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

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

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

Collective migration under hydrodynamic interactions: a computational approach

We consider a generic model for cell motility. Even if a comprehensive understanding of cell motility remains elusive, progress has been achieved in its modelling using a whole-cell physical model. The model takes into account the main mechanisms of cell motility, actin polymerization, actin-myosin dynamics and substrate mediated adhesion (if applicable), and combines them with steric cell-cell and hydrodynamic interactions. The model predicts the onset of collective cell migration, which emerges spontaneously as a result of inelastic collisions of neighbouring cells. Each cell here modelled as an active polar gel is accomplished with two vortices if it moves. Upon collision of two cells, the two vortices which come close to each other annihilate. This leads to a rotation of the cells and together with the deformation and the reorientation of the actin filaments in each cell induces alignment of these cells and leads to persistent translational collective migration. The effect for low Reynolds numbers is as strong as in the non-hydrodynamic model, but it decreases with increasing Reynolds number.

Prediction of traction forces of motile cells

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.

Persistence of fan-shaped keratocytes is a matrix-rigidity-dependent mechanism that requires α5β1 integrin engagement

Despite the importance of matrix rigidity on cell functions, many aspects of the mechanosensing process in highly migratory cells remain elusive. Here, we studied the migration of highly motile keratocytes on culture substrates with similar biochemical properties and rigidities spanning the range between soft tissues (~kPa) and stiff culture substrates (~GPa). We show that morphology, polarization and persistence of motile keratocytes are regulated by the matrix stiffness over seven orders of magnitude, without changing the cell spreading area. Increasing the matrix rigidity leads to more F-actin in the lamellipodia and to the formation of mature contractile actomyosin fibers that control the cell rear retraction. Keratocytes remain rounded and form nascent adhesions on compliant substrates, whereas large and uniformly distributed focal adhesions are formed on fan-shaped keratocytes migrating on rigid surfaces. By combining poly-L-lysine, fibronectin and vitronectin coatings with selective blocking of α_vβ₃ or α₅β₁ integrins, we show that α_Vβ₃ integrins permit the spreading of keratocytes but are not sufficient for polarization and rigidity sensing that require the engagement of α₅β₁ integrins. Our study demonstrates a matrix rigidity-dependent regulation of the directional persistence in motile keratocytes and refines the role of α_vβ₃ and α₅β₁ integrins in the molecular clutch model.

Focal Adhesion-Independent Cell Migration

Cell migration is central to a multitude of physiological processes, including embryonic development, immune surveillance, and wound healing, and deregulated migration is key to cancer dissemination. Decades of investigations have uncovered many of the molecular and physical mechanisms underlying cell migration. Together with protrusion extension and cell body retraction, adhesion to the substrate via specific focal adhesion points has long been considered an essential step in cell migration. Although this is true for cells moving on two-dimensional substrates, recent studies have demonstrated that focal adhesions are not required for cells moving in three dimensions, in which confinement is sufficient to maintain a cell in contact with its substrate. Here, we review the investigations that have led to challenging the requirement of specific adhesions for migration, discuss the physical mechanisms proposed for cell body translocation during focal adhesion-independent migration, and highlight the remaining open questions for the future.

Hybrid mechanosensing system to generate the polarity needed for migration in fish keratocytes

Crawling cells can generate polarity for migration in response to forces applied from the substratum. Such reaction varies according to cell type: there are both fast- and slow-crawling cells. In response to periodic stretching of the elastic substratum, the intracellular stress fibers in slow-crawling cells, such as fibroblasts, rearrange themselves perpendicular to the direction of stretching, with the result that the shape of the cells extends in that direction; whereas fast-crawling cells, such as neutrophil-like differentiated HL-60 cells and Dictyostelium cells, which have no stress fibers, migrate perpendicular to the stretching direction. Fish epidermal keratocytes are another type of fast-crawling cell. However, they have stress fibers in the cell body, which gives them a typical slow-crawling cell structure. In response to periodic stretching of the elastic substratum, intact keratocytes rearrange their stress fibers perpendicular to the direction of stretching in the same way as fibroblasts and migrate parallel to the stretching direction, while blebbistatin-treated stress fiber-less keratocytes migrate perpendicular to the stretching direction, in the same way as seen in HL-60 cells and Dictyostelium cells. Our results indicate that keratocytes have a hybrid mechanosensing system that comprises elements of both fast- and slow-crawling cells, to generate the polarity needed for migration.

Mathematical modeling of Myosin induced bistability of Lamellipodial fragments

For various cell types and for lamellipodial fragments on flat surfaces, externally induced and spontaneous transitions between symmetric nonmoving states and polarized migration have been observed. This behavior is indicative of bistability of the cytoskeleton dynamics. In this work, the Filament Based Lamellipodium Model (FBLM), a two-dimensional, anisotropic, two-phase continuum model for the dynamics of the actin filament network in lamellipodia, is extended by a new description of actin–myosin interaction. For appropriately chosen parameter values, the resulting model has bistable dynamics with stable states showing the qualitative features observed in experiments. This is demonstrated by numerical simulations and by an analysis of a strongly simplified version of the FBLM with rigid filaments and planar lamellipodia at the cell front and rear.

