Cell response to substrate rigidity is regulated by active and passive cytoskeletal stress

We used a microfabricated array of flexible polydimethylsiloxane (PDMS) pillars to measure the traction forces exerted by the cell while simultaneously observing the organization of the actin cytoskeleton (Fig. 1A). By tuning the height of the pillar, we also changed the stiffness of the pillar (in a cantilever bending definition) while maintaining constant Young’s modulus (∼2 MPa) of the PDMS and similar diameter (∼2 μm) (SI Appendix, Fig. S1A). The top surface of the pillar substrate was coated with fibronectin via microcontact printing, and the sidewalls were passivated (Materials and Methods) such that cells only attached to the pillar tops. We seeded wild-type REF52 (REF52-WT) fibroblasts onto pillar substrates with stiffness 4 nN/μm and 55 nN/μm for 5 h and performed immunostaining to observe the actin organization (Fig. 1B) and protein localization (Fig. 1C). Consistent with previous studies (12, 13), on soft pillars, actin organized into a system of radial and transverse fibers with circular symmetry; on stiff pillars, it globally aligned into polarized, ventral stress fibers.

On soft substrates, ACTN4 concentrated along short radial fibers nearby focal adhesions and, to a lesser extent, along the transverse fibers (Fig. 1C), whereas myosin IIA only concentrated along transverse fibers. This was similar to fibroblasts spreading into circular patterns at early times (22). On stiff substrates, both myosin IIA and ACTN4 localized along ventral stress fibers (Fig. 1B), consistent with other studies (29). While ACTN binds integrin and has been shown to play a role in focal adhesions (30), we observed that the peak ACTN intensity was roughly 1 μm toward the adhesion proximal end from the peak intensity of paxillin and fibronectin (SI Appendix, Fig. S1B). As both the organization of actin as well as the localization of myosin IIA and ACTN4 changed as a function of substrate stiffness, we questioned whether these proteins that relocated during polarization were also mechanistically involved in rigidity sensing.

To perform live cell experiments and facilitate simultaneous monitoring of both actin organization and cell traction forces, we generated a REF52 line stably expressing tdTomato-F-tractin (REF52-Ftractin), an f-actin reporter (31). We seeded the cells onto soft and stiff pillars and quantified the organization of the actin cytoskeleton at the cell scale by the nematic order parameter (10, 13) (Fig. 2A), which is zero when actin is isotropic or circular and one when actin is polarized along a single axis (Materials and Methods), and the cellular traction forces (Fig. 2B).

We treated cells with varying concentrations of blebbistatin to test the effect of myosin II on polarization and traction force generation (Fig. 2 C–E). Cells treated with high concentrations (>20 μM) displayed markedly reduced traction stresses and a disorganized actin network on both pillar stiffnesses, while cells treated with very low concentrations (<1 μM) exhibited similar rigidity-dependent ordering of actin and traction stress patterns as in untreated cells. Surprisingly, at intermediate concentrations (2.5–10 μM), traction stresses were moderately attenuated and cells on soft pillars formed ventral stress fibers and polarized. While it was counterintuitive that reducing myosin II activity promoted ventral stress fiber formation, Oakes et al. observed stress fiber formation despite large (∼75%) reductions in cytoskeletal tension (32). Cells treated with 5 μM blebbistatin retained stress fibers and localization of both ACTN4 and myosin IIA to the cell lamella (SI Appendix, Fig. S2 A and B). Cells on soft pillars treated with varying amounts of the Rho-associated protein kinase (ROCK) inhibitor Y-27632 behaved similarly (SI Appendix, Fig. S2 C and D); traction force magnitudes inversely scaled with Y-27632 concentration, at intermediate concentrations actin organized into ventral stress fibers with global alignment, and actin organization was lost at high concentrations. Furthermore, treating cells with either nocodazole or calyculin A to increase contractility resulted in lower nematic ordering on both soft and stiff substrates (SI Appendix, Fig. S2 E and F).

