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Proc. Nati. Acad. Sci. USA Vol. 86, pp. 5825-5829, August 1989 Biophysics

Effects of lipid packing on polymorphic phase behavior and membrane properties (phospholipid/hydration/bending energy/cholesterol/membrane proteins)

SEK-WEN HuI

AND

ARINDAM SEN

Department of Biophysics, Roswell Park Memorial Institute, Buffalo, NY 14263

Communicated by David Harker, May 5, 1989 (received for review August 9, 1988)

ABSTRACT The self assembly of phospholipid molecules in the bilayer form was considered in terms of equivalent molecular shapes representing intermolecular forces. The equivalent size of each phospholipid headgroup was approximated by the net atomic volume plus the volume of the associated water molecules, which was derived from water/ hydrocarbon partitioning experiments. The equivalent lengths ofunsaturated acyl chains were derived from the retention time data from chromatographic measurements. The spontaneous curvature of various phospholipid monolayers was calculated from their equivalent molecular shapes, and the energy required to flatten them to the bilayer plane was calculated, using the known bending modulus. With increasing bending energy, the mixtures showed increasing susceptibility to phospholipase A2, facilitated lipid tansfer rate by phospholipid exchange proteins, permeability to carboxyfluorescein, incorporation of human erythrocyte proteins, and calcium transport by CaATPase from sarcoplasmic reticulum in reconstituted vesicles. When the calculation was applied to known lipid compositions of nine cellular membranes, the protein/lipid ratio and phospholipid/cholesterol ratio were found to have a positive and a negative correlation, respectively, with the latent bending energy of the phospholipids. The energy expense in conforming to a bilayer phase may be an important physical parameter regarding the activity and the biogenesis of membranes.

chains, among others (3, 4). These forces are difficult to account for analytically; therefore the quantitative assessment of the energetics of bilayer-to-nonbilayer transition is a complex task. Based on molecular shape consideration alone, Isrealachvili (5) proposed a structural model for lipid packing. The shape of each lipid molecule was described by a packing factor. Alternatively, the packing free energy of each form of self assembly may be calculated from their geometric constraints (4); the extrapolation to an unconstraint assembly then gives the value of the spontaneous curvature of a monolayer (4, 6). Unfortunately the intrinsic curvature can be determined only from measurements performed on lipids in the HI, phase under given constraints. Since a very large proportion of lipids do not form HI, structures, the direct determination of the intrinsic curvature of these lipids is not always feasible. A scheme to estimate an equivalent lipid packing factor has recently been proposed (7). Based on this concept, we present here a general, semiquantitative method that can be applied to any lipid system to estimate the latent energy in their bilayer form from the chemical structure and their hydration characteristics. The latent energy is then shown to be a factor affecting membrane properties. In addition, it is found that the molecular mismatching in membrane lipids correlates positively with the amount of membrane proteins in most biological membranes. This may explain some aspects of the diversity of membrane lipid composition and the high content of nonbilayer lipids in some active membranes.

The regulated diversity in lipid composition of biological membranes is well recognized, but the need for such diversity is not fully understood. Apparently, the lipids in biological membranes do more than provide a passive barrier and a supporting matrix for membrane proteins. There is ample evidence that changes in lipid structure can influence the activity of membranes (1). The quest for maintaining a certain "fluidity" fails to explain the diversity of membrane lipid species. It is known that not all lipids found in biological membranes form bilayers when dispersed in water. In fact, a large portion of the membrane lipids do not form bilayers at physiological conditions (pH, calcium concentration, and temperature). These so-called "nonbilayer" lipids generally prefer high curvature structures such as inverted hexagonal (HI,), inverted cubic, and "lipid particles" when dispersed in water (1, 2). However, no such structures have ever been found in functioning biomembranes. It would thus seem that the ability of these lipid mixtures to form high curvature structures upon self assembly, rather than the inverted structures themselves, is needed for the proper functioning of biological membranes. The polymorphism or phase preference of any lipid is governed by the coherence force, which is the combined result of the exclusion volume, polarity, headgroup interactions, and van der Waals interactions between hydrocarbon

CALCULATION Equivalent Packing Factor. A phospholipid molecule is considered to be composed of two parts, the headgroup region and the acyl chains. We define an equivalent lipid packing factorf following ref. 5 to be: f = v/al,

