Membranes elastic properties

Typically, the insertion induces sharp variation of the membrane profile at the distances 0.5-1.0nm from the membrane-peptide interface [79-82]. The steepness of this perturbation indicates that the short-A, behavior of membrane moduli must be important in the estimates of the elastic energy. In addition, a peptide inserted in a membrane almost certainly perturbs the membrane s elastic moduli in the immediate vicinity of the inclusion. Both these effects, membrane nonlocality and nonuniform modification of elastic properties by insertions, might play an important role in resolving the contradiction between the local calculations [80] and the experimental data for the mean lifetime of a gramicidin channel [81,109,110]. ... 

To address this issue, several researchers have developed models of chiral self-assembly. In this section, we review these models. We begin with models based on nonchiral mechanisms and argue that they all have limitations in identifying a mechanism to select a particular tubule radius. We then discuss models based on the elastic properties of chiral membranes and argue that they provide a plausible approach to understanding the formation of tubules and helical ribbons. Most of this discussion was previously presented in our recent theoretical review article.139... 

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

Another approach to explain tubule formation was taken by Lubensky and Prost as part of a general theoretical study of the relationship between orientational order and vesicle shape.173 These authors note that a membrane in an Lp/ phase has orientational order within the membrane which is lacking in the La phase. The clearest source of orientational order is the tilt of the molecules with respect to the local membrane normal The molecules select a particular tilt direction, and hence the local elastic properties of the membrane become anisotropic. A membrane might also have other types of orientational order. For example, if it is in a hexatic phase, it has order in the orientations of the intermolecular bonds (not chemical bonds but lines indicating the directions from one molecule to its nearest neighbors in the membrane). 

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. 

PVA must be cross-linked in order to be useful for a wide variety of applications. A hydrogel can be described as a hydrophilic, cross-linked polymer, which can sorbe a great amount of water by swelling, without being soluble in water. Other specific features of hydrogels are their soft elastic properties, and their good mechanical stability, independent of the shape (rods, membranes, microspheres, etc.). 

The results of interfacial tension measurements on BLM formed from five different lipid solutions are given in Table I. One of the immediate questions is whether the measured values represent the true bifacial tension of BLM. It is implicitly assumed in order to apply equation 3 that yb is a characteristic property of BLM and should be independent of the extension of the BLM area. It is generally recognized that if the BLM also possessed elastic properties, the measured yb would be different when it is stretched. To answer this question, yb was measured during both expansion and contraction of the membrane. A typical trace of pressure difference vs. time in which the membrane was being expanded and contracted is shown in Figure 3. The symmetric nature of the curve indicates that little hysteresis was present during inflation and deflation of the BLM. Therefore, it seems safe to conclude that for BLM formed from lipid materials alone the membrane does not appear to possess appreciable elastic properties. 

Cholesterol affects a large variety of membrane properties in animal cells (39). It is involved in modifying dynamical membrane properties by reducing passive permeation, slowing down the lateral diffusion of molecules in fluid-like membranes, and speeding up diffusion in gel-phase membranes. It also affects bilayer properties by condensing the bilayer, which changes its elastic properties and promotes the order of phospholipid acyl chains in the hydrophobic membrane core. In this manner, cholesterol develops the formation of the liquid-ordered... 

Hiergeist, C. and Lipowsky, R. (1996) Elastic properties of polymer decorated membranes. /. Phys. II France, 6, 1465-1481. 

The elastic membrane model, formulated in terms of elastic moduli and u r), provides a significantly reduced description of insertion phenomena. More detailed analysis should account for the orientation and displacement of the lipid molecules as well as some of their internal degrees of freedom. A step in this direction has been made, for instance, in Ref. 95. At short-length scales and near nonuniformities, lipid molecules cannot attain the normal orientations typical of their mean behavior on a macroscopic scale, which must inevitably affect their elastic properties. More detailed statistical mechanical analysis and simulational studies might provide useful insight into such behavior. 

The motility appears to be due to a passive piezoelectric behavior of the ceU plasma membrane [Kahnec and colleagues, 1992]. Iwasa and Chadwick [1992] measured the deformation of a ceU under pressure loading and voltage clamping and computed the elastic properties of the wall, assuming isotropy. It appears that for agreement with both the pressure and axial stiffness measurements, the ceU wall must be... 

E.A. Franceschini and H.R. Corti, Elastic properties of Nafion, polybenzimidazole and poly [2,5-benzimidazole] membranes determined by AFM tip nano-indentation, J. Power Sources, 188, 379-386 (2009). 

Ferroelectrics and piezoceramics Ferroelectricity, sometimes combines with elastic properties Sensors, actuators (AT), ML-AT, membranes, resonators, inkjet printer heads... 

Usually, the size separation porous membranes have cutoff values for their smallest diameter on their transmembrane path, and the cutoff diameter is not usually tunable once they are synthesized. Utilizing supercompressible and fully elastic properties, CNMs were designed with mechanically reversible tunable pores. The CNM (-300 pm thick) with an... 

Membrane materials are flexible and only stabilized by tension. Therefore the most important mechanical parameters for construction are tensile strength and elastic properties. It is essential to distinguish between stiffness and strength (with and without deterioration). 

Viswanadham, R. K., and E. J. Kramer, Elastic properties of reconstituted collagen hollow fiber membranes, Journal of Materials Science, 11(7) 1254-1262 (1976). 

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