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Large-scale curvature sensing by directional actin flow drives cellular migration mode switching

Cell migration over heterogeneous substrates during wound healing or morphogenetic processes leads to shape changes driven by different organizations of the actin cytoskeleton and by functional changes including lamellipodial protrusions and contractile actin cables. Cells distinguish between cell-sized positive and negative curvatures in their physical environment by forming protrusions at positive ones and actin cables at negative ones; however, the cellular mechanisms remain unclear. Here, we report that concave edges promote polarized actin structures with actin flow directed towards the cell edge, in contrast to well-documented retrograde flow at convex edges. Anterograde flow and contractility induce a tension anisotropy gradient. A polarized actin network is formed, accompanied by a local polymerization-depolymerization gradient, together with leading-edge contractile actin cables in the front. These cables extend onto non-adherent regions while still maintaining contact with the substrate through focal adhesions. The contraction and dynamic reorganization of this actin structure allows forward movements enabling cell migration over non-adherent regions on the substrate. These versatile functional structures may help cells sense and navigate their environment by adapting to external geometric and mechanical cues.

migration mechanisms, which help cells sense and navigate their environment and adapt to external physical cues.
We first observed the actin organization at the leading edge of epithelial cells (Madin-Darby canine kidney cells, MDCK) with model wound closure assays27, 28. The migrating front displayed either convex (positive curvature, Fig. 1a, empty arrow head) or concave edges (negative curvature, Fig. 1a, filled arrow head) showing lamellipodia-based crawling or actin cable assembly, respectively2,10. This actin cable at high negative curvature is connected to a continuous actomyosin structure, which extends into the cell and is connected to the substrate at the rear by focal adhesions (FAs) (Fig. 1b and Supplementary Fig. 1a, b).
To test whether geometrical constraint suffices to produce such actomyosin organization observed at negative curvatures, we designed flower-shaped patterns for a model wound assay27 (Fig. 1c, f; see Supplementary Fig. 2a for details on the pattern geometry). At regions of negative curvature, we observed similar organizations of actomyosin and focal adhesion structures (Fig. 1e, h), whereas at regions of positive curvature the cells showed lamellipodia protrusions (Fig. 1d, g). The structures at negative curvatures displayed a polarized organization of strong leading edge actomyosin cable, immediately followed by a region of network-like actin fibers and myosin II, and FAs at the rear connected to radially oriented actin fibers, reminiscent of a variation of lamellipodium and lamella actin organization26, 29,30. With live cell structured illumination microscopy (SIM), we observed an anterograde flow of actin fibers towards the leading edge, in contrast to the retrograde flow usually observed in lamellipodium and lamella at positive curvature (Fig. 1i, j) 25,26. We thus hypothesized that the actomysosin system could serve as a cell scale curvature sensor, establishing an anterograde flow at negatively-curved edges that accumulate actin fibers and contractile cables at the front (Fig. 1k), while lamellipodium formation is promoted by the retrograde flow of actin fibers at positively curved edges26,29.
Migration over heterogeneous substrates31 and the cooperative nature of lamellipodia crawling and actin cable contraction during gap closure2 suggest that negative curvatureinduced actin structures could facilitate monolayer migration over non-adhesive regions. To test this, MDCK cells were plated on micro-patterned substrates composed of fibronectin coated surfaces dotted with non-adherent circles (see Methods) 28. When the MDCK monolayer migrated over non-adhesive regions, actin structures were formed as negativelycurved cell edges were forced by cell crawling on either side of the circle (76.5 min-178.5 min in Fig. 11). These structures actively promoted forward cellular movements over the non-adherent region (Fig. 1l, Supplementary Fig. 1e and Supplementary Video 1). As the cell encountered the non-adherent circle and the edge of the cell front adopted negative curvature, the migration mode switched from lamellipodium (Fig. 1m, filled arrowhead) to actomyosin cable (Fig. 1m, empty arrowhead). This was accompanied by a switch from retrograde to an anterograde flow of myosin (Fig. 1m, yellow dashed lines). These processes were not confined to collective cell migration processes, but were also observed within single cells such as Hela and U2OS when responding to negative curvature induced by heterogeneous micro-patterned substrates ( Fig. 1n and Supplementary Fig. 1c, d). We also created interconnected electro-spun fiber networks to mimic 3D fibrous in vivo ( Supplementary Fig. 1f). In addition to attaching to the fibers, cells were also able to extend into empty spaces at cross-sections where a suspended (non-adherent) actin structure similar to the ones induced by negative curvature was observed (Fig. 1o).
