183

Biochimica et Biophysica Acta, 506 (1978) 183--191

© Elsevier/North-Holland Biomedical Press

BBA 77908 PHASE T R A N S I T I O N S IN PHOSPHOLIPID MODEL MEMBRANES OF D I F F E R E N T C U R V A T U R E

P.W.M. VAN DIJCK a B. DE KRUIJFF J. DE GIER a

b, P.A.M.M. AARTS a, A.J. VERKLEIJ b and

a Laboratory o f Biochemisrry and b Institute o f Molecular Biology, State University o f Utrecht, University Centre "De Uithof", Transitorium 3, Padualaan 8, Utrecht (The Netherlands)

(Received June 27th, 1977)

Summary 1. Nuclear magnetic resonance, light scattering and freeze fracturing electron microscopic techniques were used to characterize the size of unilamellar phospholipid vesicles o f 1,2-dimyristoyl-sn-glycero-3-phosphocholine. 2. Differential scanning calorimetric and light scattering analyses showed that very small unilamellar vesicles obtained by the sonication m e t h o d exhibit a d o wn war d shifted, largely broadened phase transition with a slightly decreased en th alpy change when c om par e d with multilayered liposomes. 3. The phase transition of vesicles with variable diameter as obtained by injection m e t h o d s resembled the pattern of multilayered liposomes the more the diameter was increased. 4. Repeated cycling through the lipid phase transition was shown to have a progressive effect on a fusion process. This effect was strongly increased when the osmolarity of the medium was enhanced (e.g. by the addition of cryoprotectors). F u r t h e r m o r e it was shown that ice-water transitions of the systems caused abrupt fusion o f the lipid structures. 5. Controversial results in the literature on the t h e r m o t r o p i c behaviour of vesicles could be explained in terms of these fusion processes.

Introduction Both multilayered liposomes and unilamellar vesicles are c o m m o n l y used as model membranes because t hey are chemically well defined systems. Multilayered liposomes are easily obtained, but t h ey are very heterogeneous in size and have an u n k n o w n and variable out e r surface, which complicates the interp re t a tio n of, for example, permeability studies on these systems. Unilamellar

184 vesicles have a rather narrow size distribution and consequently a well defined o u t er and inner surface, and are therefore, from a morphological point of view, preferable to multilayered liposomes. However, the strong curvature of the vesicle may affect the packing of the molecules in the interface in such a way that the physico-chemical properties are significantly different from a planar bilayer. It is in this respect that published data on lipid phase transitions in the two systems are somewhat; controversial. Differential scanning calorimetric analyses carried out in our laboratory revealed no differences between vesicles and liposomes [1]. On the o t h er hand (:lear distinctions in t h e r m o t r o p i c behaviour have been reported by other groups. The phase transition of vesicles was found to be shifted to a lower temp er atu r e by 5 l f f 'C and to be significantly broader when compared to liposomes [ 2 - 4 ] . The enthalpy change of the vesicle phase transition was found to be 1 0 - 2 0 % [2,3], 505~ [5] or even 85% [4] lower than the value f o u n d for liposomes. In the present study it will be shown that such factors as differences in vesicle size due to methods of preparation and various fusion processes are i m p o r t a n t in the explanation of the observed discrepancies. Materials and Methods 1,2-Dimyristoyl-sn-glycero-3-phosphorylcholine (14 : 0/14 : 0-glycerophosphocholine) and 1,2-dipalmitoyl-sn-glyeero-3-phosphoryleholine ( 1 6 : 0 / 1 6 : 0 glycerophosphocholine), were synthesized by Mrs. A. Lanc6e-Hermkens according to the m e t h o d of van Deenen and de Haas [6]. Multilayered liposome structures were obtained by dispersion of 100 mg of lipids in 3.0 ml 25 mM Tris/acetate, 100 mM NaC1, pH 7.0, at temperatures above the phase transition. Unilamellar vesicles were derived from the multilayered structures by subsequent ultra-sonication under nitrogen (Branson sonifier, range 4, maximal o u t p u t ) for periods of 15 s, with 1 min intervals, until the suspension became translucent (2--3 min total sonieation time). The sonicate was centrifuged for 60 rain at 37 000 ":g in order to remove titanium fragments and residual multilayered structures. All manipulations starting with the dispersion of the lipid were carried out at 35°C, or 45°C, in the case of 14 : 0/ 14 : 0- and 16 : 0/16 : 0-glycerophosphocholine, respectively. Unilamellar vesicles were also obtained by injecting lipids, dissolved in ethanol, into a water system [7]. By varying the lipid c o n c e n t r a t i o n in the ethanol and standardizing the injection velocity as described by Kremer et al. [8] monodisperse populations of vesicles with variable diameter could be obtained. Freeze fracture electron microscopy was p e r f o r m e d as described previously [9]. To prevent freeze damage, glycerol was added to the vesicles. The samples were quenched from above the phase transition t e m p e r a t u r e of the phospholipid. 31p NMR measurements were p e r f o r m e d at 35°C using a Bruker WH-90 s p e c t r o m e t e r [1]. To the sample 2H20 was added to give a final concentration of 20% (v/v). Peak intensities were measured with respect to an external trip h e n y l p h o s p h i n e standard using gated decoupling. From a comparison of the total intensity of the signal from the vesicles with the intensity of the un-

