Lipid Mesophases

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A. Aggregation of Lipids in Aqueous Solutions

Single-molecule solutions of biological lipids exist only over a negligible range of concentrations; virtually all interesting lipid properties are those of aggregate mesophases such as bilayers and micelles. Lipid molecules cluster into ordered structures to maximize hydrophilic and minimize hydrophobic interactions (72,73). These interactions include negative free energy contribution from the solvation of polar heads and van der Waals in teractions of hydrocarbon chains, competing with positive contributions such as steric, hydration, and electrostatic repulsions between polar heads. The ''hydrophobic effect,'' which causes segregation of polar and nonpolar groups, is said to be driven by the increase of the entropy of the surrounding medium.

Intrinsic to the identity of surfactant lipids is the tension between water-soluble polar groups and lipid-soluble hydrocarbon chains. There is no surprise then that the amount of water available to an amphiphile is a parameter pertinent to its modes of packing and to its ability to incorporate foreign bodies.

These interactions therefore force lipid molecules to self-assemble into different ordered microscopic structures, such as bilayers, micelles (spherical, ellipsoidal, rodlike, or disklike), which can, especially at higher concentrations, pack into macroscopically ordered phases, such as lamellar, hexagonal, inverted hexagonal, and cubic. The morphology of these macroscopic phases changes with the balance between attractive van der Waals and ion correlation forces vs. electrostatic, steric, hydration, and undulation repulsion (74).

B. The Lipid Bilayer

The workhorse of all lipid aggregates is the bilayer (Fig. 17) (73). This sandwich of two monolayers, with nonpolar hydrocarbon chains tucked in toward each other and polar groups facing water solution, is only about 20 to 30 A thick. Yet it has the physical resilience and the electrical resistance to form the plasma membrane that divides ''in'' from ''out'' in all biological cells. Its mechanical properties have been measured in terms of bending and stretching moduli. These strengths together with measured interactions between bilayers in multi-lamellar stacks have taught us to think quantitatively about the ways in which bilayers are formed and maintain their remarkable stability.

With some lipids, such as double-chain phospholipids, when there is the need to encompass hydrocarbon components voluminous compared with the size of polar groups, the small surface-to-volume ratio of spheres, ellipsoids, or even cylinders cannot suffice even at extreme dilution. Bilayers in this case are the aggregate form of choice. These may occur as single ''unilamellar'' vesicles, as onionlike multilayer vesicles, or multilamellar phases of indefinite extent. In vivo, bi-layer-forming phospholipids create the flexible but tightly sealed plasma-membrane matrix that defines the inside from the outside of a cell. In vitro, multilayers are often chosen as a matrix of choice for the incorporation of polymers. Specifically, there are tight associations between positively charged lipids that merge with negatively charged DNA in a variety of forms (see below).

The organization of lipid molecules in the bilayer itself can vary (73). At low enough temperatures or dry enough conditions the lipid tails are frozen in an all-trans conformation that minimizes the energy of molecular bonds in the alkyl tails of the lipids. Also, the positions of the lipid heads along the surface of the bilayer are frozen in 2-dimensional positional order, making the overall conformation of the lipids in

Figure 17 The lipid bilayer. A lipid molecule has a hydrophilic and a hydrophobic part (here shown is the phosphatidylserine molecule that has a charged headgroup). At high-enough densities, lipid molecules assemble into a lipid bilayer. Together with membrane proteins as its most important component the lipid bilayer is the underlying structural component of biological membranes. The degree of order of the lipids in a bilayer depends drastically on temperature and goes through a sequence of phases (see main text): crystalline, gel, and fluid, depicted in the middle drawing. The box at bottom gives sample values of bilayer bending rigidity and area compressibility for some biologically relevant lipids and one well-studied cell membrane. See the color insert for a color version of this figure.

