We model theoretically the effect of localized forces on a fluid membrane anchored to a uniform elastic medium. We use this as a simple model for the plasma membrane of a cell. The atomic force microscope (AFM) has been used to apply such forces, but large membrane perturbations occurring in vivo are also treated within the same framework. Inclusions of this nature may include cell junctions, f...

A comparison of a number of texts, descriptive of the structure of the elastic intima-the fenestrated membrane of Henleof arteries, reveals the fact that the views concerning the structure of this layer are byno means unanimous. Schafer‘ speaks of the elastic intima as follows: “The elastic tissue is represented by one distinct lamina, which is separated from the endothelium by the subendotheli...

We analyze the structure of the Föppl-von Kármán shell equations of linear elastic shell theory using surface geometry and classical invariant theory. This equation describes the buckling of a thin shell subjected to a compressive load. In particular, we analyze the role of polarized Hessian covariant, also known as second transvectant, in linear elastic shell theory and its connection to minim...

Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation...

In this paper, we consider a new kind of obstacle problem for the elastic membrane. The is made rigid body covered by soft layer that deformable and allows penetration. It assigns reactive normal pressure, which depends on interpenetration membrane obstacle, during contact process. Three equivalent descriptions are derived, namely energy form, variational inequality form differential equation f...

While modern structural biology has provided us with a rich and diverse picture of membrane proteins, the biological function of membrane proteins is often influenced by the mechanical properties of the surrounding lipid bilayer. Here we explore the relation between the shape of membrane proteins and the cooperative function of membrane proteins induced by membrane-mediated elastic interactions...

Pseudoxanthoma Elasticum is an inherited disorder characterized by generalized fragmentation and progressive calcification of the elastic tissues in the dermis, blood vessels and Bruch’s membrane of the eye. Herein, we report 3 patients in a family with pseudoxanthoma elasticum: a father and his two sons.

We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the elastic membrane to insure that the uncoupled membrane is exactly controllable. The main result is ...

The membranes of human red blood cells (RBCs) are a composite of a fluid lipid bilayer and a triangular network of semiflexible filaments (spectrin). We perform cellular microrheology using the dynamic membrane fluctuations of the RBCs to extract the elastic moduli of this composite membrane. By applying known osmotic stresses, we measure the changes in the elastic constants under imposed strai...