Cellular Contraction and Polarization Drive Collective Cellular Motion

Lost in Rotation: How TiO2 and ZnO Nanoparticles Disrupt Coordinated Epithelial Cell Rotation

Coordinated cell movement is a cardinal feature in tissue organization that highlights the importance of cells working together as a collective unit. Disruptions to this synchronization can have far-reaching pathological consequences, ranging from developmental disorders to tissue repair impairment. Herein, it is shown that metal oxide nanoparticles (NPs), even at low and non-toxic doses (1 and 10 µg mL-1), can perturb the coordinated epithelial cell rotation (CECR) in micropatterned human epithelial cell clusters via distinct nanoparticle-specific mechanisms. Zinc oxide (ZnO) NPs are found to induce significant levels of intracellular reactive oxygen species (ROS) to promote mitogenic activity. Generation of a new localized force field through changes in the cytoskeleton organization and an increase in cell density leads to the arrest of CECR. Conversely, epithelial cell clusters exposed to titanium dioxide (TiO2) NPs maintain their CECR directionality but display suppressed rotational speed in an autophagy-dependent manner. Thus, these findings reveal that nanoparticles can actively hijack the nano-adaptive responses of epithelial cells to disrupt the fundamental mechanics of cooperation and communication in a collective setting.

Stress-shape misalignment in confluent cell layers

In tissue formation and repair, the epithelium undergoes complex patterns of motion driven by the active forces produced by each cell. Although the principles governing how the forces evolve in time are not yet clear, it is often assumed that the contractile stresses within the cell layer align with the axis defined by the body of each cell. Here, we simultaneously measured the orientations of the cell shape and the cell-generated contractile stresses, observing correlated, dynamic domains in which the stresses were systematically misaligned with the cell body. We developed a continuum model that decouples the orientations of contractile stress and cell body. The model recovered the spatial and temporal dynamics of the regions of misalignment in the experiments. These findings reveal that the cell controls its contractile forces independently from its shape, suggesting that the physical rules relating cell forces and cell shape are more flexible than previously thought.

Role of viscoelasticity in the appearance of low-Reynolds turbulence: considerations for modelling

Inertial effects caused by perturbations of dynamical equilibrium during the flow of soft matter constitute a hallmark of turbulence. Such perturbations are attributable to an imbalance between energy storage and energy dissipation. During the flow of Newtonian fluids, kinetic energy can be both stored and dissipated, while the flow of viscoelastic soft matter systems, such as polymer fluids, induces the accumulation of both kinetic and elastic energies. The accumulation of elastic energy causes local stiffening of stretched polymer chains, which can destabilise the flow. Migrating multicellular systems are hugely complex and are capable of self-regulating their viscoelasticity and mechanical stress generation, as well as controlling their energy storage and energy dissipation. Since the flow perturbation of viscoelastic systems is caused by the inhomogeneous accumulation of elastic energy, rather than of kinetic energy, turbulence can occur at low Reynolds numbers.This theoretical review is focused on clarifying the role of viscoelasticity in the appearance of low-Reynolds turbulence. Three types of system are considered and compared: (1) high-Reynolds turbulent flow of Newtonian fluids, (2) low and moderate-Reynolds flow of polymer solutions, and (3) migration of epithelial collectives, discussed in terms of two model systems. The models considered involve the fusion of two epithelial aggregates, and the free expansion of epithelial monolayers on a substrate matrix.

Emergence, Pattern, and Frequency of Spontaneous Waves in Spreading Epithelial Monolayers

A striking phenomenon of collective cell motion is that they can exhibit a spontaneously emerging wave during epithelia expansions. However, the fundamental mechanism, governing the emergence and its crucial characteristics (e.g., the eigenfrequency and the pattern), remains an enigma. By introducing a mechanochemical feedback loop, we develop a highly efficient discrete vertex model to investigate the spatiotemporal evolution of spreading epithelia. We find both numerically and analytically that expanding cell monolayers display a power-law dependence of wave frequency on the local heterogeneities (i.e., cell density) with a scaling exponent of -1/2. Moreover, our study demonstrates the quantitative capability of the proposed model in capturing distinct X-, W-, and V-mode wave patterns. We unveil that the phase transition between these modes is governed by the distribution of active self-propulsion forces. Our work provides an avenue for rigorous quantitative investigations into the collective motion and pattern formation of cell groups.

