of ordinary micelles of alkyl chain surfactants. This was concluded from fluorescence studies performed by Zana and Gu¨veli15 and from experiments of solubilization of various hydrocarbons in NaC aggregates performed by Sugioka and Moroi.39 Fluorescence methods as well as the solubilization studies are invasive methods in the sense that a probe molecule is introduced into the system. However, for bile salt aggregates with their low aggregation numbers the incorporation of an additional hydrophobic molecule can easily lead to a structural perturbation or a drastic change of the structure of the aggregate. An alternative explanation is that hydrophobic cavities in contact with water are filled by the hydrophobic probe molecule leading to optimal hydrophobic contacts between the bile salt and the probe molecule. Probe molecules therefore “see” a more hydrophobic surrounding than was present originally in the unperturbed aggregate. For many ionic detergents higher aggregation numbers are observed when the ionic strength is increased (see Table 2 and discussion below). This is caused by a better shielding of the negatively charged headgroups reducing electrostatic repulsion between headgroups.2 If, as a consequence, the extent of hydration of hydrophobic surfaces would also decrease, higher ∆Cpdemic values should be expected for the demicellization process in solutions with higher salt content. However, our results show that for NaC and NaDC ∆Cpdemic does not depend (39) Sugioka, H.; Moroi, Y. Biochim. Biophys. Acta 1998, 1394, 99.

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Table 2. Thermodynamic Parameters for Demicellization of NaC and NaDC Calculated on the Basis of a Mass Action Model with Counterion Binding NaC, H2O NaC, 0.1 M NaCl NaDC, H2O NaDC, 0.1 M NaCl a

T (K)

βa

nb

∆Gdemic (kJ‚mol-1)

∆Hdemic (kJ‚mol-1)

∆Hdil (mic) (kJ‚mol-1)

∆Hdil (mon) (kJ‚mol-1)

283.8 328.1 284.3 327.9 285.8 328.2 283.1 327.8

0.08 0.08 0.15 0.15 0.3 0.3 0.3 0.3

4.7 6.1 5.5 5.4 7 5.4 12.3 7.3

6.4 7.7 8.4 9.0 12.3 12.6 14.5 15.5

-6.6 7.7 -4.7 6.5 -4.4 12.9 -4.0 11.7

1.5 -0.4 0.6 0.01 -1.5 -0.5 0.9 0.6

0 -2.2 -2.1 0.8 2.0 -3.7 2.1 -3.3

β, degree of counterion binding. b n, aggregation number in the concentration region of the cmc.

on ionic strength in the range up to 0.1 M NaCl. The small change in aggregation number n only found for NaDC when the salt concentration was increased to 0.1 M NaCl is possibly not sufficient to lead to larger changes in hydrophobic hydration. For NaC, ∆Cpdemic is almost constant across the whole temperature range studied. Also the aggregation number did not change significantly with temperature. This is different for NaDC. Here, ∆Cpdemic decreases at higher temperatures and the aggregation number decreases (see below), which shows that the larger aggregates found for NaDC at low temperature are also stabilized by hydrophobic interactions. Simulation of the Titration Curves. Our previous simulations of the calorimetric titration curves were performed using a mass action model with fixed aggregation number n and without taking counterion binding into account.21 The reason for this was that results obtained by several groups had shown that the mass action model with neglect of counterion binding to bile salt aggregates was a reasonable approximation and justified for certain cases, for instance, NaC.2,5,25,39 Because of the ongoing discussion on the nature of the bile salt aggregates and the aggregation numbers, we now improved our calculations for NaC and NaDC demicellization by performing simulations of the titration curves at different temperatures, by also taking the aggregation number n in the mass action model as a variable parameter, and by additionally taking into account counterion binding to the aggregates. The formation of a micelle Mn with n monomers S- and βn bound counterions B+ is given by2,18,19,25

n S- + βnB+ h Mn-(1-β)n -(1-β)n

[S-],

(4)

[B+],

The concentrations [Mn ], and the total surfactant concentration ctS and the total counterion concentration ctB, with ctS ) ctB ) ct, are related by:

ct ) [S-] + n‚[Mn-(1-β)n] ) [B+] + βn‚ [Mn-(1-β)n] (5) With the equilibrium constant K being defined by:

K ) [Mn-(1-β)n]/([S-]n[B+]βn)

(6)

one arrives at the following equation:

[Mn-(1-β)n] ) [S-]n{ct(1 - β) + β [S-]}βn K

(7)

