Cellular Contraction and Polarization Drive Collective Cellular Motion

Relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer

The relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer are currently unknown. Ten years ago, a method known as monolayer stress microscopy (MSM) was suggested from which intercellular stresses could be computed for a given traction field. The core assumption of MSM is that intercellular stresses within the monolayer obey a linear and passive constitutive law. Examples of these include a Hookean solid (an elastic sheet) or a Newtonian fluid (thin fluid film), which imply a specific relation between the displacements or velocities and the tractions. Due to the lack of independently measured intercellular stresses, a direct validation of the 2D stresses predicted by a linear passive MSM model is presently not possible. An alternative approach, which we give here and denote as the Stokes method, is based on simultaneous measurements of the monolayer velocity field and the cell-substrate tractions. Using the same assumptions as those underlying MSM, namely, a linear and passive constitutive law, the velocity field suffices to compute tractions, from which we can then compare with those measured by traction force microscopy. We find that the calculated tractions and measured tractions are uncorrelated. Since the classical MSM and the Stokes approach both depend on the linear and passive constitutive law, it follows that some serious modification of the underling rheology is needed. One possible modification is the inclusion of an active force. In the special case where this is additive to the linear passive rheology, we have a new relationship between the active force density and the measured velocity (or displacement) field and tractions, which by Newton's laws, must be obeyed.

A theoretical model of collective cell polarization and alignment

Collective cell polarization and alignment play important roles in tissue morphogenesis, wound healing and cancer metastasis. How cells sense the direction and position in these processes, however, has not been fully understood. Here we construct a theoretical model based on describing cell layer as a nemato-elastic medium, by which the cell polarization, cell alignment and cell active contraction are explicitly expressed as functions of components of the nematic order parameter. To determine the order parameter we derive two sets of governing equations, one for the force equilibrium of the system, and the other for the minimization of the system's free energy including the energy of cell polarization and alignment. By solving these coupled governing equations, we can predict the effects of substrate stiffness, geometries of cell layers, external forces and myosin activity on the direction- and position-dependent cell aspect ratio and cell orientation. Moreover, the axisymmetric problem with cells on a ring-like pattern is solved analytically, and the analytical solution for cell aspect ratio are governed by parameter groups which include the stiffness of the cell and the substrate, the strength of myosin activity and the external forces. Our predictions of the cell aspect ratio and orientation are generally comparable to experimental observations. These results show that the pattern of cell polarization is determined by the anisotropic degree of active contractile stress, and suggest a stress-driven polarization mechanism that enables cells to sense their spatial positions to develop direction- and position-dependent behavior. This, in turn, sheds light on the ways to control pattern formation in tissue engineering for potential biomedical applications.

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.

Active nematics with anisotropic friction: the decisive role of the flow aligning parameter

We use continuum simulations to study the impact of anisotropic hydrodynamic friction on the emergent flows of active nematics. We show that, depending on whether the active particles align with or tumble in their collectively self-induced flows, anisotropic friction can result in markedly different patterns of motion. In a flow-aligning regime and at high anisotropic friction, the otherwise chaotic flows are streamlined into flow lanes with alternating directions, reproducing the experimental laning state that has been obtained by interfacing microtubule-motor protein mixtures with smectic liquid crystals. Within a flow-tumbling regime, however, we find that no such laning state is possible. Instead, the synergistic effects of friction anisotropy and flow tumbling can lead to the emergence of bound pairs of topological defects that align at an angle to the easy flow direction and navigate together throughout the domain. In addition to confirming the mechanism behind the laning states observed in experiments, our findings emphasise the role of the flow aligning parameter in the dynamics of active nematics.

Oriented Active Solids

We present a complete analysis of the linearized dynamics of active solids with uniaxial orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include a purely active response of two-dimensional orientationally ordered solids to shear, the possibility of stable active solids with quasi-long-range order in two dimensions and long-range order in three dimensions, generic instability of the solid for one sign of active forcing, and the instability of the uniaxially ordered phase in momentum-conserved systems for large active forcing irrespective of its sign.

Two-Dimensional Culture Systems to Enable Mechanics-Based Assays for Stem Cell-Derived Cardiomyocytes

Well-controlled 2D cell culture systems advance basic investigations in cell biology and provide innovative platforms for drug development, toxicity testing, and diagnostic assays. These cell culture systems have become more advanced in order to provide and to quantify the appropriate biomechanical and biochemical cues that mimic the milieu of conditions present in vivo. Here we present an innovative 2D cell culture system to investigate human stem cell-derived cardiomyocytes, the muscle cells of the heart responsible for pumping blood throughout the body. We designed our 2D cell culture platform to control intracellular features to produce adult-like cardiomyocyte organization with connectivity and anisotropic conduction comparable to the native heart, and combined it with optical microscopy to quantify cell-cell and cell-substrate mechanical interactions. We show the measurement of forces and displacements that occur within individual cells, between neighboring cells, and between cells and their surrounding matrix. This system has broad potential to expand our understanding of tissue physiology, with particular advantages for the study of the mechanically active heart. Furthermore, this technique should prove valuable in screening potential drugs for efficacy and testing for toxicity.

