Elasticity bending

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

Here B is again a compressional elastic constant, is a bend elastic constant and tire elastic constant C results from an elliptical defonnation of tire rods (tliis tenn is absent if tire column is liquid). 

Characteristic Rouse times for chains with bending elasticity Terminal time for reptation Crossover time Rouse, local reptation Characteristic Rouse times for the all-rotational model Rouse time... 

L.T. Lee, D. Langevin, J. Meunier, K. Wong, and B. Cabane Film Bending Elasticity in Microemulsions Made with Nonionic Surfactants. Prog. Colloid Polymer Sci. 81, 209 (1990). 

Sathyanarayana P, Mathew M, Sastry VSS, Kundu B, Le KV, Takezoe H, Dhara S (2010) Splay bend elasticity of a bent-core nematic liquid crystal. Phys Rev E (Rapid) 81 010702(R)-... 

Helfrich, Wolfgang, Bending Elasticity of Fluid Membranes, 6, 51 see also Klosgen, Beate, 6, 243 see also Thimmel, Johannes, 6, 253. 

E. A. Evans and W. Rawicz, "Entropy-driven tension and bending elasticity in condensed-fluid membranes," Phys. Rev. Lett., 64, 2094-7 (1990) E. A. Evans, "Entropy-driven tension in vesicle membranes and unbinding of adherent vesicles," Langmuir, 7, 1900-8 (1991). 

For an external fidd paraDel to the helicoidal axis, the cholesteric pitdi varies dependit on the relative ma tudes of 22 and 33 (the bending elastic coistant ) (5J). 

We note that the elasticity discussed above is only for planar bilayers under compression or tension and does not extend to the bending of bilayers. On the contrary, our analysis has shown that the bending of a bilayer is favoured down to the critical packing radius (assuming that the lipids can freely rearrange by lateral movement and/or flip-flop), and that bending elasticity sets in only for radii smaller than this critical value. The elasticity of a fluid bilayer is therefore seen to be profoundly different from that of a classical elastic plate or shell. 

In this equation, 8 is the dielectric anisotropy, K - (K +K j)/ is an average splay-bend elastic modulus, and E is the applied electric field. In this presentation, the curve must be linear when the Rapini approximation for the... 

In the later stage of fusion, the neck expansion velocity slows down by more than two orders of magnitude. Here the dynamics is mainly governed by the displacement of the volume of fluid around the fusion neck between the fused vesicles. The restoring force is related to the bending elasticity of the lipid bilayer [36, 37]. 

Engelhardt, H., Duwe, H.P., and Sackmann, E. (1985) Bilayer bending elasticity measured by Fourier analysis of thermally excited surface undulations of flaccid vesicles. Journal of Physics Letters, 46 (8). L395-L400. 

Bending elasticity and thermal fluctuations of lipid membranes-theoretical and experimental requirements. Journal of Physics. 50 (17), 2389-2414. 

Evans, E. and Rawicz, W. (2094) 1990) Entropy-driven tension and bending elasticity in condensed-fluid membranes. Physical Review Letters, 64 (17), 2097. 

Meleard, P., Gerbeaud, C., Pott, T., FernandezPuente, L., Bivas, L, Mitov, M.D., Dufourcq, J., and Bothorel, P. (1997) Bending elasticities of model membranes influences of temperature and sterol content. Biophysical Journal,... 

Fletcher, P.D.I. and Horsup, D.I. (1992) Droplet dynamics in water-in-oil microemulsions and macroemulsions stabilized by non-ionic surfactants - correlation of measured rates with monolayer bending elasticity. /. Chem. Soc. Faraday Trans., 88, 855-864. 

---