Aggregate Properties of Sodium Deoxycholate and ... - ACS Publications

J. Phys. Chem. B 2008, 112, 3997-4008

3997

Aggregate Properties of Sodium Deoxycholate and Dimyristoylphosphatidylcholine Mixed Micelles Jasmeet Singh, Zuleyha Unlu, and Radha Ranganathan* Department of Physics and Center for Supramolecular Studies, California State UniVersity, Northridge, California 91330-8268

Peter Griffiths School of Chemistry, Cardiff UniVersity, Main Building, Park Place, Cardiff, CF10 3AT U.K. ReceiVed: September 13, 2007; In Final Form: January 9, 2008

Mixed micelles of the phospholipid dimyristoylphosphatidylcholine (DMPC) and bile salts of sodium deoxycholate (NaDC) were investigated by a combination of techniques, including time-resolved fluorescence quenching (TRFQ), electron spin resonance (ESR), viscometry, pulsed-gradient spin-echo NMR (PGSENMR), and surface tensiometry. Aggregation numbers, and bimolecular collision rate constants of guest molecules confined in the micelles (by TRFQ), interfacial hydration index and microviscosity, (by ESR), axial ratio (from solution viscosity), micelle self-diffusion coefficient (by PGSE-NMR), and the critical micelle concentrations (from surface tension) were determined for various molar compositions defined by the ratio R ≡ [NaDC]/[DMPC] and concentrations ([NaDC]+[DMPC]). The data interpretation showed the micelles to be polydisperse rods. Aggregate properties depend on the ratio, R and reveal behavior unlike that in micelles of surfactants with aliphatic nonpolar chains. With increase in concentration from [NaDC] ) 0.010 M to [NaDC] ) 0.200 M, the hydration index and the aggregation number exhibit non-monotonic variations. Formulation of a polar shell model for cylindrical micelles yielded a set of nonlinear equations for the structural features of the micelle. The solutions give the microstructural description of the mixed micelle that includes the length, diameter, number of water molecules in the hydration shell, and the monomer organization in the micelle.

Introduction The self-assembly of bile salts and lipids are of interest primarily because the mixed micelles formed by the solubilization of dietary lipids in bile salt aggregates in the digestive tract are natural substrates for lipid hydrolysis by enzymes.1,2 The efficiency of lipolytic enzymes toward degradation of lipids in aggregated forms is significantly stronger (more than 1000fold) than that toward monomeric lipid substrates; hence the importance of the aggregate and the interface in enzymatic hydrolysis.1-5 To uncover the existence of any correlation between micelle structure and enzyme function, the fundamental micelle structure must first be characterized. Thus with the eventual goal of using the aggregates for investigating enzyme activity and the motivation of finding the specific connection, if any, between aggregate properties and lipolytic activity, we have first conducted physicochemical characterization experiments on aggregates of sodium deoxycholate (NaDC) containing solubilized phospholipids of dimyristoylphosphatidylcholine (DMPC). Bile salt/lipid/water systems typically show a variety of structures (lamellar, vesicles, worm-like micelles, globular, and rod-like micelles) depending on the relative amounts of the three components.6 The investigations in this work are conducted for concentrations and compositions where the aggregates formed are mixed micelles. The experiments include surface tension to determine the critical micelle concentration (cmc); time-resolved * Corresponding author.

fluorescence quenching (TRFQ) to determine aggregation numbers and fluorescence quenching rate constants; electron spin resonance (ESR) to determine micelle hydration and microviscosity; pulsed-gradient spin-echo NMR (PGSE-NMR) to determine the micelle self-diffusion coefficient; and viscometry to determine solution viscosity. Other than characterizing the micelles for their purported use as substrates, the goal of this work is also to understand the power of applying complementary techniques to arrive at a complete microstructural description of the micelle. Each of the techniques probes a different facet of the self-associated system, and is largely independent of the others. The results are combined together in a molecular space-filling model, referred to as the polar shell model, to structurally define the micelle aggregate. A set of nonlinear equations in the variables defining the micelle structure is derived, to which solutions are obtained by an iterative procedure, leading to greater detail on the micelle structure and dynamics. Mixed surfactant aggregate properties are expressed as functions of the solution mole fraction, described by the ratio R of the component concentrations and the total surfactant concentration CT:

[NaDC] [DMPC] CT ≡ [NaDC] + [DMPC] R≡

10.1021/jp077380w CCC: $40.75 © 2008 American Chemical Society Published on Web 03/12/2008

(1)

3998 J. Phys. Chem. B, Vol. 112, No. 13, 2008

R≡

Singh et al.