The relation between K and ∆G is

∆G ) -R‚T ln K ) n‚∆G0

(8)

with ∆G0 being the Gibbs energy change of a transfer of a monomer from water into the aggregate. In our simulations we made the approximation of using concentrations instead of the essentially necessary activities. The activity coefficients can be calculated as suggested by Coello et al.18,19 A test calculation for the activity

coefficients showed that in the concentration range up to 35 mM, as used in our experiments, the activity coefficients range from unity to 0.83. In the range of the cmc, the corrections are smaller, namely 5-10%. The approximation of using concentrations instead of activities is therefore within the limits of precision of our data. Eqs 5 and 7 are the basis for the simulations of the titration curves. For given values of n, β, and ∆G0, the surfactant monomer concentration [S-], and the micelle concentration [Mn-(1-β)n] is obtained as a function of ct by solving these equations. In the course of the titration experiment, the concentrations ct, [S-], and [Mn-(1-β)n] in the cell change because of the addition of aliquots of micellar solution from the syringe. Therefore, one needs to calculate the total change in concentration of monomers ∆[S-] or micelles ∆[Mn-(1-β)n] in the reaction cell after injection of an aliquot of a micellar solution from the syringe as a function of ct. This change in total number of aggregates in the cell and in the syringe is in a first approximation proportional to the observed heat effect for dissociation of the aggregates. In addition, however, the total observed heat contains dilution terms for monomer and micelle dilution. Fortunately, these are usually small, can be measured separately, and even if they are not negligible, do not influence the determination of the other parameters. For the simulation of the titration curves five adjustable parameters, namely the aggregation number n, ∆G0, the enthalpy ∆Hdemic, the dilution enthalpy of monomers ∆Hdil(mon), and the dilution enthalpy of micelles ∆Hdil(mic), were used. The degree of counterion binding β was introduced as a fixed parameter, and values for β were taken from the literature.18,19 Because ∆G0, n, and β are correlated, using β as an additional variable parameter led to inconclusive results. In the simulations it was observed that an increase of β mainly led to a decrease of the parameter n, whereas the steepness of the sigmoidal titration curves was mainly determined by ∆G0 together with the aggregation number n. The levels of the reaction enthalpy below and above the cmc are sensitive to the heats of dilution and the difference in levels to ∆Hdemic. The experimental curves were simulated using the nonlinear least-squares fitting procedure of the computer program SCIENTIST (see Materials and Methods). The experimental and simulated curves are shown in Figure 6. The parameters obtained from the simulations are summarized in Table 2 with ∆Gdemic ) -∆G0. As seen from Figure 6, the fit to the experimental curves is quite satisfactory, thus indicating that the assumed model can describe the aggregation process of bile salts quite well. Figure 7 shows the monomer and micellar concentrations of the two bile salts as a function of the total concentration for measurements at low temperature (T ) 284 K) as obtained from the simulations. The curves show that the monomer concentration continuously increases well above the cmc, particularly when no additional salt

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Garidel et al.

Figure 6. Experimental (open and filled squares) and calculated (lines) titration curves for the demicellization process of NaC (left column) and NaDC (right column) in H2O and 0.1 M NaCl (pH 7.5) at low and high temperatures. The simulations were performed using the mass action model with the parameters indicated in Table 2.

is present. This again shows that the pseudo-phaseseparation model, in which a constant monomer concentration above the cmc is assumed, is not appropriate. Because the heat effects mainly arise from a change in the exposure of hydrophobic surfaces (see above), titration calorimetry is only sensitive to the formation of primary aggregates with low aggregation numbers and not to secondary growth of the aggregates by interactions through hydrogen bonds. For this process, no significant changes in exposure of hydrophobic surfaces occur. Therefore, if secondary aggregates are formed in the investigated concentration range, we would not be able to detect it by calorimetry. For NaC, the best fits yielded aggregation numbers between 4.7 and 6.1 at low and high temperatures for the concentration range around the cmc. A possible dependence of n on total concentration cannot be ruled out, because in the model only a fixed aggregation number is assumed. A clear dependence on the salt concentration up to 0.1 M NaCl was not observed. Our values for n are in agreement with previous observations by other groups. Sugioka and Moroi39 recently reported the mean aggregation number for NaC as a function of the total cholate concentration. For ctotal ) 16-20 mM, their values for n are 4-6, in excellent agreement with our analysis. Coello et al.18,19 reported an average aggregation number of 3 for

