Complementary molecular shapes and additivity of the packing

Transcription

1 Proc. Natl. Acad. Sci. USA VO1. 88, pp , January 1991 Biophysics Complementary molecular shapes and additivity of the packing parameter of lipids (chain length/phase preference/theory) V. V. KUMAR The Hormel Institute, University of Minnesota, th Avenue NE, Austin, MN Communicated by Ralph T. Holman, October 15, 1990 (received for review March 19, 1990) ABSTRACT Physical dimensions of a membrane component influence its phase preference upon hydration. A dimensionless packing parameter, S, given by S = V/al, where V is the hydrocarbon volume, a is the area of the head group, and I is the critical length of the hydrocarbon chain, is useful in determining the phase preference of a lipid, and the value of S usually lies between 0.5 and 1 for bilayers. Here, the value of S is calculated for phosphatidylcholine (PC) and lysophosphatidylcholine (lysopc) as a function of chain length, and it is shown that diacylpc having an S value of <0.74 does not form bilayers. For example, diacylpc, up to a chain length of eight carbon atoms, forms only micelles, whereas higher homologs with S > 0.74 form bilayers. It is also shown that when lipid molecules having complementary shapes associate, the value of S becomes additive. Using the additivity of S, a number of experimental results for lipid mixtures can be explained. For example, lysopc and cholesterol form lamellar structures between 45 and "40 mol% cholesterol, and the additive value of S for this region is between 0.74 and 1. Similarly, the additivity of S shows that the maximum amount of cholesterol that can be incorporated into PC bilayers is 50 mol%, in agreement with experimental studies. Molecular shape is an important consideration in membrane modeling. Based on the physical dimensions of a membrane component, its phase presence upon hydration and its location in the membrane can often be predicted. Taking into account interaction free energies, molecular geometry, and entropy, theoreticians have developed a dimensionless packing parameter, S, that is useful in determining the size and shape of lipid aggregates. S is given by S = V/al, where V is the hydrocarbon volume, a is the area of head group, and 1 is the critical length of the hydrocarbon chain (1-3). a, V, and I are all estimable or measurable (4), and the value of S can be calculated. The value of S determines the aggregate formed by lipids or any amphiphiles upon hydration. It has been shown that lipids aggregate to form spherical micelles (S < 1/3), nonspherical (cylindrical) micelles (1/3 < S < 1/2), bilayers (1/2 < S < 1), and reverse micelles or hexagonal (HI,) phases (S > 1). However, theoreticians caution that the above predicted limits set on the values of S are relatively insensitive to the exact values of V and a but are strongly dependent upon the choice of 1 (5). The packing parameter S has successfully predicted that single-chain lipids like lysophosphatidylcholine (lysopc) (S = 1/3 to 1/2) having an inverted cone or wedge shape form micelles, double-chain lipids with large head group areas and fluid chains like phosphatidylcholines (PCs) (S = 1/2 to 1) having a cylindrical shape form bilayers, and, finally, cholesterol (Chol) and some double-chain lipids with small head group areas like unsaturated phosphatidylethanolamines The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C solely to indicate this fact. (PEs) (S > 1) having a truncated cone shape adopt hexagonal HI, phases upon hydration (1-3). Cylindrical and wedge-shaped molecules have been shown to be essential for spontaneous vesiculation (6) as well as bilayer stabilization (7, 8). It has also been shown experimentally that molecules having complementary molecular shapes can form bilayer structures. Inverted cone (wedge)- shaped lysopc and cone-shaped Chol or unsaturated PE can interact stoichiometrically to form bilayer structures (9-12). lysopc and fatty acids in equimolar proportion were shown to form bilayer structures and, in this case, fatty acid complexes with lysopc to produce PC-type molecules (13). In all of the above examples, the resulting complexes were assumed to be cylindrical in shape, leading to bilayerformation. Although it is not explicitly shown above, it is implied that the value of S is additive in producing a cylindrical complex from a mixture of cone-shaped and inverted cone-shaped molecules. The present paper supports the hypothesis of the additivity of S values when two or more lipids of different shapes are present in a model system. It was concluded that the additivity rule applies, and from this a number of experimental observations can be explained. The additivity of S values was tested on a number of binary and ternary lipid systems, and the results of these calculations and their implications on experimental results