Contact dynamics during keratocyte motility

On the adhesion-velocity relation and length adaptation of motile cells on stepped fibronectin lanes

The biphasic adhesion-velocity relation is a universal observation in mesenchymal cell motility. It has been explained by adhesion-promoted forces pushing the front and resisting motion at the rear. Yet, there is little quantitative understanding of how these forces control cell velocity. We study motion of MDA-MB-231 cells on microlanes with fields of alternating Fibronectin densities to address this topic and derive a mathematical model from the leading-edge force balance and the force-dependent polymerization rate. It reproduces quantitatively our measured adhesion-velocity relation and results with keratocytes, PtK1 cells, and CHO cells. Our results confirm that the force pushing the leading-edge membrane drives lamellipodial retrograde flow. Forces resisting motion originate along the whole cell length. All motion-related forces are controlled by adhesion and velocity, which allows motion, even with higher Fibronectin density at the rear than at the front. We find the pathway from Fibronectin density to adhesion structures to involve strong positive feedbacks. Suppressing myosin activity reduces the positive feedback. At transitions between different Fibronectin densities, steady motion is perturbed and leads to changes of cell length and front and rear velocity. Cells exhibit an intrinsic length set by adhesion strength, which, together with the length dynamics, suggests a spring-like front-rear interaction force. We provide a quantitative mechanistic picture of the adhesion-velocity relation and cell response to adhesion changes integrating force-dependent polymerization, retrograde flow, positive feedback from integrin to adhesion structures, and spring-like front-rear interaction.

The excitable signal transduction networks: movers and shapers of eukaryotic cell migration

In response to a variety of external cues, eukaryotic cells display varied migratory modes to perform their physiological functions during development and in the adult. Aberrations in cell migration result in embryonic defects and cancer metastasis. The molecular components involved in cell migration are remarkably conserved between the social amoeba Dictyostelium and mammalian cells. This makes the amoeba an excellent model system for studies of eukaryotic cell migration. These migration-associated components can be grouped into three networks: input, signal transduction and cytoskeletal. In migrating cells, signal transduction events such as Ras or PI3K activity occur at the protrusion tips, referred to as 'front', whereas events such as dissociation of PTEN from these regions are referred to as 'back'. Asymmetric distribution of such front and back events is crucial for establishing polarity and guiding cell migration. The triggering of these signaling events displays properties of biochemical excitability including all-or-nothing responsiveness to suprathreshold stimuli, refractoriness, and wave propagation. These signal transduction waves originate from a point and propagate towards the edge of the cell, thereby driving cytoskeletal activity and cellular protrusions. Any change in the threshold for network activation alters the range of the propagating waves and the size of cellular protrusions which gives rise to various migratory modes in cells. Thus, this review highlights excitable signal transduction networks as key players for coordinating cytoskeletal activities to drive cell migration in all eukaryotes.

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.

The bioenergetics of integrin-based adhesion, from single molecule dynamics to stability of macromolecular complexes

The forces actively generated by motile cells must be transmitted to their environment in a spatiotemporally regulated manner, in order to produce directional cellular motion. This task is accomplished through integrin-based adhesions, large macromolecular complexes that link the actin-cytoskelton inside the cell to its external environment. Despite their relatively large size, adhesions exhibit rapid dynamics, switching between assembly and disassembly in response to chemical and mechanical cues exerted by cytoplasmic biochemical signals, and intracellular/extracellular forces, respectively. While in material science, force typically disrupts adhesive contact, in this biological system, force has a more nuanced effect, capable of causing assembly or disassembly. This initially puzzled experimentalists and theorists alike, but investigation into the mechanisms regulating adhesion dynamics have progressively elucidated the origin of these phenomena. This review provides an overview of recent studies focused on the theoretical understanding of adhesion assembly and disassembly as well as the experimental studies that motivated them. We first concentrate on the kinetics of integrin receptors, which exhibit a complex response to force, and then investigate how this response manifests itself in macromolecular adhesion complexes. We then turn our attention to studies of adhesion plaque dynamics that link integrins to the actin-cytoskeleton, and explain how force can influence the assembly/disassembly of these macromolecular structure. Subsequently, we analyze the effect of force on integrins populations across lengthscales larger than single adhesions. Finally, we cover some theoretical studies that have considered both integrins and the adhesion plaque and discuss some potential future avenues of research.

Micromanipulation Techniques Allowing Analysis of Morphogenetic Dynamics and Turnover of Cytoskeletal Regulators