Figure 17 The lipid bilayer. A lipid molecule has a hydrophilic and a hydrophobic part (here shown is the phosphatidylserine molecule that has a charged headgroup). At high-enough densities, lipid molecules assemble into a lipid bilayer. Together with membrane proteins as its most important component the lipid bilayer is the underlying structural component of biological membranes. The degree of order of the lipids in a bilayer depends drastically on temperature and goes through a sequence of phases (see main text): crystalline, gel, and fluid, depicted in the middle drawing. The box at bottom gives sample values of bilayer bending rigidity and area compressibility for some biologically relevant lipids and one well-studied cell membrane. See the color insert for a color version of this figure.

the bilayer crystal (LC). The chains can either be oriented perpendicular to the bilayer surface (Lp and Lp) or be tilted (crystalline phase LC or ripple phase Pp). Such a crystalline bilayer cannot exist by itself but assembles with others to make a real 3-dimensional crystal.

Upon heating, various rearrangements in the 2-dimensional crystalline bilayers occur, first the positional order of the head-groups melts leading to a loss of 2-dimensional order (Lp) and tilt (Lp), then, at the gel-liquid crystal phase transition the untilted or rippled (Pp phase) bilayer changes into a bilayer membrane with disordered polar heads in 2 dimensions and conformationaly frozen hydrocarbon chains, allowing them to spin around the long axes of the molecules, the so-called La phase. At still higher temperatures, the thermal disorder finally also destroys the ordered configuration of the alkyl chains, leading to a fluidlike bilayer phase. The fluid bilayer phase creates the fundamental matrix that according to the fluid mosaic model (72) contains different other ingredients of biological membranes (e.g., membrane proteins, channels, etc.).

Not only bilayers in multilamellar arrays but also liposome bilayers can undergo such phase transitions; electron microscopy has revealed fluid phase, rippled, and crystalline phase in which spherical liposomes transform into polyhedra due to very high values of bending elasticity of crystallized bilayers (75).

The fluid phase of the lipid bilayer is highly flexible. This flexibility makes it prone to pronounced thermal fluctuations, resulting in large excursions away from a planar shape. This flexibility of the bilayer is essential for understanding the zoo of equilibrium shapes that can arise in closed bilayer (vesicles) systems (76). Also, just as in the case of flexible DNA, it eventually leads to configurational entropic interactions between bilayers that have been crammed together (41). Bilayers and linear polyelectrolytes thus share a substantial amount of fundamentally similar physics that allows us to analyze their behavior in the same framework.

C. Lipid Polymorphism

Low temperature phases (77) are normally lamellar with frozen hydrocarbon chains tilted (crystalline phase LC or ripple phase Pp) or nontilted (Lp and Lp' form three-, two-, or one-D crystalline or gel phases) with respect to the plane of the lipid bilayers. Terminology from thermotropic liquid crystals phenomenology (50) can be used efficiently in this context: these phases are smectic, and SmA describes 2-dimensional fluid with no tilt while a variety of SmC phases with various indices encompass tilted phases with various degrees of 2-dimensional order. Upon melting, liquid crystalline phases with 1- (lamellar La), 2- (hexagonal II), or 3-dimensional (cubic) positional order can form.

The most frequently formed phases are micellar, lamellar, and hexagonal (Fig. 14). Normal hexagonal phase consists of long cylindrical micelles ordered in a hexagonal array, while in the inverse hexagonal II (HII) phase water channels of inverse micelles are packed hexagonally with lipid tails filling the interstices. In excess water, such arrays are coated by a lipid monolayer. The morphology of these phases can be maintained upon their (mechanical) dispersal into colloidal dispersions. Despite that energy has to be used to generate dispersed mesophases relatively stable colloidal dispersions of particles with lamellar, hexagonal, or cubic symmetry can be formed.

Many phospholipids found in lamellar cell membranes, after extraction, purification, and resuspension, prefer an inverted hexagonal geometry (Fig. 18) (77). Under excess-water conditions different lipids will assume different most-favored spontaneous radii for the water cylinder of this inverted phase (78). An immediate implication is that different lipids are strained to different degrees when forced into lamellar pack-

Figure 18 Different lipids are strained to different degrees when forced into lamellar packing. Relaxation of this strain contributes to the conditions for lamellar-to-inverted hexagonal phase transitions that depend on temperature, hydration, and salt concentration (for charged lipids). See the color insert for a color version of this figure.

