Imaging viscoelastic properties of live cells by AFM: power-law rheology on the nanoscale

Abstract

We developed force clamp force mapping (FCFM), an atomic force microscopy (AFM) technique for measuring the viscoelastic creep behavior of live cells with sub-micrometer spatial resolution. FCFM combines force-distance curves with an added force clamp phase during tip-sample contact. From the creep behavior measured during the force clamp phase, quantitative viscoelastic sample properties are extracted. We validate FCFM on soft polyacrylamide gels. We find that the creep behavior of living cells conforms to a power-law material model. By recording short (50-60 ms) force clamp measurements in rapid succession, we generate, for the first time, two-dimensional maps of power-law exponent and modulus scaling parameter. Although these maps reveal large spatial variations of both parameters across the cell surface, we obtain robust mean values from the several hundreds of measurements performed on each cell. Measurements on mouse embryonic fibroblasts show that the mean power-law exponents and the mean modulus scaling parameters differ greatly among individual cells, but both parameters are highly correlated: stiffer cells consistently show a smaller power-law exponent. This correlation allows us to distinguish between wild-type cells and cells that lack vinculin, a dominant protein of the focal adhesion complex, even though the mean values of viscoelastic properties between wildtype and knockout cells did not differ significantly. Therefore, FCFM spatially resolves viscoelastic sample properties and can uncover subtle mechanical signatures of proteins in living cells.

Mapping intracellular mechanics on micropatterned substrates

“…However, the cell interior is an extremely heterogeneous medium characterized by length scales varying on several orders of magnitude from the nanometer scale to the micrometer scale. As a consequence, the intracellular viscoelasticity strongly depends on the position probed within the cell cytoplasm (33)(34)(35). The spatial variations of intracellular mechanics are hidden when only cellaveraged parameters are measured, whereas they clearly contain relevant information regarding the internal organization of the cell.…”

“…Recently experiments with atomic force microscopy (AFM) (34) and AFM or magnetic twisting cytometry combined with micropatterning (37,38) have been performed but did not discriminate between the mechanical contribution of the prestressed cell cortex and that of the cell interior. In contrast, our approach isolates the contribution of the cell interior.…”

Atomic force microscopy studies on cellular elastic and viscoelastic properties

“…where υ is the Poisson ratio of cell; cells are often considered as incompressible material and thus υ=0.5 (Vargas-Pinto et al, 2013;Nijenhuis et al, 2014;Hecht et al, 2015). F is the applied loading force of AFM probe; δ is the indentation depth; E is the Young's modulus of the celll θ is the half-opening angle of the conical tip; and R is the radius of spherical tip.…”

Atomic Force Microscopy in Characterizing Cell Mechanics for Biomedical Applications: A Review

“…The histograms of mechanical parameters (e.g., Young's modulus) extracted from these force curves are then plotted. The histograms are often well fitted with the normal distribution (for symmetric histograms) [46], [54] or log-normal distribution (for non-symmetric histograms) [61]- [63]. The mean value and standard deviation are acquired from the normal/log-normal distribution fitting, which statistically quantify the different mechanical properties of cells.…”

“…The rheological parameters of cells can be extracted by fitting the stress relaxation curves with several models, such as power-law model [52]- [54] and Maxwell spring-dashpot model [55]- [57]. The formula of power-law model [53], [58] is:…”