Examining the spatiotemporal dynamics of proteins can reveal their functional importance in various contexts. In this article, it is discussed how fluorescent recovery after photobleaching (FRAP) and photoactivation techniques can be used to study the spatiotemporal dynamics of proteins in subcellular locations. We also show how these techniques enable straightforward determination of various parameters linked to actin cytoskeletal regulation and cell motility. Moreover, the microinjection of cells is additionally described as an alternative treatment (potentially preceding or complementing the aforementioned photomanipulation techniques) to trigger instantaneous effects of translocated proteins on cell morphology and function. Micromanipulation such as protein injection or local application of plasma membrane-permeable drugs or cytoskeletal inhibitors can serve as powerful tool to record immediate consequences of a given treatment on cell behavior at the single cell and subcellular level. This is exemplified here by immediate induction of lamellipodial cell edge protrusion by the injection of recombinant Rac1 protein, as established a quarter-century ago. In addition, we provide a protocol for determining the turnover of enhanced green fluorescent protein (EGFP)-VASP, an actin filament polymerase prominently accumulating at lamellipodial tips of B16-F1 cells, employing FRAP and including associated data analysis and curve fitting. We also present guidelines for estimating the rates of lamellipodial actin network polymerization, as exemplified by cells expressing EGFP-tagged β-actin. Finally, instructions are given for how to investigate the rates of actin monomer mobility within the cell cytoplasm, followed by actin incorporation at sites of rapid filament assembly, such as the tips of protruding lamellipodia, using photoactivation approaches. None of these protocols is restricted to components or regulators of the actin cytoskeleton, but can easily be extended to explore in analogous fashion the spatiotemporal dynamics and function of proteins in various different subcellular structures or functional contexts.

Membrane tension: A challenging but universal physical parameter in cell biology

The plasma membrane separates the interior of cells from the outside environment. The membrane tension, defined as the force per unit length acting on a cross-section of membrane, regulates many vital biological processes. In this review, we summarize the first historical findings and the latest advances, showing membrane tension as an important physical parameter in cell biology. We also discuss how this parameter must be better integrated and we propose experimental approaches for key unanswered questions.

Excitable Signal Transduction Networks in Directed Cell Migration

Although directed migration of eukaryotic cells may have evolved to escape nutrient depletion, it has been adopted for an extensive range of physiological events during development and in the adult organism. The subversion of these movements results in disease, such as cancer. Mechanisms of propulsion and sensing are extremely diverse, but most eukaryotic cells move by extending actin-filled protrusions termed macropinosomes, pseudopodia, or lamellipodia or by extension of blebs. In addition to motility, directed migration involves polarity and directional sensing. The hundreds of gene products involved in these processes are organized into networks of parallel and interconnected pathways. Many of these components are activated or inhibited coordinately with stimulation and on each spontaneously extended protrusion. Moreover, these networks display hallmarks of excitability, including all-or-nothing responsiveness and wave propagation. Cellular protrusions result from signal transduction waves that propagate outwardly from an origin and drive cytoskeletal activity. The range of the propagating waves and hence the size of the protrusions can be altered by lowering or raising the threshold for network activation, with larger and wider protrusions favoring gliding or oscillatory behavior over amoeboid migration. Here, we evaluate the variety of models of excitable networks controlling directed migration and outline critical tests. We also discuss the utility of this emerging view in producing cell migration and in integrating the various extrinsic cues that direct migration.

Frustrated Phagocytic Spreading of J774A-1 Macrophages Ends in Myosin II-Dependent Contraction

Conventional studies of dynamic phagocytic behavior have been limited in terms of spatial and temporal resolution due to the inherent three-dimensionality and small features of phagocytosis. To overcome these issues, we use a series of frustrated phagocytosis assays to quantitatively characterize phagocytic spreading dynamics. Our investigation reveals that frustrated phagocytic spreading occurs in phases and is punctuated by a distinct period of contraction. The spreading duration and peak contact areas are independent of the surface opsonin density, although the opsonin density does affect the likelihood that a cell will spread. This reinforces the idea that phagocytosis dynamics are primarily dictated by cytoskeletal activity. Structured illumination microscopy reveals that F-actin is reorganized during the course of frustrated phagocytosis. F-actin in early stages is consistent with that observed in lamellipodial protrusions. During the contraction phase, it is bundled into fibers that surround the cell and is reminiscent of a contractile belt. Using traction force microscopy, we show that cells exert significant strain on the underlying substrate during the contraction phase but little strain during the spreading phase, demonstrating that phagocytes actively constrict during late-stage phagocytosis. We also find that late-stage contraction initiates after the cell surface area increases by 225%, which is consistent with the point at which cortical tension begins to rise. Moreover, reducing tension by exposing cells to hypertonic buffer shifts the onset of contraction to occur in larger contact areas. Together, these findings provide further evidence that tension plays a significant role in signaling late-stage phagocytic activity.

Adhesion-Dependent Wave Generation in Crawling Cells

Dynamic actin networks are excitable. In migrating cells, feedback loops can amplify stochastic fluctuations in actin dynamics, often resulting in traveling waves of protrusion. The precise contributions of various molecular and mechanical interactions to wave generation have been difficult to disentangle, in part due to complex cellular morphodynamics. Here we used a relatively simple cell type-the fish epithelial keratocyte-to define a set of mechanochemical feedback loops underlying actin network excitability and wave generation. Although keratocytes are normally characterized by the persistent protrusion of a broad leading edge, increasing cell-substrate adhesion strength results in waving protrusion of a short leading edge. We show that protrusion waves are due to fluctuations in actin polymerization rates and that overexpression of VASP, an actin anti-capping protein that promotes actin polymerization, switches highly adherent keratocytes from waving to persistent protrusion. Moreover, VASP localizes both to adhesion complexes and to the leading edge. Based on these results, we developed a mathematical model for protrusion waves in which local depletion of VASP from the leading edge by adhesions-along with lateral propagation of protrusion due to the branched architecture of the actin network and negative mechanical feedback from the cell membrane-results in regular protrusion waves. Consistent with our model simulations, we show that VASP localization at the leading edge oscillates, with VASP leading-edge enrichment greatest just prior to protrusion initiation. We propose that the mechanochemical feedbacks underlying wave generation in keratocytes may constitute a general module for establishing excitable actin dynamics in other cellular contexts.

