Introduction

Cell migration is essential to myriads of physiological and pathological processes including cancer dissemination (1). As the mechanical properties of tumor microenvironment being gradually unveiled, waves of studies have focused on the contribution of mechanical force - in forms of proliferation generated cell jamming (2) and fibrosis induced tissue stiffening - on tumor expansion as well as invasion (3). The ability of cells to sense and navigate along higher substrate stiffness has been coined as “durotaxis” in the early 2000s (4) with important pathophysiological implications (5). Over the past two decades, accumulating in vitro and in vivo evidence has demonstrated durotaxis in tumor epithelial sheets and single mesenchymal cells (6–10), and revealed mechanisms including focal adhesion tugging or probing of the local substrate by actin-based protrusions to underlie this specialized directional cell migration (6, 11–13). However, compared to tumor cells that harness the capacity to durotax, little is known about whether microenvironmental stiffness difference could determine the destination of immune cells.

In contrast to mesenchymal migration adopted by some tumor cells, immune cells mainly undergo rapid single cell crawling referred to as “amoeboid” migration, without formation of stable focal adhesions but can achieve migration ten times faster (14). Modeling on amoeboid migration suggested that myosin contractility may play an important role when mechanical anchoring are less evident (15). In this model, actomyosin was described as an active gel whose polarity dictates the alignment of actin fibers (15). Moreover, in silico simulation suggested that actomyosin contractility can lead to collective internal flows of actin, which, in turn, propels the cell body forward (16). Meanwhile, experiments have also revealed that protrusive flowing of the anterior actin network drives the adhesion-independent cell migration.

During development and immune surveillance, chemotactic cues have been reported to globally prescribe the migratory direction and destination of immune cells (17). Using mammalian leukocytes and lymphocytes (18, 19) as well as the protista Dictyostelium (20), mechanisms of amoeboid chemotaxis have been extensively studied . Instead, little is known about whether these amoeboid cells would undergo durotactic migration. Previous studies have shown that inflamed, stiffened endothelial cells could induce more neutrophil transmigration (21), and that once adhered to the endothelium, transmigrating neutrophils may exert durotactic sensing to search for stiffer sites (22). In addition, lymphocytes such as CD4⁺ Naïve T cells increased spreading area when plated on stiffer substrates (23), indicative of the capacity to sense external mechanical signal. The above evidence argue that amoeboid cells, albeit without strong adhesions, are able to sense and respond to environmental stiffness.

Here we developed an imaging-based cell migration device that provided both spatial confinement and stiffness gradient. By tracking live cell trajectory and analyzing the directionality of CD4⁺ Naïve T cells and neutrophils, we observed that amoeboid cells can durotax. We further uncovered the underlying mechanism to be NMII (non-muscle myosin II) dependent. Based on our observations that NMIIA was polarized towards the soft-end in cells on stiffness gradient gel, we mathematically simulated amoeboid cells as active droplets, predicting that durotaxis can be strengthened on the softer region of the gradient substrate which was then verified experimentally. Moreover, we demonstrated the evolutionary conservation of amoeboid migration in the protista Dictyostelium. Together, the identification that rigidity-guided migration existed in low-adhesive, fast moving amoeboid cells may provide new insights in focal adhesion-independent mechanosensing, and may shed new lights on immune surveillance and cancer metastasis.

Results

T cells and neutrophils undergo durotactic migration

T cells and neutrophils exert amoeboid migration in vivo and in vitro under confinement (24, 25). To probe whether amoeboid cells would undergo durotaxis, we manufactured an imaging-based cell migration device which provided spatial confinement to maintain amoeboid cell migration (24, 26, 27) and stiffness gradient to provide durotactic cue (Fig. 1A). Typically, cells were sandwiched between two polyacrylamide (PA) gels (Fig. 1A iv) with stiffness gradient (20.77 kPa/mm, Fig. S1A) or uniform stiffness (28). Cell migration trajectories from time-lapse imaging were then generated (Fig. 1A v) and analyzed for directionality (Fig. 1A vi). We employed the Forward Migration Index (FMI), for which the displacement value was divided by the total displacement the cell underwent (Fig. 1A vi) (7, 19, 28, 29). This FMI is decoupled with cell velocity and differed from persistence (Fig. S2A-C).

Fig. 1:

We then performed time-lapse imaging to record CD4⁺ Naïve T cell motility and generated trajectories for direction analysis. As reported previously (14), we observed that T cells underwent typical amoeboid migration with relatively high speed (the mean velocity was 16.21 μm/min) (Fig. 1B, E, Movie 1, 2), distinguished from mesenchymal migration which is usually below 1 μm/min (30). When we stained these T cells for focal adhesion marker paxillin (29), we detected diffused signals by ultrastructure expansion microscopy (U-ExM) (Fig. S1B), distinguished from the plaque-like structure in mesenchymal cells such as the MDA-MB-231 (Fig. S1C).

The trajectories of T cells on the uniform gel did not show biased direction (Fig. 1B-D, Movie 1), while in striking contrast, a majority of cells on the gradient gel exhibited movement towards the stiff-end (Fig. 1B-D, Movie 2). FMI for cells on the uniform gel was around zero (indicating random motility) (Fig. 1E), while it displayed a positive value for cells on the stiffness gradient gel and significantly exceeded that of cells on the uniform gel (Fig. 1E). Angular displacement comparison also revealed that T cells migrated towards the stiff end in this experimental setting (Fig. 1D). Besides, no obvious difference in velocity was detected when comparing T cells moving on uniform vs gradient gel (Fig. 1E), indicating that stiffness gradient did not enhance motility but rather increased forward migratory tendency.