Next, we confined cells on flower-shaped patterns to immobilize cells and control cell geometry ( Fig. 2a and Supplementary Fig. 2a). Cells responded to the curvature imposed by the pattern by consistently forming lamellipodial protrusions at positive curvatures and suspended actin cables at negative ones ( Fig. 2b and Supplementary Video 2). The side view shows a difference in the 3D structure between opposite curvatures: a suspended cell part over the non-adherent region, with actin accumulation at its tip and continuous actomyosin staining along the ventral surface, for negative curvatures; and a lamellipodial protrusion close to the pattern edge for positive curvatures (Fig. 2c).
We then analyzed the organization and the dynamics of the actin cytoskeleton at sub-cellular levels within regions abutting these negatively curved edges. Using SIM, we confirmed our previous observation that a polarized actin organization with radially oriented actin fibers (RFs) at the rear, transversely oriented actin fibers (TFs) near the front, and a suspended actin cable at the leading edge emerge in concave regions (Fig. 2d, see also Fig. 3a and Fig.  5q). As the actin structure occupies only part of the cell, the front and rear here and henceforth refer only to the actin structure and not the whole cell. This actin organization was quantified by the nematic order parameter S=<cos (2θ)> (where θ denotes the angle between the normal to the cell edge and the local actin filament orientation), which ranged from positive values at the rear to negative values at the front (Fig. 2d, e and Supplementary  Fig. 2b, c), suggesting anisotropic actin organization33. TFs exhibited sarcomeric patterns of α-actinin and myosin IIA (Fig. 2f, g and Supplementary Fig. 2d), whereas RFs were associated with α-actinin and connected to focal adhesions (FAs) at the rear ( Supplementary  Fig. 2e). This structure recalls the lamella, where transverse arcs glide on radially oriented fibers30,34, yet presents a reversed organization. Similarly, the RFs connected to the FAs at the rear remained non-contractile as shown by the absence of myosin IIA in this region, but the front part displayed concentration gradients of both actin and myosin IIA, suggesting increased contractility (Fig. 2h, i).
At negative curvatures anterograde flow of TFs was observed in the cell, and which coalesced at the front with the leading edge actin cable (  Fig. 3c). The flow velocity of the TFs appeared to depend on the curvature magnitude, which was varied by changing the size of the pattern ( Supplementary Fig. 3d). In order to investigate the relationship between flow velocity and curvature magnitude, we designed patterned surfaces with edges comprised of semicircular shapes with a set of positive and negative curvatures separated by regions of flat edges ( Supplementary Fig. 3e, f). By imaging cells transfected with mEos3.2 myosin IIA (see Methods), we measured the myosin flow velocity at different curvatures. This quantity showed a bi-phasic behavior with an optimum value at curvature radii 15 and -20 μm, which is of the order of the cell size (Fig. 3c). This non-monotonic dependence of flow velocity on curvature can be explained in the framework of the physical model based on active gels (SI). The anterograde flow at negative curvature was not restricted to the TFs, but occurred throughout the entire actin structure. First, photo-conversion of RFs in mEos2-actin transfected cells revealed that RFs were engaged in anterograde flow (Fig. 3d-f and Supplementary Video 4). Then, by combining fluorescent speckle microscopy (FSM)35 (Fig. 3g, h and Supplementary Video 5) and direct TF tracking, we measured the flow profile across the entire actin structure. The actin flow velocity decreased from the rear (0.38±0.05 μm/min starting from the RF region) to the front (0.17±0.04 μm/min starting from the TF region) of the structure leading to the contractile cable at the edge (Fig. 3i). In comparison, the actin flow at positive curvature, where lamellipodia formation is preferred, increased from the rear to the front ( Supplementary Fig. 3g-i and Supplementary Video 6). Altogether, these results show that concave regions promoted reverse actin flow patterns with rear-to-front actomyosin gradients, suggesting that these polarized structures may result from cell-generated active forces24.
