6266
J. Phys. Chem. B 2001, 105, 6266-6272
Zwitterion Headgroup Orientation Correlation and Mobility and the Domain Structure of Membranes W. Schrader and U. Kaatze* Drittes Physikalisches Institut, Georg-August-UniVersita¨ t, Bu¨ rgerstrasse 42-44, 37073 Go¨ ttingen, Germany ReceiVed: February 9, 2001; In Final Form: April 20, 2001
Complex electric permittivity spectra of aqueous vesicle solutions, prepared by extrusion of lecithin suspensions, have been measured as a function of temperature in order to study the dielectric relaxation of the dipolar phospholipid headgroups. Solutions of unilamellar liposomes from dimyristoylphosphatidylcholine and from a mixture of dimyristoyl- and dipalmitoylphosphatidylcholine (mole fraction x ) 0.5) have been investigated. Based on a theoretical model that considers the internal electric fields of the dielectrically heterogeneous liquids, the vesicle radius, the zwitterion relaxation time, a relaxation time distribution parameter, and a quantity that is directly related to the dipole orientation correlation factor are calculated from the measured spectra. The radii indicate a noticeable swelling when T exceeds the gel/fluid phase transition temperatures Tm of the membranes. There clearly exists an effect of correlation of dipole orientations. Either the dipole orientation correlation factor or the radius of the circular path of headgroup motions around the phosphate group is substantially higher at T > Tm than at T < Tm. The headgroup mobility in bilayers is smaller than in micellar systems made of lysolecithins, but it also increases noticeably when T exceeds Tm. With lecithin mixtures, in addition to the fluctuations in the domain structure, the clustering of like and unlike lipid molecules obviously also contributes to the broadness of the relaxation time distribution.
Introduction The domain structure of lipid bilayers is currently discussed with much enthusiasm because of its potential relevance in the biological functions of membranes.1-4 Interest is particularly directed toward the lateral differentiation of the physicochemical membrane properties. Large domains exist near phase transitions, preferably at the main phase transition where domains constitute small subphases of fluid membrane in an ordered gellike matrix and vice versa. Hence near the main phase transition temperature Tm the domain structure is predominantly promoted by structural isomerization of the lipid acyl chains. Due to the coupling of the acyl chain isomerization to the lateral membrane area per lipid molecule, fluctuations on the hydrocarbon phase of the membrane will be correlated to the molecular order and microdynamics of the dipolar headgroups, located on the bilayer surface. On the other hand, variations of the electrostatic interactions at the bilayer surface may exercise an influence on the lateral area per lipid molecule and, mediated by rotational isomerization of the acyl chains, on the domain structure of the membrane. The possibility to, via the dipolar bilayer surface, control the membrane domain structure by external parameters, such as the ionic strength or the pH of the suspending liquids, is offered thereby.5 It is, therefore, interesting to investigate the molecular order and reorientational motions of the dipolar headgroups on the bilayer surface. A powerful method to study the molecular structure and motions of the dipolar groups is provided by dielectric spectrometry. Previous investigations6-13 revealed the suitability of the method though conflicting conclusions have been drawn from the measured spectra. An example of a broadband complex dielectric spectrum (i2 ) -1)
(ν) ) ′(ν) - i′′(ν) * Author to whom corrrespondence should be addressed.
(1)
Figure 1. Real part ′(b) and negative imaginary part ′′(O) of the complex electric permittivity of a 0.17 M (100 mg/mL) solution of DMPC in water at 30 °C plotted versus frequency ν.9
of an aqueous vesicle solution of 1,2-dimyristoyl-L-3-phosphatidylcholine (DMPC, C14-lecithin) is displayed in Figure 1. The real part ′ of the electric permittivity exhibits two dispersion (d′(ν)/dν < 0) regions, corresponding with two dielectric loss (′′(ν) > 0) regions in the negative imaginary part ′′. These dispersion/dielectric loss regions reflect the relaxation associated with the reorientational motions of the water molecules (relaxation frequency at around 20 GHz) and that due to the hindered reorientations of the lipid dipolar headgroups (relaxation frequency around 80 MHz). In eq 1 ′′ denotes the dielectric contribution to the total loss
′′tot(ν) ) ′′(ν) +
σ 0ω
(2)
where σ is the dc electrical conductivity of the sample, 0 ) 8.854 × 10-12 As/Vm is the electric field constant, and ω ) 2πν is the angular frequency.
