A simple force-motion relation for migrating cells revealed by multipole analysis of traction stress

Membrane to cortex attachment determines different mechanical phenotypes in LGR5+ and LGR5- colorectal cancer cells

Colorectal cancer (CRC) tumors are composed of heterogeneous and plastic cell populations, including a pool of cancer stem cells that express LGR5. Whether these distinct cell populations display different mechanical properties, and how these properties might contribute to metastasis is poorly understood. Using CRC patient derived organoids (PDOs), we find that compared to LGR5- cells, LGR5+ cancer stem cells are stiffer, adhere better to the extracellular matrix (ECM), move slower both as single cells and clusters, display higher nuclear YAP, show a higher survival rate in response to mechanical confinement, and form larger transendothelial gaps. These differences are largely explained by the downregulation of the membrane to cortex attachment proteins Ezrin/Radixin/Moesin (ERMs) in the LGR5+ cells. By analyzing single cell RNA-sequencing (scRNA-seq) expression patterns from a patient cohort, we show that this downregulation is a robust signature of colorectal tumors. Our results show that LGR5- cells display a mechanically dynamic phenotype suitable for dissemination from the primary tumor whereas LGR5+ cells display a mechanically stable and resilient phenotype suitable for extravasation and metastatic growth.

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.

Reversible Host-Guest Crosslinks in Supramolecular Hydrogels for On-Demand Mechanical Stimulation of Human Mesenchymal Stem Cells

Stem cells are regulated not only by biochemical signals but also by biophysical properties of extracellular matrix (ECM). The ECM is constantly monitored and remodeled because the fate of stem cells can be misdirected when the mechanical interaction between cells and ECM is imbalanced. A well-defined ECM model for bone marrow-derived human mesenchymal stem cells (hMSCs) based on supramolecular hydrogels containing reversible host-guest crosslinks is fabricated. The stiffness (Young's modulus E) of the hydrogels can be switched reversibly by altering the concentration of non-cytotoxic, free guest molecules dissolved in the culture medium. Fine-adjustment of substrate stiffness enables the authors to determine the critical stiffness level E* at which hMSCs turn the mechano-sensory machinery on or off. Next, the substrate stiffness across E* is switched and the dynamic adaptation characteristics such as morphology, traction force, and YAP/TAZ signaling of hMSCs are monitored. These data demonstrate the instantaneous switching of traction force, which is followed by YAP/TAZ signaling and morphological adaptation. Periodical switching of the substrate stiffness across E* proves that frequent applications of mechanical stimuli drastically suppress hMSC proliferation. Mechanical stimulation across E* level using dynamic hydrogels is a promising strategy for the on-demand control of hMSC transcription and proliferation.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

2.5D Traction Force Microscopy: Imaging three-dimensional cell forces at interfaces and biological applications

The forces that cells, tissues, and organisms exert on the surface of a soft substrate can be measured using Traction Force Microscopy (TFM), an important and well-established technique in Mechanobiology. The usual TFM technique (two-dimensional, 2D TFM) treats only the in-plane component of the traction forces and omits the out-of-plane forces at the substrate interfaces (2.5D) that turn out to be important in many biological processes such as tissue migration and tumour invasion. Here, we review the imaging, material, and analytical tools to perform "2.5D TFM" and explain how they are different from 2D TFM. Challenges in 2.5D TFM arise primarily from the need to work with a lower imaging resolution in the z-direction, track fiducial markers in three-dimensions, and reliably and efficiently reconstruct mechanical stress from substrate deformation fields. We also discuss how 2.5D TFM can be used to image, map, and understand the complete force vectors in various important biological events of various length-scales happening at two-dimensional interfaces, including focal adhesions forces, cell diapedesis across tissue monolayers, the formation of three-dimensional tissue structures, and the locomotion of large multicellular organisms. We close with future perspectives including the use of new materials, imaging and machine learning techniques to continuously improve the 2.5D TFM in terms of imaging resolution, speed, and faithfulness of the force reconstruction procedure.