are presented. RESULTS Selection of a, V, and I for a given lipid is of paramount importance in the calculations presented. The head group area chosen was 71.7 A2 for PC and lysopc, 42 A2 for PE, and 19 A2 for Chol (5, 14). The value selected for PC is in agreement with the 71 A2 value determined for PCs with saturated acyl chains (14). The hydrocarbon volume and the length chosen for Chol are 400 A3 and A, respectively (5). Correct estimation of V for a series of PCs can be obtained from densities and partial specific volumes. Nagle and Wilkinson (15), Laggner and Stabinger (16), and Melchoir et al. (17) measured the densities and partial specific volumes for a number of PCs, and Knoll (18) measured the values for deuterated PCs. Small (19) used the dilatometric data of Nagle and Wilkinson (15) to calculate the molecular volumes of PCs as a function of chain length for the L<, and Ph phases and also at a constant temperature of 55 C. The molecular volumes were generally lower in the gel state and at 55 C than those in the liquid crystalline state, and no appreciable differences in the volumes were detected between sonicated and unsonicated forms of PCs (19). The volume per -CH2 Abbreviations: PC, phosphatidylcholine; lysopc, lysophosphatidylcholine; PE, phosphatidylethanolamine; Chol, cholesterol; S, packing parameter; V, volume of hydrocarbon chain; a, area of head group; 1, length of hydrocarbon chain; cmc, critical micelle concentration. 444

2 Biophysics: Kumar group calculated ranged from 27 A3 at 550C and also in the P~ state to 30.9 A3 in the La state. The volume of 27 A3 per -CH2 group at 550C is very low compared to the volume in alkanes, fatty alcohols, and fatty acids in the liquid state. Small (19) indicated that at 550C all of the lipids are in a single phase with an extra degree offreedom in the system. Short-chain PCs are more expanded than long-chain PCs, giving a low increase in volume for each -CH2 group increment. However, at the phase transition temperature, this additional degree of freedom is eliminated (19). It is therefore reasonable to assume a value of 30.9 A3 per -CH2 group, and using this value the hydrocarbon volumes for PCs as a function of chain length are calculated. The S values calculated using this value of molecular volume explain a number of experimental observations (see Discussion). The value of I is calculated using the equation I = n', where n' is the number of carbon atoms of the hydrocarbon chain that are embedded in the hydrocarbon core and is usually less than nc, the total number of carbon atoms in the hydrocarbon chain (4). The value of 1 is 80% of the fully extended chain length. Hence, the S values reported are calculated using 80% of the extended chain length. As discussed above, V and I can be calculated for PC and lysopc with different hydrocarbon chain lengths. These values of Vand 1, along with the values ofa mentioned earlier, are utilized to calculate S for PC and lysopc as a function of chain length. In Fig. 1, S is plotted as a function of chain length for PC and lysopc having saturated acyl chains. It can be seen from Fig. 1 that the S value increases rapidly for both PC and lysopc having short chain lengths, whereas it remains practically constant for lipids with long chain lengths. For PC, the value of S remains constant from about 10 carbon atoms in each of the fatty acyl chains. Experimental evidence indicates that PC molecules having 8 or less carbon atoms in each of the acyl chains form only micelles (20, 21), whereas higher homologs form bilayer structures (22). Extrapolation of the straight-line region of the curve for PC in Fig. 1 (circles) from a carbon chain length of 10 to S results in an S value of Therefore, the value of S for diacytpc should be for bilayer structures to form. For lysopc, the value ofs remains constant from about 8 carbon atoms (see Fig. 1, squares). Here, also, experimental evidence indicates that lysopc molecules with 8 or more carbon atoms in the fatty acyl chain form micelles, whereas lower homologs do not because of their very high critical micelle concentration (cmc) values Proc. Natl. Acad. Sci. USA 88 (1991) 445 (V.V.K. and W. J. Baumann, unpublished observations). Extrapolation of the straight-line region of the curve for lysopc in Fig. 1 (squares) from a carbon length of 8 to S gives an S value of0.34. Therefore, the value ofs for lysopc should be.0.34 for micelle formation. In fact, the value of S for C4- and C2-lysoPC lies below 0.34, indicating that these lysophospholipids do not form micelles. It is our experience that C6-lysoPC did not form micelles even at very high concentrations (-0.7 M) (V.V.K. and W. J. Baumann, unpublished observations). In this case, the solubility limit of the lipid precedes the cmc and, hence, no micelle formation occurs. The results presented in Fig. 1 indicate that an S value