Random Traction Yielding Transition in Epithelial Tissues

We investigate how randomly oriented cell traction forces lead to fluidization in a vertex model of epithelial tissues. We find that the fluidization occurs at a critical value of the traction force magnitude $F_c$. We show that this transition exhibits critical behavior, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidization mechanism through active force generation that could be relevant in biological tissues.

Figure 1

(a) Spherical vertex model tissue with $N=200$ cells with randomly oriented traction forces (red arrows). (b) Traction force is generated by extending a spring of stiffness $\kappa$ at speed $v$ in direction of the polarity ${\mathit{p}}_{\alpha }$. (c) Example of the tissue traction force magnitude dynamics $F$ as a function of spring displacement $vt$. (d) Dynamics of ensemble-averaged tissue traction force magnitude. As the spring extension speed $v$ approaches the quasistatic driving limit $v\to 0$, the traction force magnitude averaged over ensemble realisations $⟨F⟩$ converges to its critical value $F_c$ marked by the dashed line (see SM [37]).

Figure 2

Avalanche statistics. (a) Avalanche size has a power-law distribution $P(S)\sim S^{-\tau }$, with exponent $\tau =1.35\pm 0.11$. (b) Avalanche duration $T$ scales with avalanche size $S$ with exponent $z/d_f=0.68\pm 0.04$.

Figure 3

Density of plastic excitations in the tissue. (a) Additional tension $\mathrm{\Delta }f$ required to collapse the bond as a function of bond length $\ell$. A linear scaling is observed (solid line). (b) Cumulative bond length distribution $C(\ell )$ in the steady state for $v=2\times {10}^{-4}$. The predicted value of the exponent $\theta \approx 0.32$ is indicated by the solid line. At low $\ell$ we observe a linear scaling of $C(\ell )$ (dashed line), corresponding to a constant bond length distribution, as expected at finite $v$ and for finite system sizes.

Figure 4

Steady-state flow curve measured in spherical vertex model networks with $N=100$ (blue squares) and $N=200$ (orange circles). Curves show best fit to $v\sim (⟨F⟩-F_c{)}^{1.41}$ for $N=100$ (dashed line) and $N=200$ (solid line); see SM [37] for discussion of $F_c$ finite-size scaling.