Avalanches during epithelial tissue growth; Uniform Growth and a drosophila eye disc model

Abstract

Epithelial tissues constitute an exotic type of active matter with non-linear properties reminiscent of amorphous materials. In the context of a proliferating epithelium, modeled by the quasistatic vertex model, we identify novel discrete tissue scale rearrangements, i.e. cellular rearrangement avalanches, which are a form of collective cell movement. During the avalanches, the vast majority of cells retain their neighbors, and the resulting cellular trajectories are radial in the periphery, a vortex in the core. After the onset of these avalanches, the epithelial area grows discontinuously. The avalanches are found to be stochastic, and their strength is correlated with the density of cells in the tissue. Overall, avalanches redistribute accumulated local spatial pressure along the tissue. Furthermore, the distribution of avalanche magnitudes is found to obey a power law, with an exponent consistent with sheer induced avalanches in amorphous materials. To understand the role of avalanches in organ development, we simulate epithelial growth of the Drosophila eye disc during the third instar using a computational model, which includes both chemical and mechanistic signaling. During the third instar, the morphogenetic furrow (MF), a ~10 cell wide wave of apical area constriction propagates through the epithelium. These simulations are used to understand the details of the growth process, the effect of the MF on the growth dynamics on the tissue scale, and to make predictions for experimental observations. The avalanches are found to depend on the strength of the apical constriction of cells in the MF, with a stronger apical constriction leading to less frequent and more pronounced avalanches. The results herein highlight the dependence of simulated tissue growth dynamics on relaxation timescales, and serve as a guide for in vitro experiments. Author summary Epithelial tissues have interesting properties. They are often described as viscoelastic materials, behaving like an elastic solid on short time scales and as a liquid on long time scales. When tissues proliferate, cell division requires the cells to rearrange and displace each other. To relieve proliferative stress, cells are equipped with machinery that allows them to respond to mechanical cues and rearrange. Herein, we perform computational simulations, based on the vertex model, to investigate epithelial growth. In our simulations, when the tissue size reaches thousands of cells, we observe the prevalence of stochastic step-like growth discontinuities. These newly identified events, which we term avalanches, involve the collective rearrangement of all cells in the tissue, and they are accompanied with localized cellular pressure redistribution and a collective net radial displacement of cells. We study their properties in the simple setting of a spatially uniform and time independent growth model and in the context of an experimentally calibrated Drosophila eye disc growth model. Utilizing the eye disc growth model, we also investigate the relationship between localized cellular mechanical deformations and global growth dynamics. We conclude that avalanches constitute a macroscopic pathway for epithelial tissues to release accumulated proliferative stress when local processes are insufficient.