water-mixtures

R. Henze, Dielectric relaxation in lecithinlcholesterol-bilayers

167

the first run of measurements (approx. 2 h after sonication) measurements wer.e immediately repeated at one single temperature, and the whole run was repeated 24 h later. Errors of the data are less than 1.5% in ~' and 5% in ~". Temperature stability was better than 0.1°C.

Results in terms of a Debye relaxation function

Description o[ the measured permittivity data by a Debye relaxation [unction In Fig. 1 the real part ~' and the negative imaginary part excluding conductivity contributions, ~" - 2o-/~,, is plotted against frequency v for three dimyristoyl-lecithin solutions with cholesterol mole fractions of xc = 0, 0.03 and 0.05. Within the limits of experimental error the measured permittivity spectra can be analytically represented by the function: ¢(v) = Cn(m)+ eD(O)-- ~t~(~) i 2try 1 + i2~rv'rD v

(1)

Since the dielectric relaxation of the solvent water occurs at frequencies well above 50MHz [12,13], the extrapolated high frequency permittivity ~t~(~) reflects two contributions to the static permittivity ~(0): those of the orientation polarization of water and of fast solute and solvent distortion polarization mechanisms. The second term of Eqn. 1 represents a Debye relaxation which is characterized by a single relaxation time ~'r~. Previous experiments [12--14] led to the conclusion that this relaxation is due to the restricted diffusive motions of the zwitterionic lecithin head groups. The third term takes into account ohmic conductivity contributions to the total imaginary part - C 0 , ) of the permittivity. Function (1) was fitted to the experimental data by means of a nonlinear least-squares procedure.

Temperature dependence of the Debye-function parameters The temperature dependence of the Debye-function parameters is qualitatively the same for the solutions of lecithin/cholesterol-mixtures as it is for the solutions of pure lecithins which have b6en discussed previously [12,13]. A general decrease of Cr~(~o) with increasing temperature is found, an increase of the relaxation strength ~r~(0)-~D(oo), a slight decrease of ~'t~ and an increase of ~D. The increase of ~r,(0)- ~(~o) vanishes for cholesterol mole fractions xc -> 0.1. Distinct changes of the parameters at the phase transition temperature were found in the pure lecithin solutions only, they have been described and discussed previously [12--14]. ..

R. Henze, Dielectric relaxation in lecithin/cholesterol-bilayers

168 I

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~ = Fig. I. Real part of the complex permittivity ~' and negative ima~nary pa~ excluding conductivity contributions, ~"--2~D/~ plotted against frequency ~ for aqueous solutions of dimyristoyl-lecithin/cholesterol mixtures with cholesterol mole fractions x~ = 0 (~); 0.03 (~) and 0.05 (~). ~ e leothin ~n~ntration is CL =0.14mol/l and the temperature T = 3 ~ C . ~e dotted lines indicate the high (~D(~)) and low frequency (~D(0)) limiting value of ~' and the relaxation frequen~ vn = I / 2 ~ (for x~ = 0).

Cholesterol concentration dependence of the Debye-function parameters In Fig. 2 the quantities eD(0)-- ~D(O0), eD(~0) and ~'o are plotted against the cholesterol mole fraction xc in the range of xc = 0 to 0.5 for the dimyristoyland dipalmitoyl-lecithin/cholesterol-mixtures at T = 30°C and 48°C respectively. For all solutions ~D(OO)is distinctly smaller than the 'static' permittivity Cw(0) of pure water at the same temperature (see Fig. 2b). ffD(0~)

R. Henze, Dielectric relaxation in lecithinlcholesterol-bilayers I

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Fig. 2. The Debye-function parameters eD(0)-- ~D(°°) (a), ~D(00) (b) and TD (C) plotted against the mole fraction of cholesterol x~ for 0.14 molar dimyristoyl-lecithin solutions at T = 30~C (0, ) and for 0.13 molar dipalmitoyl-lecithin solutions at T = 48"C (O, - - - ) . The horizontal lines indicate the values at x~ -- 0. ~,~(0): static permittivity of pur~ water.

