Dynamics of Traction Stress Field during Cell Division

We report a quantitative measurement of traction stress exerted by dividing eukaryotic cells. The stress field was highly dynamic and sequentially changed as follows: (1) strong and localized as two spots, (2) weak and broadly distributed, and (3) strong and localized as four spots. At the final stage of cytokinesis, the dividing cells exerted strong tensile force on the intercellular bridge. The asymmetry of the traction stress and the orientation of the division axis matched throughout the division process, suggesting the possible role of the mechanical force as a “store” of the orientational information.

Figure 1

Morphological change of a dividing Dictyostelium cell. Left: Snapshots of a dividing cell. Transmission images of a dividing Dictyostelium cell are shown. The cleavage furrow appeared around $t=-2\min$, and $t=-0.1\min$ corresponded with the instant just before cleavage furrow abscission ($t=0$ is the instant when the sister cells separate). Number indicates the time in minutes. Right: Sequential cellular outlines. The outlines of a dividing cell (the same cell appeared in the left) are drawn.

Figure 2

Traction stress during cell division. The traction stress exerted by a dividing cell was measured in a time interval of 6 sec. The stress vectors (white arrow), their amplitudes (color), and the cellular outline (white line) were plotted for every 1 min. Upper color bar indicates three phases of the dividing process (see main text): phase 0 (pro- and metaphase [11], green bar), phase 1 (meta- and anaphase, blue bar), and phase 2 (ana- and telophase, red bar). Bar: $10\mu \mathrm{m}$.

Figure 3

Quantification of traction stress dynamics. The total absolute force [(blue), colors noted from top to bottom], the absolute forces parallel (red) and perpendicular (green) to the division axis, the amplitudes of the force dipole (brown, major; yellow, minor), and the orientation of the dipole axis [(light blue), dotted line corresponds to a continuous curve; see the Supplemental Material [14]] are plotted as a function of time. Color bar indicates the three dividing phases.

Figure 4

Tug-of-war behavior. (a) Phase of traction stress vectors. The center of the stress field was detected using Eq. (3). There was one single defect in this phase space (black circle). Bar: $10\mu \mathrm{m}$. (b) Number of force center. The number was almost kept at one until completing cytokinesis. After separating, each of the two daughter cells has one force center for each; thus, the total number was two.

Figure 5

Orientational relationship between traction stress asymmetry and division axis. (a) PDF of angle difference. The PDF of the angle formed by the dipole and the division axes is shown. $N=5$ cells. (b) Orientational relationship between dipole and division axes. A scatter plot of the orientations of the dipole and the division axes is shown. (c) Model. The traction stress $|\overrightarrow{T}|$ is assumed to apply pulling force $\overrightarrow{F}$ to an imaginary spindle placed at the center of a dividing cell. (d) Effective potential of the system. The calculated effective potential $W(\varphi )$ is plotted as a function of the spindle orientation $\varphi$. Broken line indicates the real division axis orientation. We set the spindle length $2L=6\mu \mathrm{m}$.