Separation of propulsive and adhesive traction stresses in locomoting keratocytes

Electromagnetic Modulation of Cell Behavior: Unraveling the Positive Impacts in a Comprehensive Review

There are numerous effective procedures for cell signaling, in which humans directly transmit detectable signals to cells to govern their essential behaviors. From a biomedical perspective, the cellular response to the combined influence of electrical and magnetic fields holds significant promise in various domains, such as cancer treatment, targeted drug delivery, gene therapy, and wound healing. Among these modern cell signaling methods, electromagnetic fields (EMFs) play a pivotal role; however, there remains a paucity of knowledge concerning the effects of EMFs across all wavelengths. It's worth noting that most wavelengths are incompatible with human cells, and as such, this study excludes them from consideration. In this review, we aim to comprehensively explore the most effective and current EMFs, along with their therapeutic impacts on various cell types. Specifically, we delve into the influence of alternating electromagnetic fields (AEMFs) on diverse cell behaviors, encompassing proliferation, differentiation, biomineralization, cell death, and cell migration. Our findings underscore the substantial potential of these pivotal cellular behaviors in advancing the treatment of numerous diseases. Moreover, AEMFs wield a significant role in the realms of biomaterials and tissue engineering, given their capacity to decisively influence biomaterials, facilitate non-invasive procedures, ensure biocompatibility, and exhibit substantial efficacy. It is worth mentioning that AEMFs often serve as a last-resort treatment option for various diseases. Much about electromagnetic fields remains a mystery to the scientific community, and we have yet to unravel the precise mechanisms through which wavelengths control cellular fate. Consequently, our understanding and knowledge in this domain predominantly stem from repeated experiments yielding similar effects. In the ensuing sections of this article, we delve deeper into our extended experiments and research.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Crawling, waving, inch worming, dilating, and pivoting mechanics of migrating cells: Lessons from Ken Jacobson

Research on the locomotion of single cells on hard, flat surfaces brought insight into the mechanisms of leading-edge protrusion, spatially graded adhesion, front-rear coordination, and how intracellular and traction forces are harnessed to execute various maneuvers. Here, we highlight how, by studying a variety of cell types, shapes, and movements, Ken Jacobson and his collaborators made several discoveries that triggered the mechanistic understanding of cell motility. We then review the recent advancements and current perspectives in this field.

Confined keratocytes mimic in vivo migration and reveal volume-speed relationship

Fish basal epidermal cells, known as keratocytes, are well-suited for cell migration studies. In vitro, isolated keratocytes adopt a stereotyped shape with a large fan-shaped lamellipodium and a nearly spherical cell body. However, in their native in vivo environment, these cells adopt a significantly different shape during their rapid migration toward wounds. Within the epidermis, keratocytes experience two-dimensional (2D) confinement between the outer epidermal cell layer and the basement membrane; these two deformable surfaces constrain keratocyte cell bodies to be flatter in vivo than in isolation. In vivo keratocytes also exhibit a relative elongation of the front-to-back axis and substantially more lamellipodial ruffling, as compared to isolated cells. We have explored the effects of 2D confinement, separated from other in vivo environmental cues, by overlaying isolated cells with an agarose hydrogel with occasional spacers, or with a ceiling made of polydimethylsiloxane (PDMS) elastomer. Under these conditions, isolated keratocytes more closely resemble the in vivo migratory shape phenotype, displaying a flatter apical-basal axis and a longer front-to-back axis than unconfined keratocytes. We propose that 2D confinement contributes to multiple dimensions of in vivo keratocyte shape determination. Further analysis demonstrates that confinement causes a synchronous 20% decrease in both cell speed and volume. Interestingly, we were able to replicate the 20% decrease in speed using a sorbitol hypertonic shock to shrink the cell volume, which did not affect other aspects of cell shape. Collectively, our results suggest that environmentally imposed changes in cell volume may influence cell migration speed, potentially by perturbing physical properties of the cytoplasm.

