Showing papers by "Udo Seifert published in 1994"

Budding transitions of fluid-bilayer vesicles: the effect of area-difference elasticity

Abstract: Budding and vesiculation are prominent shape transformations of fluid lipid-bilayer vesicles. We discuss these transitions within the context of a curvature model which contains two types of bending energy. In addition to the usual local curvature elasticity \ensuremath{\kappa}, we include the effect of a relative areal stretching of the two monolayers. This area-difference elasticity leads to an effective nonlocal curvature energy characterized by another parameter \ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{}. We argue that the two contributions to the curvature energy are typically comparable in magnitude. The model interpolates smoothly between the spontaneous-curvature model (\ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{}=0) and the bilayer-couple model (\ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}\ensuremath{\infty}), discussed previously in the literature. Conceptually, this model is not new; however, neither its consequences nor its relation to experiment has previously been explored in detail. In particular, budding is discontinuous (first order) for small \ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{} but changes via a tricritical point to continuous (second order) for large \ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{}. The order of the budding transition depends on both the ratio \ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{}/\ensuremath{\kappa} (which is a material parameter) and the initial area difference between the inner and outer monolayers (which can be modified by appropriate treatment of the vesicle). Estimates suggest that, under typical laboratory conditions, the budding process should be discontinuous, in apparent disagreement with some recent experiments. Possible reasons for this discrepancy are discussed. We propose, in particular, that hysteretic effects are important and that the observed behavior may reflect a spinodal instability.

Shape equations for axisymmetric vesicles : a clarification

Abstract: We derive the shape equations for axisymmetric vesicles and show that they are identical to the general shape equation [Ou-Yang Zhong-Can and W. Helfrich, Phys. Rev. A 39, 5280 (1989)] specialized to axisymmetry. We consider three different topologies (an axisymmetric membrane segment suspended between two circular rings and closed vesicles of spherical and toroidal topology.) We point out that the shape equations are independent of the variational method used.

Dynamics of a bound membrane.

Abstract: The dispersion relation for the overdamped bending modes of a membrane bound to a substrate by an attractive potential is determined. The damping rate γ as a function of the wave vector q behaves, for small q, like γ∼q2 arising from the interplay between the hydrodynamic damping by the surrounding liquid and the restoring force in the binding potential. With increasing wave vector q, various crossovers can occur, leading to the possibility of nonmonotonic damping where γ decreases with q as ∼1/q.

Relaxation modes of an adhering bilayer membrane

Abstract: We determine the relaxational dynamics of the shape fluctuations of a fluid membrane in the vicinity of a substrate. Extending the "classical" description, we include the coupling between the local shape and the difference of the two monolayer densities as well as a lateral tension in the membrane. These extensions introduce additional length scales to the problem. The asymptotic behavior of the dispersion relation and the correlation functions can be understood from limiting cases in which either a free bilayer or a bound incompressible membrane is considered. In many cases, however, the relevant length scales do not separate very well, so that the full dispersion relation will be needed for the interpretation of experiments. It is shown that in addition to the damping due to bulk viscosity the dissipation due to friction between the monolayers is observable and indeed dominates the long-time behavior of the dynamical height correlation function for large wave vectors. As demonstrated with typical sets of parameters, the transition to this regime will be accessible by optical techniques only for weak adhesion and strong friction between the monolayers.

La physique des liposomes

Abstract: Les liposomes ont acquis leur renommee surtout grâce a certains produits cosmetiques ou a leur utilisation possible pour transporter des medicaments. Mais ces minuscules vesicules bien flasques, dont la membrane est une double couche de molecules lipidiques, constituent aussi un systeme modele pour la physique des membranes fluides, voire celle des membranes biologiques. En particulier, les chercheurs s'interessent beaucoup a la morphologie des liposomes, lesquels peuvent ressembler a une poire, a un anneau, a un bouton a deux trous, passer d'une forme a l'autre, fusionner ou se scinder, etc. Comment est determinee la geometrie des liposomes, quelles sont les formes et les metamorphoses possibles, telles sont quelques-unes des questions auxquelles les physiciens ont reussi a repondre ces dernieres annees.

Hydrodynamics of a membrane bound to a substrate

Abstract: We briefly review recent theoretical work on the dynamical equilibrium shape fluctuations of membrane interaction, with a substrate. Solving the hydrodynamical equations we determine the damping rate γ(q) as a function of the wave-vector q. For small q, we find universally γ=q². In an intermediate q-range, the damping rate behaves like either γ-q 6 (monotonic damping) or γ~1/q (non-monotonic damping) depending on the relative sizes of the mean separation and the parallel correlation length, which are both determined by the adhesion potential. For large q, one recovers the behavior γ~q³ of a free membrane. A numerical solution of the dispersion relation is presented for a membrane subject to electrostatic repulsion in a linear attractive potential.