Dynamic shape transformations of fluid 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

Physical Review E, 1998

Physical Review Letters, 2004

The dynamics of phase separation in multi-component bilayer fluid vesicles is investigated by means of large-scale dissipative particle dynamics. The model explicitly accounts for solvent particles, thereby allowing for the very first numerical investigation of the effects of hydrodynamics and area-to-volume constraints. We observed regimes corresponding to coalescence of flat patches, budding and vesiculation, and coalescence of caps. We point out that the area-to-volume constraint has a strong influence on crossovers between these regimes. 64.75.+g, 68.05.Cf Apart from partitioning the inner and outer environments of the cell, biomembranes also act as support for complex and specialized molecular machinery, crucial for various physiological functions and trans-membrane transport . It is believed that membranes maintain inplane compositional organization that is essential for its function. Though biological membranes are very complex and can in general be far from equilibrium, knowledge of the equilibrium properties of simple model membranes will be extremely useful in providing understanding of this molecular machinery. Such a study should also be essential for developing new applications involving liposomes. This has recently resulted in a surge of theoretical and experimental investigations on domain formation in multicomponent vesicles .

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.

Life

The understanding of the shape-change dynamics leading to the budding and division of artificial cells has gained much attention in the past few decades due to an increased interest in designing stimuli-responsive synthetic systems and minimal models of biological self-reproduction. In this respect, membranes and their composition play a fundamental role in many aspects related to the stability of the vesicles: permeability, elasticity, rigidity, tunability and response to external changes. In this review, we summarise recent experimental and theoretical work dealing with shape deformation and division of (giant) vesicles made of phospholipids and/or fatty acids membranes. Following a classic approach, we divide the strategies used to destabilise the membranes into two different types, physical (osmotic stress, temperature and light) and chemical (addition of amphiphiles, the addition of reactive molecules and pH changes) even though they often act in synergy when leading to a compl...

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.

Journal of chemical theory and computation, 2014

We have developed an algorithm to determine membrane structure, area per lipid, and bending rigidity from molecular dynamics simulations of lipid vesicles. Current methods to extract structure from vesicle simulations define densities relative to the global center of mass of the vesicle. This approach ignores the long-wavelength fluctuations (undulations) that develop across the sphere and broaden the underlying structure. Our method establishes a local reference frame by defining a radially undulating reference surface (URS) and thereby removes the broadening effect of the undulations. Using an arc-length low-pass filter, we render the URS by defining the bilayer midplane on an equi-angular θ, ϕ-grid (colatitude, longitude). This surface is then expanded onto a truncated series of spherical harmonics. The spherical harmonic coefficients characterize the long-wavelength fluctuations that define both the local reference frame-used to determine the bilayer's structure-and the area...

Journal of Fluid Mechanics, 2014

When a flexible vesicle is placed in an extensional flow (planar or uniaxial), it undergoes two unique sets of shape transitions that to the best of the authors' knowledge have not been observed for droplets. At intermediate reduced volumes (i.e. intermediate particle aspect ratio) and high extension rates, the vesicle stretches into an asymmetric dumbbell separated by a long, cylindrical thread. At low reduced volumes (i.e. high particle aspect ratio), the vesicle extends symmetrically without bound, in a manner similar to the breakup of liquid droplets. During this 'burst' phase, 'pearling' occasionally occurs, where the vesicle develops a series of periodic beads in its central neck. In this paper, we describe the physical mechanisms behind these seemingly unrelated instabilities by solving the Stokes flow equations around a single, fluid-filled particle whose interfacial dynamics is governed by a Helfrich energy (i.e. the membranes are inextensible with bending resistance). By examining the linear stability of the steady-state shapes, we determine that vesicles are destabilized by curvature changes on its interface, similar to the Rayleigh-Plateau phenomenon. This result suggests that the vesicle's initial geometry plays a large role in its shape transitions under tension. The stability criteria calculated by our simulations and scaling analyses agree well with available experiments. We hope that this work will lend insight into the stretching dynamics of other types of biological particles with nearly incompressible membranes, such as cells.

Physical Review E, 1994

Under appropriate conditions fiuid lipid-bilayer vesicles in aqueous solution take the form of two (or more) compact shapes connected by a narrow neck (or necks). We study the limit {termed "vesiculation") in which the neck radius a approaches zero. On the basis of elastic equations, derived originally by Deuling and Helfrich [J. Phys. (Paris) 37, 1335 (1976)] for a bending-energy model (the spontaneouscurvature model), we show analytically that, at vesiculation, the local curvatures of the two regions joined by the neck satisfy a simple, universal "kissing" (osculation) condition. Furthermore, for points near but not at the vesiculation limit, a is small but nonzero and there is characteristic scaling behavior. For example, in the surface tension {0) and pressure (p) variables, the vesiculation boundary is a line in the (o,p) plane, and the quantity a lna scales linearly with the distance (Lcr, hp) from the boundary. These relations have been observed numerically, but no analytic discussion has previously appeared in the literature. Results for the spontaneous-curvature model generalize easily to other (more physical) bending-energy models.

Origins of Life and Evolution of Biospheres, 2004

The appearance of compartmentalization is recognized as a key step in biogenesis. The study of the dynamical behaviour of amphiphilic close membranes at equilibrium or under some external stress (osmotic pressure or dehydration process) can be useful in order to better elucidate the role of vesicles in the origin of life and to get insight into the molecular and membrane properties that bring to a spontaneous vesicle division. A Monte Carlo approach to simulate the evolution of close membranes under an external stress will be presented. This approach is mainly based on the accepted surface energy model introduced by Helfrich (1973) and Seifert (1997a). Some preliminary results will be also illustrated and possible developments and limits of this method discussed.