Universal Area Distributions in the Monolayers of Confluent Mammalian Cells

When mammalian cells form confluent monolayers completely filling a plane, these apparently random “tilings” show regularity in the statistics of cell areas for various types of epithelial and endothelial cells. The observed distributions are reproduced by a model which accounts for cell growth and division, with the latter treated stochastically both in terms of the sizes of the dividing cells as well as the sizes of the “newborn” ones—remarkably, the modeled and experimental distributions fit well when all free parameters are estimated directly from experiments.

Figure 1

Unpatterned and U.S. patterned cells and their traced contours. (a) Unpatterned glass slides plated with PtK1 cells. Cell nuclei were dyed blue, and cell borders were visualized using a fluorescent antibody to E-cadherin (red regions). The scale bar is $100\mu \mathrm{m}$. (b) Cell borders were traced to obtain a binary image for image processing. (c) A PtK1 confluent layer grown on a micropatterned island whose shape corresponds to the continental U.S.. The scale bar is $100\mu \mathrm{m}$. (d) The corresponding digitized image.

Figure 2

Distributions of cell areas from unpatterned monolayers on glass substrates. Markers give the probability distributions based on the experimental data (numbers of cells: $N_{\text{PtK}1}=1484$, $N_{\text{CPAE}}=1187$, $N_{\text{MDCK}}=1634$) and images of cell monolayers found in the literature ($N_{\text{CHO}}=226$, $N_{\text{MCF}10\text{A}}=190$, $N_{\text{PPAEC}}=403$). Cell areas are nondimensionalized with respect to the average area of a cell in a monolayer $A_{\text{ave}}$. The line is based on the steady-state model described in the main text with parameters derived directly from experiments (with $\mu =0.7$, $\sigma =0.5$, and nondimensionalized cell areas $A_{\max }=7.0$, $A_{\min }=0.4$, and $g=0.5{\mathrm{h}}^{-1}$).

Figure 3

Dependence of the steady-state distributions on various parameter values (a) $A_{\max }$ and (b) $A_{\min }$ defining function $B(A)$ and (c) $\mu$ and (d) $\sigma$ defining function $R(A)$. The plot in (e) has three continuous probability distributions tested for the robustness of $R(A)$. (f) All three distributions lead to very similar distributions of cell areas $p(A)$.