Collective durotaxis along a self-generated mobile stiffness gradient in vivo

A crucial aspect of tissue self-organization during morphogenesis, wound healing, and cancer invasion is directed migration of cell collectives. The majority of in vivo directed migration has been guided by chemotaxis, whereby cells follow a chemical gradient. In certain situations, migrating cell collectives can also self-generate the stiffness gradient in the surrounding tissue, which can have a feedback effect on the directionality of the migration. The phenomenon has been observed during collective durotaxis in vivo. Along the biointerface between neighbouring tissues, heterotypic cell-cell interactions are the main cause of this self-generated stiffness gradient. The physical processes in charge of tissue self-organization along the biointerface, which are related to the interplay between cell signalling and the formation of heterotypic cell-cell adhesion contacts, are less well-developed than the biological mechanisms of the cellular interactions. This complex phenomenon is discussed here in the model system, such as collective migration of neural crest cells between ectodermal placode and mesoderm subpopulations within Xenopus embryos by pointing to the role of the dynamics along the biointerface between adjacent cell subpopulations on the subpopulation stiffness.

Segregation of co-cultured multicellular systems: review and modeling consideration

Cell segregation caused by collective cell migration (CCM) is crucial for morphogenesis, functional development of tissue parts, and is an important aspect in other diseases such as cancer and its metastasis process. Efficiency of the cell segregation depends on the interplay between: (1) biochemical processes such as cell signaling and gene expression and (2) physical interactions between cells. Despite extensive research devoted to study the segregation of various co-cultured systems, we still do not understand the role of physical interactions in cell segregation. Cumulative effects of these physical interactions appear in the form of physical parameters such as: (1) tissue surface tension, (2) viscoelasticity caused by CCM, and (3) solid stress accumulated in multicellular systems. These parameters primarily depend on the interplay between the state of cell-cell adhesion contacts and cell contractility. The role of these physical parameters on the segregation efficiency is discussed on model systems such as co-cultured breast cell spheroids consisting of two subpopulations that are in contact. This review study aims to: (1) summarize biological aspects related to cell segregation, mechanical properties of cell collectives, effects along the biointerface between cell subpopulations and (2) describe from a biophysical/mathematical perspective the same biological aspects summarized before. So that overall it can illustrate the complexity of the biological systems that translate into very complex biophysical/mathematical equations. Moreover, by presenting in parallel these two seemingly different parts (biology vs. equations), this review aims to emphasize the need for experiments to estimate the variety of parameters entering the resulting complex biophysical/mathematical models.

Machine learning interpretable models of cell mechanics from protein images

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

Cell jamming-to-unjamming transitions and vice versa in development: Physical aspects

Collective cell migration is essential for a wide range of biological processes such as: morphogenesis, wound healing, and cancer spreading. However, it is well known that migrating epithelial collectives frequently undergo jamming, stay trapped some period of time, and then start migration again. Consequently, only a part of epithelial cells actively contributes to the tissue development. In contrast to epithelial cells, migrating mesenchymal collectives successfully avoid the jamming. It has been confirmed that the epithelial unjamming cannot be treated as the epithelial-to-mesenchymal transition. Some other mechanism is responsible for the epithelial jamming/unjamming. Despite extensive research devoted to study the cell jamming/unjamming, we still do not understand the origin of this phenomenon. The origin is connected to physical factors such as: the cell compressive residual stress accumulation and surface characteristics of migrating (unjamming) and resting (jamming) epithelial clusters which depend primarily on the strength of cell-cell adhesion contacts and cell contractility. The main goal of this theoretical consideration is to clarify these cause-consequence relations.

Physics of collective cell migration

Movement of cell clusters along extracellular matrices (ECM) during tissue development, wound healing, and early stage of cancer invasion involve various inter-connected migration modes such as: (1) cell movement within clusters, (2) cluster extension (wetting) and compression (de-wetting), and (3) directional cluster movement. It has become increasingly evident that dilational and volumetric viscoelasticity of cell clusters and their surrounding substrate significantly influence these migration modes through physical parameters such as: tissue and matrix surface tensions, interfacial tension between cells and substrate, gradients of surface and interfacial tensions, as well as, the accumulation of cell and matrix residual stresses. Inhomogeneous distribution of tissue surface tension along the cell-matrix biointerface can appear as a consequence of different contractility of various cluster regions. While the directional cell migration caused by the matrix stiffness gradient (i.e., durotaxis) has been widely elaborated, the structural changes of matrix surface caused by cell tractions which lead to the generation of the matrix surface tension gradient has not been considered yet. The main goal of this theoretical consideration is to clarify the roles of various physical parameters in collective cell migration based on the formulation of a biophysical model. This complex phenomenon is discussed with the help of model systems such as the movement of cell clusters on a collagen I gel matrix, simultaneously reviewing various experimental data with and without cells.