[NaDC] [NaDC] + [DMPC]

The data showed the mixed micelles to be small with total aggregation numbers, including that of the bile salt and the lipid monomers, in the range of 15-100. The micelle hydration decreases with total concentration for all compositions studied. The experimental data from the various techniques when interpreted together showed the mixed micelles to be short polydisperse rods with axial ratios that depend on composition and concentration. The length and diameter of the rods were calculated. Experimental Methods and Materials Surfactants and Lipids. The lipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) was obtained from Avanti Polar Lipids as a lyophilized powder. The bile salt sodium deoxycholate (NaDC) was obtained from Sigma and was used without further purification. Figure 1 is a scheme of the two surfactants. The purity of the bile salt is an issue in the determination of cmc and is therefore of concern when working close to the cmc and for calculations of surface properties such as area per molecule and other thermodynamic functions.7 In this work, the as-received nature of the salt is not believed to be an issue because the studies are on mixed micelles at concentrations greater than 20 times the cmc, and bulk rather than surface properties of micellar solutions are of interest. Fluorescent Probes and Quenchers for Steady-State Fluorescence and TRFQ, and Spin Probes for ESR. The fluorescent probe pyrene (optical grade, 99%) and the quencher 3,4-dimethyl benzophenone (DMBP, 99%), employed in the TRFQ studies, were obtained from Aldrich Chemicals and used as received. The spin probe 5-doxyl stearic acid methyl ester (5DSE; 99% Sigma) was used in the ESR experiments. Determination of cmc from Surface Tension. The surface tensions of mixtures of [NaDC] and [DMPC] were measured with a Wilhelmy plate, using a Kru¨ss K12 tensiometer, at an ambient temperature of 23 °C and 37 °C in steps at several concentrations starting with water for each of the ratios, R (≡ [NaDC]/[DMPC]): 20, 10, 5, 2.5, and 1 and also for [NaDC] alone. The surface tension decreases from its value in water as the surfactant mixture is added. The cmc is defined as the intercept between a relatively constant limiting tension at higher surfactant concentrations and a power law dependence of surface tension on concentration at lower surfactant concentrations. Mixed Micelle Solution Preparation. The solution compositions studied ranged from the molar ratio R ≡ [NaDC]/[DMPC] ) 1 to 20. For each of the compositions, the effect of total ([NaDC] + [DMPC]) concentration was studied by starting with an initial high concentration of [NaDC] + [DMPC] and conducting measurements at various dilutions. This is referred to as a dilution series. The concentration dependence was investigated for 0.010 M e [NaDC] e 0.200 M for each of the molar ratios R. All solutions, except those for NMR experiments, were prepared in double distilled water. The pyrene concentration in the samples prepared for TRFQ experiments was kept at about one hundredth of the concentration of micelles. This ensures that the fraction of micelles with two or more pyrene is negligible. The quencher (DMBP) concentration was such that the resulting value of the average number of quenchers per micelle was between 0.8 and 1.8 as determined by TRFQ. The appropriate amounts of stock solutions each of pyrene and DMBP in ethanol were added to measured amounts of DMPC powder. The resulting ethanol solution mixture was vortexed

Figure 1. Structural formulas of (a) DMPC and (b) NaDC. (c) Molecular arrangement of polar head groups and nonpolar rings of NaDC. (d) Bond lengths and bond angles of the -COO- group of NaDC (ChemDraw 3D Ultra 6.0).

Figure 2. Schematic representation of (a) the components: water, NaDC, and DMPC molecules, and (b) NaDC + DMPC mixed micelle.

thoroughly to produce a clear solution, which was then dried under dry N2 flux to produce a film of DMPC, pyrene, and DMBP. Thereafter, the required amount of the NaDC surfactant and water was added to the dry film to achieve the final concentrations. The solution was stirred overnight to ensure the complete solubilization of phospholipid in surfactant micellar solution. The samples for ESR were similarly prepared with 5DSE as the spin probe at a concentration of 0.003CT. The medium of the solutions for NMR experiments was D2O. Time-Resolved Fluorescence Quenching. In the TRFQ method, fluorescence probes and quenchers, being themselves hydrophobic, are dispersed in micelles, and the quenched timedecay of the probe fluorescence is measured. Under the conditions that (i) micelle size is monodisperse, (ii) probes and quenchers occupy the micelles according to Poisson statistics, (iii) the probes and quenchers do not migrate between micelles within the lifetime of the probe fluorescence, and (iv) the

Aggregate Properties of NaDC/DMPC Mixed Micelles

J. Phys. Chem. B, Vol. 112, No. 13, 2008 3999

micelles are globular and not long cylinders, the quenched decay of the fluorescence, F(t), is given by the Infelta-Tachiya model:8-10

F(t) ) F(0) exp[-k1t - A3{1 - exp(-kqt)}]

(2)