Focal adhesion-mediated cell anchoring and migration: from in vitro to in vivo

Cell-extracellular matrix interactions have been studied extensively using cells cultured in vitro. These studies indicate that focal adhesion (FA)-based cell-extracellular matrix interactions are essential for cell anchoring and cell migration. Whether FAs play a similarly important role in vivo is less clear. Here, we summarize the formation and function of FAs in cultured cells and review how FAs transmit and sense force in vitro. Using examples from animal studies, we also describe the role of FAs in cell anchoring during morphogenetic movements and cell migration in vivo. Finally, we conclude by discussing similarities and differences in how FAs function in vitro and in vivo.

Elastic wrinkling of keratocyte lamellipodia driven by myosin-induced contractile stress

During actin-based cell migration, the actin cytoskeleton in the lamellipodium both generates and responds to force, which has functional consequences for the ability of the cell to extend protrusions. However, the material properties of the lamellipodial actin network and its response to stress on the timescale of motility are incompletely understood. Here, we describe a dynamic wrinkling phenotype in the lamellipodium of fish keratocytes, in which the actin sheet buckles upward away from the ventral membrane of the cell, forming a periodic pattern of wrinkles perpendicular to the cell's leading edge. Cells maintain an approximately constant wrinkle wavelength over time despite new wrinkle formation and the lateral movement of wrinkles in the cell frame of reference, suggesting that cells have a preferred or characteristic wrinkle wavelength. Generation of wrinkles is dependent upon myosin contractility, and their wavelength scales directly with the density of the actin network and inversely with cell adhesion. These results are consistent with a simple physical model for wrinkling in an elastic sheet under compression and suggest that the lamellipodial cytoskeleton behaves as an elastic material on the timescale of cell migration despite rapid actin turnover.

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.

Cell Mechanics at the Rear Act to Steer the Direction of Cell Migration

Motile cells navigate complex environments by changing their direction of travel, generating left-right asymmetries in their mechanical subsystems to physically turn. Currently, little is known about how external directional cues are propagated along the length scale of the whole cell and integrated with its force-generating apparatus to steer migration mechanically. We examine the mechanics of spontaneous cell turning in fish epidermal keratocytes and find that the mechanical asymmetries responsible for turning behavior predominate at the rear of the cell, where there is asymmetric centripetal actin flow. Using experimental perturbations, we identify two linked feedback loops connecting myosin II contractility, adhesion strength and actin network flow in turning cells that are sufficient to explain the observed cell shapes and trajectories. Notably, asymmetries in actin polymerization at the cell leading edge play only a minor role in the mechanics of cell turning-that is, cells steer from the rear.

Influence of myosin activity and mechanical impact on keratocyte polarization

In cell migration, polarization is the process by which a stationary cell breaks symmetry and initiates motion. Although a lot is known about the mechanisms involved in cell polarization, the role played by myosin contraction remains unclear. In addition, cell polarization by mechanical impact has received little attention. Here, we study the influence of myosin activity on cell polarization and the initiation of motion induced by mechanical cues using a computational model for keratocytes. The model accounts for cell deformation, the dynamics of myosin and the signaling protein RhoA (a member of the Rho GTPases family), as well as the forces acting on the actomyosin network. Our results show that the attainment of a steady polarized state depends on the strength of myosin down- or up-regulation and that myosin upregulation favors cell polarization. Our results also confirm the existence of a threshold level for cell polarization, which is determined by the level of polarization of the Rho GTPases at the time the external stimuli vanish. In all, this paper shows that capturing the interactions between the signaling proteins (Rho GTPases for keratocytes) and the compounds of the motile machinery in a moving cell is crucial to study cell polarization.

A minimal mechanosensing model predicts keratocyte evolution on flexible substrates

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behaviour of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and travelling waves in the lamellipodium leading edge, (iii) response to remote mechanical stress externally applied to the substrate (tensotaxis) and (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis).

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.

