Phospholipid

18464

J. Phys. Chem. 1996, 100, 18464-18473

Concentration-Dependent Diffusion of Bile Salt/Phospholipid Aggregates Ching-Yuan Li and Timothy S. Wiedmann* Department of Pharmaceutics, College of Pharmacy, UniVersity of Minnesota, 308 HarVard Street SE, Minneapolis, Minnesota 55455 ReceiVed: May 29, 1996; In Final Form: September 10, 1996X

Bile salt/phospholipid aggregates are present as concentrated, anionic colloids in the gallbladder. After mixing with dietary lipids, these aggregates diffuse through the hydrated, negatively charged glycoprotein network at the intestinal surface prior to absorption. Analysis of these complicated processes requires a characterization of the lipid aggregate as well as its diffusion. Moreover, the excluded-volume effects on the lipid aggregate diffusion need to be addressed. Thus, the diffusion coefficients of bile salt, phospholipid, and water were obtained from four series of lipid dilutions by a Fourier transform pulsed-field gradient spin-echo 1H NMR diffusion method. Dialysis experiments were performed to provide an independent estimate of the intermicellar concentration. Four lipid solutions with different total phospholipid/bile salt ratios were then diluted with bile salt solutions containing the approximate intermicellar concentration. With these four series of solutions, the isopotential specific volume of the micelle, calculated from density measurements, was found to increase with increasing phospholipid/bile salt (PC/BS) molar ratio in the micelle. The hydration of micelle and intermicellar concentration decreased with increasing PC/BS molar ratio in the micelle but was independent of the micellar concentration, as deduced from the NMR measurements. After the theoretical correction for the excluded-volume effect was applied, the size of the micelle was found to increase significantly upon dilution in relation to the corresponding decrease of the PC/BS ratio in the micelle. Series 1 fit well with an excluded volume factor based on hard core spheres. Series 2 yielded physically unreasonable sizes when either spherical or rod corrections were applied. Series 3 and 4 were well fit by rod-shaped excluded volume corrections but only if the flexibility and possible interpenetrability of the micelles were considered.

Introduction Bile is an aqueous secretion produced in the canaliculi of the hepatocytes of the liver.1 In canaliculi, bile salts (BS) and long-chain phospholipids (lecithin, PC) are believed to spontaneously aggregate to form mixed micelles or vesicles, depending on the ratio of these two components.2 In hepatic bile, lecithin-rich vesicles are the major carriers of cholesterol. When bile is not needed for digestion, it is diverted to the gallbladder for storage.3 During the storage in the gallbladder, bile is concentrated and the vesicles transform into mixed micelles. The transition from vesicles to mixed micelles may induce nucleation of cholesterol crystals which is a crucial step in gallstone formation.4,5 After a meal, the dilution of bile upon emptying into the duodenum causes the cholesterol carriers to revert to lecithin-rich vesicles. Therefore, a complex interplay of concentration and dilution of the cholesterol carriers occurs in ViVo. Characterization of lipid aggregates in human bile and measurement of their interactions and stability are important both for an understanding of the cause of gallstone formation and for guiding their potential application in the design of oral drug-delivery systems for poorly soluble drugs. In spite of theoretical and experimental efforts devoted to their physicochemical characterization, the structure and properties of mixed BS/PC micelles are still controversial issues. However, a consensus has developed that the micelles are spherical at lower PC/BS ratios but rods at higher PC/BS ratios.6-12 There have been two models proposed for the arrangement of the phospholipid and bile salt components in the rodlike micelles. * To whom correspondence should be addressed at the University of Minnesota. Tel: (612) 624-5457. Fax: (612) 626-2125. E-mail address: [email protected]. X Abstract published in AdVance ACS Abstracts, November 1, 1996.

S0022-3654(96)01562-6 CCC: $12.00

Models with the phospholipid assembled parallel to the rod axis depict the mixed micelle rods as being made up of stacked disks.6,7 Each disk consists of a phospholipid bilayer surrounded by a ribbon of bile salts with hydrophobic portions of the bile salt interacting with the fatty acid chains of the phospholipid. This model was first proposed by Shankland7 and uses the disklike structure of the mixed disk model proposed by Small6 to describe the morphology of the basic repeating unit making up the rod. The alternative model with radially-oriented phospholipid was introduced by Ulmius et al.8,9 and by Nichols and Ozarowski10 and Hjelm et al.11 In these models, the fatty acid tails of the phospholipid are more or less radially-arranged in the interior of the rod with the phospholipid head groups in a shell on the surface. However, the bile salt is arranged differently in these two rod models. In the model of Nichols and Ozarowski, some of the bile salt is inserted between the fatty acid tails with their axes perpendicular to the rod axis.10 In the model of Ulmius et al., the bile salts are arrayed on the surface between the head groups with the cylindrical axes of the molecules parallel to the micelle rod axis.8,9 In this study, the capped-rod model of Nichols and Ozarowski was adapted to interpret the data. There is still limited quantitative information available on the dependence of the micellar size, polydispersity, and flexibility as a function of the solution composition despite an increasing number of experimental reports supporting a cylindrical structure for this system. This led us to examine the size as deduced from diffusion measurements of the BS/PC system. However, bile salts are anionic surfactants, so electrostatic interactions13 and excluded-volume interactions (potential and hydrodynamic interactions) are present in concentrated micellar solutions.14 Therefore, characterization of interparticle interactions in bile salt solution is a complex problem, and unless the © 1996 American Chemical Society