Dynamics of Cell Ensembles on Adhesive Micropatterns: Bridging the Gap between Single Cell Spreading and Collective Cell Migration

The collective dynamics of multicellular systems arise from the interplay of a few fundamental elements: growth, division and apoptosis of single cells; their mechanical and adhesive interactions with neighboring cells and the extracellular matrix; and the tendency of polarized cells to move. Micropatterned substrates are increasingly used to dissect the relative roles of these fundamental processes and to control the resulting dynamics. Here we show that a unifying computational framework based on the cellular Potts model can describe the experimentally observed cell dynamics over all relevant length scales. For single cells, the model correctly predicts the statistical distribution of the orientation of the cell division axis as well as the final organisation of the two daughters on a large range of micropatterns, including those situations in which a stable configuration is not achieved and rotation ensues. Large ensembles migrating in heterogeneous environments form non-adhesive regions of inward-curved arcs like in epithelial bridge formation. Collective migration leads to swirl formation with variations in cell area as observed experimentally. In each case, we also use our model to predict cell dynamics on patterns that have not been studied before.

Toward the reconstitution of synthetic cell motility

Cellular motility is a fundamental process essential for embryonic development, wound healing, immune responses, and tissues development. Cells are mostly moving by crawling on external, or inside, substrates which can differ in their surface composition, geometry, and dimensionality. Cells can adopt different migration phenotypes, e.g., bleb-based and protrusion-based, depending on myosin contractility, surface adhesion, and cell confinement. In the few past decades, research on cell motility has focused on uncovering the major molecular players and their order of events. Despite major progresses, our ability to infer on the collective behavior from the molecular properties remains a major challenge, especially because cell migration integrates numerous chemical and mechanical processes that are coupled via feedbacks that span over large range of time and length scales. For this reason, reconstituted model systems were developed. These systems allow for full control of the molecular constituents and various system parameters, thereby providing insight into their individual roles and functions. In this review we describe the various reconstituted model systems that were developed in the past decades. Because of the multiple steps involved in cell motility and the complexity of the overall process, most of the model systems focus on very specific aspects of the individual steps of cell motility. Here we describe the main advancement in cell motility reconstitution and discuss the main challenges toward the realization of a synthetic motile cell.

Shape and Area of Keratocytes Are Related to the Distribution and Magnitude of Their Traction Forces

Fish epidermal keratocytes maintain an overall fan shape during their crawling migration. The shape-determination mechanism has been described theoretically and experimentally on the basis of graded radial extension of the leading edge, but the relationship between shape and traction forces has not been clarified. Migrating keratocytes can be divided into fragments by treatment with the protein kinase inhibitor staurosporine. Fragments containing a nucleus and cytoplasm behave as mini-keratocytes and maintain the same fan shape as the original cells. We measured the shape of the leading edge, together with the areas of the ventral region and traction forces, of keratocytes and mini-keratocytes. The shapes of keratocytes and mini-keratocytes were similar. Mini-keratocytes exerted traction forces at the rear left and right ends, just like keratocytes. The magnitude of the traction forces was proportional to the area of the keratocytes and mini-keratocytes. The myosin II ATPase inhibitor blebbistatin decreased the forces at the rear left and right ends of the keratocytes and expanded their shape laterally. These results suggest that keratocyte shape depends on the distribution of the traction forces, and that the magnitude of the traction forces depends on the area of the cells.

Cell-ECM Interactions in Tumor Invasion

The cancer cells obtain their invasion potential not only by genetic mutations, but also by changing their cellular biophysical and biomechanical features and adapting to the surrounding microenvironments. The extracellular matrix, as a crucial component of the tumor microenvironment, provides the mechanical support for the tissue, mediates the cell-microenvironment interactions, and plays a key role in cancer cell invasion. The biomechanics of the extracellular matrix, particularly collagen, have been extensively studied in the biomechanics community. Cell migration has also enjoyed much attention from both the experimental and modeling efforts. However, the detailed mechanistic understanding of tumor cell-ECM interactions, especially during cancer invasion, has been unclear. This chapter reviews the recent advances in the studies of ECM biomechanics, cell migration, and cell-ECM interactions in the context of cancer invasion.

T Lymphocyte Migration: An Action Movie Starring the Actin and Associated Actors

The actin cytoskeleton is composed of a dynamic filament meshwork that builds the architecture of the cell to sustain its fundamental properties. This physical structure is characterized by a continuous remodeling, which allows cells to accomplish complex motility steps such as directed migration, crossing of biological barriers, and interaction with other cells. T lymphocytes excel in these motility steps to ensure their immune surveillance duties. In particular, actin cytoskeleton remodeling is a key to facilitate the journey of T lymphocytes through distinct tissue environments and to tune their stop and go behavior during the scanning of antigen-presenting cells. The molecular mechanisms controlling actin cytoskeleton remodeling during T lymphocyte motility have been only partially unraveled, since the function of many actin regulators has not yet been assessed in these cells. Our review aims to integrate the current knowledge into a comprehensive picture of how the actin cytoskeleton drives T lymphocyte migration. We will present the molecular actors that control actin cytoskeleton remodeling, as well as their role in the different T lymphocyte motile steps. We will also highlight which challenges remain to be addressed experimentally and which approaches appear promising to tackle them.

