Characteristic frequencies of localized stress relaxation in scaling-law rheology of living cells.

Living cells are known to exhibit power-law viscoelastic responses and localized stress relaxation behaviors in frequency spectrum. However, the precise interplay between molecular scale cytoskeletal dynamics and macroscale dynamical rheological responses remains elusive. Here, we propose a mechanism-based general theoretical model showing that cytoskeleton dissociation generates a peak in the loss modulus as a function of frequency, while the cytoplasmic viscosity promotes its recovery, producing a subsequent trough. We define two characteristic frequencies ( ω_c1 and ω_c2 ) related to the dissociation rate of crosslinkers and the viscosity of the cytoplasm, where the loss modulus (1) exhibits peak and trough values for ω_c1>ω_c2 , and (2) monotonically increases with frequency for ω_c1>ω_c2. Furthermore, the characteristic frequency ω_c1 exhibits a biphasic stress-dependent behavior, with a local minimum at sufficiently high stress due to the stress-dependent dissociation rate. Moreover, the characteristic frequency ω_c2 evolves with age, following a power-law relationship. The predictions of the DMM model align well with experimental observations. Our model provides a comprehensive description of the dynamical viscoelastic behaviors of cells and cell-like materials.