Diffusion of Bile Salt/Phospholipid Aggregates interparticle interactions are properly accounted for, the analysis of experimental results is erroneous. In view of the importance of understanding this BS/PC system, a multicomponent self-diffusion study by the Fourier transform pulsed-field gradient spin-echo (FT-PGSE) 1H NMR diffusion technique was performed in order to examine the concentration dependence of the aggregate diffusivity with the purpose of expanding the knowledge of the ternary phase diagram. With this technique, it is possible to simultaneously determine the self-diffusion coefficients of all constituent molecules of the BS/PC system. The FT-PGSE method has proven to be a very powerful method15 for obtaining selfassociation and structural data in microemulsion,16 micellar systems,17, and solubilization studies.18 It also has been demonstrated to be a useful tool for investigating the fairly complex BS simple and BS/PC mixed micellar systems.19 Our approach was to dilute bile salt/phospholipid solutions by a bile salt solution containing the approximate intermicellar concentration (IMC). By doing so, the excluded-volume effect can be deduced with a series of solutions that vary with concentration but are relatively homogeneous with respect to the properties of the micelles. After the excluded-volume effect was taken into account in the data analysis of NMR experiments, the appropriateness of the hydration, IMC, and micellar size were examined. Experimental Section Materials. The experiments were conducted with sodium taurocholate (NaTC) (Sigma Chemical Co., St. Louis, MO) after recrystallization from ethanol/ethyl acetate. The recrystallized surfactant was stored in Teflon-lined screw cap test tubes. Egg phosphatidylcholine (egg PC) was obtained from Avanti Polar Lipids (Alabaster, AL). Both NaTC and egg PC moved as single spots on silica plates with a mobile phase of 65:35:5 chloroform:methanol:water. Deuterium oxide (99.9 atom %) used in the diffusion measurement was purchased from Cambridge Isotope Laboratories and was used as supplied. Cellulose ester (CE) molecular porous dialysis membranes (Spectra/Por, Houston, TX) with 1000 and 5000 molecular weight cutoffs (MWCO) were used in this study. Great care was taken to exclude moisture from the samples and to prevent contact with water in order to minimize any proton NMR signal from the exchange reaction with deuterium oxide. All glassware was dried in the oven overnight before use. Sample Preparation. Sample preparation was conducted by first lyophilizing egg PC from an ethanol/cyclohexane solution. From the measured dry weight, the appropriate weight of NaTC in 0.9% NaCl/D2O solution was added to achieve the desired molar ratio of NaTC:egg PC. Each sample was purged with argon and equilibrated in excess of 24 h at room temperature before the dialysis experiments. Dialysis Experiments. The dialysis membranes were washed with distilled water three to five times, soaked in distilled water overnight, and then soaked in D2O overnight before use. The inner dialysis membrane with 1000 MWCO was tied at one end with surgical silk thread. The receiver (0.9% NaCl/D2O) solution was pipetted into the bag. Then, the other end of the tubing was tied. The inner dialysis bag was then placed inside a larger diameter dialysis bag (5000 MWCO) along with the NaTC/egg PC donor solution. The larger diameter dialysis bag was then placed inside the outer receiver solution (0.9% NaCl/ D2O) in a screw-capped test tube. The system was flushed with argon and wrapped with paraffin film. The tube was equilibrated in a shaking water bath at 37 °C. The bile salt concentration in the outer receiver-side solution was determined

J. Phys. Chem., Vol. 100, No. 47, 1996 18465 at various times by HPLC20 to determine when the system had reached equilibrium. After equilibrium, the dialysis bags were taken out, and the weight and NaTC concentration of donor and inner and outer receiver solutions were measured. Finally a series of dilutions was prepared by weight with the equilibrated bile salt/phospholipid solution and the outer dialyzate containing the appropriate intermicellar concentration. Density Measurements. The densities of the dialyzate and specific diluted solutions were measured by a pycnometer (ACE Glass Incorporated, Vineland, NJ). The volume of the pycnometer was calibrated with distilled water. The sample solutions were first heated to 40 °C for 10 min and then exposed to reduced vacuum for 10 min followed by equilibration in a water bath at 37 ( 0.5 °C for 30 min. The pycnometer was preincubated in a water bath at 37 ( 0.5 °C for 10 min. The sample solution was then introduced to the pycnometer and incubated in the water bath for another 10 min. The pycnometer was then taken out and capped to prevent water evaporation before weighing. The concentrations of bile salt and phospholipid were calculated from the volume dilution

CBS ) [gl(CBS(l))/Fl + gd(CBS(d))/Fd]/(gl/Fl + gd/Fd) (1) CPC ) [gl(CPC(l))/Fl]/(gl/Fl + gd/Fd)

(2)

where gl, Cl, Fl and gd, Cd, Fd represent the amount (g), concentration (g/mL) and density (g/mL), of equilibrated lipid solution (l) and dialyzate (d), respectively. The densities of a series of diluted solutions, F, were plotted as a function of micellar concentration, c2, to yield the value of (∂F/∂c2)µ. The isopotential specific volume of micelle, V2, was then calculated by the following equation21

V2 ) (1/Fs)[1 - (∂F/∂c2)µ]

(3)

where Fs is the density of the solvent. NMR Spectroscopy. The Fourier transform pulsed-field gradient spin-echo (PGSE) 1H NMR diffusion measurements were performed on nonspinning samples in thin-wall 5-mm tubes on a Nicolet 300 spectrometer (Nicolet Magnetic Corporation, Madison, WI) equipped with a pulse field gradient NMR proton probe (Doty Scientific, Inc., Columbia, SC). The sample temperature was controlled at 37 ( 0.2 °C by a versatile digital PID temperature controller (T-3000 Cryo Controller, Tri Research, Inc., St. Paul, MN). The magnetic field gradient pulses were generated by a home-built electronic apparatus. The standard spin-echo pulse sequence was used, and the transformed intensity was analyzed by the following equation22

A(2τ) ) A(0) exp(-2τ/T2) exp{-(γGδ)2D(∆ - δ/3)}

(4)

where A(2τ) is the peak intensity at time 2τ, A(0) is the peak intensity at time 0, τ is the time interval between 90° and 180° pulses, T2 is the spin-spin relaxation time, γ is the gyromagnetic ratio, G is the strength of the field gradient, δ is the duration of the field gradient, D is the diffusion coefficient, and ∆ is the time interval between first and second gradient pulses. The diffusion experiments were performed at constant τ (11 ms), ∆ (11 ms), and G values. A series of 10 δ values between 0.2 and 2 ms were used. To obtain absolute values for the selfdiffusion coefficients, the field gradient strength was calibrated from measurements of reference H2O, D2O, and SDS samples at 37 °C. The spectra were evaluated off-line by nonlinear leastsquares fitting of the peak heights using MacNMR 5.0 with NMRscript software (Tecmag, Inc., Houston, TX) on a personal

18466 J. Phys. Chem., Vol. 100, No. 47, 1996

Li and Wiedmann

computer. The average and standard deviations were calculated from different proton groups in a particular molecule.

nor the local diffusion coefficient, DC ) 0 for r < b and β ) 1. Therefore

Data Analysis The experimental observables include the density of the micellar solution and diffusivities of water, bile salt, and micelle. The calculated parameters were the IMC, hydration, sphere radius, and rod length. In analyzing the data, the following steps were taken. The isopotential specific volume yielded the hydrated volume. The diffusion of water yielded the direct hydration effect and the obstruction effect of hard core spheres and rigid rods. The diffusion of bile salt yielded the distribution of bile salts and obstruction effect of hard core spheres and rigid rods. Moreover, the diffusion of micelles required correction for the excluded-volume effect of hard core spheres and rigid rods; thus an iterative process was needed. Finally, it was evident that for concentrated rodlike micelles, further consideration of the flexibility and interpenetrability was needed; otherwise, unreasonable values of the size were obtained. Diffusion of Water. The self-diffusion coefficient of water in micellar solutions is smaller than that in pure water for two reasons.23 First, the large and almost stationary (compared to the Brownian motion of the water molecules) aggregates obstruct the path of water molecules; i.e., the water molecules near an aggregate have to diffuse along a longer path in order to reach other side of the aggregate. This is the so-called “obstruction effect”. The other reason is that a fraction of the water molecules are bound to the aggregates and therefore do not contribute to the rate of self-diffusion of water. This is referred to as “direct hydration effect” and is distinguished from the effect of hydration on the volume of hydrated aggregates. The Obstruction Effect. The obstruction effect was obtained from the extended cell model of Jo¨nsson et al.24 The model is based upon the concept of dividing a macroscopic system into small cells in such a way that they together may represent the macroscopic properties. The shape of these cells is further idealized to a simple form of a sphere. To calculate the effective self-diffusion coefficient for a component i in a cell, the local variation of the product of the self-diffusion coefficient (D) and the equilibrium concentration (C) must be known. A function U(r) is introduced in the cell-diffusion model in order to obtain a simple formalism for diffusion calculations. The connection between the local DC profile and the effective self-diffusion coefficient for a spherically symmetric system may be written as