Response of cells and tissues to shear stress

Shear stress is essential for normal physiology and malignancy. Common physiological processes - such as blood flow, particle flow in the gut, or contact between migratory cell clusters and their substrate - produce shear stress that can have an impact on the behavior of different tissues. In addition, shear stress has roles in processes of biomedical interest, such as wound healing, cancer and fibrosis induced by soft implants. Thus, understanding how cells react and adapt to shear stress is important. In this Review, we discuss in vivo and in vitro data obtained from vascular and epithelial models; highlight the insights these have afforded regarding the general mechanisms through which cells sense, transduce and respond to shear stress at the cellular levels; and outline how the changes cells experience in response to shear stress impact tissue organization. Finally, we discuss the role of shear stress in collective cell migration, which is only starting to be appreciated. We review our current understanding of the effects of shear stress in the context of embryo development, cancer and fibrosis, and invite the scientific community to further investigate the role of shear stress in these scenarios.

Engineering tools for quantifying and manipulating forces in epithelia

The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.

Multi-scale nature of the tissue surface tension: Theoretical consideration on tissue model systems

Tissue surface tension is one of the key parameters that govern tissue rearrangement, shaping, and segregation within various compartments during organogenesis, wound healing, and cancer diseases. Deeper insight into the relationship between tissue surface tension and cell residual stress accumulation caused by collective cell migration can help us to understand the multi-scale nature of cell rearrangement with pronounced oscillatory trend. Oscillatory change of cell velocity that caused strain and generated cell residual stress were discussed in the context of mechanical waves. The tissue surface tension also showed oscillatory behaviour. The main goal of this theoretical consideration is to emphasize an inter-relation between various scenarios of cell rearrangement and tissue surface tension by distinguishing liquid-like and solid-like surfaces. This complex phenomenon is discussed in the context of an artificial tissue model system, namely cell aggregate rounding after uni-axial compression between parallel plates. Experimentally obtained oscillatory changes in the cell aggregate shape during the aggregate rounding, which is accompanied by oscillatory decrease in the aggregate surface area, points to oscillatory changes in the tissue surface tension. Besides long-time oscillations, cell surface tension can perform short time relaxation cycles. This behaviour of the tissue surface tension distinguishes living matter from other soft matter systems. This complex phenomenon is discussed based on dilatational viscoelasticity and thermodynamic approach.

Collective Behaviors of Active Matter Learning from Natural Taxes Across Scales

Taxis orientation is common in microorganisms, and it provides feasible strategies to operate active colloids as small-scale robots. Collective taxes involve numerous units that collectively perform taxis motion, whereby the collective cooperation between individuals enables the group to perform efficiently, adaptively, and robustly. Hence, analyzing and designing collectives is crucial for developing and advancing microswarm toward practical or clinical applications. In this review, natural taxis behaviors are categorized and synthetic microrobotic collectives are discussed as bio-inspired realizations, aiming at closing the gap between taxis strategies of living creatures and those of functional active microswarms. As collective behaviors emerge within a group, the global taxis to external stimuli guides the group to conduct overall tasks, whereas the local taxis between individuals induces synchronization and global patterns. By encoding the local orientations and programming the global stimuli, various paradigms can be introduced for coordinating and controlling such collective microrobots, from the viewpoints of fundamental science and practical applications. Therefore, by discussing the key points and difficulties associated with collective taxes of different paradigms, this review potentially offers insights into mimicking natural collective behaviors and constructing intelligent microrobotic systems for on-demand control and preassigned tasks.