To investigate the role of mechanics in the establishment and the maintenance of these actin structures, we laser ablated actin fibers at different locations. Ablation of TFs resulted in recoil ( Tension in the radial direction decreased from rear to front whereas it increased in the transverse direction, resulting in a tension anisotropy gradient (Fig. 4f, g and Supplementary  Fig. 4e, f) correlating well with the variation of actin order parameter (Fig. 2e). This anisotropy gradient has also been shown to couple to actin flow36-38. We then used traction force microscopy (TFM)39 to visualize forces exerted by cells on the substrate along the edges of the pattern (Fig. 4h). We observed large traction forces along the actin cables at the edge ( Fig. 4i, filled arrow heads). In contrast, outward pointing forces were generated at highly negative curvatures (Fig. 4i, empty arrow head) resulting from the tension within the actin gel exerting pulling forces on FAs localized at the edge of the pattern. In comparison, inward pointing forces are usually observed for cells crawling or spreading with positively curved outer edges ( Fig. 4h) 6,40. Here, the distinctive geometry of the actin structure led to cell traction forces at FA sites that are directed outward towards the cell edge, in agreement with force patterns observed during in vitro wound healing39.
To further test our hypothesis of a coupling between tension anisotropy at negative curvatures and actin flow, we developed a model that describes the actin cytoskeleton as a 2D active nematic gel41 (see Supplementary Information (SI) for details). We summarize here a 1-dimensional analysis along the rear/front axis x of the suspended region (along the radial direction in Fig. 2d); a 2D numerical analysis of the stress field in the actin structure was also performed (Fig. 4j). The rear (i.e., edge of the adhesive pattern) is given by x = 0, and the front (i.e., edge of the suspended cell) is x = l. Following active gel theory38,41, the action of myosin II motors leads to an active contractile stress parameterized by positive constants ζ and ζ'. We allow the isotropic part ζ, which can be understood as a negative pressure42, to depend on the bound density of myosin motors c m , whereas, for simplicity, adherent, we neglect friction forces with both membrane and cytosol as compared to viscous forces, as justified in43 (see also SI). Thus, calling σ the tension along x in the gel, force balance is given by ∂ x σ = 0. As a result, we find σ = λ/R, where λ is the line tension of the front stress fiber and R the radius of curvature of the actin structure front. Next, σ can be related to contractile activity and to the viscous stress η∂ x v, where v(x) is the actin flow field along x; furthermore, due to fast actin turnover, pressure forces are neglected38; see SI.
Thus, we find the following linear equation that determines the flow profile (see SI): In addition, our active gel model provides a prescription for determining the nematic order parameter S(x), as described in SI.