Having identified durotaxis in T cells, we next sought to evaluate in other amoeboid cells such as neutrophils whether they also possess the durotactic capacity. Bone marrow-derived neutrophils were isolated by Percoll gradient and confined between two stiffness gradient gels. In line with our observations with T cells, neutrophils displayed random gliding on the uniform gel while appeared to durotax on the gradient gel, as revealed by the FMI and angular displacement analysis (Fig. 1F-I, Movie 3). This prominent stiff-end directed movement may result from (1) initial cell polarization upon seeding, exemplified by subsequent persistent migration towards the cell front; or (2) cells frequently exploring and re-steering to the stiffer side of the substrate. When analyzing live cell trajectories, we found that some cells indeed exhibited highly persistent migration (Fig. S1D, Track 1, 7, 9, 14, Movie 4). However, we also detected cells that frequently changed directions but showed stiff-end biased migration on the whole (Fig. S1D, Track 4, 5, 8, 10, Movie 4). These observations indicated that neutrophils were able to sense stiffness difference and re-polarize to durotax. Analysis of the bulk cell population revealed that neutrophils on stiffness gradient gel did not elevate their persistence compared to those on the uniform gel (Fig. 1I). We also employed an immortalized promyelocytic leukemia cell line HL-60 in addition to the mouse derived neutrophils. In agreement with previous reports, we detected that HL-60 employs amoeboid migration when differentiated into neutrophil-like cells (dHL-60) (31) (Fig. 1J, Fig. S3A, Movie 5). dHL-60 cells migrated randomly on the uniform gel while moved towards the stiff end on gradient gel (Fig. 1J-M, Movie 5) under confinement.

Together, these phenomena indicate that amoeboid cells such as T cells and neutrophils, although lacking stable focal adhesions, are capable to sense the stiffness gradient and orchestrate directional migration towards the stiffer side.

Amoeboid durotaxis may not be propelled by differential actin flow

Having observed that amoeboid cells can exert durotactic migration, we then interrogated the molecular underpinnings. Classic molecular clutch model attributed both single and collective mesenchymal durotaxis to the differential adhesion strength on distinct substrate stiffness (11, 13, 32). Enhanced traction strain energy on stiffer matrix (32, 33) indicates the presence of increased motors and clutches, which may then slow down the actin flow at adhesion sites by friction (32). In this sense, actin flow is mechanosensitive – with low speed on stiff substrate and high speed on soft matrix. To test the rigidity sensitivity of actin flow in amoeboid cells, we performed quantitative fluorescent speckle microscopy (qFSM) to monitor fluorescent particle movement in dHL-60 cells stained with the actin-specific dye SiR-Actin. Retrograde flow analysis (34) revealed that actin flow velocity dropped sharply when cells were plated on stiffer substrate (160 kPa) compared to the soft gel (4 kPa) (Fig. 2A, Movie 6, 7). Moreover, a descending trend of actin flow speed was detected with increasing substrate stiffness (Fig. 2A, Movie 6-10), suggesting that actin flow in amoeboid cells can indeed respond to stiffness.

Fig. 2:

Actin flow is generated by monomer assembly at the leading edge and myosin contraction at the cell rear, while is slowed down by traction stress between the cell bottom and the substrate (35). Strain energy from the halting of actin flow then transduces into protruding force to counteract membrane tension at the cell front (24, 36). Thus, the protrusion rate is inversely related to the actin retrograde flow (37). It has been suggested that continuous cycles of protrusion support forward cell migration (38). Considering the negatively correlated actin flow speed and substrate stiffness (Fig. 2A), we postulated that differential actin flow velocity (high speed in the down-gradient vs low speed in the up-gradient region) may promote stiff end biased cell migration by inducing more protrusive events in the up-gradient cell region. To test this, we divided the cell body area into up- and down-gradient halves for respective actin flow analysis. However, against our hypothesis, actin flow in these two regions appeared similar in speed (Fig. 2B, Movie 11). To further explore the role of actin flow in durotaxis, we took advantage of CK-666, an Arp2/3 complex inhibitor that prevents branched actin formation, to decrease actin flow speed without changing NMII localization (39, 40). Upon CK-666 treatment, we observed significant decrease in actin flow speed (Fig. 2C) while the durotactic behavior were not impacted (Fig. 2D), indicating that actin flow may not play a crucial role in amoeboid durotaxis.

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

Current mechanistic models explaining directional cell migration along or against a stiffness gradient such as focal adhesion tugging are not plausible in the setting of amoeboid cells. The microtubule dynamics has been reported to impact amoeboid migration (41). Besides, we previously found that perturbation of the microtubule network - especially loss of the Golgi microtubules - abrogated single cell durotaxis in HRPE cells (28). However, no obvious alterations in durotactic FMI were detected under treatments of either the microtubule polymerization inhibitor Nocodazole or the depolymerization inhibitor Taxol (Fig. 2E, Fig. S3B, Movie 12, 13) (28, 42), indicating that similar influence of the microtubule network on mesenchymal cells may not apply to amoeboid durotaxis.

