a,b, Speeds of MDA-MB-231 cells (a) and other indicated cell types (b) inside confining channels at prescribed viscosities. The red lines represent the median of ≥69 cells from ≥3 experiments. c, Cell trajectories on 2D collagen-coated surfaces after 10 h. d, Cells disseminating from 3D spheroids. e, The time required for the first cell dissociation from each spheroid (n ≥ 53) from 3 experiments. f, Airyscan images of phalloidin stained cells on collagen-coated substrates. The red arrow indicates high F-actin staining along the cell edge. g, The fraction of cell-projected area with a Lifeact–GFP-rich lamella for n ≥ 28 cells from 3 experiments. h, The leading edge of Lifeact–GFP-expressing cells on collagen-coated surfaces at t = 0 min (red) and t = 2 min (cyan) (left). Right, leading-edge lamella growth in n ≥ 19 cells from 3 experiments. Data are the moving average ± s.e.m. P < 0.05 for all points t ≥ 50 s. Time is shown as min:s. i,j, STORM reconstruction (i) and density quantification (j) of F-actin for cells (n ≥ 13) on substrates from 2 experiments. k, The average actin density over time from 20 stochastic simulations. Viscous forces were applied at t = 6 s (red arrow) and maintained until the end of the simulation. l, Confocal images of cells expressing Lifeact–GFP and ARP3–mCherry in confinement. The red arrow indicates high ARP3 intensity at leading-edge protrusions at 8 cP. m, The relative ARP3–mCherry intensity along normalized cell length in confined cells. Data are the moving average ± s.e.m. for n = 21 cells from 4 experiments. ***P < 0.001 for all comparisons at normalized cell length > 0.96. The x axis is discontinued between 0.25 and 0.75 to highlight differences at the cell edges. n, Confined migration speeds of SC versus ARP3/ARPC4 double-knockdown cells (n = 90) from 3 experiments. For e, g, j and n, data are mean ± s.d. Unless otherwise indicated, statistical comparison was performed with respect to 0.77 cP. Statistical analysis was performed using Kruskal–Wallis tests followed by Dunn’s test (a and n), Mann–Whitney U-tests (BrM2 only) or unpaired t-tests after log-transformation (other cells) (b), unpaired t-tests (e, g and j) and two-way analysis of variance (ANOVA) followed by Šidák’s test (h and m). Scale bars, 250 μm (c), 50 μm (d), 25 µm (f, white), 3 µm (f, red), 10 µm (h), 2 µm (i), 20 µm (l). The cell model was MDA-MB-231 unless otherwise indicated. *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001.

Source data

a, The volume of Lifeact–GFP-labelled MDA-MB-231 cells (n ≥ 28) at the indicated viscosities from 3 experiments. b, Confocal images of confined MDA-MB-231 cells stained for NHE1 and phalloidin. c, Front-to-rear NHE1 intensity ratio in NHE1-immunostained cells (n ≥ 16) from 3 experiments. d, The rate of pH recovery in pHRed-expressing MDA-MB-231 cells (n ≥ 29) from 5 experiments. e, The volume of SC and shNHE1 Lifeact–GFP-tagged MDA-MB-231 cells (n ≥ 36) from 3 experiments. f, Confined migration speeds of SC and shNHE1 MDA-MB-231 cells (n ≥ 113) from 3 experiments compared with the two-phase model predictions. g, The elevated Flipper-TR lifetimes in MDA-MB-231 cells on 2D surfaces indicate high membrane tension. h, The membrane tension in wild-type MDA-MB-231 cells after treatment with vehicle (veh.), CK666 or EIPA, and in SC or shTRPV4 cells (n ≥ 58) from 3 experiments. i, The number of calcium flashes in SC, shTRPV4 or shNHE1 MDA-MB-231 cells (n ≥ 52) on 2D surfaces from 3 experiments. j,l, TRPV4 currents (I) in SC- and shTRPV4 (j) or shNHE1 (l) MDA-MB-231 cells (n ≥ 3) with or without the TRPV4 inhibitor HC-067047 from ≥3 experiments. k, Confined migration speeds of SC and shTRPV4 MDA-MB-231 cells (n ≥ 129) from 3 experiments. m, The time required for the first cell dissociation from each spheroid (n ≥ 57) after treatment with vehicle control or the TRPV4 inhibitor GSK 2193874 (GSK2) from 3 experiments. n, The number of calcium flashes in MDA-MB-231 cells (n ≥ 29) treated with the ARP2/3 inhibitor CK666 from 2 experiments. o, Confocal images of confined MDA-MB-231 cells stained for NHE1, ezrin and phalloidin. p, Front-to-rear NHE1 or ezrin intensity ratio from immunostained cells (n ≥ 24) from 2 experiments. Data are mean ± s.d. (a, c–f, h, i, k, m, n and p) and mean ± s.e.m. (j and l). Statistical analysis was performed using unpaired t-tests after log-transformation (a, c and d), one-way ANOVA followed by Tukey’s test after log-transformation (e and m), Kruskal–Wallis tests followed by Dunn’s test (f, h, i, k and n), one-way ANOVA followed by Holm–Šidák’s test (j and l) and Mann–Whitney U-tests (p). Scale bars, 20 µm (b and o) and 10 µm (g).

