Figure 4. Spatiotemporal dynamics of cell density during epithelial expansion.

(A) Averaged kymographs of cell density for small (left, n = 11) and large (right, n = 9) tissues. Small tissues develop a central low-density region that persist more than 20 hr. (B) Cell density, ρ, at the center of large tissues increases gradually, while cell density at the center of small tissues has non-monotonic evolution. (C) For different initial tissue sizes and densities, the evolution of the cell density, ρ, at the boundary zone converges to similar values at about 12 hr, which coincides with the end of the overshoot of edge radial velocity in Figure 1D. Center and boundary zones are defined as in Figure 2B. (D) Simulated evolution of cell densities obtained from the numerical solution of the continuity equation using the average radial velocity measurements $v_r(r,t)$ (Figure 2B) and a uniform and constant cell proliferation rate corresponding to a 16 h cell doubling time. In (B,C) the initial cell density ranges and number of replicates ${\rho }_1$, ${\rho }_2$, and ${\rho }_3$ are the same as in Figure 1D.

Figure 4—figure supplement 1. Large vortices co-occur with regions of low cell density.

A region of low cell density co-occurs with the vortex in representative small and large tissues, centered and off-centered. Representative tissues include small tissues with vortex/low density region in the center-right (A) and center (B) as well large tissues with vortex/low density region the center (C) and right-of-center (D). In both small (E) and large (F) tissues, high-vorticity large-scale flows (high values on the vertical axis) tend to occur close to the center of the tissue, and in regions of low cell density. In panels (E) and (F), marker color indicates the distance of each point relative to the center of the tissue. For data analysis details, see Methods.