Theoretical Analysis of Membrane Tension in Moving Cells

Lateral tension in cell plasma membranes plays an essential role in regulation of a number of membrane-related intracellular processes and cell motion. Understanding the physical factors generating the lateral tension and quantitative determination of the tension distribution along the cell membrane is an emerging topic of cell biophysics. Although experimental data are accumulating on membrane tension values in several cell types, the tension distribution along the membranes of moving cells remains largely unexplored. Here we suggest and analyze a theoretical model predicting the tension distribution along the membrane of a cell crawling on a flat substrate. We consider the tension to be generated by the force of actin network polymerization against the membrane at the cell leading edge. The three major factors determining the tension distribution are the membrane interaction with anchors connecting the actin network to the lipid bilayer, the membrane interaction with cell adhesions, and the force developing at the rear boundary due to the detachment of the remaining cell adhesion from the substrate in the course of cell crawling. Our model recovers the experimentally measured values of the tension in fish keratocytes and their dependence on the number of adhesions. The model predicts, quantitatively, the tension distribution between the leading and rear membrane edges as a function of the area fractions of the anchors and the adhesions.     

Front-to-Rear Membrane Tension Gradient in Rapidly Moving Cells

Membrane tension is becoming recognized as an important mechanical regulator of motile cell behavior. Although membrane-tension measurements have been performed in various cell types, the tension distribution along the plasma membrane of motile cells has been largely unexplored. Here, we present an experimental study of the distribution of tension in the plasma membrane of rapidly moving fish epithelial keratocytes. We find that during steady movement the apparent membrane tension is ∼30% higher at the leading edge than at the trailing edge. Similar tension differences between the front and the rear of the cell are found in keratocyte fragments that lack a cell body. This front-to-rear tension variation likely reflects a tension gradient developed in the plasma membrane along the direction of movement due to viscous friction between the membrane and the cytoskeleton-attached protein anchors embedded in the membrane matrix. Theoretical modeling allows us to estimate the area density of these membrane anchors. Overall, our results indicate that even though membrane tension equilibrates rapidly and mechanically couples local boundary dynamics over cellular scales, steady-state variations in tension can exist in the plasma membranes of moving cells.     

Physical model for self-organization of actin cytoskeleton and adhesion complexes at the cell front

Cell motion is driven by interplay between the actin cytoskeleton and the cell adhesions in the front part of the cell. The actin network segregates into lamellipodium and lamellum, whereas the adhesion complexes are characteristically distributed underneath the actin system. Here, we suggest a computational model for this characteristic organization of the actin-adhesion system. The model is based on the ability of the adhesion complexes to sense mechanical forces, the stick-slip character of the interaction between the adhesions and the moving actin network, and a hypothetical propensity of the actin network to disintegrate upon sufficiently strong stretching stresses. We identify numerically three possible types of system organization, all observed in living cells: two states in which the actin network exhibits segregation into lamellipodium and lamellum, whereas the cell edge either remains stationary or moves, and a state where the actin network does not undergo segregation. The model recovers the asynchronous fluctuations and outward bulging of the cell edge, and the dependence of the edge protrusion velocity on the rate of the nascent adhesion generation, the membrane tension, and the substrate rigidity.     

Intracellular stress transmission through actin stress fiber network in adherent vascular cells

Intracellular stress transmission through subcellular structural components has been proposed to affect activation of localized mechano-sensing sites such as focal adhesions in adherent cells. Previous studies reported that physiological extracellular forces produced heterogeneous spatial distributions of cytoplasmic strain. However, mechanical signaling pathway involved in intracellular force transmission through basal actin stress fibers (SFs), a mechano-responsive cytoskeletal structure, remains elusive. In the present study, we investigated force balance within the basal SFs of cultured smooth muscle cells and endothelial cells by (i) removing the cell membrane and cytoplasmic constituents except for materials physically attaching to the substrate (i.e., SF-focal adhesion complexities) or (ii) dislodging either mechanically or chemically the cell processes of the cells expressing fluorescent proteins-labeled actin and focal adhesions in order, to examine stress-release-induced deformation of the basal SFs. The result showed that a removal of mechanical restrictions for SFs resulted in a decrease in the length of the remaining SFs, which means SFs bear tension. In addition, a release of the preexisting tension in a single SF was transmitted to another SF physically linked to the former, but not transmitted to the other ones physically independent of the former, suggesting that the prestress is balanced in tensed SF networks. These results support a hypothesis regarding cell structural architecture that physiological extracellular forces can produce in the basal SF network a directional intracellular stress or strain distribution. Therefore, consideration of the coexistence of the directional stretching strain along the axial direction of SFs and the heterogeneous strain in the other cytoplasmic region will be essential for understanding intracellular stress transmission in the adherent cells.     