Mechanochemical subcellular-element model of crawling cells

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Unified multiscale theory of cellular mechanical adaptations to substrate stiffness

Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.

The role of cellular traction forces in deciphering nuclear mechanics

Cellular forces exerted on the extracellular matrix (ECM) during adhesion and migration under physiological and pathological conditions regulate not only the overall cell morphology but also nuclear deformation. Nuclear deformation can alter gene expression, integrity of the nuclear envelope, nucleus-cytoskeletal connection, chromatin architecture, and, in some cases, DNA damage responses. Although nuclear deformation is caused by the transfer of forces from the ECM to the nucleus, the role of intracellular organelles in force transfer remains unclear and a challenging area of study. To elucidate nuclear mechanics, various factors such as appropriate biomaterial properties, processing route, cellular force measurement technique, and micromanipulation of nuclear forces must be understood. In the initial phase of this review, we focused on various engineered biomaterials (natural and synthetic extracellular matrices) and their manufacturing routes along with the properties required to mimic the tumor microenvironment. Furthermore, we discussed the principle of tools used to measure the cellular traction force generated during cell adhesion and migration, followed by recently developed techniques to gauge nuclear mechanics. In the last phase of this review, we outlined the principle of traction force microscopy (TFM), challenges in the remodeling of traction forces, microbead displacement tracking algorithm, data transformation from bead movement, and extension of 2-dimensional TFM to multiscale TFM.

3D single cell migration driven by temporal correlation between oscillating force dipoles

Directional cell locomotion requires symmetry breaking between the front and rear of the cell. In some cells, symmetry breaking manifests itself in a directional flow of actin from the front to the rear of the cell. Many cells, especially in physiological 3D matrices do not show such coherent actin dynamics and present seemingly competing protrusion/retraction dynamics at their front and back. How symmetry breaking manifests itself for such cells is therefore elusive. We take inspiration from the scallop theorem proposed by Purcell for micro-swimmers in Newtonian fluids: self-propelled objects undergoing persistent motion at low Reynolds number must follow a cycle of shape changes that breaks temporal symmetry. We report similar observations for cells crawling in 3D. We quantified cell motion using a combination of 3D live cell imaging, visualization of the matrix displacement and a minimal model with multipolar expansion. We show that our cells embedded in a 3D matrix form myosin-driven force dipoles at both sides of the nucleus, that locally and periodically pinch the matrix. The existence of a phase shift between the two dipoles is required for directed cell motion which manifests itself as cycles with finite area in the dipole-quadrupole diagram, a formal equivalence to the Purcell cycle. We confirm this mechanism by triggering local dipolar contractions with a laser. This leads to directed motion. Our study reveals that these cells control their motility by synchronizing dipolar forces distributed at front and back. This result opens new strategies to externally control cell motion as well as for the design of micro-crawlers.

Avoiding tensional equilibrium in cells migrating on a matrix with cell-scale stiffness-heterogeneity

Intracellular stresses affect various cell functions, including proliferation, differentiation and movement, which are dynamically modulated in migrating cells through continuous cell-shaping and remodeling of the cytoskeletal architecture induced by spatiotemporal interactions with extracellular matrix stiffness. When cells migrate on a matrix with cell-scale stiffness-heterogeneity, which is a common situation in living tissues, what intracellular stress dynamics (ISD) emerge? In this study, to explore this issue, finite element method-based traction force microscopy was applied to cells migrating on microelastically patterned gels. Two model systems of microelastically patterned gels (stiff/soft stripe and stiff triangular patterns) were designed to characterize the effects of a spatial constraint on cell-shaping and of the presence of different types of cues to induce competing cellular taxis (usual and reverse durotaxis) on the ISD, respectively. As the main result, the prolonged fluctuation of traction stress on a whole-cell scale was markedly enhanced on single cell-size triangular stiff patterns compared with homogeneous gels. Such ISD enhancement was found to be derived from the interplay between the nomadic migration of cells to regions with different degrees of stiffness and domain shape-dependent traction force dynamics, which should be an essential factor for keeping cells far from tensional equilibrium.