Figure 18 Different lipids are strained to different degrees when forced into lamellar packing. Relaxation of this strain contributes to the conditions for lamellar-to-inverted hexagonal phase transitions that depend on temperature, hydration, and salt concentration (for charged lipids). See the color insert for a color version of this figure.

ing. There are lamellar-inverted hexagonal phase transitions that occur with varied temperature, hydration, and salt concentration (for charged lipids) that form in order to alleviate this strain (see Fig. 18).

In the presence of an immiscible organic phase emulsion, droplets can assemble (79). In regions of phase diagram that are rich in water, oil-in-water emulsions and microemulsions (c > 0) can be formed, while in oil-rich regions these spherical particles have negative curvature and are therefore water-in-oil emulsions. The intermediate phase between the two is a bicontinuous emulsion that has zero average curvature and an anomalously low value of the surface tension (usually brought about the use of different cosurfactants) between the two immiscible components. Only microemulsions can form spontaneously (analogously to micelle formation) while for the formation of a homogeneous emulsion some energy has to be dissipated into the system.

The detailed structure of these phases as well as the size and shape of colloidal particles are probably dominated by:

• The average molecular geometry of lipid molecules

• Their aqueous solubility and effective charge

• Weaker interactions such as intra- and intermolecular hydrogen bonds

• Stereoisomerism as well as interactions within the medium

All depend on the temperature, lipid concentration, and electrostatic and van der Waals interactions with the solvent and solutes. With charged lipids, counterions, especially anions, may also be important. Ionotropic transitions have been observed with negatively charged phospholipids in the presence of metal ions leading to aggregation and fusion (80). In ca-tionic amphiphiles, it was shown that simple exchange of counterions can induce micelle-vesicle transition. Lipid polymorphism is very rich and even single-component lipid systems can form a variety of other phases, including ribbonlike phases, coexisting regions and various stacks of micelles of different shapes.

D. Forces in Multilamellar Bilayer Arrays

Except for differences in dimensionality, forces between bi-layers are remarkably similar to those between DNA. At very great separations between lamellae, the sheetlike structures flex and ''crumple'' because of (thermal) Brownian motion (41). Just as an isolated flexible linear polymer can escape from its 1 linear dimension into the 3 dimensions of the volume in which it is bathed, so can 2-dimensional flexible sheets. In the most dilute solution, biological phospholipids will typically form huge floppy closed vesicles; these vesicles enjoy flexibility while satisfying the need to keep all greasy nonpolar chains comfortably covered by polar groups rather than exposed at open edges. For this reason, in very dilute solution, the interactions between phospholipid bilayers are usually space wars of collision and volume occupation. This steric competition is always seen for neutral lipids; it is not always true for charged lipids (74).

Especially in the absence of any added salt, planar surfaces emit far-ranging electrostatic fields (27) that couple to thermally excited elastic excursions to create very long-range repulsion (44,83). As with DNA, this repulsion is a mixture of direct electrostatic forces and soft collisions mediated by electrostatic forces rather than by actual bilayer contact. In some cases electrostatic repulsion is strong enough to snuff out bilayer bending when bilayers form ordered arrays with periodicities as high as hundreds of A (82).

Almost always bilayers align into well-formed stacks when their concentration approaches ~50 to 60 weight percent and their separation is brought down to a few tens of A. In this region charged layers are quite orderly with little lamellar undulation. In fact, bilayers of many neutral phospholipids often spontaneously fall out of dilute suspension to form arrays with bilayer separations between 20 and 30 A. These spontaneous spacings are believed to reflect a balance between van der Waals attraction and undulation-enhanced hydration repulsion (74). One way to test for the presence of van der Waals forces has been to add solutes such as ethylene glycol, glucose, or sucrose to the bathing solutions. It is possible then to correlate the changes in spacing with changes in van der Waals forces due to the changes in dielectric susceptibility as described above (83). More convincing, there have been direct measurements of the work to pull apart bilayers that sit at spontaneously assumed spacings. This work of separation is of the magnitude expected for van der Waals attraction. (84).

