Cells test substrate rigidity by local contractions on submicrometer pillars

Abstract

Cell growth and differentiation are critically dependent upon matrix rigidity, yet many aspects of the cellular rigidity-sensing mechanism are not understood. Here, we analyze matrix forces after initial cell–matrix contact, when early rigidity-sensing events occur, using a series of elastomeric pillar arrays with dimensions extending to the submicron scale (2, 1, and 0.5 μm in diameter covering a range of stiffnesses). We observe that the cellular response is fundamentally different on micron-scale and submicron pillars. On 2-μm diameter pillars, adhesions form at the pillar periphery, forces are directed toward the center of the cell, and a constant maximum force is applied independent of stiffness. On 0.5-μm diameter pillars, adhesions form on the pillar tops, and local contractions between neighboring pillars are observed with a maximum displacement of ∼60 nm, independent of stiffness. Because mutants in rigidity sensing show no detectable displacement on 0.5-μm diameter pillars, there is a correlation between local contractions to 60 nm and rigidity sensing. Localization of myosin between submicron pillars demonstrates that submicron scale myosin filaments can cause these local contractions. Finally, submicron pillars can capture many details of cellular force generation that are missed on larger pillars and more closely mimic continuous surfaces.

The rigidity of matrix substrates provides important signals that determine cell growth (1), differentiation (2, 3), adhesion (4), or motility (5), among others. How the cellular motility machinery can sense matrix rigidity is unknown, but the mechanism(s) of rigidity sensing must be constrained by the size of the rigidity sensing machinery and the physical quantity “measured” by the cell (6). Arrays of elastomeric micropillars have proven to be a valuable tool in measuring cellular forces: optical microscopy can be used to precisely measure pillar displacement and generate real-time force maps across entire cells (7, 8). For example, over the time scale of hours to days, fibroblasts on arrays of 1- and 2-μm diameter pillars generate average displacements on the order of 100 nm independent of the pillar stiffness over a range of 2–130 nN/μm, i.e., the cells respond to rigidity by measuring the force required to produce a constant displacement (9). However, no studies have examined forces during the initial contact between the cell and the substrate, when the first rigidity-sensing events take place (10). Moreover, in studies of the minimal cell–substrate contact area needed to sense rigidity and assemble adhesions, fibroblasts assembled adhesion contacts at the edges of beads with contact areas of more than ∼1 μm², whereas with submicron beads, adhesion contacts only assembled after force from a rigid laser tweezers was applied (11). Analysis of bead displacement with laser tweezers also suggests that cells measure the force required for local displacements of ∼100 nm to deduce rigidity, i.e., a constant displacement mechanism (10).

Here, we concentrate on force dynamics in fibroblasts during the initial spreading phase, which represents the first exposure of the cell to the matrix rigidity, and extend the micropillar force measurement technique to the submicron regime. To follow the adhesion sites of the cells with the pillars, we examined localization of adhesion (paxillin) and contractile (myosin) molecules. Using high-resolution force spectroscopy, we investigated how the spatial pattern of force vectors changes with pillar diameter from 2 to 0.5 μm to determine the length scales over which initial forces are applied. We further measured the scaling of force and displacement with pillar diameter, as well as stiffness, to understand whether the cells control force or strain in rigidity sensing. To estimate the corresponding time scales involved in the process, we also examined the dynamics of pillar displacement and force generation. In fact, the measurement of rigidity must be either transient or periodic because of the plasticity of normal cells (6). In particular, it was reported that the forces generated by fibroblast cells are not constant but oscillate on timescales of 1 min (12), and in more recent work, periodic contractions of the cell leading edge during the early spreading phase appeared to be related with the sensing of the ECM rigidity (13). Finally, to more firmly establish a link between the observed behavior and cellular rigidity sensing, we examined the behavior of mutant cell lines with an altered rigidity response.