This model reproduces key experimental features. (i) Equation (1) shows that the actin flow is generated by myosin activity, and as long as isotropic contractility is dominant, one finds ∂ x v < 0. This, together with the boundary condition v(l) = 0 -which assumes no boundaryspecific sources of actin turnover -shows that contractility induces an anterograde flow in the actin structure, as observed experimentally. Quantitatively, flow measurements reveal that the flow profile is fitted well by a linear dependence on x (Fig. 3i), which suggests that contractile terms in Eq. (3) can be assumed constant. The maximal flow speed can then be estimated as lζ/η, which gives 0.4 μm/min with standard values of ζ~10 3 Pa and η~10 5 Pa.s44,45, in agreement with observations. (ii) This estimate of the maximal flow speed captures the effect of geometry through the dependence on l, which can be estimated as l L c 2 C for L c < 1/|C|, where C is the substrate curvature and L c the typical cell size, and l~1/| C| for L c > 1/|C|. This predicted non-monotonic dependence on curvature is observed experimentally (Fig 3c). (iii) It is shown in SI that S(x) can be analytically determined, yielding a linear behavior in the limit of a large nematic correlation length, in agreement with observations (Fig, 2e). (iv) Last, the model also predicts the observed tension anisotropy (Fig. 4f) as shown in SI. This theoretical analysis finally indicates that the hallmarks of the actin structure at negative curvature-tension anisotropy gradient, actin order parameter gradient, and anterograde flow-result mainly from the contractile behavior of the cytoskeleton and of the geometry characterized by the negative curvature of the forward edge.
We next sought to find mechanisms of actin dynamics regulation different from the one previously observed in lamellipodium-based protrusions25,46. Photo-conversion of mEos2-Actin ( Fig. 5a-c and Supplementary Video 9) within the structure at negative curvature (see Methods) revealed that actin depolymerization increased from the rear to the front, whereas polymerization peaked in the center of the structure behind the depolymerization region. It resulted in a local polymerization-depolymerization gradient, accompanying the anterograde actin flow and in contrast to polymerization gradient previously described in cell protrusions at positive curvatures25 (Fig. 5d, e). Correspondingly, Arp2/3 was mainly localized in the transition region between radial and transverse fibers (Fig. 5f, h), whereas cofilin, an actin depolymerization factor, co-localized with the actomyosin contractile cable at the cell front ( Fig. 5g, h). In addition, N-WASP clusters were observed in the same transition region ( Supplementary Fig. 5a), where we also observed highly dynamic random motion of actin ( Fig. 5i, left panel). The inhibition of Arp2/3 activity (200 μM CK666 treatment) immediately abolished such activity (Fig. 5i, middle panel) and eventually led to the depletion of transverse fibers, which could be rescued by CK666 washout (Fig. 5i, right panel and Supplementary Video 10). The inhibition of the upstream regulator of the Arp2/3 complex, N-WASP, with wiskostatin led to the same observation ( Supplementary Fig. 5b).
To perturb actin depolymerization, we treated cells with 1 nM jasplakinolide, which caused the actin structure to collapse (Supplementary Fig. 5e and Supplementary Video 11), suggesting that actin turnover is important in maintaining the dynamic stability of the structure. The effect is irreversible and could not be rescued by washout.
We then asked how Arp2/3-dependent actin polymerization could be localized to the transition region. Actin polymerization in the lamellipodia is reported to be downstream of FA signaling, where FAK activates N-WASP and Arp2/347. Noticing that radial fibers were connected to FAs and also underwent anterograde flow, we hypothesized that the polymerization signal could be transported by actin flow along radial fibers from FAs to the transition region23, 37,48,49. To test this, laser ablation of radial fibers was performed, Arp2/3 was subsequently recruited to the rear of the ablation site ( Since the radial fibers are connected to FAs, we wondered whether the radial fibers also could mediate the transport of signaling protein complexes. Indeed, with the YFP-PBD biosensor50, we observed that the active small GTPases Rac/cdc42 can be transported forward at negative curvature (Fig. 5l, m). FAK localizes along radial fibers (Fig. 5n) and FAK clusters remained mostly stationary on FN patterns (Fig. 5p, empty arrow head) but could be mobilized and then flow towards the front with the radial fibers over non-adherent regions (Fig. 5p, filled arrow head).