Nanograting structure promotes lamellipodia-based cell collective migration and wound healing

Wound healing is a dynamic and complex process of replacing missing or dead cell structures and tissue layers. The aim of this research is to discover biocompatible materials and drugs that can promote cell migration in the wound area and thus enhance desirable wound healing effects. In this paper, we report that PDMS nanogratings could accelerate the migration of epithelial cells along the grating axis, and the addition of Imatinib could further increase the epithelial cell wound healing speed to 1.6 times the speed of control cells. We also demonstrate that this migration is mediated by lamellipodia protrusion, and is Rac1-GTPase activity dependent. Lastly, we discuss the potential application and prospect of different nanostructured biomaterials for wound healing studies.

Quantifying Modes of 3D Cell Migration

Although it is widely appreciated that cells migrate in a variety of diverse environments in vivo, we are only now beginning to use experimental workflows that yield images with sufficient spatiotemporal resolution to study the molecular processes governing cell migration in 3D environments. Since cell migration is a dynamic process, it is usually studied via microscopy, but 3D movies of 3D processes are difficult to interpret by visual inspection. In this review, we discuss the technologies required to study the diversity of 3D cell migration modes with a focus on the visualization and computational analysis tools needed to study cell migration quantitatively at a level comparable to the analyses performed today on cells crawling on flat substrates.

Virus Nanoparticles Mediated Osteogenic Differentiation of Bone Derived Mesenchymal Stem Cells

There are few methodologies that allow manipulating a biomaterial surface at nanometer scale, which controllably influence different cellular functions. In this study, virus nanoparticles with different structural features are selected to prepare 2D substrates with defined nanoscale topographies and the cellular responses are investigated. It is demonstrated that the viral nanoparticle based substrates could accelerate and enhance osteogenesis of bone derived mesenchymal stem cells as indicated by the upregulation of osteogenic markers, including bone morphogenetic protein-2, osteocalcin, and osteopontin, at both gene and protein expression levels. Moreover, alkaline phosphatase activity and calcium mineralization, both indicators for a -successful bone formation, are also increased in cells grown on these nanoscale possessed substrates. These discoveries and developments present a new paradigm for nanoscale engineering of a biomaterial surface.

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

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

Two-Phase Acto-Cytosolic Fluid Flow in a Moving Keratocyte: A 2D Continuum Model

The F-actin network and cytosol in the lamellipodia of crawling cells flow in a centripetal pattern and spout-like form, respectively. We have numerically studied this two-phase flow in the realistic geometry of a moving keratocyte. Cytosol has been treated as a low viscosity Newtonian fluid flowing through the high viscosity porous medium of F-actin network. Other involved phenomena including myosin activity, adhesion friction, and interphase interaction are also discussed to provide an overall view of this problem. Adopting a two-phase coupled model by myosin concentration, we have found new accurate perspectives of acto-cytosolic flow and pressure fields, myosin distribution, as well as the distribution of effective forces across the lamellipodia of a keratocyte with stationary shape. The order of magnitude method is also used to determine the contribution of forces in the internal dynamics of lamellipodia.

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.

Disentangling Membrane Dynamics and Cell Migration; Differential Influences of F-actin and Cell-Matrix Adhesions

Cell migration is heavily interconnected with plasma membrane protrusion and retraction (collectively termed “membrane dynamics”). This makes it difficult to distinguish regulatory mechanisms that differentially influence migration and membrane dynamics. Yet such distinctions may be valuable given evidence that cancer cell invasion in 3D may be better predicted by 2D membrane dynamics than by 2D cell migration, implying a degree of functional independence between these processes. Here, we applied multi-scale single cell imaging and a systematic statistical approach to disentangle regulatory associations underlying either migration or membrane dynamics. This revealed preferential correlations between membrane dynamics and F-actin features, contrasting with an enrichment of links between cell migration and adhesion complex properties. These correlative linkages were often non-linear and therefore context-dependent, strengthening or weakening with spontaneous heterogeneity in cell behavior. More broadly, we observed that slow moving cells tend to increase in area, while fast moving cells tend to shrink, and that the size of dynamic membrane domains is independent of cell area. Overall, we define macromolecular features preferentially associated with either cell migration or membrane dynamics, enabling more specific interrogation and targeting of these processes in future.

Motile Human Neutrophils Sense Ligand Density Over Their Entire Contact Area

Neutrophils are key components of the immune system and motility is central their function during the inflammatory response. We have previously demonstrated that neutrophils are capable of switching their motile phenotype between amoeboid-like and keratocyte-like in response to the ligand density of adhesion molecules (Henry et al. in Int Biol 6:348-356, 2014). In this study, we engineered planar micropatterned surfaces that presented adhesion molecules in local islands of high density, separated by regions largely devoid of ligands. By controlling the geometry of islands we made arrays in which the local (on island) adhesion density was high but the global (multi-island) adhesion density over the entire cell-substrate interface was low. Neutrophils in contact with these island arrays assumed a well-spread and directionally-persistent motile phenotype (keratocyte-like) in contrast to the classical amoeboid morphology they display on uniform fields of high adhesion density. By virtue of our rationally designed substrates, we were able to conclude that neutrophils were integrating the stimulation received across their entire contact interface; furthermore, they were able to mount this whole cell response on the timescale of seconds. This work demonstrates the capacity of adhesive microenvironments to direct the phenotype of cell motility, which has broader implications in physiologic processes such as inflammation and cancer metastasis.

Myosin light chain kinase regulates cell polarization independently of membrane tension or Rho kinase

Use of embryonic zebrafish keratocytes as a model system shows that increased myosin light chain kinase (MLCK) activity promotes the formation of multiple protrusions independently of ROCK by increasing myosin accumulation in lamellipodia.

