Traction Forces Control Cell-Edge Dynamics and Mediate Distance Sensitivity during Cell Polarization.

Traction forces are generated by cellular actin-myosin system and transmitted to the environment through adhesions. They are believed to drive cell motion, shape changes, and extracellular matrix remodeling [1-3]. However, most of the traction force analysis has been performed on stationary cells, investigating forces at the level of individual focal adhesions or linking them to static cell parameters, such as area and edge curvature [4-10]. It is not well understood how traction forces are related to shape changes and motion, e.g., forces were reported to either increase or drop prior to cell retraction [11-15]. Here, we analyze the dynamics of traction forces during the protrusion-retraction cycle of polarizing fish epidermal keratocytes and find that forces fluctuate together with the cycle, increasing during protrusion and reaching maximum at the beginning of retraction. We relate force dynamics to the recently discovered phenomenological rule [16] that governs cell-edge behavior during keratocyte polarization: both traction forces and probability of switch from protrusion to retraction increase with the distance from the cell center. Diminishing forces with cell contractility inhibitor leads to decreased edge fluctuations and abnormal polarization, although externally applied force can induce protrusion-retraction switch. These results suggest that forces mediate distance sensitivity of the edge dynamics and organize cell-edge behavior, leading to spontaneous polarization. Actin flow rate did not exhibit the same distance dependence as traction stress, arguing against its role in organizing edge dynamics. Finally, using a simple model of actin-myosin network, we show that force-distance relationship might be an emergent feature of such networks.

Microsurgery-aided in-situ force probing reveals extensibility and viscoelastic properties of individual stress fibers.

Actin-myosin filament bundles (stress fibers) are critical for tension generation and cell shape, but their mechanical properties are difficult to access. Here we propose a novel approach to probe individual peripheral stress fibers in living cells through a microsurgically generated opening in the cytoplasm. By applying large deformations with a soft cantilever we were able to fully characterize the mechanical response of the fibers and evaluate their tension, extensibility, elastic and viscous properties.

The mechanisms of spatial and temporal patterning of cell-edge dynamics.

Adherent cells migrate and change their shape by means of protrusion and retraction at their edges. When and where these activities occur defines the shape of the cell and the way it moves. Despite a great deal of knowledge about the structural organization, components, and biochemical reactions involved in protrusion and retraction, the origins of their spatial and temporal patterns are still poorly understood. Chemical signaling circuitry is believed to be an important source of patterning, but recent studies highlighted mechanisms based on physical forces, motion, and mechanical feedback.

Cell shape dynamics reveal balance of elasticity and contractility in peripheral arcs.

The mechanical interaction between adherent cells and their substrate relies on the formation of adhesion sites and on the stabilization of contractile acto-myosin bundles, or stress fibers. The shape of the cell and the orientation of these fibers can be controlled by adhesive patterning. On nonadhesive gaps, fibroblasts develop thick peripheral stress fibers, with a concave curvature. The radius of curvature of these arcs results from the balance of the line tension in the arc and of the surface tension in the cell bulk. However, the nature of these forces, and in particular the contribution of myosin-dependent contractility, is not clear. To get insight into the force balance, we inhibit myosin activity and simultaneously monitor the dynamics of peripheral arc radii and traction forces. We use these measurements to estimate line and surface tension. We found that myosin inhibition led to a decrease in the traction forces and an increase in arc radius, indicating that both line tension and surface tension dropped, but the line tension decreased to a lesser extent than surface tension. These results suggest that myosin-independent force contributes to tension in the peripheral arcs. We propose a simple physical model in which the peripheral arc line tension is due to the combination of myosin II contractility and a passive elastic component, while surface tension is largely due to active contractility. Numerical solutions of this model reproduce well the experimental data and allow estimation of the contributions of elasticity and contractility to the arc line tension.

Ultra-soft cantilevers and 3-D micro-patterned substrates for contractile bundle tension measurement in living cells.

