Contractility and retrograde flow in lamellipodium motion

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.

Physical biomarkers for human hematopoietic stem and progenitor cells

Adhesion of hematopoietic stem and progenitor cells (HSPCs) to the bone marrow niche plays critical roles in the maintenance of the most primitive HSPCs. The interactions of HSPC-niche interactions are clinically relevant in acute myeloid leukemia (AML), because (i) leukemia-initiating cells adhered to the marrow niche are protected from the cytotoxic effect by chemotherapy and (ii) mobilization of HSPCs from healthy donors' bone marrow is crucial for the effective stem cell transplantation. However, although many clinical agents have been developed for the HSPC mobilization, the effects caused by the extrinsic molecular cues were traditionally evaluated based on phenomenological observations. This review highlights the recent interdisciplinary challenges of hematologists, biophysicists and cell biologists towards the design of defined in vitro niche models and the development of physical biomarkers for quantitative indexing of differential effects of clinical agents on human HSPCs.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Incompressible Polar Active Fluids with Quenched Random Field Disorder in Dimensions d>2

We present a hydrodynamic theory of incompressible polar active fluids with quenched random field disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a nonzero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.

Self-organization in amoeboid motility

Amoeboid motility has come to refer to a spectrum of cell migration modes enabling a cell to move in the absence of strong, specific adhesion. To do so, cells have evolved a range of motile surface movements whose physical principles are now coming into view. In response to external cues, many cells—and some single-celled-organisms—have the capacity to turn off their default migration mode. and switch to an amoeboid mode. This implies a restructuring of the migration machinery at the cell scale and suggests a close link between cell polarization and migration mediated by self-organizing mechanisms. Here, I review recent theoretical models with the aim of providing an integrative, physical picture of amoeboid migration.

Interfacial friction and substrate deformation mediate long-range signal propagation in tissues

Tissue layers can generally slide at the interface, accompanied by the dissipation due to friction. Nevertheless, it remains elusive how force could propagate in a tissue with such interfacial friction. Here, we elaborate the force dynamics in a prototypical multilayer system in which an epithelial monolayer was cultivated upon an elastic substrate in contact with a hard surface, and discover a novel mechanism of pronounced force propagation over a long distance due to interfacial dynamics between substrate layers. We derived an analytical model for the dynamics of the elastic substrate under the shear stress provided by the cell layer at the surface boundary and the friction at bottom. The model reveals that sliding between substrate layers leads to an expanding stretch regime from a shear regime of substrate deformation in time and space. The regime boundary propagating diffusively with a speed depending on the stiffness, thickness, and slipperiness of the substrate, is a robust nature of a deformed elastic sheet with interfacial friction. These results shed new light on force propagation in tissues and our model could serve as a basis for studies of such propagation in a more complex tissue environment.

Optimal transport and control of active drops

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural "gather-move-spread" strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

Mechanical processes underlying precise and robust cell matching

During the development of complicated multicellular organisms, the robust formation of specific cell-cell connections (cell matching) is required for the generation of precise tissue structures. Mismatches or misconnections can lead to various diseases. Diverse mechanical cues, including differential adhesion and temporally varying cell contractility, are involved in regulating the process of cell-cell recognition and contact formation. Cells often start the process of cell matching through contact via filopodia protrusions, mediated by specific adhesion interactions at the cell surface. These adhesion interactions give rise to differential mechanical signals that can be further perceived by the cells. In conjunction with contractions generated by the actomyosin networks within the cells, this differentially coded adhesion information can be translated to reposition and sort cells. Here, we review the role of these different cell matching components and suggest how these mechanical factors cooperate with each other to facilitate specificity in cell-cell contact formation.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Integer topological defects of cell monolayers: Mechanics and flows

Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the timescales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical patterns at integer topological defects. Our description includes three distinct sources of activity: traction forces accounting for cell-substrate interactions as well as anisotropic and isotropic active nematic stresses accounting for cell-cell interactions. We apply our approach to C2C12 cell monolayers in small circular confinements, which form isolated aster or spiral topological defects. By analyzing the velocity and orientational order fields in spirals as well as the forces and cell number density fields in asters, we determine mechanical parameters of C2C12 cell monolayers. Our work shows how topological defects can be used to fully characterize the mechanical properties of biological active matter.

