The mechanical properties of cells influence their cellular and subcellular functions, including cell adhesion, migration, polarization, and differentiation, as well as organelle organization and trafficking inside the cytoplasm. Yet reported values of cell stiffness and viscosity vary substantially, which suggests differences in how the results of different methods are obtained or analyzed by different groups. To address this issue and illustrate the complementarity of certain approaches, here we present, analyze, and critically compare measurements obtained by means of some of the most widely used methods for cell mechanics: atomic force microscopy, magnetic twisting cytometry, particle-tracking microrheology, parallel-plate rheometry, cell monolayer rheology, and optical stretching. These measurements highlight how elastic and viscous moduli of MCF-7 breast cancer cells can vary 1,000-fold and 100-fold, respectively. We discuss the sources of these variations, including the level of applied mechanical stress, the rate of deformation, the geometry of the probe, the location probed in the cell, and the extracellular microenvironment.

Here we investigated the question whether cells, being highly heterogeneous objects, could be described with the elastic modulus (effective Young's modulus) in a self-consistent way. We performed a comparative analysis of the elastic modulus derived from the indentation data obtained with atomic force microscopy (AFM) on human cervical epithelial cells (both normal and cancerous). Both sharp (cone) and dull (2500-nm radius sphere) AFM probes were used. The indentation data were processed through different elastic models. The cell was approximated as a homogeneous elastic medium that had either 1), smooth hemispherical boundary (Hertz/Sneddon models) or 2), the boundary covered with a layer of glycocalyx and membrane protrusions ("brush" models). Consistency of these approximations was investigated. Specifically, we tested the independence of the elastic modulus of the indentation depth, which is assumed in these models. We demonstrated that only one model showed consistency in treating cells as a homogeneous elastic medium, namely, the brush model, when processing the indentation data collected with the dull AFM probe. The elastic modulus demonstrated strong depth dependence in all models: Hertz/Sneddon models (no brush taken into account), and when the brush model was applied to the data collected with sharp conical probes. We conclude that it is possible to describe the elastic properties of the cell body by means of an effective elastic modulus, used in a self-consistent way, when using the brush model to analyze data collected with a dull AFM probe. The nature of these results is discussed.

The modulus of elasticity of soft materials on the nanoscale is of interest when studying thin films, nanocomposites, and biomaterials. Two novel modes of atomic force microscopy (AFM) have been introduced recently: HarmoniX and PeakForce QNM. Both modes produce distribution maps of the elastic modulus over the sample surface. Here we investigate the question of how quantitative these maps are when studying soft materials. Three different polymers with a macroscopic Young's modulus of 0.6-0.7 GPa (polyurethanes) and 2.7 GPa (polystyrene) are analyzed using these new modes. The moduli obtained are compared to the data measured with the other commonly used techniques, dynamic mechanical analyzer (DMA), regular AFM, and nanoindenter. We show that the elastic modulus is overestimated in both the HarmoniX and PeakForce QNM modes when using regular sharp probes because of excessively overstressed material in the samples. We further demonstrate that both AFM modes can work in the linear stress-strain regime when using a relatively dull indentation probe (starting from ~210 nm). The analysis of the elasticity models to be used shows that the JKR model should be used for the samples considered here instead of the DMT model, which is currently implemented in HarmoniX and PeakForce QNM modes. Using the JKR model and ~240 nm AFM probe in the PeakForce QNM mode, we demonstrate that a quantitative mapping of the elastic modulus of polymeric materials is possible. A spatial resolution of ~50 nm and a minimum 2 to 3 nm indentation depth are achieved.

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It is of interest to measure the modulus of rigidity at small indentation depths for many systems, such as thin films, nanocomposites, biomaterials, etc. Depth-dependence of the rigidity modulus of homogeneous soft materials is broadly observed in nanoindentation experiments. Typically, the modulus reaches its bulk value only when the indentation depth becomes relatively large. Nature of this effect (we suggest to call this "skin-effect" for short) is not well understood. It is not even clear if this is a real effect or an artifact. Here we present the results of precise indentation measurements based on the use of atomic force microscopy (AFM), which suggest that the skin-effect may be an artifact. It can be eliminated, and the bulk modulus can be measured at nanometer indentations if one (a) takes into account adhesion between the indenter and surface of interest, and (b) operates mostly within the linear stress−strain regime. To demonstrate it, we used three AFM probes of well-defined geometry (radii of the apex were 22, 810, and 1030 nm) to study the indentation of three different polymers of the bulk rigidity of 0.6−0.7 GPa (polyurethanes) and 2.8 GPa (polystyrene). The obtained force−indentation curves were processed through the Oliver− Pharr, Hertz, Johnson−Kendall−Roberts (JKR) and Derjaguin−Muller−Toporov (DMT) models. We found that the skin-effect disappeared when using dull (810 and 1030 nm) probes and processing the force-deformation data with either of the adhesion models (JKR or DMT). Moreover, the measured moduli were independent of the indentation depth. The values of the rigidity modulus were very close to the bulk values starting from the indentations of 2−3 nm. Such a small indentation seems to be the smallest one for soft materials at which the bulk modulus has been reached. When using the sharp (22 nm) probe, we were not able to reach the bulk moduli up to the maximum possible indentation allowed by the instrument 90 nm. The other sources of possible error in the modulus measurements are discussed. We conclude that the skin-effect originates mainly at both nonlinearity of stress−strain relation (occurs when using excessively sharp probes) and if the probe−surface adhesion is not taken into account (like in Oliver−Pharr and Hertz models).