Cells polarize to a single front and rear to achieve rapid actin-based motility, but the mechanisms preventing the formation of multiple fronts are unclear. We developed embryonic zebrafish keratocytes as a model system for investigating establishment of a single axis. We observed that, although keratocytes from 2 d postfertilization (dpf) embryos resembled canonical fan-shaped keratocytes, keratocytes from 4 dpf embryos often formed multiple protrusions despite unchanged membrane tension. Using genomic, genetic, and pharmacological approaches, we determined that the multiple-protrusion phenotype was primarily due to increased myosin light chain kinase (MLCK) expression. MLCK activity influences cell polarity by increasing myosin accumulation in lamellipodia, which locally decreases protrusion lifetime, limiting lamellipodial size and allowing for multiple protrusions to coexist within the context of membrane tension limiting protrusion globally. In contrast, Rho kinase (ROCK) regulates myosin accumulation at the cell rear and does not determine protrusion size. These results suggest a novel MLCK-specific mechanism for controlling cell polarity via regulation of myosin activity in protrusions.

Spatial trigger waves: positive feedback gets you a long way

Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances. Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs. Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely used in physics and theoretical biology, to examine different types of trigger waves-spatial switches, pulses, and oscillations-and to show how they arise.

Mechanical properties of branched actin filaments

Cells moving on a two dimensional substrate generate motion by polymerizing actin filament networks inside a flat membrane protrusion. New filaments are generated by branching off existing ones, giving rise to branched network structures. We investigate the force-extension relation of branched filaments, grafted on an elastic structure at one end and pushing with the free ends against the leading edge cell membrane. Single filaments are modeled as worm-like chains, whose thermal bending fluctuations are restricted by the leading edge cell membrane, resulting in an effective force. Branching can increase the stiffness considerably; however the effect depends on branch point position and filament orientation, being most pronounced for intermediate tilt angles and intermediate branch point positions. We describe filament networks without cross-linkers to focus on the effect of branching. We use randomly positioned branch points, as generated in the process of treadmilling, and orientation distributions as measured in lamellipodia. These networks reproduce both the weak and strong force response of lamellipodia as measured in force-velocity experiments. We compare properties of branched and unbranched networks. The ratio of the network average of the force per branched filament to the average force per unbranched filament depends on the orientation distribution of the filaments. The ratio exhibits compression dependence and may go up to about 4.5 in networks with a narrow orientation distribution. With orientation distributions measured in lamellipodia, it is about two and essentially independent from network compression, graft elasticity and filament persistence length.

Actin-myosin spatial patterns from a simplified isotropic viscoelastic model

F-actin networks are involved in cell mechanical processes ranging from motility to endocytosis. The mesoscale architecture of assemblies of individual F-actin polymers that gives rise to micrometer-scale rheological properties is poorly understood, despite numerous in vivo and vitro studies. In vitro networks have been shown to organize into spatial patterns when spatially confined, including dense spherical shells inside spherical emulsion droplets. Here we develop a simplified model of an isotropic, compressible, viscoelastic material continually assembling and disassembling. We demonstrate that spherical shells emerge naturally when the strain relaxation rate (corresponding to internal network reorganization) is slower than the disassembly rate (corresponding to F-actin depolymerization). These patterns are consistent with recent experiments, including a collapse of shells to a central high-density focus of F-actin when either assembly or disassembly is reduced with drugs. Our results demonstrate how complex spatio-temporal patterns can emerge without spatially distributed force generation, polar alignment of F-actin polymers, or spatially nonuniform regulation of F-actin by upstream biochemical networks.

Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells

The mesenchymal-amoeboid transition (MAT) was proposed as a mechanism for cancer cells to adapt their migration mode to their environment. While the molecular pathways involved in this transition are well documented, the role of the microenvironment in the MAT is still poorly understood. Here, we investigated how confinement and adhesion affect this transition. We report that, in the absence of focal adhesions and under conditions of confinement, mesenchymal cells can spontaneously switch to a fast amoeboid migration phenotype. We identified two main types of fast migration--one involving a local protrusion and a second involving a myosin-II-dependent mechanical instability of the cell cortex that leads to a global cortical flow. Interestingly, transformed cells are more prone to adopt this fast migration mode. Finally, we propose a generic model that explains migration transitions and predicts a phase diagram of migration phenotypes based on three main control parameters: confinement, adhesion, and contractility.

Balance between cell-substrate adhesion and myosin contraction determines the frequency of motility initiation in fish keratocytes

Cells are dynamic systems capable of spontaneously switching among stable states. One striking example of this is spontaneous symmetry breaking and motility initiation in fish epithelial keratocytes. Although the biochemical and mechanical mechanisms that control steady-state migration in these cells have been well characterized, the mechanisms underlying symmetry breaking are less well understood. In this work, we have combined experimental manipulations of cell-substrate adhesion strength and myosin activity, traction force measurements, and mathematical modeling to develop a comprehensive mechanical model for symmetry breaking and motility initiation in fish epithelial keratocytes. Our results suggest that stochastic fluctuations in adhesion strength and myosin localization drive actin network flow rates in the prospective cell rear above a critical threshold. Above this threshold, high actin flow rates induce a nonlinear switch in adhesion strength, locally switching adhesions from gripping to slipping and further accelerating actin flow in the prospective cell rear, resulting in rear retraction and motility initiation. We further show, both experimentally and with model simulations, that the global levels of adhesion strength and myosin activity control the stability of the stationary state: The frequency of symmetry breaking decreases with increasing adhesion strength and increases with increasing myosin contraction. Thus, the relative strengths of two opposing mechanical forces--contractility and cell-substrate adhesion--determine the likelihood of spontaneous symmetry breaking and motility initiation.