Actin-myosin microfilament bundles or stress-fibers are the principal tension-generating structures in the cell. Their mechanical properties are critical for cell shape, motion, and interaction with other cells and extracellular matrix, but were so far difficult to access in a living cell. Here we propose a micro-fabricated two-component setup for direct tension measurement on a peripheral bundle within an intact cell. We used 3-D substrates made of silicon elastomer to elevate the cell making the filament bundle at its border accessible from the side, and employed an ultra-soft (spring constant 0.78 nN µm(-1)) epoxy-based cantilever for mechanical probing. With this setup we were able for the first time to measure the tension in peripheral actin bundles in living primary fibroblasts spread on a rigid substrate.

Contact angle at the leading edge controls cell protrusion rate.

Plasma membrane tension and the pressure generated by actin polymerization are two antagonistic forces believed to define the protrusion rate at the leading edge of migrating cells [1-5]. Quantitatively, resistance to actin protrusion is a product of membrane tension and mean local curvature (Laplace's law); thus, it depends on the local geometry of the membrane interface. However, the role of the geometry of the leading edge in protrusion control has not been yet investigated. Here, we manipulate both the cell shape and substrate topography in the model system of persistently migrating fish epidermal keratocytes. We find that the protrusion rate does not correlate with membrane tension, but, instead, strongly correlates with cell roundness, and that the leading edge of the cell exhibits pinning on substrate ridges-a phenomenon characteristic of spreading of liquid drops. These results indicate that the leading edge could be considered a triple interface between the substrate, membrane, and extracellular medium and that the contact angle between the membrane and the substrate determines the load on actin polymerization and, therefore, the protrusion rate. Our findings thus illuminate a novel relationship between the 3D shape of the cell and its dynamics, which may have implications for cell migration in 3D environments.

Cell polarization: mechanical switch for a chemical reaction.

Anterior-posterior polarity in the Caenorhabditis elegans zygote depends on two groups of PAR proteins, as well as on cortical flow. Recent work now demonstrates that this polarization results from a transition in a bistable reaction-diffusion system of PAR proteins that is triggered by cortical flow.

Dynamic measurement of the height and volume of migrating cells by a novel fluorescence microscopy technique.

We propose a new technique to measure the volume of adherent migrating cells. The method is based on a negative staining where a fluorescent, non-cell-permeant dye is added to the extracellular medium. The specimen is observed with a conventional fluorescence microscope in a chamber of uniform height. Given that the fluorescence signal depends on the thickness of the emitting layer, the objects excluding the fluorescent dye (i.e., cells) appear dark, and the decrease of the fluorescent signal with respect to the background is expected to give information about the height and the volume of the object. Using a glass microfabricated pattern with steps of defined heights, we show that the drop in fluorescence intensity is indeed proportional to the height of the step and obtain calibration curves relating fluorescence intensity to height. The technique, termed the fluorescence displacement method, is further validated by comparing our measurements with the ones obtained by atomic force microscopy (AFM). We apply our method to measure the real-time volume dynamics of migrating fish epidermal keratocytes subjected to osmotic stress. The fluorescence displacement technique allows fast and precise monitoring of cell height and volume, thus providing a valuable tool for characterizing the three-dimensional behaviour of migrating cells.

Cell-matrix adhesion: slip and immobilization under force.

When force is applied to cell-matrix adhesion complexes, they respond by growing larger and stronger. It emerges that strengthening involves transient motion of the transmembrane integrin receptors and their eventual immobilization to the extracellular matrix.

Force transmission in migrating cells.

During cell migration, forces generated by the actin cytoskeleton are transmitted through adhesion complexes to the substrate. To investigate the mechanism of force generation and transmission, we analyzed the relationship between actin network velocity and traction forces at the substrate in a model system of persistently migrating fish epidermal keratocytes. Front and lateral sides of the cell exhibited much stronger coupling between actin motion and traction forces than the trailing cell body. Further analysis of the traction-velocity relationship suggested that the force transmission mechanisms were different in different cell regions: at the front, traction was generated by a gripping of the actin network to the substrate, whereas at the sides and back, it was produced by the network's slipping over the substrate. Treatment with inhibitors of the actin-myosin system demonstrated that the cell body translocation could be powered by either of the two different processes, actomyosin contraction or actin assembly, with the former associated with significantly larger traction forces than the latter.