170

R. Henze, Dielectric relaxation in lecithin/cholesterol-bilayers

decreases slightly with increasing cholesterol concentration. Both relaxation strength tD(0)--eD(~) and relaxation time ~'o decrease with increasing cholesterol concentration. For the dimyristoyl-lecithin solutions ~D(0)- eD(o~) and zt~ decrease drastically in the cholesterol mole fraction range xc-0 . . . 0.075. Another remarkable result are the noticeable higher values of these parameters for pure dimyristoyl-lecithin than for dipalmitoyl-lecithin. The dc conductivity ¢rD increases along with increasing cholesterol concentration only for the dimyristoyl-lecithin solutions while it is not dependent on cholesterol concentration for the dipalmitoyl-lecithin solutions.

A special solution model Parameter values of the phenomenologically defined Debye-function (Eqn. 1) describe macroscopic dielectric properties. Conclusions concerning molecular behaviour can be drawn from these parameters in simple cases only. In lameilar lecithin solutions the heterogeneity of the solute particles-bilayer aggregates which consist of highly polar (water) and non-polar (bilayer interior) materials with the zwitterionic head groups at the interface in between--gives rise to internal depolarizing fields. These fields have to be taken into consideration if statements concerning molecular properties are requested. The strong reduction of the solvent contribution to the permittivity (eD(~)/~W(0)= 0.75), which cannot be explained by a simple dilution of the solvent, shows, that these effects must not be neglected. Moreover, polarization contributions which occur when ions (salt impurities) are diffusion restricted at a bilayer-water interface ('Maxwell-Wagner'-relaxation) can be of importance. Details of the model function, which describes the permittivity of a solution of multilamellar bilayer aggregates with polarizable bilayer surfaces have been dealt with in previous papers [12,13]. As regards to the interesting permittivity contribution of the lecithin head groups it has to be noted that the phosphatidylcholine group is assumed to lie within the plane of the bilayer surface (as suggeste d in [7,15--17]). The trimethylammonium group is assumed to rotate on a circular path of radius ~ around the phosphate group. A frequency dependent polarizability density ACI~I

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of the bilayer is found in this case. gi represents an orientation correlation factor which specifies the number of neighbouring head groups with the same orientation, ~i~ is the mean surface number density of the lecithin molecules, eo the elementary charge, k Boltzmann's constant and T the temperature on

R. Henze, Dielectric relaxation in lecithin/cholesterol-bilayers

171

the Kelvin scale. ~'i represents the relaxation time of the ionic surface polarization. The fit of the model function yields the quantities Aot~, ~'i and the mean radius ~ of the bilayer aggregates, which are assumed to be spherically shaped. The orientation correlation factor gt can be calculated from the relaxation strength Aot~ (see Eqn. 2). For this purpose ti~ = 1/60A -2 [18] has been inserted for the lecithin molecule surface number density. Any dependence of ti~ on temperature and cholesterol concentration [18] could be neglected in so far as numerical estimations showed that it affects gi(Xc)values only within the limit of experimental uncertainty. The rotation radius was assumed to be ~ = 5 ~ [19], which is the length of the extended phosphorylcholine grou~p. This value yields minimum values for g~, since ~ may be smaller than 5 A (especially at small cholesterol concentrations).

Discussion of the influence of cholesterol on the lecithin head groups Orientation correlation