The morphology of the cells was also affected by treatment with blebbistatin, with intermediately treated cells having higher area and aspect ratio (SI Appendix, Fig. S3 A–D). To test if increasing cell area directly caused the enhanced nematic ordering in myosin-inhibited cells, we seeded cells onto pillars stamped with fibronectin in circular (diameter = 60 μm) and teardrop patterns to confine the cell (SI Appendix, Fig. S3 E–G). On soft pillars, untreated cells displayed the usual system of circular transverse arcs and radial stress fibers, and cells treated with 5 μM blebbistatin had globally aligned ventral stress fibers. Therefore, we concluded that actin organization in myosin II-inhibited cells on various pillars stiffnesses was a consequence of cytoskeletal properties rather than solely cell shape changes, which has been previously explored (33).

The maximum traction force on a single soft pillar was lower than that on stiff pillars, although the traction forces on soft pillars were broadly distributed under the cell and along the entire perimeter, whereas the traction forces on stiff pillars condensed onto a subset of pillars at the cell edge on its long axis. We quantified the total traction force exerted by the cell (Materials and Methods) and observed that the total traction force on stiff pillars was about 50% higher than on soft (2.8 ± 0.3 vs. 1.9 ± 0.3 μN for untreated cells on stiff and soft, respectively) (Fig. 2F). Thus, cells were able to deflect a larger amount of soft pillars to a larger distance than stiff pillars to achieve a similar order of magnitude of traction force despite the pillar stiffness being drastically different, which indicated a coupling of both adhesion- and cell-scale mechanosensitivity.

We saw a strong correlation between traction stresses and alignment of actin filaments, whereby actin aligned at high traction stresses on stiff substrates (Fig. 2E); however, on soft substrates, actin only globally aligned at intermediate traction stresses (Fig. 2D). As myosin was inhibited, the active stress in the actin network decreased and its passive rheological response was modified as well. Because the global mechanical response of cells was controlled by the coupled action of active and passive cross-linkers (34), we sought to disentangle such effects and examine the role of passive cross-linking in rigidity sensing.

We tuned the amounts of passive ACTN cross-linking by small interfering RNA (siRNA)-mediated knockdowns of ACTN1, ACTN4, or both ACTN1 and ACTN4 simultaneously (pan-ACTN), or by transient overexpression of ACTN1-EGFP or ACTN4-EGFP (SI Appendix, Fig. S4 A–C). As a control, cells transfected with nontargeting (NT) siRNA exhibited a rigidity-dependent propensity to polarize (Fig. 3 A and B) and spatial organization of traction forces. Cells with ACTN4 or pan-ACTN knockdown formed bundled ventral stress fibers, consistent with other studies (29, 35, 36), and had increased nematic organization of actin on soft substrates. The pan-ACTN knockdown resulted in stress fibers that had less global ordering than ACTN4 knockdown or control cells on stiff substrates. Cells overexpressing ACTN4-EGFP preserved a system of radial and transverse actin fibers and had reduced nematic ordering on all substrates. In addition, the actin network was more uniformly dense with few bundles. Knockdown of only ACTN1 did not affect rigidity sensing or actin bundling; however, overexpressing ACTN1-EGFP had a similar phenotype as overexpressing ACTN4-EGFP (SI Appendix, Fig. S4 D and E). Furthermore, we overexpressed ACTN1-ABDdel-EGFP (30), a dominant-negative mutant in which the actin binding domain is deleted but will still form dimers with endogenous ACTN (both ACTN1 and ACTN4; ref. 37) to inhibit cross-linking (SI Appendix, Fig. S4 D and E). This resulted in a phenotype similar to the pan-ACTN knockdown whereby ventral stress fibers formed on all stiffness, had increased ordering compared to control cells on soft substrates, and decreased ordering on stiff substrates. The ACTN4 knockdown phenotype was rescued by overexpression of either ACTN1-EGFP or ACTN4-EGFP, and we observed a strong negative correlation between ACTN expression level and nematic order parameter (SI Appendix, Fig. S5), which also accounted for cell-to-cell variability in protein overexpression amount. Morphologically, the aspect ratio of the cell shape exhibited a similar trend as the actin nematic order parameter (SI Appendix, Fig. S4F). Therefore, we concluded that actin organization was regulated by ACTN and that an optimal amount of cross-linking promoted polarization on various substrate stiffnesses; too much cross-linking resulted in unpolarized cells on all stiffness and too little resulted in isotropic actin networks, with cells on soft substrates requiring less ACTN cross-linking to polarize.