Similar to DNA, multilayers of charged or neutral lipids subjected to strong osmotic stress reveal exponential variation in osmotic pressure vs. bilayer separation (74). Typically at separations between dry ''contact'' and 20 A, exponential decay lengths are 2 to 3 A in distilled water or in salt solution, whether phospholipids are charged or neutral. Lipid bilayer repulsion in this range is believed to be due to the work of polar group dehydration sometimes enhanced by lamellar collisions from thermal agitation (85). Normalized per area of interacting surface the strength of hydration force acting in lamellar lipid arrays and DNA arrays is directly comparable.

Given excess water, neutral lipids will usually find the above-mentioned separation of 20 to 30 A at which this hydration repulsion is balanced by van der Waals attraction. Charged lipids, unless placed in solutions of high salt concentration, will swell to take up indefinitely high amounts of water. Stiff charged bilayers will repel with exponentially varying electrostatic double layer interactions, but most charged bilayers will undulate at separations where direct electrostatic repulsion has weakened. In that case, similar to what has been described for DNA, electrostatic repulsion is enhanced by thermal undulations (86).

E. Equation of State of Lipid Mesophases

Lipid polymorphism shows much less universality that DNA. This is of course expected because lipid molecules come in many different varieties (73) with strong idiosyncrasies in terms of the detailed nature of their phase diagrams. One thus can not achieve the same degree of generality and universality in the description of lipid phase diagram and consequent equations of state as was the case for DNA.

Nevertheless, recent extremely careful and detailed work on PCs by J. Nagle and his group (87) points strongly to the conclusion that at least in the lamellar part of the phase diagram of neutral lipids the main features of the DNA and lipid membrane assembly physics indeed is the same (85). This statement however demands qualification. The physics is the same, provided one first disregards the dimensionality of the aggregates—1 dimensional in the case of DNA and 2 dimensional in the case of lipid membranes—and takes into account the fact that while van der Waals forces in DNA arrays are negligible, they are essential in lipid membrane force equilibria. One of the reasons for this state of affairs is the large difference, unlike in the case of DNA, between the static dielectric constant of hydrophobic bilayer interior, composed of alkyl lipid tails, and the aqueous solution bathing the aggregate.

We have already pointed out that in the case of DNA arrays quantitative agreement between theory, based on hydration and electrostatic forces augmented by thermal undulation forces, and experiment has been obtained and extensively tested (7,42). The work on neutral lipids (85) claims that the same level of quantitative accuracy can be achieved also in lipid membrane assemblies if one takes into account hydration and van der Waals forces again augmented by thermal undulations. Of course, the nature of the fluctuations in the 2 systems is different and is set by the dimensionality of the fluctuating aggregates—1- vs. 2-dimensional.

The case of lipids adds an additional twist to the quantitative link between theory and experiments. DNA in the line hexatic as well as cholesteric phases (where reliable data for the equation of state exist) is essentially fluid as far as positional order is concerned and thus has unbounded positional fluctuations. Lipid membranes in the smectic multilamellar phase are quite different in this respect. They are not really fluid as far as positional order is concerned but show something called quasilong range (QLR) order, meaning that they are in certain respects somewhere between a crystal and a fluid (50,67). The quasi long-range positional order makes itself recognizable through the shape of the X-ray diffraction peaks in the form of persistent (Caille) tails (67).

In a crystal one would ideally expect infinitely sharp peaks with Gaussian broadening only because of finite accuracy of the experimental setup. Lipid multilamellar phases, however, show peaks with very broad, non-Gaussian, and extended tails that are one of the consequences of QLR positional order. The thickness of these peaks for different orders of X-ray reflexions varies in a characteristic way with the order of the reflexion (67). It is this property that allows us to measure not only the average spacing between the molecules, but also the amount of fluctuation around this average spacing. Luckily, the theory also predicts that and without any free parameters (all of them being already determined from the equation of state) the comparison between predicted and measured magnitude in positional fluctuations of membranes in a multi-lamellar assembly is more than satisfactory (85).

In summing up, the level of understanding of the equation of state reached for DNA and neutral lipid membrane arrays is pleasing.

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