Stiffening and softening in the power-law rheological behaviors of cells

Abstract

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.