The equivalence of two approaches to the variational theory of cell-membrane equilibria which have been proposed in the literature is demonstrated. Both assume a constraint on surface area, global in one formulation and local in the alternative, in accordance with measurements which reveal negligible surface dilation in the presence of membrane deformation. We thus address a potential controversy in the mathematical modeling of an important problem in biophysics.

The equations describing the behaviour of a hyperelastic dielectric under pre-existing mechanical and electrical fields are derived. The associated differential system is shown to be self-adjoint. This property, in turn, is used to establish the equivalence of linear static and dynamic stability criteria.

The goal of this work is to study the properties of living cells and cell membranes by using atomic force microscopy. During atomic force microscopy (AFM) measurement, there is a strong mechanical coupling between the AFM tip and the cell. The purpose of this paper is to present a model of the overall mechanical response of the cell that allows us to separate out the mechanical response of the cell from the local surface interactions we wish to quantify. These local interactions include recognition (or binding) events between molecules bound to an AFM tip (e.g., an antibody) and molecules or receptors on the cell surface (e.g., the respective antigen). The computational model differs from traditional Hertzian contact models by explicitly taking into account the mechanics of the biomembrane and cytoskeleton. The model also accounts for the mechanical response of the living cell during arbitrary deformation. The indentation of a bovine sperm cell is used to test the validity of this model, and further experiments are proposed to fully parameterize the model.