Avalanches During Epithelial Tissue Growth; Uniform Growth and a Drosophila Eye Disc Model

Abstract

In the physicists’ perspective, epithelial tissues constitute an exotic type of active matter with non-linear properties reminiscent of amorphous materials. In the context of a circular proliferating epithelium, modeled by the quasistatic vertex model, we identify novel discrete tissue scale rearrangements, i.e. flow avalanches, which accomplish more compact tissue via cell slipping. After the onset of these avalanches, the epithelial area grows discontinuously. The avalanches are found to be stochastic, and their strength is determined by the density of cells in the tissue. Overall, avalanches regularize the spatial tension distribution along tissue. Furthermore, the avalanche distribution is found to obey a power law, with an exponent consistent with sheer induced avalanches in amorphous materials. To decipher 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 signaling and mechanistic signalling. During the third instar, the morphogenetic furrow (MF), a ~10 cell wide wave of apical area constriction propagates through the epithelium, making it a system with interesting mechanical properties. 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. The avalanches are found to depend on the strength of the apical constriction of cells in the MF, with 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, motivate in vitro explorations and serve as a guide for future simulation implementations.