T cells and neutrophils undergo durotactic migration.

(A) Illustration of the imaging-based cell migration device and yFMI value calculation.

(B) Representative time-lapse images of single CD4+ Naïve T cells migrating on ICAM-1 coated polyacrylamide gels with uniform stiffness (top, 30 kPa) and stiffness gradient (bottom, with greater stiffness towards the top, 20.77 kPa/mm). Color lines indicated the migration trajectories of single cell. Scare bar: 50 μm.

(C) Representative tracks of migrating CD4+ Naïve T cells on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top). Note that a higher proportion of cells migrate toward the stiffer end of the gradient substrate (black tracks) compared to cells migrating opposite to the gradient (red tracks). Tracks on the uniform substrate showed equal proportion for each part.

(D) Angular displacement of CD4+ Naïve T cells on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top).

(E) y-FMI (Forward Migration Index), velocity and migration persistence of CD4+ Naïve T cells cultured on uniform substrate or gradient substrate (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by Student’s t-test.

(F) Representative time-lapse images of single neutrophils derived from mouse bone marrow migrating on fibronectin-coated polyacrylamide gels with uniform stiffness (top) or stiffness gradient (bottom). Color lines indicated the migration trajectories of single cell. Scare bar: 50 μm.

(G) Representative tracks of migrating neutrophils on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top).

(H) Angular displacement of neutrophils on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top).

(I) y-FMI, velocity and migration persistence of neutrophils cultured on uniform substrate or gradient substrate (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by Student’s t-test.

(J) Representative time-lapse images of differentiated HL-60 (dHL-60) cells migrating on fibronectin-coated polyacrylamide gels with uniform stiffness (top) or stiffness gradient (bottom). Color lines indicated the migration trajectories of single cell. Scare bar: 50 μm.

(K) Representative tracks of migrating dHL-60 cells on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top).

(L) Angular displacement of dHL-60 cells on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top).

(M) y-FMI, velocity and migration persistence of dHL-60 cells cultured on uniform substrate or gradient substrate (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by Student’s t-test.

Amoeboid durotaxis may not be propelled by differential actin flow.

(A) Actin flow speed of dHL-60 cells adhered on different substrate stiffness (4 kPa, 40 kPa, 75 kPa, 120 kPa and 160 kPa). Each plot indicated the average actin flow speed of every individual cell adhered on polyacrylamide gel. All error bars are SEM. *, P < 0.05, ****, P < 0.0001, by One-way ANOVA.

(B) Actin flow speed of softer side and stiffer side of the dHL-60 cells adhered on gradient substrate. Each plot indicated the average actin flow speed of softer or stiffer part of a cell adhered on stiffness gradient gel. All error bars are SEM. ns, not significant, by Student’s t-test.

(C) Actin flow speed of control (DMSO) and CK-666 (100 μM, pre-treated for 5 h) treated CD4+ Naïve T cells moving on stiffness gradient gel (n = 20 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, by Student’s t-test.

(D) y-FMI of control (DMSO) and CK-666 (100 μM, pre-treated for 5 h) treated CD4+ Naïve T cells moving on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ns, not significant, by Student’s t-test.

(E) y-FMI, velocity and migration persistence of control (DMSO), nocodazole (Noco, 32 μM, pre-treated for 10 min) treated and taxol (70 nM, pre-treated for 10 min) treated CD4+ Naïve T cells moving on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ns, not significant, by One-way ANOVA.

(F) y-FMI, velocity and migration persistence of control (DMSO), blebbistatin (Bleb, 10 μM, pre-treated for 10 min) treated and Rho activator II (Rho, 0.25 μg/ml, pre-treated for 2 h) treated CD4+ Naïve T cells moving on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ***, P < 0.001, ****, P < 0.0001, ns, not significant, by One-way ANOVA. All drugs were incubated for the whole experiment.

(G) y-FMI, velocity and migration persistence of control (DMSO), blebbistatin (Bleb, 10 μM, pre-treated for 10 min) treated and Rho activator II (Rho, 0.25 μg/ml, pre-treated for 2 h) treated neutrophils moving on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. *, P < 0.05, ****, P < 0.0001, ns, not significant, by One-way ANOVA. All drugs were incubated for the whole experiment.