Since the polarized actin structure can form in both single cells ( Fig. 1n and Supplementary  Fig. 1c, d) and individual cells within an epithelial monolayer ( Fig. 2a-d), we hypothesized that cell-cell junctions may enable the formation of multicellular actin structures at negative curvatures with large curvature radii. To test this, we seeded either MDCK WT or MDCK cells with stable α-catenin knockdown (KD) where cell-cell junctions are weakened ( Fig.  6d-f)51 on fibronectin patterns with varying curvatures (Fig. 6a-f and Supplementary Fig.  6a). Both WT and α-catenin KD cells could form suspended actin structures on patterns with radii of curvature equal to or smaller than 15 μm (Fig. 6b, e). However, while the WT cells could form suspended multicellular actin structures connected by E-cadherin adhesions (Fig. 6c, white arrowhead) on patterns with curvature radii 15 to 100 μm ( Supplementary  Fig. 6a), α-catenin KD cells could not and failed to extend out of the fibronectin pattern ( Fig. 6f and Supplementary Fig. 6a). Laser ablation of the actin cables at the edge ( Fig. 6g and Supplementary Video 13) led to their retraction, indicating that the mechanical tension exerted by the actin cables are important for the multicellular actin structures to extend over non-adherent areas. The retraction was significantly larger when the ablation was performed in the non-adherent region than when it was done in the adherent region (Fig. 6h), suggesting that the actin structures were mechanically coupled in the non-adherent region but were uncoupled in the adherent one, potentially due to the connection of actin cables to focal adhesions in the adherent regions.
There could be a maximum non-adherent circle size beyond which the cells could not migrate over it as a coherent monolayer22. Indeed, for 100 μm diameter non-adherent circles, although the cells could occasionally extend partially into the non-adherent region with multicellular actin structures (Fig. 6l, filled arrowheads), the monolayer failed to migrate over the non-adherent circle even after 45 hours ( Fig. 6l and Supplementary Video 14). On the other hand, when the size of the non-adherent pattern is small compared to the size of single cells, α-catenin KD cells could also migrate over it, albeit with less coordination compared to the WT cells ( Supplementary Fig. 6b and Supplementary Video 15). These results suggest that the cell-cell junction is not required for curvature sensing and actin structure formation for single cells or individual cells in a monolayer when the radius of curvature is small, but is essential for the formation and maintenance of multicellular actin structures when the radius of curvature is larger than the size of individual cells.
Our study demonstrates that migrating cells sense large-scale curvatures through the spatiotemporal adaptation of the flow and tension distribution within the actin cytoskeleton as a direct result of the physical constraint imposed by the geometry of the cell and substrate. The unique range of curvature sensing at the scale of 10 μm to tens of microns (Fig. 3c) is distinct from that of molecular curvature sensors such as BAR domain proteins and septins. Nevertheless, curvature sensing mechanisms at scales beyond tens of microns remains elusive and may involve tissue tension sensing52. Apart from sensing the sign of the curvature, the cells also show different actin flow velocities in response to different magnitudes of curvatures (Fig. 3c). Our theoretical analysis suggests that this dependence could reflect the size of the actin structure, characterized by the length of the suspended part l, which naturally varies with the change of curvature (see Model).
Formins are also important actin polymerization factors; however, we did not observe noticeable differences in actin dynamics and organization when cells were treated with the formin inhibitor SMIFH2 (25 μM concentration, data not shown). Nevertheless, formins have been shown to help polymerize actin in the radial fibers30 and the difference between measured actin polymerization activity (Fig. 5d) and Arp2/3 profile (Fig. 5h) at the rear of the actin structure indicates that formins could play a minor role here. The inhibition of actin depolymerization by Jasplakinolide resulted in the rapid break-up of the actin structure. This could be due to the high contractility inside the suspended structure, which in the absence of depolymerization builds up tension inside the actin network and leads to its collapse. On the other hand, the stabilization of F-actin by Jasplakinolide treatment could also reduce G-actin concentration in the cytosol and in turn inhibit the polymerization rate of actin53. This suggests that the active maintenance of the actin structure depends on the dynamic turnover of the cytoskeleton.