The molecular dynamics of crawling migration in microtubule-disrupted keratocytes

Cell-crawling migration plays an essential role in complex biological phenomena. It is now generally believed that many processes essential to such migration are regulated by microtubules in many cells, including fibroblasts and neurons. However, keratocytes treated with nocodazole, which is an inhibitor of microtubule polymerization – and even keratocyte fragments that contain no microtubules – migrate at the same velocity and with the same directionality as normal keratocytes. In this study, we discovered that not only these migration properties, but also the molecular dynamics that regulate such properties, such as the retrograde flow rate of actin filaments, distributions of vinculin and myosin II, and traction forces, are also the same in nocodazole-treated keratocytes as those in untreated keratocytes. These results suggest that microtubules are not in fact required for crawling migration of keratocytes, either in terms of migrating properties or of intracellular molecular dynamics.

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.

Traction force microscopy in rapidly moving cells reveals separate roles for ROCK and MLCK in the mechanics of retraction

Retraction is a major rate-limiting step in cell motility, particularly in slow moving cell types that form large stable adhesions. Myosin II dependent contractile forces are thought to facilitate detachment by physically pulling up the rear edge. However, retraction can occur in the absence of myosin II activity in cell types that form small labile adhesions. To investigate the role of contractile force generation in retraction, we performed traction force microscopy during the movement of fish epithelial keratocytes. By correlating changes in local traction stress at the rear with the area retracted, we identified four distinct modes of retraction. "Recoil" retractions are preceded by a rise in local traction stress, while rear edge is temporarily stuck, followed by a sharp drop in traction stress upon detachment. This retraction type was most common in cells generating high average traction stress. In "pull" type retractions local traction stress and area retracted increase concomitantly. This was the predominant type of retraction in keratocytes and was observed mostly in cells generating low average traction stress. "Continuous" type retractions occur without any detectable change in traction stress, and are seen in cells generating low average traction stress. In contrast, to many other cell types, "release" type retractions occur in keratocytes following a decrease in local traction stress. Our identification of distinct modes of retraction suggests that contractile forces may play different roles in detachment that are related to rear adhesion strength. To determine how the regulation of contractility via MLCK or Rho kinase contributes to the mechanics of detachment, inhibitors were used to block or augment these pathways. Modulation of MLCK activity led to the most rapid change in local traction stress suggesting its importance in regulating attachment strength. Surprisingly, Rho kinase was not required for detachment, but was essential for localizing retraction to the rear. We suggest that in keratocytes MLCK and Rho kinase play distinct, complementary roles in the respective temporal and spatial control of rear detachment that is essential for maintaining rapid motility.

Cell migration

Cell migration is fundamental to establishing and maintaining the proper organization of multicellular organisms. Morphogenesis can be viewed as a consequence, in part, of cell locomotion, from large-scale migrations of epithelial sheets during gastrulation, to the movement of individual cells during development of the nervous system. In an adult organism, cell migration is essential for proper immune response, wound repair, and tissue homeostasis, while aberrant cell migration is found in various pathologies. Indeed, as our knowledge of migration increases, we can look forward to, for example, abating the spread of highly malignant cancer cells, retarding the invasion of white cells in the inflammatory process, or enhancing the healing of wounds. This article is organized in two main sections. The first section is devoted to the single-cell migrating in isolation such as occurs when leukocytes migrate during the immune response or when fibroblasts squeeze through connective tissue. The second section is devoted to cells collectively migrating as part of multicellular clusters or sheets. This second type of migration is prevalent in development, wound healing, and in some forms of cancer metastasis.

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.

Cell migration

Cell migration is fundamental to establishing and maintaining the proper organization of multicellular organisms. Morphogenesis can be viewed as a consequence, in part, of cell locomotion, from large-scale migrations of epithelial sheets during gastrulation, to the movement of individual cells during development of the nervous system. In an adult organism, cell migration is essential for proper immune response, wound repair, and tissue homeostasis, while aberrant cell migration is found in various pathologies. Indeed, as our knowledge of migration increases, we can look forward to, for example, abating the spread of highly malignant cancer cells, retarding the invasion of white cells in the inflammatory process, or enhancing the healing of wounds. This article is organized in two main sections. The first section is devoted to the single-cell migrating in isolation such as occurs when leukocytes migrate during the immune response or when fibroblasts squeeze through connective tissue. The second section is devoted to cells collectively migrating as part of multicellular clusters or sheets. This second type of migration is prevalent in development, wound healing, and in some forms of cancer metastasis.

Coupling actin flow, adhesion, and morphology in a computational cell motility model

Cell migration is a pervasive process in many biology systems and involves protrusive forces generated by actin polymerization, myosin dependent contractile forces, and force transmission between the cell and the substrate through adhesion sites. Here we develop a computational model for cell motion that uses the phase-field method to solve for the moving boundary with physical membrane properties. It includes a reaction-diffusion model for the actin-myosin machinery and discrete adhesion sites which can be in a "gripping" or "slipping" mode and integrates the adhesion dynamics with the dynamics of the actin filaments, modeled as a viscous network. To test this model, we apply it to fish keratocytes, fast moving cells that maintain their morphology, and show that we are able to reproduce recent experimental results on actin flow and stress patterns. Furthermore, we explore the phase diagram of cell motility by varying myosin II activity and adhesion strength. Our model suggests that the pattern of the actin flow inside the cell, the cell velocity, and the cell morphology are determined by the integration of actin polymerization, myosin contraction, adhesion forces, and membrane forces.