Dfeff )

D(R) C(R) U(R) C h

(5)

where U(R) is the value of the function U(r) at the cell boundary. The DC value may be assumed to be constant in a region of the cell which is specified as follows

D(r) C(r) ) D1C1

rb

(6)

1 - βΦ 1 + βΦ/2

D2C2 (1 - Φ) 1 ) D2 C h (1 + Φ/2) (1 + Φ/2)

(8)

where the average concentration is calculated relative to the total volume, i.e., C h ) C2(1 - Φ). When the colloidal particles are markedly asymmetric, it is no longer appropriate to use spherical cells, particularly at higher concentrations. Therefore, a useful generalization was also derived to consider spheroidal particles in cells of spheroidal symmetry.20 Consider the coordinates ξ, ν, and φ defined through the relations

x ) A(ξ12 ( 1)1/2 sin ν cos φ y ) A(ξ12 ( 1)1/2 sin ν sin φ z ) Aξ1 cos ν

(9)

where 2A is the distance between two foci of the prolate (sign) or oblate (+ sign) ellipsoid and ξ1 is a function of axial ratio of the ellipsoids. An analogous expression to eq 5 can be written as

Dηeff )

D(ξR) C(ξR) Uη(ξR) C h

(10)

where U(ξR) is the value of the function U(ξ1) at the boundary of the cell and the subscript η either represents the direction along the symmetry axis of the cell, the z axis, or the direction perpendicular to the symmetry axis, the x and y axes. The product D(ξ1) C(ξ1) is specified as follows

D(ξ1) C(ξ1) ) D1C1 D(ξ1) C(ξ1) ) D2C2

ξ1 < ξb ξb e ξ1 e ξR

(11)

where ξb is the value of ξ1 at the boundary of the particle. The two equations for Uη(ξR), where η ) z or x, may be written as

Uz(ξR) ) Ux(ξR) )

γ - h(ξb) + Φ[h(ξR) - 1]

(12)

γ - h(ξb) + Φh(ξR)

1 - 2γ - h(ξb) + Φ[h(ξR) + 1] 1 - 2γ - h(ξb) + Φ[h(ξR) - 1]

(

(7)

where Φ ) b3/R3 and β ) (D2C2 - D1C1)/(D2C2 + D1C1/2). When the particle is obstructing the diffusion of the studied species but otherwise not influencing the concentration profile

(13)

where γ ) D2C2/(D2C2 - D1C1), Φ is the volume fraction of the particles, and h(ξ1) is the scale factor. For an oblate particle

π h(ξ1) ) (ξ12 + 1) ξ1 arctan ξ1 + 1 - ξ1 2

then U(R) may be written as

U(R) )

Dfeff )

)

(14)

and for a prolate particle

(

h(ξ1) ) -(ξ12 - 1)

)

ξ1 ξ 1 - 1 ln +1 2 ξ1 + 1

(15)

Diffusion of Bile Salt/Phospholipid Aggregates

J. Phys. Chem., Vol. 100, No. 47, 1996 18467

For an isotropic system, the diffusion over large distance is obtained as an average

excluded-volume effect of micelles in a system of hard spheres can be written as follows27

1 Dfeff ) (Dxeff + Dyeff + Dzeff) 3 1 C(ξR) 1 - 2γ - h(ξb) + Φ[h(ξR) + 1] ) D2 2 + 3 1 - 2γ - h(ξb) + Φ[h(ξR) - 1] C h

Dmic ) Dmic° [1 - 2.10(rH/R)3] ) Dmic° (1 - 2.10Φ)

{

}

γ - h(ξb) + Φ[h(ξR) - 1] γ - h(ξb) + Φh(ξR)

(16)

This is the explicit expression for the effective diffusion coefficient in this fairly complex geometry. When C1 ) 0 (γ ) 1), the obstruction effect can then be calculated for the spheroid. To account for the obstruction effect of a rodlike micelle, the ratio of rod length to rod diameter was converted to the axial ratio of the prolate by equating their volumes. Direct Hydration Effect. The evaluation of the direct hydration effect is complicated by the rate of exchange between “bound” and “free” water molecules. Therefore, the analysis of the water diffusion data was based on the two-site model18 involving free water with a diffusion coefficient, Df, and water bound to the micellar aggregate with a diffusion coefficient, Db. For the condition of fast exchange, the observed diffusion coefficient, Dw, is given by

Dw ) Db fb + Df (1 - fb)

(17)

where fb is the fraction of bound water. The contribution to Dw from water bound to bile salt monomer is very small and was omitted in the analysis. Db is equal to the micellar diffusion coefficient, Dmic. Df was obtained from eqs 8 and 16 for the spherical and rodlike aggregates, respectively. The selfdiffusion coefficient of pure water (D2) was taken to be 3.04 × 10-5 cm2/s at 37 °C.25 It is important to point out that the volume fraction, Φ, includes both the BS/PC micelles and associated water of hydration. Therefore

Φ ) Cmic (V2 + NhV1) ) (Clipid - CBSmon) (V2 + NhV1)

(18)

where Cmic, Clipid, and CBSmon are the micellar concentration, total lipid concentration, and intermicellar concentration (IMC) in g/mL, respectively, V2 and V1 are the specific volumes of anhydrous micelle and pure water, respectively, and Nh is the hydration number expressed in grams of water molecules per gram of lipid in the micelle diffusing with the micelle as a kinetic entity. Diffusion of Micelles Sphere Model. The diffusivity of a spherical aggregate (Dmic°) at infinite dilution is described by Stokes-Einstein equation

Dmic° ) kBT/6πη0rH

(19)

where kBT is the Boltzmann factor, η0 is the viscosity of the solvent (0.9% NaCl/D2O) which was taken to be 0.8497 cP,26 and rH is the hydrodynamic radius which is the sum of aggregate radius (r) and hydration layer thickness (t). The diffusion coefficients obtained by NMR measurements correspond to socalled long-time self-diffusion coefficients. At higher concentrations, the diffusion coefficient is reduced due to interparticle and hydrodynamic interactions. Using the cell model, the

