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A structure-based cellular model reveals power-law rheology and stiffening of living cells under shear stress

基于结构的细胞模型揭示了剪应力下活细胞的幂律 流变学和硬化特性

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Abstract

Shear stress plays a crucial role in many physiological processes, such as atherosclerosis, angiogenesis, and metastasis. However, how cells respond to static and dynamical shear stresses remains poorly understood. Here, we propose a structure-based cellular model, consisting of cell membrane, cytoplasm, and cytoskeleton, to explore the shear rheology of cells. By simulating the mechanical responses of a single cell under shear stress, we find that this model can reproduce both the universal power-law rheology at small deformations and stress stiffening at large deformations. Besides, the loss moduli of cells at high frequencies exhibit a stronger frequency dependence than the storage moduli. Moreover, we present two master relations: one is between the power-law exponent and cell stiffness; the other is between cell stiffness and external forces. Our results are in broad agreement with experiments. The self-similar hierarchical theory offers a physical explanation of the power-law responses of cells under shear stress. In addition, we consider the geometrical nonlinearity of single filaments to account for the stress stiffening of cells. The present model can be used to examine the effects of shear flow on living cells in physiological environments.

摘要

剪应力在许多生理过程中都起着至关重要的作用, 例如动脉粥样硬化、血管生成和肿瘤转移等. 然而, 细胞对静态和动态剪应 力的响应仍然知之甚少. 考虑细胞膜、细胞质和细胞骨架等结构特征, 本文提出了一个基于结构的细胞模型以探究细胞的剪切流变学. 通过模拟单个细胞在剪应力下的力学响应, 我们发现该模型可以再现细胞小变形时的幂律流变学和大变形时的应力硬化特性. 此外, 细胞在高频下的损耗模量表现出比存储模量更强的频率依赖性. 进而, 我们提出了两个重要关系: 一个是幂律指数和细胞刚度之间的 关系; 另一个是在细胞刚度和外力之间的关系. 我们的预测结果与很多实验结果一致. 自相似多级理论为细胞在剪应力下的幂律响应 提供了物理解释. 此外, 我们考虑了单根纤维的几何非线性, 以便解释细胞的应力硬化. 本模型可用于研究剪切流动对生理环境下活细 胞的影响.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant No. 12072252), and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Dong Liang  (梁栋), Jiu-Tao Hang  (杭久涛) & Guang-Kui Xu  (徐光魁)

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  1. Dong Liang  (梁栋)
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  2. Jiu-Tao Hang  (杭久涛)
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  3. Guang-Kui Xu  (徐光魁)
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Contributions

Dong Liang: Software, Validation, Formal analysis, Investigation, Data curation, Writing–original draft, Visualization. Jiu-Tao Hang: Conceptualization, Formal analysis, Writing–original draft, Writing–review & editing. Guang-Kui Xu: Conceptualization, Methodology, Formal analysis, Resources, Data curation, Writing–original draft, Writing–review & editing, Visualization, Project administration, Funding acquisition.

Corresponding author

Correspondence to Guang-Kui Xu  (徐光魁).

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Liang, D., Hang, JT. & Xu, GK. A structure-based cellular model reveals power-law rheology and stiffening of living cells under shear stress. Acta Mech. Sin. 39, 623129 (2023). https://doi.org/10.1007/s10409-023-23129-x

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