Quantitative mapping of averaged focal adhesion dynamics in migrating cells by shape normalization

The spatially ordered formation and disassembly of focal adhesions is a basic requirement for effective cell locomotion. Because focal adhesions couple the contractile actin-myosin network to the substrate, their distribution determines the pattern of traction forces propelling the cell in a certain direction. In the present study, we quantitatively analyzed the spatial patterning of cell-substrate adhesion in migrating cells by mapping averaged focal adhesion growth dynamics to a standardized cell coordinate system. These maps revealed distinct zones of focal adhesion assembly, disassembly and stability and were strongly interrelated with corresponding actin flow and traction force patterns. Moreover, the mapping technique enables precise detection of even minute responses of adhesion dynamics upon targeted signaling perturbations. For example, the partial inhibition of vinculin phosphorylation was followed by the reduced number of newly formed adhesions, whereas growth dynamics of existing adhesions remained unaffected.

High-resolution cell outline segmentation and tracking from phase-contrast microscopy images

Accurate extraction of cell outlines from microscopy images is essential for analysing the dynamics of migrating cells. Phase-contrast microscopy is one of the most common and convenient imaging modalities for observing cell motility because it does not require exogenous labelling and uses only moderate light levels with generally negligible phototoxicity effects. Automatic extraction and tracking of high-resolution cell outlines from phase-contrast images, however, is difficult due to complex and non-uniform edge intensity. We present a novel image-processing method based on refined level-set segmentation for accurate extraction of cell outlines from high-resolution phase-contrast images. The algorithm is validated on synthetic images of defined noise levels and applied to real image sequences of polarizing and persistently migrating keratocyte cells. We demonstrate that the algorithm is able to reliably reveal fine features in the cell edge dynamics.

Regulation of cell migration by dynamic microtubules

Microtubules define the architecture and internal organization of cells by positioning organelles and activities, as well as by supporting cell shape and mechanics. One of the major functions of microtubules is the control of polarized cell motility. In order to support the asymmetry of polarized cells, microtubules have to be organized asymmetrically themselves. Asymmetry in microtubule distribution and stability is regulated by multiple molecular factors, most of which are microtubule-associated proteins that locally control microtubule nucleation and dynamics. At the same time, the dynamic state of microtubules is key to the regulatory mechanisms by which microtubules regulate cell polarity, modulate cell adhesion and control force-production by the actin cytoskeleton. Here, we propose that even small alterations in microtubule dynamics can influence cell migration via several different microtubule-dependent pathways. We discuss regulatory factors, potential feedback mechanisms due to functional microtubule-actin crosstalk and implications for cancer cell motility.

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.

Cell migration is important for many biological processes: white blood cells chase down and kill bacteria to guard against infection, epithelial cells crawl across open wounds to promote healing, and embryonic cells move collectively to form organs and tissues during embryogenesis. In all of these cases, migration depends on the spatial and temporal organization of multiple forces, including actin-driven protrusion of the cell membrane, membrane tension, cell-substrate adhesion, and myosin-mediated contraction of the actin network. In this work, we have used a simple cell type, the fish epithelial keratocyte, as a model system to investigate the manner in which these forces are integrated to give rise to large-scale emergent properties such as cell shape and movement. Keratocytes are normally fan-shaped and fast-moving, but we have found that keratocytes migrate more slowly and assume round or asymmetric shapes when cell-substrate adhesion strength is too high or too low. By correlating measurements of adhesion-dependent changes in cell shape and speed with measurements of adhesion and myosin localization patterns and actin network organization, we have developed a mechanical model in which keratocyte shape and movement emerge from adhesion and myosin-dependent regulation of the dynamic actin cytoskeleton.

Modeling myosin-dependent rearrangement and force generation in an actomyosin network

Actomyosin contractility is a major force-generating mechanism that drives rearrangement of actomyosin networks; it is fundamental to cellular functions such as cellular reshaping and movement. Thus, to clarify the mechanochemical foundation of the emergence of cellular functions, understanding the relationship between actomyosin contractility and rearrangement of actomyosin networks is crucial. For this purpose, in this study, we present a new particulate-based model for simulating the motions of actin, non-muscle myosin II, and α-actinin. To confirm the model's validity, we successfully simulated sliding and bending motions of actomyosin filaments, which are observed as fundamental behaviors in dynamic rearrangement of actomyosin networks in migrating keratocytes. Next, we simulated the dynamic rearrangement of actomyosin networks. Our simulation results indicate that an increase in the density fraction of myosin induces a higher-order structural transition of actomyosin filaments from networks to bundles, in addition to increasing the force generated by actomyosin filaments in the network. We compare our simulation results with experimental results and confirm that actomyosin bundles bridging focal adhesions and the characteristics of myosin-dependent rearrangement of actomyosin networks agree qualitatively with those observed experimentally.