Dual role of the nucleus in cell migration on planar substrates

Cell migration is essential to sustain life. There have been significant advances in the understanding of the mechanisms that control cell crawling, but the role of the nucleus remains poorly understood. The nucleus exerts a tight control of cell migration in 3D environments, but its influence in 2D migration on planar substrates remains unclear. Here, we study the role of the cell nucleus in 2D cell migration using a computational model of fish keratocytes. Our results indicate that the apparently minor role played by the nucleus emerges from two antagonist effects: While the nucleus modifies the spatial distributions of actin and myosin in a way that reduces cell velocity (e.g., the nucleus displaces myosin to the sides and front of the cell), its mechanical connection with the cytoskeleton alters the intracellular stresses promoting cell migration. Overall, the favorable effect of the nucleus-cytoskeleton connection prevails, which may explain why regular cells usually move faster than enucleated cells.

Force and Collective Epithelial Activities

Cells apply forces to their surroundings to perform basic biological activities, including division, adhesion, and migration. Similarly, cell populations in epithelial tissues coordinate forces in physiological processes of morphogenesis and repair. These activities are highly regulated to yield the correct development and function of the body. The modification of this order is at the onset of pathological events and malfunctions. Mechanical forces and their translation into biological signals are the focus of an emerging field of research, shaping as a central discipline in the study of life and gathering knowledge at the interface of engineering, physics, biology and medicine. Novel engineering methods are needed to complement the classic instruments developed by molecular biology, physics and medicine. These should enable the measurement of forces at the cellular and multicellular level, and at a temporal and spatial resolution which is fully compatible with the ranges experienced by cells in vivo.

Spontaneous migration of cellular aggregates from giant keratocytes to running spheroids

Despite extensive knowledge on the mechanisms that drive single-cell migration, those governing the migration of cell clusters, as occurring during embryonic development and cancer metastasis, remain poorly understood. Here, we investigate the collective migration of cell on adhesive gels with variable rigidity, using 3D cellular aggregates as a model system. After initial adhesion to the substrate, aggregates spread by expanding outward a cell monolayer, whose dynamics is optimal in a narrow range of rigidities. Fast expansion gives rise to the accumulation of mechanical tension that leads to the rupture of cell-cell contacts and the nucleation of holes within the monolayer, which becomes unstable and undergoes dewetting like a liquid film. This leads to a symmetry breaking and causes the entire aggregate to move as a single entity. Varying the substrate rigidity modulates the extent of dewetting and induces different modes of aggregate motion: "giant keratocytes," where the lamellipodium is a cell monolayer that expands at the front and retracts at the back; "penguins," characterized by bipedal locomotion; and "running spheroids," for nonspreading aggregates. We characterize these diverse modes of collective migration by quantifying the flows and forces that drive them, and we unveil the fundamental physical principles that govern these behaviors, which underscore the biological predisposition of living material to migrate, independent of length scale.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

Control of Mechanotransduction by Molecular Clutch Dynamics

The linkage of cells to their microenvironment is mediated by a series of bonds that dynamically engage and disengage, in what has been conceptualized as the molecular clutch model. Whereas this model has long been employed to describe actin cytoskeleton and cell migration dynamics, it has recently been proposed to also explain mechanotransduction (i.e., the process by which cells convert mechanical signals from their environment into biochemical signals). Here we review the current understanding on how cell dynamics and mechanotransduction are driven by molecular clutch dynamics and its master regulator, the force loading rate. Throughout this Review, we place a specific emphasis on the quantitative prediction of cell response enabled by combined experimental and theoretical approaches.

Dynamic Mechano-Regulation of Myoblast Cells on Supramolecular Hydrogels Cross-Linked by Reversible Host-Guest Interactions

A new class of supramolecular hydrogels, cross-linked by host-guest interactions between β-cyclodextrin (βCD) and adamantane, were designed for the dynamic regulation of cell-substrate interactions. The initial substrate elasticity can be optimized by selecting the molar fraction of host- and guest monomers for the target cells. Moreover, owing to the reversible nature of host-guest interactions, the magnitude of softening and stiffening of the substrate can be modulated by varying the concentrations of free, competing host molecules (βCD) in solutions. By changing the substrate elasticity at a desired time point, it is possible to switch the micromechanical environments of cells. We demonstrated that the Young's modulus of our "host-guest gels", 4-11 kPa, lies in an optimal range not only for static (ex situ) but also for dynamic (in situ) regulation of cell morphology and cytoskeletal ordering of myoblasts. Compared to other stimulus-responsive materials that can either change the elasticity only in one direction or rely on less biocompatible stimuli such as UV light and temperature change, our supramolecular hydrogel enables to reversibly apply mechanical cues to various cell types in vitro without interfering cell viability.