Silica-Coated Magnetic Nanoparticles Decrease Human Bone Marrow-Derived Mesenchymal Stem Cell Migratory Activity by Reducing Membrane Fluidity and Impairing Focal Adhesion

For stem cell-based therapies, the fate and distribution of stem cells should be traced using non-invasive or histological methods and a nanomaterial-based labelling agent. However, evaluation of the biophysical effects and related biological functions of nanomaterials in stem cells remains challenging. Here, we aimed to investigate the biophysical effects of nanomaterials on stem cells, including those on membrane fluidity, using total internal reflection fluorescence microscopy, and traction force, using micropillars of human bone marrow-derived mesenchymal stem cells (hBM-MSCs) labelled with silica-coated magnetic nanoparticles incorporating rhodamine B isothiocyanate (MNPs@SiO₂(RITC)). Furthermore, to evaluate the biological functions related to these biophysical changes, we assessed the cell viability, reactive oxygen species (ROS) generation, intracellular cytoskeleton, and the migratory activity of MNPs@SiO₂(RITC)-treated hBM-MSCs. Compared to that in the control, cell viability decreased by 10% and intracellular ROS increased by 2-fold due to the induction of 20% higher peroxidized lipid in hBM-MSCs treated with 1.0 µg/µL MNPs@SiO₂(RITC). Membrane fluidity was reduced by MNPs@SiO₂(RITC)-induced lipid oxidation in a concentration-dependent manner. In addition, cell shrinkage with abnormal formation of focal adhesions and ~30% decreased total traction force were observed in cells treated with 1.0 µg/µL MNPs@SiO₂(RITC) without specific interaction between MNPs@SiO₂(RITC) and cytoskeletal proteins. Furthermore, the migratory activity of hBM-MSCs, which was highly related to membrane fluidity and cytoskeletal abnormality, decreased significantly after MNPs@SiO₂(RITC) treatment. These observations indicated that the migratory activity of hBM-MSCs was impaired by MNPs@SiO₂(RITC) treatment due to changes in stem-cell biophysical properties and related biological functions, highlighting the important mechanisms via which nanoparticles impair migration of hBM-MSCs. Our findings indicate that nanoparticles used for stem cell trafficking or clinical applications should be labelled using optimal nanoparticle concentrations to preserve hBM-MSC migratory activity and ensure successful outcomes following stem cell localisation.

Traction Microscopy Integrated with Microfluidics for Chemotactic Collective Migration

Cells change migration patterns in response to chemical stimuli, including the gradients of the stimuli. Cellular migration in the direction of a chemical gradient, known as chemotaxis, plays an important role in development, the immune response, wound healing, and cancer metastasis. While chemotaxis modulates the migration of single cells as well as collections of cells in vivo, in vitro research focuses on single-cell chemotaxis, partly due to the lack of the proper experimental tools. To fill that gap, described here is a unique experimental system that combines microfluidics and micropatterning to demonstrate the effects of chemical gradients on collective cell migration. Furthermore, traction microscopy and monolayer stress microscopy are incorporated into the system to characterize changes in cellular force on the substrate as well as between neighboring cells. As proof-of-concept, the migration of micropatterned circular islands of Madin-Darby canine kidney (MDCK) cells is tested under a gradient of hepatocyte growth factor (HGF), a known scattering factor. It is found that cells located near the higher concentration of HGF migrate faster than those on the opposite side within a cell island. Within the same island, cellular traction is similar on both sides, but intercellular stress is much lower on the side of higher HGF concentration. This novel experimental system can provide new opportunities to studying the mechanics of chemotactic migration by cellular collectives.

Jamming state transition and collective cell migration

Jamming state transition has been used in literature to describe migrating-to-resting cell state transition during collective cell migration without proper rheological confirmation. Yield stress often has been used as an indicator of a jamming state. Yield stress points to the liquid-to-solid state transition, but not a priori to jamming state transition. Various solid states such as elastic solid and viscoelastic solids can be considered in the context of their ability to relax. The relaxation time for (1) an elastic solid tends to zero, (2) Kelvin-Voigt viscoelastic solid is finite, and (3) jamming state tends to infinity.

In order to clarify the meaning of jamming state from the rheological standpoint we formulated the constitutive model of this state based on following conditions (1) migration of the system constituents is much damped such that the diffusion coefficient tends to zero, (2) relaxation time tends to infinity, (3) storage and loss moduli satisfy the condition G^′(ω)/G^"(ω) = const > 1. Jamming state represents the non-linear viscoelastic solid state. The main characteristic of this state is that the system cannot relax.