These measurements reveal the existence of submicron contractions that may be used by cells to sense rigidity locally by measuring the force required to generate displacements of the order of 60 nm on a timescale of 1 min. The existence of these contractions, as well as relative localization of paxillin and myosin with respect to the pillar position, indicates that these molecules are the key constituents of a local contractile complex with a minimal length of ∼1 μm.

Results

Poly(dimethylsiloxane) (PDMS) elastomer pillars with diameters of 2, 1, and 0.5 μm were prepared in hexagonal arrays by molding in etched silicon wafers. For each array, the center-to-center distance was twice the pillar diameter to keep the matrix contact area at 19% of the total spread area (Fig. 1 and Fig. S1). For each diameter, three different heights were also prepared to produce about the same range of bending stiffness (roughly 2–31 nN/μm; Table S1). As an example, a scanning electron micrograph of the 0.5-μm pillar array is shown in Fig. 1A, and a schematic representation of hexagonal arrays of pillars is shown in Fig. 1B.

Fig. 1.

(A) Scanning electron micrograph of 0.5-μm diameter PDMS pillars. (Scale bar, 1 μm.) (B) Schematic representation of the hexagonal pillar arrays. Center-to-center distance is twice the diameter.

Mouse embryonic fibroblasts (MEFs) were placed on fibronectin-coated pillar substrates and observed during the initial phase of spreading (<30 min). The cells adopted normal spread morphologies, and the pillars were dense enough, so that cells attached only to the pillar tops, as verified by scanning electron microscopy.

To investigate the interaction of the cells with the pillar substrates, we examined the distribution of the focal adhesion protein paxillin on pillars with diameters of 2 and 0.5 μm but with similar stiffness after 25 min of spreading. On 2-μm pillars, paxillin was relatively depleted on the pillar tops, and had the highest concentration in a ring around the pillars (Fig. 2A). On 0.5-μm pillars, in contrast, paxillin was localized on the pillar tops (Fig. 2B). We also examined the distribution of phosphorylated myosin light chain (p-MLC). p-MLC is an indicator of active force-generating myosin II molecules (14), which exert traction forces and contribute to building a cohesive actomyosin network within the cytoplasm (15, 16). P-MLC localized in small clusters at the edges of 2-μm pillars (Fig. 2C), and in the spaces between 0.5-μm pillars (Fig. 2D). A quantification of relative fluorescence intensity for several cells and pillars (chosen at random in a region 1–4 μm from the cell edge) confirmed that paxillin and p-MLC had similar radial distributions on 2-μm pillars (Fig. 2G), with a peak in intensity near the pillar periphery. In contrast, the two proteins showed opposite trends on 0.5-μm pillars: the maximum paxillin intensity was at the pillar tops, whereas the maximum p-MLC intensity was between the pillars (Fig. 2H). All of the individual pillars observed showed a similar pattern, with the SD of the data reflected in the error bars. Scanning electron micrograph imaging of the pillars (Fig. S1) showed that the shapes of the tops were similar for both sizes, excluding differences in local curvature as a possible mechanism for the differing paxillin distribution. Thus, both the images and morphometric analysis confirmed that cellular responses changed dramatically as the pillar size reached the submicron range. The size of the smallest adhesive unit was the same (about 600 ± 200 nm) on 2- and 0.5-μm pillars and also on flat substrates (Fig. S2A). On flat substrates and small pillars, however, these units combined to form elongated adhesions aligned toward the cell center that could extend to >3 μm (Fig. 2 I–K; quantification in Fig. S2B). On 2-μm pillars, in contrast, long adhesions were randomly aligned (Fig. 2I and Fig. S2B). Thus, the distribution of adhesions on flat substrates was reproduced to a certain extent on 0.5-μm pillars but disrupted on 2-μm pillars.

Fig. 2.

