We have analysed the response of cells on a bed of micro-posts idealized as a Winkler foundation using a homeostatic mechanics framework. The framework enables quantitative estimates of the stochastic response of cells along with the coupled analysis of cell spreading, contractility and mechano-sensitivity. In particular the model is shown to accurately predict that: (i) the extent of cell spreading, actin polymerisation as well as the traction forces that cells exert increase with increasing stiffness of the foundation; (ii) the traction forces that cells exert are primarily concentrated along the cell periphery; and (iii) while the total tractions increase with increasing cell area the average tractions are reasonably independent of cell area, i.e. for a given substrate stiffness, the average tractions that are normalized by cell area do not vary strongly with cell size. These results thus suggest that the increased foundation stiffness causes both the cell area and the average tractions that the cells exert to increase through higher levels of stress-fibre polymerization rather than the enhanced total tractions being directly linked through causation to the larger cell areas. A defining feature of the model is that its predictions are statistical in the form of probability distributions of observables such as the traction forces and cell area. In contrast, most existing models present solutions to specific boundary value problems where the cell morphology is imposed a priori. In particular, in line with observations we predict that the diversity of cell shapes, sizes and measured traction forces increase with increasing foundation stiffness. The homeostatic mechanics framework thus suggests that the diversity of observations in in vitro experiments is inherent to the homeostatic equilibrium of cells rather than being a result of experimental errors.

中文翻译：

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细胞对密集微柱阵列的反应

我们已经使用稳态力学框架分析了理想化为 Winkler 基础的微柱床上的细胞响应。该框架能够定量估计细胞的随机反应以及细胞扩散、收缩性和机械敏感性的耦合分析。特别地，该模型显示准确预测：(i) 细胞扩散的程度、肌动蛋白聚合以及细胞施加的牵引力随着基础刚度的增加而增加；(ii) 细胞施加的牵引力主要集中在细胞外围；(iii) 虽然总牵引力随着单元面积的增加而增加，但平均牵引力合理地独立于单元面积，即对于给定的基材刚度，按细胞面积归一化的平均牵引力不随细胞大小变化很大。因此，这些结果表明，增加的基础刚度导致细胞面积和细胞施加的平均牵引力通过更高水平的应力纤维聚合而增加，而不是通过因果关系直接与更大的细胞面积相关联的增强的总牵引力。该模型的一个定义特征是，它的预测是以可观察值的概率分布的形式进行统计的，例如牵引力和单元格面积。相比之下，大多数现有模型都针对特定的边界值问题提供了解决方案，其中细胞形态是先验的。特别是，根据观察，我们预测细胞形状的多样性，尺寸和测得的牵引力随着基础刚度的增加而增加。因此，稳态力学框架表明，体外实验中观察的多样性是细胞稳态平衡所固有的，而不是实验错误的结果。