Bipedal locomotion in crawling cells

Many complex cellular processes from mitosis to cell motility depend on the ability of the cytoskeleton to generate force. Force-generating systems that act on elastic cytoskeletal elements are prone to oscillating instabilities. In this work, we have measured spontaneous shape and movement oscillations in motile fish epithelial keratocytes. In persistently polarized, fan-shaped cells, retraction of the trailing edge on one side of the cell body is out of phase with retraction on the other side, resulting in periodic lateral oscillation of the cell body. We present a physical description of keratocyte oscillation in which periodic retraction of the trailing edge is the result of elastic coupling with the leading edge. Consistent with the predictions of this model, the observed frequency of oscillation correlates with cell speed. In addition, decreasing the strength of adhesion to the substrate reduces the elastic force required for retraction, causing cells to oscillate with higher frequency at relatively lower speeds. These results demonstrate that simple elastic coupling between movement at the front of the cell and movement at the rear can generate large-scale mechanical integration of cell behavior.

Actin disassembly 'clock' and membrane tension determine cell shape and turning: a mathematical model

Motile cells regulate their shape and movements largely by remodeling the actin cytoskeleton. Principles of this regulation are becoming clear for simple-shaped steadily crawling cells, such as fish keratocytes. In particular, the shape of the leading edge and sides of the lamellipodium-cell motile appendage-is determined by graded actin distribution at the cell boundary, so that the denser actin network at the front grows, while sparser actin filaments at the sides are stalled by membrane tension. Shaping of the cell rear is less understood. Here we theoretically examine the hypothesis that the cell rear is shaped by the disassembly clock: the front-to-rear lamellipodial width is defined by the time needed for the actin-adhesion network to disassemble to the point at which the membrane tension can crush this network. We demonstrate that the theory predicts the observed cell shapes. Furthermore, turning of the cells can be explained by biases in the actin distribution. We discuss experimental implications of this hypothesis.

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.

The shape of motile cells

Motile cells - fan-like keratocytes, hand-shaped nerve growth cones, polygonal fibroblasts, to name but a few - come in different shapes and sizes. We discuss the origins of this diversity as well as what shape tells us about the physics and biochemistry underlying cell movement. We start with geometric rules describing cell-edge kinetics that govern cell shape, followed by a discussion of the underlying biophysics; we consider actin treadmilling, actin-myosin contraction, cell-membrane deformations, adhesion, and the complex interactions between these modules, as well as their regulation by microtubules and Rho GTPases. Focusing on several different cell types, including keratocytes and fibroblasts, we discuss how dynamic cell morphology emerges from the interplay between the different motility modules and the environment.

What makes cells move: requirements and obstacles for spontaneous cell motility

Movement of individual cells and of cellular cohorts, chains or sheets requires physical forces that are established through interactions of cells with their environment. In vivo, migration occurs extensively during embryonic development and in adults during wound healing and tumorigenesis. In order to identify the molecular events involved in cell movement, in vitro systems have been developed. These have contributed to the definition of a number of molecular pathways put into play in the course of migratory behaviours, such as mesenchymal and amoeboid movement. More recently, our knowledge of migratory modes has been enriched by analyses of cells exploring and moving through three-dimensional (3D) matrices. While the cells' morphologies differ in 2D and 3D environments, the basic mechanisms that put a cellular body into motion are remarkably similar. Thus, in both 2D and 3D, the polarity of the migrating cell is initially defined by a specific subcellular localization of signalling molecules and components of molecular machines required for motion. While the polarization can be initiated either in response to extracellular signalling or be a chance occurrence, it is reinforced and sustained by positive feedback loops of signalling molecules. Second, adhesion to a substratum is necessary to generate forces that will propel the cell engaged in either mesenchymal or ameboid migration. For collective cell movement, intercellular coordination constitutes an additional requirement: a cell cohort remains stationary if individual cells pull in opposite directions. Finally, the availability of space to move into is a general requirement to set cells into motion. Lack of free space is probably the main obstacle for migration of most healthy cells in an adult multicellular organism. Thus, the requirements for cell movement are both intrinsic to the cell, involving coordinated signalling and interactions with molecular machines, and extrinsic, imposed by the physicochemical nature of the environment. In particular, the geometry and stiffness of the support act on a range of signalling pathways that induce specific cell migratory responses. These issues are discussed in the present review in the context of published work and our own data on collective migration of hepatocyte cohorts.

Cytoskeletal mechanisms for breaking cellular symmetry

Cytoskeletal systems are networks of polymers found in all eukaryotic and many prokaryotic cells. Their purpose is to transmit and integrate information across cellular dimensions and help turn a disorderly mob of macromolecules into a spatially organized, living cell. Information, in this context, includes physical and chemical properties relevant to cellular physiology, including: the number and activity of macromolecules, cell shape, and mechanical force. Most animal cells are 10-50 microns in diameter, whereas the macromolecules that comprise them are 10,000-fold smaller (2-20 nm). To establish long-range order over cellular length scales, individual molecules must, therefore, self-assemble into larger polymers, with lengths (0.1-20 m) comparable to the size of a cell. These polymers must then be cross-linked into organized networks that fill the cytoplasm. Such cell-spanning polymer networks enable different parts of the cytoplasm to communicate directly with each other, either by transmitting forces or by carrying cargo from one spot to another.