(20)

where Dmic is the measured diffusion coefficient, R is the radius of the cell, and Φ is calculated by eq 18. Rod Model. The transport properties for rigid rods at infinite dilution have been presented by several investigators.28-31 For rods, it is necessary to treat diffusion parallel to and perpendicular to the rod axis separately, because motion along the axis is faster than in either of the two equivalent orthogonal directions. The expressions obtained numerically by Tirado et al.28 appear to be more accurate, at least when compared with experiments of short DNA fragments. The rod was modeled as a linear array of beads, and the interactions among the beads in the Oseen approximation was calculated. For a rod of length L and diameter d the translational diffusion coefficient (Dmic°) can be expressed as follows

Dmic° ) (kBT/3πη0L) [ln(p) + V]

(21)

p ) L/d

(22)

V ) 0.312 + 0.565/p - 0.100/p2

(23)

where V is the so-called end-effect correction, which is a function of p and converges to asymptotic values when p f ∞. These expressions are valid in the approximate range of 2 < p < 30. At higher concentrations, an analogous expression to eq 20 for rodlike aggregates can be derived through the following step using eqs 19 and 2132

() ( ( )(

) )( ) ( ) [( )(

rH 3 L/2[ln(p) + V] 3 ) ) R R 2 1 L 3 [ln(p) + V]3 d

2

πd2L/4 ) 4πR3/3

)]

2 1 p2 Φ 3 [ln(p) + V]3 (24)

Therefore, the concentration dependence of the diffusion of rodlike micelles can be described by the following expression

{ [ ( )(

Dmic ) Dmic° 1 - (2.10)

)]}

2 1 p2 Φ ) 3 [ln(p) + V]3 Dmic° (1 - kΦ) (25)

Further assuming a uniform hydration layer (t) around the micelle, L, d (54 Å), and p were replaced by (L + 2t), (d + 2t), and [(L + 2t)/(d + 2t)], respectively. Model Comparison. In Figure 1, the micellar self-diffusion coefficient calculated from eqs 20 and 25 is plotted as a function of the volume fraction of spherical micelles and rodlike micelles with different L/d ratios, respectively. It is clear that a nonspherical shape leads to a larger excluded-volume effect in comparison to a sphere. In addition, the excluded-volume effect increases with the length of the rod. Diffusion of Bile Salt Analysis of the diffusivity of bile salt was conducted as follows. Since the monomers contribute substantially to the measured total diffusion of bile salt, DsBS, the diffusion of egg PC was used as the measure of the micellar diffusion coefficient of bile salt, DsBS,mic. The measured diffusion coefficient of bile salt in the dialyzate solution, DsBS,dia, should approximate the bile salt monomer diffusion coefficient, DsBS,mon; however, a

18468 J. Phys. Chem., Vol. 100, No. 47, 1996

Figure 1. Relative self-diffusion coefficient of the micelle calculated from eqs 20 and 25 for the sphere model (solid line) and the rod model (broken lines), respectively. s, sphere; ‚‚‚, p (length to diameter ratio) ) 2; - - -, p ) 5; - ‚ - , p ) 10; - - - , p ) 20.

small correction due to the obstruction effect from the micelle and bound water is required. This can be done by applying the obstruction factor (Deff/D2) in eq 8 (sphere model) and eq 16 (rod model) to the diffusivity of bile salt in the dialyzate solution. With the assumption of fast exchange between these two sites, the diffusivity of bile salt can be described by the following equation

CBS DsBS ) CBSmon DsBS,mon + (CBS - CBSmon) DsBS,mic (26) Results and Discussion The main focus of this paper was to determine the effect of concentration on the diffusivity of the BS/PC micelle. Therefore, series of dilutions were prepared from four BS/PC solutions. With this approach, the resulting dilutions would contain micelles of approximately equal sizes but in progressively smaller concentrations. Dialysis Experiments. The dialysis experiments were carried out mainly to obtain a bile salt solution containing the approximate IMC. The time to reach equilibrium was determined by periodically assaying the outer solution concentration for bile salt. These time-course experiments were conducted by dialyzing four donor solutions with the same total lipid concentration (125 mg/mL) but different total egg PC/NaTC molar ratios (0.6, 0.8, 0.9, and 1.0) against 0.9% NaCl/D2O receiver solutions. For all four phospholipid/bile salt systems, there was a relatively rapid increase in the NaTC concentration of the outer receiver solution in 24 h followed by a gradual leveling off. Equilibrium between donor and receiver sides appeared to be reached in 3 days (data not shown). The donor and receiver solutions were assayed after reaching equilibrium. The results are given in Table 1. The concentration of phospholipid in the equilibrated donor solution was adjusted by the volume expansion after the dialysis experiment. The total amount of NaTC in the equilibrated donor and both of the receiver solutions was close to that in the original donor solution (data not shown). The total egg PC/NaTC molar ratios of the equilibrated donor solutions were 0.70, 0.93, 1.04, and 1.16 for series 1, 2, 3, and 4, respectively. The measured IMCs (by HPLC) were 7.33, 5.44, 5.31, and 4.56 mM for the total egg PC/NaTC molar ratios of 0.70, 0.93, 1.04, and 1.16, respectively. These values are comparable in magnitude to the original dialysis work by Duane given that his experiments were conducted with 0.1 N NaCl/H2O at room temperature instead of 0.15 N NaCl/D2O at 37 °C.33 The IMCs were approximately

