Nestor-Bergmann Alexander, Goddard Georgina, Woolner Sarah, Jensen Oliver E
School of Mathematics, University of Manchester, Manchester, UK.
Faculty of Biology, Medicine and Health, Wellcome Trust Centre for Cell-Matrix Research, University of Manchester, Manchester, UK.
Math Med Biol. 2018 Mar 16;35(suppl_1):1-27. doi: 10.1093/imammb/dqx008.
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.
使用一种流行的基于顶点的模型来描述空间无序的平面上皮单层，我们在细胞和组织水平上研究细胞形状与机械应力之间的关系。从模型的能量公式出发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，并且当单层在组织水平上各向同性时，我们确定了整体有效组织压力。通过对不受周边应力的单层进行模拟，我们将模型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产生介观模式，这些模式在细胞形状上表现出长程相关性。该模型还表明，在真实上皮组织中，诸如细胞分裂等过程的机械和几何线索的取向可能高度相关。文中突出了该模型在捕捉非洲爪蟾上皮细胞几何特征方面的一些局限性。
