Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy.

Viscoelasticity of the leading edge, i.e., the lamellipodium, of a cell is the key property for a deeper understanding of the active extension of a cell's leading edge. The fact that the lamellipodium of a cell is very thin (<1000 nm) imparts special challenges for accurate measurements of its viscoelastic behavior. It requires addressing strong substrate effects and comparatively high stresses (>1 kPa) on thin samples. We present the method for an atomic force microscopy-based microrheology that allows us to fully quantify the viscoelastic constants (elastic storage modulus, viscous loss modulus, and the Poisson ratio) of thin areas of a cell (<1000 nm) as well as those of thick areas. We account for substrate effects by applying two different models-a model for well-adhered regions (Chen model) and a model for nonadhered regions (Tu model). This method also provides detailed information about the adhered regions of a cell. The very thin regions relatively near the edge of NIH 3T3 fibroblasts can be identified by the Chen model as strongly adherent with an elastic strength of approximately 1.6 +/- 0.2 kPa and with an experimentally determined Poisson ratio of approximately 0.4 to 0.5. Further from the edge of these cells, the adherence decreases, and the Tu model is effective in evaluating its elastic strength ( approximately 0.6 +/- 0.1 kPa). Thus, our AFM-based microrheology allows us to correlate two key parameters of cell motility by relating elastic strength and the Poisson ratio to the adhesive state of a cell. This frequency-dependent measurement allows for the decomposition of the elastic modulus into loss and storage modulus. Applying this decomposition and Tu's and Chen's finite depth models allow us to obtain viscoelastic signatures in a frequency range from 50 to 300 Hz, showing a rubber plateau-like behavior.

Friction and fracture.

Consider a block placed on a table and pushed sideways until it begins to slide. Amontons and Coulomb found that the force required to initiate sliding is proportional to the weight of the block (the constant of proportionality being the static coefficient of friction), but independent of the area of contact. This is commonly explained by asserting that, owing to the presence of asperities on the two surfaces, the actual area in physical contact is much smaller than it seems, and grows in proportion to the applied compressive force. Here we present an alternative picture of the static friction coefficient, which starts with an atomic description of surfaces in contact and then employs a multiscale analysis technique to describe how sliding occurs for large objects. We demonstrate the existence of self-healing cracks that have been postulated to solve geophysical paradoxes about heat generated by earthquakes, and we show that, when such cracks are present at the atomic scale, they result in solids that slip in accord with Coulomb's law of friction. We expect that this mechanism for friction will be found to operate at many length scales, and that our approach for connecting atomic and continuum descriptions will enable more realistic first-principles calculations of friction coefficients.