Linear and nonlinear mechanical responses can be quite different in models for biological tissues
Linear and nonlinear mechanical responses can be quite different in models for biological tissues
复制标题
生物组织模型中的线性和非线性机械响应可能有很大不同
DOI：
10.1039/c9sm01068h
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发表时间：
2020
期刊：
影响因子：
3.4
通讯作者：
Manning, M. Lisa
中科院分区：
文献类型：
--
作者：
Sahu, Preeti;Kang, Janice;Erdemci-Tandogan, Gonca;Manning, M. Lisa
生物组织的流动性——细胞是否可以改变邻居和重新排列——对它们的功能很重要。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会表现为流体。同样，在融合生物组织的无序二维顶点模型中，当细胞可以改变邻居和组织流化时，剪切模量正好变为零，控制参数为50 * = 3.81。然而，在较低的控制参数值（3.72）下，二维顶点模型的有序基态变得线性不稳定，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地预测这些系统的非线性行为：当控制参数在3.72和3.81之间时，即使剪切模量为零，单元也不能自由地改变邻居。这些结果强调，不应期望顶点模型的线性响应一般预测其流变性。我们开发了一个简单的几何ansatz，可以正确地预测非线性响应，这可以作为在其他类顶点模型中进行非线性预测的框架。
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 s0* = 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.