Pre-stress of actin cortices is important for the viscoelastic response of living cells

Shape, dynamics, and viscoelastic properties of eukaryotic cells are primarily governed by a thin, reversibly cross-linked actomyosin cortex located directly beneath the plasma membrane. We obtain time-dependent rheological responses of fibroblasts and MDCK II cells from deformation-relaxation curves using an atomic force microscope to access the dependence of cortex fluidity on pre-stress. We introduce a viscoelastic model that treats the cell as a composite shell and assumes that relaxation of the cortex follows a power law giving access to cortical pre-stress, area compressibility modulus, and the power law (fluidity) exponent. Cortex fluidity is modulated by interfering with myosin activity. We find that the power law exponent of the cell cortex decreases with increasing intrinsic pre-stress and area compressibility modulus, in accordance with previous finding for isolated actin networks subject to external stress. Extrapolation to zero tension returns the theoretically predicted power law exponent for transiently cross-linked polymer networks. In contrast to the widely used Hertzian mechanics, our model provides viscoelastic parameters independent of indenter geometry and compression velocity.