Critical role of lipid membranes in polarization and migration of cells: a biophysical view

Cell migration plays vital roles in many biologically relevant processes such as tissue morphogenesis and cancer metastasis, and it has fascinated biophysicists over the past several decades. However, despite an increasing number of studies highlighting the orchestration of proteins involved in different signaling pathways, the functional roles of lipid membranes have been essentially overlooked. Lipid membranes are generally considered to be a functionless two-dimensional matrix of proteins, although many proteins regulating cell migration gain functions only after they are recruited to the membrane surface and self-organize their functional domains. In this review, we summarize how the logistical recruitment and release of proteins to and from lipid membranes coordinates complex spatiotemporal molecular processes. As predicted from the classical framework of the Smoluchowski equation of diffusion, lipid/protein membranes serve as a 2D reaction hub that contributes to the effective and robust regulation of polarization and migration of cells involving several competing pathways.

Actomyosin Contraction Induces In-Bulk Motility of Cells and Droplets

Cell crawling on two-dimensional surfaces is a relatively well-understood phenomenon that is based on actin polymerization at a cell's front edge and anchoring on a substrate, allowing the cell to pull itself forward. However, some cells, such as cancer cells invading a three-dimensional matrigel, can also swim in the bulk, where surface adhesion is impossible. Although there is strong evidence that the self-organized engine that drives cells forward in the bulk involves myosin, the specific propulsion mechanism remains largely unclear. Here, we propose a minimal model for in-bulk self-motility of a droplet containing an isotropic and compressible contractile gel, representing a cell extract containing a disordered actomyosin network. In our model, contraction mediates a feedback loop between myosin-induced flow and advection-induced myosin accumulation, which leads to clustering and locally enhanced flow. The symmetry of such flow is then spontaneously broken through actomyosin-membrane interactions, leading to self-organized droplet motility relative to the underlying solvent. Depending on the balance between contraction, diffusion, detachment rate of myosin, and effective surface tension, this motion can be either straight or circular. Our simulations and analytical results shed new light on in-bulk myosin-driven cell motility in living cells and provide a framework to design a novel type of synthetic active matter droplet potentially resembling the motility mechanism of biological cells.

Tuning Cell Motility via Cell Tension with a Mechanochemical Cell Migration Model

Cell migration is orchestrated by a complicated mechanochemical system. However, few cell migration models take into account the coupling between the biochemical network and mechanical factors. Here, we construct a mechanochemical cell migration model to study the cell tension effect on cell migration. Our model incorporates the interactions between Rac-GTP, Rac-GDP, F-actin, myosin, and cell tension, and it is very convenient in capturing the change of cell shape by taking the phase field approach. This model captures the characteristic features of cell polarization, cell shape change, and cell migration modes. It shows that cell tension inhibits migration ability monotonically when cells are applied with persistent external stimuli. On the other hand, if random internal noise is significant, the regulation of cell tension exerts a nonmonotonic effect on cell migration. Because the increase of cell tension hinders the formation of multiple protrusions, migration ability could be maximized at intermediate cell tension under random internal noise. These model predictions are consistent with our single-cell experiments and other experimental results.

How many ways a cell can move: the modes of self-propulsion of an active drop

Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms based on general physical principles, showing that crawling is not the only way for cells to move on a substrate. We consider a thin drop of active matter on a planar substrate and fully characterize its autonomous motion for all three possible sources of driving: (i) the stresses induced in the bulk by active components, which allow in particular tractionless motion, (ii) the self-propulsion of active components at the substrate, which gives rise to crawling motion, and (iii) a net capillary force, possibly self-generated, and coupled to internal activity. We determine travelling-wave solutions to the lubrication equations as a function of a dimensionless activity parameter for each mode of motion. Numerical simulations are used to characterize the drop motion over a wide range of activity magnitudes, and explicit analytical solutions in excellent agreement with the simulations are derived in the weak-activity regime.

Dense active matter model of motion patterns in confluent cell monolayers

Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.

Motility and morphodynamics of confined cells

We introduce a minimal hydrodynamic model of polarization, migration, and deformation of a biological cell confined between two parallel surfaces. In our model, the cell is driven out of equilibrium by an active cytsokeleton force that acts on the membrane. The cell cytoplasm, described as a viscous droplet in the Darcy flow regime, contains a diffusive solute that actively transduces the applied cytoskeleton force. While fairly simple and analytically tractable, this quasi-two-dimensional model predicts a range of compelling dynamic behaviours. A linear stability analysis of the system reveals that solute activity first destabilizes a global polarization-translation mode, prompting cell motility through spontaneous symmetry breaking. At higher activity, the system crosses a series of Hopf bifurcations leading to coupled oscillations of droplet shape and solute concentration profiles. At the nonlinear level, we find traveling-wave solutions associated with unique polarized shapes that resemble experimental observations. Altogether, this model offers an analytical paradigm of active deformable systems in which viscous hydrodynamics are coupled to diffusive force transducers.

