Membranes curvature elasticity

There is one final major difference with the 1-dimensional case. Membrane curvature elasticity does not a priori define any persistence length. It displays... 

Figure 4 The modified stalk mechanism of membrane fusion and inverted phase formation, (a) planar lamellar (La) phase bilayers (b) the stalk intermediate the stalk is cylindrically-symmetrical about the dashed vertical axis (c) the TMC (trans monolayer contact) or hemifusion structure the TMC can rupture to form a fusion pore, referred to as interlamellar attachment, ILA (d) (e) If ILAs accumulate in large numbers, they can rearrange to form Qn phases, (f) For systems close to the La/H phase boundary, TMCs can also aggregate to form H precursors and assemble Into H domains. The balance between Qn and H phase formation Is dictated by the value of the Gaussian curvature elastic modulus of the bIlayer (reproduced from (25) with permission of the Biophysical Society) The stalk in (b) is structural unit of the rhombohedral phase (b ) electron density distribution for the stalk fragment of the rhombohedral phase, along with a cartoon of a stalk with two lipid monolayers merged to form a hourglass structure (reproduced from (26) with permission of the Biophysical Society).

Gruner SM. Coupling between bilayer curvature elasticity and membrane-protein activity. In Biomembrane Electrochemistry, Volume 235. Blank M, Vodyanoy I, eds. 1994. American Chemical Society, Washington, DC. pp. 129-149. 

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... 

An application of the optical microscopy to the detennination of the curvature elastic-modulus of biological and model membranes. Journal of Physics, 48 (5). 855-867. 

Coupling between Bilayer Curvature Elasticity and Membrane Protein Activity... 

The purpose of this chapter is to summarize some recent developments in the physics of lipid bilayers that demonstrate the existence of curvature-elastic stresses in bilayers and to review mechanisms whereby the resultant forces may couple to membrane protein conformations (see also references 1-3 for reviews). A consequence of these forces is that membrane proteins may have mechanistic themes that are qualitatively different from themes operative in aqueous proteins. Moreover, because these forces are directed generally parallel to the membrane surface, the actual conformational motions to which the forces couple may ultimately be simpler to understand than the complex conformations of aqueous proteins. 

Under this assumption, the bending energy Eg can be represented in terms of the membrane s curvature. For this reason. Eg is also referred to as the curvature elastic energy. The curvature of smooth surfaces is characterized by two functions that depend on the local canonical curvatures, h t) and h lr), in a surface element dS centered at r. These functions are the mean curvature, H = ( 1 + hi) , and the Gaussian curvature, K = hih2- In general, H and K change with the point r. 

Bivas, P. Hanusse, P. Bothorel, J. Lalanne, and O. Aguerre-Chariol,/. Phys. (Paris), 48,855 (1987). An Application of the Optical Microscopy to the Determination of the Curvature Elastic Modulus of Biological and Model Membranes. 

Find the tangent-tangent correlation function and persistence length for a polymeric chain with curvature elasticity — i.e., a one-dimensional membrane embedded in a three-dimensional space. This is applicable to the physics of a flexible rod undergoing thermal fluctuations. Contrast the results with those of a two-dimensional membrane. 

The situation is also very different with regard to curvature elasticity when we compare 2-dimensional membranes with giant 1-dimensional micelles. The most general expression for the curvature elasticity of a 2-dimensional fluid film is [5.9]... 

These scaling relations are an immediate consequence of the scale invariance noted for the curvature elasticity (5.9) of fluid membranes. An isotropic dilation of factor A transforms Ci and to Ci/A and C2/A, respectively, whilst dA transforms to A dA. The whole thing leaves d ei unchanged. 

When aggregation produces very extended objects (giant 1-dimensional micelles or 2-dimensional fluid membranes), the degrees of freedom associated with their curvature elasticity play an essential role in determining phase properties. The situation is very different depending on how many dimensions the object has. 

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