Source data

a, The lifetimes of the RHOA activity biosensor in MDA-MB-231 cells on a 2D surface at the indicated viscosities. b, The subcellular distribution of RHOA activity in n ≥ 30 cells on a 2D surface from 4 experiments. c, RHOA activity in SC and shTRPV4 MDA-MB-231 cells (n ≥ 21) on a 2D surface from 3 experiments. d, Confocal images of GFP–AHD-expressing MDA-MB-231 cells in confinement. The red arrowheads indicate regions of active RHOA. e, GFP–AHD intensity in different segments of confined MDA-MB-231 cells (n ≥ 33) at 8 cP in the presence of vehicle control or NHE1 inhibitor from ≥3 experiments. f, GFP–AHD intensity in different segments of confined MDA-MB-231 cells (n ≥ 33) after treatment with vehicle control or the TRPV4 inhibitor GSK 2193874 (GSK2) from 3 experiments. The intensity in each segment was normalized to the mean intensity of the entire cell in e and f. g, Confocal images of MIIA–GFP-expressing and Lifeact–Ruby-expressing MDA-MB-231 cells migrating in confinement. The red arrowheads indicate regions of intense MIIA localization. h, The confined migration speeds of SC and MIIA and MIIB single- or double-knockdown MDA-MB-231 cells (n ≥ 38) from 2 experiments. Data are mean ± s.d. i, Schematic of the proposed viscosity-sensing pathway. OEM, osmotic engine model. The schematic in i was created using Servier Medical Art. Statistical analysis was performed using unpaired t-tests (b), Kruskal–Wallis tests followed by Dunn’s test (c and h) and two-way ANOVA followed by Tukey’s test (e and f). Scale bars, 20 µm (a, d and g).

Source data

a, Illustration of cell preconditioning at the indicated viscosities. b, Confined migration speeds of preconditioned cells (0.77 or 8 cP for 6 days) resuspended at the indicated migration viscosity. Data are mean ± s.d. for n ≥ 140 cells from 3 experiments. c, The confined migration speeds of preconditioned SC or shTRPV4 cells allowed to migrate at 0.77 cP. Data are mean ± s.d. for n ≥ 146 cells from 3 experiments. d, Confocal image of 3 day post-fertilization (d.p.f.) zebrafish ISVs with measurements of vessel width (top). Bottom, experimental design of migration studies in zebrafish. e,f, Time-lapse confocal images (e) and average speeds (f) of preconditioned cells (n ≥ 77) inside ISVs from 3 experiments. The red lines indicate the median (thick) and quartiles (thin). g, The experimental design of mouse tail-vein experiments. h, The number of human vimentin-positive colonies in the lungs 48 h after injection. Data are mean ± s.e.m. for 8 mice per group from 2 experiments. i,j, Confocal images of lung sections (i) and quantification of human vimentin-positive metastatic colonies (j) 3 weeks after injection. Data are mean ± s.e.m. for a total of ≥7 mice per group from 2 experiments. k,l, The number of human vimentin-positive metastatic colonies in the lungs 48 h (k) and 3 weeks (l) after injection. Data are mean ± s.e.m. for ≥9 mice per group from 2 experiments. The squares represent experiments with PVP as the medium additive. m,n, qPCR detection of human DNA in the lungs of mice 48 h (m) or 3 weeks (n) after injection. Data are mean ± s.d. for ≥9 mice per group. Squares are from experiments with PVP. Statistical analysis was performed using Kruskal–Wallis tests followed by Dunn’s test (b and c), Mann–Whitney U-tests (f), unpaired t-tests (h and j), one-way ANOVA followed by Tukey’s test (l–n) and one-way ANOVA followed by Tukey’s test on log-transformed data (k). Scale bars, 20 µm (d), 30 µm (e) and 200 µm (i). The schematics in a, d and g were created using Servier Medical Art.

Source data