A mechanical model is presented to analyze the mechanics and dynamics of the cell cortex during indentation. We investigate the impact of active contraction on the cross-linked actin network for different probe sizes and indentation rates. The essential molecular mechanisms of filament stretching, cross-linking and motor activity, are represented by an active and viscous mechanical continuum. The filaments behave as worm-like chains linked either by passive rigid linkers or by myosin motors. In the first example, the effects of probe size and loading rate are evaluated using the model for an idealized rounded cell shape in which properties are based on the results of parallel-plate rheometry available in the literature. Extreme cases of probe size and indentation rate are taken into account. Afterward, AFM experiments were done by engaging smooth muscle cells with both sharp and spherical probes. By inverse analysis with finite element software, our simulations mimicking the experimental conditions show the model is capable of fitting the AFM data. The results provide spatiotemporal dependence on the size and rate of the mechanical stimuli. The model captures the general features of the cell response. It characterizes the actomyosin cortex as an active solid at short timescales and as a fluid at longer timescales by showing (1) higher levels of contraction in the zones of high curvature; (2) larger indentation forces as the probe size increases; and (3) increase in the apparent modulus with the indentation depth but no dependence on the rate of the mechanical stimuli. The methodology presented in this work can be used to address and predict microstructural dependence on the force generation of living cells, which can contribute to understanding the broad spectrum of results in cell experiments.

中文翻译：

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关于细胞压痕过程中肌动球蛋白皮层的机械反应。

提出了一个力学模型来分析压痕过程中细胞皮层的力学和动力学。我们研究了主动收缩对不同探针尺寸和压痕率的交联肌动蛋白网络的影响。长丝拉伸、交联和运动活动的基本分子机制由活跃和粘性的机械连续体表示。细丝表现为蠕虫状链，由被动刚性连接器或肌球蛋白马达连接。在第一个示例中，使用理想化圆形单元形状的模型评估探针尺寸和加载速率的影响，其中属性基于文献中可用的平行板流变测量结果。考虑了探头尺寸和压痕率的极端情况。之后，AFM 实验是通过将平滑肌细胞与尖锐和球形探针结合来完成的。通过有限元软件的逆向分析，我们模拟实验条件的模拟表明该模型能够拟合 AFM 数据。结果提供了对机械刺激的大小和速率的时空依赖性。该模型捕捉细胞反应的一般特征。它通过显示 (1) 在高曲率区域的更高水平的收缩来表征肌动球蛋白皮层在短时间尺度上作为活性固体和在较长时间尺度上作为流体；(2) 随着探头尺寸的增加，压痕力也越大；(3) 表观模量随着压痕深度的增加而增加，但不依赖于机械刺激的速率。