(A–F) Immunofluorescence staining of paxillin (A and B), p-MLC (C and D), and merge images (E and F) of cells spread for 25 min on 2- and 0.5-μm pillars. (Scale bar, 2 μm.) For reference, red circles show the localization of one pillar. (G and H) Normalized average fluorescence intensities of paxillin and p-MLC on 2-μm pillars (G) and 0.5 μm pillars (H), as a function of radial distance from the pillar center, averaged over all angles. r = 0, pillar center; r = 2,000/500, midpoint between 2 μm/0.5 μm pillars. Data correspond to the average distributions of ≥15 pillars from ≥3 cells, for both paxillin and p-MLC. For both paxillin and p-MLC, protein localization was significantly different on 0.5-μm pillars between pillar center and interpillar space (P < 0.001) and on 2-μm pillars between pillar center and pillar edge (P < 0.001). (I–K) Paxillin immunofluorescence staining showing entire cells spread on pillars of 2 μm (I) and 0.5 μm (J) with stiffnesses of 2.1 and 2.7 nN/μm, respectively, and on a flat substrate (K). [Scale bar, 10 μm (I)]. Insets show magnified views of the areas marked with white rectangles.

The spatial distribution of forces exerted (Fig. 3) also changed dramatically on the submicron pillars. On micron-scale pillars, all of the force vectors were oriented inward, toward the center of the cell (Fig. 3 A and C). This behavior was consistent with previous observations (8, 17) and indicated that the balancing forces were generated on the opposite half of the cell. In contrast, the 0.5-μm pillars showed heretofore unobserved local contractile areas in which neighboring pillars were deflected toward each other (Fig. 3 B and D and Movie S1). To quantify the extent of these local contractions, we measured the vector force exerted on pillars in a defined region at the cell edge containing several pillars. For each image, we computed a directionality parameter γ, defined as the magnitude of the sum of the force vectors divided by the sum of their magnitudes. This directionality parameter is γ = 1 for parallel forces and γ = 0 for forces balanced locally. A histogram of the values of γ collected for 100 frames confirms the pattern observed in Fig. 3. γ was significantly larger for 2- and 1-μm pillars (0.9 ± 0.04, mean ± SD) than for 0.5-μm pillars (0.4 ± 0.08) (Fig. 3E). The measured value of γ = 0.4 for the 0.5-μm pillars likely reflects a combination of local contractions (γ = 0) and long-range inward forces (γ = 1). Thus, the local contractile forces were not evident in the displacements of the larger pillars but constituted a significant fraction of the total force for the submicron pillars.

Fig. 3.

(A and B) Spatial force distribution (red arrows) near the edge of a single cell on pillars with diameters of 1 μm (A) and 0.5 μm (B). The yellow line represents the approximate cell boundary. (Scale bar, 5 μm.) (C) Magnified view of forces on 1μm pillars. (D) Magnified view of forces on 0.5-μm pillars. The arrow lengths corresponding to 1 nN in C and D are shown at the bottom of each image. (E) Histogram of directionality γ (magnitude of vectorial sum of forces/sum of force magnitudes) for areas of 34.5 μm² on the edges of n = 6 cells. γ = 1: parallel forces; γ = 0: forces balanced locally. Differences in γ on 0.5- vs. 2-μm pillars were significant (P < 0.001).

We next examined whether the changes in direction of pulling described above were accompanied by quantitative changes in the time-dependent pillar displacements. For each cell, the time-varying displacement of pillars was measured. To have a zero force reference, only pillars that were initially outside the cell were analyzed. For each of the nine arrays studied, at least 50 pillars in total (from 2 to 4 cells) were analyzed. Fig. 4 shows displacement vs. time traces for representative pillars from the nine arrays, starting just before the time of first cell–pillar contact. For a given pillar, the displacement was zero outside the cell and then would rise to a maximum value after initial contact, followed by a gradual decrease as the spreading edge moved away from the pillar. Additional displacement oscillations also appeared on top of this broad pattern. We estimated that the maximum uncertainty in these displacement measurements was Δd ∼25 nm, attributable primarily to optical lensing effects. Error analysis is discussed in detail in Materials and Methods (Fig. S3) and established that the lensing effects could not account for the observed displacements. Furthermore, differences in cell type caused dramatic differences in the observed displacements, even though lensing and other noise parameters were constant. All of the measured maximum displacements were significantly larger than this measurement uncertainty.