10.1021/jp010525t CCC: $20.00 © 2001 American Chemical Society Published on Web 06/07/2001
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J. Phys. Chem. B, Vol. 105, No. 26, 2001 6267
Figure 2. Sound velocity number u (eq 3) as a function of temperature T displayed for aqueous solutions of DMPC (∆) and DMPC/DPPC, x ) 0.5 (O). The total lipid content of the samples is 4 mg/mL.
The former spectrum9 shown in Figure 1 clearly evidences the suitability of dielectric spectrometry as a tool for the study of the molecular dynamics of native bilayer systems. Meanwhile, much more sophisticated dielectric spectrometers are available. In addition, the techniques of producing unilamellar vesicles have been improved. Therefore, it seemed to be promising to us to perform systematic dielectric spectrometry as a function of sample temperature using phospholipid/water suspensions with narrow size distribution of nearly spherically shaped unilamellar vesicles. Here we report on results for a DMPC suspension and for an aqueous suspension of vesicles made from an equimolar mixture of DMPC with 1,2-dipalmitoyl-L-3phosphatidylcholine (DPPC, C16-lecithin). The latter system is included to look for any effect in the phosphoryl choline headgroup order and dynamics as due to the domain structure induced by the mixing of lipids with different length of acyl chains. Materials and Methods Liposome Solutions. At Tm DMPC vesicle solutions of high water content exhibit a thermotropic transition from an ordered “gel” phase of the bilayer to a disordered “fluid” phase. The phase diagram of DMPC/DPPC systems has a lens-like shape and suggests almost ideal binary liquid mixtures with an only small tendency of clustering of like molecules.14 Sound velocity number profiles of aqueous solutions of DMPC and DMPC/ DPPC vesicles (Figure 2) show relative minima at the transition temperatures (Tm ≈ 24°, DMPC, Tm ≈ 33 °C, DMPC/DPPC x ) 0.5; x ) mole fraction of DMPC). For the pseudobinary lipid mixture the temperature range of the transition is somewhat broader than for the DMPC system, indicating a reduced cooperativity in the ordered-gel phase transition of the mixture. The sound velocity number u, defined by15,16
u)
cs - cs0 cs0cˆ
(3)
is the relative deviation, per solute concentration in mg/mL, of the sound velocity of the solution
cs ) (Fκs)-1/2
(4)
from that of the solvent (cs0). In eq 4 F is the density and κs the adiabatic (volume) compressibility. The sound velocity measurements have been performed at around 2.3 MHz using a computer-controlled twin resonator ultrasonic velocimeter.17 A detailed description of the cs data will be given in a forthcoming article in which particular attention will be paid to the correlation
between sound velocity and heat capacity profiles of membrane systems as predicted theoretically.16,18 Large unilamellar liposomes were prepared from DMPC and DPPC using an extrusion method19-21 that produces almost spherically shaped vesicles with a relatively small size distribution.21 The lipids (>99%; Fluka, Deisenhofen, Germany) were used without additional purification. Water was deionized, doubly distilled, and UV sterilized. To obtain a homogeneous DMPC/DPPC mixture both lipids were first dissolved in trichloromethane (>99%; Merck, Darmstadt, Germany). The organic solvent was vaporized at reduced pressure in a desiccator cabinet and the resulting film of dry lipid was dissolved in a preweighted amount of water. Samples with rather high total lipid concentration (60 mg/mL = 0.1 mol/L) were prepared in order to reach a sufficiently clear effect from the phosphatidyl choline headgroups in the dielectric spectra. In the extrusion procedure a LipoFast-Basic extruder (Milsch Equipment, Laudenbach, Germany) was used, containing a polycarbonate filter (Poretics, Livermore, CA), the pores of which were about 100 nm in diameter. During the extrusion procedure the vesicle solutions were kept at a temperature at least 10 K above the transition temperature Tm. With the DMPC/ DPPC mixture the extrusion procedure was difficult to perform, due to the high lipid concentration and to the high transition temperature. Hence with that mixture there may be a small amount of multilamellar vesicles left. Dielectric Spectrometry. Since we are interested in the reorientational motions of the lipid headgroups (Figure 1), measurements have been performed at frequencies from 300 kHz to 3GHz, thus covering the frequency range of dipolar headgroup relaxation. At these frequencies the wavelengths within the sample are sufficiently large to allow for a quasistatic approach. Input impedance measurements of suitable sample cells have thus been performed, utilizing a computer-controlled network analyzer (HP 8753A), combined with a reflection test set (HP 85044A). Specimen cells of the cutoff variety have been used.22 In this type of cell the sample is contained in a coaxial line/circular waveguide transition. The diameter of the cell (7 mm) was sufficiently small to excite the piece of waveguide below the cutoff frequency of the TM01 field mode so that only an evanescent field exists in this section. We used two different cells. One cell, matched to the frequency range below 100 MHz, was provided with an impedance-matched dielectric window and the length l of the inner conductor of the coaxial line filled with liquid was 16 mm. The other cell was more appropriate for measurements at high frequencies (ν > 100 MHz). To minimize electrical field inhomogeneities, in this cell the liquid was separated from the feeding coaxial line by an unmatched window. The length l was set at zero. Repeated sample permittivity measurements using cells of different lengths l and measurements of reference liquids with known permittivity resulted in the following relative errors: ∆′/ ′ ) 0.02, ∆′′/′′ ) 0.03, ν < 5 MHz; ∆′/′ ) 0.01, ∆′′/′′ ) 0.01, 5 MHz e ν e 1 GHz; ∆′/′ ) 0.05, ∆′′/′′ ) 0.07, ν > 1 GHz. The error in the frequency of measurement was smaller than ∆ν/ν ) 0.001. The temperature of the sample was controlled to within 0.02 K and was measured with an error of 0.01K. The effect of this temperature error in the complex permittivity data was negligibly small. Results and Treatment of Data Between 300 kHz and 3GHz the complex dielectric spectrum of a DMPC vesicle solution is displayed in Figure 3. Only the
6268 J. Phys. Chem. B, Vol. 105, No. 26, 2001
Schrader and Kaatze TABLE 1: Parameters of the Relaxation Spectral Function Defined by Eq 5 for the 0.1 M DMPC Solution (60 mg/mL) at Various Temperatures T (Here E(∞) ≡ 5 and hI ≡ 0 throughout) ∆I τI, µs σ, mS/m ∆w τw, ps ∆z τz, ns hz (0.5% (5% (2% (3% (5% (50% (50% (3%
T, °C 18 21 23 23.5 24 24.5 25 26 28 31 Figure 3. Complex dielectric spectrum at 31 °C of a 0.1 M (60 mg/ mL) aqueous solution of DMPC made by extrusion. Figure symbols indicate different sample cells. Spectra for the solution of the DMPC/ DPPC mixture look quite similar.
dielectric contribution to the total loss is shown. Besides the dielectric relaxation of the zwitterionic headgroups (“Z”), located in the center of our measuring range, additional relaxations emerge at higher and lower frequencies. The former is doubtlessly due to the reorientational motions of the solvent water and will be indicated by “W” further on. The low frequency relaxation (“I”) reflects restricted motions of electrically charged species,23 due to small traces of ionic impurities.24 We have complemented the former studies23,24 of the effects from interfacial ionic polarization mechanisms by a systematic investigation in which small amounts of the ionic lipid 1,2dimyristoyl-DL-3-glycerol, sodium salt25,26 were added to DMPC membranes. It was found that the dielectric spectra of the ionic vesicles solutions can be well represented by the Dukhin and Shilov theory27 if, in contrast to many other heterogeneous systems, convection is taken into acount. Considering the results for the ionic vesicle solutions23-26 the above assignment of spectral regions to different molecular motions of the membrane systems follows conclusively. Hence, evidently the dielectric contribution to the complex permittivity spectrum has to be represented by three relaxation terms. We found a Debye-type relaxation with discrete relaxation time28 suitable to describe the low-frequency branches of the water contribution to the spectrum (Figure 3). With both, the one-component DMPC membrane system and the pseudo-binary DMPC/DPPC mixture, the zwitterion relaxation is subject to a relaxation time distribution. With the DMPC/DPPC mixture, also the low-frequency I relaxation extends over a broader frequency range than characteristic for a process with discrete relaxation time. We assumed an underlying continuous distribution of relaxation times. Among various distribution functions the Cole-Cole29 relaxation time distribution GCC(s) was empirically found most suitable. When plotted versus log(s) function sGCC(s) is symmetrically bell shaped. Here s ) τ/τCC, where τCC is the relaxation time with strongest weight. Considering, in addition, the contribution from the d.c. conductivity σ the relaxation spectral function