Membrane tension controls adhesion positioning at the leading edge of cells

Pontes et al. show that plasma membrane mechanics exerts an upstream control during cell motility. Variations in plasma membrane tension orchestrate the behavior of the cell leading edge, with increase–decrease cycles in tension promoting adhesion row positioning.

Cell migration is dependent on adhesion dynamics and actin cytoskeleton remodeling at the leading edge. These events may be physically constrained by the plasma membrane. Here, we show that the mechanical signal produced by an increase in plasma membrane tension triggers the positioning of new rows of adhesions at the leading edge. During protrusion, as membrane tension increases, velocity slows, and the lamellipodium buckles upward in a myosin II–independent manner. The buckling occurs between the front of the lamellipodium, where nascent adhesions are positioned in rows, and the base of the lamellipodium, where a vinculin-dependent clutch couples actin to previously positioned adhesions. As membrane tension decreases, protrusion resumes and buckling disappears, until the next cycle. We propose that the mechanical signal of membrane tension exerts upstream control in mechanotransduction by periodically compressing and relaxing the lamellipodium, leading to the positioning of adhesions at the leading edge of cells.

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.

Cell mediated contraction in 3D cell-matrix constructs leads to spatially regulated osteogenic differentiation

During embryonic development, morphogenetic processes give rise to a variety of shapes and patterns that lead to functional tissues and organs. While the impact of chemical signals on these processes is widely studied, the role of physical cues is less understood. The aim of this study was to test the hypothesis that the interplay of cell mediated contraction and mechanical boundary conditions alone can result in spatially regulated differentiation in simple 3D constructs. An experimental model consisting of a 3D cell-gel construct and a finite element (FE) model were used to study the effect of cellular traction exerted by mesenchymal stem cells (MSCs) on an initially homogeneous matrix under inhomogeneous boundary conditions. A robust shape change is observed due to contraction under time-varying mechanical boundary conditions, which is explained by the finite element model. Furthermore, distinct local differences in osteogenic differentiation are observed, with a spatial pattern independent of osteogenic factors in the culture medium. Regions that are predicted to have experienced relatively high shear stress at any time during contraction correlate with the regions of distinct osteogenesis. Taken together, these results support the underlying hypothesis that cellular contractility and mechanical boundary conditions alone can result in spatially regulated differentiation. These results will have important implications for tissue engineering and regeneration.

Kisspeptin/KISS1R signaling potentiates extravillous trophoblast adhesion to type-I collagen in a PKC- and ERK1/2-dependent manner

During the first trimester of human pregnancy, cytotrophoblasts proliferate within the tips of the chorionic villi to form cell columns that anchor the placenta to the uterus. This migration coincides with a widespread change in the adhesion molecule repertoire of these trophoblasts. Kisspeptin and its receptor, KISS1R, are best known as potent triggers of gonadotropin-releasing hormone secretion. The kisspeptin/KISS1R signaling system is also highly expressed in the human placenta, where it was demonstrated to inhibit extra-villous trophoblast (EVT) migration and invasion in vitro. Here we show that kisspeptin, in a dose- and time-dependent manner, induces increased adhesion of human EVTs to type-I collagen, a major component of the human placenta. This increased adhesion was both rapid and transient, suggesting that it likely occurred through the activation of KISS1R secondary effectors such as PKC and ERK, which underwent rapid and transient kisspeptin-dependent activation in EVTs. We then showed that inhibition of both PKC and ERK1/2 attenuated the kisspeptin-dependent increase in EVT adhesion, suggesting that these molecules are key positive regulators of trophoblast adhesion. We therefore propose that kisspeptin/KISS1R signaling potentiates EVT adhesion to type-I collagen via "inside-out signaling." Furthermore, kisspeptin treatment increased mouse blastocyst adhesion to collagen I, suggesting that kisspeptin signaling is a key regulator of trophoblast function during implantation as well as early placentation.

