Free energy of closed membrane with anisotropic inclusions

Abstract

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...

Membrane Skeleton Detachment in Spherical and Cylindrical Microexovesicles

“…A boundary condition should be stated, such as a requirement for a fixed radius of the cylinder. For λ A = 0 we have chosen the cylindrical solution of equation (7) which is consistent with recent theoretical predictions (Fournier, 1996;Kralj-Iglič et al, 1999) and with experimental results indicating that anisotropic amphiphilic molecules have the capacity to induce predominantly cylindrical microexovesicles [ Fig. 1(b)].…”

“…If both of them are possible it should be distinguished which of them would be energetically more favourable. Therefore, the free energy of the budding segment under consideration (Israelachvili et al, 1976;Wiese et al, 1992;Bukman et al, 1996;Boulbitch, 1998;Kralj-Iglič et al, 1999) should be minimized, taking into account the local composition of the segment. This is, however, beyond the scope of this work.…”

“…1(b)]. Namely, it has been shown recently that the orientational ordering of anisotropic molecules embedded in the membrane may favour a thin cylindrical shape in order to minimize the membrane free energy (Fournier, 1996;Kralj-Iglič et al, 1999).…”

“…The exovesicle is spherical if the area of the budding segment A is fixed during the budding process (Iglič and Hägerstrand, 1999) and cylindrical if the area of the budding segment A increases during the budding due to the influx of the anisotropic membrane constituents (Israelachvili et al, 1976;Kralj-Iglič et al, 1999) to the region of the segment.…”

“…The redistributions of other membrane components, i.e., membrane lipids and integral membrane proteins, during the vesiculation process (Allan et al, 1976;Discher et al, 1994;Hägerstrand and Isomaa, 1994;Knowles et al, 1997) may play an important role in stabilization of the microexovesicle shape (Lipowsky, 1993;Kralj-Iglič et al, 1996;Seifert, 1997;Kralj-Iglič et al, 1999).…”