Bilayer bending

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... 

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. 

Under osmotic stress, the aqueous compartment shrinks and the mono-layer around the water cylinder bends. The osmotic work can be translated into monolayer- and bilayer-bending moduli (7) to yield a bilayer value of about 1.5 X 10 12 erg, which is in qualitative agreement with measurements from bilayer mechanics (38). It is possible to refine the analysis of Hn dehydration to include the change in area per lipid molecule and to extract both a bending modulus and a lateral compressibility moduli. This refinement gives moduli in close quantitative agreement with other measures of mechanical deformation (39). 

FIGURE 8.82 Cyclic voltammetry at 5 mV/s for a 3 p.m thick film showing potential (top), current (upper middle), and film thickness (lower middle). Bilayer bending (bottom) at 2 mV/s is shown for comparison (the timescale is therefore 5/2 longer), (a) First reduction cycle, (b) Third reduction cycle. The currents have been corrected to reflect only that from the PPy by subtracting the current drawn by a bare gold reference surface. (From Smela, E., and Gadegaard, N., Adv. Mater., 11, 953, 1999. With permission.)... 

Alben, S., Balakrisnan, B. Smela, E. Edge effects determine the direction of bilayer bending. Nano Lett. 2011,11, 2280-2285. 

This section concludes with a few words on bilayers that are asymmetric because their monolayers consist of different molecules. In such cases a reasonable choice of the bilayer bending surface may be the middle between the monolayer bending surfaces. It ensures that bilayer bending without stretching conserves the sum of the monolayer bending surface areas for arbitrary cylindrical curvature. The bending rigidity and the spontaneous curvature of the bilayer may be expected to obey... 

Any dilation of the bilayer bending surface due to Gaussian curvature is proportional to C C2 and therefore does not affect Hookean elasticity. Substituting (z - z ) +Zj, for z in eq. (30) leads to... 

The same primitive model using no more than two of the five relevant fourth-order invariants listed above seems to be sufficient to understand both graininess and knotted sticks. Its bilayer bending energy density is expressed by... 

The last experimental study presents some recent experiments on the deformation of giant vesicles induced by electric fields. These observations represent the first part of a work to study the electric interaction with lipid bilayers, as a function of the frequency of the applied electric field (from 100 Hz to 10 kHz). This paper, focuses on the low frequency regime (< 1 kHz) when pure water can be considered as a conductive medium while the membrane is an insulator. The observed large shape changes of giant vesicles are related to their bilayer bending properties. 

Fig. 36.2 Scheme of the movement of an artificial muscle formed by a polypyrrole film/nonconducting plastic tape bilayer during current flow, starting from the vertical position. The flow of cathodic current through the conducting film promotes its reduction accompanied by the expulsion of counterions and water. The polypyrrole shrinks, and the bilayer bends to the left. The opposite processes and movements occur during oxidation. 

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