S(ν) ) (∞) +
Z
1 + (iωτI)1-hI
10.5 10.3 9.9 9.8 9.6 9.6 9.5 9.4 9.2 8.8
5.2 4.9 4.9 4.6 4.7 4.6 4.7 4.5 4.4 4.2
12.7 11.2 8.2 6.2 4.6 3.9 3.8 3.4 3.0 2.6
0.39 0.37 0.36 0.31 0.29 0.25 0.26 0.23 0.22 0.20
3 3 1 3 3 4 7 5 4 6
0.4 0.5 0.2 0.4 0.4 0.5 0.6 0.5 0.4 0.4
1.08 1.31 1.35 1.31 1.33 1.35 1.34 1.38 1.44 1.52
TABLE 2: Parameters of the Relaxation Spectral Function Defined by Eq 5 for the 0.1 M Aqueous Solution of the DMPC/DPPC Mixture with Mole Fraction x ) 0.5 of the lipids (E(∞) ≡ 5 throughout) ∆I τI, ns T, ∆w τw, ps ∆z τz, ns hz hI σ, mS/m °C (1% (10% (50% (50% (50% (20% (20% (30% (0.5% 25 28 30 31 32 33 34 35 37 40
60.6 59.3 57.9 57.0 55.7 54.4 52.8 52.1 50.8 49.8
9.6 9.2 8.9 8.8 8.7 8.5 8.2 8.4 8.1 8.0
3 3 3 3 2 3.3 3 3.6 3.4 3
30 30 25 7 2 4 3 3 2 2
0.3 0.3 0.3 0.3 0.1 0.3 0.3 0.2 0.2 0.2
11 12 13 12 13 12 13 10 12 14
57 69 82 84 64 68 62 60 60 60
0.3 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.2 0.2
16.42 17.28 17.75 17.95 17.93 17.95 17.73 17.88 18.38 19.28
In eq 5 parameter e(∞) denotes the extrapolated high frequency permittivity due to distortion polarization mechanisms. Since we did not measure at sufficiently high frequencies to be able to properly account for that high-frequency permittivity contribution, this parameter has been fixed at the reasonable value8 (∞) ) 5 in the regression analysis of the measured spectra. Parameters τZ and τI denote the characteristic Cole-Cole relaxation times of the Z and I terms, respectively, and hZ and hI are related to the width of the relaxation time distribution function corresponding with these terms. In the DMPC spectra hI ≡ 0 throughout. The values for the unknown parameters have been found using a nonlinear least- squares regression analysis minimizing the reduced variance
χ2 )
1 N-P-1
∑
[(
) (
S′(νn) - ′(νn) ∆′(νn)
2
+
)]
S′′(νn) - ′′(νn) ∆′′(νn)
2
(6)
Here the νn, n ) 1, ..., N, denotes the frequencies of measurement, P is the number of adjustable parameters of S, and the inverse experimental errors 1/∆′(νn) and 1/∆′′(νn) are used as weighing factors. The values for the parameters of the spectral function (eq 5) are presented in Tables 1 and 2. Discussion
∆W ∆Z + + 1 + iωτW 1 + (iωτ )1-hZ ∆I
63.1 62.5 61.4 60.6 59.4 59.0 58.7 58.4 57.8 56.9
-i
σ (5) 0ω
has been used to analytically represent the measured spectra.
Internal Electric Fields. Due to the spatial distribution of material with substantially different permittivity and d.c. electrical conductivity noticeable effects from internal polarizing and depolarizing fields exist in the vesicle solutions. Therefore, the relaxation parameters as well as the static permittivity parameters of the phospholipid systems, in addition to the molecular
Headgroup Relaxation of Lipid Membranes
J. Phys. Chem. B, Vol. 105, No. 26, 2001 6269 and
R((ω) ) R((∞) +
∆R(
(9)
1 + (iωτ()1-h(
from the diffusional reorientation of the zwitterionic phospholipid headgroups and the restricted motions of ionic species, respectively, as sketched in part A of Figure 4. Here again the Cole-Cole term turned out to favorably account for any relaxation time distribution in the measured spectra. We also evaluated the experimental spectra assuming other continuous relaxation time distributions. Due to the preference that has been recently made to represent the “Z” region of the spectra of egg lecithin solutions31 particular attention has been given to the unsymmetric Davidson-Cole relaxation distribution.32 For our spectra the symmetrical sGCC(s) function was found somewhat superior. In deriving eq 8 it has been assumed that the cationic lecithin group moves tangentially to the vesicle surfaces on circular paths relative to the anionic phosphate group. If the radius of this path is denoted by ξ and the cation mobility in this motion by u
∆Rξ )
njg(e0ξ)2 2kT
(10)
and
τξ ) Figure 4. Sketch of the model of vesicle solutions.
