Vesicle shapes

Mesoscopic structures and phases vesicles and vesicle shapes, structured phases and phase behavior of amphiphilic systems. 

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). 

Dobereiner, Hans-Gtinther, Fluctuating Vesicle Shapes, 6, 149 see also Xu, Liyu, 6, 181 Petrov, Peter G.,... 

Another force [57, 58] occurs in a multilayered system, like a swollen lamellar phase of surfactant bilayers or phospholipid vesicles. Shape fluctuations in the bilayers can give rise to steric effects that are supposed to stabilise such systems where the van der Waals and double-layer forces are very weak, as they often are. The magnitude of such fluctuations depends on the "stiffness" of die bilayer. The status of these forces is the subject of an active debate and imclear. 

Peterlin, P., Svetina, S., and Zeks, B. (2000) The frequency dependence of phospholipid vesicle shapes in an external electric field. Pfluegers Archiv/ European Journal of Physiology, 439, R139-R140. 

Murphy SM, Pilowsky PM, Llewellyn-Smith IJ (1996) Vesicle shape and amino acids in synaptic inputs to phrenic motoneurons do all inputs contain either glutamate or GABA . J Comp Neurol 575 200-219. 

Deuling H, Helfrich W (1976) The curvature elasticity of fluid membranes a catalogue of vesicle shapes. J Phys (France) 37 1335-1345... 

Phase Diagram. As the surface area A is usually fixed for vesicle after its preparation, it is useful to consider an area-equivalent radius R = (A/4jr)V, which is defined vm the radius of a spherical vesicle with the same siuface area A. Using the radius R the reduced spontaneous curvature co, the reduced volume v, the reduced optimal area difference Aoo, and the effective reduced area difference Ado are introduced which are given in Table 4. Reduced quantities are convenient measures of vesicles shapes irrespective of vesicle size. 

Pig. 14. (a) Theoretical phase diagram of vesicle shapes. From Ref 3, with permission from Elsevier BV. (b) Experimentally observed vesicle shapes of PB-PEO block copolymer vesicles. From Ref 144. Lipid and block copolymer vesicles show the same structural polymorphism. 

For most bilayer systems the constant has values of a = 1. A large area difference Ado > 1 tends to curve the membrane outward, whereas a smaller or negative value leads to inward curvature or invaginated vesicle shapes. 

Polymorphism. As during vesicle preparation the number of amphiphiles in the outer and inner monolayer and thus AN is fixed for each vesicle, each vesicle carries its own value of Ado and thus its own shape. This often leads to a zoo of different vesicle shapes within the same vesicle preparation. From the definition of Aao and equation 12, it follows that... 

R/2d) 10. The pol5miorphism of vesicle shapes is quite commonly observed for large, micron-sized vesicles. 

Another problem must be taken into account in the description of the induced potential modulation. The vesicle shape is not a sphere for cells. A spheroid is a more accurate description. The effect of the field is therefore dependent on the ratio of the relative axis of the spheroid and on the orientation of the field relative to the main axis. Recent simulations predicted complex cell responses that were fairly assayed experimentally [24]. 

Nenmaim E, Kakorin S (1996) Electroptics of membrane electropraatimi and vesicle shape deformation. Curr Opin Colloid Interface 1 790-799... 

FIG. 19 Vesicle adhered to a substrate located at z = 0, A is the surface area of the whole droplet including the surface area O that is in contact with the substrate. The vesicle shape is assumed to be axisymmetric around the z-axis. 

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.)... 

Finally, we note that by using Eq. (53) and varying the parameters yo, //q, kc, and A/, a number of more complex vesicle shapes have been derived [34], and that theoretical schemes based on the pressure tensor in the interface have been worked out to derive the bending constants and kc [35,36]. 

The changes of vesicle shapes are due to temperature or pressure changes, the addition of various amphiphiles or adsorbents, mechanical, electrical or magnetic treatments, or to adhesion [14,22,23,25,47]. Temperature changes induce area/ volume differences due to the different expansion coefficients of lipid and water, as well as to the two- and three-dimensional response of the system to external stress. 

In these studies vesicle shape is influenced either by change in temperature or composition [22,29,47,48,54-57]. Similar topological changes of GUV under various physical and chemical stresses are extensively studied by Monger s group. They study hydration, adhesion, aggregation, fusion, fission, and disintegration of vesicles, which they refer to as cytomimetic supramolecular chemistry [58,59]. 

Based on the concepts of bending energy and broken sytnmetry of the two leaflets comprising the membrane, several models of vesicle shapes have been established [22,25,27-30]. 

The following is a brief introduction to fluid membrane bending elasticity. The emphasis is on some basic ideas and not on particular models or applications. The theory of vesicle shapes is treated in Chapter 7. A subject to be included in the following is non-Hookean bending elasticity, i.e. energy terms of higher than... 

Spontaneous curvature of a symmetric bilayer can also arise from differences between the aqueous media inside and outside the vesicle such as different solutes and concentrations. (Any dependence of Cq on local curvature Cj + C2 is absorbed in k). This kind of spontaneous curvature does not depend on vesicle shape and is sometimes regarded as the true spontaneous curvature. 

Giant vesicles constitute a paradigmatic soft-matter system. The characteristic interplay between energy and entropy, i.e. between deterministic forces and fluctuations that is one of the key features of soft matter, becomes visible in the microscope. Rarely in physics, are the relevant phenomena observable so directly, rather than requiring deconvolution of intricate data. Even though only a few parameters determine the state of such a vesicle, these vesicles can exhibit an amazing variety of phenomena. Therefore, their quantitative explanation becomes a real challenge because a simple model must contain and reflect this diversity. Due to the smallness of the parameter space of these systems, a fairly complete elucidation of the equilibrium properties of vesicle shapes has become possible. 

The vesicle shapes can be obtained by minimizing the appropriate curvature energy subject to the geometric constraints. Video microscopy reveals that these shapes typically exhibit thermal fluctuations. How can these fluctuations be described ... 

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