Scaling-laws are ubiquitous as universal physical principles in physics, biological systems, and human behavior. The scaling-law rheological responses of viscoelastic and plastic deformations and rate-dependent softening and stiffening during dynamic loading are remarkable characteristics of living cells and cell-like materials; however, the underlying mechanisms remain poorly understood. Here, we first propose a cellular structural model with 3-dimensional anisotropic discrete and plastic cytoskeletal networks to study the scaling-law rheological responses of cells. Besides the scaling-law invariance observed in cellular plastic deformation and viscoelastic deformation under large force ranges, there is evidence of scaling-law variance under relatively small force ranges. We develop a minimal mechanical model to elucidate the origins of scaling-law variance and invariance of cellular viscoelastic and plastic deformations. Interestingly, we find that cell materials can transition from fluid to solid over time and from elasticity to plasticity with increasing force. Furthermore, it is shown that the heterogeneity of three-dimensional cytoskeletal network dominates the anisotropic viscoplastic behavior of cells. We show that the stress-strain curves of cells with plastic cytoskeletons can be collapsed onto a single master curve of cells with elastic cytoskeletons. Moreover, we discover and derive a novel scaling-law wherein the extent of force relaxation on cells during cyclical mechanical stimuli follows the same power-law dependence on the loading rate, as creep compliance on time. Our findings provide evidence that structure-based simulation and theoretical models can naturally capture the scaling-law invariance and variance of cellular deformations, in agreement with many experimental findings.

中文翻译：

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细胞可塑性的标度律方差和不变性

标度定律作为物理学、生物系统和人类行为中的普遍物理原理无处不在。动态加载过程中粘弹性和塑性变形的比例律流变响应以及速率相关的软化和硬化是活细胞和类细胞材料的显着特征；然而，其根本机制仍然知之甚少。在这里，我们首先提出了一种具有 3 维各向异性离散和塑料细胞骨架网络的细胞结构模型，以研究细胞的标度律流变响应。除了在大力范围下在细胞塑性变形和粘弹性变形中观察到的标度律不变性之外，还有在相对较小的力范围下标度律方差的证据。我们开发了一个最小力学模型来阐明尺度定律方差和细胞粘弹性和塑性变形不变性的起源。有趣的是，我们发现细胞材料可以随着时间的推移从流体转变为固体，并随着力的增加从弹性转变为可塑性。此外，研究表明三维细胞骨架网络的异质性主导着细胞的各向异性粘塑性行为。我们表明，具有塑性细胞骨架的细胞的应力-应变曲线可以折叠到具有弹性细胞骨架的细胞的单个主曲线上。此外，我们发现并推导了一种新的标度律，其中循环机械刺激期间细胞上的力松弛程度遵循与蠕变顺应性对时间相同的幂律依赖于加载速率。我们的研究结果提供了证据，表明基于结构的模拟和理论模型可以自然地捕获细胞变形的标度律不变性和方差，这与许多实验结果一致。