4402
J. Phys. Chem. 1994,98, 4402-4410
Characterization of Lecithin-Taurodeoxycholate Mixed Micelles Using Small-Angle Neutron Scattering and Static and Dynamic Light Scattering Michelle A. Long,* Eric W. Kaler,’**Sum P. Lee$ and George D. Wignallt Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716; VA Medical Center, Seattle, Washington 98108; and Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830-6393 Received: January 25, 1994’
We have used small-angle neutron scattering (SANS) to probe the structure and interparticle interactions of
lecithin-taurodeoxycholate mixed micelles. The data are fit to a core-shell model that provides the micelle composition and dimensions. The effects on the scattering spectra of electrostatic and excluded-volumeinteractions are explored in terms of the decoupling approximation (Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983,79, 2461) and the random phase approximation (Shimada, T.; Doi, M.; Okano, K. J. Chem. Phys. 1988,88,2815). We found the TDC-lecithin micelles are cylindrical particles with an average cross-sectional radius of 26.7 f 0.4 A. The coreshell structure is found to be an appropriate model for the highly hydrated micelles. The micelle length increases dramatically with an increase in added electrolyte, but not with decreasing concentration as previously reported. The SANS data analysis shows that particles in 0.05 M NaCl grow by less than 15% with a 3-fold decrease in the total surfactant concentration. This is in contrast to the simple interpretation of dynamic light scattering of the same samples that shows an apparent doubling of the micelle length with the same decrease in surfactant concentration. This discrepancy is attributed to neglect of the thermodynamic and hydrodynamic interactions in the analysis of the dynamic light scattering data. Corrections for the thermodynamic interactions are determined from the static data and applied to the interpretation of dynamic light scattering measurements. The strength of hydrodynamic and entanglement interactions is also discussed in relation to existing models for both semidilute polymer solutions and spherical particles.
Lecithin and bile salt are the two major cholesterol-solubilizing agents found in gallbladder bile. Lecithin is a double-tailed zwitterionic surfactantwell-known for its tendency to form bilayers in solution. Bile salts are derived from cholesterol, and the four fused rings of the steroid backbone impose a “planar” structure on the surfactant. One face of the bile salt molecule is hydrophobic, while the other face is hydrophilic because of the presence of hydroxyl groups. Bile salt species differ in the number and position of hydroxyl groups and conjugation of the short hydrophilic tail with taurine or glycine. Like other surfactants, most bile salts self-associateto form either globular or cylindrical micelles.14 In gallbladder and hepatic bile, lecithin and bile salt together will form mixed aggregates (micelles or vesicles) that solubilize cholesterol. The liver continuouslyproduces hepatic bile, which is a dilute (3 g/dL) solution of lecithin, bile salt, and cholesterol. In hepatic bile the insoluble cholesterol is carried by unilamellar, lecithinrich vesicles.s When bile is not needed for digestion, it is stored in the gallbladder for future use. Water is extracted during storage, and the resulting high concentrations of bile salt drive a microstructural transition from vesicular aggregates to mixed micelles of lecithin, bile salt, and cholesterol. Mixed micelles are less efficient than vesicles for carrying cholesterol,6 and the transition from vesicles to micelles may induce nucleation of cholesterolcrystals. The presence of microcrystalsof cholesterol is the necessary precursor to the formationof cholesterolgallstones. The long residence times in the gallbladder allow comparison of the state of native bile with the appropriate equilibrium phase diagram.’ Thus, investigation of the equilibrium state of model bile could provide an initial step toward discovering the cause of cholesterol gallstone disease.
* To whom correspondence should be addressed. 8
Department of Chemical Engineering, University of Delaware.
I V A Medical Center, Seattle.
Solid State Division, Oak Ridge National Laboratory. Abstract published in Aduance ACS Absrracrs, March 15, 1994.