Jamming state transition of multicellular systems caused by collective cell migration is discussed on a model system such as cell aggregate rounding after uni-axial compression between parallel plates based on the data from the literature. Cell aggregate rounding occurs via successive relaxation cycles. Every cycle corresponds to a different scenario of cell migration. Three scenarios were established depending on the magnitude of mechanical and biochemical perturbations (1) ordered scenario with reduced perturbations corresponds to the case that most of the cells migrate, (2) disordered scenario corresponds to the case that some cell groups migrate while the others (at the same time) stay in resting state (corresponds to medium perturbations), and (3) highly suppressed cell migration under large perturbations corresponds to the viscoelastic solid under jamming state. If cells reach the jamming state in one cycle, they are able to overcome this undesirable state and start migrating again in the next cycle by achieving the first or second scenarios again.

Sustained Oscillations of Epithelial Cell Sheets

Morphological changes during development, tissue repair, and disease largely rely on coordinated cell movements and are controlled by the tissue environment. Epithelial cell sheets are often subjected to large-scale deformation during tissue formation. The active mechanical environment in which epithelial cells operate have the ability to promote collective oscillations, but how these cellular movements are generated and relate to collective migration remains unclear. Here, combining in vitro experiments and computational modeling, we describe a form of collective oscillations in confined epithelial tissues in which the oscillatory motion is the dominant contribution to the cellular movements. We show that epithelial cells exhibit large-scale coherent oscillations when constrained within micropatterns of varying shapes and sizes and that their period and amplitude are set by the smallest confinement dimension. Using molecular perturbations, we then demonstrate that force transmission at cell-cell junctions and its coupling to cell polarity are pivotal for the generation of these collective movements. We find that the resulting tissue deformations are sufficient to trigger osillatory mechanotransduction of YAP within cells, potentially affecting a wide range of cellular processes.

Functional Epithelium Remodeling in Response to Applied Stress under In Vitro Conditions

Mathematical modeling is often used in tissue engineering in order to overcome one of its major challenges: transformation of complex biological and rheological behaviors of cells and tissue in a mathematically predictive and physically manipulative engineering process. The successive accomplishment of this task will greatly help in quantifying and optimizing clinical application of the tissue engineering products. One of the problems emerging in this area is the relation between resting and migrating cell groups, as well as between different configurations of migrating cells and viscoelasticity. A deeper comprehension of the relation between various configurations of migrating cells and viscoelasticity at the supracellular level represents the prerequisite for optimization of the performance of the artificial epithelium. Since resting and migrating cell groups have a considerable difference in stiffness, a change in their mutual volume ratio and distribution may affect the viscoelasticity of multicellular surfaces. If those cell groups are treated as different phases, then an analogous model may be applied to represent such systems. In this work, a two-step Eyring model is developed in order to demonstrate the main mechanical and biochemical factors that influence configurations of migrating cells. This model could be also used for considering the long-time cell rearrangement under various types of applied stress. The results of this theoretical analysis point out the cause-consequence relationship between the configuration of migrating cells and rheological behavior of multicellular surfaces. Configuration of migrating cells is influenced by mechanical and biochemical perturbations, difficult to measure experimentally, which lead to uncorrelated motility. Uncorrelated motility results in (1) decrease of the volume fraction of migrating cells, (2) change of their configuration, and (3) softening of multicellular surfaces.

Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods

Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is associated with some biomechanical particularities such as restructuring of extracellular matrix (ECM), stress and force distribution profiles, and reorganization of the cytoskeleton. Therefore, the phenomenon could be understood by an in-depth study of cells' behavior determinants, including but not limited to mechanical cues from the environment and from fellow "travelers". This review article aims to cover the recent development of experimental and computational methods for studying the biomechanics of collective cell migration during cancer progression and invasion. We also summarized the tested hypotheses regarding the mechanism underlying collective cell migration enabled by these methods. Together, the paper enables a broad overview on the methods and tools currently available to unravel the biophysical mechanisms pertinent to cell collective migration as well as providing perspectives on future development toward eventually deciphering the key mechanisms behind the most lethal feature of cancer.

Confinement-Induced Transition between Wavelike Collective Cell Migration Modes

The structural and functional organization of biological tissues relies on the intricate interplay between chemical and mechanical signaling. Whereas the role of constant and transient mechanical perturbations is generally accepted, several studies recently highlighted the existence of long-range mechanical excitations (i.e., waves) at the supracellular level. Here, we confine epithelial cell monolayers to quasi-one-dimensional geometries, to force the establishment of tissue-level waves of well-defined wavelength and period. Numerical simulations based on a self-propelled Voronoi model reproduce the observed waves and exhibit a phase transition between a global and a multinodal wave, controlled by the confinement size. We confirm experimentally the existence of such a phase transition, and show that wavelength and period are independent of the confinement length. Together, these results demonstrate the intrinsic origin of tissue oscillations, which could provide cells with a mechanism to accurately measure distances at the supracellular level.

