Bilayer membranes curvature

Baumgartner and coworkers [145,146] study lipid-protein interactions in lipid bilayers. The lipids are modeled as chains of hard spheres with heads tethered to two virtual surfaces, representing the two sides of the bilayer. Within this model, Baumgartner [145] has investigated the influence of membrane curvature on the conformations of a long embedded chain (a protein ). He predicts that the protein spontaneously localizes on the inner side of the membrane, due to the larger fluctuations of lipid density there. Sintes and Baumgartner [146] have calculated the lipid-mediated interactions between cylindrical inclusions ( proteins ). Apart from the... 

The experiments discussed in this chapter have shown that a variety of chiral molecules self-assemble into cylindrical tubules and helical ribbons. These are indeed surprising structures because of their high curvature. One would normally expect the lowest energy state of a bilayer membrane to be flat or to have the minimum curvature needed to close off the edges of the membrane. By contrast, these structures have a high curvature, with a characteristic radius that depends on the material but is always fairly small compared with vesicles or other membrane structures. Thus, the key issue in understanding the formation of tubules and helical ribbons is how to explain the morphology with a characteristic radius. 

More recently, Smith et al. have developed another model based on spontaneous curvature.163 Their analysis is motivated by a remarkable experimental study of the elastic properties of individual helical ribbons formed in model biles. As mentioned in Section 5.2, they measure the change in pitch angle and radius for helical ribbons stretched between a rigid rod and a movable cantilever. They find that the results are inconsistent with the following set of three assumptions (a) The helix is in equilibrium, so that the number of helical turns between the contacts is free to relax, (b) The tilt direction is uniform, as will be discussed below in Section 6.3. (c) The free energy is given by the chiral model of Eq. (5). For that reason, they eliminate assumption (c) and consider an alternative model in which the curvature is favored not by a chiral asymmetry but by an asymmetry between the two sides of the bilayer membrane, that is, by a spontaneous curvature of the bilayer. With this assumption, they are able to explain the measurements of elastic properties. 

Dynamic heterogeneity produces weakening of the mechanical properties, i.e. the compressibility and bending rigidity of the bilayer, because they are linked to the local membrane curvature. 

Bozic and Svetina [36] analysed a different situation, where addition of membrane constituents happens from the external milieu, and there is no metabolism inside, but there is limited permeability. They supposed that the membrane assumes spontaneous membrane curvature. This is non-zero if the properties of the inside and outside solutions differ, or if the two layers of a bilayer membrane differ in composition, or if some membrane-embedded constituents are asymmetrically shaped. They were able to show that under these assumptions membrane division is possible provided TLkC4 > 1.85, where T is the time taken to double the membrane area, L is the hydraulic permeability of the membrane, k is the bending modulus, and C is the spontaneous membrane curvature. In this model growing vesicles first retain spherical shape, then are distorted to a dumbbell, then to a pair of asymmetric vesicles coupled by a narrow neck, and finally to a pair of spherical vesicles linked by a narrow neck. Separation of the two daughter vesicles occurs as a result of mechanical agitation in the solution. 

A biologic reason for the abundance of nonlamellar lipids in membranes is that they possess the ability to modulate the activities of membrane proteins (15, 16). It has been recognized that membranes exist in a state of curvature frustration, which may be sufficiently large to have significant effect on certain protein conformations (17). Many examples show that the lipid bilayer elastic curvature stress indeed couples to conformational changes of membrane proteins (15, 18, 19). Protein kinase C is one such example of an enzyme activated by lipids that exhibit a propensity for nonlamellar phase formation (20). The activity of Ca " -ATPase from sarcoplasmic reticulum membranes also strongly correlates with the occurrence of nonbilayer lipids in the membrane and increases with the increase of their amount. It is noteworthy that the protein activity does not depend on the chemical structure of the lipids but only on their phase propensity thus specific binding interactions are ruled out. The list of proteins with activities that depend on the phase properties... 

This (local) double twist configuration clearly involves a hyperbolic deformation of the imaginary layers. In contrast to the hyperbolic layers found in bicontinuous bilayer lyotropic mesophases, the molecules within these chiral thermotropic mesophases are oriented parallel to the layers, to achieve nonzero average twist. The magnitude of this twist is deternuned by the direction along which the molecules lie (relative to the principal directions on the surface), and a function of the local curvatures of the layers (K1-K2), cf. eq. 1.4. Just as the molecular shape of (achiral) surfactant molecules determines the membrane curvatures, the chirality of these molecules induces a preferred curvature-orientation relation, via the geodesic torsion of the layer. 