A former study showed that after laser severing of the actin cable at the edge of a MDCK monolayer, it can transform into a lamellipodium protrusion12. However, in our setup, the Europe PMC Funders Author Manuscripts actin cable could repair rapidly after laser ablation and repeated laser ablation induced the collapse of the actin structure which can be explained by the fact that non-adherent pattern may serve to prevent lamellipodium protrusion formation after ablation. In addition, the switching of migration mode after laser ablation of the actin cable could also be regulated by curvature. Indeed, when we ablated actin cables at the edge of a MDCK monolayer on a continuously adhesive substrate, 71% (5 out of 7) of the cells transformed into lamellipodium protrusion when the edges were of positive curvature whereas 89% (8 out of 9) of the cells repaired the cable when the edges were of negative curvature ( Supplementary  Fig. 4g In light of these results, curvature sensing by actin flow appears to be the fundamental mechanism of migration mode switching, although the curvature itself might be generated by diverse environmental and cellular conditions in vivo. Cells were cultured in DMEM medium (Invitrogen) supplied with 10% FBS (Invitrogen) and changed to Leibovitz imaging medium (Invitrogen) supplied with 10% FBS before imaging.

Materials and
Transfection of plasmids was performed with a Neon electroporation system (Invitrogen) as per the manufacturer's instructions.

b Drug treatment
Drug treatments were performed on stage by exchanging normal imaging medium with the same amount of medium containing drugs pre-warmed to 37°C. Concentrations of drugs used were as follows: (-) Blebbistatin (Selleckchem) 25 μM, CK666 (Millipore) 200 μM, Wiskostatin (Sigma) 50 μM, Jasplakinolide (Sigma) 1 nM. Washout of drugs was performed on stage by rinsing with 10 ml imaging medium 3 times. The interval between consecutive time-lapse imagings due to drug addition or washout is generally between 5 min to 10 min.

c Model wound closure assay and MDCK monolayer expansion assay
Model wound closure experiment was performed on a continuous fibronectin-coated substrate as described before 2,27 with the flower-shaped block to induce positive and negative curvatures at the edge of the gap. Cells were fixed 15 min after the removal of the block followed by immunostaining. For the freely expanding MDCK monolayer assay, a rectangular Polydimethylsiloxane (PDMS) (Sylgard 184, Dow Corning) block (approx. 0.5 cm by 1 cm) was placed in the center of the dish and MDCK cells were allowed to grow to confluence around the block before the block was removed and the expansion of the monolayer into the empty space was initiated. Images in Fig. 1a, b were taken approx. 10 hours after the removal of the block.

d Micro-patterning of glass substrate
Silicon wafers with custom designed micro patterns were made with soft-lithography. PDMS pillars were cast from the wafers and used to pattern glass surfaces to make islands of fibronectin (20 μg/ml human plasma fibronectin mixed with 1-5% Atto-674 conjugated fibronectin in MQ water) surrounded by PLL-g-PEG (1mg/ml PLL(20)-g[3.5]-PEG(2), SuSoS, dissolved in PBS) with a modified protocol based on plasma micro-contact patterning (PμCP)54. Briefly, PDMS pillars were placed with their features down in contact with glass, and the unblocked part of the glass was activated with a low power oxygen plasma (Harrick Plasma) for 20min. 20ul of PLL-g-PEG solution was then added and incubated at room temperature for 1 hour, after which the stencil was removed vertically with a tweezer and the glass was rinsed once with MQ water to remove the excess PLL-g-PEG. Then, fibronectin solution was added to coat the previously blocked surface at 37°C for 30 min and rinsed 3 times with MQ water. Cells were then seeded on the patterned substrate and allowed to attach for 30-35 minutes, rinsed with DMEM to remove unattached cells, and imaged the following day. Patterns with near-confluent colonies were selected for imaging to minimize movement of cells within patterns as well as over-crowding effect.

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Europe PMC Funders Author Manuscripts imaged with 100 ms exposure and 1-2 minutes per frame. For fast dynamics of actin, cells were imaged with 30-50ms exposure and 10-15 seconds per frame. Image reconstruction was done with the NIS Elements software as per the manufacturer's instruction.