Traction microscopy with integrated microfluidics: responses of the multi-cellular island to gradients of HGF

Collective cellular migration plays a central role in development, regeneration, and metastasis. In these processes, mechanical interactions between cells are fundamental but measurement of these interactions is often hampered by technical limitations. To overcome some of these limitations, here we describe a system that integrates microfluidics with traction microscopy (TM). Using this system we can measure simultaneously, and in real time, migration speeds, tractions, and intercellular tension throughout an island of confluent Madin-Darby canine kidney (MDCK) cells. The cell island is exposed to hepatocyte growth factor (HGF) at a controlled gradient of concentrations; HGF is known to elicit epithelial-to-mesenchymal transition (EMT) and cell scattering. As expected, the rate of expansion of the cell island was dependent on the concentration of HGF. Higher concentrations of HGF reduced intercellular tensions, as expected during EMT. A novel finding, however, is that the effects of HGF concentration and its gradient were seen within an island. This integrated experimental system thus provides an integrated tool to better understand cellular forces during collective cellular migration under chemical gradients.

Influence of proliferation on the motions of epithelial monolayers invading adherent strips

Biological systems integrate dynamics at many scales, from molecules, protein complexes and genes, to cells, tissues and organisms. At every step of the way, mechanics, biochemistry and genetics offer complementary approaches to understand these dynamics. At the tissue scale, in vitro monolayers of epithelial cells provide a model to capture the influence of various factors on the motions of the tissue, in order to understand in vivo processes from morphogenesis, cancer progression and tissue remodelling. Ongoing efforts include research aimed at deciphering the roles of the cytoskeleton, of cell-substrate and cell-cell adhesions, and of cell proliferation-the point we investigate here. We show that confined to adherent strips, and on the time scale of a day or two, monolayers move with a characteristic front speed independent of proliferation, but that the motion is accompanied by persistent velocity waves, only in the absence of cell divisions. Here we show that the long-range transmission of physical signals is strongly coupled to cell density and proliferation. We interpret our results from a kinematic and mechanical perspective. Our study provides a framework to understand density-driven mechanisms of collective cell migration.

Active wetting of epithelial tissues

Development, regeneration and cancer involve drastic transitions in tissue morphology. In analogy with the behavior of inert fluids, some of these transitions have been interpreted as wetting transitions. The validity and scope of this analogy are unclear, however, because the active cellular forces that drive tissue wetting have been neither measured nor theoretically accounted for. Here we show that the transition between two-dimensional epithelial monolayers and three-dimensional spheroidal aggregates can be understood as an active wetting transition whose physics differs fundamentally from that of passive wetting phenomena. By combining an active polar fluid model with measurements of physical forces as a function of tissue size, contractility, cell-cell and cell-substrate adhesion, and substrate stiffness, we show that the wetting transition results from the competition between traction forces and contractile intercellular stresses. This competition defines a new intrinsic lengthscale that gives rise to a critical size for the wetting transition in tissues, a striking feature that has no counterpart in classical wetting. Finally, we show that active shape fluctuations are dynamically amplified during tissue dewetting. Overall, we conclude that tissue spreading constitutes a prominent example of active wetting - a novel physical scenario that may explain morphological transitions during tissue morphogenesis and tumor progression.

Continuum Models of Collective Cell Migration

Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key biological question is how cells integrate molecular activities for force generation on multicellular scales. In this review we discuss recent advances in modeling collective cell migration using quantitative tools and approaches rooted in soft matter physics. We focus on theoretical models of cell aggregates as continuous active media, where the feedback between mechanical forces and regulatory biochemistry gives rise to rich collective dynamical behavior. This class of models provides a powerful predictive framework for the physiological dynamics that underlies many developmental processes, where cells need to collectively migrate like a viscous fluid to reach a target region, and then stiffen to support mechanical stresses and maintain tissue cohesion.

Fingering instabilities in tissue invasion: an active fluid model

Metastatic tumours often invade healthy neighbouring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model of a self-propelled, growing biological tissue. The theory involves only four mechanical parameters and remains analytically trackable in various settings. As an application of the model, we study the evolution of a two-dimensional circular droplet made of our active and expanding fluid, and embedded in a passive non-growing tissue. This system could be used to model the evolution of a carcinoma in an epithelial layer. We find that our description can explain the propensity of tumour tissues to fingering instabilities, as conditioned by the magnitude of active traction and the growth kinetics. We are also able to derive predictions for the tumour size at the onset of metastasis, and for the number of subsequent invasive fingers. Our active fluid model may help describe a wider range of biological processes, including wound healing and developmental patterning.

Force localization modes in dynamic epithelial colonies

Collective cell behaviors, including tissue remodeling, morphogenesis, and cancer metastasis, rely on dynamics among cells, their neighbors, and the extracellular matrix. The lack of quantitative models precludes understanding of how cell-cell and cell-matrix interactions regulate tissue-scale force transmission to guide morphogenic processes. We integrate biophysical measurements on model epithelial tissues and computational modeling to explore how cell-level dynamics alter mechanical stress organization at multicellular scales. We show that traction stress distribution in epithelial colonies can vary widely for identical geometries. For colonies with peripheral localization of traction stresses, we recapitulate previously described mechanical behavior of cohesive tissues with a continuum model. By contrast, highly motile cells within colonies produce traction stresses that fluctuate in space and time. To predict the traction force dynamics, we introduce an active adherent vertex model (AAVM) for epithelial monolayers. AAVM predicts that increased cellular motility and reduced intercellular mechanical coupling localize traction stresses in the colony interior, in agreement with our experimental data. Furthermore, the model captures a wide spectrum of localized stress production modes that arise from individual cell activities including cell division, rotation, and polarized migration. This approach provides a robust quantitative framework to study how cell-scale dynamics influence force transmission in epithelial tissues.