Response of adherent cells to mechanical perturbations of the surrounding matrix

We present a generic and unified theory to explain how cells respond to perturbations of their mechanical environment such as the presence of neighboring cells, slowly applied stretch, or gradients of matrix rigidity. Motivated by experiments, we calculate the local balance of forces that give rise to a tendency for the cell to locally move or reorient, with a focus on the contribution of feedback and homeostasis to cell contractility (manifested by a fixed displacement, strain or stress) that acts on the adhesions at the cell boundary. These forces can be either reinforced or diminished by elastic stresses due to mechanical perturbations of the matrix. Our model predicts these changes and how their balance with local protrusive forces that act on the cell's leading edge either increase or decrease the tendency of the cell to locally move (toward neighboring cells or rigidity gradients) or reorient (in the direction of slowly applied stretch or rigidity gradients).

A minimal physical model captures the shapes of crawling cells

Cell motility in higher organisms (eukaryotes) is crucial to biological functions ranging from wound healing to immune response, and also implicated in diseases such as cancer. For cells crawling on hard surfaces, significant insights into motility have been gained from experiments replicating such motion in vitro. Such experiments show that crawling uses a combination of actin treadmilling (polymerization), which pushes the front of a cell forward, and myosin-induced stress (contractility), which retracts the rear. Here we present a simplified physical model of a crawling cell, consisting of a droplet of active polar fluid with contractility throughout, but treadmilling connected to a thin layer near the supporting wall. The model shows a variety of shapes and/or motility regimes, some closely resembling cases seen experimentally. Our work strongly supports the view that cellular motility exploits autonomous physical mechanisms whose operation does not need continuous regulatory effort.

Collective cell migration induced by mechanical stress and substrate adhesiveness

Mechanical stress normal to the boundary of a tissue sheet can arise in both constrained as well as unconstrained epithelial layers through pushing and pulling of surrounding tissue and substrate adhesiveness, respectively. A continuum model is used to investigate how such stress influences the epithelial dynamics. Four types of spreading and motility can be identified: a uniformly stretched stationary state, uniform sheet migration, active stress compensation by polarization close to the boundary, and a wormlike progression by deformation waves. Analytical and numerical solutions are presented along with bifurcation diagrams using normal stress and active force as control parameters.

Self-organizing actomyosin patterns on the cell cortex at epithelial cell-cell junctions

The behavior of actomyosin critically determines morphologically distinct patterns of contractility found at the interface between adherent cells. One such pattern is found at the apical region (zonula adherens) of cell-cell junctions in epithelia, where clusters of the adhesion molecule E-cadherin concentrate in a static pattern. Meanwhile, E-cadherin clusters throughout lateral cell-cell contacts display dynamic movements in the plane of the junctions. To gain insight into the principles that determine the nature and organization of these dynamic structures, we analyze this behavior by modeling the 2D actomyosin cell cortex as an active fluid medium. The numerical simulations show that the stability of the actin filaments influences the spatial structure and dynamics of the system. We find that in addition to static Turing-type patterns, persistent dynamic behavior occurs in a wide range of parameters. In the 2D model, mechanical stress-dependent actin breakdown is shown to produce a continuously changing network of actin bridges, whereas with a constant breakdown rate, more isolated clusters of actomyosin tend to form. The model qualitatively reproduces the dynamic and stable patterns experimentally observed at the junctions between epithelial cells.

Modes and mechanisms of T cell motility: roles for confinement and Myosin-IIA

T cells are charged with surveying tissues for evidence of their cognate foreign antigens. Subsequently, they must navigate to effector sites, which they enter through the process of trans-endothelial migration (TEM). During interstitial migration, T cells migrate according to one of two modes that are distinguished by the strength and sequence of adhesions and the requirement for Myosin-IIA. In contrast during TEM, T cells require Myosin-IIA for the final process of pushing their nucleus through the endothelium. A generalized model emerges with dual roles for Myosin-IIA: This motor protein acts like a tensioning or expansion spring, transmitting force across the cell cortex to sites of surface contact and also optimizing the frictional coupling with substrata by modulating the surface area of the contact. The phosphorylation and deactivation of this motor following TCR engagement can allow T cells to rapidly alter the degree to which they adhere to surfaces and to switch to a mode of interaction with surfaces that is more conducive to forming a synapse with an antigen-presenting cell.

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.

Alex Mogilner: math illuminates biology

Mogilner uses modeling to probe and explain the behavior of cells and their cytoskeleton.

