Membranes elastic

The most successful continuum description of membrane elasticity, dynamics, and thermodynamics is based on the smectic bilayer model (for examples of different versions and applications of this approach see Ref. 76-82 and references therein). We introduce this model in conjunction with the question of membrane undulations. 

The Helfrich-Prost model was extended in a pair of papers by Ou-Yang and Liu.181182 These authors draw an explicit analogy between tilted chiral lipid bilayers and cholesteric liquid crystals. The main significance of this analogy is that the two-dimensional membrane elastic constants of Eq. (5) can be interpreted in terms of the three-dimensional Frank constants of a liquid crystal. In particular, the kHp term that favors membrane twist in Eq. (5) corresponds to the term in the Frank free energy that favors a helical pitch in a cholesteric liquid crystal. Consistent with this analogy, the authors point out that the typical radius of lipid tubules and helical ribbons is similar to the typical pitch of cholesteric liquid crystals. In addition, they use the three-dimensional liquid crystal approach to derive the structure of helical ribbons in mathematical detail. Their results are consistent with the three conclusions from the Helfrich-Prost model outlined above. 

In Fig. Ic is seen a preparation made by repeatedly autoclaving material of the tunica media of bovine aorta. The particles of purified elastin were dried, embedded in wax, and then sectioned. The sections were mounted and stained with Verhoeff s hematoxylin. Examination of the sections showed that much of the membranous elastic material had been resolved into flat bundles of fine fibrils, arranged parallel, and in registerlike locks of wavy hair. 

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... 

Lipids and Membranes. Mastoparan X was studied by both high-resolution and solid-state NMR techniques to determine the structure and orientation of MPX when associated with bicelles. Membrane elasticity in the presence of cholesterol and detergents. 

The membrane elastic behavior of PEO-PEE giant polymersomes has been studied by a micropipette aspiration method [5], The results showed that the polymer membrane elasticity is comparable to fluid-state lipid membranes however the vesicles could sustain a greater strain before rupture, proving an enhanced polymersome toughness, which originates from membrane thickness. 

Section III describes the mechanical influence that a membrane can have on channel stabilization, focusing on simple physical models used to understand the mechanism of membrane-peptide interaction. We describe the elastic interaction between a membrane and an inserted peptide, focusing on GA, and first provide a brief overview of the basics of the elastic theory of membranes, demonstrating the formal equivalence of these issues to a classical problem in mechanical engineering. We then consider different descriptions of the interaction of a membrane with an inclusion and follow with a discussion of lipids influences on channel lifetimes. Finally, we describe a new perspective for describing the membrane-inclusion interaction. It emphasizes the inclusion-induced perturbation of membrane elastic constants at the lipid-peptide interface. 

The idea that membrane elastic constants could be modified by the insertion is not a new one. It was suggested [76,89] that, on the molecular scale involved in the insertion energetics, the elasticity coefficients might differ from their macroscopic values (see also Ref. 114). Furthermore, membranes material constants are nonlocal [115-117] (see also similar predictions for the interfacial tension [118]), which implies that their behavior on short-length scales differs from the macroscopic limit even for uniform membranes, as has been recently observed experimentally [119,120]. 

Fig. 9 C-DARR spectra of the aliphatic regions of U-[ C, NKwhyfi-PR at 273 (blue, gel phase) and 313 K (red, liquid crystal phase) (a) and the modified homology model of green PR (b). Helical residues influenced by changes in membrane elasticity (labeled in blue) are found in helices C, E, F, and G as well as in loops EC and EF. These residues disappear in the fluid membrane but are visible in the gel phase. This indicates that especially helices C and G but also E and F undergo thermal equilibrium fluctuations in the ground state of PR. Adapted from [41] with permission from the American Chemical Society...

Subsequent to these original formulations, a number of refinements to these relationships have been proposed. Observations of persistent deformations after micropipette aspiration for extended periods of time formed the basis for the development of a model for long-term stress relaxation [Markle et al., 1983]. The characteristic times for these relaxations were on the order of 1 to 2 h, and they were thought to correlate with permanent rearrangements of the membrane elastic network. 

These fields differ quite substantially in their theoretical description concentrations are scalar variables, orientations are vectors, and differential geometry is at heart a tensor theory but, aU of them are known to mediate interactions. For instance, the fact that proteins might prefer one lipid composition over another and thus aggregate [217-220] is central to an important mechanism attributed to lipid rafts. Tilt-mediated protein interactions have also been studied in multiple contexts [32, 33, 159, 221-223]. It is even possible to describe all these phenomena within a common language [224], using the framework of covariant surface stresses [154, 155, 157-161]. However, in the present review we will restrict the discussion to only two examples, both related to membrane elasticity in Sect. 3.1 we will discuss interactions due to hydrophobic mismatch, and in Sect. 3.2 we will look at interactions mediated by the large-scale curvature deformation of the membrane. 

Fournier JB (1999) Microscopic membrane elasticity and interactions among membrane inclusions interplay between the shape, dilation, tilt and tilt-difference modes. Eur Phys JB 11 261-272... 

Baumgart T, Das S, Webb WW, Jenkins JT (2005) Membrane elasticity in giant vesicles with fluid phase coexistence. Biophys J 89(2) 1067-1080... 

Desemo M (2009) Membrane elasticity and mediated interactions in continuum theory a differential geometric approach. In Faiier R, Jue T, Longo ML, Risbud SH (eds) Biomembrane frontiers nanostmctures, models, and the design of life, vol 2. Springer, New York, pp 41-74... 

Membrane Elasticity. For a vesicle with fixed volume V = Vo. area A = Aq, and genus the curvature energy of the bilayer membrane reduces to the sum of the remaining two terms of equation 9... 

The emphasis of this review of membrane elasticity is on the fluid plate model of the amphiphilic monolayer. The homogeneous fluid plate is used for some elementary considerations and estimates. Plates modeling actual monolayers will possess a nonvanishing stress profile even when undeformed, i.e. in the flat state at zero lateral tension. 

After particle adhesion, the membrane is cooled down to about 15°C, well in the gel state domain, while holding the two particles at fixed distance d. Then the trap separation was slowly increased to a distance + e. In response to this perturbation, the interparticle distance, d (initially d = d ) increases slightly. The new distance, d = d, is found < do- -e because of the membrane elasticity. Here the membrane can be modeled as a spring of stiflhess binding the two particles. The value of df is simply found by balancing radiation pressure (fc p) and membrane (fc ) forces ... 

The random network model explains differences in abCk) relations for various sulfonated ionomer membranes (Eikerling et al., 1997). It rationalizes effects of membrane elasticity and swelling behavior on performances under varying degrees of... 

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