properties of the subspheres, also reflect structural characteristics of the subphases. The evaluation of relaxation amplitudes and relaxation times in terms of dipole moment densities and dipolar group mobilities thus requires a theoretical model relating the measured parameters to the molecular properties of the dielectrically heterogeneous systems. Here we shall treat the data in terms of a specially matched model23 in which the shape of the vesicles is assumed to be perfectly spherical (Figure 4). The radius of the water core is denoted by rc and the outer vesicle radius by r ) rc + db, where db denotes the bilayer thickness. Previous dielectric spectrometry up to 40 GHz of phospholipid vesicle solutions with lipid concentration up to 0.37 mol/L revealed a water relaxation very close to that of pure water (Figure 1). The present relaxation times of the “W” term (Tables 1,2) also almost agree with the values for pure water at the same temperature.30 We thus attributed the frequency dependent permittivity
w(ω) )
w0(0) - w0(∞) σc -i 1 + iωτw0 0ω
(7)
to the water core (B, Figure 4). The subscript “0” indicates pure water values and σc denotes a possible small d.c. conductivity of the solvent within the water core. The bilayer headgroup region is dielectrically characterized by surface polarizability densities
Rξ(ω) ) Rξ(∞) +
∆Rξ 1 + (iωτξ)1-hξ
(8)
ξ2 ukT
(11)
Here nj is the mean surface number density of the zwitterions, g has regard to possible correlations in the orientation of neighboring zwitterions, and the other quantities have their usual meaning. Let R ) Rξ + R( denote the sum of the zwitterion polarizability density and of the less interesting polarizability contribution from restricted motions of ionic species. The surface polarizability contribution can be combined with the core permittivity to yield a resulting permittivity23
c(ω) ) w(ω) +
8πR(ω) rc
(12)
of the vesicle core together with the inner polar surface layer of the membrane (C, Figure 4). Using the Wagner mixture relation27 the permittivity
v(ω) ) e
(2e + c(ω))r3 - 2(e - c(ω))r3c (2e + c(ω))r + (e 3
c(ω))r3c
+
8πR(ω) r (13)
of the homogeneous sphere dielectric substitute of an isolated vesicle follows (D, Figure 4). The first term on the right-hand side of eq 13 represents the resulting permittivity of the vesicle core (c, eq 12) and of the nonpolar hydrocarbon region of the lipid bilayer with (predominantly electronic) polarizability e ) 2. The second term on the right-hand side of this equation considers the surface polarizability of the outer polar shell of the vesicle. Using the permittivity v(ω) of the homogeneous sphere dielectric substitute of a vesicle and applying the Wagner mixture formula accordingly, the permittivity m(ω) of the mixture (E, Figure 4) of vesicles in solvent with permittivity w(ω) (eq 7) results as
6270 J. Phys. Chem. B, Vol. 105, No. 26, 2001
Schrader and Kaatze
m(ν) ) w(ν) + 3Vvw(ν)
v(ν) - w(ν) 2w(ν) + v(ν) + Vv(w(ν) - v(ν))
(14)
where
Vv )
Vr3 r3 - r3c
(15)
denotes the volume fraction of the vesicles and V that of the phospholipid within the solutions. Interesting quantities of this model are (i) the radius of the vesicles, (ii) the relaxation time distribution parameter hξ (eq 8), corresponding with parameter hz (eq 5), (iii) the product gξ2 (eq 10), which is related to the relaxation strength ∆Z (eq 5), and (iv) the zwitterion relaxation time τξ (eq 11), corresponding with the macroscopic dielectric relaxation time τZ (eq 5). The values of these quantities as obtained from a regression analysis of the measured spectra in terms of the model relaxation spectral function m(ν) will be discussed in the following. Solvent Contribution to the Static Permittivity. Radius of Micelles. The radius of the vesicles acts as noticeable influence on the internal electric fields (eqs 12, 13, 15) and thus on the permittivity spectrum m(ν) of the phospholipid solutions. This influence is particularly reflected by the permittivity s ) (∞) + ∆w representing the solvent contribution to the static permittivity of the measured spectra (Figures 1, 3). As shown by Figure 5 the s values are substantially smaller than the pure water static permittivity w0(0) at the same temperature, not only due to the dilution of the dipolar water by the bilayer material but also due to the aforementioned internal fields within the dielectrically heterogeneous liquids, tending to screen the core water. With both phospholipid systems the s/w0(0) data decrease at the respective transition temperature Tm, indicating an increase in the micellar radius. The effect is much stronger with the DMPC/DPPC mixture than