Active wetting of epithelial tissues: modeling considerations

Morphogenesis, tissue regeneration, and cancer invasion involve transitions in tissue morphology. These transitions, caused by collective cell migration (CCM), have been interpreted as active wetting/de-wetting transitions. This phenomenon is considered based on a model system as wetting of a cell aggregate on a rigid substrate, which includes cell aggregate movement and isotropic/anisotropic spreading of a cell monolayer around the aggregate depending on the substrate rigidity and aggregate size. This model system accounts for the transition between 3D epithelial aggregate and 2D cell monolayer as a product of: (1) tissue surface tension, (2) surface tension of substrate matrix, (3) cell-matrix interfacial tension, (4) interfacial tension gradient, (5) viscoelasticity caused by CCM, and (6) viscoelasticity of substrate matrix. These physical parameters depend on the cell contractility and state of cell-cell and cell-matrix adhesion contacts, as well as the stretching/compression of cellular systems caused by CCM. Despite extensive research devoted to study cell wetting, we still do not understand the interplay among these physical parameters which induces an oscillatory trend of cell rearrangement. This review focuses on these physical parameters in governing the cell rearrangement in the context of epithelial aggregate wetting/de-wetting, and on modeling approaches aimed at reproducing and understanding these biological systems. In this context, we not only review previously published biophysical models for cell rearrangement caused by CCM, but also propose new extensions of those models to point out the interrelation between cell-matrix interfacial tension and epithelial viscoelasticity and the role of the interfacial tension gradient in cell spreading.

Low-intensity continuous ultrasound to inhibit cancer cell migration

In recent years, it has been verified that collective cell migration is a fundamental step in tumor spreading and metastatic processes. In this paper, we demonstrate for the first time how low-intensity ultrasound produces long-term inhibition of collective migration of epithelial cancer cells in wound healing processes. In particular, we show how pancreatic tumor cells, PANC-1, grown as monolayers in vitro respond to these waves at frequencies close to 1 MHz and low intensities (<100 mW cm^-2) for 48-72 h of culture after some minutes of a single ultrasound irradiation. This new strategy opens a new line of action to block the spread of malignant cells in cancer processes. Despite relevant spatial variations of the acoustic pressure amplitude induced in the assay, the cells behave as a whole, showing a collective dynamic response to acoustic performance. Experiments carried out with samples without previous starving showed remarkable effects of the LICUs from the first hours of culture, more prominent than those with experiments with monolayers subjected to fasting prior to the experiments. This new strategy to control cell migration demonstrating the effectiveness of LICUS on not starved cells opens a new line of action to study effects of in vivo ultrasonic actuation on tumor tissues with malignant cells. This is a proof-of-concept study to demonstrate the physical effects of ultrasound stimulation on tumor cell migration. An in-depth biological study of the effects of ultrasounds and underlying biological mechanisms is on-going but out of the scope of this article.

The dynamics along the biointerface between the epithelial and cancer mesenchymal cells: Modeling consideration

Epithelial cancer is the one of most lethal cancer type worldwide. Targeting the early stage of disease would allow dramatic improvements in the survival of cancer patients. The early stage of the disease is related to cancer cell spreading across surrounding healthy epithelium. Consequently, deeper insight into cell dynamics along the biointerface between epithelial and cancer (mesenchymal) cells is necessary in order to control the disease as soon as possible. Cell dynamics along this epithelial-cancer biointerface is the result of the interplay between various biological and physical mechanisms. Despite extensive research devoted to study cancer cell spreading across the epithelium, we still do not understand the physical mechanisms which influences the dynamics along the biointerface. These physical mechanisms are related to the interplay between physical parameters such as: (1) interfacial tension between cancer and epithelial subpopulations, (2) established interfacial tension gradients, (3) the bending rigidity of the biointerface and its impact on the interfacial tension, (4) surface tension of the subpopulations, (5) viscoelasticity caused by collective cell migration, and (6) cell residual stress accumulation. The main goal of this study is to review some of these physical parameters in the context of the epithelial/cancer biointerface elaborated on the model system such as the biointerface between breast epithelial MCF-10A cells and cancer MDA-MB-231 cells and then to incorporate these parameters into a new biophysical model that could describe the dynamics of the biointerface. We conclude by discussing three biophysical scenarios for cell dynamics along the biointerface, which can occur depending on the magnitude of the generated shear stress: a smooth biointerface, a slightly-perturbed biointerface and an intensively-perturbed biointerface in the context of the Kelvin-Helmholtz instability. These scenarios are related to the probability of cancer invasion.

Cell segregation via differential collision modes between heterotypic cell populations

In tissue development and regeneration, the establishment of sharp boundaries between heterotypic cells is essential for the differentiation of tissue functions. During the dynamic rearrangements of constituent cells that result from cell division and collective migration, the segregation boundary encounters various challenges. Several studies have suggested that cortical actomyosin structures play a crucial role in the maintenance of the boundary interface of segregated cell populations, implicating actin-mediated stresses. Examining physical cellular properties such as motility, traction, and intercellular stress, we investigated the formation and maintenance of the stable segregation between epithelial and mesenchymal cell populations devoid of heterotypic adhesions. At the contact boundary, the homotypic adhesion-mediated epithelial aggregates exerted collision-mediated compression against the surrounding mesenchymal cells. Our results demonstrated that heterotypic cell populations established a robust interfacial boundary by accumulating stress from active collisions and repulsions between two dissimilar cell types. Furthermore, the moment of the heterotypic collisions was identified by the existence of a sharp rise in maximum shear stress within the cell cluster.