185 shifted inside resonance in the presence of 3 mM Nd 3÷ the outside-inside distribution was determined, which enabled the vesicle size to be calculated. Vesicle size was also measured by angular-dependent light scattering, using a FICA light scattering p h o t o m e t e r and techniques recently described by Kremer et al. [8]. The light scattering recorded at 90 ° versus t em perat ure also enabled us to analyse the phase transition. In these experiments the t e m p e r a t u r e of the cuvet was raised or lowered at a speed of 5°/h. Differential scanning calorimetric measurements were carried out using a Perkin-Elmer 2 calorimeter cooled by a Perkin-Elmer Intracooler 1. The expansion ch amb er of the Intracooler is in direct c o n t a c t with the sample holder enclosure block which is t h e r e b y kept at --50°C; in this way the sample comp a r t men ts can be cooled if necessary. The advantage of using the Intracooler instead o f cooling by liquid nitrogen will be discussed. Heating and cooling rates were 5°C/min. Calibration of the temperature and the peak area and the calculation of the heat c o n t e n t of the transition were p e r f o r m e d as described previously [ 10]. Results and Discussion

Vesicle size The phospholipid distribution over the inside and outside of the vesicle could be determined by means of 3~p NMR. In an earlier study [1] an inside/ outside ratio of 0.38 was f o u n d for 14 : 0/14 : 0-glycerophosphocholine vesicles. In t hat study both the unshifted inside signal and the shifted outside signal (corrected for the Nuclear Overhauser Effect by a factor derived from experiments with egg lecithin) were used. In the present experiments the total intensity w i t h o u t shift reagent and the inside intensity after adding shift reagent were used in the calculation. This gave an inside/outside ratio of 0.32 ± 0.01, which we think is a m or e reliable value. Assuming an identical packing density for the inside and outside layer and a m em brane thickness of 35 A [11] it can be calculated [1] that the sonicated vesicles have an average diameter o f 220 ± 10 A. Considering this value it should be not ed t hat in the absence of shift reagent only 84--88% of the total a m o u n t of lipid phosphate was observable in the spectrum as a narrow signal with a linewidth of 9 Hz. This can be explained if the remaining fraction of the phospholipid molecules was present as larger vesicles with a 31p signal which was t oo broad to be observed under the conditions employed. This interpretation is supported by the observation that u p o n c h r o m a t o g r a p h y of the vesicles over a Sepharose 4B column a b o u t 15% of the phosphorus appeared in the void volume, indicating the presence o f a fraction consisting of larger structures. Typical results of the light scattering analyses are given in Fig. 1, in which the reciprocal value of the Rayleigh ratio at angle 0 (corrected for the use of unpolarised light) is plotted against sin 2 0/2. As discussed elsewhere [8] the intercept obtained by extrapolation of the experimental curve to angle 0 = 0 gives a p p r o x i m a t e l y 1/M, in which M is the total lipid molecular weight of the vesicle. At lower angles small fractions of larger vesicles cause deviations from linearity, and e x t r a p o l a t i o n is therefore made from high angles [8]. Using M and assuming an area per molecule of 60 A 2 and a bilayer thickness of 35 A