Nuclear motility in glioma cells reveals a cell-line dependent role of various cytoskeletal components

Nuclear migration is a general term for the movement of the nucleus towards a specific site in the cell. These movements are involved in a number of fundamental biological processes, such as fertilization, cell division, and embryonic development. Despite of its importance, the mechanism of nuclear migration is still poorly understood in mammalian cells. In order to shed light on the mechanical processes underlying nuclear movements, we adapted a micro-patterning based assay. C6 rat and U87 human glioma cells seeded on fibronectin patterns - thereby forced into a bipolar morphology - displayed oscillatory movements of the nucleus or the whole cell, respectively. We found that both the actomyosin system and microtubules are involved in the nuclear/cellular movements of both cell lines, but their contributions are cell-/migration-type specific. Dynein activity was necessary for nuclear migration of C6 cells but active myosin-II was dispensable. On the other hand, coupled nuclear and cellular movements of U87 cells were driven by actomyosin contraction. We explain these cell-line dependent effects by the intrinsic differences in the overall mechanical tension due to the various cytoskeletal elements inside the cell. Our observations showed that the movements of the nucleus and the centrosome are strongly correlated and display large variation, indicating a tight but flexible coupling between them. The data also indicate that the forces responsible for nuclear movements are not acting directly via the centrosome. Based on our observations, we propose a new model for nuclear oscillations in C6 cells in which dynein and microtubule dynamics are the main drivers of nuclear movements. This mechanism is similar to the meiotic nuclear oscillations of Schizosaccharomyces pombe and may be evolutionary conserved.

Determinants of maximal force transmission in a motor-clutch model of cell traction in a compliant microenvironment

The mechanical stiffness of a cell's environment exerts a strong, but variable, influence on cell behavior and fate. For example, different cell types cultured on compliant substrates have opposite trends of cell migration and traction as a function of substrate stiffness. Here, we describe how a motor-clutch model of cell traction, which exhibits a maximum in traction force with respect to substrate stiffness, may provide a mechanistic basis for understanding how cells are tuned to sense the stiffness of specific microenvironments. We find that the optimal stiffness is generally more sensitive to clutch parameters than to motor parameters, but that single parameter changes are generally only effective over a small range of values. By contrast, dual parameter changes, such as coordinately increasing the numbers of both motors and clutches offer a larger dynamic range for tuning the optimum. The model exhibits distinct regimes: at high substrate stiffness, clutches quickly build force and fail (so-called frictional slippage), whereas at low substrate stiffness, clutches fail spontaneously before the motors can load the substrate appreciably (a second regime of frictional slippage). Between the two extremes, we find the maximum traction force, which occurs when the substrate load-and-fail cycle time equals the expected time for all clutches to bind. At this stiffness, clutches are used to their fullest extent, and motors are therefore resisted to their fullest extent. The analysis suggests that coordinate parameter shifts, such as increasing the numbers of motors and clutches, could underlie tumor progression and collective cell migration.

Modeling crawling cell movement on soft engineered substrates

Self-propelled motion, emerging spontaneously or in response to external cues, is a hallmark of living organisms. Systems of self-propelled synthetic particles are also relevant for multiple applications, from targeted drug delivery to the design of self-healing materials. Self-propulsion relies on the force transfer to the surrounding. While self-propelled swimming in the bulk of liquids is fairly well characterized, many open questions remain in our understanding of self-propelled motion along substrates, such as in the case of crawling cells or related biomimetic objects. How is the force transfer organized and how does it interplay with the deformability of the moving object and the substrate? How do the spatially dependent traction distribution and adhesion dynamics give rise to complex cell behavior? How can we engineer a specific cell response on synthetic compliant substrates? Here we generalize our recently developed model for a crawling cell by incorporating locally resolved traction forces and substrate deformations. The model captures the generic structure of the traction force distribution and faithfully reproduces experimental observations, like the response of a cell on a gradient in substrate elasticity (durotaxis). It also exhibits complex modes of cell movement such as "bipedal" motion. Our work may guide experiments on cell traction force microscopy and substrate-based cell sorting and can be helpful for the design of biomimetic "crawlers" and active and reconfigurable self-healing materials.

Ligand density elicits a phenotypic switch in human neutrophils

Neutrophils are mediators of innate immunity and motility is critical to their function. We used microcontact printing to investigate the relationship between density of adhesive ligands and the dynamics of neutrophil motility. We show that neutrophils adopt a well-spread morphology without a uropod on moderate densities of adhesion ligand. As density is increased, the morphology switches to a classic amoeboid shape. In addition to the morphological differences, the dynamics of motility were quantitatively distinct. Well-spread cells without uropods glide slowly with high persistence, while amoeboid cells made frequent directional changes migrating quickly with low persistence. Using an antibody panel against various integrin chains, we show that adhesion and motility on fibronectin are mediated by MAC-1 (αMβ2). The phenotypic switch could be generalized to other surface ligands, such as bovine serum albumin, to which the promiscuous MAC-1 also binds. These results suggest that neutrophils are capable of displaying multiple modes of motility as dictated by their adhesive environment.

Plasticity in the macromolecular-scale causal networks of cell migration

Heterogeneous and dynamic single cell migration behaviours arise from a complex multi-scale signalling network comprising both molecular components and macromolecular modules, among which cell-matrix adhesions and F-actin directly mediate migration. To date, the global wiring architecture characterizing this network remains poorly defined. It is also unclear whether such a wiring pattern may be stable and generalizable to different conditions, or plastic and context dependent. Here, synchronous imaging-based quantification of migration system organization, represented by 87 morphological and dynamic macromolecular module features, and migration system behaviour, i.e., migration speed, facilitated Granger causality analysis. We thereby leveraged natural cellular heterogeneity to begin mapping the directionally specific causal wiring between organizational and behavioural features of the cell migration system. This represents an important advance on commonly used correlative analyses that do not resolve causal directionality. We identified organizational features such as adhesion stability and adhesion F-actin content that, as anticipated, causally influenced cell migration speed. Strikingly, we also found that cell speed can exert causal influence over organizational features, including cell shape and adhesion complex location, thus revealing causality in directions contradictory to previous expectations. Importantly, by comparing unperturbed and signalling-modulated cells, we provide proof-of-principle that causal interaction patterns are in fact plastic and context dependent, rather than stable and generalizable.