Interplay between substrate rigidity and tissue fluidity regulates cell monolayer spreading

Coordinated and cooperative motion of cells is essential for embryonic development, tissue morphogenesis, wound healing and cancer invasion. A predictive understanding of the emergent mechanical behaviors in collective cell motion is challenging due to the complex interplay between cell-cell interactions, cell-matrix adhesions and active cell behaviors. To overcome this challenge, we develop a predictive cellular vertex model that can delineate the relative roles of substrate rigidity, tissue mechanics and active cell properties on the movement of cell collectives. We apply the model to the specific case of collective motion in cell aggregates as they spread into a two-dimensional cell monolayer adherent to a soft elastic matrix. Consistent with recent experiments, we find that substrate stiffness regulates the driving forces for the spreading of cellular monolayer, which can be pressure-driven or crawling-based depending on substrate rigidity. On soft substrates, cell monolayer spreading is driven by an active pressure due to the influx of cells coming from the aggregate, whereas on stiff substrates, cell spreading is driven primarily by active crawling forces. Our model predicts that cooperation of cell crawling and tissue pressure drives faster spreading, while the spreading rate is sensitive to the mechanical properties of the tissue. We find that solid tissues spread faster on stiff substrates, with spreading rate increasing with tissue tension. By contrast, the spreading of fluid tissues is independent of substrate stiffness and is slower than solid tissues. We compare our theoretical results with experimental results on traction force generation and spreading kinetics of cell monolayers, and provide new predictions on the role of tissue fluidity and substrate rigidity on collective cell motion.

Pulsations and flows in tissues as two collective dynamics with simple cellular rules

Collective motions of epithelial cells are essential for morphogenesis. Tissues elongate, contract, flow, and oscillate, thus sculpting embryos. These tissue level dynamics are known, but the physical mechanisms at the cellular level are unclear. Here, we demonstrate that a single epithelial monolayer of MDCK cells can exhibit two types of local tissue kinematics, pulsations and long range coherent flows, characterized by using quantitative live imaging. We report that these motions can be controlled with internal and external cues such as specific inhibitors and substrate friction modulation. We demonstrate the associated mechanisms with a unified vertex model. When cell velocity alignment and random diffusion of cell polarization are comparable, a pulsatile flow emerges whereas tissue undergoes long-range flows when velocity alignment dominates which is consistent with cytoskeletal dynamics measurements. We propose that environmental friction, acto-myosin distributions, and cell polarization kinetics are important in regulating dynamics of tissue morphogenesis.

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Two collective cell motions, pulsations and flows, coexist in MDCK monolayers

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Each collective movement is identified using divergence and velocity correlations

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Motion is controlled by the regulation of substrate friction and cytoskeleton

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A vertex model recapitulates the motion by tuning velocity and polarity alignment

The rearrangement of co-cultured cellular model systems via collective cell migration

Cancer invasion through the surrounding epithelium and extracellular matrix (ECM) is the one of the main characteristics of cancer progression. While significant effort has been made to predict cancer cells response under various drug therapies, much less attention has been paid to understand the physical interactions between cancer cells and their microenvironment, which are essential for cancer invasion. Considering these physical interactions on various co-cultured in vitro model systems by emphasizing the role of viscoelasticity, the tissue surface tension, solid stress, and their inter-relations is a prerequisite for establishing the main factors that influence cancer cell spread and develop an efficient strategy to suppress it. This review focuses on the role of viscoelasticity caused by collective cell migration (CCM) in the context of mono-cultured and co-cultured cancer systems, and on the modeling approaches aimed at reproducing and understanding these biological systems. In this context, we do not only review previously-published biophysics models for collective cell migration, but also propose new extensions of those models to include solid stress accumulated within the spheroid core region and cell residual stress accumulation caused by CCM.

Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population

Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it is challenging to infer the interaction rules directly from data. In the field of equation discovery, the weak-form sparse identification of nonlinear dynamics (WSINDy) methodology has been shown to be computationally efficient for identifying the governing equations of complex systems from noisy data. Motivated by the success of IPS models to describe the spatial movement of organisms, we develop WSINDy for the second-order IPS to learn equations for communities of cells. Our approach learns the directional interaction rules for each individual cell that in aggregate govern the dynamics of a heterogeneous population of migrating cells. To sort a cell according to the active classes present in its model, we also develop a novel ad hoc classification scheme (which accounts for the fact that some cells do not have enough evidence to accurately infer a model). Aggregated models are then constructed hierarchically to simultaneously identify different species of cells present in the population and determine best-fit models for each species. We demonstrate the efficiency and proficiency of the method on several test scenarios, motivated by common cell migration experiments.

The role of viscoelasticity in long time cell rearrangement

Cell rearrangement caused by collective cell migration (CCM) during free expansion of epithelial monolayers has become a landmark in our current understanding of fundamental biological processes such as tissue development, regeneration, wound healing or cancer invasion. Cell spreading causes formation of mechanical waves which has a feedback effect on cell rearrangement and can lead to the cell jamming state. The mechanical waves describe oscillatory changes in cell velocity, as well as, the rheological parameters that affect them. The velocity oscillations, obtained at a time scale of hours, are in the form of forward and backward flows. Collision of forward and backward flows can induce an increase in the cell compressive stress accompanied with cell packing density which have a feedback impact on cell mobility, tissue viscoelasticity and alters the tissue stiffness. The tissue stiffness depends on the cell packing density and the active/passive (i.e. migrating/resting) state of single cells and can be used as an indicator of cell jamming state transition. Since cell stiffness can be measured it may directly show in which state the multicellular system is. In this work a review of existing modeling approaches is given along with assortment of published experimental findings, in order to invite experimentalists to test given theoretical considerations in multicellular systems.

Marangoni effect and cell spreading

Cells are very sensitive to the shear stress (SS). However, undesirable SS is generated during physiological process such as collective cell migration (CCM) and influences the biological processes such as morphogenesis, wound healing and cancer invasion. Despite extensive research devoted to study the SS generation caused by CCM, we still do not fully understand the main cause of SS appearance. An attempt is made here to offer some answers to these questions by considering the rearrangement of cell monolayers. The SS generation represents a consequence of natural and forced convection. While forced convection is dependent on cell speed, the natural convection is induced by the gradient of tissue surface tension. The phenomenon is known as the Marangoni effect. The gradient of tissue surface tension induces directed cell spreading from the regions of lower tissue surface tension to the regions of higher tissue surface tension and leads to the cell sorting. This directional cell migration is described by the Marangoni flux. The phenomenon has been recognized during the rearrangement of (1) epithelial cell monolayers and (2) mixed cell monolayers made by epithelial and mesenchymal cells. The consequence of the Marangoni effect is an intensive spreading of cancer cells through an epithelium. In this work, a review of existing literature about SS generation caused by CCM is given along with the assortment of published experimental findings, to invite experimentalists to test given theoretical considerations in multicellular systems.

A physical model for dynamic assembly of human salivary stem/progenitor microstructures

The in vitro reconstructions of human salivary glands in service of their eventual medical use represent a challenge for tissue engineering. Here, we present a theoretical approach to the dynamical formation of acinar structures from human salivary cells, focusing on observed stick-slip radial expansion as well as possible growth instabilities. Our findings demonstrate the critical importance of basement membrane remodeling in controlling the growth process.

Mechanical coupling of supracellular stress amplification and tissue fluidization during exit from quiescence

Most cells in the human body reside in a dormant state characterized by slow growth and minimal motility. During episodes such as wound healing, stem cell activation, and cancer growth, cells adapt to a more dynamic behavior characterized by proliferation and migration. However, little is known about the mechanical forces controlling the transition from static to motile following exit from dormancy. We demonstrate that keratinocyte monolayers install a mechanical system during dormancy that produces a coordinated burst of intercellular mechanical tension only minutes after dormancy exit. The activated forces are essential for large-scale displacements of otherwise motility-restricted cell sheets. Thus, cells sustain a mechanical system during dormancy that idles in anticipation of cell cycle entry and prompt activation of motion.

