Related papers: Lipid membranes with free edges
Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary…
This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the…
A cell membrane can be simply regarded as composite material consisting of lipid bilayer, membrane cytoskeleton beneath lipid bilayer, and proteins embedded in lipid bilayer and linked with membrane cytoskeleton if one only concerns its…
Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes…
Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric…
Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an…
This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact…
Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic…
Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian…
Common models for two-phase lipid bilayer membranes are based on an energy that consists of an elastic term for each lipid phase and a line energy at interfaces. Although such an energy controls only the length of interfaces, the membrane…
The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free…
Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a…
The adhesion of a lipid membrane vesicle to a fixed substrate is examined from a geometrical point of view. This vesicle is described by the Helfrich hamiltonian quadratic in mean curvature; it interacts by contact with the substrate, with…
In this article we review the present knowledge on the elastic properties of membranes of biological origin. Assuming the fluid mosaic hypothesis, we consider the phospholipid bilayer as the structural base of a biological membrane. We…
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting…
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…
We propose a continuum model to describe the molecular alignment in thin nematic shells. By contrast with previous accounts, the two-dimensional free energy, aimed at describing the physics of thin films of nematics deposited on curved…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…
The entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers are obtained by scaling analysis. It is found that the elastic free energy of the membrane has the form of the in-plane…