is necessary for micelle formation by saturated lysopc, whereas an S value.0.74 is essential for bilayer formation by saturated diacylpcs. A critical test for the limits proposed for S values is to calculate the values of S for different lipid mixtures and compare the bilayer limits set by the value of S with experimentally known bilayer limits. For example, in a PC/Chol system the two lipids form bilayer structures only up to 50 mol% Chol (23). Similarly, lysopc and Chol form bilayer structures only when the mol% of Chol is between 45 and 80 (11, 24, 25). In Fig. 2, the value of S is plotted for C16-lysoPC and dicj6pc as a function of mol% Chol. S values are calculated assuming the additivity of S. For example, at 50 mol% Chol in a C16-lysoPC/Chol system the value of S would be [0.5 x (S value for lysopc)] + [0.5 x 1.21 (S value for Chol)] = Similarly, S is calculated for other lysopc/chol and dic16pc/chol mixtures. It can be seen from Fig. 2 that for the dic16pc/chol system, the value of S begins at at 0 mol% Chol and reaches 1 at 50 mol% Chol. It was shown that dic16pc and Chol form lamellar structures up to 50 mol% Chol and any excess Chol forms a separate crystalline Chol phase (23). The theoretical value of S presented in Fig. 2 as well as the experimental evidence indicates that dic16pc/chol mixtures remain in the bilayer state up to 50 mol% Chol. Finally, Chol is known to exhibit a "condensing effect" in saturated PC/Chol systems. This condensing would have little or no effect on the calculations presented here, and an excellent theoretical analysis of this was reported earlier (26). It is also shown in Fig. 2 that the value of S increases linearly with increasing mol% Chol for the C16-lysoPC/Chol system. The value ofs remains in the lamellar phase between 45 and =80 mol% Chol. It was observed by freeze-fracture electron microscopy (27) and x-ray diffraction (25) that lysopc/chol mixtures form lamellar structures with F F 0.4 F F LE-31 E3 LE-3 w Chain length FIG. 1. Changes in calculated S values as a function of chain length for PC (o) and IysoPC (o) mol% Chol FIG. 2. S values for PC (o) and lysopc (o) as a function of mol% Chol. S value for mixtures is calculated as described in Results.

3 446 Biophysics: Kumar mol% Chol. NMR spectroscopic evidence indicates that lysopc and Chol in equimolar proportion, as well as up to 60 mol% Chol, upon sonication form stable vesicles (9, 10, 28). Thus, the theoretical values of S as well as the experimental data support the fact that C16-lysoPC/Chol produces bilayer structures only when Chol is present at mol%. In Fig. 3, changes in the additive S are plotted for PC/PE (circles) and lysopc/pe (squares) systems with increasing mol% of PE. It is shown in Fig. 3 that the lysopc/pe mixture remains in the bilayer state from 35 to 60 mol% PE. It was shown by 31P NMR that lysopc and PE form bilayer structures up to 50 mol% PE due to their complementary molecular shapes (12). In a similar fashion, it was shown by 31p NMR that PE and PC remain in the bilayer state up to 50 mol% PE (29). The results shown in Fig. 3 (circles) are in agreement with these experimental results. In Fig. 4, changes in the S values for the dic16pc/c16- lysopc system as a function of lysopc mol% are presented. It is shown in Fig. 4 that the value of S falls below 0.74 when the mol% of lysopc is between 15 and 20, indicating that dic16pc and lysopc do not form stable lamellar structures when the mol% of lysopc exceeds 20. It was shown experimentally that the maximum amount of lysopc that can be incorporated into dic16pc small unilamellar vesicles (SUV) without the loss of ionic permeability barrier is about 21.8 mol% (30). Similarly, the amount of lysopc that was shown to be incorporated into dic16pc multilamellar vesicles (MLV) was 30 mol% (11). Although there is some variation between the theoretical predictions and the experimental observations, it should be noted that the amount of lysopc that can be incorporated into PC vesicles (both MLV and SUV) varies over a considerable range depending upon the nature of PC and lysopc (31). The S value calculated for the system dic6pc and C6-lysoPC as a function of mol% of C6-lysoPC always lies below 0.74, indicating that these two lipids (in any proportion) do not form bilayers. 31P NMR spectroscopy and freeze-fracture electron microscopy failed to reveal the presence of lamellar structures in these mixtures (V.V.K. and W. J. Baumann, unpublished observations). Similarly, the additive packing parameter for the system dic6pc/c16- lysopc is always below 0.74, indicating that these two lipids in any proportion do not form bilayers. 