Cellular quiescence is a state of reversible cell cycle arrest that is associated with tissue dormancy. Timely regulated entry into and exit from quiescence is important for processes such as tissue homeostasis, tissue repair, stem cell maintenance, developmental processes, and immunity. However, little is known about processes that control the mechanical adaption to cell behavior changes during the transition from quiescence to proliferation. Here, we show that quiescent human keratinocyte monolayers sustain an actinomyosin-based system that facilitates global cell sheet displacements upon serum-stimulated exit from quiescence. Mechanistically, exposure of quiescent cells to serum-borne mitogens leads to rapid amplification of preexisting contractile sites, leading to a burst in monolayer tension that subsequently drives large-scale displacements of otherwise motility-restricted monolayers. The stress level after quiescence exit correlates with the level of quiescence depth at the time of activation, and a critical stress magnitude must be reached to overcome the cell sheet displacement barrier. The study shows that static quiescent cell monolayers are mechanically poised for motility, and it identifies global stress amplification as a mechanism for overcoming motility restrictions in confined confluent cell monolayers.

Active nonreciprocal attraction between motile particles in an elastic medium

We show from experiments and simulations on vibration-activated granular matter that self-propelled polar rods in an elastic medium on a substrate turn and move towards each other. We account for this effective attraction through a coarse-grained theory of a motile particle as a moving point-force density that creates elastic strains in the medium that reorient other particles. Our measurements confirm qualitatively the predicted features of the distortions created by the rods, including the |x|^{-1/2} tail of the trailing displacement field and nonreciprocal sensing and pursuit. A discrepancy between the magnitudes of displacements along and transverse to the direction of motion remains. Our theory should be of relevance to the interaction of motile cells in the extracellular matrix or in a supported layer of gel or tissue.

Interplay between cell height variations and planar pulsations in epithelial monolayers

Biological tissues change their shapes through collective interactions of cells. This coordination sets length and time scales for dynamics where precision is essential, in particular during morphogenetic events. However, how these scales emerge remains unclear. Here, we address this question using the pulsatile domains observed in confluent epithelial MDCK monolayers where cells exhibit synchronous contraction and extension cycles of [Formula: see text] h duration and [Formula: see text] length scale. We report that the monolayer thickness changes gradually in space and time by more than twofold in order to counterbalance the contraction and extension of the incompressible cytoplasm. We recapitulate these pulsatile dynamics using a continuum model and show that incorporation of cell stiffness dependent height variations is critical both for generating temporal pulsations and establishing the domain size. We propose that this feedback between height and mechanics could be important in coordinating the length scales of tissue dynamics.

Condensation of the Drosophila nerve cord is oscillatory and depends on coordinated mechanical interactions

During development, organs reach precise shapes and sizes. Organ morphology is not always obtained through growth; a classic counterexample is the condensation of the nervous system during Drosophila embryogenesis. The mechanics underlying such condensation remain poorly understood. Here, we characterize the condensation of the embryonic ventral nerve cord (VNC) at both subcellular and tissue scales. This analysis reveals that condensation is not a unidirectional continuous process but instead occurs through oscillatory contractions. The VNC mechanical properties spatially and temporally vary, and forces along its longitudinal axis are spatially heterogeneous. We demonstrate that the process of VNC condensation is dependent on the coordinated mechanical activities of neurons and glia. These outcomes are consistent with a viscoelastic model of condensation, which incorporates time delays and effective frictional interactions. In summary, we have defined the progressive mechanics driving VNC condensation, providing insights into how a highly viscous tissue can autonomously change shape and size.

Effect of substrate stiffness on friction in collective cell migration

In collective cell migration, the motion results from forces produced by each cell and transmitted to the neighboring cells and to the substrate. Because inertia is negligible and the migration occurs over long time scales, the cell layer exhibits viscous behavior, where force and motion are connected by an apparent friction that results from the breaking and forming of adhesive bonds at the cell–cell and cell–substrate interfaces. Most theoretical models for collective migration include an apparent friction to connect force and motion, with many models making predictions that depend on the ratio of cell–cell and cell–substrate friction. However, little is known about factors that affect friction, leaving predictions of many theoretical models untested. Here, we considered how substrate stiffness and the number of adhesions affected friction at the cell–substrate interface. The experimental data were interpreted through prior theoretical models, which led to the same conclusion, that increased substrate stiffness increased the number of cell–substrate adhesions and caused increased cell–substrate friction. In turn, the friction affected the collective migration by altering the curvature at the edge of the cell layer. By revealing underlying factors affecting friction and demonstrating how friction perturbs the collective migration, this work provides experimental evidence supporting prior theoretical models and motivates the study of other ways to alter the collective migration by changing friction.