(H) y-FMI, velocity and migration persistence of control (DMSO), blebbistatin (Bleb, 10 μM, pre-treated for 10 min) treated and Rho activator II (Rho, 0.25 μg/ml, pre-treated for 2 h) treated dHL-60 cells moving on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant by One-way ANOVA.

Durotaxis of T cells and neutrophils is regulated by polarized actomyosin activity.

(A) Western blot showing the protein level of NMIIA (left) and NMIIB (right) in negative control (Ctrl), NMIIA knocked down (NMIIAKD) and NMIIB knocked down (NMIIBKD) HL-60 cells. α-tubulin was used as loading control. Numbers below the ladders were the relative intensity versus α-tubulin.

(B) Representative time-lapse images of NMIIAKD (top) and NMIIBKD (bottom) dHL-60 cells migrating on polyacrylamide gels with stiffness gradient. Color lines indicated the migration trajectories of single cell. Scare bar: 50 μm

(C) Representative tracks of migrating NMIIAKD (top) and NMIIBKD (bottom) dHL-60 cells on stiffness gradient gels.

(D) Angular displacement of NMIIAKD (top) and NMIIBKD (bottom) dHL-60 cells on stiffness gradient gels (with greater stiffness towards the top).

(E) y-FMI, velocity and migration persistence of control, NMIIAKD and NMIIBKD dHL-60 cells migrating on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by One-way ANOVA.

(F) Representative immunofluorescent staining of NMIIA (left) and NMIIB (right) of dHL-60 cells on stiffness gradient gel (with greater stiffness towards the top). The yellow triangles indicated the location of NMIIA and NMIIB. Scale bar: 10 μm.

(G) Fluorescent intensity ratio of NMIIA or NMIIB in cell softer part to stiffer part in Fig. 3F. All error bars are SEM. ****, P < 0.0001, by Student’s t-test.

(H) Fluorescent intensity ration of NMIIA in softer part to stiffer part of neutrophils and CD4+ Naïve T cells in Fig. S4B, C. All error bars are SEM. ns, not significant, by Student’s t test.

Amoeboid durotaxis is evolutionarily conserved.

(A) Representative time-lapse images of Dictysotelium on polyacrylamide gels with uniform stiffness (top) or stiffness gradient (bottom). Color lines indicated the migration trajectories of single cell. Scare bar: 50 μm.

(B) Representative tracks of migrating Dictysotelium on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top).

(C) Angular displacement of Dictysotelium on the uniform stiffness gels (top) or stiffness gradient gels (bottom, with greater stiffness towards the top).

(D) y-FMI, velocity and migration persistence for Dictysotelium cultured on uniform substrate or gradient substrate (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by Student’s t-test.

(E) y-FMI, velocity and migration persistence of control (DMSO), blebbistatin (Bleb,10 μM, pre-treated for 10 min) treated and Rho activator II (Rho, 0.25 μg/ml, pre-treated for 2 h) treated Dictysotelium moving on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by One-way ANOVA.

(F) y-FMI, velocity and migration persistence of control (DMSO), nocodazole (Noco, 32 μM, pre-treated for 10 min) treated and taxol (70 nM, pre-treated for 10 min) treated Dictysotelium moving on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by One-way ANOVA.

Mechanosensing active gel model of amoeboid durotaxis.

(A) Illustration of an amoeboid cell crawling on the PA gel with stiffness gradient.

(B) Details of the mechanosensing active gel model. The blue circle represented an amoeboid cell. The position of the blue circle was defined by actin density (green) with given polarization field. To recapitulate cell migration, myosin contractility (red), and hydrodynamic flow velocity (black) were illustrated in the model.

(C) Initial density and polarization field of actin. The background color indicated the density of actin both inside and outside of the cell border. The red arrows indicated the polarization field of actin.

(D) Density and polarization field of actin during amoeboid durotaxis. The background color indicated the density of actin both inside and outside of the cell border. The red arrows indicated the polarization field of actin.

(E) Spatial distribution of NMIIA (blue line) and actin (red line) along the direction of stiffness gradient. The cell position was marked with the blue rectangle.

Regulation of amoeboid durotaxis by cell contractility and substrate stiffness.

(A) Illustration of different regions (soft, middle and stiff) on gradient substrates with the greater stiffness towards right.

(B) Trajectories of migrating amoeboid cells with no contractility on middle region of gradient substrates, and the substrate stiffness of the initial cell centroid was set as E = 70 kPa.