Deterministic actin waves as generators of cell polarization cues

Dendritic cells "patrol" the human body to detect pathogens. In their search, dendritic cells perform a random walk by amoeboid migration. The efficiency of pathogen detection depends on the properties of the random walk. It is not known how the dendritic cells control these properties. Here, we quantify dendritic cell migration under well-defined 2-dimensional confinement and in a 3-dimensional collagen matrix through recording their long-term trajectories. We find 2 different migration states: persistent migration, during which the dendritic cells move along curved paths, and diffusive migration, which is characterized by successive sharp turns. These states exhibit differences in the actin distributions. Our theoretical and experimental analyses indicate that this kind of motion can be generated by spontaneous actin polymerization waves that contribute to dendritic cell polarization and migration. The relative distributions of persistent and diffusive migration can be changed by modification of the molecular actin filament nucleation and assembly rates. Thus, dendritic cells can control their migration patterns and adapt to specific environments. Our study offers an additional perspective on how dendritic cells tune their searches for pathogens.

Tractionless Self-Propulsion of Active Drops

We report on a new mode of self-propulsion exhibited by compact drops of active liquids on a substrate which, remarkably, is tractionless, i.e., which imparts no mechanical stress locally on the surface. We show, both analytically and by numerical simulation, that the equations of motion for an active nematic drop possess a simple self-propelling solution, with no traction on the solid surface and in which the direction of motion is controlled by the winding of the nematic director field across the drop height. The physics underlying this mode of motion has the same origins as that giving rise to the zero viscosity observed in bacterial suspensions. This topologically protected tractionless self-propusion provides a robust physical mechanism for efficient cell migration in crowded environments like tissues.

Stick-slip dynamics of migrating cells on viscoelastic substrates

Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviors have previously been investigated typically using purely elastic substrates. For a more realistic understanding of this phenomenon, we propose a theoretical model to study the dynamics on a viscoelastic substrate. Our model, based on a reaction-diffusion framework, incorporates known important interactions such as retrograde flow of actin, myosin contractility, force-dependent assembly, and disassembly of focal adhesions coupled with cell-substrate interaction. We show that consideration of a viscoelastic substrate not only captures the usually observed stick-slip jumps but also predicts the existence of an optimal substrate viscosity corresponding to maximum traction force and minimum retrograde flow which was hitherto unexplored. Moreover, our theory predicts the time evolution of individual bond force that characterizes the stick-slip patterns on soft versus stiff substrates. Our analysis also elucidates how the duration of the stick-slip cycles are affected by various cellular parameters.

Network Contractility During Cytokinesis-from Molecular to Global Views

Cytokinesis is the last stage of cell division, which partitions the mother cell into two daughter cells. It requires the assembly and constriction of a contractile ring that consists of a filamentous contractile network of actin and myosin. Network contractility depends on network architecture, level of connectivity and myosin motor activity, but how exactly is the contractile ring network organized or interconnected and how much it depends on motor activity remains unclear. Moreover, the contractile ring is not an isolated entity; rather, it is integrated into the surrounding cortex. Therefore, the mechanical properties of the cell cortex and cortical behaviors are expected to impact contractile ring functioning. Due to the complexity of the process, experimental approaches have been coupled to theoretical modeling in order to advance its global understanding. While earlier coarse-grained descriptions attempted to provide an integrated view of the process, recent models have mostly focused on understanding the behavior of an isolated contractile ring. Here we provide an overview of the organization and dynamics of the actomyosin network during cytokinesis and discuss existing theoretical models in light of cortical behaviors and experimental evidence from several systems. Our view on what is missing in current models and should be tested in the future is provided.

Cell motility dependence on adhesive wetting

Adhesive cell-substrate interactions are crucial for cell motility and are responsible for the necessary traction that propels cells. These interactions can also change the shape of the cell, analogous to liquid droplet wetting on adhesive substrates. To address how these shape changes affect cell migration and cell speed we model motility using deformable, 2D cross-sections of cells in which adhesion and frictional forces between cell and substrate can be varied separately. Our simulations show that increasing the adhesion results in increased spreading of cells and larger cell speeds. We propose an analytical model which shows that the cell speed is inversely proportional to an effective height of the cell and that increasing this height results in increased internal shear stress. The numerical and analytical results are confirmed in experiments on motile eukaryotic cells.