The decay rate k1 is the rate constant of pyrene fluorescence decay in micelles with zero quencher occupation; kq is the quenching rate constant due to quenching by one quencher. If condition (iii) is satisfied, then k1 ) k0, the unquenched pyrene fluorescence decay rate constant, which would be observed in the complete absence of quenchers. The quantity A3 is the average number of quenchers per micelle. TRFQ measurements were conducted on mixtures of DMPC and NaDC at 37 °C. The fluorescence decay was measured over a time of 2 µs by time-correlated single photon counting using an FL900 lifetime measurement spectrometer of Edinburgh Analytical Instruments (EAI) with nanosecond flash lamp excitation. The decay curves, corrected for instrument response, were fitted to the InfeltaTachiya model (eq 2)8-10 using the Level 2 analysis software of EAI. The fit returns k1, kq, and A3. To eliminate pyrene fluorescence quenching due to the dissolved oxygen, some of the TRFQ samples were degassed by three freeze, pump, and thaw cycles to remove the dissolved oxygen, which would otherwise shorten pyrene fluorescence lifetime. This is expected to improve fitting precision. The lifetime, T0 ()1/k0), of unquenched pyrene fluorescence depends on the ratio R and was found to be about 290 to 350 ns. However, when samples were not degassed, T0 was about 250-320 ns. Degassing did not appear to provide tangible gain in fitting precision. Therefore not all samples were subjected to degassing. In all samples, k1 was ∼k0. The physicochemical properties of micelles, qualified by a subscript q in anticipation that they may be dependent on quencher concentration in the event of the existence of polydispersity, which can then be derived from the fitting, are as follows: 1. Concentration of Micelles, [micelles]. The quencher concentration, [Q], is a known sample parameter. Using the fitted value of A3 and the known [Q], the concentration of micelles may be calculated from

[micelles]q )

[Q] A3

(3)

The aqueous quencher concentration is estimated to be 10 mM. 3. Quenching Rate Constant. Quenching in micelles is diffusion controlled, and thus the quenching constant kq is the pseudo first-order bimolecular collision rate constant of guest molecules confined to micelles.13-16 4. Micelle Polydispersity. For a Gaussian micelle size distribution, the quencher averaged aggregation number Nq, for any particular [Q] derived by a fit of the decay to eq 2, is written as a series in the quencher concentration.16,17 The series limited to the first term is

N q ≈ NW -

[Q] σ2 2 CT - cmc

(6)

where NW is the weight averaged aggregation number defined as

NW )

∑n n2Xn ∑n

Xn

)

∑n n2Xn CT - cmc

(7)

σ is the standard deviation in the aggregation number n, and Xn is the distribution function. The intercept of Nq vs (1/2)([Q]/ (CT - cmc)) yields the true or weight averaged aggregation number, NW, and the slope yields the variance of the aggregation number distribution.17,18 A quencher concentration dependence of the TRFQ decay was conducted, and eq 6 was used on data for A3 in the range of 0.8-1.8. This range is chosen because most reliable fits are obtained when the resulting A3 is about 1. At very low quencher concentrations, the fits to the decay curves are subject to a higher error and have been found to overestimate the aggregation numbers, sometimes as high as 15%.19-21 At high quencher concentrations there are problems due to the solubility of quenchers and non-Poisson distributions, which may underestimate the aggregation numbers. 5. Micelle Concentration. The micelle concentration is then calculated using NW as below:

[micelles] )

CT - cmc NW

(8)

Electron Spin Resonance. Line shape analysis of the ESR spectra of spin-probes incorporated into micelles yields the hyperfine splitting constant and the linewidths and thereby the polarity and microviscosity of the spin-probe environment.22,23 The hydration index defines the polarity of the micelle/water interface and is denoted by H. Therefore the hyperfine splitting constant denoted by A+ in this work and H are related and are found to bear a linear relation in mixtures of methanol and water.24,25 Thus, using the calibration relation between A+ and H obtained for the selected probe in methanol/water mixtures, H in micelles can be obtained from the observed A+ in micelles.23,26


Singh et al.

The interface region, also called the polar shell, has a volume denoted by Vshell. H is given by the volume fraction of OH dipoles in the polar shell of the micelle. Each of the NaDC monomers in a micelle contributes two OH, and the rest of the OH is from the interfacial water. Therefore,

H)

VOH Vshell - Vdry ) Vshell Vshell

(9)

where VOH is the volume occupied in the shell by the OH dipoles from water and the NaDC monomers of the micelle, and Vdry is the volume in the polar shell inaccessible to water. In the simple continuum model that has thus far proved to be successful,15,23,25,27-30 Vdry is the sum of the volumes of the polar headgroups (including the headgroup of the phospholipid and the COO- of NaDC), the counterions, and any nonpolar portion of the surfactants, including the hydrocarbons from the alkyl chains of the lipids and the steroid ring of NaDC that may be part of the shell.30 The rotational correlation time, τ, of the spin probe, given by the width of the ESR lines that is obtained by fitting, is used to calculate the microviscosity, ηmicro, from the Debye-StokesEinstein equation:31,32

τ)

