Cell proliferation maintains cell area polydispersity in the growing fruit fly wing epithelium

TL;DR

The paper investigates how cell proliferation and mechanical forces shape cell-area heterogeneity in a growing Drosophila wing epithelium. It combines direct measurements of size-dependent growth $\gamma(a_0)$, division $\omega(a_0)$, and mechanical noise with a minimal stochastic model linking target-area growth, division, and pressure fluctuations to observed area distributions; no fitting parameters are used. A log-normal conditional distribution $p(a|a_0)$ arising from pressure fluctuations related by $\Pi = -K \ln(a/a_0)$, integrated over the target-area distribution $p_0(a_0)$, accurately reproduces the universal normalized cell-area distribution $p(a)$ (high $R^2$ values) and predicts spatial pressure gradients consistent with experiments. The key finding is that about $85\%$ of the area variance stems from proliferation, with the remaining from mechanical fluctuations, and the framework extends to predicting tissue-scale pressure patterns and can be applied to other developing epithelia.

Abstract

Developing epithelial tissues coordinate cell proliferation and mechanical forces to achieve proper size and shape. As epithelial cells tightly adhere together to form the confluent tissue, the distribution of cell areas significantly influences possible patterns of cellular packing and thereby also the mechanics of the epithelium. Therefore, it is important to understand the origin of cell area heterogeneity in developing tissues and, if possible, how to control it. Previous models of cell growth and division have been successful in accounting for experimentally observed area distributions in cultured cells and bacterial colonies, but developing tissues present additional complexity due to self-organized patterns of mechanical stresses that guide morphogenesis. Here, we address this challenge focusing on the D. melanogaster wing disc epithelium. We consider a simple model that couples cell cycle dynamics to tissue mechanics. From time-lapse imaging of the cellular network, we extract all model parameters - cell growth rates, division rates, and mechanical fluctuations - revealing that they all depend on cell size. With these independently measured parameters, our model quantitatively reproduces the observed cell area distribution without any fitting parameters and further predicts tissue pressure gradients, in quantitative agreement with previously published data. Importantly, we find that cell proliferation accounts for 85% of cell area variance, establishing it as the dominant source of packing disorder that influences tissue mechanics and organization.

Figures (5)

• Figure 1: Cell area distribution in the Drosophila wing imaginal disc. (a) Image of the Drosophila wing disc epithelium. The yellow circle highlights the region of the wing disc analysed. The scale bar shows 100 $\mu m$. (b) Segmented cells are divided in radial bins based on their distance from the center of the tissue dye2021self, as indicated by different colors. Light gray cells are not analysed as they belong to the DV boundary region and have been shown to have different material properties dye2021self. Dark gray cells are outside the region of interest. (c) Probability density of cell areas by distance from the center, for bins of width 2 $\mu m^2$. (d) Probability density of cell area normalised by mean area within the bin, for bins of width 0.4.
• Figure 2: Quantification of cell area dynamics: growth, division and noise. (a) An example cell area trajectory over time. Dark blue line shows the normalised cell area $a(t)$. Light blue line is the one hour moving average of the cell area $a_{c,0}(t)$. (b) Normalised cell area variance in a $1\text{hr}$ moving time-window $S^2$ against the cell target area $a_0$, defined as the average cell area in the moving window. Data points show the mean values from experiments $\pm$ standard error binned by $a_0$ in bins of width 0.2. Solid line is the quadratic function $s^2(a_0)$ we use to represent the data. (c) Cell growth rate $\Gamma$ against $a_0$. Data points show the mean values from experiments $\pm$ standard error binned by $a_0$. Solid line is the linear function $\gamma(a_0)$ used to represent the data in the model. (d) Cell division rate $\Omega$ against $a_0$. Data points show the mean values from experiments $\pm$ standard error binned by $a_0$. Solid line shows the function $\omega(a_0)$. For each statistic, n=296036 data points were used, consisting of 3686 unique cells across 4 experiments.
• Figure 3: Cell area theory captures the experimental distribution. (a) Schematic showing a model cell area trajectory. The target area grows and can halve at the time of cell division for each of the daughter cells, while the actual area fluctuates about the target area. (b) Normalised target area probability density $p_0(a_0)$ against target area $a_0$ for different growth rates. (c) Conditional probability density of normalised cell area $p(a|a_0)$ given different target areas $a_0$. (d) Normalised cell area distribution $p(a)$. Dots show experimental data. The line shows the model prediction.
• Figure 4: Spatial patterns of area are captured by varying pressure. (a) Probability distribution for cell area at different radii. Dots show experimental data. Lines show model predictions. (b) Model probability for cell area across the whole wing disc. Dots show experimental data. The line shows model predictions. (c) Relative area pressure $\Pi / K$ against radius from model predictions and laser ablation experiments from Ref. dye2021self. Blue dots show the experimental data and the blue line is linear fit to the data. Shaded region corresponds to the uncertainty of the linear fit, and the dashed line is the extrapolation of the linear fit beyond the experimental range. Black dots show the model prediction.
• Figure 5: (a) Normalised cell area variance in a $1\text{hr}$ moving time-window $S^2$ against the cell target area $a_0$, defined as the average cell area in the moving window. Data points show the mean values from experiments binned by $a_0$ in bins of width 0.2. Different colors correspond to radial distances from the wing disc center. Solid line is the quadratic function $s^2(a_0)$ we use to represent the data in the main text. (b) Cell growth rate $\Gamma$ against $a_0$. Data points show the mean values from experiments binned by $a_0$. Different colors correspond to radial distances from the wing disc center. Solid line is the linear function $\gamma(a_0)$ used to represent the data in the main text. (c) Cell division rate $\Omega$ against $a_0$. Data points show the mean values from experiments binned by $a_0$. Different colors correspond to radial distances from the wing disc center. Solid line shows the function $\omega(a_0)$ we use to represent the data in the main text.