Durotaxis: The Hard Path from In Vitro to In Vivo

Durotaxis, the process by which cells follow gradients of extracellular mechanical stiffness, has been proposed as a mechanism driving directed migration. Despite the lack of evidence for its existence in vivo, durotaxis has become an active field of research, focusing on the mechanism by which cells respond to mechanical stimuli from the environment. In this review, we describe the technical and conceptual advances in the study of durotaxis in vitro, discuss to what extent the evidence suggests durotaxis may occur in vivo, and emphasize the urgent need for in vivo demonstration of durotaxis.

Traction Forces Control Cell-Edge Dynamics and Mediate Distance Sensitivity during Cell Polarization

Traction forces are generated by cellular actin-myosin system and transmitted to the environment through adhesions. They are believed to drive cell motion, shape changes, and extracellular matrix remodeling [1-3]. However, most of the traction force analysis has been performed on stationary cells, investigating forces at the level of individual focal adhesions or linking them to static cell parameters, such as area and edge curvature [4-10]. It is not well understood how traction forces are related to shape changes and motion, e.g., forces were reported to either increase or drop prior to cell retraction [11-15]. Here, we analyze the dynamics of traction forces during the protrusion-retraction cycle of polarizing fish epidermal keratocytes and find that forces fluctuate together with the cycle, increasing during protrusion and reaching maximum at the beginning of retraction. We relate force dynamics to the recently discovered phenomenological rule [16] that governs cell-edge behavior during keratocyte polarization: both traction forces and probability of switch from protrusion to retraction increase with the distance from the cell center. Diminishing forces with cell contractility inhibitor leads to decreased edge fluctuations and abnormal polarization, although externally applied force can induce protrusion-retraction switch. These results suggest that forces mediate distance sensitivity of the edge dynamics and organize cell-edge behavior, leading to spontaneous polarization. Actin flow rate did not exhibit the same distance dependence as traction stress, arguing against its role in organizing edge dynamics. Finally, using a simple model of actin-myosin network, we show that force-distance relationship might be an emergent feature of such networks.

Generation of fluorescent cell-derived-matrix to study 3D cell migration

Cell migration is involved in key phenomena in biology, ranging from development to cancer. Fibroblasts move between organs in 3D polymeric networks. So far, motile cells were mainly tracked in vitro on Petri dishes or on coverslips, i.e., 2D flat surfaces, which made the extrapolation to 3D physiological environments difficult. We therefore prepared 3D Cell Derived Matrices (CDM) with specific characteristics with the goal of extracting the main readouts required to measure and characterize cell motion: cell specific matrix deformation through the tracking of fluorescent fibronectin within CDM, focal contacts as the cell anchor and acto-myosin cytoskeleton which applies cellular forces. We report our method for generating this assay of physiological-like gel with relevant readouts together with its potential impact in explaining cell motility in vivo.

The Interplay Between Cell-Cell and Cell-Matrix Forces Regulates Cell Migration Dynamics

Cells in vivo encounter and exert forces as they interact with the extracellular matrix (ECM) and neighboring cells during migration. These mechanical forces play crucial roles in regulating cell migratory behaviors. Although a variety of studies have focused on describing single-cell or the collective cell migration behaviors, a fully mechanistic understanding of how the cell-cell (intercellular) and cell-ECM (extracellular) traction forces individually and cooperatively regulate single-cell migration and coordinate multicellular movement in a cellular monolayer is still lacking. Here, we developed an integrated experimental and analytical system to examine both the intercellular and extracellular traction forces acting on individual cells within an endothelial cell colony as well as their roles in guiding cell migratory behaviors (i.e., cell translation and rotation). Combined with force, multipole, and moment analysis, our results revealed that traction force dominates in regulating cell active translation, whereas intercellular force actively modulates cell rotation. Our findings advance the understanding of the intricacies of cell-cell and cell-ECM forces in regulating cellular migratory behaviors that occur during the monolayer development and may yield deeper insights into the single-cell dynamic behaviors during tissue development, embryogenesis, and wound healing.

