A procedure is developed to calculate red blood cell and phospholipid vesicle shapes within the bilayer couple model of the membrane. The membrane is assumed to consist of two laterally incompressible leaflets which are in close contact but unconnected. Shapes are determined by minimizing the membrane bending energy at a given volume of a cell (V), given average membrane area (A) and given difference of the areas of two leaflets (delta A). Different classes of shapes exist in parts of the v/delta a phase diagram, where v and delta a are the volume and the leaflet area difference relative to the sphere with area A. The limiting shapes are composed of sections of spheres with only two values allowed for their radii. Two low energy axisymmetrical classes, which include discocyte and stomatocyte shapes are studied and their phase diagrams are analyzed. For v= 0.6, the discocyte is the lowest energy shape, which transforms by decreasing delta a continuously into a stomatocyte. The spontaneous membrane curvature (C0) and compressibility of membrane leaflets can be incorporated into the model. A model, where delta A is free and C0 determines the shapes at given V and A, is also studied. In this case, by decreasing C0, a discocyte transforms discontinuously into an almost closed stomatocyte.
Abstract. Phospholipid membrane forming a closed surface and decorated with anisotropic inclusions is considered. The inclusions are free to redistribute laterally over the membrane and to orient in the plane of the membrane according to the local membrane curvature. A phenomenological expression for the energy of the interaction between an inclusion and local curvature of the surrounding membrane is proposed. Considering this single-inclusion energy, and assuming thermodynamic equilibrium, the free energy of the inclusions, and the consistently related lateral and orientational distributions of the inclusions are obtained using statistical mechanical methods. For a vesicle shape with given surface area, enclosed volume, and total amount of inclusions, the free energy is in general given in a nonlocal form (i.e. it can not be expressed as an integral of its area density over the membrane area). The limits of weak and strong orientational ordering are considered. Specifically, it is shown that in the shape sequence representing the formation of an exovesicle the effect of the membrane curvature on the orientation of the inclusions may stabilize the shape where the exovesicle and the cell are connected by a narrow neck. PACS. 05.70.Np Interface and surface thermodynamics -87.16.Dg Membranes, bilayers and vesiclesThe system considered is composed of a continuum of phospholipid molecules into which anisotropic laterally mobile molecules are embedded. It was determined that embedding a molecule into the membrane may involve several kT of energy [1]. Thus it can be expected that the embedded molecules may considerably influence the membrane free energy and also the equilibrium vesicle shape. The effect of the embedded molecules on the vesicle shape was also observed in experiments [2,3].In previous works, nonuniform lateral distribution of the embedded molecules was theoretically described by taking into account the interdependence between the local membrane curvature and the lateral density of the embedded molecules [4,5], while orientation of the anisotropic embedded molecules in the local curvature field was studied [6] by considering the area density of the embedded molecules to be uniform. In this work we present a consistent description of both, the nonuniform lateral distribution and the orientational ordering of the membrane constituents.Below we employ the term inclusion for an entity consisting of the embedded molecule and some lipids that are significantly distorted due to the presence of the embeda e-mail: vera.kralj-iglic@biofiz.mf.uni-lj.si b Present address: Dept. of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215, USA ded molecule. It is imagined that there exists a local membrane shape (and orientation) which fits the inclusion. We will refer to this shape as to the intrinsic shape of the inclusion. As the region where the configuration of the lipid molecules is significantly distorted is small with respect to the lateral membrane dimensions [7], the inclusions are fo...
Underdamped soft tunnelling modes, which disappear on deuteration, are observed in KHZP04 type crystals below Tc in addition to a central mode which exists both above and below Tc. These results can be understood in terms of a Bloch type description of pseudo‐spin motion.
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