A structure-based cellular model reveals power-law rheology and stiffening of living cells under shear stress

Shear stress plays a crucial role in many physiological processes, such as atherosclerosis, angiogenesis, and metastasis. However, how cells respond to static and dynamical shear stresses remains poorly understood. Here, we propose a structure-based cellular model, consisting of cell membrane, cytoplasm, and cytoskeleton, to explore the shear rheology of cells. By simulating the mechanical responses of a single cell under shear stress, we find that this model can reproduce both the universal power-law rheology at small deformations and stress stiffening at large deformations. Besides, the loss moduli of cells at high frequencies exhibit a stronger frequency dependence than the storage moduli. Moreover, we present two master relations: one is between the power-law exponent and cell stiffness; the other is between cell stiffness and external forces. Our results are in broad agreement with experiments. The self-similar hierarchical theory offers a physical explanation of the power-law responses of cells under shear stress. In addition, we consider the geometrical nonlinearity of single filaments to account for the stress stiffening of cells. The present model can be used to examine the effects of shear flow on living cells in physiological environments.