On the force between "rafts".

"Rafts" in the plasma membrane are nanoscopic domains rich in sphingolipids and cholesterol. Groups of them are thought to provide stable platforms for various proteins. How several rafts can form a larger stable platform has yet to be made clear. Here, we show that in the microemulsion theory of rafts, in which they, and the sea in which they float, are characterized by a naturally occurring length, rafts separated by a sea larger than this length will attract one another, thus making the sea smaller. Similarly, if rafts are separated by a sea that is smaller than the characteristic size, they will repel one another thus allowing the sea to increase in size. Such an elastic force can clearly stabilize a platform of many rafts.

Lipid redistribution in the highly curved footprint of Piezo1.

We investigate the effects on the distribution of lipids in the plasma membrane that are caused by the insertion of a protein, Piezo1, that significantly distorts the membrane toward the cytosol. From coarse-grained molecular dynamics simulations, we find that the major effects occur in the outer, extracellular, leaflet. The mol fraction of cholesterol increases significantly in the curved region of the membrane close to Piezo1, while those of phosphatidylcholine and of sphingomyelin decrease. In the inner leaflet, mol fractions of cholesterol and of phosphatidylethanolamine decrease slightly as the protein is approached, while that of phosphatidylserine increases slightly. The mol fraction of phosphatidylcholine decreases markedly as the protein is approached. Most of these results are understood in the context of a theoretical model that utilizes two elements: 1) a coupling between the leaflets' actual curvatures and their compositionally dependent spontaneous curvatures and 2) the dependence of the spontaneous curvatures not only on the mol fractions of the phospholipids, but also on the effect that cholesterol has on the spontaneous curvatures of the phospholipids.

A Theoretical Basis for Nanodomains.

We review the current theories of nanodomain, or "raft," formation. We emphasize that the idea that they are co-exisiting Lo and Ld phases is fraught with difficulties, as is the closely related idea that they are due to critical fluctuations. We then review an alternate theory that the plasma membrane is a two-dimensional microemulsion, and that the mechanism that drives to zero the line tension between Lo and Ld phases is the coupling of height and composition fluctuations. The theory yields rafts of SM and cholesterol in the outer leaf and POPS and POPC in the inner leaf. The "sea" between rafts consists of POPC in the outer leaf and POPE and cholesterol in the inner leaf. The characteristic size of the domain structures is tens of nanometers.

Cholesterol-Dependent Bending Energy Is Important in Cholesterol Distribution of the Plasma Membrane.

We consider the plasma membrane that contains a cholesterol molar fraction of 0.4 and ask how that cholesterol is distributed between the two leaves. Because of the rapid flip-flop of cholesterol between leaves, we assume that its distribution is determined by the equality of its chemical potentials in the two leaves. When we consider only the contributions of entropy and interactions to the cholesterol chemical potential in our model system, we find, not surprisingly, that the cholesterol is mostly in the outer leaf because of the strong attraction between cholesterol and sphingomyelin (SM), which is predominantly in that leaf. We find 72% there. We then include the contribution from the bending energy in each leaf that must be overcome to join the leaves in a flat bilayer. The product of bending modulus and spontaneous curvature is obtained from simulation. We find that the addition of cholesterol to the outer leaf reduces the spontaneous curvature, which is initially positive, until it passes through zero when the molar fraction of cholesterol in the outer leaf is 0.28. Additional cholesterol is driven toward the inner leaf by the sphingomyelin phosphatidylcholine mixture. This is resisted by the bending energy contribution to the inner leaf. We find, again by simulation, that the addition of cholesterol monotonically increases the magnitude of the spontaneous curvature of the inner leaf, which is negative. This increases its bending energy. We conclude that, as a result of these competing effects, the percentage of cholesterol in the outer leaf is reduced to ∼63 ± 6%.

Light scattering study of the "pseudo-layer" compression elastic constant in a twist-bend nematic liquid crystal.

The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or "pseudo-layers", each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining "layer" compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant K. The magnitude of K is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼106 Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the "pseudo-layer" structure of the TB phase with Beff in the range 103-104 Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director.

Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers.

The nematic twist-bend (NTB) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase - the first distinct nematic variant discovered in many years. The NTB phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The NTB structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, NTB-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like "pseudo-layers", defined by planes of equivalent phase in a coarse-grained description of the NTB state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two.

Dynamic light scattering study of biaxial ordering in a thermotropic liquid crystal.

Dynamic light scattering from orientational order fluctuations in a liquid crystalline tetrapode reveals successive, weakly first-order isotropic to uniaxial and uniaxial to biaxial nematic phase transitions. The order parameter relaxation rates exhibit temperature dependences consistent with Landau-de Gennes mean field theory. Combined with previous evidence of a second-order uniaxial-biaxial transition in a closely related tetrapode, the present study supports the existence of a nematic-nematic tricritical point in thermotropic liquid crystals.

Phase separation in bilayer lipid membranes: effects on the inner leaf due to coupling to the outer leaf.

The combined effects of the tendency of cholesterol to order lipids in the liquid phase and the coupling between lipids in the two leaves of a bilayer are investigated theoretically utilizing a Landau free energy. We show that as a consequence of these combined effects, lateral phase separation in the outer leaf between cholesterol-rich and -poor liquids causes a similar, but weaker, phase separation in the inner leaf. Just as the areal density of lipids in the outer leaf increases in the cholesterol-rich regions, so the areal density of lipids also increases in the inner leaf. Thus, the areal density in the inner leaf varies spatially, reflecting spatial variations of the areal density in the outer leaf. This provides a mechanism for proteins attached to the inner leaf via a hydrocarbon tether to respond to variations in the composition of the outer leaf. We also note that the effect of coupling between the leaves should be observable in artificial bilayers.

Geometrical optics approach in liquid crystal films with three-dimensional director variations.

A formal geometrical optics approach (GOA) to the optics of nematic liquid crystals whose optic axis (director) varies in more than one dimension is described. The GOA is applied to the propagation of light through liquid crystal films whose director varies in three spatial dimensions. As an example, the GOA is applied to the calculation of light transmittance for the case of a liquid crystal cell which exhibits the homeotropic to multidomainlike transition (HMD cell). Properties of the GOA solution are explored, and comparison with the Jones calculus solution is also made. For variations on a smaller scale, where the Jones calculus breaks down, the GOA provides a fast, accurate method for calculating light transmittance. The results of light transmittance calculations for the HMD cell based on the director patterns provided by two methods, direct computer calculation and a previously developed simplified model, are in good agreement.

Pseudo-Casimir effect in untwisted chiral nematic liquid crystals.

We investigate theoretically the pseudo-Casimir force between parallel plates immersed in a chiral nematic liquid crystal. We focus on small-separation limit where the director configuration between the plates inducing strong homeotropic anchoring is uniform. We find that the force is attractive at separations smaller than the crossover distance and repulsive otherwise, and that it diverges logarithmically at the critical distance where the uniform structure is replaced by a distorted structure. We also analyze modifications to the force introduced by magnetic field and comment on the possible detection of the effect.

Surface states in nearly modulated systems.

A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid-crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a nonwet layer having a small deviation from bulk order, and a different nonwet layer with a large deviation from bulk order that decays nonmonotonically as the distance from the wall increases. In particular, the large deviation nonwet layer is a feature of systems at the Lifshitz point and also those systems having only homogeneous bulk phases.