Long-time viscoelasticity of multicellular surfaces caused by collective cell migration - Multi-scale modeling considerations

Long-time viscoelasticity of multicellular surfaces caused by collective cell migration depends on: (1) the volume fraction and configuration of migrating cells and the rate of its change, (2) the viscoelasticity of migrating cell groups, and (3) the viscoelasticity of surrounding resting cells. The key parameter that influences the viscoelasticity is the size, shape, and thickness of the biointerface between migrating and resting cell sub-populations. The multi-scale nature of the biointerface dynamics represents the product of: (1) the local changes of the size and shape of migrating cell groups, (2) the local accumulation of resistance stress within the core regions of migrating cell groups (internal effects), (3) the collision of the velocity fronts (external effects). The local changes of the size and shape of migrating cell groups induces additional energy dissipation. The accumulated stress could induce disordering of migrating cell groups and consequently migrating-to-resting cell state transition. The collision of the velocity fronts could lead to stagnant zone formation and local increase of the volume fraction of resting cells. Herein, an attempt is made to discuss and connect various modeling approaches from the stand point of thermodynamics and rheology obtained at: (1) cellular level, (2) biointerface between migrating cell group and surrounding resting cells, and (3) a part of multicellular surfaces. These complex phenomena are discussed on the model system such as cell aggregate rounding after uni-axial compression under in vitro conditions at characteristic times such as: (1) cell shape relaxation time under stretching/compression, (2) contact time between migrating cell group and surrounding resting cells, (3) cell persistence time, (4) the lifetime of migrating cell groups, (5) cell rearrangement time (i.e. the process time), and (6) the stress and strain relaxation times of perturbed multicellular surface parts. The results of this theoretical analysis point to the relationship between interfacial size, mechanical coupling mode and rheological behavior of multicellular surfaces. Multi scale dynamics at the biointerface is a key parameter which influences mechanical behavior of multicellular surfaces. Consequently, the shape of migrating cell groups and their distribution are not random characteristics of the multicellular surface but rather influenced by cause-consequence relations between biochemical processes at the cellular level and surface stiffness distribution at the mesoscopic level.

Volumetric optical coherence microscopy with a high space-bandwidth-time product enabled by hybrid adaptive optics

Optical coherence microscopy (OCM) is a promising modality for high resolution imaging, but has limited ability to capture large-scale volumetric information about dynamic biological processes with cellular resolution. To enhance the throughput of OCM, we implemented a hybrid adaptive optics (hyAO) approach that combines computational adaptive optics with an intentionally aberrated imaging beam generated via hardware adaptive optics. Using hyAO, we demonstrate the depth-equalized illumination and collection ability of an astigmatic beam compared to a Gaussian beam for cellular-resolution imaging. With this advantage, we achieved volumetric OCM with a higher space-bandwidth-time product compared to Gaussian-beam acquisition that employed focus-scanning across depth. HyAO was also used to perform volumetric time-lapse OCM imaging of cellular dynamics over a 1mm × 1mm × 1mm field-of-view with 2 μm isotropic spatial resolution and 3-minute temporal resolution. As hyAO is compatible with both spectral-domain and swept-source beam-scanning OCM systems, significant further improvements in absolute volumetric throughput are possible by use of ultrahigh-speed swept sources.

Keratinocyte Motility Is Affected by UVA Radiation-A Comparison between Normal and Dysplastic Cells

UVA radiation induces multiple and complex changes in the skin, affecting epidermal cell behavior. This study reports the effects of UVA exposure on normal (HaCaT) and dysplastic (DOK) keratinocytes. The adherence, spreading and proliferation were investigated by time-lapse measurement of cell layer impedance on different matrix proteins. Prior to UVA exposure, the time required for adherence and spreading did not differ significantly for HaCaT and DOK cells, while spreading areas were larger for HaCaT cells. Under UVA exposure, HaCaT and DOK cells behavior differed in terms of movement and proliferation. The cells' ability to cover the denuded surface and individual cell trajectories were recorded by time-lapse videomicroscopy, during wound healing experiments. Dysplastic keratinocytes showed more sensitivity to UVA, exhibiting transient deficiencies in directionality of movement and a delay in re-coating the denuded area. The actin cytoskeleton displayed a cortical organization immediately after irradiation, in both cell lines, similar to mock-irradiated cells. Post-irradiation, DOK cells displayed a better organization of stress fibers, persistent filopodia, and new, stronger focal contacts. In conclusion, after UVA exposure HaCaT and DOK cells showed a different behavior in terms of adherence, spreading, motility, proliferation, and actin cytoskeleton dynamics, with the dyplastic keratinocytes being more sensitive.