4πηr3 3kT

(10)

where r is the hydrodynamic radius of the spin label () 4.68 Å for 5DSE),25,33 k is the Boltzmann constant, and T is the sample temperature. The details of the instrument and the method are given in previous publications and are not repeated here.25,28,34,35 Both TRFQ and ESR are methods that employ invasive probes. The quencher-to-surfactant ratio (given by [Q]/([NaDC] + [DMPC] - cmc)) was thus kept constant for any particular dilution series to afford some measure of normalization for evaluation of the behavior at any constant R. Viscosity. The viscosities of the micellar solutions relative to the solution at the cmc were measured with a Cannon Polyvisc Viscometer, with a precision of 0.5% (determined as the standard deviation in the data from repeated experiments). The capillary tube used was such that the flow time for water was about 50 s at 37°C ( 0.02 °C. The densities of the solutions were determined with an Anton-Paar density meter DMA 5000. The relative viscosity given by the instrument is then multiplied by the ratio of the density of the solution to the density of the solution at the cmc. The viscosity data are treated with model equations that consider hydrodynamic interactions alone as well as those that include the electroviscous effects. These are the dominant interactions in colloidal suspensions.36 When considering the presence of only hydrodynamic interactions, the relative viscosity, ηr, data were fit to the power series up to the cubic term in the volume fraction of micelles, φ:37

ηr ) 1 + νφ + κ1(νφ)2 + κ2 (νφ)3

(11a)

where ν is a shape factor given by

ν ) 2.5 + 0.407(J - 1)1.508, 1 < J < 15 and

J)p

( ) 2

1 3p

0.5

;p)

L d

(12)

where p is the axial ratio of the length L to the diameter d of the micelle. The constants, κ1 and κ2, account for hydrodynamic interactions. The value of κ1 for rigid rods or prolate ellipsoids is taken to be 0.75.37,38 Equations 11a and 12 have been used widelyintreatingsolutionviscositydataoncolloidalsuspensions.38-41 Electroviscous effects cause the viscosity to increase, and derivations show that these effects may be incorporated into eq 11a, by replacing ν with ν(1 + δ), where δ is the electroviscous coefficient, so that42,43

ηr ) 1 + ν(1 + δ)φ + κ1(ν(1 + δ)φ)2 + κ2(ν(1 + δ)φ)3 (11b) Model calculations yield numerical values for δ, the use of which in eq 11b and its subsequent application permits an examination of the effect of charge.44 The combined contributions of the hydrodynamic and electroviscous effects are thus calculated. Pulsed-Gradient Spin-Echo NMR. Measurements were conducted on a Bruker AMX360 NMR spectrometer using a stimulated echo-sequence as described elsewhere.45 This configuration uses a 5 mm diffusion probe (Cryomagnet Systems, Indianapolis, IN) and a Bruker gradient spectroscopy accessory unit. A series of 1H NMR spectra were recorded with increasing gradient duration. The normal procedure for measuring the selfdiffusion coefficient (denoted by Ds) of a species in a multicomponent solution is to isolate a resolvable peak, extract the peak integral (intensity) or height for the series of spectra separated in time, and fit the resultant exponential time decay to the equation:46

A(δ,G,∆) ) Ao exp[(-kDs)]

(13)

where A is the signal amplitude in the absence (A0) or presence of the field gradient pulses A(δ,G,∆),

k)

(

-γ2G2

)

30∆(δ + σ)2 - (10δ3 + 30σδ2 + 35σ2δ + 14σ3) 30

given that γ is the magnetogyric ratio, ∆ is the diffusion time, σ is the gradient ramp time, δ is the gradient pulse length, and G is the gradient field strength. When spectral overlap is present, as in the case of mixtures of structurally similar species, a powerful approach to extracting the pure diffusion coefficients for each component present within the multicomponent mixture is that developed by Stilbs, termed CORE.47 In the CORE analysis (COmponent REsolved (CORE) PGSE-NMR), the data implicit within the NMR line shape is retained rather than averaged to a single intensity or integral. Each datum comprising the line shape constitutes an exponential decay, the time constant of which is the diffusion coefficient. Therefore, a complex line shape may contain thousands of points and thus exponential decays that may be fitted individually to maximize the accuracy of the diffusion coefficient so obtained. The CORE analysis, unlike, say, DOSY, assumes that a discrete number of species are present (e.g., 1, 2, or 3), and thus limits the number of accessible diffusion coefficients. The program then returns more accurate estimates of these diffusion coefficients and, concomitantly, the contribution each diffusion coefficient makes to the overall line shape, thus permitting the


Figure 3. Variation of the surface tension, γ, of NaDC and mixed solutions of NaDC and DMPC with the concentration of NaDC for different molar ratios; R ≡ [NaDC]/[DMPC] in the range of 1-20 at 37 °C. The concentration at which γ is a minimum (R g 5) or becomes a constant (R < 5) is taken to be the cmc.

Figure 4. Variation of the relative viscosity, ηr, ((0.5%) of mixed solutions of DMPC and NaDC with φ0 (micelle volume fraction excluding hydration water; eq A8), for three different molar ratios: R ≡ [NaDC]/[DMPC] )1, 2.5, and 5 at 37 °C.

extraction of fitted line shapes to facilitate unequivocal spectra and diffusion coefficient assignment.