Geometry Regulates Traction Stresses in Adherent Cells

Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell’s mechanical output over a wide range of cell geometries.     

Geometry Regulates Traction Stresses in Adherent Cells

Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell’s mechanical output over a wide range of cell geometries.     

The Role of Stress Fibers in the Shape Determination Mechanism of Fish Keratocytes

Crawling cells have characteristic shapes that are a function of their cell types. How their different shapes are determined is an interesting question. Fish epithelial keratocytes are an ideal material for investigating cell shape determination, because they maintain a nearly constant fan shape during their crawling locomotion. We compared the shape and related molecular mechanisms in keratocytes from different fish species to elucidate the key mechanisms that determine cell shape. Wide keratocytes from cichlids applied large traction forces at the rear due to large focal adhesions, and showed a spatially loose gradient associated with actin retrograde flow rate, whereas round keratocytes from black tetra applied low traction forces at the rear small focal adhesions and showed a spatially steep gradient of actin retrograde flow rate. Laser ablation of stress fibers (contractile fibers connected to rear focal adhesions) in wide keratocytes from cichlids increased the actin retrograde flow rate and led to slowed leading-edge extension near the ablated region. Thus, stress fibers might play an important role in the mechanism of maintaining cell shape by regulating the actin retrograde flow rate.     

An adhesion-dependent switch between mechanisms that determine motile cell shape

Keratocytes are fast-moving cells in which adhesion dynamics are tightly coupled to the actin polymerization motor that drives migration, resulting in highly coordinated cell movement. We have found that modifying the adhesive properties of the underlying substrate has a dramatic effect on keratocyte morphology. Cells crawling at intermediate adhesion strengths resembled stereotypical keratocytes, characterized by a broad, fan-shaped lamellipodium, clearly defined leading and trailing edges, and persistent rates of protrusion and retraction. Cells at low adhesion strength were small and round with highly variable protrusion and retraction rates, and cells at high adhesion strength were large and asymmetrical and, strikingly, exhibited traveling waves of protrusion. To elucidate the mechanisms by which adhesion strength determines cell behavior, we examined the organization of adhesions, myosin II, and the actin network in keratocytes migrating on substrates with different adhesion strengths. On the whole, our results are consistent with a quantitative physical model in which keratocyte shape and migratory behavior emerge from the self-organization of actin, adhesions, and myosin, and quantitative changes in either adhesion strength or myosin contraction can switch keratocytes among qualitatively distinct migration regimes.     

Actin,microtubules and focal adhesion dynamics during cell migration

Cell migration is a complex cellular behavior that results from the coordinated changes in the actin cytoskeleton and the controlled formation and dispersal of cell-substrate adhesion sites. While the actin cytoskeleton provides the driving force at the cell front, the microtubule network assumes a regulatory function in coordinating rear retraction. The polarity within migrating cells is further highlighted by the stationary behavior of focal adhesions in the front and their sliding in trailing ends. We discuss here the cross-talk of the actin cytoskeleton with the microtubule network and the potential mechanisms that control the differential behavior of focal adhesions sites during cell migration.     

VASP governs actin dynamics by modulating filament anchoring

Actin filament dynamics at the cell membrane are important for cell-matrix and cell-cell adhesions and the protrusion of the leading edge. Since actin filaments must be connected to the cell membrane to exert forces but must also detach from the membrane to allow it to move and evolve, the balance between actin filament tethering and detachment at adhesion sites and the leading edge is key for cell shape changes and motility. How this fine tuning is performed in cells remains an open question, but possible candidates are the Drosophila enabled/vasodilator-stimulated phosphoprotein (Ena/VASP) family of proteins, which localize to dynamic actin structures in the cell. Here we study VASP-mediated actin-related proteins 2/3 (Arp2/3) complex-dependent actin dynamics using a substrate that mimics the fluid properties of the cell membrane: an oil-water interface. We show evidence that polymerization activators undergo diffusion and convection on the fluid surface, due to continual attachment and detachment to the actin network. These dynamics are enhanced in the presence of VASP, and we observe cycles of catastrophic detachment of the actin network from the surface, resulting in stop-and-go motion. These results point to a role for VASP in the modulation of filament anchoring, with implications for actin dynamics at cell adhesions and at the leading edge of the cell.     