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.

Locomotion guidance by extracellular matrix is adaptive and can be restored by a transient change in Ca2+ level

Navigation of cell locomotion by gradients of soluble factors can be desensitized if the concentration of the chemo-attractant stays unchanged. It remains obscure if the guidance by immobilized extracellular matrix (ECM) as the substrate is also adaptive and if so, how can the desensitized ECM guidance be resensitized. When first interacting with a substrate containing micron-scale fibronectin (FBN) trails, highly motile fish keratocytes selectively adhere and migrate along the FBN paths. However, such guided motion become adaptive after about 10 min and the cells start to migrate out of the ECM trails. We found that a burst increase of intracellular calcium created by an uncaging technique immediately halts the undirected migration by disrupting the ECM-cytoskeleton coupling, as evidenced by the appearance of retrograde F-actin flow. When the motility later resumes, the activated integrin receptors render the cell selectively binding to the FBN path and reinitiates signaling events, including tyrosine phosphorylation of paxillin, that couple retrograde F-actin flow to the substrate. Thus, the calcium-resensitized cell can undergo a period of ECM-navigated movement, which later becomes desensitized. Our results also suggest that endogenous calcium transients as occur during spontaneous calcium oscillations may exert a cycling resensitization-desensitization control over cell's sensing of substrate guiding cues.

Intracellular fluid flow in rapidly moving cells

Cytosolic fluid dynamics have been implicated in cell motility because of the hydrodynamic forces they induce and because of their influence on transport of components of the actin machinery to the leading edge. To investigate the existence and the direction of fluid flow in rapidly moving cells, we introduced inert quantum dots into the lamellipodia of fish epithelial keratocytes and analysed their distribution and motion. Our results indicate that fluid flow is directed from the cell body towards the leading edge in the cell frame of reference, at about 40% of cell speed. We propose that this forward-directed flow is driven by increased hydrostatic pressure generated at the rear of the cell by myosin contraction, and show that inhibition of myosin II activity by blebbistatin reverses the direction of fluid flow and leads to a decrease in keratocyte speed. We present a physical model for fluid pressure and flow in moving cells that quantitatively accounts for our experimental data.

Multi-scale models of cell and tissue dynamics

Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. The early development of multi-cellular organisms involves individual and collective cell movement; leukocytes must migrate towards sites of infection as part of the immune response; and in cancer, directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell- or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper, we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumour growth in which each cell is treated individually, and a hybrid continuum-discrete model of the later stages of tumour growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.

Actomyosin contractility spatiotemporally regulates actin network dynamics in migrating cells

Coupling interactions among mechanical and biochemical factors are important for the realization of various cellular processes that determine cell migration. Although F-actin network dynamics has been the focus of many studies, it is not yet clear how mechanical forces generated by actomyosin contractility spatiotemporally regulate this fundamental aspect of cell migration. In this study, using a combination of fluorescent speckle microscopy and particle imaging velocimetry techniques, we perturbed the actomyosin system and examined quantitatively the consequence of actomyosin contractility on F-actin network flow and deformation in the lamellipodia of actively migrating fish keratocytes. F-actin flow fields were characterized by retrograde flow at the front and anterograde flow at the back of the lamellipodia, and the two flows merged to form a convergence zone of reduced flow intensity. Interestingly, activating or inhibiting actomyosin contractility altered network flow intensity and convergence, suggesting that network dynamics is directly regulated by actomyosin contractility. Moreover, quantitative analysis of F-actin network deformation revealed that the deformation was significantly negative and predominant in the direction of cell migration. Furthermore, perturbation experiments revealed that the deformation was a function of actomyosin contractility. Based on these results, we suggest that the actin cytoskeletal structure is a mechanically self-regulating system, and we propose an elaborate pathway for the spatiotemporal self-regulation of the actin cytoskeletal structure during cell migration. In the proposed pathway, mechanical forces generated by actomyosin interactions are considered central to the realization of the various mechanochemical processes that determine cell motility.

Quantifying cell-matrix adhesion dynamics in living cells using interference reflection microscopy

Focal adhesions and podosomes are integrin-mediated cell-substratum contacts that can be visualized using interference reflection microscopy (IRM). Here, we have developed automated image-processing procedures to quantify adhesion turnover from IRM images of live cells. Using time sequences of images, we produce adhesion maps that reveal the spatial changes of adhesions and contain additional information on the time sequence of these changes. Such maps were used to characterize focal adhesion dynamics in mouse embryo fibroblasts lacking one or both alleles of the vinculin gene. Loss of vinculin expression resulted in increased assembly, disassembly and/or in increased translocation of focal adhesions, suggesting that vinculin is important for stabilizing focal adhesions. This method is also useful for studying the rapid dynamics of podosomes as observed in primary mouse dendritic cells.

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.