Figure 5. Variation of the micelle self-diffusion coefficient, Dmic s , ((2.5%) of mixed solutions of DMPC and NaDC with total surfactant concentration, CT, for three different molar ratios; R ≡ [NaDC]/[DMPC] ) 1, 2.5, and 5 at 37 °C.

of viscosity is more nonlinear and steeper than for R ) 2.5 and R ) 5.38,49-51 Self-Diffusion Coefficient. Figure 5 shows the variation of the self-diffusion coefficient, Dmic s , at 37 °C as a function of concentration. Over the majority of the composition range, the self-diffusion coefficient decreases with increasing concentration and decreasing R. The values of Dmic also indicate that the s micelles are small, typically a few nanometers. The CORE program described in the Methods section was used to extract the micelle self-diffusion coefficient. The resonances in the observed spectra are from DMPC (DMPC-1H) and NaDC (NaDC-1H) and include their overlap. DMPC is not present in monomeric form, but NaDC is at about the cmc concentration. If there is no overlap, the DDMPC determined from the decay of s DC DMPC-1H resonances would be the micellar Dmic s , and the Ds determined from NaDC-1H would be a combination of the micellar Dmic and the monomeric self-diffusion coefficient, s 46 These statements are summarized below. Dmic . Dmon s s DMPC Dmic s ) Ds mon + pmicDmic DDC s ) pmonDs s

Results Determining cmc from Surface Tension. The observed surface tension profiles with the concentration of mixtures of [NaDC] and [DMPC] at 37 °C are displayed in Figure 3 and used to extract the cmc.The surface tension falls steeply from its value at low concentration, and then is relatively constant with further increase in concentration. A sharp minimum is exhibited for R g 5, an effect signifying the presence of impurities.26,48 The cmc values at 23 °C and 37 °C thus determined are tabulated in Table 2. The concentration referred to in Figure 3 is the [NaDC] in the mixture. The cmc decreases with increase in the composition of the more hydrophobic lipid component. These estimates are used in the calculation of the aggregation numbers from TRFQ (eqs 4-7). Viscosity. The relative viscosity of micellar solutions at 37 °C measured relative to the viscosity at the cmc is examined in Figure 4 as a function of the micelle volume fraction (excluding the hydration water) φ0, (given by eq A8 in the Appendix). The observed increase is nonlinear, and the values of ηr are small and thus do not indicate the presence of large or worm-like micelles, except perhaps for the molar ratio, R ) 1, containing [NaDC] > 0.150 M, for which the rate of increase

(14)

pmon )

[NaDC] - cmc cmc ; pmic ) [NaDC] [NaDC]

(15)

where pmon and pmic are the molar fractions of monomers of NaDC and micelles, respectively, both of which are measured in this work, by surface tension and TRFQ. The contribution of the monomer diffusion would make DDC > DDMPC )Dmic s s s . The time decay of the spectra was fit to single and double exponentials. The double exponential fits gave very close values (to within 5%) of Dmic s , indicating that the decay was effectively a single exponential for the compositions with R ) 1 at all concentrations, R ) 2.5 for [NaDC] > 0.025 M, and for R ) 5 for [NaDC] > 0.100 M. So, for these concentrations, single-exponential decays were assumed, and Dmic was calcus lated using eqs 14 and 15. A value of 7 × 10-10 m2/s was used 52 For other concentrations, the double exponential for Dmon s . fits showed a difference of about 50% between the two fit Ds values. The lower Ds was taken to be that of the DMPC-1H and therefore that of the micelle (eq 14), with the rationale that the higher Ds must be that of NaDC-1H because the NaDC monomers contribute to a higher DDC s .


Singh et al.

TABLE 1: Notation for the Various Volumes and Some Numerical Values for Appropriate Molecular Fragments volume/linear dimension

notation VDMPC hc VDMPC hg

lipid hydrocarbon tail lipid headgroup lipid steroid rings of NaDC NaDC excluding Na NaDC excluding OH & Na DMPC headgroup thickness NaDC headgroup thickness polar shell thickness OH (from water and NaDC) water molecule OH in NaDC micelle core shell

VL ) VDMPC + VDMPC hc hg DC Vhc VDC VDC-OH

s VOH Vw VOH Vmic Vcore Vshell

numerical value (Å3 or Å)a 452 275 727 353 406 385 9b 1.4c mic d + 1.4Xmic (9XDMPC DC ) 30 16

a van der Waals volumes calculated following the method of Zhao et al.64 b From simulations.26,65 c Sum of height of triangle formed by CdO and C-O- and one-half of C-C bond length (Figure 1). d Linear combination of headgroup thicknesses of DC and DMPC according to composition.

TABLE 2: Critical Micelle Concentration (cmc) of Solutions of Binary Mixtures of NaDC and DMPC at Various Molar Compositions Specified Here by the Molar Ratio R ≡ [NaDC]/[DMPC]a R ≡ [NaDC]/[DMPC]

cmc (23 °C) mM

cmc (37 °C) mM

1 2.5 5 10 20 NaDC only

0.09 0.13 0.5 1.08 2.6 3.7

0.11 0.16 0.68 1.1 2.7 3.8

a Measurements were conducted at 23 °C and 37 °C by surface tension using a platinum plate.