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.

On the relation between filament density, force generation, and protrusion rate in mesenchymal cell motility

Lamellipodia are flat membrane protrusions formed during mesenchymal motion. Polymerization at the leading edge assembles the actin filament network and generates protrusion force. How this force is supported by the network and how the assembly rate is shared between protrusion and network retrograde flow determines the protrusion rate. We use mathematical modeling to understand experiments changing the F-actin density in lamellipodia of B16-F1 melanoma cells by modulation of Arp2/3 complex activity or knockout of the formins FMNL2 and FMNL3. Cells respond to a reduction of density with a decrease of protrusion velocity, an increase in the ratio of force to filament number, but constant network assembly rate. The relation between protrusion force and tension gradient in the F-actin network and the density dependency of friction, elasticity, and viscosity of the network explain the experimental observations. The formins act as filament nucleators and elongators with differential rates. Modulation of their activity suggests an effect on network assembly rate. Contrary to these expectations, the effect of changes in elongator composition is much weaker than the consequences of the density change. We conclude that the force acting on the leading edge membrane is the force required to drive F-actin network retrograde flow.

Eukaryotic Cell Dynamics from Crawlers to Swimmers

Movement requires force transmission to the environment, and motile cells are robustly, though not elegantly, designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission used. As with humans, the available modes range from momentary attachment to a substrate when crawling, to shape deformations when swimming, and at the cellular level this involves sensing the mechanical properties of the environment and altering the mode appropriately. While many types of cells can adapt their mode of movement to their microenvironment (ME), our understanding of how they detect, transduce and process information from the ME to determine the optimal mode is still rudimentary. The shape and integrity of a cell is determined by its cytoskeleton (CSK), and thus the shape changes that may be required to move involve controlled remodeling of the CSK. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of motility in even simple cells such as bacteria is not at hand. In this review we discuss recent advances in our understanding of cell motility and some of the problems remaining to be solved.

Simple Physical Model Unravels Influences of Chemokine on Shape Deformation and Migration of Human Hematopoietic Stem Cells

We studied the dynamic behavior of human hematopoietic stem cells (HSC) on the in vitro model of bone marrow surfaces in the absence and presence of chemokine (SDF1α). The deformation and migration of cells were investigated by varying the chemokine concentration and surface density of ligand molecules. Since HSC used in this study were primary cells extracted from the human umbilical cord blood, it is not possible to introduce molecular reporter systems before or during the live cell imaging. To account for the experimental observations, we propose a simple and general theoretical model for cell crawling. In contrast to other theoretical models reported previously, our model focuses on the nonlinear coupling between shape deformation and translational motion and is free from any molecular-level process. Therefore, it is ideally suited for the comparison with our experimental results. We have demonstrated that the results in the absence of SDF1α were well recapitulated by the linear model, while the nonlinear model is necessary to reproduce the elongated migration observed in the presence of SDF1α. The combination of the simple theoretical model and the label-free, live cell observations of human primary cells opens a large potential to numerically identify the differential effects of extrinsic factors such as chemokines, growth factors, and clinical drugs on dynamic phenotypes of primary cells.

Hydrodynamic theory of active matter

We review the general hydrodynamic theory of active soft materials that is motivated in particular by biological matter. We present basic concepts of irreversible thermodynamics of spatially extended multicomponent active systems. Starting from the rate of entropy production, we identify conjugate thermodynamic fluxes and forces and present generic constitutive equations of polar active fluids and active gels. We also discuss angular momentum conservation which plays a role in the the physics of active chiral gels. The irreversible thermodynamics of active gels provides a general framework to discuss the physics that underlies a wide variety of biological processes in cells and in multicellular tissues.

A nonequilibrium force can stabilize 2D active nematics

Suspensions of actively driven anisotropic objects exhibit distinctively nonequilibrium behaviors, and current theories predict that they are incapable of sustaining orientational order at high activity. By contrast, here we show that nematic suspensions on a substrate can display order at arbitrarily high activity due to a previously unreported, potentially stabilizing active force. This force moreover emerges inevitably in theories of active orientable fluids under geometric confinement. The resulting nonequilibrium ordered phase displays robust giant number fluctuations that cannot be suppressed even by an incompressible solvent. Our results apply to virtually all experimental assays used to investigate the active nematic ordering of self-propelled colloids, bacterial suspensions, and the cytoskeleton and have testable implications in interpreting their nonequilibrium behaviors.