Lamellipodial contractions during crawling and spreading

Most eukaryotic cells can crawl over surfaces. In general, this motility requires three distinct actions: polymerization at the leading edge, adhesion to the substrate, and retraction at the rear. Recent experiments with mouse embryonic fibroblasts showed that during spreading and crawling the lamellipodium undergoes periodic contractions that are substrate-dependent. Here I show that a simple model incorporating stick-slip adhesion and a simplified mechanism for the generation of contractile forces is sufficient to explain periodic lamellipodial contractions. This model also explains why treatment of cells with latrunculin modifies the period of these contractions. In addition, by coupling a diffusing chemical species that can bind actin, such as myosin light-chain kinase, with the contractile model leads to periodic rows and waves in the chemical species, similar to what is observed in experiments. This model provides a novel and simple explanation for the generation of contractile waves during cell spreading and crawling that is only dependent on stick-slip adhesion and the generation of contractile force and suggests new experiments to test this mechanism.     

Mechanotransduction of mesenchymal melanoma cell invasion into 3D collagen lattices: Filopod-mediated extension–relaxation cycles and force anisotropy

Mesenchymal cell migration in interstitial tissue is a cyclic process of coordinated leading edge protrusion, adhesive interaction with extracellular matrix (ECM) ligands, cell contraction followed by retraction and movement of the cell rear. During migration through 3D tissue, the force fields generated by moving cells are non-isotropic and polarized between leading and trailing edge, however the integration of protrusion formation, cell–substrate adhesion, traction force generation and cell translocation in time and space remain unclear. Using high-resolution 3D confocal reflectance and fluorescence microscopy in GFP/actin expressing melanoma cells, we here employ time-resolved subcellular coregistration of cell morphology, interaction and alignment of actin-rich protrusions engaged with individual collagen fibrils. Using single fibril displacement as sensitive measure for force generated by the leading edge, we show how a dominant protrusion generates extension–retraction cycles transmitted through multiple actin-rich filopods that move along the scaffold in a hand-over-hand manner. The resulting traction force is oscillatory, occurs in parallel to cell elongation and, with maximum elongation reached, is followed by rear retraction and movement of the cell body. Combined live-cell fluorescence and reflection microscopy of the leading edge thus reveals step-wise caterpillar-like extension–retraction cycles that underlie mesenchymal migration in 3D tissue.     

Boyden chamber-based method for characterizing the distribution of adhesions and cytoskeletal structure in HT1080 fibrosarcoma cells

A 2D model was previously presented that describes the gliding motility of human fibrosarcoma cells. The model was based on the observation that adhesions are present only on the outer rim of the leading lamella of the semicircular cell. The present model describes the organization of adhesions and the cytoskeleton of migrating HT1080 fibrosarcoma and LX2 hepatic stellate cells in three dimensions. The migration assays were performed in a modified Boyden chamber using fibronectin, Matrigel, or collagen I as chemoattractants. The distribution of the adhesions was analyzed by confocal laser scanning microscope, and following decoration with heavy meromyosin, the organization of actin filaments was analyzed by electron microscopy. Double labeling was performed to study the relationship of the actin and vimentin filament network in the moving cells. Vinculin containing adhesions were observed only at the front of the cell in the form of a ring while passing through a filter pore of the Boyden chamber. Actin filaments were present only below the plasma membrane, except the very tip of the leading lamella. Vimentin intermediate filaments were localized around the cell nucleus behind the actin filament-rich lamella.

This paper describes a model of the organization of adhesions and the cytoskeleton of migrating cells in the Boyden chamber. The model is based on the observation that adhesions are present only at the leading edge of the cell. The results extend the earlier 2D model of cell locomotion into 3D.     

Computational Tension Mapping of Adherent Cells Based on Actin Imaging

Forces transiting through the cytoskeleton are known to play a role in adherent cell activity. Up to now few approaches haves been able to determine theses intracellular forces. We thus developed a computational mechanical model based on a reconstruction of the cytoskeleton of an adherent cell from fluorescence staining of the actin network and focal adhesions (FA). Our custom made algorithm converted the 2D image of an actin network into a map of contractile interactions inside a 2D node grid, each node representing a group of pixels. We assumed that actin filaments observed under fluorescence microscopy, appear brighter when thicker, we thus presumed that nodes corresponding to pixels with higher actin density were linked by stiffer interactions. This enabled us to create a system of heterogeneous interactions which represent the spatial organization of the contractile actin network. The contractility of this interaction system was then adapted to match the level of force the cell truly exerted on focal adhesions; forces on focal adhesions were estimated from their vinculin expressed size. This enabled the model to compute consistent mechanical forces transiting throughout the cell. After computation, we applied a graphical approach on the original actin image, which enabled us to calculate tension forces throughout the cell, or in a particular region or even in single stress fibers. It also enabled us to study different scenarios which may indicate the mechanical role of other cytoskeletal components such as microtubules. For instance, our results stated that the ratio between intra and extra cellular compression is inversely proportional to intracellular tension.     