A mechanochromic luminescent material with aggregation-induced emission: Application for pressure sensing and mapping

In this study, we report a new compound, (E)-4-(((2-hydroxynaphthalen-1-yl)methylene)amino)-3-methylbenzoic acid (HNMB), which shows aggregation-induced emission property as well as intramolecular charge transfer (ICT) nature. In addition, it exhibits unique mechanochromic luminescence (MCL). The HNMB solid powder emits strong emission but shows quenching effect together with bathochromic-shift after grinding, suggesting a high contrast ratio up to 1420%. Through crystallographic analysis, the relationship between MCL nature and molecular packing mode is verified: Molecules in crystalline phase adopt the J-type coupling based on less overlapped π⋯π stacking, in which multiple intermolecular interactions mainly including C-H⋯π, C-H⋯O and hydrogen bonding, help to stabilize such packing mode. When these interactions are destructed by mechanical force, the packing would be disassembled, activating the MCL behavior. Such working mechanism only needs weak external force capable of destructing intermolecular interactions, rendering the MCL material highly sensitive to pressure. As a practical application, a film sensor for pressure detection is designed based on HNMB, which gives a linear relation between the emission intensity and the external pressure in a lower range. The detection limit of the film sensor is 27.24 Mpa, suggesting high sensitivity. In addition, pressure mapping with high contrast ratio is obtained by surface plot, making this pressure sensor a reliable candidate to be instrumented for various applications.

Spontaneous spatiotemporal ordering of shape oscillations enhances cell migration

The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence collective properties. Here we demonstrate, using numerical simulations, that the interplay of directed motion, shape oscillations, and excluded volume enables cells to locally "synchronize" their motion and thus enhance collective migration. Our model captures elongation and contraction of crawling ameboid cells controlled by an internal clock with a fixed period, mimicking the internal cycle of biological cells. We show that shape oscillations are crucial for local rearrangements that induce ordering of neighboring cells according to their internal clocks even in the absence of signaling and regularization. Our findings reveal a novel, purely physical mechanism through which the internal dynamics of cells influences their collective behavior, which is distinct from well known mechanisms like chemotaxis, cell division, and cell-cell adhesion.

Substrate mediated interaction between pairs of keratocytes: Multipole traction force models describe their migratory behavior

A series of traction force microscopy experiments involving pairs of keratocytes migrating on compliant substrates were analyzed. We observed several instances where keratocytes that are about to collide turn before they touch. We term this phenomenon collision avoidance behavior and we propose that the turning is caused by the substrate mediated elastic interactions between the cells. A multipole analysis of the cell traction reveals that the left-right symmetry of the keratocyte traction pattern is broken during collision avoidance events. The analysis further shows that the cell migration direction reorients before the principal traction dipoles as the cells turn. Linear elasticity theory is used to derive the cell-cell interaction energy between pairs of keratocytes. The traction force applied by each cell is modeled as a two points (dipole) or three points (tripod) force model. We show that both models predict that cells that are about to collide in a head-on manner will turn before touching. The tripod model is further able to account for the quadrupole components of the traction force profile that we observed experimentally. Also, the tripod model proposes a mechanism that may explain why cells tend to scatter with a finite angle after a collision avoidance event. A relationship between the scattering angle and the traction force quadrupole moment is also established. Dynamical simulations of migrating model cells are further used to explain the emergence of other cell pair trajectories that we observed experimentally.

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.