0022-3654/94/2098-4402%04.50/0
The formation and transformations of mixed micelles in solutions of lecithin and bile salt have been studied widely. In a comprehensive paper, Mazer et a1.*used static and quasielastic light scattering to support the “mixed disk” model of micelle structure. The mixed disk body consists of a central lecithin bilayer interspersedwith bile salt dimers. The hydrophobicedges of the body are shielded from aqueous solution by a ring of bile salt. The dynamic light scattering data indicated a hyperbolic increase of the hydrodynamic radius of the micelles with decreasing total lipid concentration, and this increase was interpreted as evidence of radial growth of the disk-shaped particles. Mazer and co-workers proposed that as a concentrated micellar mixture is diluted, bile salt is leached from the perimeter of the structure to maintain an intermicellar concentration of monomer (IMC). The newly exposed lecithin tails will cause micelles to fuse into larger aggregates while preserving a constant ratio of lecithin and bile salt dimers within the body of the disk. Once the bile salt can no longer adequately surround the bilayer, hydrophobic interactions between the exposed lecithin tails at the edges of the disks and the aqueous solution will cause the large disks or sheets to spontaneously fold into vesicles. The mixed disk model was challenged by small-angle neutron scattering (SANS) measurementsof aqueous solutions containing lecithin and the trihydroxy bile salt glycocholate. From theshape of the scattering curves, Hjelm et al.9J0determinedthat the mixed micelles found at higher concentrations were not disklike but instead are elongated with a radius of approximately 27 A. With dilution, the cylindrical particles give way to extended sheetlike structures, and ultimately unilamellar vesicles form in highly dilute solutions. Reconsideration of the analysis of the hydrodynamic measure ments of the mixed micelles showed that growth of cylindrical micelles through elongation can equally well describethe observed hyperbolic increase of the hydrodynamic radius.” The new micelle model proposes that the lecithin molecules are arranged radially along axis of the micelle (Figure 1). The body of the 0 1994 American Chemical Society
Lecithin-Taurodeoxycholate Mixed Micelles
Figure 1. Core-shell model of cylindrical micelle. The micelle shell is defined to include the lecithin headgroup, the bile salt molecules, and any water of hydration. The core is made up of the lecithin tails. The final scattered intensity is a weighted average of the contributionsof the two regions. The molecular structures of lecithin and bile salt are given at the top.
cylinder is mostly lecithin, and the rod ends are capped by bile salts. A similar model was proposed for the infinitely long rods making up the more concentrated hexagonal phase.12 Axial growth of the capped cylinders occurs with dilution because of the need to balance the amount of bile salt availableto the endcap with the IMC. While the predictions of the capped cylinder model correlate well with the measured hydrodynamicradii obtained by dynamic light scattering, there still remains a lack of understanding of the effects of intermicellar interactions on the measured light scattering signals. These important effects are mostly ignored in the analysis of dynamic light scattering measurements of these micelles. The diffusion coefficient derived from dynamic light scattering measurements is an apparent value and reflects the effects of electrostatic and excluded-volume thermodynamic interactions as well as hydrodynamic interactions. These interactions impose a nonrandom distribution of the particles within the solution and directly affect both the amplitude and the correlations of the scattered intensity. Unless interparticle interactions are properly accounted for, scattering experiments yield erroneous results. Interparticle interactions are not negligible in bile. Bile salts are anionic surfactants, so bile salt micelles exhibitelectrostatic interactions,13 and excluded-volume interactionsare present in any concentrated micellar solution. Characterization of the interparticle interactions in bile salt solutions is a complex problem because the mixed micelles are elongated, and the "simple" solutions to the statistical mechanical problem of calculating the magnitude and range of interactions have been reserved for spherical particles. Static light scattering and small-angle neutron scattering are complementary techniques that can provide information about micellar structure and intermicellar interactions. This information can then be employed for the accurate interpretation of dynamic light scattering measurements. A small-angle scattering experiment measures the intensity pattern of coherently scattered radiation that is constructed by the arrangement of scattering centers in solution. The scattered intensity is reported in terms of the magnitude of the scattering vector q = 4rIX sin(e/2), where 6 is the scattering angle defined by the instrument geometry and Xis the wavelength of the incident radiation. Becauseofthe long wavelengthsofvisible light (-5000 A), the magnitude of q available in a light scattering experiment is limited to values less than 0.003 A-1, while the shorter wavelengths of neutrons allow SANS measurementsup to q value of 0.2 A-1 or more. The scattering vector has units of inverse distance and is inversely proportional to the length scales probed in the experiment. As a result, the intensity at low values of q is sensitive to long-range structure in the solution caused by interparticle interactions; this is especially significant in the light