Altering ACTN cross-linking also perturbed the magnitude and spatial patterns of traction forces (Fig. 3 A and C). Consistent with other studies (35, 38), the total traction force exerted by the cell was highest in ACTN4 knockdown (Fig. 3C). On soft substrates, the order parameter of the traction force vectors was higher for ACTN4 or pan-ACTN knockdown cells, whereas it was lowest on all substrates with ACTN4-EGFP overexpressing cells (SI Appendix, Fig. S4G). Both the amount of cell traction forces pointing toward the cell center of mass (SI Appendix, Fig. S4H) as well as the spatial correlation of traction force vectors (SI Appendix, Fig. S4I) was highest in ACTN4-EGFP overexpressing cells and decreased as ACTN cross-linking was reduced, which implied that the spatial symmetry of traction forces was controlled by ACTN concentration, in line with another study (28).

We next performed time lapse imaging of the cells to observe the dynamics of traction forces and actin (Movies S1–S4). As previously observed (13), control cells on soft pillars had a combined system of radial and transverse fibers that flowed inwards from the cell boundary. In contrast, cells on stiff pillars formed ventral stress fibers that were stable throughout a 40-min imaging window (SI Appendix, Fig. S6 A–C). We observed that the force fluctuation magnitude was higher in pan-ACTN knockdown cells compared to control (SI Appendix, Fig. S6D). While static traction forces were radially directed toward the center of mass, we observed that the direction of the dynamic traction forces on soft pillars was more orthoradial (SI Appendix, Fig. S6F). On stiff substrates, control cells formed ventral stress fibers and the traction forces fluctuated in the same direction as the static forces (SI Appendix, Fig. S6E). In pan-ACTN knockdown cells, the stability of ventral stress fibers that formed on soft pillars was similar to those on stiff and the dynamic forces fluctuated along the same direction as the static (SI Appendix, Fig. S6 A and F).

Our experimental results of actin organization on micropillars are summarized in Fig. 3D. When the substrate is soft, or ACTN is overexpressed, cells retain a circular shape with a combination of radial and transverse fibers that flow inward and myosin motors indirectly develop traction forces. When the substrate stiffness is high, ACTN4 is knocked down, or myosin II is inhibited with small concentrations of blebbistatin, then circular symmetry is broken, ventral stress fibers form, and the cytoskeleton is more polarized. When the ACTN cross-linking is highly attenuated (pan-ACTN knockdown or ACTN1-ABDdel overexpression), or contractile activity is depleted by a large concentration of blebbistatin, then the cytoskeleton is more isotropic, although ACTN depletion promotes ventral stress fiber formation and large concentrations of blebbistatin abolish stress fiber formation.

We observed increased actin ordering at an optimal amount of either myosin II activity or ACTN cross-linking. However, the magnitude of traction stress at which order arose on a given stiffness was not the same in the two scenarios as blebbistatin treatment reduced traction forces while ACTN knockdown increased traction forces. We next considered how myosin II and ACTN affected the rheology of the cell; the elasticity of a single cell correlates with traction force (39) and for an actin network scales with cross-linker concentration (23). As both passive and active cross-linking contribute to cell rheological properties, we considered that the ordering of the cytoskeleton might be more generally governed by the actin network stiffness.

