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. cellular flow avalanches, which are a form of collective cell movement. During the avalanches, the cellular trajectories are radial in the periphery and form 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 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, and serve as a guide for in vitro experiments.

中文翻译：

---

上皮组织生长过程中的雪崩；均匀生长和果蝇眼盘模型

从物理学家的角度来看，上皮组织是一种奇异的活性物质，具有非线性性质，让人联想到非晶态材料。在由准静态顶点模型建模的圆形增殖上皮中，我们确定了新颖的离散组织规模重排，即细胞流动性雪崩，这是集体细胞运动的一种形式。在雪崩期间，细胞轨迹在外围呈放射状，并在核心形成涡旋。这些雪崩发作后，上皮区域不连续生长。发现雪崩是随机的，其强度取决于组织中细胞的密度。总的来说，雪崩使沿着组织的空间张力分布规则化。此外，发现雪崩分布服从幂定律，其指数与无定形材料中纯粹的雪崩现象一致。为了解释雪崩在器官发育中的作用，我们使用计算模型（包括信号传导和机制信号传导）模拟了第三龄期果蝇眼盘的上皮生长。在第三龄期，形态发生犁沟（MF），约10个细胞宽的顶端区域收缩波通过上皮传播，使其成为具有有趣机械特性的系统。这些模拟用于了解生长过程的细节，MF对组织尺度上生长动态的影响，并进行预测。发现雪崩取决于MF中细胞顶部收缩的强度，顶端收缩变强，导致雪崩的发生频率降低且更加明显。本文的结果突出了模拟的组织生长动力学对松弛时间尺度的依赖性，并用作体外实验的指南。