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4403 scattering q range. The intensity at higher values of q enables determination of particle shapes and dimensions. Because the expandedq range of SANS extendsbeyond the range of influence of interparticle interactions, SANS provides more conclusive measures of particle structures than those available from a light scattering experiment. The information obtained from the combination of these techniques aids in the construction of a more realistic model of the surfactant microstructure transitions found in the physiological pathway of bile. In this paper we begin with a descriptionof the static scattering theory for cylindrical particles. Emphasis is placed on the discussionof two models availablefor the calculationof the effects of interparticle interactions on the scattering spectra. The first model is the decouplingappr~ximationl~ that treats the ordering and orientation effects of interparticle interactions separately. The second model, the random phase approximation (RPA15J6), avoids explicit consideration of relative particle position and orientation by using a mean-field interaction. This expression, originally developed for polymer melts, provides a good description of theeffects of intermicellarinteractions on the scattered intensity spectra for the elongated micelles of this study. We then briefly summarize the established expressions quantifying the influence of thermodynamic and hydrodynamic interactions on dynamic light scattering (DLS) measurements of dilute and semidilute solutions. Next are presented scattering measurements of a series of lecithin-taurodeoxycholate mixed micelle samples that vary in total surfactant concentrationand the amount of added electrolyte. Thesevariables were chosen to assess the degreeto which excludedvolume and electrostatic interactions contribute to the q dependence of the scattered intensity. At high q values interparticle interactions do not affect the scattering spectra, and fitting the data begins with the applicationof a core-shell model to determine the intramicellar structure. The analysis yields the radial dimensions of the micelle, the relative ratio of lecithin to bile salt in the micelle, and the amount of water interspersed around the headgroup. This informationis then used to model the scattering over the entireq range, and we determinethe limits of applicability of the decoupling approximation and the RPA. The structural and thermodynamicinformationobtained from the static intensity data is then incorporated into a predictive model of the diffusion of interacting cylindricalparticles and compared to experimental dynamic light scattering measurements. These results show the potential for misinterpretationof DLS data when thermodynamic and hydrodynamic interactions are ignored.
Scattering Models for Colloidal Particles In this experiment, the measuredSANS intensity was converted (see below) to an absolute differential scattering cross section per unit soid angle, per unit volume of material Z(q). This quantity has units of cm-l and is given by N
The summation is the total scattering amplitude of N scattering centers. Each center 1has coherent scattering amplitude b, (the atomic scattering length for neutron scattering or the molecular polarizability for light scattering) and is found at position rrrelative to an arbitrary origin. The intensity is defined as the product of the amplitude and its complex conjugate representedsymbolically by I...I2. The actual measured intensity is the orientationalaverage (( ...)) of the scattered intensity at each value of q. B is the q-independent contribution of incoherent scattering that in a SANS experiment is attributed mainly to hydrogen in the sample. For a dispersion of particles it is convenient to separate the distribution of scattering centers within a particle from the distribution of particles within solution. The particle form factor
4404
The Journal of Physical Chemistry, Vol. 98, No. 16,1994
accounts for the position of a scattering center within a particle. The form factor varies with particle size and shape and can be calculated either analytically or n~merically.’~ The amplitude form factor for each particle j is
