Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
Soft Matter. 2020 Feb 21;16(7):1850-1856. doi: 10.1039/c9sm01068h. Epub 2020 Jan 27.
The fluidity of biological tissues - whether cells can change neighbors and rearrange - is important for their function. In traditional materials, researchers have used linear response functions, such as the shear modulus, to accurately predict whether a material will behave as a fluid. Similarly, in disordered 2D vertex models for confluent biological tissues, the shear modulus becomes zero precisely when the cells can change neighbors and the tissue fluidizes, at a critical value of control parameter s* = 3.81. However, the ordered ground states of 2D vertex models become linearly unstable at a lower value of control parameter (3.72), suggesting that there may be a decoupling between linear and nonlinear response. We demonstrate that the linear response does not correctly predict the nonlinear behavior in these systems: when the control parameter is between 3.72 and 3.81, cells cannot freely change neighbors even though the shear modulus is zero. These results highlight that the linear response of vertex models should not be expected to generically predict their rheology. We develop a simple geometric ansatz that correctly predicts the nonlinear response, which may serve as a framework for making nonlinear predictions in other vertex-like models.
生物组织的流动性——即细胞是否能够改变邻居并重新排列——对于它们的功能很重要。在传统材料中，研究人员使用线性响应函数，如剪切模量，来准确预测材料是否表现为流体。同样，在连通生物组织的无序二维顶点模型中，当细胞可以改变邻居并且组织液化时，剪切模量在控制参数 s*=3.81 时恰好变为零。然而，二维顶点模型的有序基态在较低的控制参数（3.72）下变得线性不稳定，这表明线性和非线性响应之间可能存在解耦。我们证明了线性响应不能正确预测这些系统中的非线性行为：当控制参数在 3.72 和 3.81 之间时，即使剪切模量为零，细胞也不能自由改变邻居。这些结果强调了顶点模型的线性响应不应被期望普遍预测它们的流变学。我们提出了一个简单的几何假设，可以正确预测非线性响应，这可能为在其他类似顶点的模型中进行非线性预测提供一个框架。