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.

Mechanism of cell rear retraction in migrating cells

For decades, ever growing data on myosin II provides strong evidence that interaction of myosin-II-motor-domain with actin filaments within cells retracts the cell rear during actin-based cell migration. Now it is clear myosin II motor-activity is not the sole force involved. Alternative force-generating mechanisms within cells clearly also exist to power cell rear retraction during actin-based cell migration. Given that nematode sperm cells migrate without actin and without cytoskeletal motor proteins it is perhaps not surprising other types of force power cell rear retraction in actin-based systems. Here, cell rear retraction driven by actin filament depolymerisation, actin filament crosslinking, cell front protrusion and possibly apparent membrane tension and their importance relative to myosin II-motor-based contractility are discussed.

Deformation gradients imprint the direction and speed of en masse fibroblast migration for fast healing

En masse cell migration is more relevant than single cell migration in physiological processes of tissue formation, such as embryogenesis, morphogenesis and wound healing. In these situations, cells are influenced by the proximity of other cells including interactions facilitated by substrate mechanics. Here we found that when fibroblasts migrated en masse over a hydrogel, they established a well-defined deformation field by traction forces and migrated along a trajectory defined by field gradients. The mechanics of the hydrogel determined the magnitude of the gradient. For materials stiff enough to withstand deformation related to cellular traction forces, such patterns did not form. Furthermore, migration patterns functioned poorly on very soft matrices where only a minimal traction gradient could be established. The largest degree of alignment and migration velocity occurred on the gels with the largest gradients. Granulation tissue formation in punch wounds of juvenile pigs was correlated strongly with the modulus of the implanted gel in agreement with in vitro en masse cell migration studies. These findings provide basic insight into the biomechanical influences on fibroblast movement in early wounds and relevant design criteria for development of tissue-engineered constructs that aim to stimulate en masse cell recruitment for rapid wound healing.

Myosin IIA deficient cells migrate efficiently despite reduced traction forces at cell periphery

Cell motility is a cornerstone of embryogenesis, tissue remodeling and repair, and cancer cell invasion. It is generally thought that migrating cells grab and exert traction force onto the extracellular matrix in order to pull the cell body forward. While previous studies have shown that myosin II deficient cells migrate efficiently, whether these cells exert traction forces during cell migration in the absence of the major contractile machinery is currently unknown. Using an array of micron-sized pillars as a force sensor and shRNA specific to each myosin II isoform (A and B), we analyzed how myosin IIA and IIB individually regulate cell migration and traction force generation. Myosin IIA and IIB localized preferentially to the leading edge where traction force was greatest, and the trailing edge, respectively. When individual myosin II isoforms were depleted by shRNA, myosin IIA deficient cells lost actin stress fibers and focal adhesions, whereas myosin IIB deficient cells maintained similar actin organization and focal adhesions as wild-type cells. Interestingly, myosin IIA deficient cells migrated faster than wild-type or myosin IIB deficient cells on both a rigid surface and a pillar array, yet myosin IIA deficient cells exerted significantly less traction force at the leading edge than wild-type or myosin IIB deficient cells. These results suggest that, in the absence of myosin IIA mediated force-generating machinery, cells move with minimal traction forces at the cell periphery, thus demonstrating the remarkable ability of cells to adapt and migrate.

Gleevec, an Abl family inhibitor, produces a profound change in cell shape and migration

The issue of how contractility and adhesion are related to cell shape and migration pattern remains largely unresolved. In this paper we report that Gleevec (Imatinib), an Abl family kinase inhibitor, produces a profound change in the shape and migration of rat bladder tumor cells (NBTII) plated on collagen-coated substrates. Cells treated with Gleevec adopt a highly spread D-shape and migrate more rapidly with greater persistence. Accompanying this more spread state is an increase in integrin-mediated adhesion coupled with increases in the size and number of discrete adhesions. In addition, both total internal reflection fluorescence microscopy (TIRFM) and interference reflection microscopy (IRM) revealed a band of small punctate adhesions with rapid turnover near the cell leading margin. These changes led to an increase in global cell-substrate adhesion strength, as assessed by laminar flow experiments. Gleevec-treated cells have greater RhoA activity which, via myosin activation, led to an increase in the magnitude of total traction force applied to the substrate. These chemical and physical alterations upon Gleevec treatment produce the dramatic change in morphology and migration that is observed.