In Fig. 3a the head group orientation correlation factor g~ is plotted against the cholesterol mole fraction xc for the dimyristoyl-lecithin/cholesterol mixtures. For pure lecithin (xc = 0) the value of gt is 65, indicating that the bilayer surface is built up by domains of 65 head groups in which the phosphate-trimethylammonium vectors are strongly correlated in their orientation. The correlation factor gt decreases with increasing cholesterol mole fraction, which means that the addition of cholesterol disrupts the bilayer surface structure. This view is supported by other data, indicating that cholesterol reduces the interaction of the polar lecithin head groups. Measurements of the nuclear Overhauser effect in 3tP-NMR spectra [6,10] have shown that the intermolecular interaction between the phosphate region and the trimethylammonium group will be reduced when cholesterol concentration increases. X-ray data [20] indicate that the distance between the head groups increases. The increase in the lateral distance of the lecithin molecules however is unlikely to be the only reason for the strong reduction in the head group domain size which decreases from 65 at x¢ = 0 to about 4 molecules at xc = 0.075. Since the cholesterol molecule is embedded in the inner hydrocarbon phase of the bilayer it seems reasonable to expect that the drastic influence on the surface order is also mediated by an intramolecular interaction between the hydrophilic and the hydrophobic part of the lecithin molecule, the latter of which being mainly affected by cholesterol. X-ray and calorimetric (dsc) measurements [21] of solutions of dipalmitoyl-lecithin/cholesterol mixtures led to the conclusion that the arrangement of the hydrocarbon chains changes from a tilted (58° with

R. Henze, Dielectric relaxation in lecithin/cholesterol-bilayers

172

80 ~ T - - ~

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R. Henze, Dielectric relaxation in lecithin/cholesteroi-bilayers

173

respect to the lipid water interface) to a vertical configuration at cholesterol mole fraction exceeding x~ = 0.075. This is accompanied by an increase of the interlameilar water layer thickness, indicating a change in the hydration state of the bilayer surface, which may be caused by a change in the charge distribution of the head group layer. Concluding it can be guessed that the alignment of the chains parallel to the bilayer surface normal is possibly related to the disrupture of the head group order. With increasing temperature, g~ increases for cholesterol mole fractions xc-< 0.075 (of. Fig. 3a) while being independent of temperature at higher cholesterol mole fractions. Qualitatively, the slope of the g~(x~)-relation is the same for the dipalmitoyl-lecithin solutions as it is for dimyristoyllecithin. As a remarkable difference the value at x~ --- 0 is g~ = 17.

Relaxation time of the ionic surface polarizability Associated to the reduction of gi is a distinct decrease of the surface polarizability relaxation time ~-~(Fig. 3b), indicating that the size reduction is related to a faster reorientation of the head group domains. A further decrease of ~'~ is to be observed when x~ exceeds 0.3. At high cholesterol mole fractions (Xc >~0.4), where the head group order is almost completely disrupted ( g ~ - 1 . . . 2 ) , the head groups can be assumed to rotate independently from one another. In this case ~'g follows the equation ~[

~'~ = u i k T '

(3)

in which u~ represents the mobility of the trimethylammonium Group, rotating on a circular path around the phosphate group. At ~ = 5 A this equation yields u~ ~-20.106 s/g, which value is in the same order of magnitude as it was found in micelles built up by lysolecithin (50.106 s/g [22]), and it is approximately one order of magnitude smaller than the mobility of the free tetramethylammonium ion in water (290. l& s/g, T = 25°C, cf. Ref. 23).

Influence of the curvature of the bilayer surface In Fig. 3c the values for the mean vesicle radius ~ are plotted against the cholesterol mole fraction Xc for the dimyristoyl- and dipamitoyl-lecithin solutions. For dimyristoyl-lecithin ? decreases with increasing xc from a value of 2400 ,~ at xc = 0 to approx. 300 ,~ at Xc = 0.5. This decrease is likely to be the reason for the increase of the conductivity trt) (see above). For dipalmitoyl-lecithin the ?(x~)-curve remains constant f f ~ 4 0 0 , ~ ) at small cholesterol mole fractions (x~ < 0.2) and approaches the curve of dimyristoyllecithin at xc exceeding 0.2. In a previous paper [14] an almost linear relation

R. Henze, Dielectric relaxation in lecithin/cholesterol-bilayers

174

5

i

i

i

t --

0 0.01

,

,

0.02 0.03

I

0.05

~

i _

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Xc ~ Pig. 4. ~afiO O[ lhe correlation ~ac~or g~ and ~he mean vesicle radius ~ plo~ed agains~ [he choleslerol mole ~racfion z~ ~or lhe dimyris~oyl- (~) and dipalmffoyVleci~hin (0) solutions a[ T = 35°C.