Fig. 4.

(A–C) Deflection as a function of time for pillars with diameters of 2 μm (A), 1 μm (B), and 0.5 μm (C) and with three different stiffnesses for each diameter. (D) Averaged maximum deflection of individual pillars as a function of substrate rigidity. (E) Averaged maximum shear stress on single pillars as a function of substrate rigidity. (F) Average period of single pillar deflection peaks. Blue, green, and red points represent pillars with diameters of 2, 1, and 0.5 μm, respectively. Pillars (50 to ∼100) from 2 to 4 cells were analyzed per value shown. The effect of pillar stiffness on F_max/A was significant for 0.5- and 1-μm pillars (P < 0.05) but not for 2-μm pillars. The effect of pillar stiffness on d_max and period was significant for 1- and 2-μm pillars (P < 0.05) but not for 0.5-μm pillars (two-way ANOVA).

Pillar-deflection patterns were markedly affected by pillar stiffness and diameter. For 2-μm pillars, displacement decreased dramatically with increasing stiffness (Fig. 4A). This effect was diminished for 1-μm pillars (Fig. 4B), and 0.5-μm pillars (Fig. 4C) had peak displacements of about 60 nm independent of rigidity. The kinetics of pillar pulling was also a function of pillar size: micron-scale pillars showed an inverse correlation between pillar stiffness and displacement period, whereas submicron pillars had a constant period of displacement.

To quantify the variation in pillar deflection with diameter and stiffness, we calculated the maximum deflection, d_max, for each of the pillars examined on each substrate. Fig. 4D shows the average value of d_max for all of the pillars (>50 pillars and 2–4 cells) examined on each substrate, as a function of pillar stiffness. Confirming the trend seen in Figs. 4 A–C, d_max decreased with pillar stiffness for micron-scale pillars, whereas it was roughly constant (49, 62, and 59 ± 25 nm for 2.7, 13.9, and 21.8 nN/mm pillars, respectively) (mean ± Δd) for 0.5-μm pillars of different stiffness (Fig. 4D and Fig. S4). Fig. 4E shows the shear stress (lateral force corresponding to maximal deflection divided by top pillar area: F_max/A) as a function of the stiffness. For 2-μm pillars, this value was unaffected by stiffness (∼1 nN/μm² for all stiffnesses). Thus, for large pillars force scales approximately with adhesive area, as suggested previously (7, 18). For submicron pillars, F_max/A had a significant linear increase with pillar stiffness (12-fold, reaching a maximum value of about 8 nN/μm²), reflecting the constant displacement. To explore the extent of the trend of constant displacement, we fabricated one additional set of 0.5-μm diameter pillars with a stiffness of 90 nN/μm. These pillars showed d_max = 76 ± 25 nm (mean ± Δd), consistent with the picture of constant displacement (Fig. S5 A and B). For 1-μm pillars, F_max/A slightly increased with stiffness, thereby showing an intermediate behavior. It must be noted that a mechanical model that takes into account the elasticity of the PDMS substrate (19) can be used to more accurately determine the pillar stiffness. Using this model, the correction to the stiffness of the 1- and 2-μm pillars is negligible, whereas stiffness of the 0.5-μm pillars is up to 40% smaller (Fig. S5C). The correction does not affect the trends observed with either pillar size or stiffness. To quantify the kinetic component, the average value of the period of the force peaks was also calculated (Fig. 4F). The period of pulling decreased with decreasing pillar diameter and decreased with increasing stiffness for larger pillars but not for submicron pillars, confirming the qualitative change in behavior. The force loading and unloading rate in pN/s (which should increase with pillar stiffness and d_max but decrease with the pulling period) was calculated for all of the pillar substrates, showing a faster loading on stiffer pillars, irrespective of pillar diameter (Fig. S6). Thus, similar trends in d_max and pulling period with diameter (Fig. 4 D and F) probably cancelled each other to result in no net effect of pillar diameter on loading rate. Force generation and reinforcement, however, were enhanced in stiffer substrates, as shown previously, although rates of movement were significantly slower than rates of myosin contraction or actin transport inward (20).