We seeded cells onto plastic dishes and performed atomic force microscopy (AFM) nanoindentation (Fig. 4A and SI Appendix, Fig. S7) in a rapid force-volume scanning mode with high lateral resolution (Materials and Methods) and with different conditions of ACTN knockdown (ACTN4, pan-ACTN, NT control), overexpression (ACTN4-EGFP), and cells treated with 5 μM blebbistatin. The local elastic modulus in the cytoskeleton strongly depended on the precise location probed; points on a stress fiber were about an order of magnitude stiffer than indentation points between the stress fibers (SI Appendix, Fig. S7D). Further, by correlating the local elastic modulus with the local height, we observed that very thin lamellipodial and thick nuclear regions were both softer than the lamella region (SI Appendix, Fig. S7E). We found that ACTN4-EGFP overexpression resulted in the stiffest lamella (here defined as locations with height <2 μm), followed by control, ACTN4 knockdown, and pan-ACTN knockdown, indicating that the mean lamella stiffness positively correlated with ACTN concentration (Fig. 4 B and C). By scanning we resolved the stiffness of stress fibers within a cell (Fig. 4D) and found that the stress fiber stiffness decreased with blebbistatin treatment. As the protein localization of ACTN4 and myosin IIA remained on stress fibers after blebbistatin treatment (SI Appendix, Fig. S2 A and B), we attributed this stiffness decrease to a loss of contractility. Cells with ACTN4 knockdown had stress fibers with similar stiffness as control; however, there were more soft regions between the fibers as they became more bundled. Cells with ACTN4-EGFP overexpression were unpolarized and exhibited the stiffest lamella; however, the nuclear region of these cells was softer than in the other conditions, which may have been indicative of a defect in the perinuclear actin cap which control cells could form.

Control cells on soft substrates or cells with ACTN overexpression appeared to be incapable of undergoing a symmetry breaking process which cells must first undergo to establish polarity, whereas control cells on stiff substrates, ACTN knockdown cells, or cells with intermediate myosin II inhibition had broken symmetry. This behavior can be recapitulated in a phenomenological physical model, whose main ingredients are summarized below (see SI Appendix for details). The model provides a minimal coarse grained description of the actin cytoskeleton of a cell seeded on a surface as a two-dimensional layer of active gel that can undergo an isotropic to nematic transition upon increasing actin filament density ρ, analogous to that of lyotropic liquid crystals (13, 40). We adopt the simplest mean-field description where variables are assumed to be uniform in space. The alignment of actin filaments can then be quantified by the cell-averaged nematic order parameter S, which satisfies close to the isotropic-nematic transition:for ρ > ρ_c while S = 0 for ρ < ρ_c, where $\propto$ denotes proportionality and ρ_c is the critical actin density required for symmetry breaking. Qualitatively, this yields a negligible actin ordering at low density (ρ < ρ_c) and an increasing ordering with density for ρ > ρ_c. We assume below that cells remain close to the isotropic-nematic transition. As opposed to classical equilibrium systems, the model assumes that the filament density is actively regulated by the total averaged stress σ^s at the cell-substrate interface. To linear order in σ^s (limit of low activity), this can be written ρ = ρ₀ + χTr(σ^s), where χ > 0 is a phenomenological coupling constant that encodes the mechanosensitive response to stress and ρ₀ is a reference density in absence of stress; under this hypothesis, the mean actin filament density increases when the pulling stress increases at the cell-substrate interface. This is qualitatively supported at the level of focal adhesions, which are expected to mediate such mechanosensitive response; fluorescence recovery after photobleaching of GFP-talin showed an increased stability of focal adhesions on stiff pillars or with higher pillar traction force compared to soft pillars or lower traction forces (SI Appendix, Fig. S8 and Movie S5), thus the stability of focal adhesions and, hence, actin filament density, was indeed gated by local force.

