Cell Shape Emerges from Motion

TL;DR

The paper addresses how mobile confluent epithelial monolayers produce a broad, positively skewed shape-parameter distribution $P({\cal A})$ with ${\cal A}=p^2/(4\pi a)$. It combines automated cell segmentation with two deformable-particle models: a fixed-shape Model 1 and an adaptive-perimeter Model 2, showing that only the adaptive perimeter reproduces the observed $P({\cal A})$ across MDCK and HaCaT cells, with robust moments and a distribution well described by a shifted gamma. The key finding is that ${\cal A}$ is an emergent property of collective motion rather than a fixed input, and perimeter relaxation is a central mechanism for shaping $P({\cal A})$ in fluidized monolayers. This work links cell motility, density, and mechanical relaxation to the emergence of a characteristic, broad shape distribution, offering insights into solid-fluid transitions in tissues and guiding future explorations of tissue mechanics.

Abstract

We perform cell segmentation on images from experimental studies of confluent, mobile cells in epithelial monolayers and show that these systems possess a broad, positively-skewed shape parameter distribution $P(\mathcal{A})$, where $\mathcal{A}=p^2/4πa$, $p$ is the perimeter, and $a$ is area of each cell. $P(\mathcal{A})$ is peaked at a value higher than the typical shape parameter $\mathcal{A}^* \sim 1.15$ that occurs for randomly packed, static confluent cell monolayers. The distribution does not arise from a heterogeneous population of cells with different fixed $\mathcal{A}$, nor can it arise from cell shape fluctuations from strains below the elastic limit. Instead, we find that all cells in each monolayer sample $\mathcal{A}$ values that span the full shape parameter distribution. We develop a deformable particle model that allows cell perimeter to adapt to local forces during cell motion, and this model recovers $P(\mathcal{A})$ to within $5\%$ for both MDCK and HaCaT epithelial cell monolayers. These results emphasize that confluent epithelial monolayers of mobile cells generate a well-defined broad shape parameter distribution that is independent of the initial cell shapes.

Figures (15)

• Figure 1: (a) A segmented section of a phase contrast image of a low-density island of MDCK epithelial cells. The cyan borders mark the cell boundaries. (b) The highlighted magenta cell in (a), showing the pixels that make up the cell and the $N_v$ boundary vertices (black points) that are used to calculate the cell shape parameter $\mathcal{A}= p^2 / 4\pi a \approx 1.22$, where $p$ is the perimeter, $a$ is the area, and $l_i$ is the distance between consecutive vertices $i$ and $i+1$.
• Figure 1: Descriptions of the six datasets of epithelial cells including the cell line, imaging technique, number of images, total number of segmented cells, and average cell density of the monolayer.
• Figure 2: Probability distributions of the cell shape parameter $P(\cal{A})$ from the segmentation of low-density islands of MDCK epithelial cells using Cellpose (black solid) and Voronoi tessellations of the centers of mass of the cell masks from the segmentation (red dashed).
• Figure 2: Listing of the (left) physical quantities, (center) associated dimensionless parameters, and (right) the values that were used in the deformable particle simulations of epithelial cell monolayers for Models $1$ and $2$.
• Figure 3: (a) Three example shapes for a deformable particle with $U_{\mu,{\rm shape},0} \approx 0$ with preferred shape parameter $\mathcal{A}_0=1.15$, $N_v=8$ vertices, and bending energy $\epsilon_b=0$. The rightmost shape has an invagination. The inset describes the geometry of the particle surface, where $\vec{r}_{\mu (i-1)}$, $\vec{r}_{\mu i}$, and $\vec{r}_{\mu (i+1)}$ are the positions of the vertices $i-1$, $i$, and $i+1$ and $\theta_{\mu i}$ is the angle between the bond vectors ${\hat{l}}_{\mu i}$ and ${\hat{l}}_{\mu(i-1)}$. (b) The minimum energy configurations for single deformable particles with $\epsilon_b/(k_l\sigma^2)=10^{-3}$, where $\sigma$ is the vertex diameter, $N_v=50$, and $\mathcal{A}_0=1.15$, $1.4$, and $2$ from left to right.