(C) Trajectories of migrating amoeboid cells with normal contractility on middle region of gradient substrates, and the substrate stiffness of the initial cell centroid was set as E = 70 kPa.

(D) Trajectories of migrating amoeboid cells with normal contractility on soft region of gradient substrates, and the substrate stiffness of the initial cell centroid was set as E = 30 kPa.

(E) Trajectories of migrating amoeboid cells with normal contractility on stiff region of gradient substrates, and the substrate stiffness of the initial cell centroid was set as E = 200 kPa.

(F) The FMI with different contractility strength and different initial substrate stiffness of cell centroid. (G-I) yFMI, velocity and migration persistence of CD4+ Naïve T cells migrating on different regions illustrated in Fig. 6A (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. ****, P < 0.0001, ns, not significant, by One-way ANOVA.

(A) Representative stiffness gradient of polyacrylamide gels measured by atomic force microscope was plotted (20.77 kPa/mm). All error bars are SEM. (n = 3 regions, replicates are biological).

(B) Left: Representative immunofluorescence images (obtained by confocal imaging) of CD4+ naïve T cells stained with Paxillin antibody and Alexa Fluor 555-conjugated secondary antibody. Right: Representative immunofluorescence images (obtained by expansion microscopy) of CD4+ naïve T cells stained with Paxillin antibody and Alexa Fluor 488-conjugated secondary antibody. Scale bar: 10 μm.

(C) Representative immunofluorescence images (obtained by confocal imaging) of MDA-MB-231 cells stained with Paxillin antibody and Alexa Fluor 555-conjugated secondary antibody. Scale bar: 10 μm.

(D) Representative tracks of migrating neutrophils on stiffness gradient gel with greater stiffness towards the top. Color lines and numbers indicated the migration trajectories of single cell. Scare bar: 50 μm.

Representative trajectories of three different conditions (A, B and C) of persistence value when the yFMI1 > yFMI2. In all conditions, the single cell migrated the same locomotion, which means L1 = L2. t1 and t2 can be regarded as the two consecutive time points during cell migration. Each graph showed one condition for a migrating single cell. In all three conditions, yFMI on left was greater than the right. But the persistence on left was less (A), equal (B) or greater (C) than the right.

(A) Representative immunofluorescence images (obtained by confocal imaging) of dHL-60 cells stained with Paxillin antibody and Alexa Fluor 555-conjugated secondary antibody. Scale bar: 10 μm.

(B) Representative immunofluorescence images (obtained by expansion microscopy) of CD4+ naïve T cells stained with α-Tubulin antibody and Alexa Fluor 488-conjugated secondary antibody. Left: control (DMSO) cells. Middle: Nocodazole (32 μM, pre-treated for 10 min) treated cells. Right: Taxol (70 nM, pre-treated for 10 min) treated cells. Scale bar: 10 μm.

(A) Quantification of protein level in Fig. 3A. α-tubulin was used as loading control. Bar chart shows quantification of protein levels normalized to α-tubulin in each condition (n = 3 independent experiments, replicates are biological). All error bars are SEM. **, P < 0.01, ****, P < 0.0001; by Student’s t-test.

(B) Representative immunofluorescent staining of NMIIA of CD4+ Naïve T cells on stiffness gradient gel (with greater stiffness towards the top). Scale bar: 5 μm.

(C) Representative immunofluorescent staining of NMIIA of neutrophils on stiffness gradient gel (with greater stiffness towards the top). Scale bar: 10 μm.

(A) Representative time-lapse images of GFP-NMIIA dHL-60 cells migrating on gradient gel with greater stiffness towards the top. Scale bar: 10 μm.

(B) y-FMI, velocity and migration persistence of control (DMSO) and SMIFH2 (15 μM, pre-treated for 5 h) treated CD4+ Naïve T cells migrating on stiffness gradient gel (n ≥ 30 tracks were analyzed for each experiment, N = 3 independent experiments for each condition, replicates are biological). All error bars are SEM. *, P < 0.05, ns, not significant, by Student’s t-test.

(C) Representative confocal image of dHL-60 cells stained with 0.1 μM SiR-Actin on gradient gel. Scale bar: 5μm.

(D) Quantification of contact angle of cell soft end and stiff end (n =26). Error bars are SEM. ****, P < 0.0001, by Student’s t-test.

Parameters used in simulations.