g Particle image velocimetry (PIV) analysis
Velocity measurement of myosin flow at different negative curvature patterns was performed by imaging cells transfected with mEos3.2 Myosin IIA. Before the acquisition, a 405 laser was used to photo-switch a fraction of the fluorophores from green to red fluorescence, such that the images of Myosin IIA display locally distinctive patterns that can be tracked by the image cross-correlation through PIV. Images were acquired with a Nikon NSTORM microscope in TIRF mode with a 1.49 N.A. 100X oil immersion objective. The open source software MatPIV was used to process the images with a 16-by-16 pixel sampling window and 75% overlap. The results were further passed through a median filter to reduce noise. A custom written MATLAB (mathworks) code was used to define an analysis ROI in the center of the actin structure for each experiment and average the signal over space and time to produce the mean radial flow velocity. Outliers, defined as 3 times standard deviation from medium, were removed.

h Fluorescent speckle microscopy
Cells were transfected with low concentration of mEmerald-actin plasmid (0.1 μg DNA for a 100μl electroporation experiment) and imaged on a Nikon Nstorm microscope with a 1.49 N.A. 100X oil immersion objective with TIRF illumination. Images were acquired with 500 ms exposure and a frame rate of 3 seconds per frame to measure the flow of actin. Images were processed with the openly available QFSM software provided by Gaudenz Danuser lab55, to measure the flow velocity. Then the output data was collected and analyzed to compute the averaged radial velocity with MATLAB.

i Laser ablation
An ultraviolet laser (355 nm, 300 ps pulse duration, 1 kHz repetition rate, PowerChip PNV-0150-100, team photonics) was interfaced to a Nikon A1R MP confocal microscope. The UV laser was integrated into a Nikon ECLIPSE Ti microscope body through a customized optical path and a customized dichroic filter, and were co-aligned with the optical axis of the microscope. The position of the laser was controlled by a mirror mounted on two linear actuators (TRA12CC, Newport), and the exposure time of the laser was controlled by a mechanical shutter (VS25S2ZM0, Uniblitz). The actuators (through the actuator controller, ESP301-3G, Newport) and shutter were controlled by custom ImageJ plug-ins from a PC. The laser ablation system, which is independent from imaging microscope, allows us to perform an ablation during imaging. MDCK GFP MRLC cells were used and for measurement of tension anisotropy, a point ablation (with laser power of 25nW at the back aperture of the objective, 300 ms duration) was performed at different positions within the myosin-rich region. Images were then analyzed with a custom-written MATLAB code to calculate the recoil in radial and transverse direction 5 seconds after the ablation. The relative distance of the ablation site was calculated with respect to the rear of the region as 0 and front of it as 1. For ablation of TFs or RFs, a ROI line was drawn and a line ablation was performed during continuous image acquisition. For measurement of actin structure retraction after laser ablation of actin cables either on or out of fibronectin pattern, a point ablation was performed to sever the actin cables at different locations and a customwritten MATLAB code was used to calculate the retraction distance, which was defined by d before -d after, while d before and d after are the furthest distance from the edge of the cell to the fibronectin pattern before and 10 seconds after the ablation.

j Traction force microscopy
Traction force microscopy was performed as described before56 with some modifications, using soft PDMS gels (1:1 mixture of CY52-276A and CY52-276B (Dow Corning Toray) resulting in a elastic modulus of ~8 kPa) spin-coated (700 rpm) on glass bottom dishes (Iwaki) and cured at 80 °C for 2 hours. The substrate was then functionalized with 5% aminopropyl triethoxysilane (Sigma) in methanol for 5 min, rinsed 3 times with ethanol, and cured at 80 °C for 20 min. Then a diluted (1:500) solution of 100 nm carboxylated red fluorescent beads (Invitrogen) in MQ water was added, incubated for 15 min and rinsed 4 times with MQ water to remove excessive beads. For fibronectin patterning of the gel, PDMS (Sylgard 184, Dow Corning) stencils with pillars of the given shapes were treated with UV for 20 min and coated with a solution of 50 μg/ml human plasma fibronectin mixed with 10% Atto647 conjugated fibronectin in MQ water for 1 hour. Afterwards, the solution was removed with suction and stencil was inverted and directly stamped on a previously prepared Polyvinyl Alcohol (PVA) membrane (Sigma). Then the PVA membrane was gently placed face down on the soft PDMS substrate. After 1 hour, a 0.2% solution of Pluronics F-127 (Sigma) in MQ water was added to dissolve the PVA and block the uncoated area.
