Anisotropy vs isotropy in living cell indentation with AFM

Abstract

The measurement of local mechanical properties of living cells by nano/micro indentation relies on the foundational assumption of locally isotropic cellular deformation. As a consequence of assumed isotropy, the cell membrane and underlying cytoskeleton are expected to locally deform axisymmetrically when indented by a spherical tip. Here, we directly observe the local geometry of deformation of membrane and cytoskeleton of different living adherent cells during nanoindentation with the integrated Atomic Force (AFM) and spinning disk confocal (SDC) microscope. We show that the presence of the perinuclear actin cap (apical stress fibers), such as those encountered in cells subject to physiological forces, causes a strongly non-axisymmetric membrane deformation during indentation reflecting local mechanical anisotropy. In contrast, axisymmetric membrane deformation reflecting mechanical isotropy was found in cells without actin cap: cancerous cells MDA-MB-231, which naturally lack the actin cap, and NIH 3T3 cells in which the actin cap is disrupted by latrunculin A. Careful studies were undertaken to quantify the effect of the live cell fluorescent stains on the measured mechanical properties. Using finite element computations and the numerical analysis, we explored the capability of one of the simplest anisotropic models - transverse isotropy model with three local mechanical parameters (longitudinal and transverse modulus and planar shear modulus) - to capture the observed non-axisymmetric deformation. These results help identifying which cell types are likely to exhibit non-isotropic properties, how to measure and quantify cellular deformation during AFM indentation using live cell stains and SDC, and suggest modelling guidelines to recover quantitative estimates of the mechanical properties of living cells.

Figure 1

Morphology and mechanical properties of fibroblasts and cancer cells. (a) F-actin (SiR-actin) structure in NIH 3T3 and MDA-MB-231 cells, the height is colour coded with respect to the scaling shown in the colour scale bars. Vertical cross-sections along the marked lines shows that F-actin is mostly localized in the submembranous region (CellMask staining for plasma membrane). Scale bars 10 μm in the horizontal direction and 2 μm in the vertical direction. (b) Box plots of cell height, Young’s relaxation modulus scale factor E₁, and power-law exponent α. The differences between all distributions are significant at the p < 0.001 level.

Figure 2

Correlation between perinuclear actin cap structure and mechanical properties of NIH 3T3 fibroblasts. (a) Typical distribution of actin in fibroblasts with well-developed actin cap (cap), sparse cap, and with no cap (SiR-actin staining). The height is colour coded with respect to the scaling shown in the colour scale bars. Scale bars 10 μm. (b) Box plots of cell height, Young’s relaxation modulus scale factor E₁, and power-law exponent α (Data for the cells with SiR-actin staining). The differences between all distributions except the one marked in the last panel are significant at the p < 0.01 level.

Figure 3

Deformation of single apical stress fibers in NIH 3T3 fibroblasts (a,b) causes anisotropic (non-axisymmetric) indentation profile (e,f), while isotropic indentation profile is presented in MDA-MB-231 cells (c,d,g,h). Single-plane recording experiment (protocol 2, see Supplementary Information, Section B). SiR-Actin (a–d) and CellMask (e–h) staining for F-actin and the plasma membrane, respectively. The cantilever is above the cell in (a,e,c,g); the bead indents the cell in (b,d,f,h) and its location is marked with red triangles. The perinuclear actin cap fibers located underneath the bead deformed most, going deeper out of the focal plane (b). Anisotropic deformation pattern was also observed with membrane staining as a decrease in the dye intensity along the fiber direction and an extension in the perpendicular direction (f). In MDA-MB-231 cells, isotropic deformation pattern was observed with both stainings revealing a circular indentation profile. Scale bars 10 μm.

Figure 4

Anisotropic and isotropic indentation profiles in NIH 3T3 (a–c) and MDA-MB-231 (d–f) cells, respectively. Full z-stacks were obtained before and during the hold period (protocol 1, see Supplementary Information, Section B). SiR-actin staining (a,d) reveals actin stress fiber orientation and CellMask staining (b,e) shows the membrane deformation (surface displacement profile). (a,d) Colour coded z-projections of the SiR-actin staining. (b,e) Reconstructed vertical cross-sections along the marked lines, before (top) and during (middle) indentation. (c,f) The calculated position of the membrane showing the anisotropic indentation profile in NIH 3T3 cells but not in MDA-MB-231 cells. Scale bars: 10 μm for the z-projections; 10 μm in the horizontal direction and 2 μm in the vertical direction for the cross-sections.

Figure 5

Examples of the surface displacement profiles for the different cells. The red line is the profile along the apical cap fibers and/or the main cell axis, the blue line is the profile perpendicular to it. The number near the profile is the calculated degree of anisotropy (D.A.). Surface displacement profiles for NIH 3T3 fibroblasts with a well-developed actin cap (a–c), without actin cap (d), after Latrunculin A (LatA) treatment (e) and typical for MDA-MB-231 cell (f) are presented. In (a), the microsphere used as an AFM probe is shown with green for the reference (it has an elliptical shape due to different x-y scaling), and two widths measured at half-depth for calculation of the D.A. are shown with arrows.

Figure 6

Finite element simulation of the indentation of the transversely isotropic material. (a) A schematic representation of the transversely isotropic material. Subscripts “a” and “t” are used for axial and transverse material properties respectively. Indentation axis is parallel to the plane of isotropy. (b) Vertical displacement obtained with the three-dimensional finite element model for incompressible transversely isotropic material with E_a/E_t = 100 and G_a/E_t = 4. A quarter of the geometry has been cut to show the displacement field inside the material. (c) Examples of the surface displacement profiles for material with different parameter ratios. The value of D.A. is shown near profiles. (d) The surface plot of the degree of anisotropy (D.A.) versus G_a/E_t (linear scale) and E_a/E_t (log scale) ratios. G_a/E_t ratio affects D.A. stronger than E_a/E_t ratio, while the combined effect is even more significant. The average D.A. value for the fibroblasts with actin cap fibers (2.1) is marked with the yellow plane.

Figure 7

Phenotypes of soft and stiff cells. (a) Soft cells could be characterized by higher height, low level of spreading and more viscous and mostly isotropic behaviour. (b) Stiff cells have well-developed apical stress fibers, flattened nucleus, they are highly spread and demonstrate more elastic and highly anisotropic mechanical properties.