These data demonstrated that, during early spreading, cells applied local contractions to the substrate, with local displacements of ∼60 nm per pillar. To test whether these local displacements were linked to rigidity sensing, we measured force generation on 0.5-μm pillars by cells missing the receptor-like protein tyrosine phosphatase α (RPTPα^−/−). These cells lacked the ability to sense substrate rigidity (10). Pillar displacements by RPTPα^−/− cells were below our experimental error (Fig. 5 A–C). Expression of RPTPα-YFP in RPTPα^−/− cells restored the ability of those cells to pull the 0.5-μm pillars to the same displacements as controls (Fig. 5D). Therefore, we propose that pillar displacements of 60 nm are a critical step in rigidity sensing.

Fig. 5.

(A) Deflection of pillars with diameters 0.5 μm and two different stiffnesses as a function of time. Green and red traces represent RPTPα^−/− cells and control (RPTPα^+/+), respectively. (B–D) Histograms of maximum deflection of submicron pillars with two different values of the stiffness for RPTPα^−/− cells (B), RPTPα^+/+ cells (C), and RPTPα^−/− cells rescued with RPTPα-YFP (D). Values represent means ± SD. Differences between RPTPα^−/− cells and either RPTPα^+/+ cells or RPTPα^−/− cells rescued with RPTPα-YFP were significant under pillars of both stiffnesses (P < 0.05).

Discussion

In these studies, we find two different modes of pillar displacement, one for the submicron and another for micron-scale and larger pillars. Displacements of submicron pillars are primarily by local contractions that are balanced locally, whereas displacements of larger pillars are balanced primarily by distant forces. These differences are indicative of two different processes: rigidity sensing for adhesion formation and the coupling of formed adhesions with inward actin flow. In rigidity sensing for adhesion formation, there are contractile complexes that generate displacements of ∼60 nm on the scale of ∼1 μm that then lead to adhesion formation. Once adhesions are formed, they couple to the rearward actin flow, which produces a centripetally directed force that increases with pillar diameter. The localization of myosin between 0.5-μm pillars suggests that the contractile complex consists of bipolar myosin filaments (with lengths of 0.3 to ∼0.4 μm) (21, 22), attached to actin filaments that polymerize from adhesion sites as recently observed (23).

For 0.5-μm pillars, the contractile complex is too large to span a single pillar and, instead, bridges neighboring pillars (Fig. 6A). Thus, paxillin is localized on the pillar tops, whereas myosin filaments bridge between pillars and myosin contractions displace nearby pillars toward each other, i.e., the local contractions test the bending rigidity of the pillars. In this regime, the local contractions dominate over linkage to the actin rearward flow because the adhesions are just forming and rearward force scales with pillar area.

Fig. 6.

Schematic representation of local contractile units in which myosin filaments (green dots) pull either from two adhesions located on neighboring 0.5-μm pillars (red dots) (A) or from adhesions distributed at the edge of 2-μm pillars (red circle) (B).

When the diameter of the pillar is larger than the minimal contractile complex size (≥1 μm, from our results), the adhesion complexes form initially along the edges of individual pillars (Fig. 6B). Because the stiffness of individual pillar tops to compression is much greater than the pillar bending stiffness, assembly of contractile units around pillar tops, rather than between them is favored. This is shown by the localization of paxillin at the pillar edges and the localization of small clusters of p-MLC on the edge of 2-μm pillars (Fig. 2 C and E). We postulate that the majority of the local contractions would be applied within individual pillars and, therefore, would sense the very high rigidity of the PDMS itself, rather than the pillar bending stiffness. These contractions across individual pillars would not be observed in our system. The number of the matrix adhesion complexes on the top of the pillars that can couple with the actin flow should increase with pillar diameter. Because of this scaling, large pillar deflections are attributable to rearward actin flow, rather than local contractions between pillars, resulting in the observed centripetal displacements.

