Flat and sigmoidally curved contact zones in vesicle–vesicle adhesion

Abstract

Using the membrane-bending elasticity theory and a simple effective model of adhesion, we study the morphology of lipid vesicle doublets. In the weak adhesion regime, we find flat-contact axisymmetric doublets, whereas at large adhesion strengths, the vesicle aggregates are nonaxisymmetric and characterized by a sigmoidally curved, S-shaped contact zone with a single invagination and a complementary evagination on each vesicle. The sigmoid-contact doublets agree very well with the experimentally observed shapes of erythrocyte aggregates. Our results show that in identical vesicles with large to moderate surface-to-volume ratio, the sigmoid-contact shape is the only bound morphology. We also discuss the role of sigmoid contacts in the formation of multicellular aggregates such as erythrocyte rouleaux.lipid vesicle ͉ vesicle doublet ͉ sigmoid-contact doublet ͉ rouleau E lastic theory of shapes of phospholipid vesicles (1) is a very successful model. Its phase diagram, now explored in considerable detail, comprises a broad spectrum of shapes such as stomatocytes, discocytes, dumbbells, pears, torocytes, starfish, rackets, etc. (2-5). A large majority of the predicted shapes has been observed experimentally (6), and some of them correspond very closely to the different normal and abnormal forms of a mammalian erythrocyte, a simple anucleate eukaryotic cell. If the theory is extended to include the shear elasticity of the membrane skeleton, the agreement between the calculated and the actual shapes is truly striking, even in very deformed erythrocytes such as echinocytes (7).These results give hope that the approach can be extended to describe not only single vesicles but also their aggregates. With some exceptions, theoretical studies of aggregates rely on the simplest model of the intermembrane attraction where the adhesion energy is proportional to the contact area (8-10). In the first analyses of erythrocyte doublets and rouleaux, the contact zone was assumed to be flat (10-12), but at large adhesion strengths, this hypothesis was found to disagree with experiments (10); so far no explanation of the observed shapes has been available.Here we fill this gap by studying vesicle-vesicle adhesion within a fully numerical model free of all symmetry constraints, and we focus on vesicle doublets as the most elementary aggregates. Our central result is a doublet morphology with a sigmoid shape of the contact zone, which closely reproduces the large-scale features of erythrocyte doublets (10-16). In vesicles of volume and area of a human erythrocyte, this doublet is the stable shape at large enough adhesion strengths, whereas immediately beyond the aggregation threshold, a flat-contact doublet is found. We show that with increasing surface-to-volume ratio, the range of adhesion strengths corresponding to the flat-contact doublet should diminish and eventually vanish, leaving the sigmoid-contact doublet as the only stable bound morphology. These findings also provide an insight into the mechanics of aggregates of more than ...

Structure–property relationships of cell clusters in biotissues: 2D analysis

“…Simulation also indicates this phase transformation can be found in the whole volume region (0 < v < 1). Actually, similar results have been reported [17] to explain the erythrocyte stacking structures. If ω is fixed, the energy in Equation 53 has the minimum at a suitable volume.…”

“…Following the increase of v, the amplitude of the structure will increase and the period length tends to decrease. It means the cell number contained in one period is negatively related to v. Similar symmetry breaking induced by changing adhesion potential ware found between two red blood cells [17]. For fixed ω, we find there is an optimal v, at which the energy reaches its minimum.…”

“…To study the complicate adhesion system, we use the software Surface Evolver [34] which has been generally applied to simulate the equilibrium shapes of single vesicle [35,36], cell adhesion system [17], random foam [37] and droplet adhesion structure [38]. First, it needs to build an initial geometric model for the structure.…”

“…In past two decades, their theory has been generally used to investigate vesicle adhesion configurations and great progress has been achieved. It explained the adhesion shape composed by several red blood cells [17]. Deserno et al [18] developed a general geometrical framework to derive the equilibrium shape equations and boundary conditions, which makes it possible to reveal the complex structures composed by a large number of cells.…”

Topological instabilities of spherical vesicles

“…1(a)] distinguishes double bubbles from dumbbells or pear-shaped vesicles that were extensively studied in phase-separated sys tems [6]. Two adhering vesicles may look similar to a double bubble, but they have different topology because the mem brane S2 is composed of two interacting membranes [7]. Hence, when vesicles adhere there is no change in topology and the Euler characteristic [8] remains unchanged as for two single vesicles (^= 4 ), whereas a double bubble has x= 3 [9] that is neither the topology of two single vesicles nor the one of a larger sphere (^= 2 ).…”