The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

中文翻译：

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将细胞皮层流变学映射到组织流变学，反之亦然

生物组织的力学主要来源于细胞皮层流变学。皮层流变学和组织流变学之间的直接、明确的联系仍然缺乏，但有助于理解皮层力学的调制如何影响组织力学行为。使用基于 3D 六边形不可压缩细胞的有序几何结构，我们构建了将皮质流变学与单层组织流变学相关联的映射。我们的方法表明，组织低频弹性模量与皮层的静止张力成正比，正如液体泡沫和张拉整体结构的物理学所预期的那样。预计分数粘-收缩皮层流变学会产生高频分数式粘弹性单层流变学，最近在每个尺度上分别通过实验观察到这种分数行为。在特定情况下，映射可以反转，从而允许从给定的组织流变学中推导出潜在的皮层流变学。有趣的是，将相同的方法应用于二维六边形拼贴失败，这表明基于平面细胞皮层的模型的二维特征可能不适合解释真实的单层流变学。我们提供定量预测，通过皮层成分的标准扰动试验进行实验测试，并希望促进新的、具有挑战性的细胞单层机械实验。将相同的方法应用于 2D 六边形拼贴失败，这表明基于平面细胞皮层的模型的 2D 特征可能不适合解释实际的单层流变学。我们提供定量预测，通过皮层成分的标准扰动试验进行实验测试，并希望促进新的、具有挑战性的细胞单层机械实验。将相同的方法应用于 2D 六边形拼贴失败，这表明基于平面细胞皮层的模型的 2D 特征可能不适合解释实际的单层流变学。我们提供定量预测，通过皮层成分的标准扰动试验进行实验测试，并希望促进新的、具有挑战性的细胞单层机械实验。