Dictyostelium cells migrate similarly on surfaces of varying chemical composition

During cell migration, cell-substrate binding is required for pseudopod anchoring to move the cell forward, yet the interactions with the substrate must be sufficiently weak to allow parts of the cell to de-adhere in a controlled manner during typical protrusion/retraction cycles. Mammalian cells actively control cell-substrate binding and respond to extracellular conditions with localized integrin-containing focal adhesions mediating mechanotransduction. We asked whether mechanotransduction also occurs during non-integrin mediated migration by examining the motion of the social amoeba Dictyostelium discoideum, which is thought to bind non-specifically to surfaces. We discovered that Dictyostelium cells are able to regulate forces generated by the actomyosin cortex to maintain optimal cell-surface contact area and adhesion on surfaces of various chemical composition and that individual cells migrate with similar speed and contact area on the different surfaces. In contrast, during collective migration, as observed in wound healing and metastasis, the balance between surface forces and protrusive forces is altered. We found that Dictyostelium collective migration dynamics are strongly affected when cells are plated on different surfaces. These results suggest that the presence of cell-cell contacts, which appear as Dictyostelium cells enter development, alter the mechanism cells use to migrate on surfaces of varying composition.

Formation of transient lamellipodia

Cell motility driven by actin polymerization is pivotal to the development and survival of organisms and individual cells. Motile cells plated on flat substrates form membrane protrusions called lamellipodia. The protrusions repeatedly appear and retract in all directions. If a lamellipodium is stabilized and lasts for some time, it can take over the lead and determine the direction of cell motion. Protrusions traveling along the cell perimeter have also been observed. Their initiation is in some situations the effect of the dynamics of the pathway linking plasma membrane receptors to actin filament nucleation, e.g. in chemotaxis. However, lamellipodia are also formed in many cells incessantly during motion with a constant state of the signaling pathways upstream from nucleation promoting factors (NPFs), or spontaneously in resting cells. These observations strongly suggest protrusion formation can also be a consequence of the dynamics downstream from NPFs, with signaling setting the dynamic regime but not initiating the formation of individual protrusions. A quantitative mechanism for this kind of lamellipodium dynamics has not been suggested yet. Here, we present a model exhibiting excitable actin network dynamics. Individual lamellipodia form due to random supercritical filament nucleation events amplified by autocatalytic branching. They last for about 30 seconds to many minutes and are terminated by filament bundling, severing and capping. We show the relevance of the model mechanism for experimentally observed protrusion dynamics by reproducing in very good approximation the repetitive protrusion formation measured by Burnette et al. with respect to the velocities of leading edge protrusion and retrograde flow, oscillation amplitudes, periods and shape, as well as the phase relation between protrusion and retrograde flow. Our modeling results agree with the mechanism of actin bundle formation during lamellipodium retraction suggested by Burnette et al. and Koestler et al.

Computational estimates of membrane flow and tension gradient in motile cells

All parts of motile cells, including the plasma membrane, have to translocate in the direction of locomotion. Both directed intracellular membrane transport coupled with polarized endo- and exocytosis and fluid flow in the plane of the plasma membrane can contribute to this overall plasma membrane translocation. It remains unclear how strong a force is required to generate this flow. We numerically solve Stokes equations for the viscous membrane flow across a flat plasma membrane surface in the presence of transmembrane proteins attached to the cytoskeleton and find the membrane tension gradient associated with this flow. This gradient is sensitive to the size and density of the transmembrane proteins attached to the cytoskeleton and can become significant enough to slow down cell movement. We estimate the influence of intracellular membrane transport and actin growth and contraction on the tension gradient, and discuss possible ‘tank tread’ flow at ventral and dorsal surfaces.

Impact of MACC1 on human malignant glioma progression and patients' unfavorable prognosis

BACKGROUND

Metastasis-associated in colon cancer 1 (MACC1) has been established as an independent prognostic indicator of metastasis formation and metastasis-free survival for patients with colon cancer and other solid tumors. However, no data are available concerning MACC1 expression in human astrocytic tumors. Glioblastoma multiforme (GBM) is the most prevalent primary brain tumor of adulthood, and due to its invasive and rapid growth, patients have unfavorable prognoses. Although these tumors rarely metastasize, their invasive and migratory behavior is similar to those of metastatic cells of tumors of different origin. Thus, we hypothesized that MACC1 may be involved in progression of human gliomas.

METHODS

We performed real-time measurements of proliferation and migration in MACC1-transfected GBM cell lines (U138, U251) and evaluated tumor formation in organotypic hippocampal slice cultures of mice. Semiquantitative and quantitative real-time reverse transcription PCR analyses were performed for MACC1 and for its transcriptional target c-Met in human astrocytoma of World Health Organization grade II (low-grade astrocytoma) and GBM biopsies. Data were validated by MACC1 immunohistochemistry in independent matched samples of low-grade astrocytoma and GBM.