Cell migration: mechanisms of rear detachment and the formation of migration tracks

Cell migration is central to many biological and pathological processes, including embryogenesis, tissue repair and regeneration as well as cancer and the inflammatory response. In general, cell migration can be usefully conceptualized as a cyclic process. The initial response of a cell to a migration-promoting agent is to polarize and extend protrusions in the direction of migration. These protrusions can be large, broad lamellipodia or spike-like filopodia, are usually driven by actin polymerization, and are stabilized by adhering to the extracellular matrix (ECM) via transmembrane receptors of the integrin family linked to the actin cytoskeleton. These adhesions serve as traction sites for migration as the cell moves forward over them, and they must be disassembled at the cell rear, allowing it to detach. The mechanisms of rear detachment and the regulatory processes involved are not well understood. The disassembly of adhesions that is required for detachment depends on a coordinated interaction of actin and actin-binding proteins, signaling molecules and effector enzymes including proteases, kinases and phosphatases. Originally, the biochemically regulated processes leading to rear detachment of migrating cells were thought not to be necessarily accompanied by any loss of cell material. However, it has been shown that during rear detachment long tubular extensions, the retracting fibers, are formed and that "membrane ripping" occurs at the cell rear. By this process, a major fraction of integrin-containing cellular material is left behind forming characteristic migration tracks that exactly mark the way a cell has taken.     

Depolymerization-driven flow in nematode spermatozoa relates crawling speed to size and shape

Cell crawling is an inherently physical process that includes protrusion of the leading edge, adhesion to the substrate, and advance of the trailing cell body. Research into advance of the cell body has focused on actomyosin contraction, with cytoskeletal disassembly regarded as incidental, rather than causative; however, extracts from nematode spermatozoa, which use Major Sperm Protein rather than actin, provide at least one example where cytoskeletal disassembly apparently generates force in the absence of molecular motors. To test whether depolymerization can explain force production during nematode sperm crawling, we constructed a mathematical model that simultaneously describes the dynamics of both the cytoskeleton and the cytosol. We also performed corresponding experiments using motile Caenorhabditis elegans spermatozoa. Our experiments reveal that crawling speed is an increasing function of both cell size and anterior-posterior elongation. The quantitative, depolymerization-driven model robustly predicts that cell speed should increase with cell size and yields a cytoskeletal disassembly rate that is consistent with previous measurements. Notably, the model requires anisotropic elasticity, with the cell being stiffer along the direction of motion, to accurately reproduce the dependence of speed on elongation. Our simulations also predict that speed should increase with cytoskeletal anisotropy and disassembly rate.     

The key feature for early migratory processes

Migration of cells is one of the most essential prerequisites to form higher organisms and depends on a strongly coordinated sequence of processes. Early migratory events include substrate sensing, adhesion formation, actin bundle assembly and force generation. While substrate sensing was ascribed to filopodia, all other processes were believed to depend mainly on lamellipodia of migrating cells. In this work we show for motile keratinocytes that all processes from substrate sensing to force generation strongly depend on filopodial focal complexes as well as on filopodial actin bundles. In a coordinated step by step process filopodial focal complexes have to be tightly adhered to the substrate and to filopodial actin bundles to enlarge upon lamellipodial contact forming classical focal adhesions. Lamellipodial actin filaments attached to those focal adhesions originate from filopodia. Upon cell progression, the incorporation of filopodial actin bundles into the lamellipodium goes along with a complete change in actin cross-linker composition from filopodial fascin to lamellipodial α-actinin. α-Actinin in turn is replaced by myosin II and becomes incorporated directly behind the leading edge. Myosin II activity makes this class of actin bundles with their attached FAs the major source of force generation and transmission at the cell front. Furthermore, connection of FAs to force generating actin bundles leads to their stabilization and further enlargement. Consequently, adhesion sites formed independently of filopodia are not connected to detectable actin bundles, transmit weak forces to the substrate and disassemble within a few minutes without having been increased in size.     

Dynamic coupling between actin network flow and turnover revealed by flow mapping in the lamella of crawling fragments

Dynamic turnover and transport of actin filament network is essential for protrusive force generation and traction force development during cell migration. To elucidate the dynamic coupling between actin network flow and turnover, we focused on flow dynamics in the lamella of one of the simplest but elegant motility systems; crawling fragments derived from fish keratocytes. Interestingly, we show that actin network in the lamella of fragments is not stationary as earlier reported, but exhibits a flow dynamics that is strikingly similar to that reported for higher order cells, suggesting that network flow is an intrinsic property of the actin cytoskeleton that is fundamental to cell migration. We also demonstrate that whereas polymerization mediates network assembly at the front, surprisingly, network flow convergence modulates network disassembly toward the rear of the lamella, suggesting that flow and turnover are coupled during migration. These results obtained using simple motility systems are significant to the understanding of actin network dynamics in migrating cells, and they will be found useful for developing biophysical models for elucidating the fundamental mechanisms of cell migration.