where p(r) is the scattering length density and is defined as the average of the atomic scattering lengths per unit volume. In practice, the measured intensity includes the q-independent contribution of the solvent, so the scattering length density difference between the particle and the solvent (pIIv)is used to calculate the form factor. Experimentally, thesolvent contribution is measured separately and subtracted to yield the excess particle scattering. If a solution of particles is dilute, the form factor alone describes the scattered intensity. On the other hand, in a solution of interacting particles the position of each particle will depend on the position of all others. Interparticle interactions can have a significant effect on the q dependence of the scattered intensity. Repulsive particle-particle interactions cause a reduction of the intensity at low q and ultimately can produce a maximum in the scattered intensity when the particles strongly interact. When these interactions do not depend on the relative orientation of the particles, the intensity can be factored into separate intra- and interparticle functions. In addition, when all orientations of the scattering centers in solution are equally probable, the intensity is a function of only the magnitude of the scattering vector q. These assumptions lead to the well-known expression Z(q) = Np P(q) S(q) where P(q) = (IW2) and
S(q),the solution structure factor, is the Fourier transform of the
pair correlation function, which in turn depends on the form and strength of the interparticle interactions.18 There are closedform expressions of S(q) for dispersions of spherical particles interacting via excluded-~olume~~ or electrostatic potentials.20 The above separation of the particle shape and interaction contributionsto the scattering spectra is exact for a monodisperse solution of spherically symmetric particles. However, mixed micelles of lecithin and bile salt are cylindrical, and description of their scattering spectra is more complicated. The “decoupling approximation” is a first-order correction that allows application of the structure factor expressions for spherical particles to solutions of polydisperse or elongated parti~1es.l~ The particles are redefined as equivalent spheres for calculation of S(q),which is then modified by the effects of orientation or polydispersity through a parameter (3(q). This procedure allows expression of theintensityasZ(q) = NpP(q)S’(q),whereagainP(q) = (IF(q)12) and
In the case of elongated particles, the radius of the equivalent sphere is determined by equating the second virial coefficient of the elongated particle21 to the second virial coefficient of a hard sphere dispersion. The decoupling approximation is expected to give reliable estimates of the effects of interparticle interactions on the scattering of elongated particles only in a dilute regime, where each particle occupies its own distinct volume element. The decoupling approximation is likely to fail when the particle concentration reaches the point where contact or entanglement
Long et al. occurs. This “semidilute” regime exists for cylindrical particles of length L, radius R, and number density N p when the volume fraction 9, is between N 4 3 and N&2R.22 The scattering from a semidilute solution of cylindrical particles can be modeled using tools developed to describe polymer melts. The random phase approximation (RPA) uses a mean-field approach to model the effects of segment-segment interactions within a volume element.15J6.23 The RPA result for the static scattering of the solution is proportional to the Fourier transform of the segment concentration distribution rather than the Fourier transform of the pair correlation function as described in the decoupling approximation. The RPA expression is
where A is a constant proportionalto the scattering length density difference and the number of particles and v is an excludedvolume parameter.24 Po(q) is derived from the reference state of the concentration distribution defined in the limit of no interactions. Po(q) is thus equivalent to P(q). Equation 6 was derived for flexible polymers where interactions are a function only of distance and not of relative orientation. If the scattering units are rigid, the relative orientation of two interacting units must be included in the calculation of the concentration distribution function. The RPA with the corrections for rigid particles has been applied to static and dynamic light scattering of rigid p0lymers,2”~ and the static intensity is
where Po(q) is the form factor of a cylinder and function Ro(q) contains the effects of relative particleorientati~n.~~ When there are no orientation effects, the function &(q) = 0, and eq 6 is recovered. Before attempting to fit a detailed model to the scattered intensity, we obtained preliminary information about the micelles using asymptotic expressions of Z(q). The cylinder radius can be estimated from the data at high q, where the effects of interparticle interactions are minimal. For q > 1/15, the scattered intensity is insensitive to I5 and depends only on the cross-sectional size and internal structure.28 For homogeneous cylinders,
