Figure 4.

Force-relaxation experiments on MDCK II cysts. (A) Schematic of the experimental procedures is shown: the approach phase (a and b) is same as that in cyst elasticity measurements; the cantilever is held at a fixed position for 40 s when the target force, F_M, is reached (b and c), and then, retracted from the cyst (c and d). (B) Typical force-relaxation curves obtained for MDCK II cysts, featuring three distinct regions: approach (black; a and b), relaxation (red; b and c), and retraction (blue; c and d); v = 1, 10, and 100 μm/s. (C) Population-averaged force-relaxation curves (b and c) obtained for MDCK II cysts at distinct loading velocities (shaded lines), plotted in a log-log scale. The force-relaxation curves do not reach a plateau within 40 s. Curves are averages of N = 8, 7, and 4 MDCK II cysts (n = 4) for loading velocities of v = 1, 10, and 100 μm/s, respectively. The black dot-dashed lines and red dashed lines are the fittings of the experimental force relaxation with the poroelastic and power-law relaxations, respectively. To obtain the best fitting for the poroelastic fit, we selected the first 6, 3, and 0.2 s (t < t_trans) of the averaged force relaxation with loading velocities of v = 1, 10, and 100 μm/s, respectively. R² = 0.976, 0.971, and 0.971, respectively. For the power-law fit, the ranges of the selected data were set as follows: relaxation time t = 6–40, 3–40, and 0.2–40 s (t_trans < t < 40 s) for v = 1, 10, and 100 μm/s, with power-law exponent β = 0.128, 0.133, and 0.138, and R² = 0.996, 0.995, and 0.993, respectively. (D) Effects of aquaporin blocking on cyst-size change upon consecutive replacement of the external buffering solution with the hypertonic solution (425 mOsm) and isotonic solution (320 mOsm) are shown. Cysts pretreated with 0.1 μM HgCl₂ (N = 4, n = 4) or 10 μM TEA⁺ (N = 3, n = 3) displayed a similar reduction in size (∼25%) upon hypertonic challenge that was less than that of control cysts (∼40%; N = 5, n = 5), which indicated that aquaporins were partially blocked by HgCl₂ or TEA⁺ treatment. (E) Population-averaged force-relaxation curves obtained for MDCK II cysts before and after treatment with 0.1 μM HgCl₂, under loading velocity v = 1 μm/s and target force F_M = 150 nN are shown. The dashed curves are the fittings to the poroelastic model, with the range of the selected data optimized as t = 0–23 s. R² = 0.968 and 0.965 for cysts before and after Hg²⁺ treatment, respectively. The shaded areas above and below the average curves represent the SD(±) of the data; N = 5, n = 5. The inset shows the percentage error, defined as |F(t) − F_fit|/F(t). To see this figure in color, go online.