Gel Phase Vesicles Buckle into Specific Shapes

International audienceOsmotic deflation of giant vesicles in the rippled gel phase P 0 gives rise to a large variety of novel faceted shapes. These shapes are also found from a numerical approach by using an elastic surface model. A shape diagram is proposed based on the model that accounts for the vesicle size and ratios of three mechanical constants: in-plane shear elasticity and compressibility (usually neglected) and out-of-plane bending of the membrane. The comparison between experimental and simulated vesicle morphologies reveals that they are governed by a typical elasticity length, of the order of 1 m, and must be described with a large Poisson's ratio. Probing the structural and mechanical properties of soft shells by noncontact techniques is a challenging approach in soft matter and in cell biology, where contacts may trigger surface and/or cell adhesion and bias results [1]. For instance, morphological changes of fluid-phase lipid vesicles under osmotic or temperature variations have been largely studied for the past 30 years. They have shown that vesicle shapes are governed by the bending energy, the spontaneous curvature of the two monolayers of the membrane [2] and by their area difference [3]. Surprisingly, very few studies have concerned the shapes of gel-phase vesicles [4-6]. In addition to the bending stiffness and the stretching elasticity, the existence in the gel state of a lipid bilayer of a nonzero shear modulus is likely to generate specific deformations and new vesicle shapes. This was indeed observed in the model of coupled bilayer cytoskeleton proposed in [7-9] for red blood cells, and in the buckling instability that occurs under large local external forces on actin-coated [10] and on gel-phase vesicles [11]. Here, we report observations of buckling induced by a nonlocal constraint on gel-phase giant uni-lamellar vesicles (GUVs, diameter >500 nm) upon deflation induced by applying an isotropic osmotic pressure. We propose a simple model that captures the major observed morphologies. The study highlights the relationship between the elastic properties of the lipid membrane and the specific faceted shapes taken by the vesicles. Deflation experiments were performed on DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) GUVs in the rippled gel phase P 0 at 15 C. GUVs were prepared by electroformation [12] above the main acyl chain crystal-lization temperature T m ¼ 23:6 C [13] in a 100 mM su-crose solution, and by slowly decreasing the temperature down to 15 C with a cooling rate of 0:05 C= min. In order to prevent the breaking of the lipid membrane at the transition, the volume of vesicles was decreased to adjust to their loss of surface area ($ 28% between the L fluid and the P 0 rippled phases [14]) by adding a controlled sucrose solution in the external solution. Gel-phase GUVs obtained with this protocol were spherical and presented no observable defects in the membrane. Finally, GUVs sedimented in an iso-osmolar glucose solution were kept at 15 C and osmotically deflated by adding controlled amounts of glucose solution of suitable concentration in the external solution. GUVs were observed by phase contrast microscopy. The obtained shapes displayed in Fig. 1 line (a) show obvious differences with the classical shapes observed on vesicles in the fluid state [15]. Subjected to the osmotic shock, gel-phase GUVs shrink and develop a large variety of morphologies, from stoma-tocytes to concave polyhedra (i.e., sphere paved with depressions). The final faceted state is reached around 40 min after the beginning of the deflation (the whole process is limited by diffusion of glucose molecules in the surrounding medium), and, thereafter, no shape modification is observed over several hours, when temperature and osmo-larity are kept constant. In order to quantitatively understand these specific shapes, we model the 2D gel-phase membrane by a surface with an in-plane Hooke elasticity [16] determined by two 2D phenomenological constants, the Young modulus Y 2D and the 2D Poisson's ratio 2D , and by an out-of-plane bending elasticity. We describe the bending contribution by the Helfrich model [2] that involves only two constants, the spontaneous curvature C 0 and the bending modulus of the membrane. An initial vesicle is considered as a spherical surface of radius R, enclosing a volume V 0. As the vesicle remains spherical during the phase transition towards the P 0 phase, we consider that the vesicle remains unstrained, which implies C 0 ¼ 2=R. Dimensional analysis reveals that three dimensionless parameters control the shape of the vesicle when its volume decreases from V 0 to PRL 108