Technion - Israel Institute of Technology, Haifa, 32000, Israel.
Soft Matter. 2020 Dec 28;16(48):10781-10808. doi: 10.1039/d0sm01451f. Epub 2020 Dec 8.
We review continuum elastic models for the transmission of both external forces and internal active cellular forces in biopolymer gels, and relate them to recent experiments. Rather than being exhaustive, we focus on continuum elastic models for small affine deformations and intend to provide a systematic continuum method and some analytical perspectives on the study of force transmission in biopolymer gels. We start from a very brief review of the nonlinear mechanics of individual biopolymers and a summary of constitutive models for the nonlinear elasticity of biopolymer gels. We next show that the simple 3-chain model can give predictions that fit well the shear experiments of some biopolymer gels, including the effects of strain-stiffening and negative normal stress. We then review continuum models for the transmission of internal active forces that are induced by a spherically contracting cell embedded in a three-dimensional biopolymer gel. Various scaling regimes for the decay of cell-induced displacements are identified for linear isotropic and anisotropic materials, and for biopolymer gels with nonlinear compressive-softening and strain-stiffening elasticity, respectively. After that, we present (using an energetic approach) the generic and unified continuum theory proposed in [D. Ben-Yaakov et al., Soft Matter, 2015, 11, 1412] about how the transmission of forces in the biogel matrix can mediate long-range interactions between cells with mechanical homeostasis. We show the predictions of the theory in a special hexagonal multicellular array, and relate them to recent experiments. Finally, we conclude this paper with comments on the limitations and outlook of continuum modeling, and highlight the need for complementary theoretical approaches, such as discrete network simulations, to force transmission in biopolymer gels and phenomenological active gel theories for multicellular systems.
我们回顾了生物聚合物凝胶中外部力和内部活性细胞力传递的连续弹性模型，并将它们与最近的实验联系起来。我们不是面面俱到，而是专注于小仿射变形的连续弹性模型，并旨在为生物聚合物凝胶中力传递的研究提供一种系统的连续方法和一些分析视角。我们从单个生物聚合物的非线性力学的简要回顾和生物聚合物凝胶非线性弹性的本构模型的总结开始。接下来，我们展示了简单的 3 链模型可以给出与某些生物聚合物凝胶的剪切实验吻合良好的预测，包括应变硬化和负法向应力的影响。然后，我们回顾了用于传递由嵌入三维生物聚合物凝胶中的球形收缩细胞引起的内部主动力的连续体模型。对于线性各向同性和各向异性材料，以及具有非线性压缩软化和应变硬化弹性的生物聚合物凝胶，分别确定了细胞诱导位移衰减的各种比例规则。之后，我们使用能量方法介绍了 [D. Ben-Yaakov 等人，Soft Matter，2015，11，1412] 中提出的关于生物凝胶基质中力传递如何介导具有机械稳态的细胞之间长程相互作用的通用和统一连续体理论。我们在特殊的六边形多细胞阵列中展示了该理论的预测，并将其与最近的实验联系起来。最后，我们以对连续体建模的局限性和展望的评论结束本文，并强调需要互补的理论方法，如离散网络模拟，以研究生物聚合物凝胶中的力传递和多细胞系统的现象学活性凝胶理论。