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.

Force field evolution during human blood platelet activation

Contraction at the cellular level is vital for living organisms. The most prominent type of contractile cells are heart muscle cells, a less-well-known example is blood platelets. Blood platelets activate and interlink at injured blood vessel sites, finally contracting to form a compact blood clot. They are ideal model cells to study the mechanisms of cellular contraction, as they are simple, having no nucleus, and their activation can be triggered and synchronized by the addition of thrombin. We have studied contraction using human blood platelets, employing traction force microscopy, a single-cell technique that enables time-resolved measurements of cellular forces on soft substrates with elasticities in the physiological range (∼4 kPa). We found that platelet contraction reaches a steady state after 25 min with total forces of ∼34 nN. These forces are considerably larger than what was previously reported for platelets in aggregates, demonstrating the importance of a single-cell approach for studies of platelet contraction. Compared with other contractile cells, we find that platelets are unique, because force fields are nearly isotropic, with forces pointing toward the center of the cell area.

Membrane tension, myosin force, and actin turnover maintain actin treadmill in the nerve growth cone

A growth cone is a motile structure at the tips of axons that is driven by the actin network and guides axon extension. Low actin adhesion to the substrate creates a stationary actin treadmill that allows leading-edge protrusion when adhesion increases in response to guidance cues. We use experimental measurements in the Aplysia bag growth cone to develop and constrain a simple mechanical model of the actin treadmill. We show that actin retrograde flow is primarily generated by myosin contractile forces, but when myosin is inhibited, leading-edge membrane tension increases and drives the flow. By comparing predictions of the model with previous experimental measurements, we demonstrate that lamellipodial and filopodial filament breaking contribute equally to the resistance to the flow. The fully constrained model clarifies the role of actin turnover in the mechanical balance driving the actin treadmill and reproduces the recent experimental observation that inhibition of actin depolymerization causes retrograde flow to slow exponentially with time. We estimate forces in the actin treadmill, and we demonstrate that measured G-actin distributions are consistent with the existence of a forward-directed fluid flow that transports G-actin to the leading edge.

A three-component mechanism for fibroblast migration with a contractile cell body that couples a myosin II-independent propulsive anterior to a myosin II-dependent resistive tail

Frontal, cell body, and rear regions perform distinct functions in the complex process of cell migration. A low-capacity, directional mechanism in the front coupled to a high-capacity, nondirectional mechanism in the middle represents a highly appealing model for driving cell migration under high mechanical load.

To understand the mechanism of cell migration, we cultured fibroblasts on micropatterned tracks to induce persistent migration with a highly elongated morphology and well-defined polarity, which allows microfluidic pharmacological manipulations of regional functions. The function of myosin II was probed by applying inhibitors either globally or locally. Of interest, although global inhibition of myosin II inhibited tail retraction and caused dramatic elongation of the posterior region, localized inhibition of the cell body inhibited nuclear translocation and caused elongation of the anterior region. In addition, local application of cytochalasin D at the tip inhibited frontal extension without inhibiting forward movement of the cell nucleus, whereas local treatment posterior to the nucleus caused reversal of nuclear movement. Imaging of cortical dynamics indicated that the region around the nucleus is a distinct compression zone where activities of anterior and posterior regions converge. These observations suggest a three-component model of cell migration in which a contractile middle section is responsible for the movement of a bulky cell body and the detachment/retraction of a resistive tail, thereby allowing these regions to undergo coordinated movement with a moving anterior region that carries little load.

