The response of the living cell membranes probed with Atomic Force Microscope is investigated. The general theory of fluid membranes with local bending resistance is used to obtain the equations that describe axisymmetric equilibrium states. The membrane is assumed to enclose a fluid medium, which transmits hydrostatic pressure to the membrane, and a point load is applied at the pole of the membrane to simulate an AFM probe. Both types of loading are associated with a potential and the problem is then cast in a variational setting. The equilibrium equations and boundary conditions are obtained by applying standard variational procedures, resulting in a pair of coupled fourth-order differential equations to be solved for the shape of the meridian. Further refinements associated with global constraints on the enclosed volume and contact with a rigid substrate are introduced and a solution strategy is proposed which relies on an iterative scheme for calculating the associated Lagrange multipliers. A procedure is also given for identifying material constants for the cell membrane through correlation with AFM data.
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