Within this model, we suggest that local rigidity sensing is accomplished by measuring the level of myosin contraction required to displace neighboring pillars by ∼60 nm. In such a case, the parallel activation of myosin and a diffusive signaling molecule could produce a response proportional to substrate rigidity (6). In terms of the mechanism by which the cell can limit the displacement of the pillars to 60 nm, single proteins can easily span such distances, and mechanical displacements of >100 nm have been reported for adhesion proteins (24, 25). Thus, we suggest that localized (1–2 μm) contractions recruit active myosin until the matrix is displaced by a defined amount (very rigid surfaces would exceed the range of the system). The loss of RPTPα reduces the activation of Src family kinases that are critical for rigidity sensing (26–28) and reduces the displacement in the local contractions. Thus, we suggest that the Src family kinases are coupled with localized contraction and force sensing that are integral parts of the rigidity sensing process.

It is important to note that the effects observed in this work represent rigidity-sensing events upon initial cell–substrate contact, before mature adhesions and stress fibers are formed. At later times, cell traction forces on large areas (or at the whole cell level) have also been reported to increase with substrate stiffness as well (9, 29, 30). This contrasts with the constant stress observed here for 2-μm pillars and shows that initial rigidity sensing events are clearly distinct from later adaptive responses to substrate rigidity.

The work presented here shows that there exists a rigidity-sensing system that can be localized to matrix contacts separated by 1–2 μm and that cells will adjust the force needed to produce a constant displacement of the matrix. Such early adhesion complexes will couple with rearward actin flow, generating a shear force that scales roughly with area. These findings greatly constrain molecular models of the rigidity-sensing system and provide ways to test for proteins such as RPTPα that are critical components in the process of early rigidity sensing (6). These experiments also demonstrate the qualitative and quantitative difference between micron-scale and submicron pillar arrays and suggest that submicron pillars can accurately mimic continuous substrates of a specified rigidity.

Materials and Methods

Pillar Fabrication.

Conventional high-resolution photolithography was used to fabricate arrays of holes in a silicon substrate. A 5× reduction autostepper (GCA Autostep 200 DSW i-line, Integrated Solutions Inc) was used to pattern the photoresist. A C₄F₈/SF₄-based deep reactive ion etch (DRIE) was performed on the wafers to etch holes to the desired depth. After stripping of photoresist, the silicon masters were cleaned with piranha solution (3:1 H₂SO₄/H₂O₂), followed by 1 min of O₂ plasma cleaning and then silanized with (tridecafluoro-1,1,2,2,-tetrahydrooctyl)-1-trichlorosilane (United Chemical Technologies) overnight under vacuum. PDMS (mixed at 10:1 with its curing agent, Sylgard 184; Dow Corning) was then poured over the silicon mold, cured at 70 °C for 12 h to reach a Young modulus of 2 ± 0.1 MPa, and peeled off while immersed in ethanol. Pillar arrays were hexagonal, with center-to-center spacing set to twice the pillar diameter to maintain constant areal density. Pillar tops were also very flat, with a variation in height at the pillar tops that was only ∼10% of pillar diameter (Fig. S1). Pillar bending stiffness was calculated by Euler–Bernoulli beam theory:

where D, L, and E are the diameter, length, and Young modulus of the pillar, respectively (31). Pillar dimensions and resulting bending stiffness are in Table S1.

Cell Culture.

MEFs were cultured in DMEM supplemented with 10% (vol/vol) FBS, 2 mM l-glutamine, and 100 IU/mg penicillin-streptomycin (Invitrogen) at 37 °C and 5% CO₂ (all from Gibco). Before measurements, PDMS pillar substrates were coated with human plasma fibronectin (10 μg/mL; Roche) and incubated at 37 °C and 5% CO₂ for 1 h. Cells were then trypsinized, suspended in DMEM for 30 min at 37 °C for recovery, and plated on the substrate.

