Quantitative evaluation of mechanical properties of cell membranes: An exact solution

Abstract

Properties of cell membranes are determined by means of a single mechanical experiment involving probing of the membrane with an atomic force microscope. The membrane is modeled as a two-dimensional medium with bending resistance whose energy has three contributions: from the strain energy of the membrane itself, from the internal pressure, and from the point load applied by the microscope. The problem is cast into a variational form and the emerging Euler-Lagrange equations are linearized and solved for the shape of the deformed cell, which can be readily compared with experimental data on the deformed shape to yield the mechanical properties of the membrane.