Strain energy storage and dissipation rate in active cell mechanics

When living cells are observed at rest on a flat substrate, they can typically exhibit a rounded (symmetric) or an elongated (polarized) shape. Although the cells are apparently at rest, the active stress generated by the molecular motors continuously stretches and drifts the actin network, the cytoskeleton of the cell. In this paper we theoretically compare the energy stored and dissipated in this active system in two geometric configurations of interest: symmetric and polarized. We find that the stored energy is larger for a radially symmetric cell at low activation regime, while the polar configuration has larger strain energy when the active stress is beyond a critical threshold. Conversely, the dissipation of energy in a symmetric cell is always larger than that of a nonsymmetric one. By a combination of symmetry arguments and competition between surface and bulk stress, we argue that radial symmetry is an energetically expensive metastable state that provides access to an infinite number of lower-energy states, the polarized configurations.

A disassembly-driven mechanism explains F-actin-mediated chromosome transport in starfish oocytes

While contraction of sarcomeric actomyosin assemblies is well understood, this is not the case for disordered networks of actin filaments (F-actin) driving diverse essential processes in animal cells. For example, at the onset of meiosis in starfish oocytes a contractile F-actin network forms in the nuclear region transporting embedded chromosomes to the assembling microtubule spindle. Here, we addressed the mechanism driving contraction of this 3D disordered F-actin network by comparing quantitative observations to computational models. We analyzed 3D chromosome trajectories and imaged filament dynamics to monitor network behavior under various physical and chemical perturbations. We found no evidence of myosin activity driving network contractility. Instead, our observations are well explained by models based on a disassembly-driven contractile mechanism. We reconstitute this disassembly-based contractile system in silico revealing a simple architecture that robustly drives chromosome transport to prevent aneuploidy in the large oocyte, a prerequisite for normal embryonic development.

Effective viscosity and dynamics of spreading epithelia: a solvable model

Collective cell migration in spreading epithelia in controlled environments has become a landmark in our current understanding of fundamental biophysical processes in development, regeneration, wound healing or cancer. Epithelial monolayers are treated as thin layers of a viscous fluid that exert active traction forces on the substrate. The model is exactly solvable and shows a broad range of applicabilities for the quantitative analysis and interpretation of force microscopy data of monolayers from a variety of experiments and cell lines. In addition, the proposed model provides physical insights into how the biological regulation of the tissue is encoded in a reduced set of time-dependent physical parameters. In particular the temporal evolution of the effective viscosity entails a mechanosensitive regulation of adhesion. Besides, the observation of an effective elastic tensile modulus can be interpreted as an emergent phenomenon in an active fluid.

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.

Physical role for the nucleus in cell migration

Cell migration is important for the function of many eukaryotic cells. Recently the nucleus has been shown to play an important role in cell motility. After giving an overview of cell motility mechanisms we review what is currently known about the mechanical properties of the nucleus and the connections between it and the cytoskeleton. We also discuss connections to the extracellular matrix and mechanotransduction. We identify key physical roles of the nucleus in cell migration.

Ratchetaxis: Long-Range Directed Cell Migration by Local Cues

Directed cell migration is usually thought to depend on the presence of long-range gradients of either chemoattractants or physical properties such as stiffness or adhesion. However, in vivo, chemical or mechanical gradients have not systematically been observed. Here we review recent in vitro experiments, which show that other types of spatial guidance cues can bias cell motility. Introducing local geometrical or mechanical anisotropy in the cell environment, such as adhesive/topographical microratchets or tilted micropillars, show that local and periodic external cues can direct cell motion. Together with modeling, these experiments suggest that cell motility can be viewed as a stochastic phenomenon, which can be biased by various types of local cues, leading to directional migration.