Mechanobiology of tumor invasion: engineering meets oncology

The physical sciences and engineering have introduced novel perspectives into the study of cancer through model systems, tools, and metrics that enable integration of basic science observations with clinical data. These methods have contributed to the identification of several overarching mechanisms that drive processes during cancer progression including tumor growth, angiogenesis, and metastasis. During tumor cell invasion - the first clinically observable step of metastasis - cells demonstrate diverse and evolving physical phenotypes that cannot typically be defined by any single molecular mechanism, and mechanobiology has been used to study the physical cell behaviors that comprise the "invasive phenotype". In this review, we discuss the continually evolving pathological characterization and in vitro mechanobiological characterization of tumor invasion, with emphasis on emerging physical biology and mechanobiology strategies that have contributed to a more robust mechanistic understanding of tumor cell invasion. These physical approaches may ultimately help to better predict and identify tumor metastasis.

Staurosporine induces lamellipodial widening in locomoting fish keratocytes by abolishing the gradient from radial extension of leading edge

Fish epidermal keratocytes locomote along surfaces without overall cell size or shape changes, as kinematically described by the graded radial extension (GRE) model. We found that the cell size increased during locomotion after the addition of a low dose of staurosporine or K-252a, broad-spectrum protein-serine/threonine kinase inhibitors. Quantitative shape analysis showed that the cell size increase resulted from an increase in lamellipodial width, the maximal length perpendicular to the direction of the cell locomotion, whereas the lamellipodial length, along the locomotion direction, remained constant. Importantly, the gradient of radial extension in the leading edge disappeared during lamellipodial width increase. These results suggest that a special mechanism for producing graded radial extension of lamellipodia exists to keep cell size constant, and that a protein-serine/threonine kinase plays an important role in regulating this mechanism.

Viscoelastic gel-strip model for the simulation of migrating cells

Migrating tumor cells can exhibit both mesenchymal- and amoeboid-type behaviors. Recent studies have shown that both cellular and extracellular structural and mechanical variables control the transition of tumor cells from one mode to the other and provide them with morphological plasticity. The mesenchymal-mode migration is characterized by strong adhesion and proteolytic machinery to navigate through complex extracellular matrices. The amoeboid-mode migration is characterized by little or no adhesion and strong actomyosin contraction to squeeze through the matrices. While adhesion dependent migration has been computationally and experimentally studied in both 2D and 3D environments, quantitative models of amoeboid motion in native environments are lacking. In order to address this major gap in our understanding and to probe the mesenchymal to amoeboid transitions quantitatively and comprehensively, we have developed an axisymmetric viscoelastic gel-strip model of a single cell to investigate a cell migrating in native-like environments. In this model, cell migration and morphology are governed by internal stresses as well as external forces. The internal stresses are controlled by F-actin density distribution, protrusion strength, and contraction strength. The external forces are controlled by adhesion strength and steric resistance from the extracellular matrix. Our model predicts that the transition of the cell migration mode from mesenchymal- to amoeboid-type, and vice versa, is closely related to the loss of adhesion as well as increased contraction strength of the cells. Our results indicate that amoeboid migration is more suited for low-resistance environment while mesenchymal migration is preferred in high-resistance environment, which would explain the versatile behaviors of tumor cells in complex environments.

Mechanisms of Cell Propulsion by Active Stresses

The mechanisms by which cytoskeletal flows and cell-substrate interactions interact to generate cell motion are explored using a simplified model of the cytoskeleton as a viscous gel containing active stresses. This model yields explicit general results relating cell speed and traction forces to the distributions of active stress and cell-substrate friction. It is found that 1) the cell velocity is given by a function that quantifies the asymmetry of the active-stress distribution, 2) gradients in cell-substrate friction can induce motion even when the active stresses are symmetrically distributed, 3) the traction-force dipole is enhanced by protrusive stresses near the cell edges or contractile stresses near the center of the cell, and 4) the cell velocity depends biphasically on the cell-substrate adhesion strength if active stress is enhanced by adhesion. Specific experimental tests of the calculated dependences are proposed.