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[11] t h e d i a m e t e r o f the vesicle was calculated to be 280 ~ 20 A. Considering the a s s u m p t i o n s t h a t had to be m a d e it can be c o n c l u d e d t h a t the NMR and light scattering data are in reasonable a g r e e m e n t . T h e results c o u l d also be c o n f i r m e d by e l e c t r o n - m i c r o s c o p y . Fig. 2A shows a typical freeze f r a c t u r e e l e c t r o n m i c r o g r a p h o f a s o n i c a t e d 14 : 0 / 1 4 : 0 - g l y c e r o p h o s p h o choline vesicle p r e p a r a t i o n . F r o m such pictures it c o u l d be calculated t h a t the m a j o r i t y of the s o n i c a t e d vesicles had a d i a m e t e r b e t w e e n 200 and 300 A. In a g r e e m e n t with the results o f K r e m e r et al. [8], the injection m e t h o d o f Batzri and K o r n [7] p r o d u c e d vesicles with larger and variable diameters, d e p e n d e n t on the lipid c o n c e n t r a t i o n in the alcohol solution. As the m e t h o d gives diluted dispersions, the vesicle size c o u l d o n l y be d e t e r m i n e d by the light scattering m e t h o d . We injected l-ml samples o f 14 : 0 / 1 4 : 0 - g l y c e r o p h o s p h o choline in e t h a n o l into 10 ml o f buffer. C o n c e n t r a t i o n s o f 10 mg lipid per ml yielded vesicles with an average d i a m e t e r o f 540 h and c o n c e n t r a t i o n s o f 15 m g / m l vesicles with a d i a m e t e r of 700 A. F o r reasons which are n o t entirely clear, one o f the 540 h p r e p a r a t i o n s a p p a r e n t l y u n d e r w e n t fusion, to give a p o p u l a t i o n of 800 A vesicles, a f t e r storage in the refrigerator. A typical p l o t of the angular d e p e n d e n c e o f the scattered light o f these vesicles, o b t a i n e d by the injection m e t h o d , is s h o w n in Fig. 1 for the vesicles o f 800 A. F r o m the linearity of the p l o t it was c o n c l u d e d t h a t the vesicles were m o n o d i s p e r s e .

Analyses of the phase transition Multilayered liposomes of 14 : 0 / 1 4 : 0 - g l y c e r o p h o s p h o c h o l i n e studied by differential scanning c o l o r i m e t r y e x h i b i t e d a t h e r m o t r o p i c b e h a v i o u r as s h o w n in Figs. 3A and 3B. T h e main transition o c c u r r e d at 23.5°C and involved an e n t h a l p y change o f 6.9 + 0.1 k c a l / m o l in a g r e e m e n t with earlier r e p o r t e d values [ 1 , 2 , 4 , 1 0 ] . When a sample of sonicated 14 : 0 / 1 4 : 0 - g l y c e r o p h o s p h o c h o l i n e vesicles was placed in the sample c o m p a r t m e n t and c o o l e d to 2°C, heating and cooling curves were observed as s h o w n in Figs. 3C and 3D, respectively. A b r o a d peak is seen ranging f r o m 16 t o 28°C with a A H value o f 5.6 + 0.4 kcal/ mol, in a g r e e m e n t with the observations o f S u u r k u u s k et al. [2]. S o n i c a t e d vesicles p r e p a r e d f r o m 16 : 0 / 1 6 : 0 - g l y c e r o p h o s p h o e h o l i n e also

187

Fig. 2. E l e c t r o n m i c r o g r a p h s of 14 : 0 / 1 4 : 0 - g l y c e r o p h o s p h o e h o l i n e s o n i c a t e d vesicles. A, b e f o r e a n d B, a f t e r passing the i c e - w a t e r t r a n s i t i o n . G l y c e r o l was a d d e d t o t h e s a m p l e s (final c o n c e n t r a t i o n 30 vol%). t o P r e v e n t f r e e z e d a m a g e , b e f o r e t h e y w e r e q u e n c h e d f r o m 35°C. T h e bars in t h e figures r e p r e s e n t 0.25 ~m.

s h o w e d a b r o a d e n e d p e a k ( 3 2 - - 4 3 " C ) and a decrease in A H value ( f r o m 8.8 ± 0.2 to 7.5 _+ 0.3 k c a l / m o l ) w h e n c o m p a r e d with the c o r r e s p o n d i n g liposomes. As L a w a c z e k et al. [12] r e p o r t e d t h a t vesicles p r e p a r e d b e l o w the transition t e m p e r a t u r e are unstable and fuse readily t o f o r m larger s t r u c t u r e s we also studied the c a l o r i m e t r i c b e h a v i o u r o f 14 : 0 / 1 4 : 0- and 16 : 0 / 1 6 : 0-glycero-