Mechanism of shape determination in motile cells

The shape of motile cells is determined by many dynamic processes spanning several orders of magnitude in space and time, from local polymerization of actin monomers at subsecond timescales to global, cell-scale geometry that may persist for hours. Understanding the mechanism of shape determination in cells has proved to be extremely challenging due to the numerous components involved and the complexity of their interactions. Here we harness the natural phenotypic variability in a large population of motile epithelial keratocytes from fish (Hypsophrys nicaraguensis) to reveal mechanisms of shape determination. We find that the cells inhabit a low-dimensional, highly correlated spectrum of possible functional states. We further show that a model of actin network treadmilling in an inextensible membrane bag can quantitatively recapitulate this spectrum and predict both cell shape and speed. Our model provides a simple biochemical and biophysical basis for the observed morphology and behaviour of motile cells.

Quantitative analysis of G-actin transport in motile cells

Cell migration is based on an actin treadmill, which in turn depends on recycling of G-actin across the cell, from the rear where F-actin disassembles, to the front, where F-actin polymerizes. To analyze the rates of the actin transport, we used the Virtual Cell software to solve the diffusion-drift-reaction equations for the G-actin concentration in a realistic three-dimensional geometry of the motile cell. Numerical solutions demonstrate that F-actin disassembly at the cell rear and assembly at the front, along with diffusion, establish a G-actin gradient that transports G-actin forward "globally" across the lamellipod. Alternatively, if the F-actin assembly and disassembly are distributed throughout the lamellipod, F-/G-actin turnover is local, and diffusion plays little role. Chemical reactions and/or convective flow of cytoplasm of plausible magnitude affect the transport very little. Spatial distribution of G-actin is smooth and not sensitive to F-actin density fluctuations. Finally, we conclude that the cell body volume slows characteristic diffusion-related relaxation time in motile cell from approximately 10 to approximately 100 s. We discuss biological implications of the local and global regimes of the G-actin transport.

Propagation of mechanical stress through the actin cytoskeleton toward focal adhesions: model and experiment

We investigate both theoretically and experimentally how stress is propagated through the actin cytoskeleton of adherent cells and consequentially distributed at sites of focal adhesions (FAs). The actin cytoskeleton is modeled as a two-dimensional cable network with different lattice geometries. Both prestrain, resulting from actomyosin contractility, and central application of external force, lead to finite forces at the FAs that are largely independent of the lattice geometry, but strongly depend on the exact spatial distribution of the FAs. The simulation results compare favorably with experiments with adherent fibroblasts onto which lateral force is exerted using a microfabricated pillar. For elliptical cells, central application of external force along the long axis leads to two large stress regions located obliquely opposite to the pulling direction. For elliptical cells pulled along the short axis as well as for circular cells, there is only one region of large stress opposite to the direction of pull. If in the computer simulations FAs are allowed to rupture under force for elliptically elongated and circular cell shapes, then morphologies arise which are typical for migrating fibroblasts and keratocytes, respectively. The same effect can be obtained also by internally generated force, suggesting a mechanism by which cells can control their migration morphologies.

Locomotion of fish epidermal keratocytes on spatially selective adhesion patterns

Cell migration results from forces generated by assembly, contraction, and adhesion of the cytoskeleton. To address how these forces integrate in space and time, novel assays are required that allow spatial separation of the different force categories. We used micro-contact printing of fibronectin on glass substrates to study the effect of adhesion patterns on fish epidermal keratocytes locomotion. Cells migrated at similar speeds on homogeneously adhesive substrates and on patterns with 5 microm-wide adhesive stripes interleaved by non-adhesive stripes with a width varied between 5 and 13 microm. The leading edge protruded on adhesive stripes and lagged behind on non-adhesive stripes. On patterns with non-adhesive stripes wider than 13 microm cells halted, although the lamellipodium did not collapse. High correlation was found between the widths of protruding and lagging edge segments and the widths of the underlying stripes. We explain our data by the force balances between actin polymerization, contraction and adhesion on fibronectin stripes; and between actin polymerization, contraction and lamellipodium-internal elastic tension on non-adhesive stripes. We tested our model further by blocking lamellipodium actin network contraction and polymerization. In both experiments we observed that cells eventually lost their ability to move. However, the two perturbations induced distinct morphological responses. The data suggested that forces powering forward motion of keratocytes are largely associated with network assembly whereas contraction maintains cell polarity. This study establishes spatially selective adhesion substrates and cell morphological readouts as a means to elucidate the mechanical balance between substrate adhesion and cytoskeleton-internal tension in cell migration.

Model of polarization and bistability of cell fragments

Directed cell motility is preceded by cell polarization-development of a front-rear asymmetry of the cytoskeleton and the cell shape. Extensive studies implicated complex spatial-temporal feedbacks between multiple signaling pathways in establishing cell polarity, yet physical mechanisms of this phenomenon remain elusive. Based on observations of lamellipodial fragments of fish keratocyte cells, we suggest a purely thermodynamic (not involving signaling) quantitative model of the cell polarization and bistability. The model is based on the interplay between pushing force exerted by F-actin polymerization on the cell edges, contractile force powered by myosin II across the cell, and elastic tension in the cell membrane. We calculate the thermodynamic work produced by these intracellular forces, and show that on the short timescale, the cell mechanics can be characterized by an effective energy profile with two minima that describe two stable states separated by an energy barrier and corresponding to the nonpolarized and polarized cells. Cell dynamics implied by this energy profile is bistable-the cell is either disk-shaped and stationary, or crescent-shaped and motile-with a possible transition between them upon a finite external stimulus able to drive the system over the macroscopic energy barrier. The model accounts for the observations of the keratocyte fragments' behavior and generates quantitative predictions about relations between the intracellular forces' magnitudes and the cell geometry and motility.