Actin-myosin viscoelastic flow in the keratocyte lamellipod.

The lamellipod, the locomotory region of migratory cells, is shaped by the balance of protrusion and contraction. The latter is the result of myosin-generated centripetal flow of the viscoelastic actin network. Recently, quantitative flow data was obtained, yet there is no detailed theory explaining the flow in a realistic geometry. We introduce models of viscoelastic actin mechanics and myosin transport and solve the model equations numerically for the flat, fan-shaped lamellipodial domain of keratocytes. The solutions demonstrate that in the rapidly crawling cell, myosin concentrates at the rear boundary and pulls the actin network inward, so the centripetal actin flow is very slow at the front, and faster at the rear and at the sides. The computed flow and respective traction forces compare well with the experimental data. We also calculate the graded protrusion at the cell boundary necessary to maintain the cell shape and make a number of other testable predictions. We discuss model implications for the cell shape, speed, and bi-stability.

Role of focal adhesions and mechanical stresses in the formation and progression of the lamellipodium-lamellum interface [corrected].

Actin network in the front part of a moving cell is organized into a lamellipodium and a lamellum. A distinct lamellipodium-lamellum interface is associated with focal adhesions and consists of a series of arclike segments linking neighboring focal adhesions in the front row. The interface advances by leaping onto new rows of focal adhesions maturating underneath the lamellipodium. We propose a mechanism of the lamellipodium-lamellum boundary generation, shape formation, and progression based on the elastic stresses generated in the lamellipodial actin gel by its friction against the focal adhesions. The crucial assumption of the model is that stretching stresses trigger actin gel disintegration. We compute the stress distribution throughout the actin gel and show that the gel-disintegrating stresses drive formation of a gel boundary passing through the row of focal adhesions. Our computations recover the lamellipodium-lamellum boundary shapes detected in cells and predict the mode of the boundary transition to the row of the newly maturing focal adhesions in agreement with the experimental observations. The model fully accounts for the current phenomenology of the lamellipodium-lamellum interface formation and advancing, and makes experimentally testable predictions on the dependence of these phenomena on the sizes of the focal adhesions, the character of the focal adhesion distribution on the substrate, and the velocity of the actin retrograde flow with respect to the focal adhesions. The phase diagram resulting from the model provides a background for quantitative classification of different cell types with respect to their ability to form a lamellipodium-lamellum interface. In addition, the model suggests a mechanism of nucleation of the dorsal and arclike actin bundles found in the lamellum.

Comparative dynamics of retrograde actin flow and focal adhesions: formation of nascent adhesions triggers transition from fast to slow flow.

Dynamic actin network at the leading edge of the cell is linked to the extracellular matrix through focal adhesions (FAs), and at the same time it undergoes retrograde flow with different dynamics in two distinct zones: the lamellipodium (peripheral zone of fast flow), and the lamellum (zone of slow flow located between the lamellipodium and the cell body). Cell migration involves expansion of both the lamellipodium and the lamellum, as well as formation of new FAs, but it is largely unknown how the position of the boundary between the two flow zones is defined, and how FAs and actin flow mutually influence each other. We investigated dynamic relationship between focal adhesions and the boundary between the two flow zones in spreading cells. Nascent FAs first appeared in the lamellipodium. Within seconds after the formation of new FAs, the rate of actin flow decreased locally, and the lamellipodium/lamellum boundary advanced towards the new FAs. Blocking fast actin flow with cytochalasin D resulted in rapid dissolution of nascent FAs. In the absence of FAs (spreading on poly-L-lysine-coated surfaces) retrograde flow was uniform and the velocity transition was not observed. We conclude that formation of FAs depends on actin dynamics, and in its turn, affects the dynamics of actin flow by triggering transition from fast to slow flow. Extension of the cell edge thus proceeds through a cycle of lamellipodium protrusion, formation of new FAs, advance of the lamellum, and protrusion of the lamellipodium from the new base.

