Scaling analysis of narrow necks in curvature models of fluid lipid-bilayer vesicles (original) (raw)
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Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles
Physical Review A, 1991
According to a model introduced by Helfrich [Z. Naturforsch. 28c, 693 {1973)],the shape of a closed lipid vesicle is determined by minimization of the total bending energy at fixed surface area and enclosed volume. We show that, in the appropriate regime, this model predicts both budding (the eruption of a satellite connected to the parent volume via a neck) and vesiculation (the special case when the neck radius goes to zero). Vesiculation occurs when the minimum is located at a boundary in the space of configurations. Successive vesiculations produce multiplets, in which the minimum-energy configuration consists of several bodies coexisting through infinitesimal necks. We study the sequence of shapes and shape transitions followed by a spherical vesicle of radius Rz, large on the scale Ro set by the spontaneous curvature, as its area A increases at constant volume V =4+R&/3. Such a vesicle periodically sheds excess area into a set of smaller spheres with radii comparable to Ro. We map out this (shape) phase diagram at large volume. In this region the phase diagram is dominated by multiplets and reAects the details of the shedding process. The overall effect of successive vesiculations is to reduce the energy from a quantity of order R v down to zero or near zero when the area reaches 3 V/Ro, however, the decrease is not uniform and the energy E (A, V) is not convex. 'I'he physical origin of the spontaneous curvature under given experimental conditions is a matter of present interest and even controversy. Nonzero values of co may arise, for example, from chemical asymmetry between the interior and exterior of the membrane' or from different areas of the two leaves of the bilayer (the bilayer-couple mechanism). " Whether these mechanisms suffice to explain observed shapes is unclear. In any case, we must keep in mind that the "constant" co may depend on both microscopic (chemical) and macroscopic (geometrical) variables. In what follows, we shall study a model system in which co is taken to be constant. If under laboratory conditions co turns out to depend on the surface area A 43 6843
Budding transitions of fluid-bilayer vesicles: the effect of area-difference elasticity
Physical Review E, 1994
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~, 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 K We argue that the two contributions to the curvature energy are typically comparable in magnitude.
Budding transition for bilayer fluid vesicles with area-difference elasticity
2011
We consider a curvature model for bilayer vesicles with an area-difference elasticity or non-local bending-energy term. Such a model interpolates between the bilayer-couple and spontaneous-curvature models. We report preliminary results for the budding transition. The shape transformation between the dumbbell and the pear phases can be continuous or discontinuous depending on the ratio of the non-local to the local bending rigidities.
Spontaneous curvature of fluid vesicles induced by trans-bilayer sugar asymmetry
European Biophysics Journal, 1999
We present measurements of the effective spontaneous curvature of fluid lipid bilayers as a function of trans-bilayer asymmetry. Experiments are performed on micrometer-scale vesicles in sugar solutions with varying species across the membrane. There are two effects leading to a preferred curvature of such a vesicle. The spontaneous curvatures of the two monolayers as well as their area difference combine into an effective spontaneous curvature of the membrane. Our technique for measuring this parameter allows us to use vesicle morphology as a probe for general membrane-solute interactions affecting elasticity.
Membrane Elasticity in Giant Vesicles with Fluid Phase Coexistence
Biophysical Journal, 2005
Biological membranes are known to contain compositional heterogeneities, often termed rafts, with distinguishable composition and function, and these heterogeneities participate in vigorous transport processes. Membrane lipid phase coexistence is expected to modulate these processes through the differing mechanical properties of the bulk domains and line tension at phase boundaries. In this contribution, we compare the predictions from a shape theory derived for vesicles with fluid phase coexistence to the geometry of giant unilamellar vesicles with coexisting liquid-disordered (L d ) and liquid-ordered (L o ) phases. We find a bending modulus for the L o phase higher than that of the L d phase and a saddle-splay (Gauss) modulus difference with the Gauss modulus of the L o phase being more negative than the L d phase. The Gauss modulus critically influences membrane processes that change topology, such as vesicle fission or fusion, and could therefore be of significant biological relevance in heterogeneous membranes. Our observations of experimental vesicle geometries being modulated by Gaussian curvature moduli differences confirm the prediction by the theory of Juelicher and Lipowsky.
Curvature effects in vesicle-particle interactions
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2003
In this paper I propose a continuum model to describe the dynamics of a lipid membrane and a bead that are interacting. The bead could represent either a colloidal particle or a peripheral protein. The evolution is governed by a system of nonlinear di¬erential equations. Focusing attention on the case where the membrane is xed gives information about the forces exerted on the bead by the membrane. It turns out that the curvature and the curvature gradient of the membrane play a prominent role in the evolution of the bead, as illustrated by suitable examples.
The Effect of Variable Spontaneous Curvature on Dynamic Evolution of Two-Phase Vesicle
Journal of Advanced Chemical Engineering, 2017
This article aims to study the effect of non-uniform distribution of spontaneous curvature on shape transformation of two-phase vesicles via an evolutionary method. Their dynamic evolution is developed based on conventional Helfrich theory, considering bending of the membrane and friction in the surrounding fluid in each phase with variable spontaneous curvature. The variation of spontaneous curvature is assumed to be a function of arc length in each domain considering the effects of inducing factors (surrounding solution concentration and the membrane-protein interactions such as scaffolding and insertion). Membrane pearling from a large vesicle is simulated by the model and compared with the result of constant curvature and also with empirical observations. It can be shown that accurate simulation of some membrane deformation mechanisms depends on careful consideration of key factors such as the SC variations. In addition, the importance of different uniform and non-uniform distributions of spontaneous curvature is discussed with reference to specific cases.
Anisotropic spontaneous curvatures in lipid membranes
Symmetry restrictions due to fluidity require the strain energy in the Helfrich theory of lipid membranes to be locally isotropic in nature. Although this framework is suitable for modeling the interaction of membranes with proteins that generate spherical curvature such as clathrin, there are other important membrane-bending proteins such as BIN-amphiphysin-Rvs proteins that form a cylindrical coat with different curvatures in the longitudinal and the circumferential directions. In this work, we present a detailed mathematical treatment of the theory of lipid membranes incorporating anisotropic spontaneous curvatures. We derive the associated Euler-Lagrange equations and the edge conditions in a generalized setting that allows spatial heterogeneities in the properties of the membrane-protein system. We employ this theory to model the constriction of a membrane tubule by a cylindrical scaffold. In particular, we highlight the role of the equilibrium equation in the tangential plane in regulating the spatial variation of the surface tension field.
Physical Review E, 1995
The equilibrium shapes of fluid-phase phospholipid vesicles in an aqueous solution are controlled by bending elasticity. The regime of nonvesiculated shapes at reduced volume v) 1/v 2 involves the interplay of Bve branches of distinct stationary shapes: pears, prolates, oblates, stomatocytes, plus a branch of nonaxisymmetric shapes with the symmetry D2&. We exploit a method for calculating explicitly the stability of arbitrary axisymmetric shapes to map out in a numerically exact way both the stable phases and the metastability of the low-lying shape branches. To obtain additional required information about nonaxisymmetric shapes, we calculate these by numerical minimization of the curvature energy on a triangulated surface. Combining these two methods allows us to construct the full (shape) phase diagram and the full stability diagram in this region. We provide explicit results for values of the bending constants appropriate to stearoyl-oleoyl-phosphatidylcholine; generalization to other values is straightforward.