with the DMPC solution. In addition, with the binary liquid mixture the transition extends over a broader temperature range, thus, in conformity with the sound velocity numbers shown in Figure 2, reflecting a reduced cooperativity of the phase transition. As shown by Figure 6 the characteristics in the s/w0(0) data are reflected by the rc values resulting from the fit of the model relaxation function m(ν) to the measured spectra. The vesicle radii of the DMPC solution increase from a value of about 85 nm at T < Tm to nearly twice this value when the sample temperature exceeds Tm, indicating a swelling of the vesicles near the main transition temperature. This increase in the vesicle size is much stronger with the binary DMPC/DPPC membrane system than with the DMPC solution. It is well established that the hydrodynamic radius of vesicles made by the extrusion of lipid suspensions may exceed the nominal pore radius of the polycarbonate membranes used as filters.33 The difference between the actual radii from the dielectric spectra (85 nm, DMPC, T < Tm) and the nominal pore radius (50 nm), however, is rather large, probably due to some simplifications of the internal electric field model. First the model proceeds from the assumption of a monodisperse suspension of exactly spherically shaped vesicles. At the high lipid concentration used in the dielectric relaxation study, deviations from the spherical shape may be substantial and may result in depolarizing field effects stronger than assumed in the model, thus simulating larger vesicle radii in the treatment of spectra. In addition, since the effect of internal electric fields
Figure 5. The water contribution s to the static permittivity of the solutions normalized by the static permittivity w0(0) of pure water displayed versus temperature T.
Figure 6. Vesicle radius r as a function of temperature T.
cannot be treated rigorously, there exists a great variety of mixture formulas for composite dielectrics27,34,35 and there is thus some arbitrariness in selecting one. Finally, if a small amount of dielectrically saturated water30 exists in the phospholipid vesicle solutions, this partly irrotationally bound water also tends to decrease the s values and thus to suggest enhanced vesicle radii. Despite these limitations in the theoretical model the vesicle radii evaluated from the dielectric relaxation spectra show some interesting trends in the r data. These trends are confirmed by quasi-elastic light scattering studies using an improved version of a photon correlation spectrometer.36 This technique allows us to determine the distribution function for the diffusion coefficient D of the vesicles and, according to the Einstein-Stokes relation
r)
kT 6πηD
(16)
also the distribution of the vesicle radius r. In eq 16 η denotes
Headgroup Relaxation of Lipid Membranes
Figure 7. DC conductivity σ of the DMPC/DPPC system plotted versus temperature T.
Figure 8. Product gξ2 (eq 10) of the phospholipid bilayer systems shown as a function of temperature T.
the shear viscosity of the liquid. Preliminary measurements on solutions of small phospholipid concentration clearly indicated noticeable swelling of the vesicles when T exceeds Tm. These studies also revealed an unsymmetric broadening of the vesicle size distribution for the DMPC/DPPC systems, with a preference for radii larger than the principal value at T > Tm. The solvent uptake of vesicles around Tm is also reflected by the d.c. electrical conductivity σ (eq 5) which for the DMPC/ DPPC system is displayed as a function of temperature T in Figure 7. The overall tendency of σ to increase with T is obviously eclipsed around the transition temperature by the counteracting effect that more ions are trapped in vesicular cores and are thus unable to freely move. Zwitterion Relaxation Parameters. The product gξ2 characterizes the static bilayer surface polarizability as due to the zwitterionic headgroup reorientational motions (eq 10). The gξ2 data of the DMPC solution vary between 0.68 nm2 and 0.9 nm2 (Figure 8). These values are distinctly larger than those previously found for sonicated unilamellar vesicles with smaller radii between about 12 and 20 nm.9 Those solutions exhibited gξ2 data between 0.41 nm2 and 0.53 nm2, in conformity with micelle solutions of lysolecithins for which 0.4 nm2 e gξ2 e 0.5 nm2. Hence, in conformity with our expectations, the larger radius of curvature of the vesicles made by extrusion lead to a
J. Phys. Chem. B, Vol. 105, No. 26, 2001 6271
Figure 9. Mobility of headgroup motions, normalized to the square of the radius ξ (eq 11), displayed versus temperature T.