Cells were then seeded on the patterned substrate, let attach for 1 hour, rinsed with DMEM to remove unattached cells, and imaged on a Zeiss LSM780 confocal microscope with a 1.2 N.A. 60X water immersion objective the next day. After live imaging, a 1% SDS solution in PBS was added to lyse the cells and a resting beads image (null-force) was captured.
Analysis of traction forces based on beads displacement was performed as described previously.39

k Measurement of actin polymerization and depolymerization by photo-conversion
Cells were first transfected with mEos2-Actin-C-18 construct and seeded on the patterns. We performed photo-conversion of mEos2-Actin within the structure at negative curvature with a 405 laser in a rectangular ROI to measure the polymerization and depolymerization dynamics ( Fig. 5a and Supplementary Video 9). After the photo-conversion, hotspots of fluorescence in the green channel reappeared within the center region at the negative curvature in the green channel, suggesting newly polymerized actin filaments (Fig. 5b). In the mean time, decreasing fluorescence in the red channel was driven by depolymerization of actin filaments (Fig. 5c). Actin polymerization and depolymerization measurements based on photo-conversion experiments are calculated as follows: polymerization is computed as local average of fluorescence intensity between 20-40 seconds after photo-conversion subtracting fluorescence intensity before photo-conversion in the green channel, normalized by the difference between the fluorescence intensity immediately before and after photoconversion; depolymerization is computed as local average of fluorescence intensity between 20-40 seconds after photo-conversion subtracted from fluorescence intensity immediately after photo-conversion in the red channel, normalized by the difference between the fluorescence intensity immediately before and after photo-conversion. Assuming photo-bleaching is independent of the spatial location, there is no need to correct for photo-bleaching in order to compare the relative values between different spatial locations. We do not claim that the numerical values obtained from this measurement necessarily represent a linear mapping to the molecules of actin monomers incorporated into F-actin per unit time.
l Image processing and analysis Images shown in the figures were background subtracted and contrast enhanced for visualization. Intensity measurements were performed on raw images. Due to the nonlinearity of structure illumination microscopy images, only confocal images were used for intensity measurements, hence only structural but not intensity information should be interpreted from the SIM images.
Due to the 3D shape of the cell, intensity measurements over the whole actin structure were done by taking a 2 μm z-stack and averaging along z direction after segmentation of each slice to calculate the local fluorescence concentration, except for live imaging experiments where high time resolution is needed and a single slice was taken but with a larger pinhole size to image the entire structure.
Profiles with relative distances were calculated by measuring intensity at each point within a central region at positive or negative curvature, and its position along the radial direction (perpendicular to the edge of the fibronectin pattern), taking the rear of the radial fibers as 0 and the frontal edge of the cell as 1.
Fiber orientation analysis was performed with a custom-built MATLAB code to measure the local fiber orientation based on edge-detection of F-actin images. The order parameter was then calculated as S=<cos(2θ)> where θ is the angle at each point between the actin fiber and the radial direction.
Actin dynamics index (ADI) is measured by taking a time-lapse (15 seconds per frame) movie of GFP actin with live SIM microcopy, and calculated as ADI(i)=(I(i)-I(i-1))/std(I(i)), with image of frame i as I(i) and the standard deviation of frame i as std(I(i)). An averaged ADI for all frames is shown in the figures.

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Europe PMC Funders Author Manuscripts