The sensitivity of cells to alterations in the microenvironment and in particular to external mechanical stimuli is significant in many biological and physiological circumstances. In this regard, experimental assays demonstrated that, when a monolayer of cells cultured on an elastic substrate is subject to an external cyclic stretch with a sufficiently high frequency, a reorganization of actin stress fibres and focal adhesions happens in order to reach a stable equilibrium orientation, characterized by a precise angle between the cell major axis and the largest strain direction. To examine the frequency effect on the orientation dynamics, we propose a linear viscoelastic model that describes the coupled evolution of the cellular stress and the orientation angle. We find that cell orientation oscillates tending to an angle that is predicted by the minimization of a very general orthotropic elastic energy, as confirmed by a bifurcation analysis. Moreover, simulations show that the speed of convergence towards the predicted equilibrium orientation presents a changeover related to the viscous–elastic transition for viscoelastic materials. In particular, when the imposed oscillation period is lower than the characteristic turnover rate of the cytoskeleton and of adhesion molecules such as integrins, reorientation is significantly faster.

细胞对微环境变化的敏感性，特别是对外部机械刺激的敏感性，在许多生物学和生理环境中都很重要。在这方面，实验分析表明，当在弹性基质上培养的单层细胞受到足够高频率的外部循环拉伸时，肌动蛋白应力纤维和粘着斑会发生重组，以达到稳定的平衡取向，其特征在于细胞主轴和最大应变方向之间的精确角度。为了检查频率对取向动力学的影响，我们提出了一个线性粘弹性模型，该模型描述了细胞应力和取向角的耦合演化。我们发现细胞方向振荡倾向于一个角度，该角度通过非常普遍的正交各向异性弹性能量的最小化来预测，如分岔分析所证实的那样。此外，模拟表明，向预测的平衡方向收敛的速度呈现出与粘弹性材料的粘弹性转变相关的转换。特别是，当施加的振荡周期低于细胞骨架和粘附分子（如整联蛋白）的特征周转率时，重新定向明显更快。模拟表明，向预测的平衡方向收敛的速度呈现出与粘弹性材料的粘弹性转变相关的转换。特别是，当施加的振荡周期低于细胞骨架和粘附分子（如整联蛋白）的特征周转率时，重新定向明显更快。模拟表明，向预测的平衡方向收敛的速度呈现出与粘弹性材料的粘弹性转变相关的转换。特别是，当施加的振荡周期低于细胞骨架和粘附分子（如整联蛋白）的特征周转率时，重新定向明显更快。