Comparative maps of motion and assembly of filamentous actin and myosin II in migrating cells.

To understand the mechanism of cell migration, one needs to know how the parts of the motile machinery of the cell are assembled and how they move with respect to each other. Actin and myosin II are thought to be the major structural and force-generating components of this machinery (Mitchison and Cramer, 1996; Parent, 2004). The movement of myosin II along actin filaments is thought to generate contractile force contributing to cell translocation, but the relative motion of the two proteins has not been investigated. We use fluorescence speckle and conventional fluorescence microscopy, image analysis, and computer tracking techniques to generate comparative velocity and assembly maps of actin and myosin II over the entire cell in a simple model system of persistently migrating fish epidermal keratocytes. The results demonstrate contrasting polarized assembly patterns of the two components, indicate force generation at the lamellipodium-cell body transition zone, and suggest a mechanism of anisotropic network contraction via sliding of myosin II assemblies along divergent actin filaments.

Analysis of actin filament network organization in lamellipodia by comparing experimental and simulated images.

Protrusion of lamellipodia during cell migration depends on the assembly of actin network. The assembly mechanism, based on dendritic filament branching, has been investigated in reconstituted in vitro systems, but little is known about the dynamical and structural properties of the actin network in the lamellipodia of migrating cells. The length and orientation of filaments are difficult to measure directly in either optical or electron microscopy images because of the high filament density and overlapping of individual filaments. Here, we use the non-uniformity of optical images of the lamellipodia to extract information about the structural and dynamical properties of the underlying actin network. To determine the relationship between the image features and the properties of the network, we performed simulations of actin network assembly, based on the hypothesis of stochastic branching and capping of filaments, and produced computed ;fluorescence' and ;electron microscopy' images of the simulated network. By varying simulation parameters, in particular the actin filament density, length and orientation, we closely reproduced the contrast and the characteristic diagonal criss-cross pattern observed in the experimental optical images. Thus, matching the images of the simulated network to the experimental images allowed us to estimate parameters of actin filament network in lamellipodia.

Assembly and mechanosensory function of focal adhesions: experiments and models.

Initial integrin-mediated cell-matrix adhesions (focal complexes) appear underneath the lamellipodia, in the regions of the "fast" centripetal flow driven by actin polymerization. Once formed, these adhesions convert the flow behind them into a "slow", myosin II-driven mode. Some focal complexes then turn into elongated focal adhesions (FAs) associated with contractile actomyosin bundles (stress fibers). Myosin II inhibition does not suppress formation of focal complexes but blocks their conversion into mature FAs and further FA growth. Application of external pulling force promotes FA growth even under conditions when myosin II activity is blocked. Thus, individual FAs behave as mechanosensors responding to the application of force by directional assembly. We proposed a thermodynamic model for the mechanosensitivity of FAs, taking into account that an elastic molecular aggregate subject to pulling forces tends to grow in the direction of force application by incorporating additional subunits. This simple model can explain a variety of processes typical of FA behavior. Assembly of FAs is triggered by the small G-protein Rho via activation of two major targets, Rho-associated kinase (ROCK) and the formin homology protein, Dia1. ROCK controls creation of myosin II-driven forces, while Dia1 is involved in the response of FAs to these forces. Expression of the active form of Dia1, allows the external force-induced assembly of mature FAs, even in conditions when Rho is inhibited. Conversely, downregulation of Dia1 by siRNA prevents FA maturation even if Rho is activated. Dia1 and other formins cap barbed (fast growing) ends of actin filaments, allowing insertion of the new actin monomers. We suggested a novel mechanism of such "leaky" capping based on an assumption of elasticity of the formin/barbed end complex. Our model predicts that formin-mediated actin polymerization should be greatly enhanced by application of external pulling force. Thus, the formin-actin complex might represent an elementary mechanosensing device responding to force by enhancement of actin assembly. In addition to its role in actin polymerization, Dia1 seems to be involved in formation of links between actin filaments and microtubules affecting microtubule dynamics. Alpha-tubulin deacetylase HDAC6 cooperates with Dia1 in formation of such links. Since microtubules are known to promote FA disassembly, the Dia1-mediated effect on microtubule dynamics may possibly play a role in the negative feedback loop controlling size and turnover of FAs.