where &8 is the cross-sectional radius of gyration ( R / Afor a circular cross section), Ap2 is the square of the scattering length density difference, Vpis the cylinder volume, and $t is the particle volume fraction. A plot of ln(qZ) vs q2 is linear over the range of q > 1/ L , and the slope provides an estimateof 4.The intercept is a measure of the average scattering length density per unit length. For homogeneous particles, the scattering length density is a constant that can be factored out of the integral that defines the form factor. Incontrast, the scatteringlengthdensityofsurfactant aggregates varies within the particle. Surfactant molecules selfassociate, generally arranging their hydrophilic headgroups to shield their hydrophobic portions from contact with aqueous solution. This sets up a ”core-shell” structure with the hydrophobic tails forming a central core of radius Rc of a scattering length density pc. The core is surrounded by a shell of headgroups with scattering length density ps (Figure 1). The form factor for
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4405
Lecithin-Taurodeoxycholate Mixed Micelles a core-shell cylinder of total volume V = nR2Laveraged over all orientations y is29
where H = L/2 and Jl(x) is the first-order Bessel function. Once the static intensity data has provided the structural and thermodynamic details of the particles in solution,the information can be used to check the consistency of apparent diffusion coefficients measured by dynamic light scattering data. In an infinitely dilute solution, where there are no interparticle interactions, the diffusion coefficient is described by the Einstein relation DO= kT/J wheref is the frictional drag coefficient that depends on particle size and shape. For a spheref equals 6m&, where& is the hydrodynamic radius and Q is the solvent viscosity. The frictional coefficients of anisotropicshapes (disks or cylinders) are functions of two axial dimensions, and determination of the particle dimensions is not possible without prior knowledge of one length or the axial ratio. In concentrated solutions the apparent diffusion coefficient measured by DLS is a function of the interparticlethermodynamic interactions represented by S(q) and hydrodynamic interactions, represented by the function H(q). The apparent diffusion coefficient is
where DOis the diffusion coefficient at infinite dilution. The fit to the static scattering data provides S(q). When the thermodynamic interactions are repulsive, S(q) is less than one and D,, > DO. This increase is countered by the retarding effects of hydrodynamic interactions that occur when the flow field of one particle influences the motion of another. In the limit of q 0, expressions for D,, of spherical particles expand S(0) and H(0) in terms of the particle volume fraction. To first order in 4, S(0) = 1 - 84 for hard-sphere interactions and H ( 0 ) = 1 - 6.444,3O so
-
Dapp(q+O)= Do(l
+ 1.564 + ...)
(1 1)
Linear extrapolation of D,,(q=O) versus 4 provides Do. The particle dimensions are then determined through the friction coefficient of the Einstein relation. The particle dimensions derived from the friction coefficient are often larger than the anhydrous values because dynamic light scattering measures the center-of-massdiffusion of a particle and so includesany entrained water. A more general expression allowing the use of any interparticle potential at all q has been derived.31 The results of this detailed calculation show that H(q) increases with q to an asymptotic value of 1. The translational diffusion of a cylindrical particle is the sum of parallel and perpendicular components: Dt, = (Dl1 2D1)/3. The friction coefficients in each direction are unequal, so the direction of translation depends on the particle orientation. This effect, coupled with the orientation dependence of the cylinder scattering function, causes D,, to vary with q.22 In addition, D,, is inversely proportional to S(q)as it is for sphericalparticles. Equation 1226927incorporates the effects of both the cylinder anisotropy (through the coefficients Fl(qL) and F2(qL)22) and the interparticle interactions into a predictive equation for Dapp.
+
Dapp(q) =
+ ( ~ ' / 1 2 ) ~F,(qL) r -
[ ~ t ,
(D,, -4 ) ( ' / 3
- F,(q.Q)I/S(q) (12)
where L is the particle length and 0, is the rotational diffusion coefficient. Equation 12 is expected to overestimate the magnitude of Dapp because it does not explicitly account for either hydrodynamic or entanglement interactions. There are no satisfactorytheoretical expressions for the interparticle hydrodynamic interactions of cylindricalparticles. Entanglement effects occur when the motion of a micelle is stericallyhindered by the presence of other micelles. In this situation, the perpendicular diffusion component and the rotational diffusion coefficient are constrained while the parallel component remains ~ n a f f e c t e d . ~Both ~ hydrodynamic and entanglement effects can be quantified in terms of an empirical function fl(q), which is of order (N&3)-1, by replacing the rotational and perpendicular diffusion coefficients in eq 12 with j3(q) D, and @(q)DLeZ2 The intent of fl(q) is analogous to that of H(q), and similarly the magnitude of fl should increase with q. Because the q dependence of 0 is unknown, fl(q) is taken as a constant in a first approximation.
