Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. The model predicts that mechanical interactions can generate mesoscopic patterns within the monolayer that exhibit long-range correlations in cell shape. The model also suggests that the orientation of mechanical and geometric cues for processes such as cell division are likely to be strongly correlated in real epithelia. Some limitations of the model in capturing geometric features of Xenopus epithelial cells are highlighted.

中文翻译：

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使用基于顶点的模型关联空间无序上皮细胞的形状和机械应力。

使用流行的基于顶点的模型来描述空间无序的平面上皮单层，我们检查了细胞形状与机械应力在细胞和组织水平之间的关系。从模型的能量公式开始推导应力张量的表达式，我们表明单个细胞的应力主轴与形状主轴对齐，并且当单层在组织上各向同性时，我们确定了有效的组织总压力等级。使用不在外围应力下的单层的模拟，我们将模型的参数拟合到非洲爪蟾胚胎组织的实验数据。该模型预测机械相互作用可以在单层内生成介观模式，这些模式在细胞形状中表现出长期相关性。该模型还表明，诸如细胞分裂之类的过程的机械和几何线索的方向在真实的上皮细胞中可能密切相关。该模型在捕获非洲爪蟾上皮细胞的几何特征方面存在一些局限性。