Mechanobiology aims to establish functional relationships between the mechanical state of a living a cell and its physiology. The acquisition of force-distance curves with an AFM is by far the dominant method to characterize the nanomechanical properties of living cells. However, theoretical simulations have shown that the contact mechanics models used to determine the Young's modulus from a force-distance curve could be off by a factor 5 from its expected value. The semi-quantitative character arises from the lack of a theory that integrates the AFM data, a realistic viscoelastic model of a cell and its finitethickness. Here, we develop a method to determine the mechanical response of a cell from a force-distance curve. The method incorporates bottom-effect corrections, a power-law rheology model and the deformation history of the cell. It transforms the experimental data into viscoelastic parameters of the cell as a function of the indentation frequency. The quantitative agreement obtained between the experiments performed on living fibroblast cells and the analytical theory supports the use of force-distance curves to measure the nanorheological properties of cells. † Electronic supplementary information (ESI) available: Complete derivation of the analytical expressions for PLR and KV models, coefficients for a conical tip, correspondence between velocities and equivalent indentation frequencies, statistical analysis of the experiments performed on NIH 3T3 fibroblasts. See

The development of high-resolution, label-free, noninvasive, and subsurface microscopy methods of living cells remains a formidable problem. Force-microscopy-based stiffness measurements contribute to our understanding of single-cell nanomechanics. The elastic properties of the cell’s outer structures, such as the plasma membrane and actin cytoskeleton, dominate stiffness measurements, which in turns prevents the imaging of intracellular structures. We propose that the above limitation could be overcome by combining 2D sections of the cell’s viscoelastic properties. We show the simultaneous imaging of the outer cell’s cytoskeleton and the organelles inside the nucleus. The elastic component of interaction force carries information on the cell’s outer elements as the cortex and the actin cytoskeleton. The inelastic component is sensitive to the hydrodynamic drag of the inner structures such the nucleoli.

Single cell stiffness measurements consider cells as passive and elastic materials which react instantaneously to an external force. This approximation is at odds with the complex structure of the cell which includes solid and liquid components. Here we develop a force microscopy method to measure the time and frequency dependencies of the elastic modulus, the viscosity coefficient, the loss modulus and the relaxation time of a single live cell. These parameters have different time and frequency dependencies. At low modulation frequencies (0.2-4 Hz), the elastic modulus remains unchanged; the loss modulus increases while the viscosity and the relaxation time decrease. We have followed the evolution of a fibroblast cell subjected to the depolymerization of its F-actin cytoskeleton. The elastic modulus, the loss modulus and the viscous coefficient decrease with the exposure time to the depolymerization drug while the relaxation time increases. The latter effect reflects that the changes in the elastic response happen at a higher rate than those affecting the viscous flow. The observed behavior is compatible with a cell mechanical response described by the poroelastic model.

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