Aggregation Number, Quenching Rate Constant, and Micelle Polydispersity. The decay curves in Figure 6 are representative of the TRFQ data. A fit of eq 2 to the decay data, typified in Figure 6, yields the micellar properties listed in eqs 3-5 and kq. For solutions with 20 e R < 1 and [NaDC] e 0.200 M, and in the case of R ) 1 and [NaDC] < 0.100 M, the TRFQ data, fits, and the derived aggregation numbers and quenching rate constants exhibit characteristics of small micelles. The characteristics of long cylindrical micelles typically are as follows: they grow rapidly with change in parameters (typically added salts or mixture compositions in the case of mixtures) that cause growth,25,27,30,38 and the fluorescence decay curve for long cylindrical micelles is different and cannot be fit to a micellar quenching model.53 No such sudden rapid changes in the decay characteristics (values of T1 and T2) are observed for the set of concentrations and compositions in the present investigation, and the decay curves fit quite well to the InfeltaTachiya model of micellar quenching (eq 2). The characterization of aggregates as small in TRFQ applies to aggregates in which the lifetime, T2, of the fluorescence in the presence of one quencher in a micelle, given by the inverse of the quenching rate constant, kq, is less than and distinguishable from the lifetime, T1, of pyrene in a micelle without quencher. In most cases T2 was 0.050 M. For the neat NaDC, there appears to be a break in the nature of the variation of the microviscosity at [NaDC] ) 0.150 M. Measurements and computer simulations of bile salt aggregation find a change in the aggregation behavior from hydrophobically bound primary micelles at low concentrations to hydrogen-bonded secondary micelles at high concentrations.52 This occurs somewhere between 0.090 and 0.300 M for NaDC. It is not clear how this would affect the measured microviscosity, but it is possible that the change in the nature of the variation of microviscosity observed in this work at about [NaDC] ) 0.150 M is related to the change in aggregation behavior. Further investigations on other neat bile salt micelles are needed to establish such a correlation.


Figure 9. Variation of the (a) micelle hydration index, H, and (b) microviscosity, ηmicro, of mixed micelles of NaDC and DMPC at different constant molar compositions, R ≡ [NaDC]/[DMPC] ) 1-20 vs total surfactant concentration, CT and at 37 °C. The uncertainty in H is ( 2%, and in ηmicro it is about (1% for [NaDC] < 0.050 M.

Figure 10. Variation of the relative viscosity, ηr ((0.5%), of mixed solutions of DMPC and NaDC with micelle volume fraction, φ (eq 11a), for three different molar ratios: R ≡ [NaDC]/[DMPC] ) 1, 2.5, and 5 at 37 °C.

Results of Calculations. Application of the iterative protocol (with eq 11a for the relative viscosity) described in the Appendix shows that the mixed micelles are small rods and yields the length and diameter of the micelle, the micelle volume fraction, and the number of water molecules per micelle monomer. Figure 10 presents the relative viscosity dependence on the micelle volume fraction, φ, clearly showing that the dependence is not linear and thus the necessity to include the higher order terms of eq 11a. The geometrical properties of length of the micelle and the axial ratio decrease with φ (Figure 11a) steeply initially, followed by a weak concentration dependence that includes a

Singh et al.

Figure 11. Variation of the axial ratio, L/d ((1%), represented by open symbols, and length of micelle, L ((3%), represented by filled symbols, with micelle volume fraction, φ, for three different molar ratios: R ≡ [NaDC]/[DMPC] )1, 2.5, and 5 at 37 °C. Results are for the presence of (a) hydrodynamic interactions alone (eq 11a) and (b) hydrodynamic and electroviscous effects (eq 11b). The lines through the data points for the length L are meant as a guide to the nature of the variation. The error bars were calculated by considering a (10% error in the aggregation numbers.

shallow minimum, indicating that the micelle length again increases at higher volume fractions. The minimum occurs between φ ≈ 0.02 and 0.03 for R ) 5, and the shapes of the curves for R ) 2.5 and 1 suggest a higher value of φ where the minimum might be expected. This behavior is found to have similarities with that observed for mixed micelles of egg yolk lecithin and glycochenodeoxycholic acid sodium salts (namely, a sharp decrease in length followed by weak growth), where a minimum was found at about a solute volume fraction of ∼0.012 for R ≈ 1.54 The same procedure, but with eq 11b, was employed to examine the combined hydrodynamic and electroviscous effects on the micelle sizes. Values for the electroviscous coefficient, δ, were obtained from available model calculations for suspensions of spherical colloidal particles in salt-free solutions.44 These calculations show that δ depends on the volume fraction and surface charge density of the colloids. However, it is insensitive to the charge density for high surface charge densities. The micelles in the present case do have surface charge densities in excess of -5 µC/cm2. We have used the values of δ (denoted by p in the work cited) vs φ for -1 µC/cm2 and found a power law fit for 0.004 < φ < 0.1. This functional form for δ was inserted into eq 11b. An additional modification was introduced to account for non-spherical shapes. The electroviscous coefficient was found to be smaller for prolate ellipsoids and shown to decrease with axial ratio.55 The values of δ were found to be reduced by a factor >0.6, for an axial ratio of 3.88. We have used 0.6 as the reduction factor on the



