Extent of raft composition in a model plasma membrane.

"Rafts" are nanometer-size inhomogeneities in the plasma membrane that, in the outer leaflet, are enriched in sphingomyelin and cholesterol. They are thought to provide a platform for proteins to carry out biological processes. Here, we employ a model asymmetric plasma membrane to address the question of the range of sphingomyelin and cholesterol compositions in which one would expect the formation of rafts. We define a weight for the likelihood of raft formation and evaluate it as a function of the sphingomyelin mole fraction in the outer leaflet for three bilayers with total cholesterol mole fractions of 0.30, 0.40, and 0.50. Not surprisingly, the weight decreases when there is little sphingomyelin. Less expected, we find that the weight also decreases when there is a large mole fraction of sphingomyelin. The weight is largest in the bilayer with a total cholesterol mole fraction of 0.30 and decreases rapidly with increasing total cholesterol. We explicate the reasons for these behaviors. In the 0.30 cholesterol bilayer, the largest weight occurs at a sphingomyelin mole fraction in the outer leaflet of approximately 0.23. The weight falls to one half its maximum value at sphingomyelin mole fractions of 0.15 and 0.33. In terms of the sphingomyelin mole fraction of the asymmetric bilayer, the maximum weight occurs at 0.12 and falls to half maximum at 0.08 and 0.17.

Recent Experiments Support a Microemulsion Origin of Plasma Membrane Domains: Dependence of Domain Size on Physical Parameters.

It is widely, but not universally, believed that the lipids of the plasma membrane are not uniformly distributed, but that "rafts" of sphingolipids and cholesterol float in a "sea" of unsaturated lipids. The physical origin of such heterogeneities is often attributed to a phase coexistence between the two different domains. We argue that this explanation is untenable for several reasons. Further, we note that the results of recent experiments are inconsistent with this picture. However, they are quite consistent with an alternate explanation, namely, that the plasma membrane is a microemulsion of the two kinds of regions. To show this, we briefly review a simplified version of this theory and its phase diagram. We also explicate the dependence of the predicted domain size on four physical parameters. They are the energy cost of gradients in the composition, the spontaneous curvature of the membrane, its bending modulus and its surface tension. Taking values of the latter two from experiment, we obtain domain sizes for several different cell types that vary from 58 to 88 nm.

Model Plasma Membrane Exhibits a Microemulsion in Both Leaves Providing a Foundation for "Rafts".

We consider a model lipid plasma membrane, one that describes the outer leaf as consisting of sphingomyelin, phosphatidylcholine, and cholesterol and the inner leaf of phosphatidylethanolamine, phosphatidylserine, phosphatidylcholine, and cholesterol. Their relative compositions are taken from experiment; the cholesterol freely interchanges between leaves. Fluctuations in local composition are coupled to fluctuations in the local membrane curvature, as in the Leibler-Andelman mechanism. Structure factors of components in both leaves display a peak at nonzero wavevector. This indicates that the disordered fluid membrane is characterized by structure of the corresponding wavelength. The scale is given by membrane properties: its bending modulus and its surface tension, which arises from the membrane's connections to the cytoskeleton. From measurements on the plasma membrane, this scale is on the order of 100 nm. We find that the membrane can be divided into two different kinds of domains that differ not only in their composition but also in their curvature. The first domain in the outer, exoplasmic leaf is rich in cholesterol and sphingomyelin, whereas the inner, cytoplasmic leaf is rich in phosphatidylserine and phosphatidylcholine. The second kind of domain is rich in phosphatidylcholine in the outer leaf and in cholesterol and phosphatidylethanolamine in the inner leaf. The theory provides a tenable basis for the origin of structure in the plasma membrane and an illuminating picture of the organization of lipids therein.

The Effect of Solutes on the Temperature of Miscibility Transitions in Multicomponent Membranes.

We address questions posed by experiments that show small-chain alcohols reduce the miscibility transition temperature when added to giant plasma membrane vesicles (GPMVs), but increase that temperature when added to giant unilamellar vesicles. In giant unilamellar vesicles the change in temperature displays a definite minimum, between decanol and tetradecanol, as a function of alcohol chain length; in GPMVs there is no such minimum. To emphasize the competition between internal entropies of the components and the interactions between them, we model the system as consisting of three different linear polymers. Two of them are the constituents of a liquid, one that can undergo a miscibility transition. To this liquid is added the third polymer component, which represents the short-chain alcohol. We show that, within Flory-Huggins theory, the addition of alcohol causes an increase or decrease of the miscibility transition temperature depending upon the competition of two effects. The first is the dilution of the interactions between the two components of the liquid caused by the introduction of the alcohol. This tends to lower the transition temperature. The second effect is the preferential partitioning of the alcohol into one phase of the liquid or the other. This tends to raise the transition temperature irrespective of which phase the alcohol prefers. This second effect is the smallest, and the decrease in transition temperature the largest, when the alcohol partitions equally between the two phases. Such equal partitioning occurs when the effect of the entropic excluded volume interactions (which cause the alcohol to prefer one phase) just balances the effect of the direct interactions, which cause it to prefer the other. These results allow us to make several predictions, and to propose an explanation for the different behavior of the transition temperature in GPMVs and giant unilamellar vesicles that results from the addition of alcohols.

Predicting a polar analog of chiral blue phases in liquid crystals.

In liquid crystals, if flexoelectric couplings between polar order and director gradients are strong enough, the uniform nematic phase can become unstable to the formation of a modulated polar phase. Previous theories have predicted two types of modulation: twist bend and splay bend; the twist-bend phase has been found in recent experiments. Here, we investigate other types of modulation, using lattice simulations and Landau theory. In addition to twist bend and splay bend, we also find polar blue phases, with 2D or 3D modulations of both the director and the polar order. We compare polar blue phases with chiral blue phases, and discuss opportunities for observing them experimentally.