论文标题
开发过程中细胞表的大弯曲变形的形态弹性
Morphoelasticity of Large Bending Deformations of Cell Sheets during Development
论文作者
论文摘要
形态发生过程中细胞表的变形是由细胞分裂和细胞形状变化等发育过程驱动的。在形态弹性的发育理论中，这些过程似乎是薄弹性壳的内在几何形状的变化。但是，形态发生通常涉及大型弯曲变形，这些变形超出了这些外壳理论的形式有效性范围。在这里，通过在薄壳的极限下渐近地扩展三维不可压缩的形态弹性，我们得出了一个壳理论，用于大型固有弯曲变形，并强调所得的几何材料各向异性和细胞收缩的弹性作用。以绿色藻类Volvox为模型发育事件的内陷，我们展示了该理论的结果与经典外壳理论的结果有何不同，该理论对于这些大型弯曲变形而无效，并揭示了这些几何效应如何稳定内置。
Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. Here, by asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we derive a shell theory for large intrinsic bending deformations and emphasise the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we show how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilise invagination.