more ponounced effet of parallel ordering of the dipolar phospholipid headgroups. Since we do not know the exact value for the radius ξ of the path on which the cationic group moves relative to the anionic group of the lecithin molecule, we use ξmax ) 0.5 nm as the length of the stretched phosphorylcholine group to calculate gmin values from the product gξ2. For the DMPC vesicles 2.7 e gmin e 3.6 follows and 1.6 e gmin e 2.9 for the DMPC/DPPC system. Obviously, the degree of parallel ordering of electric dipole moments is smaller with the membranes made from the lipid mixture than with the DMPC membranes. Another remarkable result is the finding that the surface polarizability increases when T exceeds Tm. This may to the most part result from a larger radius ξ above the transition temperature rather than a larger dipole orientation correlation factor g. If the assumption about the radius ξ is true, then the stepwise enhancement of the quantity u/ξ2 (eq 11) when exceeding Tm (Figure 9) points at a remarkable increase in the mobility u of the headgroup motions. Even if the radius ξ is assumed to be independent of temperature the cationic headgroup mobility changes by a factor of about 35 (umin ) 0.1 × 109 s/g, 25 °C; umin ) 3.5 × 109 s/g, 40 °C; ξmax ) 0.5 nm). The headgroup mobility data are in fairly good agreement with the previous data for sonicated DMPC vesicle solutions for which u/ξ2 values between 60 and 120 × 106 s/g nm2 had been found.9 The results for vesicle solutions indicate a somewhat smaller mobility than lysolecithin micelle systems with u/ξ2 between 200 and 300 × 106 s/g nm2. The headgroup relaxation time distribution parameter hξ displays quite different temperature dependencies for both phospholipid systems (Figure 10). For DMPC hξ decreases substantially with T, pointing at a more pronounced heterogeneity in the headgroup dynamics below than above Tm. Since hξ corresponds with the distribution of τξ rather than u values (eq 8), the distinct heterogeneity in the headgroup dynamics may be due to both a broad distribution of the radii ξ or of the mobility u. Recently the parameter measuring the width of the DavidsonCole relaxation time distribution, used to describe dielectric spectra of solutions of egg lecithin, have been discussed in terms of a nonhomogeneous spatial distribution of dipolar headgroups.31 As egg lecithin membranes consist of a nonideal mixture of various saturated and unsaturated lipids, their microheterogeneous structure is much more complicated than that of the DMPC and DMPC/DPPC bilayers. Obviously, even the quasi-ideal mixture of DMPC and DPPC reveals a substantial heterogeneity in the headgroup reorientational motions near the
6272 J. Phys. Chem. B, Vol. 105, No. 26, 2001
Schrader and Kaatze (6) Shepherd, J. C. W.; Bu¨ldt, G. Biochim. Biophys. Acta 1978, 514, 83. (7) Shepherd, J. C. W.; Bu¨ldt, G. Biochim. Biophys. Acta 1979, 558, 41.
Figure 10. Relaxation time distribution parameter hξ for the surface polarizability from the phospholipid headgroup motions versus temperature T.
transition temperature Tm (Figure 10). We suggest the fluctuations in the domain structure near Tm of the lipid mixture to be larger than with the single lipid system, because the fluctuations of the former are not only given by fluid/gel state variations but additionally include changes in the ordering of like and unlike molecules. Acknowledgment. We thank Dr. Ralph Behrends for making his light scattering data available to us before publication. Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. References and Notes (1) Gebhardt, C.; Gruler, H.; Sackmann, E. Z. Naturforsch. 1977, 32C, 581. (2) Mouritsen, O. G.; Jørgensen, K. Chem. Phys. Lipids 1994, 73, 3. (3) Sackmann, E. In Structure and Dynamics of Membranes; Lipowski, R., Sackmann, E., Eds.; Elsevier: Amsterdam, 1995. (4) Jørgensen, K.; Mouritsen, O. G. Thermochim. Acta 1999, 328, 81. (5) Tra¨uble, H.; Eibl, H. Proc. Natl. Acad. Sci. U.S.A. 1974, 71, 214.
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