The origin of universal cell shape variability in a confluent epithelial monolayer

TL;DR

This paper develops a mean-field analytical theory explaining the universal distribution of cell shape variability in epithelial monolayers, linking it to a single parameter and verifying it through simulations and experiments.

Contribution

The study introduces a novel theoretical framework that captures the universal cell shape variability in epithelial monolayers using a single parameter, validated by simulations and experiments.

Findings

A single parameter $oldsymbol{ extalpha}$ describes the shape variability distribution.

The shape variability follows a nearly universal distribution unrelated to jamming.

The theory links shape variability to physical conditions like maturation.

Abstract

Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works reveal that shape variability in diverse epithelial monolayers follows a nearly universal distribution. However, the origin and implications of this universality are unclear. Here, assuming contractility and adhesion are crucial for cell shape, characterized via aspect ratio (AR), we develop a mean-field analytical theory for shape variability. We find that a single parameter, $\alpha$, containing all the system-specific details, describes the probability distribution function (PDF) of AR; this leads to a universal relation between the standard deviation and the average of AR. The PDF for the scaled AR is not strictly but almost universal. The functional form is not related to jamming, contrary to common beliefs, but a consequence of a mathematical property. In addition, we obtain the scaled area distribution, described by the parameter $\mu$. We show that $\alpha$ and $\mu$ together can distinguish the effects of changing physical conditions, such as maturation, on different system properties. The theory is verified in simulations of two distinct models of epithelial monolayers and agrees well with existing experiments. We demonstrate that in a confluent monolayer, average shape determines both the shape variability and dynamics. Our results imply the cell shape variability is inevitable, where a single parameter describes both statics and dynamics and provides a framework to analyze and compare diverse epithelial systems.