Recently, the cell rear-localized actomyosin network has been inferred to determine polarity re-establishment by mediating contractility underneath the plasma membrane and propels the locomotion of the cell body. We then asked whether this machinery could provide steering force for focal adhesion-independent durotaxis. Interestingly, treating T cells or neutrophils with the NMII inhibitor blebbistatin to disrupt cell contraction drastically reduced durotactic FMI towards zero (Fig. 2F, G, Movie 14). In contrast, Rho activator II, which can enhance myosin contractility, elevated the FMI of durotactic T cells and neutrophils (Fig. 2F, G), supporting the notion that NMII activation may play an important role in amoeboid durotaxis. Pharmacological perturbations in dHL-60 cells with blebbistatin or Rho activator II showed similar effects with what we observed in T cells (Fig. 2F, H), agreeing with myosin activity being pivotal for amoeboid durotaxis.

It has been documented that NMIIB is more sensitive to stiffness gradient than NMIIA in mesenchymal stem cells (6). Having observed that NMII inhibition significantly decreased FMI in T cells and neutrophils, we next set to explore the roles of specific NMII isoforms in amoeboid durotaxis. We generated HL-60 cells knocked down of NMIIA or NMIIB (Fig. 3A, Fig. S4A). Interestingly, cell trajectories on gradient gel revealed that loss of NMIIA rather than NMIIB abolished dHL-60 durotaxis (Fig. 3B-E, Movie 15), which was not in accordance with what has been reported in mesenchymal cells (6). To exclude functional compensation between these two NMII isoforms, we performed Western blot to detect protein levels of these two isoforms in NMIIA^KD and NMIIB^KD cells. The results showed that NMIIB protein level in NMIIA^KD cells doubled while there was no compensatory upregulation of NMIIA in NMIIB^KD cells (Fig. S4B, C), further suggesting NMIIA rather than NMIIB is responsible for amoeboid durotaxis since in NMIIA^KD cells, compensatory upregulation of NMIIB did not rescue the durotaxis-deficient phenotype.

Fig. 3:

Previous studies showed that when mesenchymal cells crawl on rigid glass, NMIIB is enriched at the cell rear (43), whereas NMIIA appears uniformly distributed (6). To examine the mechanism underlying the requirement for NMIIA but not NMIIB in amoeboid durotaxis, we assayed their distribution in cells on gradient gel. Strikingly, NMIIA was concentrated at the down-gradient side of dHL-60 cells, regardless of the front-rear axis of the cell (Fig. 3F, G). On the contrary, NMIIB showed much less correlation with the stiffness gradient (Fig. 3G), consistent with it playing a minor role in the establishment of durotactic direction. Similar distribution of NMIIA was also seen in T cells and neutrophils on gradient gel (Fig. 3H, Fig. S4D, E).

Previous studies suggested that localizing NMIIA to the cell rear is required to set cell polarity (6, 44). We then hypothesized that the down-gradient concentrated NMIIA may leverage the cell front towards the stiffer side, thus enabling efficient amoeboid durotaxis. To test this, we transfected HL-60 cells with GFP-NMIIA and monitored the fluorescent signal in durotaxis assays. We captured events when cells turned to align with the stiffness gradient and in these cases, the GFP-NMIIA signal stayed concentrated at the soft side, preceding re-polarization of the cell to form a new front-rear axis (Fig. S5A, Movie 16).

Amoeboid durotaxis is evolutionarily conserved

Having identified durotactic behavior in T cells and neutrophils, we then asked whether this low-adhesive, rapid moving durotaxis was evolutionarily conserved. To answer this, we switched to the protista Dictyostelium, which move in amoeboid mode when reside as single cells. After being plated on PA gel surface under confinement, Dictyostelium exhibited elongated morphology and extended convex membrane protrusions at the front as described before (45), which then alternated sideways for gliding (Fig. 4A, Movie 17). Agreeing with our previous findings with T cells and neutrophils, Dictyostelium also displayed stiff-side directed motility when seeded on the gradient gel (Fig. 4A-D, Movie 17). Blebbistatin application drastically dropped the durotactic FMI to around zero (Fig. 4E), while Rho activator II treatment significantly elevated this value (Fig. 4E). Moreover, in line with what we discovered in T cells, microtubule perturbation did not hamper the directionality of Dictyostelium durotaxis (Fig. 4F). These results suggest that the molecular mechanism underlying amoeboid durotaxis is largely conserved in Dictyostelium.

Fig. 4:

Simulation of amoeboid durotaxis with a mechanosensitive active gel model

To better characterize amoeboid durotaxis observed in our experiments, we established an active gel model (16), in which a cell is represented by an active droplet (Fig. 5A) c (r, t) composed of actin filaments with a certain density, whose polarization field is defined by P (r,t), with r and t denoting the position vector and time, respectively (Fig. 5B). The free energy F [c, P] to confine actin assembly into a droplet can be formulated as (16):

Fig. 5:

This energy ensured that a polar active actin phase c > c₀/2 (|P|> 0) and a passive solvent phase c =0 (|P| =0) coexist in this system, where c₀ denotes the average actin density. α is the stability constant and k determines the interfacial tension between actin and adjacent solvent phase. a is a phenomenological free energy amplitude to define the bulk property of the droplet, and κ describes the elastic constant of liquid-crystalline elasticity. In addition, fluid velocity v, which is involved in actin convection, is incorporated here. Cell migration is described by the spatial evolution of actin density c (r, t) and can be influenced by the fluid velocity and polarization field. The evolution of actin density is formulated as (16):

where M is thermodynamic mobility parameter, w denotes the polymerization rate of actin filament, and F, expressed by Eq. 1, is the free energy that constrains actins within the droplet. The incompressible Navier–Stokes equation is invoked to describe fluid velocity v (16, 46):

where P is the isotropic pressure and ^γ is the friction coefficient. Total hydrodynamic stress σ^total includes four parts, including viscous stress σ^vis (Materials and Methods, Active gel model, Eq. 7), elastic stress σ^ela (Materials and Methods, Active gel model, Eq. 8), interfacial stress between active and passive phase σ ^int (Materials and Methods, Active gel model, Eq. 9), and active stress σ^act (47). The active contraction of cells is represented by the active stress σ^act =ζ̅ cPP, where ζ̅ measures the contractile strength.

NMIIA is related to cell polarity establishment during cell durotaxis (6). In our amoeboid durotaxis experiments, we observed soft-end polarized NMIIA (Fig. S5A), which is involved in the present model. Thus, we propose that the density of NMIIA m evolves as (48):

where D_m (E) denotes diffusive ability of NMIIA and is related to the substrate stiffness E . The diffusion parameter D_m (E) outside the cell (c < c₀/2) is set to be uniform and defined by the basal diffusion parameter D₀ . Inside the cell, D_m (E) is defined by

where E_min and E_max are the minimum and maximum substrate stiffness locally sensed by the cell. _ζ̅thr is the thresholds of cell contractility and cooperates with the substrate stiffness to characterize the sensitivity of cells to the substrate stiffness gradient. is the average substrate stiffness sensed by the cell. E_m and E₀ are the threshold of stiffness sensitivity and the reference substrate stiffness, respectively, which regulate the most sensitive range of stiffness for cells. With density of actin and NMIIA defined above, the global polarity vector of cell is determined by the unit vector n̄_polar of , which points from the center of NMIIA to the cell centroid. As evidenced in our experiments, the local polarity of actin flow P is aligned to n̄_polar (Movie 6-10). Therefore, the evolution of actin polarity field can be formulated by (48, 49):

where and are the anti-symmetric and asymmetric part of ∇ v, respectively; Γ denotes the rotational viscosity and R_π/2 is a rotational matrix.

The proposed model successfully recapitulates amoeboid durotaxis found in our experiments (Fig. 5C-E). Initially, actin polarity P is assumed to be random (Fig. 5C). With increasing time, P tends to align along the stiffness gradient (Fig. 5D, Movie 18). In addition, asymmetric distribution of NMIIA is observed in our simulation, where NMIIA displays high concentration at the rear of the cell (Fig. 5E), consistent with our experiments (Fig. 3F).

Cell contractility and substrate stiffness concertedly regulate amoeboid durotaxis

Our experiments showed that decreasing cell contractility can inhibit amoeboid durotaxis. We theoretically demonstrate that with low cell contractility ζ̅, amoeboid durotaxis disappears and random trajectories of cells are observed (Fig. 6A). With increasing ζ̅, cells indeed perform directional migration along the stiffness gradient (Fig. 6B). To quantify amoeboid durotaxis in our model, we also calculate the FMI (Fig. 6E), similar to experimental statistics. Increased FMI indicates stronger amoeboid durotaxis. It is evident that with increasing cell contractility ζ̅, FMI elevates, accompanied by more robust amoeboid durotaxis.

Fig. 6:

Our model suggests that basal diffusion rate of NMIIA is larger on stiffer substrate, improving the mechanosensity of cells to substrate gradient. In addition, the model predicts that cells initially placed on softer region of gradient substrates exhibit stronger durotaxis (Fig. 6C-E). Furthermore, the initial local substrate stiffness may reverse cell durotaxis to adurotaxis. For example, under cell contractility ζ̅ =0.002, cells on softer region of gradient substrate, i.e., initial stiffness of cell centroid E=30 and 70 kPa, migrate directionally following the stiffness gradient (Fig. 6C), whereas the strong durotaxis gives way to random migration when the initial stiffness of cell centroid is 200 kPa (Fig. 6D), resulting in an FMI close to zero (Fig. 6E). To test our theoretical predictions, we segregated the gradient gel (ranging from 30 kPa to 210 kPa) into three equal regions (soft, middle and stiff) (Fig. 6F) for cell trajectory analysis. FMI of cells on the soft region topped, while cells in the stiff region displayed more random motility (Fig. 6G). Cell velocity and persistence showed no difference among these regions (Fig. 6H, I). These experiments agreed with our theoretical predictions, thereby confirming the robustness regulation of amoeboid durotaxis by local stiffness.

Discussion

Durotaxis based on focal adhesion dependent mechanosensing has been well studied for decades. However, whether cells can durotax using amoeboid migration strategies was asked only recently (5). In this study, we developed an imaging-based cell migration device that provided both spatial confinement and stiffness gradient, and with this device we demonstrated that amoeboid cells can durotax. We further uncovered the underlying mechanism to involve NMIIA polarization towards the soft-matrix-side but may not require differential actin flow up- or down-stiffness gradient.