31P NMR spectroscopy and freeze-fracture electron microscopy showed the presence of micellar structures, consistent with the predictions presented here. The additive S value for a 3:1 dicj6pc/ lysopc mixture in which the chain length of lysopc varied increases as the chain length of lysopc increases and finally [ Proc. Natl. Acad. Sci. USA 88 (1991) I I- u mol% lysopc FIG. 4. S value for dic16pc/c16-lysopc as a function of mol% C16-lysoPC. reaches a value between 0.75 and 0.8 when the chain length of lysopc is 16 (data not shown). From past experience, dic16pc formed stable bilayers only when the chain length of lysopc was 14 or higher (30). The slight disagreement between the experimental values and theoretical predictions in all of the examples discussed above could be due to the simplicity in calculating S. A more rigorous treatment of the additivity data, taking into account the effect of curvature, might result in a better agreement. Finally, it should be appreciated that simple additivity leads to a better understanding of which lipid mixtures form bilayers. Having established the validity of limits proposed for S for binary lipid mixtures, these limits were applied to ternary lipid mixtures. In Fig. 5 the changes in S for the ternary system of PC/lysoPC/Chol are presented. The mol% of PC decreased from 100 to 0 from left to right with increasing the mol fraction oflysopc and Chol in equimolar proportion (Fig. 5, circles). A similar explanation can be given for ternary systems in which Chol (Fig. 5, triangles) and lysopc (Fig. 5, squares) mol% decreased from 100 to 0 from left to right. Considering the PC system containing various mol fractions '5 -o io mol% PE FIG. 3. S values for PC/PE (o) and lysopc/pe (o) systems as a function of mol% PE. A1 _0 I. A I mol fraction 1.0 FIG. 5. S value for the ternary system containing PC, lysopc, and Chol. o, The mol% of PC decreases from 100 to 0 from left to right. The mol fraction of lysopc and Chol increases from left to right in equimolar proportion. o, lysopc/pc/chol system. A, Chol/PC/ lysopc system.

4 Biophysics: Kumar of lysopc and Chol (Fig. 5, circles), the value of S is always -0.8, which indicates that the system remains in the bilayer state irrespective of the mol fraction of lysopc and Chol as long as lysopc and Chol are in equimolar proportion. 31P NMR spectroscopy and barrier property measurements were utilized to show that PC remains in the bilayer state when equimolar proportions of lysopc and Chol are present in the system (11, 26, 32). For the lysopc system containing equimolar amounts of PC and Chol (Fig. 5, squares), the value of S remains below 0.74 until the mol% of lysopc reaches 40. The system then remains in the bilayer state even with no lysopc but with equimolar PC and Chol. The same resulti.e., PC and Chol up to 50 mol% Chol form bilayer structures-was also observed in Fig. 2. DISCUSSION The results presented in Figs. 1-5 indicate two important phenomena: (i) that the value of S should be for bilayer formation by saturated diacylpcs and (ii) that S is additive when lipid mixtures are present. The results presented in Fig. 1 indicate that a minimum S value of 0.74 is necessary for diacylpcs to form bilayer structures. Such an S value is possible only for diacylpcs having 10 or more carbon atoms in each of the fatty acyl chains. Experimental evidence is strongly supportive, as it has been shown that saturated diacylpcs having 8 or less carbon atoms in each of the fatty acyl chains form only micelles, whereas higher homologs form bilayers (20-22). It is interesting to point out that a similar phenomenon was observed for diacylpcs in the plots of changes in transition temperature (ATm), enthalpy (AH), entropy (AS), and volume (AV) as a function of chain length. In these plots the values of ATm, AH, AS, and AV increase more steeply for lower homologs compared to higher homologs, and extrapolation of these curves to zero Al and zero AS resulted in a chain length of 11 carbon atoms (19). Also, a transition temperature of -8.5 C was recorded for dicj0pc (33), and no data are available for dic8pc showing a chain transition. These findings indicate that a minimum of 10 carbon atoms in each of the fatty acyl chains are necessary for bilayer formation, and a similar conclusion can be drawn from the S value versus the chain length curve shown in Fig. 1. Thus, S values, changes in ATm, AH, AS, and AV, as well as experimental evidence, indicate that bilayer formation for diacylpcs is possible only when 10 or more carbon atoms are present in each of the acyl chains. The results presented in Fig. 1 (squares) also indicate that the value of S should be for lysopc to form micelles. Such an S value is possible only for lysopcs with 8 or more carbon atoms in the fatty acyl chain. Experimental evidence is strongly supportive in that C6-lysoPC and lower homologs do not form micelles because their cmc values are very high and the solubility limit of the lipid precedes the cmc (V.V.K. and W. J. Baumann, unpublished observations). It was shown earlier that C16-, C18-, and