Combined atomic force microscopy (AFM) and traction force microscopy (TFM) reveals a correlation between viscoelastic material properties and contractile prestress of living cells

Living cells exhibit a complex mechanical behavior, whose underlying mechanisms are still largely unknown. Emerging from the molecular structure and dynamics of the cytoskeleton, the mechanical behavior comprises "passive" viscoelastic material properties and "active" contractile prestress. To directly investigate the connection between these quantities at the single-cell level, we here present the combination of atomic force microscopy (AFM) with traction force microscopy (TFM). With this combination, we simultaneously measure viscoelastic material parameters (stiffness, fluidity) and contractile prestress of adherent fibroblast and epithelial cells. Although stiffness, fluidity, and contractile prestress greatly vary within a cell population, they are highly correlated: stiffer cells have a lower fluidity and a larger prestress than softer cells. We show that viscoelastic material properties and contractile prestress are both governed by the activity of the actomyosin machinery. Our results underline the connection between a cell's viscoelastic material properties and its contractile prestress and their importance in cell mechanics.

Biological Tissues as Active Nematic Liquid Crystals

Live tissues can self-organize and be described as active materials composed of cells that generate active stresses through continuous injection of energy. In vitro reconstituted molecular networks, as well as single-cell cytoskeletons show that their filamentous structures can portray nematic liquid crystalline properties and can promote nonequilibrium processes induced by active processes at the microscale. The appearance of collective patterns, the formation of topological singularities, and spontaneous phase transition within the cell cytoskeleton are emergent properties that drive cellular functions. More integrated systems such as tissues have cells that can be seen as coarse-grained active nematic particles and their interaction can dictate many important tissue processes such as epithelial cell extrusion and migration as observed in vitro and in vivo. Here, a brief introduction to the concept of active nematics is provided, and the main focus is on the use of this framework in the systematic study of predominantly 2D tissue architectures and dynamics in vitro. In addition how the nematic state is important in tissue behavior, such as epithelial expansion, tissue homeostasis, and the atherosclerosis disease state, is discussed. Finally, how the nematic organization of cells can be controlled in vitro for tissue engineering purposes is briefly discussed.

Sensing of substratum rigidity and directional migration by fast-crawling cells

Living cells sense the mechanical properties of their surrounding environment and respond accordingly. Crawling cells detect the rigidity of their substratum and migrate in certain directions. They can be classified into two categories: slow-moving and fast-moving cell types. Slow-moving cell types, such as fibroblasts, smooth muscle cells, mesenchymal stem cells, etc., move toward rigid areas on the substratum in response to a rigidity gradient. However, there is not much information on rigidity sensing in fast-moving cell types whose size is ∼10 μm and migration velocity is ∼10 μm/min. In this study, we used both isotropic substrata with different rigidities and an anisotropic substratum that is rigid on the x axis but soft on the y axis to demonstrate rigidity sensing by fast-moving Dictyostelium cells and neutrophil-like differentiated HL-60 cells. Dictyostelium cells exerted larger traction forces on a more rigid isotropic substratum. Dictyostelium cells and HL-60 cells migrated in the "soft" direction on the anisotropic substratum, although myosin II-null Dictyostelium cells migrated in random directions, indicating that rigidity sensing of fast-moving cell types differs from that of slow types and is induced by a myosin II-related process.

Persistent random deformation model of cells crawling on a gel surface

In general, cells move on a substrate through extension and contraction of the cell body. Though cell movement should be explained by taking into account the effect of such shape fluctuations, past approaches to formulate cell-crawling have not sufficiently quantified the relationship between cell movement (velocity and trajectory) and shape fluctuations based on experimental data regarding actual shaping dynamics. To clarify this relationship, we experimentally characterized cell-crawling in terms of shape fluctuations, especially extension and contraction, by using an elasticity-tunable gel substrate to modulate cell shape. As a result, an amoeboid swimmer-like relation was found to arise between the cell velocity and cell-shape dynamics. To formulate this experimentally-obtained relationship between cell movement and shaping dynamics, we established a persistent random deformation (PRD) model based on equations of a deformable self-propelled particle adopting an amoeboid swimmer-like velocity-shape relationship. The PRD model successfully explains the statistical properties of velocity, trajectory and shaping dynamics of the cells including back-and-forth motion, because the velocity equation exhibits time-reverse symmetry, which is essentially different from previous models. We discuss the possible application of this model to classify the phenotype of cell migration based on the characteristic relation between movement and shaping dynamics.