For immunostaining, cells were cultured on PDMS pillar substrates for 25 min, fixed in 4% (vol/vol) paraformaldehyde in PBS for 15 min, quenched with 50 mM ammonium chloride in PBS for 15 min, and permeabilized with 0.1% (vol/vol) Triton X-100 in PBS. Cells were then rinsed with 0.2% (vol/vol) fish gelatin in PBS and incubated with a primary antibody to paxillin (clone 349; BD Transduction Laboratories) for 1 h and then with fluorophore-conjugated secondary antibodies to IgG (Invitrogen).

Video Microscopy and Force Traction Measurements.

Time-lapse imaging of pillars was performed with bright-field microscopy using a CoolSNAP HQ (Photometrics) attached to an inverted microscope (Olympus IX-70) maintained at 37 °C. Images were recorded at 1 Hz using a 100× (1.4 NA, oil immersion; Olympus) objective for submicron pillars and a 40× (0.6 NA, air; Olympus) for micron-scale pillars. The position of each pillar in each frame was determined using the particle-tracking plugin for ImageJ software (National Institutes of Health), which employs an autocorrelation algorithm (32). In all cases, pillars were tracked before the cell spread over them, to establish an equilibrium (zero force) position. The time-dependent displacement of a given pillar was then calculated by subtracting its initial position (corresponding to zero force) from the position in a given frame. To remove stage drift, the average displacement of a set of pillars far from any cells was subtracted from the data. Finally, the position vs. time data for each pillar was low-pass-filtered with a cutoff frequency of 0.1 Hz. Traction forces were deduced by multiplying displacements by the pillar spring constant (Table S1). To calculate the period of force peaks, custom code in Matlab (MathWorks) was written to find sequential maxima and minima in the displacement traces. The directionality parameter γ was computed as the magnitude of the sum of the force vectors found in area of 34.5 μm² at the cell periphery divided by the sum of their magnitudes.

Epifluorescent imaging was performed on an Olympus IX-81 microscope with 100× (1.4 NA, oil immersion; Olympus) objective and a Cascade II camera (Photometrics), as well as an Olympus Fluoview FV500 laser-scanning confocal microscope. Imaging software was SimplePCI (C-Imaging). The radial distributions of paxillin and p-MLC were calculated by integrating the total fluorescence intensity over an annulus between r and r + Δr and dividing by the area. Step sizes of Δr = 50 nm and 120 nm were used for 0.5- and 2-μm pillars, respectively. The length of paxillin adhesions was calculated by defining their edge as the point where intensity fell to half the maximum value. To characterize elongated structures, the orientation of the two longest straight paxillin structures were measured for each cell.

Statistical and Error Analysis.

To ensure measurement accuracy for each sample, the noise of the system was measured by tracking the pillars not associated with any cells. The average background displacement of these pillars was <10 nm. To establish the accuracy of the detection technique, we also determined the apparent pillar displacement caused by optical distortions upon cell–pillar contact (lensing effect). To do this, we observed the position of ultrastiff pillars (k = 680 nN/μm) as a cell moved over them. The apparent position of these pillars (which should not be deflected at all) reflects both random noise in the image [found to be <10 nm by observation of pillars without cells (Fig. S7)] and optical lensing attributable to the cell. The maximum displacement of these pillars was measured to be 25 ± 9 nm (mean ± SD) (Fig. S3), indicating that lensing is the dominant source of error in these experiments. For all of the pillars used in this work, the distribution of maximum displacements (Fig. 5 and Fig. S4) is clearly distinct from the distribution on ultrastiff pillars, with negligible P values (<0.0001). Moreover, analysis of directionality parameter on ultrastiff pillars showed a γ value of roughly 0.7 ± 0.2, implying that the lensing error acts mostly in the same direction, toward the inside of the cell. Therefore, errors shown for maximum pillar displacement are the SD for all of the pillars measured or the experimental error Δd of 25 nm, whichever was greater. Errors in k and F_max/A were calculated using error propagation. All other data shown are means ± SD.

Statistical analysis of measured pillar displacements (Figs. 2–5) was performed with two-tailed Student t test when two cases were compared and with ANOVA tests when more cases were analyzed.