C20-lysoPC form interdigitated bilayer structures at temperatures below their bilayermicellar transition temperature (11, 34). However, the results presented in Fig. 1 (squares) indicate that these lysopcs form only micelles. This is due to the fact that the hydrocarbon volumes and, hence, S values are calculated above the transition temperature. The additive S value for dic16pc/chol mixtures, shown in Fig. 2, lies below 1 up to equimolar amounts of Chol. Experimental evidence also indicates that PC/Chol mixtures remain in the bilayer state up to 50 mol% Chol and excess Chol forms a separate crystalline phase (23). Also shown in Fig. 2 (squares) is that the additive S for lysopc/chol reaches 0.74 when the mol% of Chol is 45 and remains in the bilayer state up to -80 mol% Chol. There is ample evidence in the Proc. Natl. Acad. Sci. USA 88 (1991) 447 literature to indicate that lysopc and Chol form lamellar structures in equimolar proportions. Dervichian (35) first observed that "lysolecithin associated with cholesterol in equimolar proportions swells and gives myelinic figures as does lecithin alone." It was observed by freeze-fracture electron microscopy (27) and x-ray diffraction (25) that lysopc forms lamellar structures with mol% Chol. The formation of lamellar structures by equimolar lysopc and Chol was confirmed by differential scanning calorimetry (24), x-ray diffraction (25) and barrier property measurements (11, 32), and NMR spectroscopy (9, 10, 28). Experimental data and theoretical predictions are in agreement with each other in regard to the amount of Chol necessary for bilayer formation by lysopc. In a similar fashion, the phase adopted by PC/PE, lysopc/pe, dic16pc/c16-lysopc systems (Figs. 3 and 4) assuming additivity are in agreement with experimental r'sults as discussed earlier. A very important and interesting phenomena that emerged from the additivity of packing parameter values for lipid mixtures is a plausible model in better understanding lysopc/ Chol antagonism. The results presented in Fig. 5 clearly indicate that PC remains in the bilayer phase provided lysopc and Chol are in equimolar proportion. When lysopc is incorporated into PC bilayers it induces structural changes. These changes usually result in increased membrane permeability (36), cause membrane fusion (37), and eventually lead to lamellar disruption (38). In contrast, Chol in phospholipid lamellae behaves as if it were a truncated cone (5), and its incorporation into PC bilayers reduces membrane permeability, broadens the gel to liquid-crystalline phase transition, and decreases average molecular surface areas (39-42). It is not only that lysopc and Chol affect phospholipid bilayers quite differently, but when both are present in similar proportions, they appear to counteract each other's effect (11, 24, 32, 43). Although such a large body of experimental evidence exists for lysopc/chol antagonism, results presented in Fig. 5 offer a likely model for understanding lysopc/chol antagonism. In conclusion, the calculations shown in this paper establish that the value of S is additive when lipids with complementary molecular shapes associate to form bilayer structures, and these bilayer structures form only when the values of S lie between 0.74 and 1. The agreement between the calculated S values for the lipid mixtures to form bilayers and the experimental data is quite surprising given the simplicity of S. The results presented in this paper show that S is additive, although it was recently suggested that it is difficult to see how V/al can be applied to lipid mixtures (44). It should be noted that in addition to the Israelachvili (1-3) model to explain the phase behavior of hydrated lipids, another interesting theory called intrinsic radius of curvature was also advocated to explain the presence of bilayer and nonbilayer lipids in biological membranes (45, 46). However, it was recently suggested that the determination of intrinsic radius of curvature of bilayer lipids is not always possible (47). Bilayer structure of membranes is the most popular, and membrane permeability is the only major, functional role of lipids which may be regarded as firmly established. If so, a simple unsaturated PC species would easily satisfy such a demand. However, a simple biomembrane such as that of erythrocytes contains well over 100 different lipid species with diverse molecular shapes. In essence, membrane integrity is maintained by a delicate balance of lipids of different shapes. These different shapes may complement each other and maintain a bilayer structure although neither of two components can form bilayers by itself (Fig. 5). The additivity of S proposed here should be useful in predicting which membrane components complement their shapes and form (or maintain) bilayer structures.

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