Determination of the viscoelastic properties of a single cell cultured on a rigid support by force microscopy

Understanding the relationship between the mechanical properties of living cells and physiology is a central issue in mechanobiology. Mechanical properties are used as fingerprints of the pathological state of a single cell. The force exerted on a cell is influenced by the stiffness of the solid support needed to culture it. This effect is a consequence of the cell's boundary conditions. It causes a cell to appear with mechanical properties different from their real values. Here we develop a bottom effect viscoelastic theory to determine the viscoelastic response of a cell. The theory transforms a force-distance curve into the cell's Young's modulus, loss modulus, relaxation time or viscosity coefficient with independence of the stiffness of the rigid support. The theory predicts that, for a given indentation, the force exerted on the cell's periphery will be larger than on a perinuclear region. Results based on the use of semi-infinite contact mechanics models introduce large numerical errors in the determination of the mechanical properties. Finite element simulations confirm the theory and define its range of applicability.