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 the 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 and ω) 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<ω and 2) monotonically increases with frequency for ω>ω. Furthermore, the characteristic frequency ω 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 evolves with age, following a power-law relationship. The predictions of the dissociation-based multiscale theoretical mechanical model align well with experimental observations. Our model provides a comprehensive description of the dynamical viscoelastic behaviors of cells and cell-like materials.