Re )

( ) 3 2p2

1/3

L 2

(16)

where k is the Boltzmann constant, η0 is the viscosity of the solvent at the temperature T, and p ) L/d. Values of D0 calculated using the values of p and L (of Figure 11a) obtained from the polar shell model applied to the TRFQ, ESR, and viscosity data are compared with the measured values of the self-diffusion coefficient in Figure 13. Use of the smaller values of Figure 11b increases the ratio by 5-8%. Being the infinite dilution limit, D0 does not include the retardation in diffusion due to the finite concentration, which may vary depending on R. The comparison in Figure 13 is discussed in the following section. Discussion Figure 12. Variation of the number of water molecules per head group, nw ((4%: error calculated by considering a (10% error in the aggregation numbers), with weight average aggregation number, NW, for three different molar ratios: R ≡ [NaDC]/[DMPC] ) 1, 2.5, and 5 at 37 °C. The upper abscissa is for R ) 1, and the lower ones are for R ) 2.5 and 5 as indicated.

δ calculated for spheres. Accounting for the electroviscous effects accordingly yields the sizes as in Figure 11b. The number of water molecules per micelle monomer, nw, calculated using Vw ) 30 Å3 and VOH ) 16 Å3 in eq. A11 is examined against the aggregation number NW in Figure 12. Calculated values of nw depend on NW as well as H. For R ) 2.5 and 5, nw has its highest value for [NaDC] ) 0.050 M, where NW is minimum and H is maximum, and decreases from this value for changes in concentration (either an increase or decrease) from [NaDC] ) 0.050 M. For R ) 1, the highest nw is for [NaDC] ) 0.025 M. The lowest nw occurs for [NaDC] ) 0.010 M for which NW is 101 (R ) 2.5), 57 (R ) 5), or 107 (R ) 1). The value of nw, when using eq 11a to obtain micelle size information, is about 3-7 for R ) 2.5 and 5 and is typical of ionic and mixed micelles.23,25,27-29 For R ) 1, the micelles are quite dry, with about 1-2 molecules of water per headgroup. These numbers reduce by about 10% (R ) 5), 8% (R ) 2.5), and 6% (R ) 1) when eq 11b is used. The distribution of the nonpolar part of the monomers between the micelle core and shell region, represented by the fraction f, is about 72:28 for R ) 5, about 65:35 for R ) 2.5, and about 38:62 for R ) 1, and is about the same with either of eq 11a or 11b. With increase in the lipid component, a larger fraction of the monomer’s nonpolar part occupies the shell region. Fitting of the data of scattering experiments on bile salt and lecithin micelles at equimolar ratios also conclude that most of the bile salts are present in the shell region.6,54,56 The Stokes-Einstein model for the self-diffusion coefficient, D0, for a cylindrical particle of length L and diameter d at infinite dilution is given by57

D0 )

Ft )

kT Ft6ππ0Re

( ) 2p2 3

ln(p) + 0.312 +

1/3

0.565 0.100 + 2 p p

Bile salt/lecithin micelles have been reported to show dilutioninduced growth as the solution is diluted toward the cmc and the presence of rod-like micelles.6,54,56,58 Most bile salt/lecithin studies have concentrated on the solubilization of lecithin bilayers by the added bile salts and the structures present at about the vesicle/micelle transition. The micellar structural phase at concentrations above the transition region was shown to consist of rod-like micelles.6,56,59 Typically, at a bile salt-tolecithin molar ratio of about 1 (R ≈ 1), static and dynamic light scattering experimental data were interpreted to show small micelles with low polydispersity at concentrations that are closer to the concentrations in this work. At greater dilutions, not covered in this work, micelles were shown to be cylindrical before eventually transforming into vesicles.58 The calculations in this work, which pertains to concentrations above the micelle/ vesicle transition, show that the micelles are cylindrical and more elongated at the lower concentrations than at the higher concentrations. The outcome of including electroviscous effects in the analysis is that the changes in micelle sizes with increase in volume fraction are less pronounced (Figure 11b), and, furthermore, the axial ratio decreases upon dilution below a volume fraction of 0.02. For micelle volume fractions greater than 0.004, the electroviscous coefficient is less than 1 (for surface charge density ≈ -1 µC/cm2) and decreases with volume fraction. Its effect is to decrease the calculated values of the micelle axial ratio and length as may be noted by comparing Figure 11a with 11b.44 The values in Figure 11a may be treated as an upper limit on the micelle sizes. A better approximation of the electroviscous effect would be possible if values of the electroviscous coefficient were available for cylindrical or ellipsoidal colloids, shapes for which a decrease from the value for spherical shape is indicated.55 The changes in shape and size observed (Figure 11 a and b) are in general agreement with experimental observations in bile salt-lecithin micelles.54 The aggregation numbers and hydration variation with concentration is non-monotonic. Such a variation is unlike that in ionic micelles. Globular ionic micelles typically increase monotonically in size with aqueous counterion concentration as a slow growth power law followed by a rapid growth after transformation to cylinders.30,54 A rapid growth in aggregation number, for dilution from [NaDC] ) 0.050 M, along with a decrease in hydration is similar to observations for cylindrical micelles of surfactants with aliphatic chains.25,30,60 Empirical equations have been proposed to fit the non-monotonic size variation with concentration observed in bile salt/lipid micelles.54 The physical basis for the peculiarity of non-monotonic size variation must lie in the presence of competitive processes or


Singh et al.

