Showing papers by "Udo Seifert published in 1991"
TL;DR: Vesicle shapes of low energy are studied for two variants of a continuum model for the bending energy of the bilayer, which lead to different predictions for typical trajectories, such as budding trajectories or oblate-stomatocyte transitions.
Abstract: Vesicle shapes of low energy are studied for two variants of a continuum model for the bending energy of the bilayer: (i) the spontaneous-curvature model and (ii) the bilayer-coupling model, in which an additional constraint for the area difference of the two monolayers is imposed. We systematically investigate four branches of axisymmetric shapes: (i) the prolate-dumbbell shapes; (ii) the pear-shaped vesicles, which are intimately related to budding; (iii) the oblate-discocyte shapes; and (iv) the stomatocytes. These branches end up at limit shapes where either the membrane self-intersects or two (or more) shapes are connected by an infinitesimally narrow neck. The latter limit shape requires a certain condition between the curvatures of the adjacent shape and the spontaneous curvature. For both models, the phase diagram is determined, which is given by the shape of lowest bending energy for a given volume-to-area ratio and a given spontaneous curvature or area difference, respectively. The transitions between different shapes are continuous for the bilayer-coupling model, while most of the transitions are discontinuous in the spontaneous-curvature model. We introduce trajectories into these phase diagrams that correspond to a change in temperature and osmotic conditions. For the bilayer-coupling model, we find extreme sensitivity to an asymmetry in the monolayer expansivity. Both models lead to different predictions for typical trajectories, such as budding trajectories or oblate-stomatocyte transitions. Our study thus should provide the basis for an experimental test of both variants of the curvature model.
856 citations
TL;DR: In the presence of an attractive surface, a vesicle can undergo shape transformations between two different free states, between a free and a bound state, and between the two different bound states as discussed by the authors.
Abstract: In the presence of an attractive surface, a vesicle can undergo shape transformations between two different free states, between a free and a bound state, and between two different bound states. Adhesion can also lead to topological changes such as vesicle rupture and vesicle fusion. The interaction between the vesicle membrane and the surface is renormalized by thermally excited shape fluctuations. This renormalization leads to unbinding phenomena both for fluid and for polymerized (or solid-like) membranes.
169 citations
TL;DR: The adhesion of vesicles in two dimensions is studied by solving the shape equations that determine the state of lowest energy by exploiting fluctuations of their position, while large vesicle unbind via shape fluctuations.
Abstract: The adhesion of vesicles in two dimensions is studied by solving the shape equations that determine the state of lowest energy. Two ensembles are considered where for a fixed circumference of the vesicle either a pressure difference between the exterior and the interior is applied or the enclosed area is prescribed. First, a short discussion of the shape of free vesicles is given. Then, vesicles confined to a wall by an attractive potential are considered for two cases: (i) For a contact potential, a universal boundary condition determines the contact curvature as a function of the potential strength and the bending rigidity. Bound shapes are calculated, and an adhesion transition between bound and free states is found, which arises from the competition between bending and adhesion energy. (ii) For adhesion in a potential with finite range, the crossover from the long-ranged to the short-ranged case is studied. For a short-ranged potential, a decrease in the strength of the potential can lead to a shape transition between a bound state and a ``pinned'' state, where the vesicle acquires its free shape but remains pinned by the potential. In such a potential, fluctuations lead to unbinding for which two different cases are found. Small vesicles unbind via fluctuations of their position, while large vesicles unbind via shape fluctuations.
127 citations
TL;DR: The present study shows, however, that fluid vesicles can also be expected to form such shapes, which should even exhibit qualitatively new features not present for shapes of spherical topology.
Abstract: We consider fluid vesicles of toroidal topology. Minimization of the curvature energy at fixed volume and area leads to three different branches of axisymmetric shapes. By using conformal transformations, we identify a large region of nonaxisymmetric shapes in the phase diagram. For vanishing spontaneous curvature, the ground state is twofold degenerate in this region and corresponds to zero pressure difference across the membrane. The relation of these results to the recent observation of toroidal shapes for partially polymerized vesicles is discussed.
80 citations
TL;DR: In this article, the shape of a bound vesicle is determined by the interplay of bending and adhesion energies, which leads to adhesion transitions from a free to a bound Vesicle state even in the absence of shape fluctuations.
Abstract: We theoretically study (i) a large membrane segment and (ii) a closed membrane surface or vesicle that adhere to another surface. The membrane segment can undergo unbinding transitions as a result of thermally excited shape fluctuations. These transitions are studied by renormalization group methods and by Monte Carlo simulations. The shape of a bound vesicle is determined by the interplay of bending and adhesion energies. This interplay leads to adhesion transitions from a free to a bound vesicle state even in the absence of shape fluctuations. Our theory helps to clarify the notion of a contact angle for membranes.
71 citations
TL;DR: In this article, conformal transformations are used to derive an exact geometrical relation for equilibrium vesicle shapes within the spontaneous curvature and bilayer coupling models, and stability criteria with respect to these transformations efficiently detect instabilities related to the breaking of reflection symmetry.
Abstract: Conformal transformations are used to derive an exact geometrical relation for equilibrium vesicle shapes within the spontaneous curvature and bilayer coupling models. Stability criteria with respect to these transformations efficiently detect instabilities related to the breaking of reflection symmetry.
11 citations
01 Jan 1991
TL;DR: The lipid bilayer vesicle is the simplest possible model of biological membranes Nevertheless, it exhibits already a number of typical properties of cell membranes The most fascinating examples are the shape transitions and shape instabilities.
Abstract: The lipid bilayer vesicle is the simplest possible model of biological membranes Nevertheless, it exhibits already a number of typical properties of cell membranes The most fascinating examples are the shape transitions and shape instabilities It has been recognized long ago that shape transitions may be induced by changing the osmotic conditions or the temperature1 Apart from spherical and ellipsoidal shapes more exotic shapes such as e g discocytes, stomatocytes1, echinocytes2 or a necklace of small vesicles3 has recently been observed Up to now, our understanding of these shape transformations has been rather limited Indeed, all previous experiments have been performed with relatively complex systems containing, e g charged and unsaturated lipids, mixtures of different lipids or additional solutes such as sugar in the aqueous phase It was generally believed that these different ingredients play an essential role in determining the vesicle shape Therefore, no attempt has been reported so far to relate these experimentally observed shapes in a systematic way to theoretical calculations
1 citations