Immersed Boundary Simulations of Active Fluid Droplets

We present numerical simulations of active fluid droplets immersed in an external fluid in 2-dimensions using an Immersed Boundary method to simulate the fluid droplet interface as a Lagrangian mesh. We present results from two example systems, firstly an active isotropic fluid boundary consisting of particles that can bind and unbind from the interface and generate surface tension gradients through active contractility. Secondly, a droplet filled with an active polar fluid with homeotropic anchoring at the droplet interface. These two systems demonstrate spontaneous symmetry breaking and steady state dynamics resembling cell motility and division and show complex feedback mechanisms with minimal degrees of freedom. The simulations outlined here will be useful for quantifying the wide range of dynamics observable in these active systems and modelling the effects of confinement in a consistent and adaptable way.

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.

Cortical Flow-Driven Shapes of Nonadherent Cells

Nonadherent polarized cells have been observed to have a pearlike, elongated shape. Using a minimal model that describes the cell cortex as a thin layer of contractile active gel, we show that the anisotropy of active stresses, controlled by cortical viscosity and filament ordering, can account for this morphology. The predicted shapes can be determined from the flow pattern only; they prove to be independent of the mechanism at the origin of the cortical flow, and are only weakly sensitive to the cytoplasmic rheology. In the case of actin flows resulting from a contractile instability, we propose a phase diagram of three-dimensional cell shapes that encompasses nonpolarized spherical, elongated, as well as oblate shapes, all of which have been observed in experiment.

When cell biology meets theory

Cell biologists now have tools and knowledge to generate useful quantitative data. But how can we make sense of these data, and are we measuring the correct parameters? Moreover, how can we test hypotheses quantitatively? To answer these questions, the theory of physics is required and is essential to the future of quantitative cell biology.

Role of interfacial friction for flow instabilities in a thin polar-ordered active fluid layer

We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient Γ. Being controlled by Γ, our model provides a unified framework to describe the long-wavelength behavior of a variety of thin polar-ordered systems, ranging from wet to dry active matter and free-standing active films. Investigations of the linear instabilities around a chosen orientationally ordered uniform reference state reveal generic moving and static instabilities in the system that can depend sensitively on Γ. Based on our results, we discuss estimation of bounds on Γ in experimentally accessible systems.

Theoretical study of actin layers attachment and separation

We use the theory of active gels to study theoretically the merging and separation of two actin dense layers akin to cortical layers of animal cells. The layers bind at a distance equal to twice the thickness of a free layer, thus forming a single dense layer, similar in this sense to a lamellipodium. When that unique layer is stretched apart, it is resilient to break apart up to a critical length larger than twice the thickness of a free layer. We show that this behavior can result from the high contractile properties of the actomyosin gel due to the activity of myosin molecular motors. Furthermore, we establish that the stability of the stretched single layer is highly dependent on the properties of the gel. Indeed, the nematic order of the actin filaments along the polymerizing membranes is a destabilizing factor.

Elastic properties of epithelial cells probed by atomic force microscopy

Cellular mechanics plays a crucial role in many biological processes such as cell migration, cell growth, embryogenesis, and oncogenesis. Epithelia respond to environmental cues comprising biochemical and physical stimuli through defined changes in cell elasticity. For instance, cells can differentiate between certain properties such as viscoelasticity or topography of substrates by adapting their own elasticity and shape. A living cell is a complex viscoelastic body that not only exhibits a shell architecture composed of a membrane attached to a cytoskeleton cortex but also generates contractile forces through its actomyosin network. Here we review cellular mechanics of single cells in the context of epithelial cell layers responding to chemical and physical stimuli. This article is part of a Special Issue entitled: Mechanobiology.

Forcing cells into shape: the mechanics of actomyosin contractility

Actomyosin-mediated contractility is a highly conserved mechanism for generating mechanical stress in animal cells and underlies muscle contraction, cell migration, cell division and tissue morphogenesis. Whereas actomyosin-mediated contractility in striated muscle is well understood, the regulation of such contractility in non-muscle and smooth muscle cells is less certain. Our increased understanding of the mechanics of actomyosin arrays that lack sarcomeric organization has revealed novel modes of regulation and force transmission. This work also provides an example of how diverse mechanical behaviours at cellular scales can arise from common molecular components, underscoring the need for experiments and theories to bridge the molecular to cellular length scales.