Single Biomolecule Imaging with Frequency and Force Modulation in Tapping-Mode Atomic Force Microscopy

A new intermittent-contact atomic force microscopy (AFM) mode (frequency and force modulation AFM, FFM-AFM) has been recently proposed to characterize soft samples. This method uses excitation force frequency and amplitude modulation to eliminate bistability and reduce the tip-sample forces. This letter describes theoretical modeling of FFM-AFM applied to a single bacteriorhodopsin molecule on a substrate, showing that its cross section can be measured without damage, in contrast to conventional tapping-mode AFM. Speculations are made regarding nonideal conditions and the ability of FFM-AFM to perform quantitative nanoelasticity measurements.

Dermal matrix proteins initiate re-epithelialization but are not sufficient for coordinated epidermal outgrowth in a new fish skin culture model

We have established a new culture system to study re-epithelialization during fish epidermal wound healing. In this culture system, fetal bovine serum (FBS) stimulates the epidermal outgrowth of multi-cellular layers from scale skin mounted on a coverslip, even when cell proliferation is blocked. The rate of outgrowth is about 0.4 mm/h, and at 3 h after incubation, the area occupied by the epidermal sheet is nine times larger than the area of the original scale skin. Cells at the bottom of the outgrowth show a migratory phenotype with lamellipodia, and "purse string"-like actin bundles have been found over the leading-edge cells with polarized lamellipodia. In the superficial cells, re-development of adherens junctions and microridges has been detected, together with the appearance and translocation of phosphorylated p38 MAPK into nuclear areas. Thus, this culture system provides an excellent model to study the mechanisms of epidermal outgrowth accompanied by migration and re-differentiation. We have also examined the role of extracellular matrix proteins in the outgrowth. Type I collagen or fibronectin stimulates moderate outgrowth in the absence of FBS, but development of microridges and the distribution of phosphorylated p38 MAPK are attenuated in the superficial cells. In addition, the leading-edge cells do not have apparent "purse string"-like actin bundles. The outgrowth stimulated by FBS is inhibited by laminin. These results suggest that dermal substrates such as type I collagen and fibronectin are able to initiate epidermal outgrowth but require other factors to enhance such outgrowth, together with coordinated alterations in cellular phenotype.

The leading edge is a lipid diffusion barrier

Actin polymerization drives many cellular events, including endocytosis, pathogen rocketing, and cell spreading. Force generation and polymerization regulation are intimately linked where an actin meshwork attaches to, and pushes against, an interface. We reasoned that interaction with actin filament plus-ends might stabilize the position of components within the plasma membrane at the leading edge, thereby slowing the diffusion of lipids within the bilayer where filament growth occurs. To test this hypothesis we focally labeled the outer membrane leaflet of migrating keratocytes and compared the initial diffusion of carbocyanine dyes in the dorsal and ventral lamellipodium membranes using sequential TIRF and epi-fluorescent imaging. Global diffusion analysis shows that lateral mobility of lipids in the outer membrane leaflet is blocked at the leading edge during protrusion. Cytochalasin treatment abolished this diffusion barrier, but we found no evidence to support the involvement of membrane microdomains. Our results demonstrate the immobilization of membrane components at the leading edge, and suggest that interaction between actin filaments and the plasma membrane is mediated by densely packed molecular complexes. We propose that actin polymerization traps regulatory proteins at the leading edge in a positive-feedback loop.

The last but not the least: the origin and significance of trailing adhesions in fibroblastic cells

Mature adhesions in a motile fibroblast can be classified as stationary "towing" adhesions in the front and sliding trailing adhesions that resist the traction force. Adhesions formed at the front of motile fibroblasts rarely reach the trailing zone, due to disassembly promoted by intensive microtubule targeting. Here, we show that the majority of adhesions found at the trailing edge originate within small short-lived protrusions that extend laterally and backwards from the cell edge. These adhesions enlarge by sliding and by fusion with neighboring adhesions. A further subset of trailing adhesions is initiated at a novel site proximal to trailing stress fibre termini. Following tail retraction, trailing adhesions are actively regenerated and the stress fibre system is remodeled accordingly; the tensile forces elaborated by the contractile actin system are consequently redirected according to trailing adhesion location. We conclude that persistent and dynamic anchorage of the cell rear is needed for the maintenance of continuous unidirectional movement of fibroblasts.

Actin microridges characterized by laser scanning confocal and atomic force microscopy

We have characterized the cell surface of zebrafish stratified epithelium using a combined approach of light and atomic force microscopy under conditions which simulate wound healing. Microridges rise on average 100 nm above the surface of living epithelial cells, which correlate to bundles of cytochalasin B-insensitive actin filaments. Time-lapse microscopy revealed the bundles to form a highly dynamic network on the cell surface, in which bundles and junctions were severed and annealed on a time scale of minutes. Atomic force microscopy topographs further indicated that actin bundle junctions identified were of two types: overlaps and integrated end to side T- and Y-junctions. The surface bundle network is found only on the topmost cell layer of the explant, and never on individual locomoting cells. Possible functions of these actin bundles include cell compartmentalization of the cell surface, resistance to mechanical stress, and F-actin storage.