Holographic Traction Force Microscopy

Traction Force Microscopy (TFM) computes the forces exerted at the surface of an elastic material by measuring induced deformations in volume. It is used to determine the pattern of the adhesion forces exerted by cells or by cellular assemblies grown onto a soft deformable substrate. Typically, colloidal particles are dispersed in the substrate and their displacement is monitored by fluorescent microscopy. As with any other fluorescent techniques, the accuracy in measuring a particule's position is ultimately limited by the number of evaluated fluorescent photons. Here, we present a TFM technique based on the detection of probe particle displacements by holographic tracking microscopy. We show that nanometer scale resolutions of the particle displacements can be obtained and determine the maximum volume fraction of markers in the substrate. We demonstrate the feasibility of the technique experimentally and measure the three-dimensional force fields exerted by colorectal cancer cells cultivated onto a polyacrylamide gel substrate.

The role of talin2 in breast cancer tumorigenesis and metastasis

Recent studies show that talin2 has a higher affinity to β-integrin tails and is indispensable for traction force generation and cell invasion. However, its roles in cell migration, cancer cell metastasis and tumorigenesis remain to be determined. Here, we used MDA-MB-231 human breast cancer cells as a model to define the roles of talin2 in cell migration, invasion, metastasis and tumorigenesis. We show here that talin2 knockdown (KD) inhibited cell migration and focal adhesion dynamics, a key step in cell migration, and that talin2 knockout (KO) inhibited cell invasion and traction force generation, the latter is crucial for cell invasion. Re-expression of talin2^WT in talin2-KO cells restored traction force generation and cell invasion, but that of talin2^S339C, a β-integrin-binding deficient mutant, did not. Moreover, talin2 KO (or KD) suppressed tumorigenesis and metastasis in mouse xenograft models. However, surprisingly, re-expression of talin2^WT in talin2-KO cells did not rescue tumorigenesis. Thus, talin2 is required for breast cancer cell migration, invasion, metastasis and tumorigenesis, although exogenous expression of high levels of talin2 could inhibit tumorigenesis.

Swinging motion of active deformable particles in Poiseuille flow

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Force-induced elastic matrix-mediated interactions in the presence of a rigid wall

We consider a soft elastic matrix that contains particulate inclusions and is bounded by a rigid wall, e.g., the substrate. Such a situation arises in elastic composite materials. They may serve as soft actuators when forces are imposed on or induced between the embedded particles. We investigate how the presence of the rigid wall affects the interactions between the inclusions. First, for no-slip boundary conditions, we transfer Blake's derivation of a corresponding Green's function from low-Reynolds-number hydrodynamics to the linearly elastic case. Then, we list the general expressions to describe the situation for point-like particles in the presence of no-slip and free-slip surface conditions. To compare the effect of the different surface conditions to each other and to the bulk behavior, we address the example situation of pairwise interactions between two embedded particles. The axis through both particle centers is either aligned parallel or perpendicular to the surface. Our results suggest that walls with free-slip surface conditions are preferred when they serve as substrates for soft actuators made from elastic composite materials. As we further demonstrate, the presence of a rigid wall can qualitatively change the interactions between the inclusions. In effect, it can switch attractive interactions into repulsive ones (and vice versa). It should be straightforward to observe the effects in future experiments and to combine our results, e.g., with the modeling of biological cells and tissue on rigid surfaces.

Oscillatory motion of a camphor grain in a one-dimensional finite region

The motion of a self-propelled particle is affected by its surroundings, such as boundaries or external fields. In this paper, we investigated the bifurcation of the motion of a camphor grain, as a simple actual self-propelled system, confined in a one-dimensional finite region. A camphor grain exhibits oscillatory motion or remains at rest around the center position in a one-dimensional finite water channel, depending on the length of the water channel and the resistance coefficient. A mathematical model including the boundary effect is analytically reduced to an ordinary differential equation. Linear stability analysis reveals that the Hopf bifurcation occurs, reflecting the symmetry of the system.