A multiphysical model of cell migration integrating reaction-diffusion, membrane and cytoskeleton

Cellular motility is a complicated phenomenon that involves multiphysics, including the cytoskeleton, the plasma membrane and intracellular signal transduction. In this study, a hybrid computational model was developed for the simulation of whole-cell migration behaviors. The model integrates sub-models of reaction-diffusion, actin filaments (F-actin) and the plasma membrane. Reaction-diffusion was calculated as if enclosed by a moving membrane. Individual F-actins were reorganized on the basis of stochastic kinetic events, such as polymerization, capping, branching and severing. Membrane dynamics were modeled using an optimization of energy function that depends on cell volume, surface area, smoothness and the elasticity of F-actin against the membrane. Simulations of this model demonstrated self-organization of F-actin networks, as in lamellipodia, and chemotactic migration. Furthermore, this method was extended to address external obstacles to simulate the dynamic cellular morphological changes seen during invasive migration.

Undulation instability of epithelial tissues

Treating the epithelium as an incompressible fluid adjacent to a viscoelastic stroma, we find a novel hydrodynamic instability that leads to the formation of protrusions of the epithelium into the stroma. This instability is a candidate for epithelial fingering observed in vivo. It occurs for sufficiently large viscosity, cell-division rate and thickness of the dividing region in the epithelium. Our work provides physical insight into a potential mechanism by which interfaces between epithelia and stromas undulate and potentially by which tissue dysplasia leads to cancerous invasion.

Mechanical integration of actin and adhesion dynamics in cell migration

Directed cell migration is a physical process that requires dramatic changes in cell shape and adhesion to the extracellular matrix. For efficient movement, these processes must be spatiotemporally coordinated. To a large degree, the morphological changes and physical forces that occur during migration are generated by a dynamic filamentous actin (F-actin) cytoskeleton. Adhesion is regulated by dynamic assemblies of structural and signaling proteins that couple the F-actin cytoskeleton to the extracellular matrix. Here, we review current knowledge of the dynamic organization of the F-actin cytoskeleton in cell migration and the regulation of focal adhesion assembly and disassembly with an emphasis on how mechanical and biochemical signaling between these two systems regulate the coordination of physical processes in cell migration.

Drag force as a tool to test the active mechanical response of PC12 neurites

We investigate the mechanical response of PC12 neurites subjected to a drag force imposed by a laminar flow perpendicular to the neurite axis. The curvature of the catenary shape acquired by an initially straight neurite under the action of the drag force provides information on both elongation and tension of the neurite. This method allows us to measure the rest tension and viscoelastic parameters of PC12 neurites and active behavior of neurites. Measurement of oscillations in the strain rate of neurites at constant flow rate provides insight on the response of molecular motors and additional support for the presence of a negative strain-rate sensitivity region in the global mechanical response of PC12 neurites.

Simulation of cell motility that reproduces the force-velocity relationship

Many cells crawl by extending an actin-rich pseudopod. We have devised a simulation that describes how the polymerization kinetics of a branched actin filament network, coupled with excluded volume effects, powers the motility of crawling cells such as amoebae and fish keratocytes. Our stochastic simulation is based on the key fundamental properties of actin polymerization, namely growth, shrinkage, capping, branching, and nucleation, and also includes contributions from the creation and breaking of adhesive contacts with the substrate together with excluded volume effects related to filament packing. When reasonable values for appropriate constants were employed, this simulation generated a force-velocity relationship that resembled closely that observed experimentally. Our simulations indicated that excluded volume effects associated with actin filament branching lead to a decreased packing efficiency and resultant swelling of the cytoskeleton gel that contributes substantially to lamellipod protrusion.

The key feature for early migratory processes: Dependence of adhesion, actin bundles, force generation and transmission on filopodia

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 alpha-actinin. alpha-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.

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.

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.

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.

Multiscale modeling of cell mechanics and tissue organization

Nowadays, experimental biology gathers a large number of molecular and genetic data to understand the processes in living systems. Many of these data are evaluated on the level of cells, resulting in a changed phenotype of cells. Tools are required to translate the information on the cellular scale to the whole tissue, where multiple interacting cell types are involved. Agent-based modeling allows the investigation of properties emerging from the collective behavior of individual units. A typical agent in biology is a single cell that transports information from the intracellular level to larger scales. Mainly, two scales are relevant: changes in the dynamics of the cell, e.g. surface properties, and secreted molecules that can have effects at a distance larger than the cell diameter.