Vesicles unbinding

Deme, B., Dubois, M., Gulik-Krzywicki, T. and Zemb, Th. (2002) Giant collective fluctuations of charged membranes at the lamellar-to-vesicle unbinding transition. 1. Characterisation of a new lipid morphology by SANS, SAXS, and electron microscopy. Fangmuir, 18, 997-1004. 

FIG. 21 Schematic phase diagram for the vesicle unbinding transition (thick solid lines and thick dashed line) as calculated by Seifert and Lipowsky [47,48] as a function of the reduced volume, v, and reduced substrate adhesion energy, w. In the solid region, nonaxisymmetric vesicle shapes are relevant. The soUd lines are shape transitions of the vesicle within the bound or unbound region. (See Ref. 48 for further details.)... 

One can now also investigate other ensembles for the single vesicle adhered to a substrate such as the ensemble in which besides the volume also the surface area A is kept constant. As we discussed previously, this is the ensemble for which Seifert and Lipowsky constructed their phase diagrams of the vesicle unbinding transition. Another ensemble one might wish to consider is the constant pressure ensemble, for which Q is the appropriate free energy, in which instead of the vesicle volume the Laplace pressure difference Ap is... 

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-... 

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). 

Evans, E. (1991) Entropy-driven tension in veside membranes and unbinding of adherent vesicles. Langmuir, 7 (9), 1900-1908. 

Fig. 7 Predictions for continuous unbinding of multilamellar vesicles that have an underlying exponential repulsion = PqX I h = 10. See text for definition of other variables. Adapted from Evans [33]...

Seifert and Lipowsky [47,48] were the first to apply the Helfrich free energy for the description of the shape and free energy of such systems adhered to a solid substrate (see Fig. 19). In their analysis they calculated the phase diagram for the unbinding of a vesicle adsorbed to a substrate. In this section, we discuss the analysis by Seifert and Lipowsky [47]. First, we introduce the expression for the curvature free energy by Helfrich and derive the shape equations that minimize the Helfrich free energy for a vesicle in contact with a solid substrate. Since these shape equations cannot, in general, be solved... 

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