Collective cell migration without proliferation: density determines cell velocity and wave velocity

Collective cell migration contributes to embryogenesis, wound healing and tumour metastasis. Cell monolayer migration experiments help in understanding what determines the movement of cells far from the leading edge. Inhibiting cell proliferation limits cell density increase and prevents jamming; we observe long-duration migration and quantify space-time characteristics of the velocity profile over large length scales and time scales. Velocity waves propagate backwards and their frequency depends only on cell density at the moving front. Both cell average velocity and wave velocity increase linearly with the cell effective radius regardless of the distance to the front. Inhibiting lamellipodia decreases cell velocity while waves either disappear or have a lower frequency. Our model combines conservation laws, monolayer mechanical properties and a phenomenological coupling between strain and polarity: advancing cells pull on their followers, which then become polarized. With reasonable values of parameters, this model agrees with several of our experimental observations. Together, our experiments and model disantangle the respective contributions of active velocity and of proliferation in monolayer migration, explain how cells maintain their polarity far from the moving front, and highlight the importance of strain-polarity coupling and density in long-range information propagation.

Disease-causing mutation in α-actinin-4 promotes podocyte detachment through maladaptation to periodic stretch

α-Actinin-4 (ACTN4) bundles and cross-links actin filaments to confer mechanical resilience to the reconstituted actin network. How this resilience is built and dynamically regulated in the podocyte, and the cause of its failure in ACTN4 mutation-associated focal segmental glomerulosclerosis (FSGS), remains poorly defined. Using primary podocytes isolated from wild-type (WT) and FSGS-causing point mutant Actn4 knockin mice, we report responses to periodic stretch. While WT cells largely maintained their F-actin cytoskeleton and contraction, mutant cells developed extensive and irrecoverable reductions in these same properties. This difference was attributable to both actin material changes and a more spatially correlated intracellular stress in mutant cells. When stretched cells were further challenged using a cell adhesion assay, mutant cells were more likely to detach. Together, these data suggest a mechanism for mutant podocyte dysfunction and loss in FSGS-it is a direct consequence of mechanical responses of a cytoskeleton that is brittle.

Traction Force Microscopy for Noninvasive Imaging of Cell Forces

The forces exerted by cells on their surroundings play an integral role in both physiological processes and disease progression. Traction force microscopy is a noninvasive technique that enables the in vitro imaging and quantification of cell forces. Utilizing expertise from a variety of disciplines, recent developments in traction force microscopy are enhancing the study of cell forces in physiologically relevant model systems, and hold promise for further advancing knowledge in mechanobiology. In this chapter, we discuss the methods, capabilities, and limitations of modern approaches for traction force microscopy, and highlight ongoing efforts and challenges underlying future innovations.

Probing three-dimensional collective cancer invasion with DIGME

BACKGROUND

Multicellular pattern formation plays an important role in developmental biology, cancer metastasis and wound healing. While many physical factors have been shown to regulate these multicellular processes, the role of ECM micro-to-meso scale geometry has been poorly understood in 3D collective cancer invasion.

RESULTS

We have developed a mechanical-based strategy, Diskoid In Geometrically Micropatterned ECM (DIGME). DIGME allows easy engineering of the shape of 3D tissue organoid, the mesoscale ECM heterogeneity, and the fiber alignment of collagen-based ECM all at the same time. We have employed DIGME to study the 3D invasion of MDA-MB-231 diskoids in engineered collagen matrix. We find that the collective cancer invasion is closely regulated by the micro-to-meso scale geometry of the ECM.

CONCLUSIONS

We conclude that DIGME provides a simple yet powerful tool to probe 3D dynamics of tissue organoids in physically patterned microenvironments.

Emergence of epithelial cell density waves

Epithelial cell monolayers exhibit traveling mechanical waves. We rationalize this observation thanks to a hydrodynamic description of the monolayer as a compressible, active and polar material. We show that propagating waves of the cell density, polarity, velocity and stress fields may be due to a Hopf bifurcation occurring above threshold values of active coupling coefficients.

Hydrodynamic instabilities, waves and turbulence in spreading epithelia

We present a hydrodynamic model of spreading epithelial monolayers described as polar viscous fluids, with active contractility and traction on a substrate. The combination of both active forces generates an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. Our viscous fluid model provides a comprehensive understanding of a variety of observations on the slow dynamics of epithelial monolayers, remarkably those that seemed to be characteristic of elastic media. The model also makes simple predictions to test the non-elastic nature of the mechanical waves, and provides new insights into collective cell dynamics, explaining plithotaxis as a result of strong flow-polarity coupling, and quantifying the non-locality of force transmission. In addition, we study the nonlinear regime of waves deriving an exact map of the model into the complex Ginzburg-Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the chaotic dynamics often observed in epithelia.

