Fig. 3.

Number fluctuations and diffusion in cell colonies. (A) Exponent of number fluctuations ${\sigma }_N\sim N^{\beta }$ as a function of cell–cell adhesion ${\overline{W}}_c$ and CIL repolarization rate $\psi$. Phase-separated states feature giant number fluctuations ($\beta >1/2$) whose onset identifies the transition to the cohesive phase (triangles in Fig. 2). In the noncohesive phase, colonies of slowly repolarizing cells (low $\psi$) feature equilibrium-like fluctuations ($\beta \approx 1/2$), whereas faster repolarizations (higher $\psi$) induce a hyperuniform distribution of cells ($\beta <1/2$). (B) Cell diffusion coefficient $D$ as a function of $\psi$ for some values of ${\overline{W}}_c$. For increasing repolarization rate $\psi$, $D$ initially increases but then decreases as clusters form. The maximum of $D\left(\psi \right)$ identifies the onset of clustering (squares in Fig. 2). $D_{\text{free}}=F_m/(2{\gamma }_s{D}_r)$ is the translational diffusion coefficient of a persistent random walker with rotational diffusion (28).