Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Department of Physics and Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA.
Phys Rev Lett. 2018 Jun 29;120(26):268105. doi: 10.1103/PhysRevLett.120.268105.
We study the mechanical behavior of two-dimensional cellular tissues by formulating the continuum limit of discrete vertex models based on an energy that penalizes departures from a target area A_{0} and a target perimeter P_{0} for the component cells of the tissue. As the dimensionless target shape index s_{0}=(P_{0}/sqrt[A_{0}]) is varied, we find a transition from a soft elastic regime for a compatible target perimeter and area to a stiffer nonlinear elastic regime frustrated by geometric incompatibility. We show that the ground state in the soft regime has a family of degenerate solutions associated with zero modes for the target area and perimeter. The onset of geometric incompatibility at a critical s_{0}^{c} lifts this degeneracy. The resultant energy gap leads to a nonlinear elastic response distinct from that obtained in classical elasticity models. We draw an analogy between cellular tissues and anelastic deformations in solids.
我们通过构建基于能量的离散顶点模型的连续体极限来研究二维细胞组织的力学行为，该能量对组织中各成分细胞的目标面积 A_0 和目标周长 P_0 的偏离进行惩罚。当无量纲目标形状指数 s_0=(P_0/√[A_0])变化时，我们发现从与目标周长和面积兼容的软弹性区域到由于几何不兼容性而受阻的更硬非线性弹性区域的转变。我们表明，软区域的基态具有与目标面积和周长的零模式相关的一族简并解。在临界 s_0^c 处的几何不兼容性的出现消除了这种简并性。由此产生的能隙导致与从经典弹性模型获得的不同的非线性弹性响应。我们将细胞组织与固体中的粘弹性变形进行了类比。