[1]

where v and l are the volume and the length of the hydrocarbon chains, respectively, and a is the cross-sectional area of the equivalent headgroup (including the repulsive volume of hydration and other forces). The averaged packing factor Ffor a mixed lipid in a dispersion is then the weighted average of the equivalent packing factors of the lipids in the mixed system. F = Efi x Ni,

[2]

where Ni is the compositional fraction of the ith lipid in the mixed membrane. The value F = 1 indicates that the averaged cross section of the equivalent headgroup equals the averaged cross section of the chains, and the molecules can

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Abbreviations: [Pal,Ole]PtdCho, 1-palmitoyl-2-oleoyl phosphatidylcholine; [Lin2]PtdEth, 1,2-dilinoleoyl phosphatidylethanolamine; [Myr2]PtdCho, 1,2-dimyristoyl phosphatidylcholine.

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Proc. Natl. Acad. Sci. USA 86 (1989)

Biophysics: Hui and Sen

then be regarded as cylinders and tend to pack into a planar bilayer. F > 1 or F < 1 signifies that the averaged crosssectional area occupied by the headgroup is small or large in comparison to that of the chains. For lipids in the fluid or "liquid crystalline" state, which is the only case we consider here, these molecules tend to favor inverted (CII or HI,) phases or micellar phases, respectively. Otherwise neitherf nor F bears a simple geometric relationship to the molecular shape. Alternatively, the shape of the molecule may be approximated by a truncated cone (or an inverted truncated cone), with the headgroup cross section as its top section. A shape factor g may then be defined as g = A/a, where A is the bottom section of the cone. The value ofA, and therefore that of g, may be expressed in terms of a, v, and 1, making use of the geometry of the truncated cone. The weighted average shape factor G is defined by analogy to Eq. 2. The conditions G > 1 or G < 1 have the same indications as for F, but the g value has a geometric meaning. The cross-sectional area of the headgroup is calculated in the following manner. The van der Waals volume of the headgroup is calculated from the van der Waals bonded radii of the atoms in the headgroup approximating the atoms to spheres. The volume of water associated with the headgroup is estimated from partitioning the lipid between a water and a hexane phase and determining the water taken in the hexane phase by the lipid using 3H-labeled water (8). Care was taken to ensure that inverted micelles formed by this method attained the minimal radii so that the hydration was not overestimated. The hydration values thus obtained agreed with the values derived by other physical methods (9-12). The total headgroup volume is the sum of the van der Waals volume of the headgroup and the volume of the associated water. The cross-sectional area of the headgroup, a, is determined from the total headgroup volume and approximating the headgroup to a sphere. A cylindrical or a hemispherical model gives, respectively, 20%o or 58% higher estimate of the cross section than a spherical one. The cross-sectional area of the headgroup determined from a spherical model is closest to the values determined by x-ray diffraction measurements (9, 10, 13). The equivalent chain lengths l are based on the known lengths of trans acyl chains and the equivalent carbon number for those containing cis-double bonds as measured by retention time in chromatography (14). The volumes of the acyl chains are calculated from known densities. The measured values of a and A for cholesterol are used in our calculations (15). All quantities except the van der Waals volume of the head group atoms are experimentally determined. Spontaneous Curvature. The spontaneous curvature So of a mixed lipid monolayer is defined as the curvature of the self assembly of lipids at the least energy (the most tightly packed) configuration, without extrinsic constraint (4, 16). The geometry is depicted in Fig. 1. If ro is the isotropic radius of curvature of the hydrophilic surface,

[3] So = 1/(ro + h/2), where h = I + \/7r is the thickness of the monolayer. ro is given by either F or G through geometric relations: ro = h(3 +

\/T2IW-)/6(F

FIG. 1. Schematic drawing of a spontaneously curved monolayer of cone-shaped phospholipids.

structure. For planar bilayers, ro is infinity, and both G = 1 and F = 1. F < 1/4 or G < 3/4 gives the limit of the size of the micelle that can be described by the geometric model. F > 1 indicates inverted micelles or tubes. This model is appropriate only for monolayers with small perturbationi.e., F - 1. For F >> 1 or F