Materials and Methods Materials. Egg yolk lecithin (in chloroform) and sodium taurodeoxycholate(TDC) were obtained from Sigma Chemicals. TDC was recrystallized (to a yield of 38%) following a modification of the method of Hsd3 that included dissolving the TDC in 90% aqueous ethanol and boiling it under reflux with activated charcoal for 10 min. Without this extra step, the crystals in the final product have a yellow impurity. After the solution had cooled, chloroformwas added to precipitate any sodium chloride, and the solution was filtered through a 0.2-pm Nucleopore filter that had been boiled to remove any wetting agents. Diethylether was added until incipientcloudinesswas observed, and the solution was stored at 4 OC for 4 days. The resulting white needlelike crystals were filtered and dried in a vacuum over for 2 days. Solutions. Lecithin was dried under nitrogen in a rotating scintillationvial to produce a thin film. These films were further dried under vacuum until they reached a constant dry weight (typically 4-5 days). Appropriate amounts of dry bile salt and D20 saline solution (0.05,O. 15, or 0.6 M NaC1) were added to make stock solutions of 5.17 g/dL total lipid with an overall molar ratio of lecithin to bile salt equal to 0.9. These were then sparged with argon and stored at 25 OC for 2 days, after which they were diluted to the final concentrations used in the experiments (0.86, 1.29, and 2.59 g/dL). These samples were sparged with argon and sealed in 5-mL acid-washed ampules. All lipid stock solutions for light scattering were filtered through Gelman 0.22 pm Acrodisk-13 filters, and dilutions were made with similarly filtered saline solutions. Light scattering measurements were made of the above concentrationswith two additional dilutions per [NaCl] series at 1.03 and 1.72 g/dL. Samples measured by light scattering achieved a constant size and scattered intensity within 48 h. Methods. Light scattering measurements were made using a Brookhaven Instruments BI-2OOSM goniometer and a BI-9000 correlator. The samples were held in a temperature-controlled cell and surrounded by decalin as an index matching fluid. The radiation source was a 2-W Lexel Ar+ laser operated at 488-nm wavelength. Apparent diffusion coefficients were determined from the measured autocorrelation function using a cumulant fit.34 The time-averaged intensity as a function of q was obtained on the same apparatus, and the intensity data were put on absolute scale using benzene as a standard (Rayleigh ratio of 3 1.4 X 10-4 m-13). The refractive index increment was measured on a C. N. Wood Mfg. differential refractometer calibrated with a potassiumchloridesolutionof 6.1217 g KCl/lOOgdistilledwater. All measurements were made with 488-nm light.
4406 The Journal of Physical Chemistry, Vol. 98, No. 16, 1994
Long et al.
6 4 2
0
s8 10 5
0.0
.,
40
Figure 3. Apparent hydrodynamic radius derived from the measured diffusion coefficients. Themicellesizeappearsto decreasewith increasing concentration(0,0.05 M NaCl; A, 0.15 M NaCl; 0.6 M NaCI; lines are guides to the eye).
30
20 10
n 0.001
0.5 1.0 1.5 2.0 2.5 3.0 Surfactant Concentration (g/dl)
0.01
0.1
0.001
0.01
0.001
0.01
0.1
1
(ICY$'
Figure 2. Small-anglescattering spectra of L-TDC micelles. The solid lines are the fits to the data as described in the text. The open circles are SANS data, and the filled circles are light scattering data. (The number of SANS data points plotted has been reduced for clarity. All data points were used to fit the data.)
Small-angle neutron scattering data were collected on the W. C. Koehler 30m SANS facility36 at the Oak Ridge National Laboratory (ORNL) with a 64 X 64 cmz area detector and cell (element) size 1 cm2and a neutron wavelength of 4.75 A. The detector was placed at sampledetector distances of 3.0 and 19.0 m, and the data were corrected for instrumental backgrounds and detector efficiency on a cell-by-cell basis, prior to radial averagingto give a q range of 0.004 < q < 0.1 A-l. The coherent intensities of the sample were obtained by subtracting the intensities of the correspondingblanks (solvent plus cell), which formed only a minor correction (
