Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Phys Rev E. 2019 Feb;99(2-1):022411. doi: 10.1103/PhysRevE.99.022411.
The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning different surface tensions to the apical, basal, and lateral sides of the cells. These differential-tension models have been used to describe the deformations of epithelia in different living systems, but the underlying continuum mechanics at the scale of the epithelium are still unclear. Here, we derive a continuum theory for a simple differential-tension model of a two-dimensional epithelial monolayer and study the buckling of this epithelium under imposed compression. The analysis reveals how the cell-level properties encoded in the differential-tension model lead to linear and nonlinear elastic as well as nonlocal, nonelastic behavior at the continuum level.
上皮组织的形状源于组织中细胞的细胞骨架中的收缩力和细胞间的粘附力之间的复杂相互作用。许多离散的基于细胞的模型通过为细胞的顶端、基底和侧面分配不同的表面张力来描述这些力。这些差分张力模型已被用于描述不同生命系统中上皮的变形，但上皮的尺度下的潜在连续体力学仍然不清楚。在这里，我们为二维上皮单层的简单差分张力模型推导出一个连续体理论，并研究了在强制压缩下这种上皮的屈曲。分析揭示了差分张力模型中编码的细胞级特性如何导致连续体水平的线性和非线性弹性以及非局部、非弹性行为。