Mean deformation metrics for quantifying 3D cell-matrix interactions without requiring information about matrix material properties

Mechanobiology relates cellular processes to mechanical signals, such as determining the effect of variations in matrix stiffness with cell tractions. Cell traction recorded via traction force microscopy (TFM) commonly takes place on materials such as polyacrylamide- and polyethylene glycol-based gels. Such experiments remain limited in physiological relevance because cells natively migrate within complex tissue microenvironments that are spatially heterogeneous and hierarchical. Yet, TFM requires determination of the matrix constitutive law (stress-strain relationship), which is not always readily available. In addition, the currently achievable displacement resolution limits the accuracy of TFM for relatively small cells. To overcome these limitations, and increase the physiological relevance of in vitro experimental design, we present a new approach and a set of associated biomechanical signatures that are based purely on measurements of the matrix's displacements without requiring any knowledge of its constitutive laws. We show that our mean deformation metrics (MDM) approach can provide significant biophysical information without the need to explicitly determine cell tractions. In the process of demonstrating the use of our MDM approach, we succeeded in expanding the capability of our displacement measurement technique such that it can now measure the 3D deformations around relatively small cells (∼10 micrometers), such as neutrophils. Furthermore, we also report previously unseen deformation patterns generated by motile neutrophils in 3D collagen gels.

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.

Traction force and tension fluctuations in growing axons

Actively generated mechanical forces play a central role in axon growth and guidance, but the mechanisms that underly force generation and regulation in growing axons remain poorly understood. We report measurements of the dynamics of traction stresses from growth cones of actively advancing axons from postnatal rat DRG neurons. By tracking the movement of the growth cone and analyzing the traction stress field from a reference frame that moves with it, we are able to show that there is a clear and consistent average stress field that underlies the complex spatial stresses present at any one time. The average stress field has strong maxima on the sides of the growth cone, directed inward toward the growth cone neck. This pattern represents a contractile stress contained within the growth cone, and a net force that is balanced by the axon tension. Using high time-resolution measurements of the growth cone traction stresses, we show that the stress field is composed of fluctuating local stress peaks, with a large number peaks that live for a short time, a population of peaks whose lifetime distribution follows an exponential decay, and a small number of very long-lived peaks. We show that the high time-resolution data also reveal that the tension appears to vary randomly over short time scales, roughly consistent with the lifetime of the stress peaks, suggesting that the tension fluctuations originate from stochastic adhesion dynamics.

Force transmission during adhesion-independent migration

When cells move using integrin-based focal adhesions, they pull in the direction of motion with large, ~100 Pa, stresses that contract the substrate1. Integrin-mediated adhesions, however, are not required for in vivo confined migration2. During focal adhesion-free migration, the transmission of propelling forces, and their magnitude and orientation, are not understood. Here, we combine theory and experiments to investigate the forces involved in adhesion-free migration. Using a non-adherent blebbing cell line as a model, we show that actin cortex flows drive cell movement via non-specific substrate friction. Strikingly, the forces propelling the cell forward are several orders of magnitude lower than during focal adhesion-based motility. Moreover, the force distribution in adhesion-free migration is inverted: it acts to expand, rather than contract, the substrate in the direction of motion. This fundamentally different mode of force transmission may have implications for cell-cell and cell-substrate interactions during migration in vivo.

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.

Collision dynamics of traveling bands in systems of deformable self-propelled particles

We study the soliton-like character of traveling bands in systems of interacting deformable self-propelled particles in two dimensions. The collision dynamics of the model in which migration velocity increases with increasing local density is investigated numerically by changing the relaxation rate of deformations. The bands are unstable upon head-on collisions for larger relaxation rates. This clearly indicates that deformability plays a crucial role of the soliton-like behavior.