An intriguing question remains is how cells manage to retain NMIIA on regions that downward the stiffness gradient. One likely explanation would be that NMIIA could sense substrate stiffness (6) and then locates itself to the soft end. In our modeling, we assigned NMIIA with an initial diffusion rate which increases with higher substrate stiffness. Under this consideration, NMIIA is more diffusive on the stiff end and intended to accumulate on the soft end. To experimentally verify this, future work using single particle tracking is required to analyze NMIIA diffusion rate on substrate with different stiffness. Another possible mechanism may be that NMIIA is recruited by its upstream factors which prefer to locate at softer area. Mst1 kinase is a key component of Hippo pathway that could be regulated by substrate stiffness. It has been reported that Mst1 directly regulate NMIIA dynamics to organize high and low affinity LFA-1 to the anterior and posterior membrane during T cell migration (50). Whether Mst1 is mechanosensitive and has the capacity to recruit NMIIA to the soft end still need to be testified. The mDia1-like formin A, IQGAP-related proteins and actin-bundling protein cortexillin localize like NMII to the rear of polarized, migrating Dictyostelium cells, promoting the formation of cortical actin in the rear and allowing efficient cell migration in 2D-confined environments (51). Whether these proteins localize to the soft end of durotactic amoeboid cells and recruit NMIIA is an intriguing question. We have used formin inhibitor SMIFH2 in our durotaxis assay and found this treatment slightly decreased migration velocity but did not impact durotactic behavior of T cells (Fig. S5B). The possibility that IQGAP-related proteins and cortexillin act as upstream factors that recruit NMIIA to the softer area is still open.

Aside from NMIIA, other mechanisms may also facilitate amoeboid durotaxis. Inorganic droplets can move directionally on surfaces with stiffness gradient due to the intrinsic wettability (52, 53). Droplets with smaller and wetting contact angles move towards the soft end, while those with larger and non-wetting contact angles can durotax (52). We also measured the contact angles of dHL-60 cells at both the stiffer and softer sides on gradient gel and observed non-wetting contact angles (greater than 90 degrees) on both sides (Fig. S5C) albeit the angles on the softer side are larger (Fig. S5D). Hence, it can be postulated that the smaller, non-wetting contact angle on stiffer side are also likely contribute to amoeboid durotaxis to certain extent.

Immune cell activation is regulated not only by biochemical factors, but also by the mechano-microenvironment including substrate stiffness (54). Substrate rigidity influences differentiation (55), gene expression, cell migration, morphology, and cytokine secretion (23) in T cells. Interestingly, cytotoxic T lymphocytes (CTL) has been shown to enhance killing response when encountering stiffer target cells (56). Whether stiff tumor cells can act as a mechanical guidance for CTL durotaxis is tentative to test. Immune cells are recruited and play a crucial role in tissue repair. Tissue injuries of varying origins, including chemical, mechanical, or microbiological, initiate the processes that ultimately result in fibrosis (57). Fibrosis is characterized by tissue stiffening due to excessive extracellular matrix protein deposition and cross-linking (3). It will be intriguing to investigate whether the rigidity cues in fibrotic area may regulate immune cell migration.

The search for molecular mechanisms underlying cell durotaxis has been paralleled by the development of different types of theoretical models (32). The well-established motor-clutch model (58) and random walk model (59) demonstrate that cell durotaxis is attributable to traction or cell-substrate adhesion difference. Vertex model (60) and continuum model (53) are widely used in collective durotaxis, focusing on long-range environmental stiffness difference and force generation between adjacent cells and suggesting far more efficiency in collective durotaxis than single-cell durotaxis. The active nematic model employs active extensile or contractile agents to push or pull the fluid along their elongation axis to simulate cell flowing (61). These models, which usually ignore the asymmetric distribution of polarity markers, are more suitable for mesenchymal cells forming obvious stress fibers, but might not be applicative in low adhesive amoeboid cells. The mechanosensing active gel model established here highlights the role of polarity markers in migration of cells with low adhesion. It also provides us a novel perspective that the diffusion rate difference dependent on substrate stiffness can polarize NMIIA and subsequently induce polarized actin flow along the stiffness gradient, followed by amoeboid durotaxis.

Our study also has technical and mechanistic limitations. Cells live in complex, three-dimensional physiological or pathological microenvironments. Thus, the phenomena observed in our 2D confinement assay may not faithfully recapitulate the behavior of amoeboid cells in vivo. Further measurement of in vivo stiffness gradient sensed by immune cells and more in vivo studies can broaden our understanding of amoeboid durotaxis. In addition, mechanistic studies of amoeboid durotaxis in our research is limited. We found that soft end polarized NMIIA is crucial to amoeboid durotaxis but how NMIIA is recruited to the soft area remains to be further explored. Migrating amoeboid cells commonly form spherical protrusions called blebs at their leading edges, which facilitate cell locomotion (62). Whether these cell front positioned blebs are involved in mechanosensing and determination of migrating direction also deserves further investigation.

Materials and methods

Cell lines and cell culture

The HL-60 cell line (derived from a 36-year-old female with acute promyelocytic leukemia) was purchased form National Infrastructure of Cell Line Resource (NICR). Human embryonic kidney 293T (HEK 293T) cells were kept by our laboratory. All cells were passed no more than 10 times and were mycoplasma free. HL-60 cells were cultured in RPMI-1640 medium (Hyclone, SH30809.01) supplemented with 15% fetal bovine serum (FBS; Vistech, VIS00CU3524), 100 U/mL penicillin and 100 μg/mL streptomycin at 37 with 5% CO₂. The cultured cells were diluted once every 2-3 days into a density of 1×10⁶ cells/mL. For differentiation, HL-60 cells were diluted into RPMI-1640 medium containing 1.3% DMSO (VWR Life Science) with an initial density of 1× 10⁶ cell/mL. For all the experiments, only cells differentiated for 5-6 days were used. HEK 293T cells were cultured in Dulbecco’s modified Eagle medium (DMEM, Corning, 10-013-CRVC) supplemented with 10% FBS, 100 U/mL penicillin and 100 μg/mL streptomycin at 37 with 5% CO₂. For cell passage, cells were washed with phosphate-buffered saline (PBS, Macgene, CC010) and digested with 0.25% trypsin (Macgene, CC012).