Figure 13. Variation of the ratio of the calculated self-diffusion coefficient ((3%: error calculated by considering a (10% error in the aggregation numbers) to measured self-diffusion coefficient, ( mic mic Ds,cal )/(Ds,meas ), with micelle volume fraction, φ, for three different molar ratios: R ≡ [NaDC]/[DMPC] ) 1, 2.5, and 5 at 37 °C.

concentration-dependent transitions. The occurrence of cylindrical shapes for bile salt/lipid mixed micelles has been attributed to the difference between the architecture of the lipid and the bile salt. A rationale to understand a decrease in micelle length with concentration (Figure 11) is that long rods with all equally probable orientations are not sustainable as concentration or micelle volume fraction increases because of steric hindrances, and the system is driven by steric repulsion to decrease its length and eventually transform to an anisotropic regime in which the rods are ordered in their orientations and they can grow in length. Such a process would result in a rapid increase in the solution viscosity, as was observed as [NaDC] approached ∼0.200 M (for R ) 1; in this work, ηr was measured to be 9.16 at 37 °C).37 In the concentration region [NaDC] g 0.050 M, the increase in kq with aggregation number (Figure 7c) may be rationalized when examined in the light of the other accompanying changes occurring in the micelle: namely, the decreasing hydration index or polarity and decreasing length and axial ratio. Under these changing conditions, it is conceivable that the probe and quencher locations shift so that the overlap region of their diffusive motion increases, causing the quenching rate constant kq to increase as well.16 In recent work on the hydrodynamics of kq, the particular role of the overlap region of the diffusion domains and locations of guest molecules was examined, and it was shown that changes in these could be quantified.15,16 This brings a resolution to what at first seems to be a paradox in that both the micellar kq and aggregation number increase with concentration. The concentration dependence of the diffusion coefficient is a long standing problem of theoretical research.36 For charged colloids treated as dressed macroions, the dominant contributions to the concentration dependence are from the screened Coulomb interactions, which reduce the value of Ds, and the hydrodynamic interactions between the particles, which increase Ds. The result can be a very weak dependence on the concentration, and an explicit calculation showed this to be61

Ds ) D0(1 - 0.07φ)

(17)

where φ is the volume fraction of the colloids. Rigorous treatments need computational modeling for the particular system of interest, and, furthermore, a framework for nonspherical particles is needed. This is outside the scope of the

present work. In the present comparison of Figure 13, the concentration dependence is ignored following the general guidance of eq 17. Figure 13 illustrates that the calculated value falls short of the measured values by a factor of 0.5 at of Dmic s the lowest concentration but approaches the measured value ( mic Dmic s,cal/Ds,meas ) 1) as the concentration increases. At the highest mic concentration investigated, Dmic s,cal/Ds,meas ≈ 1. Recognition of a number of factors may explain this trend. The experimental values of Ds extracted by a fit of an exponential decay to the PGSE-NMR data is an average over the micelle and the unassociated monomer contributions. The unassociated monomer contribution in the dilute cases can be a significant part and would therefore distort the value of Dmic s , leading to an agreement that progressively becomes better with concentration, as observed. Although a double exponential fit was used at the lower concentrations, the proximity of the two Ds values makes their resolution problematic. Furthermore, eq 17 may not represent the effect of interactions. In the bile salt/lipid systems, the size and shape of the colloidal particles change with concentration or φ. Available theoretical models do not take this into account. With respect to aggregation number, experimental observations generally show that ionic micelles grow with concentration, and non-ionic and zwitterionic micelles are insensitive to concentration.62 Within such a classification, the mixed micelles in this study would qualify as ionic for R ) 5, 10, and 20, and zwitterionic for R ) 2.5 and 1. With increase in the zwitterionic lipid content, the residual micelle charge is diluted as R is decreased, and the lack of growth for R ) 2.5 and 1 suggests that the micelles with R e 2.5 acquire zwitterionic characteristics. The number of water molecules per monomer also is a clue to the zwitterionic character of the micelles. The sodium counterions contribute to nw because of their water of hydration. In SDS micelles, this number reduces from about 10 at about [SDS] ) 0.050 M to about 5 as the aggregation number increases (with increase in SDS concentration and/or the addition of salt) and the micelles transform to cylinders.25 In the present mixed micelles, where the counterion is sodium, the calculated value of nw is about 3-7 for R ) 2.5 and 5, but reduces to

Aggregate Properties of Sodium Deoxycholate and ... - ACS Publications

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