Figure 5.10 Electron micrographs of L-cells of Streptomyces hydroscopicas [73]. The freeze-fractured texture shows the periodically curved lipid bilayer. The curvature is weakly expressed in a and very distinct in fi. Two attached lamellar bodies and the imderlying membrane are shown in fe. The bar (in fi) is 500 nm.

It is now well established that proteins can induce phase transitions in lipid membranes, resulting in new structures not found in pure lipid-water systems (c/. section 5.1). However, this property is not peculiar to proteins the same effect can be induced by virtually any amphiphilic molecule. Depending on the structure and nature of proteins, their interactions with lipid bilayers can be manifested in very different ways. We may further assume that the role of proteins in the biogenesis of cubic membranes is analogous to that in condensed systems, and lipids are necessary for the formation of a cubic membrane. This assumption is supported by studies of membrane oxidation, which induce a structure-less proteinaceous mass [113]. However, the existence of a lipid bilayer by itself does not guarantee the formation of a cubic membrane, as proteins may also play an essential role in setting the membrane curvature. In this context, note that the presence of chiral components e.g. proteins) may induce saddle-shaped structures characteristic of cubic membranes. (This feature of chiral packings has been discussed briefly in section 4.14)... 

These results show clearly that most of the MgOEP is located near the inner vesicle surface although much smaller than the outer surface. A similar conclusion has been drawn previously for chlorophyll a dissolved in egg phosphatidylcholine vesicles. The inner part of the bilayer membrane of small vesicles is obviously a more suitable solvent or better liquid than the outer part, which is again reasonably explained by the much higher curvature of the inner part. Furthermore, at the centre of the bilayer, the same space is occupied by about half as many molecules. Several amphiphilic porphyrins with long side chains vesiculate upon sonification. The porphyrin then becomes part of the hydro-phobic core. ... 

Ultimately, sequestering charged lipids could potentially lead to a new stable state, in which bilayer bending forces favor membranes with local nonzero curvature. Moreover, the mechanism for coupling local lipid composition with membrane curvature may be complemented by a "local spontaneous curvature" mechanism [88], whereby the asymmetry between the spontaneous shapes of two monolayers is achieved by insertion of amphipathic N-terminal helices of certain BAR domains into the lipid polar head-groups region on one side of the membrane [7,88-95]. According to this mechanism, the insertion of an amphipathic... 

A characteristic of all membranes is an asymmetry in lipid composition across the bilayer. Although most phospholipids are present in both membrane leaflets, they are commonly more abundant in one or the other leaflet. For instance, in plasma membranes from human erythrocytes and certain canine kidney cells grown in culture, almost all the sphingomyelin and phosphatidylcholine, both of which form less fluid bilayers, are found in the exoplasmic leaflet. In contrast, phosphatidylethanolamine, phosphatidylserine, and phosphatidylinositol, which form more fluid bilayers, are preferentially located in the cytosolic leaflet. This segregation of lipids across the bilayer may influence membrane curvature (see Figure 5-8c). Unlike phospholipids, cholesterol is relatively evenly distributed in both leaflets of cellular membranes. 

The water insolubility of Cers, combined with strong intermolecular interactions, account for their participation in the water barrier of skin, where Cers are about one-third of the total lipid. In cell membranes, Cers tend to associate with rafts and caveolae and can affect membrane curvature. These may be important contributors to bilayer organization during cell signaling, for example, when SM is hydrolyzed to Cer in response to agonist activation of SMase [18]. Cer is also involved in cell signaling (as discussed in Section 5), and under certain conditions, Cers can form channels and induce leakiness in membranes, such as mitochondria, which may contribute to the induction of apoptosis (L.R. Montes, 2002 L.J. Siskind, 2006). 

The rods and tubules, described by Fuhrhop et al. [17] follow an analogous pattern to that of these the 2-directional arborols. When the racemic form of the lysine bolaphile 4 was used (Scheme 2), no rod or tubule formation was noted in contrast, the racemate of the extended bolaphile 5 produced supramolecu-lar assemblies identical to those formed by the pure enantiomers. The effect of configuration in molecular monolayers was shown to depend on membrane curvature in the same manner as in bilayers. [17]... 

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