Dictyostelium cells were maintained in HL5 medium containing G418 (10-40 μg/mL), Hygromycin (50 μg/mL), or both as needed, as described in (63).

Antibodies and reagents

The following antibodies were used in this study: anti-GAPDH (ab181602) from Abcam, anti-MYH9 (A16923) and anti-MYH10 (A12029) from ABclonal, anti-Paxillin (AB_39952) from BD_Biosciences.

The following reagents were used in this study: Blebbistatin (2946047) from EMD_Millipore, Rho activator II (CN03) and SiR-Actin (CY-SC001) from Cytoskeleton, nocodazole (M1404), CK-666 (182515) and SMIFH2 (S4826) from Sigma-Aldrich.

NMIIA and NMIIB knockdown cell line generation

The following short hairpin RNA (shRNA) primer were used to generate NMIIA and NMIIB knockdown HL-60 cell lines:

• Human shRNA forward shNMIIA, 5′-GCCAAGCTCAAGAACAAGCAT-3’.

• Human shRNA forward shNMIIB, 5’-GCCAACATTGAAACATACCTT-3’.

The plasmid, together with other helper plasmid (pCMV-VSV-G and psPAX2), were transfected to HEK 293T cells at 60-80 % confluence. The virus-containing supernatant was harvested 48 h later, and concentrated 100 folds. 1×10⁵ HL-60 cells were infected with 100 μL concentrated virus supernatant, centrifuging at 1000 g for 2 h. Polybrene (hexadimethrine bromide) was added at a final concentration of 10 μg/mL to increase infection efficiency. The knockdown efficiency was verified by Western blotting.

Drug treatment

Drug treatment was performed according to previous publications. CK-666 was used at concentration of 100 µM and pre-treated for 5 h before imaging. Blebbistatin was used at concentration of 10 μM and pre-treated for 10 min before imaging. Rho activator II was used at concentration of 0.25 μg/mL and pre-treated for 2 h before imaging. Nocodazole was used at concentration of 32 μM and pre-treated for 10 min before imaging (42). Taxol was used at concentration of 70 nM and pre-treated for 10 min before imaging (42). SMIFH2 was used at concentration of 15 µM and pre-treated for 5 h before imaging. All drugs were incubated for the whole experiment.

Isolation of murine neutrophils

Bone marrow-derived neutrophils were isolated by Percoll gradients as described by Li et al. (64). Mice were euthanized and bone marrow was extracted from the femurs by perfusing 6 mL pre-cold FACS solution (PBS with 2% FBS). Bone marrow cells were pelleted by centrifugation (300 g, 5 min, 4) and then resuspended in 2 mL FACS. Percoll solution (Pharmacia) and 10× PBS were mixed (Percoll: 10× PBS = 9:1) to obtain a 100% Percoll stock. 100% Percoll stock was diluted with 1× PBS to get 72%, 60% and 52% Percoll solutions. Bone marrow cell suspensions were loaded in the uppermost layer. After centrifugation (1100 g, 30 min, 4°C), the neutrophils were collected in the band between the 72% and 60% layers. Before experiment, the neutrophils were stimulated with 100 nM fMLP (N-formyl-methionyl-leucyl-phenylalanine) (Sigma, F3506) for 10 min.

CD4⁺ Naïve T cell purification

Mice were euthanized and the spleens were harvested and homogenized with a 40-µm cell strainer. After removing red blood cells by ACK (Ammonium-Chloride-Potassium) lysis, untouched primary naïve T cells were isolated with an EasySep Mouse T cell Isolation Kit according to the manufacturer’s protocol (BioLegend). The purified CD4⁺ Naïve T cells were stimulated with 20 ng/mL phorbol 12-myristate13-acetate (PMA) and 1 μg/mL ionomycin for 4-6 h to activate the integrin pathway before migration assay. Interaction between Lymphocyte Function-Associated Antigen 1 (LFA-1) and its ligand Intercellular Adhesion Molecule 1 (ICAM-1) has been reported to drive T cell movement by creating tangential friction between the actin cortex and the environment (24). In this case, T cells were allowed to migrate on the ICAM-1 coated surface.

Mice

Male C57BL/6 WT mice were obtained from a special pathogen-free facility at Peking University Care Industrial Park, and were used for experiments at the age of 4-6 weeks. All procedures were approved and monitored by the Animal Care and Use Committee of Peking University.