Weak force stalls protrusion at the leading edge of the lamellipodium.

Protrusion, the first step of cell migration, is driven by actin polymerization coupled to adhesion at the cell's leading edge. Polymerization and adhesive forces have been estimated, but the net protrusion force has not been measured accurately. We arrest the leading edge of a moving fish keratocyte with a hydrodynamic load generated by a fluid flow from a micropipette. The flow arrests protrusion locally as the cell approaches the pipette, causing an arc-shaped indentation and upward folding of the leading edge. The effect of the flow is reversible upon pipette removal and dependent on the flow direction, suggesting that it is a direct effect of the external force rather than a regulated cellular response. Modeling of the fluid flow gives a surprisingly low value for the arresting force of just a few piconewtons per micrometer. Enhanced phase contrast, fluorescence, and interference reflection microscopy suggest that the flow does not abolish actin polymerization and does not disrupt the adhesions formed before the arrest but rather interferes with weak nascent adhesions at the very front of the cell. We conclude that a weak external force is sufficient to reorient the growing actin network at the leading edge and to stall the protrusion.

Gradient of rigidity in the lamellipodia of migrating cells revealed by atomic force microscopy.

Changes in mechanical properties of the cytoplasm have been implicated in cell motility, but there is little information about these properties in specific regions of the cell at specific stages of the cell migration process. Fish epidermal keratocytes with their stable shape and steady motion represent an ideal system to elucidate temporal and spatial dynamics of the mechanical state of the cytoplasm. As the shape of the cell does not change during motion and actin network in the lamellipodia is nearly stationary with respect to the substrate, the spatial changes in the direction from the front to the rear of the cell reflect temporal changes in the actin network after its assembly at the leading edge. We have utilized atomic force microscopy to determine the rigidity of fish keratocyte lamellipodia as a function of time/distance from the leading edge. Although vertical thickness remained nearly constant throughout the lamellipodia, the rigidity exhibited a gradual but significant decrease from the front to the rear of the lamellipodia. The rigidity profile resembled closely the actin density profile, suggesting that the dynamics of rigidity are due to actin depolymerization. The decrease of rigidity may play a role in facilitating the contraction of the actin-myosin network at the lamellipodium/cell body transition zone.

Tracking retrograde flow in keratocytes: news from the front.

Actin assembly at the leading edge of the cell is believed to drive protrusion, whereas membrane resistance and contractile forces result in retrograde flow of the assembled actin network away from the edge. Thus, cell motion and shape changes are expected to depend on the balance of actin assembly and retrograde flow. This idea, however, has been undermined by the reported absence of flow in one of the most spectacular models of cell locomotion, fish epidermal keratocytes. Here, we use enhanced phase contrast and fluorescent speckle microscopy and particle tracking to analyze the motion of the actin network in keratocyte lamellipodia. We have detected retrograde flow throughout the lamellipodium at velocities of 1-3 microm/min and analyzed its organization and relation to the cell motion during both unobstructed, persistent migration and events of cell collision. Freely moving cells exhibited a graded flow velocity increasing toward the sides of the lamellipodium. In colliding cells, the velocity decreased markedly at the site of collision, with striking alteration of flow in other lamellipodium regions. Our findings support the universality of the flow phenomenon and indicate that the maintenance of keratocyte shape during locomotion depends on the regulation of both retrograde flow and actin polymerization.