Long-lived force patterns and deformation waves at repulsive epithelial boundaries

For an organism to develop and maintain homeostasis, cell types with distinct functions must often be separated by physical boundaries. The formation and maintenance of such boundaries are commonly attributed to mechanisms restricted to the cells lining the boundary. Here we show that, besides these local subcellular mechanisms, the formation and maintenance of tissue boundaries involves long-lived, long-ranged mechanical events. Following contact between two epithelial monolayers expressing, respectively, EphB2 and its ligand ephrinB1, both monolayers exhibit oscillatory patterns of traction forces and intercellular stresses that tend to pull cell-matrix adhesions away from the boundary. With time, monolayers jam, accompanied by the emergence of deformation waves that propagate away from the boundary. This phenomenon is not specific to EphB2/ephrinB1 repulsion but is also present during the formation of boundaries with an inert interface and during fusion of homotypic epithelial layers. Our findings thus unveil a global physical mechanism that sustains tissue separation independently of the biochemical and mechanical features of the local tissue boundary.

Cell growth, division, and death in cohesive tissues: A thermodynamic approach

Cell growth, division, and death are defining features of biological tissues that contribute to morphogenesis. In hydrodynamic descriptions of cohesive tissues, their occurrence implies a nonzero rate of variation of cell density. We show how linear nonequilibrium thermodynamics allows us to express this rate as a combination of relevant thermodynamic forces: chemical potential, velocity divergence, and activity. We illustrate the resulting effects of the nonconservation of cell density on simple examples inspired by recent experiments on cell monolayers, considering first the velocity of a spreading front, and second an instability leading to mechanical waves.

Single and collective cell migration: the mechanics of adhesions

Chemical and physical properties of the environment control cell proliferation, differentiation, or apoptosis in the long term. However, to be able to move and migrate through a complex three-dimensional environment, cells must quickly adapt in the short term to the physical properties of their surroundings. Interactions with the extracellular matrix (ECM) occur through focal adhesions or hemidesmosomes via the engagement of integrins with fibrillar ECM proteins. Cells also interact with their neighbors, and this involves various types of intercellular adhesive structures such as tight junctions, cadherin-based adherens junctions, and desmosomes. Mechanobiology studies have shown that cell-ECM and cell-cell adhesions participate in mechanosensing to transduce mechanical cues into biochemical signals and conversely are responsible for the transmission of intracellular forces to the extracellular environment. As they migrate, cells use these adhesive structures to probe their surroundings, adapt their mechanical properties, and exert the appropriate forces required for their movements. The focus of this review is to give an overview of recent developments showing the bidirectional relationship between the physical properties of the environment and the cell mechanical responses during single and collective cell migration.

Viscoelasticity of multicellular surfaces

Various modeling approaches have been applied to describe viscoelasticity of multicellular surfaces. The viscoelasticity is considered within three time regimes: (1) short time regime for milliseconds to seconds time scale which corresponds to sub-cellular level; (2) middle time regime for several tens of seconds to several minutes time scale which corresponds to cellular level; and (3) long time regime for several tens of minutes to several hours time scale which corresponds to supra-cellular level. Short and middle time regimes have been successfully elaborated in the literature, whereas long time viscoelasticity remains unclear. Long time regime accounts for collective cell migration. Collective cell migration could induce uncorrelated motility which has an impact to energy storage and dissipation during cell surface rearrangement. Uncorrelated motility influences: (1) volume fraction of migrating cells, (2) distribution of migrating cells, (3) shapes of migrating cell groups. These parameters influence mechanical coupling between migrating and resting subpopulations and consequently the constitutive model for long time regime. This modeling consideration indicates that additional experimental work is needed to confirm the feasibility of constitutive models which have been applied in literature for long time regime as: (1) relaxation of stress and strain, (2) storage and loss moduli as the function of time, (3) distribution of migrating cells.

Collective cell migration: a physics perspective

Cells have traditionally been viewed either as independently moving entities or as somewhat static parts of tissues. However, it is now clear that in many cases, multiple cells coordinate their motions and move as collective entities. Well-studied examples comprise development events, as well as physiological and pathological situations. Different ex vivo model systems have also been investigated. Several recent advances have taken place at the interface between biology and physics, and have benefitted from progress in imaging and microscopy, from the use of microfabrication techniques, as well as from the introduction of quantitative tools and models. We review these interesting developments in quantitative cell biology that also provide rich examples of collective out-of-equilibrium motion.

Successive relaxation cycles during long-time cell aggregate rounding after uni-axial compression

The mean features of cell surface rearrangement during cell aggregate rounding after uni-axial compression between parallel plates are considered. This is based on long-time rheological modeling approaches in order to shed further light on collective cell migration. Many aspects of cell migration at the supra-cellular level, such as the coordination between surrounding migrating cell groups that leads to uncorrelated motility, have remained unclear. Aggregate shape changes during rounding are considered depending on the size and homogeneity of 2-D and 3-D cell aggregates. Cell aggregate shape changes that are taking place during successive relaxation cycles have various relaxation rates per cycle. Every relaxation rate is related to the corresponding cell migrating state. If most of the cells migrate per cycle, the relaxation rate is maximal. If most of the cells are in a resting state per cycle, the relaxation rate is nearing zero. If some cell groups migrate while the others, at the same time, stay in a resting state, the relaxation rate is lower than that obtained for the migrating cells. The relaxation rates per cycles are not random, but they have a tendency to gather around two or three values indicating an organized cell migrating pattern. Such behavior suggests that uncorrelated motility during collective cell migration in one cycle induces a decrease of the relaxation rate in the next cycle caused by an accumulation of cells in the resting state. However, cells have the ability to overcome these perturbations and re-establish an ordered migrating trend in the next cycle. These perturbations of the cell migrating state are more pronounced for: (1) more mobile cells, (2) a heterogeneous cell population, and (3) a larger cell population under the same experimental conditions.

