论文标题
在活细胞表中伸展和弯曲之间的拔河
A tug-of-war between stretching and bending in living cell sheets
论文作者
论文摘要
拉伸和弯曲变形之间的平衡表征了薄弹性板的形状过渡。在拉伸主导着张力的机械响应时,弯曲在突然的扣除过渡后的压缩中占主导地位。最近,悬浮的上皮单层悬浮的实验结果表明,由于分子电动机在厚度$ e上皮的厚度$ e $中产生的表面应力的不对称性,因此此类组织的自由边缘自发卷曲外部弯曲,从而伸展了纸板,从而伸展了平面图。这表明弯曲与拉伸之间的竞争使组织边缘的形态设定了。在这项研究中,我们使用非欧几里得板的框架将活性的预算力和自发曲率融合到薄弹性壳理论中。我们表明,当板块尺度的自发曲率(如$ 1/e $)时,拉伸和弯曲能的缩放尺寸在消失的小厚度的极限中,因此都以外部张力不断改变的方式竞争,以定义组织的三维形状。
The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness $e$ of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this study, we use the framework of non-euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like $1/e$, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.