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F i g . 3. T h e r m o t r o p i c properties of 14 : 0/14 : 0-glycerophosphocholine bilayers. Liposomal preparation: a, h e a t i n g s c a n ; b , c o o l i n g s c a n . S o n i c a t e d v c s i c l e s : c, h e a t i n g s c a n ; d , c o o l i n g s c a n . S o n i c a t e d v e s i c l e s a f t e r f r e e z i n g : e, h e a t i n g s c a n ; f, c o o l i n g s c a n . S o n i c a t e d v e s i c l e s in 5 0 v o l % e t h y l e n e g l y c o l : g, h e a t i n g s c a n . F i g . 4. T e m p e r a t u r e dependency o f t h e 9 0 ° s c a t t e r e d l i g h t as o b s e r v e d f o r v a r i o u s 1 4 : 0 / 1 4 : 0 - g l y e e r o phosphocholine p r e p a r a t i o n s a, s o n i c a t e d v e s i c l e s , c o o l i n g s c a n ( e ) ; b - - d , v e s i c l e s w i t h d e f i n e d d i a m e t e r s ; b , 5 4 0 A d i a m e t e r , c o o l i n g s c a n ( o ) ; c, 7 0 0 A d i a m e t e r , c o o l i n g s c a n (X), h e a t i n g s c a n (A); d, 8 0 0 A d i a m e t e r , h e a t i n g s c a n (m).

phosphocholine vesicles obtained by sonication at 4 and 23°C, respectively. Although the transition peaks displayed a more p r o n o u n c e d sharp shoulder (10--15% o f the total peak area) the preparations exhibited a transition broadness and an enthalpy change typical of vesicles. As the vesicle preparations obtained by the injection m et hods were t oo diluted to be studied by differential scanning calorimetry, Fig, 4 shows a comparative analysis of the phase transitions as recorded by the light scattering technique. It can be concluded that the very small vesicles exhibit a very broad transition, but that the t e m per a t ur e range over which the scattering changes is rapidly reduced when the diameter of the vesicles is increased. The light scattering tracing of the sonicated vesicles suggests a somewhat smaller t e m p e r a t u r e range of transition (18--25°C) when compared with the differential scanning calorimetric analyses (16--28°C). This may be explained by the fact that the larger vesicles make a greater c o n t r i b u t i o n to light scattering intensity during the phase transition [8]. In understanding the anomalous behaviour of the small vesicles the following may be of importance: (i) It has become clear recently that in multilayered liposomes the main transition is from a La to a P~' phase whereas at the pretransition a change from P~' to L~ occurs [11,14]. Since in vesicles a P~3' phase is very unlikely it can be speculated that the broadened peak represents

189 a transition from La directly to Lfi or Pfi. This may explain the downward shift of the transition temperature. (ii) The broad transition may be explained by a distortion of the packing of the phospholipid molecules due to the high curvature of the vesicles. It has been concluded, however, that the molecular motion and the order parameters of different chain positions in vesicles is very similar to those in liposomes [1,13,15] and that there are no changes in relative number of trans and gauche isomers in both systems [16]. On the other hand NMR studies of Chan et al. [17] indicated a more disordered lipid packing in vesicles while interchain interactions were affected by sonication as deduced from Raman studies [16]. (iii)Another possibility which would account for the broad transition is a decrease in cooperativity due to the size of the vesicles. On theoretical grounds it has been argued by Marsh et al. [18], that the size of the cooperative unit per perimeter molecule at the centre of the transition is in the same range as the vesicle radius. The fact that there is only a small decrease in energy c o n t e n t of the phase transition of the vesicles compared to liposomes may favor this explanation.