between g~ and f was found in various solutions of lecithins and lecithin analogues with increased phosphorus-ammonium distance, indicating that the head group domain size decreases with decreasing curvature radius of the bilayer surface. This is the explanation of the different gt-values (65 and 17, respectively) at xc = 0 for doimyristoyl- aond dipalmitoyl-lecithin, which are related to f-values of 2400A and 400A respectively. The influence of admixed cholesterol on gt however is not mainly caused by changes of the bilayer curvature. Both are demonstrated in Fig. 4 in which the ratio g~/r~ is plotted against xc for the dimyristoyl- and dipalmitoyl-lecithin solutions. The curve for dipalmitoyl-lecithin is similar to the dimyristoyl-lecithin curve, indicating that the difference in gt at x~ = G is mainly due to different f-values. Both curves show qualitatively the same tendencies as the gt(xc)curves in Fig. 3a. This means that addition of cholesterol exercises its influence on g~ directly by changes in the molecular interaction, which have been discussed above, and not via changes in the bilayer curvature.

Acknowledgement I owe special thanks to Professor R. Pottel and Dr. U. Kaatze for valuable discussions. This work was financially supported by the Deutsche Forschungsgemeinschaft. Numerical calculations were executed by a computer at the Gesellschaft fiir Wissenschaftliche Datenverarbeitung G/Sttingen.

R. Henze, Dielectric relaxation in lecithin/cholesterol-bilayers

175

References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

D. Chapman, Biological Membranes, Vol. 2, Academic Press, New York~ 1973, p. 91. H.-J. Hinz and J.M. Sturtevant, J. Biol. Chem., 247 (1972) 3697. H. Lecuyer and D.G. Dervichian, J. Mol. Biol., 45 (1969) 39. D.M. Engelman and J.E. Rothman, J. Biol. Chem., 247 (1972) 3694. M.C. Phillips and E.G. Finer, Biochim. Biophys. Acta, 356 (1974) 199. P.L. Yeagle, W.C. Hutton, C. Huang and R.B. Martin, Proc. Natl. Acad. Sci. U.S.A., 72, No. 9 (1975) 3477. D.L. Worcester and N.P. Franks, J. Mol. Biol., 100 (1976) 359. R.A. Demel and B. de Kruyff, Biochim. Biophys. Acta, 457 (1976) 109. G.L. Jendrasiak and J.H. Hasty, Biochim. Biophys. Acta, 337 (1974) 79. P.L. Yeagle, W.C. Hutton, C. Huang and R.B. Martin, Biochemistry, 16, No. 2 (1977) 4344. U. Kaatze, R. Henze, A. Seegers and R. Pottel, Ber. Bunsenges. Phys. Chem., 79 (1975) 42. R. Henze, Thesis, Mathem. Nat. Fak. Univ. G6ttingen 1978. U. Kaatze, R. Henze and R. Pottel, Chem. Phys. Lipids, 25 (1979) 149. U. Kaatze, R. Henze and H. Eibl, Biophys. Chem., 10 (1979) 351. W. Lessauer, J.E. Cain and J.K. Blasie, Proc. Natl. Acad. Sci. U.S.A., 69 (1972) 1499. G. Biildt, H.-U. Gaily, A. Seelig and J. Seelig, Nature, 271 (1978) 182. N.P. Franks, J. Mol. Biol., 1130(1976) 345. M.C. Phillips, in J.F. Danielli, M.D. Rosenberg and D.A. Cadenhead (Eds.), Progress in Surface and Membrane Science, Vol. 5, Academic Press, New York, 1972. M.C. Phillips, E.G. Finer and H. Hauser, Biochim. Biophys. Acta, 290 (1972) 397. Y.K. Levine, Progr. Biophys. Mol. Biol., 24 (1972) I. B.D. Ladbrooke, R.M. Williams and D. Chapman, Biochim. Biophys. Acta, 150 (1968) 333. R. Pottel, U. Kaatze and St. Miiller, Ber. Bunsenges. Phys. Chem., 82 (1978) 1086. R.A. Robinson and R.H. Stokes, Electrolyte Solutions, Butterworth, London, 1959.