a, Evolution of G′_n of HASM cells after a single transient stretch of 0% (no stretch, open circles), 2.5% (green), 5% (blue) and 10% (red). The response of each bead was normalized to its pre-stretch value. b, Evolution of the phase angle after stretch application. Compare with Box 1 in Supplementary Note 7.

In every case, the closer the system was to the solid-like state (δ₀ = 0) before being subjected to transient stretch, the greater was the extent of its fluidization and, except for the case of ATP depletion, the faster was its subsequent recovery. Master curves of G′_n at the earliest time point recorded after stretch (a) and of the initial rate of stiffness recovery α versus the pre-stretch phase angle δ₀ (b). α was assessed by fitting a power-law to the first 30 s of response after stretch cessation. Error bars indicate standard errors. When plotted again over the full range possibilities (c), cells are seen to lie much closer to the solid-like (δ₀ = 0) than the fluid-like (δ₀ = π/2) state. In response to shear of similar magnitude, cells show a fluidization response comparable to but to the left of hard sphere colloids (data adapted from ref. 4). Soft glassy rheology theory5 (Supplementary Note 7) captures these trends but substantially underestimates sensitivity to changes of δ₀. n values are given in Supplementary Table 1. Colours are as in Fig. 2 with the addition of HASM PBS (dark blue), HBE Latrunculin A (orange squares), MDCK cytochalasin D (brown diamonds) and BASM tissue (green hexagons).

a, b, G′_n (a) and δ (b) of pharmacologically treated HASM cells after application of a single transient stretch of 10% amplitude (see Methods and Supplementary Table 1 for pre-stretch baseline values and treatment details). Groups are latrunculin A (orange), DBcAMP (green), ML7 (10 min incubation, bright pink; 45 min incubation, dark pink), histamine (yellow), EGTA (grey), jasplakinolide (bright blue), ATP depletion (open symbols), and untreated cells (red). G′_n (c) and δ (d) of MDCK (blue diamonds), HBE (yellow squares), HLF (black triangles) and HASM (red circles). Compare with Box 1 in Supplementary Note 7.

a, Spontaneous motions of beads bound to HASM cells at different t_w after stretch cessation (n = 1,062 beads). Waiting times are 5, 20, 35, 55, 85, 135, 195, 295, 435, 665 and 995 s from top to bottom. The red line is the MSD before stretch application. The dashed lines indicate diffusion exponents of 1 and 2. b, To characterize the progressive slowing of rearrangement kinetics, we defined a time τ at which MSD(τ)=d², where d was taken as an arbitrary threshold and τ thus represented the average time required for a bead to move (diffuse) a distance d. For any value of d, we found that τ increased with t_w as a power law τ ∝ t_w^μ with μ≈0.3, indicating that the decay was slower than any exponential process, and that within the experimental time window no steady state was achieved. Data are shown for d² = 100 nm² and the solid line is a fit to a power law with exponent μ = 0.32. c, After rescaling the time axis using with μ = 0.32, all data collapsed onto a master curve. This indicates that the kinetics at each waiting time were self-similar. In inert soft glassy materials, such slowing of rearrangement kinetics as well as the absence of a steady state is referred to as physical ageing and μ is identified as the ageing coefficient. Physical ageing can be interrupted by injection of mechanical energy through shear; shear drives inelastic structural rearrangements7,23, in which case it is presumed that elements can then ‘hop’ out of the deep energy wells in which they are trapped, erase system memory, and push the system farther from thermodynamic equilibrium. In inert soft materials these events reset system evolution to some earlier time and for that reason are called physical rejuvenation6,7.