Li and Wiedmann 8.0, 6.2, 5.7, and 5.0 mM for the same total egg PC/NaTC molar ratios as above. In addition, our data were also consistent with the light-scattering work by Mazer et al.34 where the IMCs at 40 °C were approximately 7.7, 5.1, 4.4, and 4.3 mM. The design of the dialysis apparatus allows separation of the bile salt monomers, bile salt simple micelles, and BS/PC mixed micelles. The molecular weights of NaTC and egg PC are 537.7 and 760.09, respectively. Therefore, only bile salt monomers could penetrate through the dialysis membrane with 1000 MWCO, while both bile salt monomers and simple micelles could penetrate through the dialysis membrane with 5000 MWCO. The only drawback is that bile salt dimers might be able to penetrate through the dialysis membrane with 1000 MWCO, since the size range for the dialysis membrane is (10%. The equilibrated NaTC concentration within the 1000 and 5000 MWCO dialysis membranes were not statistically different from each other (Table 1). The variation of measured IMCs was small within the four series of lipid dilutions. The results indicate that simple micelles (n g 2) are not present in the equilibrated egg PC/NaTC solution at total egg PC/NaTC molar ratios of 0.6-1.0. This is consistent with results of Mazer et al.34 and Schurtenberger and Lindman19 who reported that simple bile salt micelles and small bile salt/phospholipid mixed micelles of fixed composition coexist at PC/BS molar ratios between 0.2 and 0.4. To further demonstrate that the BS/PC aggregate remains isomorphous in each dilution series, the ternary phase diagram of the NaTC/egg PC/H2O system at high water content by Mazer et al.34 has been reconstructed and the composition of each lipid dilution has been marked (Figure 2). The phase diagram consists of three regions separated by two boundaries. The coexistence boundary separates the region where both simple and mixed micelles exist from the region where only mixed micelles are present. The mixed micellar phase boundary separates the mixed micellar region from the region where vesicles are formed. Comparing the coexistence and mixed micellar boundaries at 20 °C to those at 40 °C reveals that the temperature elevation causes both the simple/mixed micelle coexistence and micelle-vesicle transition to occur at lower PC/BS ratios. It is clear in Figure 2 that each of the four series of lipid dilutions falls into the mixed micellar region at 37 °C. The total lipid concentration and total PC/BS molar ratio of the four series of lipid dilution are also given in Table 2. As the dilution number increases, the total lipid concentration and total molar ratio of phospholipid to bile salt decrease. Density Measurements. The densities of a series of diluted solutions were measured for each series (data not shown). The isopotential specific volume of micelle was then calculated from eq 3 to be 0.87619, 0.88258, 0.88573, and 0.88904 mL/g for series 1, 2, 3, and 4, respectively. This analysis is strictly correct only for systems in which the aggregate properties remain constant. For the series of lipid dilutions, the sizes were only relatively constant as given below; however, the slight error in the specific volume did not affect the outcome of data analysis. The increase in specific volume with PC/BS molar ratio in the micelle is of interest. With an increase in the PC/BS ratio, the micelle becomes richer with respect to the PC content. Thus, the increase in specific volume may be related to the inherent differences in the molecular volumes of PC relative to BS. Alternatively, the flexible acyl chains of the PC may allow more efficient packing within the micelle than the rigid BS molecules, and thereby the packing density is increased with the increase in PC. This has also been observed by Mu¨ller.35 In his work, the apparent specific volumes of overall 1:1 PC/BS micelles are 0.912, 0.915, 0.918, and 0.919 mL/g for 10%, 5%, 2.5%,

Diffusion of Bile Salt/Phospholipid Aggregates

J. Phys. Chem., Vol. 100, No. 47, 1996 18469

TABLE 1: Lipid Composition of the Donor Solutions and Equilibrated Donor Solutions and Bile Salt Concentration of the Inner and Outer Dialyzate Solutions (Measured by HPLC) of the Four Series of Lipid Dilutions donor solution CBS (mM) CPC (mM) equilibrated donor solution CBS (mM) CPC (mM) inner dialyzate (mM) through 1000 MWCO outer dialyzate (mM) through 5000 MWCO

series 1

series 2

series 3

series 4

125.0 75.0 80.2 56.0 7.32 ( 0.21 7.33 ( 0.04

109.1 87.3 73.1 67.9 5.43 ( 0.03 5.44 ( 0.06

102.3 92.0 69.6 72.6 5.25 ( 0.08 5.31 ( 0.09

96.3 96.3 72.4 83.6 4.45 ( 0.03 4.56 ( 0.03

Figure 2. PC/BS composition of the four series of lipid dilutions. 0, series 1; [, series 2; O, series 3; 2, series 4. The simple/mixed micelle coexistence boundary and mixed micellar phase boundary are reconstructed from the light-scattering work by Mazer et al.34 ‚‚‚, 20 °C; - - -, 40 °C.

and 1.25% (all w/v), respectively. Since the micelle grows upon dilution, the apparent specific volume increases with PC/BS molar ratio in the micelle. Diffusivities of Water, Phospholipid, and Bile Salt. The observed diffusivities of water, phospholipid, and bile salt were calculated from the FT-PGSE 1H NMR experiments. Before the results are discussed, the limitations of this technique should be addressed. We have recognized that an imperfect match between the two field gradient pulses will lead to partial echo attenuations and displacement of the echo in the time domain which may erroneously be taken as a consequence of diffusion.22 A common practice in large-gradient FT-PGSE experiments is to obtain a maximum echo at the right location and with the right phase, in partial compensation for the inevitable overall imperfection of the experiment. This can be achieved by manually adjusting the width or amplitude of one of the field gradient pulses and the phase of the second rf pulses. To compensate, multiple calibration solvents were chosen in our study to adjust the two field gradient pulses at different field gradient durations to give the same calibration constant (γ2G2). The reason that H2O, D2O, and SDS were chosen was because their diffusion coefficients are in the same range as those of water, BS, and BS/PC micelles. Another issue relates to the micellar polydispersity. There have been studies showing that the polydisperse index increases upon dilution and reaches a maximum at the micellar phase limit.36-38 It has been demonstrated that it is caused by internal modes of the flexible polymer-like mixed micelles. Monitoring of diffusion is then more demanding with regard to data handling procedures than diffusion studies of pure solvents. In essence, deviations from the simple Stejskal-Tanner relation39 have to be interpreted in terms of different echo attenuation models by monitoring the echo decay over a long δ2(∆ - δ/3) interval.40 In our case, signals have been monitored up to 90% decay and

10 data points have been collected. Following the decay further becomes impractical due to the small value of the transverse relaxation, T2. Under these conditions, deviations from the simple Stejskal-Tanner relation were not detected. This is consistent with the findings by Schurtenberger and Lindman.19 The observed diffusivities of water, phospholipid, and bile salt for the four series of lipid dilutions are tabulated in Table 3. For each series, water, bile salt, and micelle diffuse more slowly as the concentration of the lipid is increased. The data of series 1 and 2 were analyzed by the sphere model, and those of series 3 and 4 were analyzed by the rod model. For the sphere model, there are two independent parameters in eqs 17 and 26, hydration of the micelle and intermicellar concentration, which were obtained by solving these equations simultaneously. The radius of the sphere can then be calculated by incorporating both parameters into eq 20. The thickness of hydration layer can be derived from the volume expansion due to the hydration effect. For the rod model, there are four independent parameters, hydration of the micelle, hydration layer thickness, rod length, and intermicellar concentration, in each of eqs 17, 25, and 26. With an additional equation (also containing four independent parameters) to account for the hydration effect on volume expansion, these parameters can be calculated by solving four equations numerically. Intermicellar Concentration. The intermicellar concentration as a function of volume fraction of the micelle is shown in Figure 3 for the four series of lipid dilutions. It decreases upon dilution for series 1 (8.66 f 7.55 mM) and series 2 (6.21 f 5.66 mM), while it increases upon dilution for series 3 (5.40 f 5.55 mM) and series 4 (4.34 f 4.70 mM). For each series, the calculated IMCs of stock and diluted solutions from NMR measurements were higher than the BS concentration of the diluent. This is the reason that the micelle grows upon dilution as will be discussed below. With knowledge of the intermicellar concentration, the PC/ BS molar ratio in the micelle was calculated. The PC/BS molar ratio in the micelle increased slightly with dilution. It ranged from 0.78 to 0.79 for series 1, from 1.02 to 1.04 for series 2, from 1.13 to 1.16 for series 3, and from 1.23 to 1.26 for series 4. The average PC/BS molar ratio in the micelle for each series was calculated for the purpose of discussion. It was 0.79, 1.03, 1.14, and 1.24 for series 1, 2, 3, and 4, respectively. Therefore, the intermicellar concentration decreases as the PC/BS molar ratio in the micelle increases. This is consistent with the findings by Mazer et al.34 They concluded that the IMC is dependent on the hydrodynamic radius which is only a function of the PC/BS molar ratio in the micelle and temperature. The IMC decreased with increasing size of micelle, or equivalently, the IMC decreased as the PC/BS molar ratio in the micelle increased. Hydration of Micelle. The hydration of the micelle was plotted as a function of volume fraction of the micelle and PC/ BS molar ratio in the micelle (Figure 4). The grams of water molecules per gram of lipid molecule in the micelle (Nh) was converted to the number of water molecules per lipid molecule in the micelle (Nh*) for the purpose of comparison with literature

