Living cells are known to exhibit power-law viscoelastic responses and localized stress relaxation behaviors in the frequency spectrum. However, the precise interplay between molecular-scale cytoskeletal dynamics and macroscale dynamical rheological responses remains elusive. Here, we propose a mechanism-based general theoretical model showing that cytoskeleton dissociation generates a peak in the loss modulus as a function of frequency, while the cytoplasmic viscosity promotes its recovery, producing a subsequent trough. We define two characteristic frequencies (ωc1 and ωc2) related to the dissociation rate of crosslinkers and the viscosity of the cytoplasm, where the loss modulus 1) exhibits peak and trough values for ωc1<ωc2 and 2) monotonically increases with frequency for ωc1>ωc2. Furthermore, the characteristic frequency ωc1 exhibits a biphasic stress-dependent behavior, with a local minimum at sufficiently high stress due to the stress-dependent dissociation rate. Moreover, the characteristic frequency ωc2 evolves with age, following a power-law relationship. The predictions of the dissociation-based multiscale theoretical mechanical model align well with experimental observations. Our model provides a comprehensive description of the dynamical viscoelastic behaviors of cells and cell-like materials.

中文翻译：

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活细胞缩放律流变学中局部应力松弛的特征频率


已知活细胞在频谱中表现出幂律粘弹性响应和局部应力松弛行为。然而，分子尺度的细胞骨架动力学和宏观尺度的动力学流变学反应之间的精确相互作用仍然难以捉摸。在这里，我们提出了一个基于机制的一般理论模型，表明细胞骨架解离在损耗模量中产生一个峰值，作为频率的函数，而细胞质粘度促进其恢复，产生随后的低谷。我们定义了两个特征频率（ωc1 和 ωc2），与交联剂的解离速率和细胞质的粘度有关，其中损耗模量 1） ωc1<ωc2 的峰值和谷值，2） ωc1>ωc2 的波动频率单调增加。此外，特征频率 ωc1 表现出双相应力依赖性行为，由于应力依赖性解离速率，在足够高的应力下具有局部最小值。此外，特征频率 ωc2 遵循幂律关系，随年龄的增长而变化。基于解离的多尺度理论力学模型的预测与实验观察结果非常吻合。我们的模型全面描述了细胞和细胞样材料的动力学粘弹性行为。