Gradient or uniform polyacrylamide (PA) gel preparation and functionalization

PA gel preparation and functionalization have been adapted from the previous work in our laboratory (28, 29). Specially, 40% acrylamide and 2% bis-acrylamide solutions were combined at 11.73% and 0.33%, respectively, to make a 55 kPa gel. 0.5% (w/v) Irgacure 2959 was added to catalyze cross-linking when exposed to UV light. Gels were cast on cover glasses which was treated with bind-silane (BioDee, Beijing, China) followed by treatment with 0.5% glutaraldehyde (Sangon Biotech, Beijing, China) solution. To ensure complete polymerization, the whole acrylamide mix solution was first exposed to the UV light for 10 min without covering (for the initial nucleation in the polymerization reaction). To make gradient stiffness, an opaque mask was put between the gels and UV light. Then the mask was removed slowly by a microinjection pump with constant speed (40 μm/s for 10 min) to produce the steep stiffness gradient gels. After polymerization, the upper coverslip was peeled off the gel, leaving a thin layer of gel on the activated surface. The PA gel was then washed extensively in PBS. The PA gel was functionalized with 2 mL soak solution (137 mM NaCl and 5% (v/v) glycerol) for 1 h at room temperature. After that, 2 mL mixed buffer (pH = 4.5) containing 15 mM 1-ethyl-3-[3-dimethylaminopropyl] carbodiimide hydrochloride (EDC), 25 mM N-hydroxysulfosuccinimide (NHS), 100 mM 2-(N-morpholino) ethane sulfonic acid (MES) and 10% (v/v) glycerol were added. The PA gel was incubated within the mixed buffer in dark at room temperature for 30 min. Then, the PA gel was coated with fibronectin (50 μg/mL) or ICAM-1 (10 μg/mL) diluted in PBS for 35 min at room temperature. The PA gel was then washed with PBS three times and stored at 4°C for up to 1 week. The stiffness was measured with atomic force microscopy (AFM).

Uniform PA gels were made from 40% acrylamide and 2% bis-acrylamide mixed with 10% ammonium persulfate and 1% TEMED, where varying ratios of acrylamide and bis-acrylamide were used to create gels of known reproducible stiffness (65). The stiffness was measured with AFM.

2D confinement assay

Cells were seeded on the functionalized gradient gel or uniform gel and settled down for about 30 min. The culture medium was aspired and a small amount of medium was left on the gel to prevent detachment and desiccation of the cells. Another gradient or uniform gel was carefully placed on top of the cells to construct a sandwich-like confinement device. This confinement device was incubated at 37 for at least 30 min allowing the cells to adapt to increased stress in the physical confinement before imaging. To avoid edge effect, fields close to the edge of the gel were not selected for imaging. Unless otherwise stated, all durotaxis assay were proceeded with this confinement device.

Immunofluorescence and imaging analysis

Cells were plated on acid-washed coverslips coated with 10 μg/mL fibronectin at room temperature for 30 min. Cells were then fixed with 4% paraformaldehyde at room temperature for 15 min, permeabilized with 0.5% Triton X-100 in PBS for 5 min, washed with PBS once for 5 min, and sequentially blocked with 10% bovine serum albumin (BSA) for 1 h at room temperature. Then, the primary antibody was appropriately diluted in PBS and cells were incubated for 1 h at room temperature. After washing with PBS three times, the cells were incubated with Alexa Fluor 488- or Alexa Fluor 555-conjugated secondary antibody (Thermo Fisher Scientific) for 1 h at room temperature. After washing with PBS three times, the coverslips were mounted with Prolong Diamond Antifade (Thermo Fisher Scientific). After mounting medium is solidified, single plane images were captured using a 63×1.4 NA objective lens on Andor Dragonfly epi-fluorescence confocal imaging system.

Ultrastructure expansion microscopy (U-ExM)

U-ExM procedure was performed as described by Gambarotto et al., 2021 (66). Briefly, CD4⁺ Naïve T cells were seeded on a gradient PA gel with another upper gel providing confinement. 4% PFA was used to fix cells for 15 min at room temperature. After fixation, the upper gradient PA gel is carefully removed and the bottom gradient PA gel with seeded cells were immersed in an anchoring solution containing 1% acrylamide and 0.7% formaldehyde (Sigma, F8775) for 5 h at 37 °C. Next, each gradient PA gel was placed on top of one drop of gelling solution (0.1% N,N’-methylenebisacrylamide, 0.5% ammonium persulfate, 0.5% N,N,N’,N’-TEMED, 10% acrylamide and 23% (w/v) sodium acrylate) with cells facing down. The gelling process was fully initiated after 5 min on ice and completed after 1 h at 37 °C. The solidified gels were then detached from the gradient PA gels and denatured in denaturation buffer (50 mM Tris-BASE, 200 mM NaCl and 200 mM SDS, pH = 9.0) for 20 min at 90 °C. In the first round of expansion, the solidified gels were immersed in ddH₂O overnight and then labeled with primary and secondary antibody. Before confocal imaging, the solidified gels were completely expanded through one more round of expansion in ddH₂O and then mounted on poly-L-lysine-coated confocal dishes.

Live cell imaging and durotaxis analysis

Time-lapse videos were acquired for 15 min at 15 s intervals using a 10× dry objective lens (NA 0.3, Olympus, Tokyo, Japan) on a deconvolution microscope (CellTIRF). Images were analyzed with “manual tracking” and “chemotaxis tool” plugins of ImageJ. Coordinates and distances of cell movement were tracked using the ‘Manual Tracking’ plugin of ImageJ, then tracking data were imported into the ‘Chemotaxis Tool’ plugin to generate statistic feature such as velocity, FMI (forward migration index), directionality and plot feature such as rose plot.