18470 J. Phys. Chem., Vol. 100, No. 47, 1996

Li and Wiedmann

TABLE 2: Total Lipid Concentration (mg/mL) and Total Molar Ratio of Phospholipid to Bile Salt of the Four Series of Lipid Dilutions series 1 stock solution dilution 1 dilution 2 dilution 3 dilution 4 dilution 5 dilution 6 dilution 7 dilution 8 dilution 9

series 2

series 3

series 4

Ctot

PC/BS

Ctot

PC/BS

Ctot

PC/BS

Ctot

PC/BS

81.7 73.5 65.0 56.9 49.2 40.8 32.5 24.7 16.4 8.4

0.70 0.69 0.68 0.67 0.66 0.64 0.61 0.57 0.51 0.39

88.0 79.2 69.7 61.6 53.2 44.0 34.9 25.9 18.0 8.9

0.93 0.92 0.91 0.90 0.88 0.86 0.83 0.79 0.72 0.56

89.7 80.6 71.4 63.3 54.6 45.2 36.6 26.0 19.4 8.9

1.04 1.03 1.02 1.01 1.00 0.97 0.94 0.88 0.82 0.62

100.1 89.8 80.0 69.7 60.6 50.3 40.0 30.3 20.3 10.0

1.16 1.15 1.14 1.12 1.11 1.09 1.05 1.01 0.93 0.74

TABLE 3: Observed Diffusion Coefficient of Water, DW (×105 cm2/s), Egg PC, DsPC ∼ Dmic (×107 cm2/s), and Bile Salt, DsBS (×107 cm2/s), of the Four Series of Lipid Dilutions water diffusion coefficients stock solution dilution 1 dilution 2 dilution 3 dilution 4 dilution 5 dilution 6 dilution 7 dilution 8 dilution 9

PC diffusion coefficients

BS diffusion coefficients

ser. 1

ser. 2

ser. 3

ser. 4

ser. 1

ser. 2

ser. 3

ser. 4

ser. 1

ser. 2

ser. 3

ser. 4

2.54 2.59 2.64 2.69 2.74 2.79 2.84 2.89 2.94 2.99

2.57 2.61 2.66 2.71 2.75 2.80 2.85 2.90 2.94 2.99

2.64 2.68 2.73 2.76 2.80 2.84 2.88 2.92 2.95 3.00

2.65 2.69 2.73 2.77 2.81 2.84 2.89 2.92 2.96 3.00

7.91 8.04 8.19 8.31 8.44 8.57 8.70 8.83 8.95 9.08

4.79 4.88 4.96 5.03 5.09 5.18 5.26 5.34 5.41 5.49

3.14 3.18 3.23 3.27 3.31 3.36 3.40 3.45 3.48 3.54

2.51 2.55 2.59 2.63 2.66 2.70 2.74 2.77 2.81 2.85

12.2 12.7 13.1 13.7 14.5 15.7 17.1 19.3 22.4 26.7

8.70 8.88 9.11 9.75 10.3 11.6 13.0 15.5 18.9 23.9

6.60 6.88 7.44 7.90 8.55 9.90 11.1 13.6 16.5 22.6

5.30 5.50 5.80 6.47 7.10 8.00 9.50 11.7 14.8 20.1

Figure 3. Effects of micellar concentration on the intermicellar concentration of the four series of lipid dilutions. 0 series 1; [, series 2; O, series 3; 2, series 4.

values. The hydration of the micelle decreased slightly upon dilution. It also decreased with PC/BS molar ratio in the micelle. The average hydration number of the micelle was 39, 33, 22, and 18 for series 1, 2, 3, and 4, respectively. The hydration of phospholipid vesicles has been studied extensively.41-43 There has been a report that on average there are 12.4 water molecules per phospholipid molecule in a bilayer.343 Lindman et al.13,17 have investigated the dynamics in aqueous sodium cholate solution. They reported that the minimum number of water molecules per sodium cholate molecule in micelles is 20. The higher hydration number is expected given the nature of the cholate association. The rigid molecule with multiple hydroxyl moieties possesses sites for water interactions. Furthermore, hydrogen bonding among small aggregates appears to lead to the formation of larger aggregates at high cholate concentrations. The aggregate hydration number increases from 22 in a 0.1 mol/kg sodium cholate solution to 43 in a 0.2 mol/kg sodium cholate solution, while for typical micelle-forming substances the hydration numbers stay constant

Figure 4. Effects of micellar concentration on the hydration of the micelle of the four series of lipid dilutions. 0, series 1; [, series 2; O, series 3; 2, series 4.

or decrease with increasing concentration. Thus, the hydration number of BS/PC micelle should range from 20 to 40 depending on the PC/BS molar ratio in the micelle, and it should decrease with PC/BS molar ratio in the micelle. This is consistent with our data. Mu¨ller has also reported that on average each lipid molecule is associated with 28 water molecules for the overall 1:1 PC/ BS micelle at pH 9, 0.15 M NaCl solution.35 In our study, at approximately a 1:1 egg PC:NaTC molar ratio in the micelle (series 2), the estimate of water molecules per lipid molecule was 33 which is slightly larger than the literature value. When the series 3 and 4 were fitted into sphere model, the hydration of the micelle became 26 and 21, respectively. These number are larger than those fitted into rod model as given above. This may explain why the hydration of the micelle appears too large for series 2 of the lipid dilutions. Apparently, the sphere model is not suitable for the data analysis of series 2 lipid dilutions. Figure 5 shows the thickness of hydration layer as a function of volume fraction of the micelle. There is a slight increase of

Diffusion of Bile Salt/Phospholipid Aggregates

Figure 5. Effects of micellar concentration on the hydration layer thickness (Å) of the micelle of the four series of lipid dilutions. 0, series 1; [, series 2; O, series 3; 2, series 4.