Model for adhesion clutch explains biphasic relationship between actin flow and traction at the cell leading edge

Cell motility relies on the continuous reorganization of a dynamic actin-myosin-adhesion network at the leading edge of the cell, in order to generate protrusion at the leading edge and traction between the cell and its external environment. We analyze experimentally measured spatial distributions of actin flow, traction force, myosin density, and adhesion density in control and pharmacologically perturbed epithelial cells in order to develop a mechanical model of the actin-adhesion-myosin self-organization at the leading edge. A model in which the F-actin network is treated as a viscous gel, and adhesion clutch engagement is strengthened by myosin but weakened by actin flow, can explain the measured molecular distributions and correctly predict the spatial distributions of the actin flow and traction stress. We test the model by comparing its predictions with measurements of the actin flow and traction stress in cells with fast and slow actin polymerization rates. The model predicts how the location of the lamellipodium-lamellum boundary depends on the actin viscosity and adhesion strength. The model further predicts that the location of the lamellipodium-lamellum boundary is not very sensitive to the level of myosin contraction.

A conserved region within interferon regulatory factor 5 controls breast cancer cell migration through a cytoplasmic and transcription-independent mechanism

Background

Migration of breast cancer cells out of a duct or lobule is a prerequisite for invasion and metastasis. However, the factors controlling breast cancer cell migration are not fully elucidated. We previously found that expression of the transcription factor interferon regulatory factor 5 (IRF5) is significantly decreased as a breast lesion progresses from a non-malignant stage to ductal carcinoma in situ and is eventually lost in ~80% of invasive ductal carcinomas examined. Human in vitro and murine in vivo models of invasive breast cancer confirmed an important role for IRF5 in regulating cell motility, invasion and/or metastasis; yet, the mechanism(s) by which this occurs is not known. Since IRF5 is primarily expressed in the cytoplasm of human mammary epithelial cells, we hypothesized that IRF5 may function in a transcription-independent manner to control intrinsic cell migration.

Results

A series of IRF5 deletion mutants were tested in cell motility, invasion and migration assays. A novel, conserved 10 amino acid domain was identified that regulates mammary epithelial cell migration. This region (∆115-125) is downstream of IRF5′s DNA binding domain and therefore when absent, retains IRF5 transcription activity but loses cell migration control. An IRF5 construct with a mutated nuclear localization signal further confirmed that IRF5 controls migration in a cytoplasmic and transcription-independent manner. Candidate cytoskeletal molecules were identified in MDA-MB-231 cells to interact with IRF5 by immunoprecipitation and mass spectrometry analysis. α6-tubulin was independently confirmed to interact with endogenous IRF5 in MCF-10A cells. Alterations in F-actin bundling after staining EV- and IRF5-231 cells with phalloidin suggests that IRF5 may control cell migration/motility through its interaction with cytoskeletal molecules that contribute to the formation of F-actin networks. Last and most notably, we found that IRF5′s control of cell migration is not restricted to mammary epithelial cells but functions in other epithelial cell types suggesting a more global role for this newly identified cell migratory function of IRF5.

Conclusions

These findings are significant as they identify a new regulator of epithelial cell migration and provide specific insight into the mechanism(s) by which loss of IRF5 expression in mammary epithelial cells contributes to breast cancer metastasis.

Polarization of cells and soft objects driven by mechanical interactions: consequences for migration and chemotaxis

We study a generic model for the polarization and motility of self-propelled soft objects, biological cells, or biomimetic systems, interacting with a viscous substrate. The active forces generated by the cell on the substrate are modeled by means of oscillating force multipoles at the cell-substrate interface. Symmetry breaking and cell polarization for a range of cell sizes naturally "emerge" from long range mechanical interactions between oscillating units, mediated both by the intracellular medium and the substrate. However, the harnessing of cell polarization for motility requires substrate-mediated interactions. Motility can be optimized by adapting the oscillation frequency to the relaxation time of the system or when the substrate and cell viscosities match. Cellular noise can destroy mechanical coordination between force-generating elements within the cell, resulting in sudden changes of polarization. The persistence of the cell's motion is found to depend on the cell size and the substrate viscosity. Within such a model, chemotactic guidance of cell motion is obtained by directionally modulating the persistence of motion, rather than by modulating the instantaneous cell velocity, in a way that resembles the run and tumble chemotaxis of bacteria.

Generation of stationary and moving vortices in active polar fluids in the planar Taylor-Couette geometry

We study the dynamics of an active polar fluid in the interstitial space between two fixed coaxial cylinders. For sufficiently large expansive or contractive active stresses, the fluid presents roll instabilities of axially symmetric states leading to the spontaneous formation of vortices in the flow field. These vortices are either stationary or travel around the inner cylinder. Increasing the activity further, our numerical solutions indicate the existence of active turbulence that coexists with regular vortex solutions.