Fusogenic conditions During this study it appeared that a number of experimental conditions greatly affect the apparent results of the differential scanning calorimetric analyses and explain earlier findings [ 1]. In the braod transition of the sonicated vesicles as shown by differential scanning calorimetry (Figs. 3C and 5A) a slight shoulder could normally be observed, which we think is due to the small fraction of larger structures present in the preparation. The intensity of this shoulder increased slowly upon repeated scanning. In one of the experiments the intensity of the shoulder increased from 5.6 to 36% of the total peak area after 25 cycles through the transition (Fig. 5B and insert). The dynamic change of the liquid crystalline into the gel state and the return must be responsible for this effect, for it appeared that incubations at constant temperature, chosen in, above or below the phase transition region (Figs. 5B, 5C and 5D), did not give a strong enhancement of the shoulder peak in the subsequent analyses. It is possible that variations in the vesicle volume as a consequence of changes in membrane area, due to the phase transition, cause osmotic forces that break up the continuous bilayer and create conditions favourable for fusion. This view is supported by the finding that cryoprotectors greatly enhance the rate of fusion upon passing the phase transition. In our differential scanning calorimetric analyses of vesicles prepared in 50 vol% ethyleneglycol a pattern completely comparable to that of liposomes was found (Fig. 3G). The hypothesis that vesicles prepared in 50 vol% ethyleneglycol fuse upon passing through the phase transition can also be deduced from the disappearance of the sharp signal seen by 31p NMR (Cullis, P.R., unpublished results). By the use of an Intracooler instead of liquid nitrogen as employed in earlier studies [1], the equilibration of the vesicle sample at 2°C, prior to the start of the differential scanning calorimetry scan, could carefully be controlled and any freezing effects prevented. To observe the effect of an ice-water transition in the system, a vesicle sample was cooled in order to induce such an ice-water transition prior to differential scanning calorimetric analyses. The results given

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Fig. 5. T h e r m o t r o p i c p r o p e r t i e s of s o n i c a t e d 14 : 0 / 1 4 : O - g l y c e r o p h o s p h o c h o l i n e v e s i c l e s u n d e r v a r i o u s c o n d i t i o n s , a, h e a t i n g scan t a k e n i m m e d i a t e l y a f t e r p r e p a r a t i o n ; b, h e a t i n g scan a f t e r 25 c y c l e s t h r o u g h t h e t r a n s i t i o n r e g i o n ( h e a t i n g r a t e 5 ° C ] m i n , c o o l i n g r a t e 4 0 ° C / m i n ; s c a n n i n g r a n g e 2---47°C; c, h e a t i n g scan of t h e v e s i c l e s a f t e r i n c u b a t i o n for t h e s a m e p e r i o d of t i m e as b at 35°C ( 2 6 5 m i n ) ; d, h e a t i n g scan of t h e v e s i c l e s a f t e r i n c u b a t i o n f o r t h e s a m e p e r i o d of t i m e as b at 4°C ( 2 6 5 rain); e, h e a t i n g scan of t h e v e s i c l e s a f t e r i n c u b a t i o n for 90 rain at 20°C. In the i n s e r t the i n t e n s i t y of t h e s h a r p s h o u l d e r r e l a t i v e t o t h e t o t a l p e a k area is p l o t t e d against t h e t i m e of i n c u b a t i o n , e, C y c l i n g t h r o u g h t h e t r a n s i t i o n region; J, i n c u b a t i o n at 4°C; ×, i n c u b a t i o n at 35°C.

in Figs. 3E and 3F shows a sharp peak at around 24°C with a AH of 6.9 kcal/ mol in agreement with observations of Suurkuusk et al. [2]. Electron microscopy on this sample (compare Fig. 2B) showed that under these conditions the vesicles had been fused to predominantly multlayered liposomes. Conventional quenching is not rapid enough to prevent the transition from the L~ to the P~' phase [19]. Therefore the multilayered liposomes display the typical band pattern. Acknowledgements We are indebted to Drs. J.M.H. Kremer and P.H. Wiersema for valuable discussions and for making the light scattering and the injection technique available to us. This study was carried out under the auspices of the Netherlands Foundation for Chemical Research (S.O.N.) and with financial aid from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). References 1 De K r u i j f f , B., Cullis, P.R. a n d R a d d a , G.K. ( 1 9 7 5 ) B i o c h e m . B i o p h y s . A c t a 4 0 6 , 6 -20 2 S u u r k u u s k , J., L e n t z , B.R., Baxenholz, Y., B i l t o n e n , R.L. a n d T h o m p s o n , T.E. ( 1 9 7 6 ) BiochcmlatLy 15, 1 3 9 3 - - 1 4 0 1

