Cytoskeletal Anisotropy Controls Geometry and Forces of Adherent Cells

We investigate the geometrical and mechanical properties of adherent cells characterized by a highly anisotropic actin cytoskeleton. Using a combination of theoretical work and experiments on micropillar arrays, we demonstrate that the shape of the cell edge is accurately described by elliptical arcs, whose eccentricity expresses the degree of anisotropy of the internal cell stresses. This results in a spatially varying tension along the cell edge, that significantly affects the traction forces exerted by the cell on the substrate. Our work highlights the strong interplay between cell mechanics and geometry and paves the way towards the reconstruction of cellular forces from geometrical data.

Figure 1

(a) A cell with an anisotropic actin cytoskeleton (epithelioid $\mathrm{GE}\beta 3$) with circles (white) fitted to its edges (green). The end points of the arcs (cyan) are identified based on the forces exerted on the pillars [31]. The actin cytoskeleton is visualized with tetramethyl isothiocyanate rhodamine phalloidin (red). Scale bar is $10\mu \mathrm{m}$. (b) The cell cortex (red line) is spanned in segments between fixed adhesion sites (blue). (c) Arc radius as a function of the sine of the angle ${\theta }_{\mathrm{SF}}-\varphi$, between the local orientation of the stress fibers and that of the distance between the adhesion points (data correspond to a sample of 285 cells and show the mean $\pm$ standard deviation).

Figure 2

(a) Schematic representation of our model for ${\theta }_{\mathrm{SF}}=\pi /2$. All cellular arcs are part of a unique ellipse of aspect ratio $a/b=\sqrt{\gamma }$. The cell exerts forces ${\mathit{F}}_0$ and ${\mathit{F}}_1$ on the adhesion sites (blue) with magnitude $\lambda ({\phi }_0)$ and $\lambda ({\phi }_1)$. (b) An epithelioid cell [$\mathrm{GE}\beta 3$; same cell as in Fig. 1] with a unique ellipse (yellow) fitted to its edges (green). The end points of the arcs (cyan) are identified based on the forces exerted on the pillars [31]. The fitted values of the ellipses’ major and minor axes are, respectively, $13.38\pm 0.04\mu \mathrm{m}$ and $9.65\pm 0.02\mu \mathrm{m}$. The major axes (yellow lines) are parallel to the stress fibers. Their orientations are found to be, in counterclockwise order from the nearly vertical ellipse in the bottom right corner, ${\theta }_{\mathrm{SF}}=93\pm 4°$, $28\pm 5°$, $110\pm 2°$, $139\pm 6°$, $127\pm 3°$, $125\pm 2°$, $133\pm 2°$, $130\pm 3°$ with respect to the horizontal axis of the image. Scale bar is $10\mu \mathrm{m}$. (c) Histogram of ${\theta }_{\text{ellipse}}-{\theta }_{\mathrm{SF}}$, with ${\theta }_{\text{ellipse}}$ the orientation of the major axis of the fitted ellipse and ${\theta }_{\mathrm{SF}}$ the measured orientation of the stress fibers. The mean of this distribution is 0° and the standard deviation is 36°.

Figure 3

(a) Enlargement of one adhesion site of the cell in the previous figures. Actin is shown in red, the cell edge in green, and the tops of the micropillars in blue. The lines represent the fitted circle (white) and ellipse (yellow). The arrows correspond to the measured forces (green) and the predicted directions (but not magnitudes) of the forces in the presence of isotropic ($\alpha =0$, white arrow) and anisotropic ($\alpha \ne 0$, yellow arrow) contractile stresses. Scale bar is $2\mu \mathrm{m}$. (b) Histogram (shown as a probability density) of ${\theta }_{\text{force}}-{\theta }_{\text{shape}}$ for isotropic (black) and anisotropic (orange) contractile stresses. Both the distributions are centered around 0°, the standard deviations are 60° and 40° for the isotropic and anisotropic models, respectively.