hydration layer thickness upon dilution for series 1 (5.82 f 6.74 Å) and series 2 (8.56 f 9.92 Å). However, the thickness of the hydration layer remains constant with dilution for series 3 and 4. The average thickness is 6.80 and 5.83 Å for series 3 and series 4, respectively. For series 1, 3, and 4, the hydration layer thickness seems to be in the range of 6-7 Å regardless of the PC/BS molar ratio in the micelle. Long et al.14 have used small-angle neutron scattering to probe the structure and interparticle interactions of phospholipid/taurodeoxycholate mixed micelles. Their results showed that the hydration layer thickness of mixed micelles was 6 ( 2 and 7 ( 4 Å for the 0.05 M NaCl series and 0.15 M NaCl series, respectively, at an overall molar ratio of PC to BS equal to 0.9. Again, the thickness of hydration layer of series 2 lipid dilutions is larger than those of series 1, 3, and 4. It is evident that micelles of series 2 lipid dilutions are not spherical. Micellar Size. The micellar size was calculated after applying the excluded-volume effect in the data analysis of the NMR diffusion experiment. For the excluded-volume effect, the classical theory of Brownian motion applies to suspensions which are so dilute that each particle is effectively alone in an infinite continuum. When the suspension is not extremely dilute, the interactions of particles will affect their migration. One type of interaction, that due to interparticle forces, has been studied extensively. The dependence of the thermodynamic quantities describing the state of a statistically homogeneous suspension or solution on the concentration of particles is known in the form of a virial expansion for various functional forms of the interaction potential. It has been theoretically shown that both the attraction and repulsion forces cause a decrease of the self-diffusion coefficients.27 The repulsive forces acting between particles prevent an individual particle from movement over the range of the interparticle distance, resulting in a negative contribution to the self-diffusion coefficient. This has been demonstrated by the computer simulation of Gaylor et al.44 Therefore, the electrostatic repulsion not only increases the hydrodynamic volume of the micelles but also decreases the effective diffusivity of the micelles. The other type of interaction is considered to be hydrodynamic and results from the fact that the movement of one particle through the fluid generates a long-range flow disturbance and velocity field which affect the motion of neighboring particles.45-47 The hydrodynamic interaction can be separated into a short-range part and long-range part. The long-range interaction can be further split into an Oseen part and a dipole part.46,47 In a hard sphere system with a screened Coulomb type repulsive potential, hydrodynamic interactions cause an

J. Phys. Chem., Vol. 100, No. 47, 1996 18471

Figure 6. Effects micellar concentration on the radius of the spherical micelle. 0, series 1; [, series 2.

increase in the self-diffusion coefficient.34 In a system of hard spheres with a Lennard-Jones attractive potential, the effect of hydrodynamic interactions on the self-diffusion coefficient depends on the surface potential. When the surface potential is small, hydrodynamic interactions cause a decrease in the selfdiffusion coefficient.27 However, when the surface potential is large, there is an increase in the self-diffusion coefficient.27 In the last decade there has been considerable development both theoretically as well as experimentally in the concentration dependence of the mutual diffusion coefficient and self-diffusion coefficient of interacting spherical particles.27,45-54 The concentration-dependent diffusion of bile salt/phospholipid mixed micelles could be much more complicated than the classical surfactants due to the very different chemical structure and surface charge of the bile salts, the shape and cooperativity of the micelles, and the interaction between the bile salt and phospholipid. On the basis of the enormous progress that polymer and colloid physics has made in recent years, the theoretical descriptions of the mutual diffusion coefficient of elongated BS/PC micelles have been developed by Egelhaaf and Schurtenberger38 and Pedersen et al.55 However, there have been no investigations indicating what the concentration dependence of self-diffusion coefficient of BS/PC micelles should be. Therefore, eq 25 was used as an approximation to estimate the excluded-volume effect of elongated BS/PC micelles in this study. For the sphere model, the radius of the micelle was calculated by subtracting the hydration layer thickness from the hydrodynamic radius. The results are given in Figure 6. There is an increase in the size of the micelle upon dilution. The radius increases from 18.4 to 21.9 Å for series 1 and from 31.9 to 37.4 Å for series 2. The hydrodynamic radius increases from 24.3 to 28.6 Å for series 1 and from 40.4 to 47.3 Å for series 2. The aggregation number was calculated to be 28-47 for series 1 and 140-230 for series 2. In the X-ray structure analysis of the structural dimorphism of BS/PC mixed micelle, Mu¨ller reported that the mixed micelles were spherical for the overall molar ratio of PC to BS equal to 0.33.35 The radius of the 1:3 PC/BS micelle was 31 Å, and the aggregation number was 48. Since the micellar size of series 1 dilutions is quite small, the use of the sphere model to analyze the NMR data is reasonable. However, the micellar size of series 2 dilutions seems to be too large to fit the sphere model. This is also supported by the results of micelle hydration as mentioned above. According to the capped-rod model by Nichols and Ozarowski,10 the rod length of the micelle for series 2 dilutions should be between 147 and 157 Å, based on the PC/BS molar ratio in the micelle.

18472 J. Phys. Chem., Vol. 100, No. 47, 1996

Figure 7. Effects of micellar concentration on the length of the rodlike micelle. O, series 3; 2, series 4.

Figure 8. Length of the rodlike micelle as a function of PC/BS molar ratio in the micelle. O, series 3; 2, series 4; - - -, calculated curve from eq 28. The parameters in eq 28 were estimated from the most diluted sample of series 3 and 4 (indicate by arrows).

Therefore, the ratio of rod length to diameter (p) is around 3. Although the expressions (eqs 21-23) by Tirado et al.28 are valid for 2 < p < 30, the NMR data of series 2 dilutions could not be fit to the rod model. The results of the data analysis of series 3 and 4 for the rod model are shown in Figure 7. The rod length was plotted as a function of volume fraction of the micelle. It is clear that the micelle grows upon dilution for series 3 (117 f 225 Å) and series 4 (176 f 369 Å). Thus, dilution of a BS/PC mixed micellar solution with a diluent containing the approximate IMC for a relatively high lipid concentration can still result in a variation of PC/BS molar ratio in the micelle and change of micellar size. For the smallest elongated micelle (rod length, 117 Å), the theoretical k value (calculated from eq 25) for rigid rods was approximately 30% larger than theoretical value for hard core sphere; for the largest micelle (rod length, 369 Å), the theoretical k value for rigid rods was more than a factor of 2 larger than theoretical value for hard core sphere. However, the theoretical k values for rigid rods led to inappropriate micellar sizes as discussed below. When the rod length is plotted as a function of PC/BS molar ratio in the micelle, an inconsistency with the expectation of size is evident. As shown in Figure 8, micelles have a sharp change in calculated length with relatively small changes in the PC/BS molar ratio. Therefore, there exists other factors in determining the self-diffusion coefficient of BS/PC micelles. Recent studies have demonstrated that the structure of BS/PC mixed micelles could be described by the wormlike chain

