This work is motivated by experimental observations that cells on stretched substrate exhibit different responses to static and dynamic loads. A model of focal adhesion that can consider the mechanics of stress fiber, adhesion bonds, and substrate was developed at the molecular level by treating the focal adhesion as an adhesion cluster. The stability of the cluster under dynamic load was studied by applying cyclic external strain on the substrate. We show that a threshold value of external strain amplitude exists beyond which the adhesion cluster disrupts quickly. In addition, our results show that the adhesion cluster is prone to losing stability under high-frequency loading, because the receptors and ligands cannot get enough contact time to form bonds due to the high-speed deformation of the substrate. At the same time, the viscoelastic stress fiber becomes rigid at high frequency, which leads to significant deformation of the bonds. Furthermore, we find that the stiffness and relaxation time of stress fibers play important roles in the stability of the adhesion cluster. The essence of this work is to connect the dynamics of the adhesion bonds (molecular level) with the cell's behavior during reorientation (cell level) through the mechanics of stress fiber. The predictions of the cluster model are consistent with experimental observations.

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Associate Editors Mian Long and Fan Yuan oversaw the review of this article.Abstract-The adhesion-based cell mechanosensitivity plays central roles in many physiological and pathological processes. Recently, quantitative understanding of cell responses to external force has been intensively pursued. However, the frequency dependent cell responses to the substrate stretching have not yet been fully understood. Here we developed a multiscale modeling framework for studying cell reorientation behaviors under substrate stretching, in which the mechano-chemical coupling at molecular, subcellular, and cellular scales was considered. The effect of matrix stiffness was also considered in a FEM based mechano-chemical coupling simulation. We showed that the collapsing time of focal adhesion decreases with the increasing of the loading frequency, however, the cell reorientation time exhibits a biphasic frequency-dependent behavior. Our results suggested that this biphasic behavior might be caused by the competition between the frequency-dependent collapsing of focal adhesions and the less frequency-dependent formation of stress fibers aligning away from the loading direction. At the low loading frequency, the collapsing of focal adhesion dominates the reorientation process, however, at the high loading frequency the polymerization of stress fiber dominates the reorientation. Moreover, we showed that the compliance of matrix may help accelerate the cell reorientation because focal adhesion is prone to be instable on soft matrix.