In the cell, the stress can be decomposed into a passive component σ^e and an active component σ^a. The passive stress is assumed to be of elastic nature and controlled mainly by the elastic modulus E_c of the actin network. Here, we assume for the sake of simplicity a classical isotropic elastic response (independent of ρ in the limit of low activity), which is expected to hold close to the isotropic-nematic transition. The cytoskeleton is described at a coarse-grained level as a uniform material, E_c is therefore the effective cell-scale stiffness, which is likely to be controlled at the microscopic scale by the local actin organization (stress fibers or cortex). σ^a is induced by myosin contractility, which is parametrized by the phenomenological constant ζ₀; the isotropic component of σ^a is then set by ρ and ζ₀ according to ${\text{σ}}_{ij}^a={\zeta }_0\rho {\delta }_{ij}$. Continuity of stress at the cell-substrate interface can then be written σ^e + σ^a = σ^s. After taking the trace and averaging over the cell contour it follows thatwhere E_s is the Young’s modulus of the substrate, assumed elastic (the pillar substrate Poisson’s ratio ν_s is assumed to be zero for simplicity), and C is a dimensionless constant that depends on cell shape and Poisson’s ratio. This equation defines the scaling function f that depends on E_s and E_c only via E_s/E_c; note however that f is not universal since it depends on the cell shape and Poisson’s ratio. The main prediction of this simple model is hence that the density and nematic organization of actin are critically controlled by the elastic modulus of the substrate relative to that of the cell E_s/E_c (SI Appendix, Fig. S9) and that the critical substrate stiffness k* (E_s when ρ = ρ_c) required for the cell to break symmetry is determined by the stiffness of the actin cytoskeleton, as was experimentally observed. Cells on soft surfaces had less bundled stress fibers and lower traction forces on individual pillars at the cell-surface interface, whereas cells on stiff substrates formed ventral stress fibers and had higher traction forces on individual pillars. When ACTN was knocked down we observed a decrease in the stiffness measured by AFM (Fig. 4) and increased local actin density, traction stress, and ordering of stress fibers on soft substrates (Fig. 3). Overexpression of ACTN resulted in the opposite phenotype; cell stiffness increased such that the critical stiffness was no longer accessible and cells remained unpolarized. Consistent with this, lowering cell stiffness with intermediate concentrations of blebbistatin while not completely abolishing contractile activity was sufficient to induce cytoskeletal order on soft substrates. This mechanosensing mechanism requires active processes and, indeed, in the regime of very low active stress with large doses of blebbistatin (ζ₀→0), the phenotypes of soft and stiff substrates converge, as intuitively expected and correctly predicted by the model. Furthermore, this mechanism requires cells to form adhesions and exert traction stresses; when this is not possible, for example in a talin knockout (41, 42), cells cannot form ventral stress fibers or polarize on any substrate.

Importantly, Eq. 1 together with Eq, 2 predict that actin ordering S depends on E_s and E_c only via E_s/E_c. The main prediction of the model was found to be in good agreement with experimental observations (Fig. 5A). Note that f determined in Eq. 2 depends in principle on the cell Poisson’s ratio, which was assumed constant in Fig. 5A; large variation of the Poisson’s ratio have however been reported and could lead to important effects (43). It should be noted that while cell stiffness measured by AFM and in the model both correlated with ACTN concentration and myosin II activity, the exact measured values were different from those used in the model due to the complex nature of cellular mechanical properties including heterogeneous, anisotropic, and unknown Poisson’s ratio of actin structures.

In our experiments, the polarization of the actin cytoskeleton and cell polarization appeared to go hand-in-hand with stress fibers spanning the long axis of the cell body. As the actin cytoskeleton is not the sole determinant of cell polarity, we questioned whether nematic organization of actin also affected the organization of the microtubule cytoskeleton. Disrupting microtubules with nocodazole resulted in decreased nematic ordering of the cytoskeleton (SI Appendix, Fig. S2 E and F), which we attributed to an increase in contractility from released GEF-H1 (44). To test this, we seeded cells onto soft and stiff pillar substrates and performed immunostaining to visualize the microtubules and quantified the order parameter in the same manner as actin. We found that the microtubule cytoskeleton became more linearly organized on stiff substrates compared to soft substrates (SI Appendix, Fig. S10) and furthermore followed the same trend as the actin cytoskeleton of soft and stiff substrates as ACTN was knocked down or overexpressed, or myosin II was inhibited. This provided evidence that the breaking of symmetry and polarization of the actin cytoskeleton also resulted in downstream cellular adaptations to substrate rigidity.