Diverse roles of guanine nucleotide exchange factors in regulating collective cell migration

Effective collective cell migration depends on delicate tuning of cell motility forces and cell–cell communication. Zaritsky, Tseng, and coworkers identified differential roles for RhoA, RhoC, and their upstream activators in mediating long-range transmission of guidance cues.

Efficient collective migration depends on a balance between contractility and cytoskeletal rearrangements, adhesion, and mechanical cell–cell communication, all controlled by GTPases of the RHO family. By comprehensive screening of guanine nucleotide exchange factors (GEFs) in human bronchial epithelial cell monolayers, we identified GEFs that are required for collective migration at large, such as SOS1 and β-PIX, and RHOA GEFs that are implicated in intercellular communication. Down-regulation of the latter GEFs differentially enhanced front-to-back propagation of guidance cues through the monolayer and was mirrored by down-regulation of RHOA expression and myosin II activity. Phenotype-based clustering of knockdown behaviors identified RHOA-ARHGEF18 and ARHGEF3-ARHGEF28-ARHGEF11 clusters, indicating that the latter may signal through other RHO-family GTPases. Indeed, knockdown of RHOC produced an intermediate between the two phenotypes. We conclude that for effective collective migration, the RHOA-GEFs → RHOA/C → actomyosin pathways must be optimally tuned to compromise between generation of motility forces and restriction of intercellular communication.

Modeling, signaling and cytoskeleton dynamics: integrated modeling-experimental frameworks in cell migration

Cell migration is a complex and multistep process involved in homeostasis maintenance, morphogenesis, and disease development, such as cancer metastasis. Modeling cell migration and the relevant cytoskeleton dynamics have profound implications for studying fundamental development and disease diagnosis. This review focuses on some recent models of both cell migration and migration-related cytoskeleton dynamics, addressing issues such as the difference between amoeboid and mesenchymal migration modes, and between single-cell migration and collective cell migration. The review also highlights the computational integration among variable external cues, especially the biochemical and mechanical signaling that affects cell migration. Finally, we aim to identify the gaps in our current knowledge and potential strategies to develop integrated modeling-experimental frameworks for multiscale behavior integrating gene expression, cell signaling, mechanics, and multicellular dynamics. WIREs Syst Biol Med 2017, 9:e1365. doi: 10.1002/wsbm.1365 For further resources related to this article, please visit the WIREs website.

Collective migration and cell jamming in asthma, cancer and development

Collective cellular migration within the epithelial layer impacts upon development, wound healing and cancer invasion, but remains poorly understood. Prevailing conceptual frameworks tend to focus on the isolated role of each particular underlying factor - taken one at a time or at most a few at a time - and thus might not be tailored to describe a cellular collective that embodies a wide palette of physical and molecular interactions that are both strong and complex. To bridge this gap, we shift the spotlight to the emerging concept of cell jamming, which points to only a small set of parameters that govern when a cellular collective might jam and rigidify like a solid, or instead unjam and flow like a fluid. As gateways to cellular migration, the unjamming transition (UJT) and the epithelial-to-mesenchymal transition (EMT) share certain superficial similarities, but their congruence - or lack thereof - remains unclear. In this Commentary, we discuss aspects of cell jamming, its established role in human epithelial cell layers derived from the airways of non-asthmatic and asthmatic donors, and its speculative but emerging roles in development and cancer cell invasion.

Contact inhibition of locomotion and mechanical cross-talk between cell-cell and cell-substrate adhesion determine the pattern of junctional tension in epithelial cell aggregates

A computational approach is used to analyze the biomechanics of epithelial cells based on their capacity to adhere to one another and to the substrate and exhibit contact inhibition of locomotion. This approach reproduces emergent properties of epithelial cell aggregates and makes predictions for experimental validation.

We used a computational approach to analyze the biomechanics of epithelial cell aggregates—islands, stripes, or entire monolayers—that combines both vertex and contact-inhibition-of-locomotion models to include cell–cell and cell–substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high-order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces, and apical aspect ratios that decreased when moving from the edge to the island center. Our in silico analysis also showed that tension on cell–cell junctions and apical stress is not homogeneous across the island. Instead, these parameters are higher at the island center and scale up with island size, which we confirmed experimentally using laser ablation assays and immunofluorescence. Without formally being a three-dimensional model, our approach has the minimal elements necessary to reproduce the distribution of cellular forces and mechanical cross-talk, as well as the distribution of principal stress in cells within epithelial cell aggregates. By making experimentally testable predictions, our approach can aid in mechanical analysis of epithelial tissues, especially when local changes in cell–cell and/or cell–substrate adhesion drive collective cell behavior.