Actin flow analysis

Quantitative fluorescence speckle microscopy (qFSM) was applied to analysis the actin flow of dHL-60 cells on PA gel. In general, dHL-60 cells pretreated with 0.1 μM SiR-Actin for 30 min were plated on PA gel as described above. Live cell movies were obtained for 10 min using a 63× 1.4 NA objective lens on Andor Dragonfly confocal imaging system. Movies were analyzed using a previously described qFSM software in MATLAB (34). Full cell masks were generated using automatic thresholding (MinMax setting). Flow analyses were performed using the flow tracking setting with a six-frame integration window. The average actin flow rate was calculated for each movie (n = 10-20 cells per group). To compare the overall fluorescence of the cells used in qFSM, an ROI encompassing the cell perimeter was made and the mean fluorescence intensity of this ROI was recorded for each cell.

Western blotting

For Western blotting, suspended HL-60 cells were harvested and centrifuged at 300 g for 5 min and then washed with PBS once. Cells were lysed in radio immunoprecipitation assay (RIPA) buffer (50 mM Tris-HCl pH 8.0, 150 mM NaCl, 1% Triton X-100, 0.5% Na-deoxycholate, 0.1% SDS, 1 mM EDTA, and protease inhibitor cocktail) for 10 min on ice. Lysates were centrifuged at 12,000 rpm for 10 min at 4, and the supernatants were collected. 5× SDS loading buffer was added to the supernatants and the mixture were boiled for 10 min at 95 °C. Protein samples were run on 10% SDS PAGE (H2O, 30% acrylamide, 1.5 M Tris-HCl pH 8.8, 10% ammonium persulphate, and tetramethylethylenediamine (TEMED)) and transferred onto nitrocellulose membranes by wet electrophoretic transfer, followed by 10% nonfat-milk blocking at room temperature for 1 h. The primary antibody incubations were at 4°C overnight or at room temperature for 2 h, followed by the secondary antibody incubations at room temperature for 1 h. The X-ray film was used to detect and record the band intensities. The fixed X-ray film was scanned, and digital images were obtained.

Atomic Force Microscope (AFM) measurement

A Bioscope Resolve atomic force microscope (AFM, NT-MDT) mounted on an Olympus IX73 inverted microscope was used to investigate the mechanical properties of polyacrylamide gels made from different formulations. The inverted microscope was used to visually position the AFM tip with respect to the specimen. Silicon nitride probes with a squared pyramid tip (DNP, nominal cantilever spring constant = 0.06 N/m, Bruker) were used in this study. After system stabilization, the thermal tune method was used to determine the exact spring constant before each experiment. The Hertz-Sneddon model for pyramid tips was used to extract Young’s modulus of the sample. For each indentation, the following parameters were used: 1 nN set point, 4.0 μm Z range, and an extend speed of 2.0 μm/s.

Active gel model

Total hydrodynamic stress σ^total includes four parts, including viscous stress σ^vis =η (∇v+(∇v)^T) (7), elastic stress σ^ela, interfacial stress between active and passive phase σ ^int, and active stress σ^act (47). ^η is the shear viscosity, and the elastic stress σ^ela is formulated as:

where ξ is a shape factor. We take ξ =1 .1, which means shear-aligning rod-like actin are considered (67). The interfacial stress between the active and passive phase is calculated as:

where I is the identity tensor and f denotes the free energy density, which has been given by the integrand in Eq. 1.

The integration is performed using a vorticity or stream-function finite difference scheme (68) on a square _{1 2 8 × 1 2 8} domain with periodic boundary conditions, whose grid spacing is _{Δ x = Δ y = 1} . The initial circular droplet with radius _{R = 7} μ m is placed at the center of square domain. At the beginning, the unit polarity field P is randomly generated and the fluid velocity v is zero. A fourth-order Runge-Kutta method with time step Δ t = 0 . 1 is employed to implement the time integration. To normalize the system, three scales are chosen as: length scale L = 1 μ m, time scale T = 1 0 m s and force scale F = 1 0 0 n N . The parameters used in the simulations are chosen from previous work (16) and our experiments, which are provided in Table S1 in the supplementary material.

Statistical analysis

All the plots and statistical tests were performed using GraphPad Prism software. The presented values were displayed as mean ± SEM for at least three independent experiments (as indicated in the figure legends). The significance was calculated using unpaired Student’s t tests or One-way ANOVA, as indicated. In all statistical test, P > 0.05 was considered as not significant.

Acknowledgements

We thank Prof. Dan Lv, Dr. Yuxing Huang, Dr. Yingxue Rong, Dr. Yuan Jin, Dr. Peng Shi, Chunlei Zhang and Xiaoyu Ren from Peking University for technical support and data discussion. We thank Prof. Xiangdong Li from Chinese Academy of Sciences for sharing the NMIIA construct.

Additional information

Funding

National Natural Science Foundation of China grant 32122029 (CW)

National Natural Science Foundation of China grant 11922207 (BL)

Author contributions

Conceptualization: CW, XY, CK

Methodology: CW, BL, XY, CK, PC, YY

Investigation: CK, XY, PC

Visualization: CK, XY, PC, DL

Supervision: CW, BL, HC

Writing—original draft: CK, PC, XY

Writing—review & editing: CW, BL, CK, XY, PC, YH

Competing interests

no competing interests.

Supplementary Material

Fig. S1

Fig. S2

Fig. S3

Fig. S4

Fig. S5

Table S1.