NaC increasing to ∼4.2 at 0.5 M NaCl with an average value of β of 0.077. This is agreement with data from Hao et al.20 of n ) 3.9 with β ) 0.21, but slightly lower than our values. For NaDC, the simulations indicate that the aggregation number n seems to increase slightly with salt concentration from n ) 7 in pure water to n ) 12.3 in 0.1 M NaCl at low temperature (284 K). A temperature dependence also seems to be present, because at higher temperature (328 K) the aggregation number decreases to 5.4 in water and 7.3 in 0.1 M NaCl, respectively (see Table 2). These findings are in good agreement with the results of other authors. Coello et al.19 reported values of ∼5.8 for saltfree solutions at low temperatures. Jover et al.4,5 found an average value of 8 ( 2 from fluorescence measurements. Kratohvil et al.40 reported values for n of 8 at 0.15 M NaCl and 11.6 at 0.6 M NaCl, indicating a slight salt dependence of n. However, Zana and Gu¨veli15 found that n had values of 11 ( 2 in the concentration range of 0.4-0.6 M NaCl, independent of the salt concentration in the regime. Besides these lower numbers for n, much higher numbers up to 20 were also reported (see Coello et al.19 for compilation of data). A detailed comparison is difficult, because the experiments were conducted under different (40) Kratohvil, J. P.; Hsu, W. P.; Kwok, D. I. Langmuir 1985, 2, 256.

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with higher aggregation numbers at low temperature also involves polar interactions. These interactions may be weaker at higher temperatures causing the observed decrease in aggregation number. However, the reduced ∆Cpdemic value observed for NaDC at higher temperatures (see above) compared with the value at low temperature shows that the larger aggregate at low temperatures is not only stabilized by polar but also by hydrophobic interactions. The simulation also yields values for ∆Hdemic (see Table 2). These values are slightly different from those determined by using the pseudo-phase-separation model. However, the differences are only about 5%. The increase of ∆Hdemic with temperature is the same as determined before and therefore the resulting values for ∆Cpdemic are also in the same range. The comparison of ∆Gdemic obtained from the simulation of the titration curves (Table 2) with those determined by the pseudo-phase-separation model shows that these values do not coincide. This is to be expected, because they were calculated based on completely different models, and the pseudo-phase-separation model is not appropriate for describing the aggregation process of bile salts.

Figure 7. Calculated values for the concentration of detergent in monomeric and micellar form for NaC and NaDC (pH 7.5) at low temperature (283-285 K). cmonomer in H2O (9) in 0.1 M NaCl (0); cmicellar in H2O (b) in 0.1 M NaCl (O). The simulations were performed using the mass action model with the parameters as shown in Table 2.

conditions and with different methods. Values for n obtained with probe methods particularly must be viewed with caution, because the introduction of probes into the aggregates can change the aggregation behavior (see above). In addition, the aggregation number n can increase with increasing total concentration as shown for NaC.39 Our values are only for the concentration region around the cmc, however. All data reported are for lower temperatures (20-30 °C), and no comparable data exist for higher temperatures. Our data show, that for NaDC n decreases with temperature. This could be because the formation of aggregates

Conclusions Isothermal titration calorimetry was used to determine the critical micellar concentration and the heat of demicellization of NaC and NaDC as a function of temperature and at two different ionic strengths. Assuming the pseudophase-separation model, the Gibbs energy change and the entropy change for the demicellization processes were calculated. The change in heat capacity ∆Cpdemic was obtained from the first derivative of the demicellization enthalpy ∆Hdemic as a function of temperature. The ∆Cpdemic values indicate relatively small changes in exposed hydrophobic surface area upon dissociation of the aggregates. A large proportion of the hydrophobic surface of the molecules in the micellar aggregates must therefore be accessible to water. We were able to simulate the experimental calorimetric titration curves using a mass action model including counterion binding. In addition to the thermodynamic parameters, we obtained values for the aggregation number n of the aggregates. Titration calorimetry has an advantage compared with other methods, because the critical micelle concentration, the thermodynamic parameters of the aggregation process, and the aggregation numbers can be determined directly from one experiment. Acknowledgment. We thank A. Kerth for critical reading of the manuscript and B. Fo¨lting for excellent technical assistance. This work was supported by grants from the Max-Planck-Gesellschaft zur Fo¨rderung der Wissenschaften (P. G. and A. B.) and the Fonds der Chemischen Industrie (A. B.). LA9912390