PDMS micropillars were fabricated as previously described (55). Briefly, 10:1 PDMS ratio was mixed and poured into deep-reactive ion etched silicon molds, degassed, and cured at 80 °C for 2 h. Human plasma fibronectin (Roche) was conjugated with Atto-647N using a protein labeling kit (catalog no. 76508, Sigma-Aldrich). Blank PDMS stamps were incubated in 50 μg/mL pure fibronectin and 1 μg/mL conjugated fibronectin in Dulbecco’s phosphate-buffered saline (DPBS) at room temperature for at least 90 min, washed once with Milli-Q water, and dried in N₂ stream. Pillars were treated in UV-ozone for 15 min (UV Ozone ProCleaner Plus, BioForce Nanosciences), and fibronectin was transferred to the pillar tops by microcontact printing, incubated with 0.2% Pluronic F-127 for 1 h, and washed multiple times with DPBS and left at 4° until ready to use. The pillar spring constant k was determined as in Schoen et al. (56); the Young’s modulus of PDMS was assumed to be 2 MPa and ν = 0.5. Pillars were arranged in a close-packed hexagonal lattice with 4 μm center-to-center distance and the dimensions of pillars (imaged by scanning electron microscopy) were: d = 2.1 μm with h = 4.1 μm (k = 55 nN/μm), d = 2.0 μm with h = 7.0 μm (k = 11 nN/μm), and d = 1.8 μm with h = 8.6 μm (k = 4.1 nN/μm).

The order parameter was calculated using a custom-built MATLAB program. Briefly, the local orientation θ of actin and coherence was determined at each pixel from the structure tensor of the image (Peter Kovesi, MATLAB and Octave Functions for Computer Vision and Image Processing, Available from: https://www.peterkovesi.com/matlabfns). Pixels with coherence less than 0.08 were discarded. The order parameter is S = <cos(2|θ − θ_avg|)>, where θ_avg is the average angle of actin. All averages were weighted by the fluorescence intensity. The radial order parameter was calculated by as S_θ = <cos(2|θ − θ_COM|)>, where θ_COM is the angle of the vector between a given position to the center of mass of the cell. Cell aspect ratio and area were calculated using the built-in MATLAB function regionprops of a binary-masked actin image.

Plastic Petri dishes (TPP) were incubated in 10 μg/mL fibronectin in PBS at 4 °C overnight on a 60-rpm shaker. Cells were seeded and allowed to adhere at least 3 h. AFM nanoindentation experiments were performed using a Nanowizard 4 (JPK Instruments) in Quantitative Imaging mode with a 37 °C Petri dish heater. The imaging buffer was Leibovitz’s L-15 medium supplemented with 10% fetal bovine serum and 1× penicillin-streptomycin. PFQNM-LC-A-CAL cantilevers (Bruker) were used; the nominal tip radius was 70 nm (confirmed by scanning electron microscopy), the spring constant for each probe was provided by the manufacturer, and the optical lever sensitivity was determined by the thermal tuning method in liquid. Force-indentation curves were collected with 100 μm/s probe velocity, 400 pN trigger force, and variable indentation-retraction distance (scanning frequency) over a (60 × 60) μm² area with 128 × 128 pixel resolution. Curves were fit in a linearization scheme (57) for the elastic modulus E/(1 − υ²) by the Hertz model modified for a thin sample adhered to an infinitely rigid substrate (58) using a custom-built MATLAB program. The height at each indentation was determined from the contact point relative to the substrate, and the Poission’s ratio was assumed to be 0.5 for rigid substrate correction only.

All data are available in the manuscript and SI Appendix.

Further information regarding experimental procedures are detailed in the accompanying SI Appendix.