RESULTS

MACC1 increases the proliferative, migratory, and tumor-formation abilities of GBM cells. The c-Met inhibitor crizotinib reduced MACC1-induced migration and tumor formation in organotypic hippocampal slice cultures of mice. Analyzing patients' biopsies, MACC1 expression increased concomitantly with increasing World Health Organization grade. Moreover, MACC1 expression levels allowed discrimination of dormant and recurrent low-grade astrocytomas and of primary and secondary GBM. Strong MACC1 expression correlated with reduced patient survival.

CONCLUSIONS

MACC1 may represent a promising biomarker for prognostication and a new target for treatment of human gliomas.

Bidirectional coupling between integrin-mediated signaling and actomyosin mechanics explains matrix-dependent intermittency of leading-edge motility

A physicochemical model is used to describe the coupling of adhesion, cytoskeletal, and signaling dynamics during cell migration. Analysis of stochastic simulations predicts relationships between measurable quantities that reflect partitioning of stress between F-actin–bound adhesions, which act as a molecular clutch, and retrograde F-actin flow.

Animal cell migration is a complex process characterized by the coupling of adhesion, cytoskeletal, and signaling dynamics. Here we model local protrusion of the cell edge as a function of the load-bearing properties of integrin-based adhesions, actin polymerization fostered by adhesion-mediated signaling, and mechanosensitive activation of RhoA that promotes myosin II–generated stress on the lamellipodial F-actin network. Analysis of stochastic model simulations illustrates how these pleiotropic functions of nascent adhesions may be integrated to govern temporal persistence and frequency of protrusions. The simulations give mechanistic insight into the documented effects of extracellular matrix density and myosin abundance, and they show characteristic, nonnormal distributions of protrusion duration times that are similar to those extracted from live-cell imaging experiments. Analysis of the model further predicts relationships between measurable quantities that reflect the partitioning of stress between tension on F-actin–bound adhesions, which act as a molecular clutch, and dissipation by retrograde F-actin flow.

Closing the loop: lamellipodia dynamics from the perspective of front propagation

We develop a simple physical model that captures the large-scale lamellipodia dynamics in crawling cells and explains the observed spectrum of fish keratocytes behavior. The main ingredients in this description are the geometrical evolution of the lamellipodium leading edge, the dynamic remodeling of the actin network, and the interconnection between them. We deviate from existing theoretical works and consider the lamellipodium leading edge as a propagating front. The agreement of our model with experimental works suggests that the large-scale morphological and migration features exhibited by keratocyte cells are a direct consequence of the closed feedback loop between the shape of the leading edge and the density of the actin network.

Migration speed and directionality switch of normal epithelial cells after TGF-β1-induced EMT (tEMT) on micro-structured polydimethylsiloxane (PDMS) substrates with variations in stiffness and topographic patterning

The epithelial to mesenchymal transition (EMT) involves several physiological and pathological phenomena and endows cells with invasive and migratory properties. However, the effects of substrate stiffness and topography on the migration of cells before or after transforming growth factor-β1 (TGF-β1)-induced EMT (tEMT) are unknown. Herein, we seed control or tEMT NMuMG cells on the 2D patterns consisted of 1 μm or 5 μm line-widths and groove or cone patterns on either 2 MPa (1.96 ± 0.48 MPa) or 4 MPa (3.70 ± 0.74 MPa) polydimethylsiloxane (PDMS) substrates. After tEMT, the increased expression of α-SMA with vinculin in focal adhesion (FA) sites led to an acceleration of tEMT cell motility. On the 2 MPa substrate, the most influenced substrate was the 1 μm, cone-patterned substrate, where the tEMT cells' motility decelerated by 0.13 μm/min (36% slower than the cells on groove pattern). However, on the 5 μm, groove-patterned substrate, where the tEMT cells demonstrated the most rapid motility relative to the control cells, with an increment of 0.18 μm/min (100%). Among the different physical cues from substrate, the cone pattern could impede the migration speed of tEMT cells. Furthermore, we recommend the groove-patterned with a 5 μm line-width substrate as a useful tool to differentiate control and tEMT cells by migration speed.

Contraction-driven cell motility

We propose a mechanism for the initiation of cell motility that is based on myosin-induced contraction and does not require actin polymerization. The translocation of a cell is induced by symmetry breaking of the motor-driven flow, and the ensuing asymmetry gives rise to a steady motion of the center of mass of a cell. The predictions of the model are consistent with observations on keratocytes.

Master equation-based analysis of a motor-clutch model for cell traction force

Microenvironmental mechanics play an important role in determining the morphology, traction, migration, proliferation, and differentiation of cells. A stochastic motor-clutch model has been proposed to describe this stiffness sensitivity. In this work, we present a master equation-based ordinary differential equation (ODE) description of the motor-clutch model, from which we derive an analytical expression to for a cell's optimum stiffness (i.e. the stiffness at which the traction force is maximal). This analytical expression provides insight into the requirements for stiffness sensing by establishing fundamental relationships between the key controlling cell-specific parameters. We find that the fundamental controlling parameters are the numbers of motors and clutches (constrained to be nearly equal), and the time scale of the on-off kinetics of the clutches (constrained to favor clutch binding over clutch unbinding). Both the ODE solution and the analytical expression show good agreement with Monte Carlo motor-clutch output, and reduce computation time by several orders of magnitude, which potentially enables long time scale behaviors (hours-days) to be studied computationally in an efficient manner. The ODE solution and the analytical expression may be incorporated into larger scale models of cellular behavior to bridge the gap from molecular time scales to cellular and tissue time scales.