Living cells are a complex soft material with fascinating mechanical properties. Confusingly, experiments have shown that cells exhibit stiffening and more solid-like behaviors under uniaxial stretches or shear, while they present softening and more fluid-like behaviors under biaxial stretches. For both of these seemingly paradoxical stiffening and softening rheological behaviors, cells often exhibit a robust power-law rheological characteristic. Here, based on the structural features, we propose a cellular structural model to investigate these rheological behaviors of cells under different loading conditions. It is found that this structural model can naturally capture the stiffening and softening behaviors in the power-law rheological responses of cells, depending on the loading conditions. Both stiffening and softening of cells originate from changes in the configuration of the discrete cytoskeleton: stiffening from the rotation of the microtubules to the loading direction and softening from the elastic buckling of individual microtubules. Moreover, for both stiffening and softening in the rheological behaviors of cells, there exists a unified relationship that the power-law exponent decreases linearly with the cellular stiffness in a semi-logarithmic coordination. We further present that a self-similar hierarchical model can be used to analyze this unified relationship. This study not only provides a discrete cellular structural model to capture the essential mechanisms of cellular rheology, but also suggests that the scaling rheological exponent may be treated as a mechanical marker for monitoring cellular healthy states.

活细胞是一种复杂的柔软材料，具有迷人的机械性能。令人困惑的是，实验表明，细胞在单轴拉伸或剪切下表现出硬化和更像固体的行为，而在双轴拉伸下它们表现出软化和更像流体的行为。对于这些看似矛盾的硬化和软化流变行为，细胞通常表现出强大的幂律流变特性。在这里，基于结构特征，我们提出了一个细胞结构模型来研究细胞在不同负载条件下的这些流变行为。发现这种结构模型可以自然地捕捉到细胞幂律流变响应中的硬化和软化行为，具体取决于加载条件。细胞的变硬和软化都源于离散细胞骨架结构的变化：从微管旋转到加载方向的变硬和单个微管的弹性屈曲变软。此外，对于细胞流变行为的变硬和软化，都存在一个统一的关系，即幂律指数与细胞刚度呈半对数坐标呈线性递减关系。我们进一步提出，自相似层次模型可用于分析这种统一关系。该研究不仅提供了一个离散的细胞结构模型来捕捉细胞流变学的基本机制，而且还表明标度流变学指数可以作为监测细胞健康状态的机械标记。