Fig. 3.

Scaling properties of the Keller–Segel instability with one morphogen. (A) Schematic of the Keller–Segel instability in a 1D tissue. Morphogen gradients generate cell volume fraction gradients (via local fluid exchanges, blue arrows in Inset), which in return cause mechanically induced self-amplifying extracellular flows that advect morphogens from morphogen-poor to morphogen-rich regions (green arrow). (B) Normalized pattern size as a function of system size in the single-morphogen case with $f=0$. (C) Morphogen concentration and cell packing fraction (Inset) profiles remain quasi-stationary as system size increases. Parameters are ${\chi }_A=0.25$, $D_m/D=10$, and ${\varphi }^{*}=0.85$.