191 3 P a p a h a d j o p o u l o s , D., H u i , S., Vail, W.J. a n d P o s t e , G. ( 1 9 7 6 ) B i o c h i m . B i o p h y s . A c t a 4 4 8 , 2 4 5 - - 2 6 4 4 K a n t o r , H . L . , M a b r e y , S., P r e s t e g a r d , J . H . a n d S t u r t e v a n t , J . M . ( 1 9 7 7 ) B i o c h i m . Biophyso A c t a 4 6 6 , 402--410 5 S t u r t e v a n t , J . M . ( 1 9 7 4 ) A n n . R e v . B i o p h y s . B i o e n g . 3, 3 5 - - 5 1 6 V a n D e e n e n , L . L . M . a n d de H a a s , G . H . ( 1 9 6 4 ) A d v . L i p i d Res. 2, 1 6 8 - - 2 2 9 7 B a t z r i , S. a n d K o r n , E . D . ( 1 9 7 3 ) B i o c h i m . B i o p h y s . A c t a 2 9 8 , 1 0 1 5 - - 1 0 1 9 8 K r e m e r , J . M . H . , v a n d e r E s k e r , M . W . J . , P a t h m a m a n o h a r a n , C. a n d W i e r s e m a , P.H. ( 1 9 7 7 ) B i o c h e m i s t r y , 16, 3932--3935 9 V e r v e r g a e r t , P . H . J . T h . , E l b e r s , P . F . , L u i t i n g h , A . J . a n d v a n d c Berg, H . J . ( 1 9 7 2 ) C y t o b i o l o g y 6, 8 6 - 96 1 0 V a n D i j c k , P.W.M., V e r v e r g a e r t , P . H . J . T h . , Verldeij, A . J . , v a n D e e n e n , L . L . M . a n d de G i e r , J. ( 1 9 7 5 ) Biochim. Biophys. Acta 406,465--478 11 J a n i a k , M.J., S m a l l , D.M. a n d S h i p l e y , G . G . ( 1 9 7 6 ) B i o c h e m i s t r y 15, 4 5 7 5 - - 4 5 8 0 1 2 L a w a c z e k , P., K a i n o s k o , M., G i r a r d e t , J . L . a n d Chart, S.I. ( 1 9 7 5 ) N a t u r e 2 5 6 , 5 8 4 - - 5 8 6 1 3 Yi, P . N . a n d M a c D o n a l d , R . C . ( 1 9 7 3 ) C h e m . P h y s . L i p i d s 11, 1 1 4 - - 1 3 4 1 4 L u n a , E.J. a n d M c C o n n e l l ( 1 9 7 7 ) B i o c h i m . B i o p h y s . A c t a 4 6 6 , 3 8 1 - - 3 9 2 1 5 M e t c a l f e , J.C. ( 1 9 7 5 ) in F u n c t i o n a l L i n k a g e in B i o m o l e c u l a x S y s t e m s ( S c h m i t t , F . O . , S c h n e i d e r , D.M. a n d C r o t h e r s , D.M., e d s . L p p . 9 0 - - 1 0 1 , R a v e n Press, N e w Y o r k 16 M e n d e l s o h n , R., S u n d e r , S. a n d B e r n s t e i n , H . J . ( 1 9 7 6 ) B i o c h i m . B i o p h y s . A c t a 4 1 9 , 5 6 3 - - 5 6 9 17 C h a n , S.I., S h e e t z , M.P., S e i t e r , C . H . A . , H s u , M., L a u n , A. a n d Y a n , Y. ( 1 9 7 5 ) A n n . N . Y . A c a d . Sci. 222,499--522 1 8 M a r s h , D., W a t t s , A. a n d K n o w l e s , P . F . ( 1 9 7 7 ) B i o c h i m . B i o p h y s . A c t a 4 6 5 , 5 0 0 - - 5 1 4 19 V e r v e r g a e r t , P . H . J . T h . , V e r k l e y , A . J . , V e r h o e v e n , J . J . a n d E l b e r s , P . F . ( 1 9 7 3 ) B i o c h i m . B i o p h y s . Acta 311,651--654

Phase transitions in phospholipid model membranes of different curvature.

183 Biochimica et Biophysica Acta, 506 (1978) 183--191 © Elsevier/North-Holland Biomedical Press BBA 77908 PHASE T R A N S I T I O N S IN PHOSPHOLI...
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