Fig. 4.

Dynamics and phase-separation kinetics in cell colonies. (A) MSD exponent ${(\mathrm{\Delta }\text{𝒙})}^2\sim t^{\alpha }$ as a function of cell–cell adhesion ${\overline{W}}_c$ and CIL repolarization rate $\psi$. The colony forms a gel-like network with subdiffusive dynamics ($\alpha <1$) at low $\psi$. Faster CIL gives rise to collective cell motion, indicated by almost ballistic dynamics ($\alpha =2$). (B) Evolution of the average domain size $𝔏\left(t\right)$, computed from the structure factor (SI Appendix), for different ${\overline{W}}_c$ at $\psi =1$. Dimensionless time reads $\overline{t}=F_m/(2R{\gamma }_s)t$. The colony phase separates for ${\overline{W}}_c\gtrsim 0.4$. CIL yields faster phase-separation kinetics than the diffusive coarsening dynamics of passive systems, for which $𝔏\left(t\right)\sim t^{1/3}$ (33). (C) Illustration of the phase separation from an initial random configuration toward the active polar liquid at $\psi =1$ and ${\overline{W}}_c=0.7$.