Li and Wiedmann model.56,57 In this model, the flexibility of the rod is characterized by a persistence length. Generally, the persistence length of polymer-like micelles ranges from about 100 Å for reverse micelles58 up to 200 Å for ionic surfactants59 at high ionic strength. In the study by Egelhaaf and Schurtenberger, the persistence length of sodium taurochenodeoxycholate/egg PC micelles ranged from 100 to 250 Å. One important finding is that the persistence length decreased as the micellar size increased. This may be due to the increase of PC/BS molar ratio in the micelle upon dilution which, in turn, results in a decrease of the relative charge density of the micelles. This allows for a greater flexibility and thus a decrease in the persistence length. Another factor leading to the failure of the theoretical predictions is the possibility of a micelle penetrating surrounding micelles. This type of penetration does not occur with polymers and is perhaps unique to micellar systems. This interpenetration would also be expected to reduce the value of k in the concentration dependence of the micellar diffusion. Since the PC/BS ratio within the micelle did not change dramatically upon dilution in each series, it is reasonable to assume that the flexibility factor in each dilution remains constant. In order to estimate the effect of interpenetration of micelles on the micellar diffusivity, the theoretical relationship derived by Nichols and Ozarowski10 was used to estimate the rod length. In this capped-rod model, the growth of the micelles occurs by elongation of the rod with a constant radius of 27 Å. The rod length (L) depends on the phospholipid to bile salt ratio in the entire micelle which can be defined by four parameters: R (number of phospholipids per length), β (number of bile salts per length of the rod portion of the micelle), a (number of phospholipids in each cap), and b (number of bile salts in each cap). Thus, the ratio of phospholipid to bile salt in the 1-palmitoyl-2-oleoylphosphatidylcholine (POPC)/deoxycholate (DC) micelle is equal to

PC RL + 2a ) BS βL + 2b

(27)

where PC and BS are the number of phospholipid and bile salt molecules in the micelle, respectively. Solving for L yields

L)

2b (PC/BS - a/b) β (R/β - PC/BS)

(28)

for a/b e PC/BS < R/β. The relationship predicts a hyperbolic increase in L as a function of PC/BS. As PC/BS approaches a/b (the ratio in the caps), L approaches zero, and as PC/BS approaches R/β (the ratio in the rod), L approaches infinity (i.e., the micellar phase limit). The best-fit parameters for this model are a/b ) 0, R/β ) 1.40, and 2b/β ) 81.6 Å. At the lowest lipid concentration of series 3 and 4, as indicated by the arrows in Figure 8, it is reasonable to assume that interpenetration of micelles play a negligible effect on the diffusivity of micelle. Therefore, assuming a/b ) 0, R/β and 2b/β were calculated to be 1.49 and 69.06 Å, respectively. The rod length of the rest of series 3 and 4 was then calculated by substituting these three parameters and PC/BS molar ratio in the micelle into eq 28. The results were a curve as shown in Figure 8. It turns out that the rod length increases upon dilution from 216 to 245 Å for series 3 and from 320 to 369 Å for series 4. Evidently, the interpenetration of micelles has a dramatic effect on the diffusivity of micelle. It is not surprising that this effect depends on both the concentration and size of the micelle. In fact, it causes a 56% and 60% decrease of the theoretical k value on the basis of the excluded-volume effect of rigid rods for the stock solutions of series 3 and 4, respectively.

Diffusion of Bile Salt/Phospholipid Aggregates Conclusion Bile salt/phospholipid aggregates have been characterized with density measurements, dialysis studies, and Fourier transform pulsed-field gradient spin-echo (FT-PGSE) 1H NMR diffusion methods. The results have provided a means to analyze the concentration-dependent diffusion of these anionic colloids. The design of the dialysis experiments allowed separation of the bile salt monomers, bile salt simple micelles, and BS/PC mixed micelles. The isopotential specific volume increased with increasing PC/BS molar ratio in the micelle. This might due to the inherent differences in the molecular volumes of PC relative to BS and/or more efficient packing and higher charge density of the larger micelles. The hydration of micelle decreased with increasing PC/BS molar ratio in the micelle or equivalently increasing size of the aggregate. This is expected given the nature of the cholate association. The rigid molecule with multiple hydroxyl moieties possesses sites for water interactions. For each series of the lipid dilutions, the micellar size increased upon dilution after correcting for the excludedvolume effect. Series 1 fit well with an excluded volume factor based on hard core spheres. Series 2 yielded physically unreasonable sizes when either spherical or rod corrections were applied. Series 3 and 4 were well fit by rod-shaped excluded volume corrections. However, the flexibility of the micelle and interpenetration of micelles are also important factors in evaluating the properties and aggregate behavior of BS/PC mixed micelles. Acknowledgment. Our thanks for the support provided by NIH RO1-CA 55493 and International Student Work Opportunity Program. We acknowledge Professor Cheryl Zimmerman for her helpful comments as well as the reviewers. References and Notes (1) Palmer, R. H. Prog. LiVer Dis. 1982, 7, 221. (2) Cabral, D. J.; Small, D. M. In Handbook of PhysiologysThe Gastrointestinal System III; Schultz, S. G., Forte, J. G., Rauner, B. B., Eds.; Waverly Press: New York, 1989; Section 6, p 621. (3) Lee, S. P.; Park, H. Z.; Madani, H.; Kaler, E. W. Am. J. Physiol. 1987, 252, G374. (4) Kibe, A.; Dudley, M. A.; Halpern, Z.; Lynn, M. P.; Breuer, A. C.; Holzbach, R. T. J. Lipid Res. 1985, 26, 1102. (5) Halpern, Z.; Dudley, M. A.; Lynn, M. P.; Nader, J. M.; Breuer, A. C.; Holzbach, R. T. J. Lipid Res. 1986, 27, 295. (6) Small, D. M. Gastroenterology 1967, 52, 607. (7) Shankland, W. Chem. Phys. Lipids 1970, 4, 109. (8) Ulmius, J.; Lindblom, G.; Wennerstrom, H.; Johansson, L. B.-A.; Fontell, K.; So¨derman, O.; Arvidson, G. Biochemistry 1982, 21, 1553. (9) Lindblom, G.; Eriksson, P.-O.; Arvidson, G. Hepatology 1984, 4, 129S. (10) Nichols, J. W.; Ozarowski, J. Biochemistry 1990, 29, 4600. (11) Hjelm, R. P.; Thiyagarajan, P.; Alkan, H. J. Phys. Chem. 1992, 96, 8653. (12) Long, M. A.; Kaler, E. W.; Lee, S. P. Biophys. J. 1994, 67, 1733. (13) Lindman, B.; Kamenka, N.; Fabre, H.; Ulmius, J.; Weiloch, T. J. Colloid Interface Sci. 1980, 73, 556. (14) Long, M. A.; Kaler, E. W.; Lee, S. P.; Wignall, G. D. J. Phys. Chem. 1994, 98, 4402. (15) Stilbs, P.; Moseley, M. E.; Lindman, B. J. Magn. Reson. 1980, 40, 401.

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