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... 

Here, the final three terms are a Ginzburg-Landau expansion in powers of i j. The coefficient t varies as a function of temperature and other control variables. When it decreases below a critical threshold, the system undergoes a chiral symmetry-breaking transition at which i becomes nonzero. The membrane then generates effective chiral coefficients kHp = k n>i f and kLS = which favor membrane curvature and tilt modulations, respec-... 

Shearman GC, Ces O, Templer RH et al (2006) Inverse lyotropic phases of lipids and membrane curvature. J Phys Condens Matter 18 S1105-S1124... 

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. 

The influence of substituent size, polarity, and location on the thermotropic properties of synthetic phosphatidylcholines has been studied by Menger et al. [18], The effect of increasing membrane curvature on the phase transition has been investigated by DSC and FTIR [19]. In addition, a data bank, LIPIDAT, on lipid phase transition temperatures and enthalpy changes is available [20, 21],... 

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. 

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. 

An apparently related effect due to membrane curvature is the phenomenon of immunosuppression induced by cationic surfactants. The cationic quaternary ammonium and pyridinium surfactants are widely used as sterilising (antibacterial) agents in an enormous variety of applications. Although the biochemical and genetic mechanism by which bacteria like streptococcus aureus develop immimity to these is not understood, it appears certain that the antiseptic effect is simply related to membrane disruption. At and above the critical micelle concentration ("cmc", discussed in Chapter 3),... 

A large number of examples have been outlined above where these structures occur spontaneously, and their transformations between flat and curved forms are evidently used expensively in nature. The approach to thinking about structure and function in terms of membrane curvature presented here allows insights into biological function that are inaccessible through the conventional view of membranes, that largely focuses on the role of proteins, to the exclusion of the lipid matrix. 

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)... 

Keywords cell signaling lipid rafts BAR domains membrane curvature membrane elasticity PIP2 diffusion mean-field model coarse-grained theory Poisson-Boltzmann theory Cahn-Hilliard equations... 

Here, and // denote respectively the local mole fraction and local electrochemical potential of the charged lipid species in that particular leaflet, g is the metric tensor defined on the leaflet surface, and Di p represents the diffusion coefficient of charged lipids. Note that Diip should not affect the equilibrium state. The local electrochemical potentials, in turn, are derived from the free energy functional that itself depends on local lipid component densities self-consistent formulation, which remains as the main computational task. 

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... 

Lipid demixing upon Amphiphysin BAR dimer adsorption is insufficient on its own to induce significant membrane curvatures... 

In order to explore whether insertions of the BAR dimer s N-helices can enhance membrane curvature, various penetration depths of N-helices were examined, and the results are illustrated in Figure 3. We observe larger membrane deformations upon deeper insertion of N-helices (represented in the model by increasing the local spontaneous curvature). By performing quantitative analysis on binding... 

Campelo, F., McMahon, H.T., Kozlov, M.M. The hydrophobic insertion mechanism of membrane curvature generation by proteins. Biophys. J. 2008, 95, 2325-39. 

Itoh, T., De Camilli, P. BAR, F-BAR (EFC) and ENTH/ANTH domains in the regulation of membrane-cytosol interfaces and membrane curvature. Biochim. Biophys. Acta 2006, 1761, 897-912. 

Masuda, M., Takeda, S., Sone, M., Ohki, T., Mori, H., Kamioka, Y., Mochizuki, N. Endophilin BAR domain drives membrane curvature by two newly identified structure-based mechanisms. EMBO J. 2006, 25, 2889-97. 

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