4D Traction Force Microscopy Reveals Asymmetric Cortical Forces in Migrating Dictyostelium Cells

We present a 4D ($x$; $y$; $z$; $t$) force map of Dictyostelium cells crawling on a soft gel substrate. Vertical forces are of the same order as the tangential ones. The cells pull the substratum upward along the cell, medium, or substratum contact line and push it downward under the cell except for the pseudopods. We demonstrate quantitatively that the variations in the asymmetry in cortical forces correlates with the variations of the direction and speed of cell displacement.

Figure 1

(a) and (b) represent a field of fluorescent beads on the upper surface of the elastomer: (a) with a cell above and (b) without it. Note the black hole in the middle of the field (a) due to the fact that beads are pushed underneath by the cell and brought out of focus. (c) represents the measured in-plane projection of the 3D bead displacements on this particular field of view (in red [medium gray] movement of bead pointing towards the cell and in green [light gray] beads that are pushed towards the interior of the gel by the cell). (d) PIV calculation (i.e., 2D) on the same field with a window size of ($16\times 16$) pixels, and a 50% overlap between windows. (e) Upper surface bead displacement in a vertical plane along the line depicted in (c). The red line depicts the upper gel surface deformation. (f) Scheme of the cell on the gel, it deforms the substrate as a droplet would do adhering on a very soft substrate.

Figure 2

(a) In-plane projection of the 3D forces calculated from the displacement vectors of Fig. 1c. The same color convention as in Fig. 1c is used (in red [medium gray] forces pointed towards the cell and in green [light gray] forces pointed toward the gel). (b) 2D forces calculated with the PIV displacements of Fig. 1d. (c) Force profile along the blue line drawn in (a).

Figure 3

Radial stress ${\sigma }_t$ is proportional to normal stress ${\sigma }_n$. The orange line is a linear fit of the data going through zero. The slope is 0.72. The inset on the left top is a scheme of the different membrane tensions acting on the membrane on the edge of the cell. ${\sigma }_1$ is the in-plane tension. ${\sigma }_2$ is the tension in the membrane going off the substrate. $\theta$ is the angle between the two membranes.

Figure 4

(a) Temporal variations of the in-plane force asymmetry compared to temporal variations of the cell speed. (b) Unbiased power spectral density of the same data.