Coordination of contractile tension and cell area changes in an epithelial cell monolayer

During tissue development and repair, cells contract and expand in coordination with their neighbors, giving rise to tissue deformations that occur on length scales far larger than that of a single cell. The biophysical mechanisms by which the contractile forces of each cell cause deformations on multicellular length scales are not fully clear. To investigate this question, we began with the principle of force equilibrium, which dictates a balance of tensile forces between neighboring cells. Based on this principle, we hypothesized that coordinated changes in cell area result from tension transmitted across the cell layer. To test this hypothesis, spatial correlations of both contractile tension and the divergence of cell velocities were measured as readouts of coordinated contractility and collective area changes, respectively. Experiments were designed to alter the spatial correlation of contractile tension using three different methods, including disrupting cell-cell adhesions, modulating the alignment of actomyosin stress fibers between neighboring cells, and changing the size of the cell monolayer. In all experiments, the spatial correlations of both tension and divergence increased or decreased together, in agreement with our hypothesis. To relate our findings to the intracellular mechanism connecting changes in cell area to contractile tension, we disrupted activation of extracellular signal-regulated kinase (ERK), which is known to mediate the intracellular relationship between cell area and contraction. Consistent with prior knowledge, a temporal cross-correlation between cell area and tension revealed that ERK was responsible for a proportional relationship between cell area and contraction. Inhibition of ERK activation reduced the spatial correlations of the divergence of cell velocity but not of tension. Together, our findings suggest that coordination of cell contraction and expansion requires transfer of cell tension over space and ERK-mediated coordination between cell area and contraction in time.

Active chemo-mechanical feedbacks dictate the collective migration of cells on patterned surfaces

Recent evidence has demonstrated that, when cultured on micro-patterned surfaces, living cells can move in a coordinated manner and form distinct migration patterns, including flowing chain, suspended propagating bridge, rotating vortex, etc. However, the fundamental question of exactly how and why cells migrate in these fashions remains elusive. Here, we present a theoretical investigation to show that the tight interplay between internal cellular activities, such as chemo-mechanical feedbacks and polarization, and external geometrical constraints are behind these intriguing experimental observations. In particular, on narrow strip patterns, strongly force-dependent cellular contractility and intercellular adhesion were found to be critical for reinforcing the leading edge of the migrating cell monolayer and eventually result in the formation of suspended cell bridges flying over nonadhesive regions. On the other hand, a weak force-contractility feedback led to the movement of cells like a flowing chain along the adhesive strip. Finally, we also showed that the random polarity forces generated in migrating cells are responsible for driving them into rotating vortices on strips with width above a threshold value (~10 times the size of the cell).

Mechanical waves caused by collective cell migration: generation

Long-timescale viscoelasticity caused by collective cell migration (CCM) significantly influences cell rearrangement and induces generation of mechanical waves. The phenomenon represents a product of the active turbulence occurring at low Reynolds number. The generation of mechanical waves has been a subject of intensive research primarily in 2D multicellular systems, while 3D systems have not been considered in this context. The aim of this contribution is to discuss the generation of mechanical waves during 3D CCM in two model systems: (1) the fusion of two-cell aggregates and (2) cell aggregate rounding after uni-axial compression, pointing out that mechanical waves represent a characteristic of CCM in general. Such perturbations are also involved in various biological processes, such as embryogenesis, wound healing and cancer invasion. The inter-relation between the viscoelasticity and the appearance of active turbulence remains poorly understood even in 2D. The phenomenon represents a consequence of the competition between the viscoelastic force and the surface tension force which induces successive stiffening and softening of parts of multicellular systems. The viscoelastic force is a product of the residual cell stress accumulation and its inhomogeneous distribution caused by CCM. This modeling consideration represents a powerful tool to address the generation of mechanical waves in CCM towards an understanding of this important but still controversial topic.

Spatio-temporal analysis of collective migrationin vivoby particle image velocimetry

Collective cell migration drives the formation of complex organ systems as well as certain tumour invasions and wound healing processes. A characteristic feature of many migrating collectives is tissue-scale polarity, whereby 'leader' cells at the tissue edge guide 'followers' cells that become assembled into polarized epithelial tissues. In this study, we employed particle image velocimetry (PIV) as a tool to quantitate local dynamics underlying the migration of the posterior lateral line primordium (pLLP) in zebrafish at a short time scale. Epithelial cadherin-EGFP was the fluorescent tracer in time-lapse images for PIV analysis. At the tissue level, global speed and directionality of the primordium were extracted from spatially averaged velocity fields. Interestingly, fluctuating velocity patterns evolve at the mesoscale level, which distinguishes the pseudo-mesenchymal leading front from the epithelialized trailing edge, and superimpose to the global deceleration of the whole primordium during the separation of a protoneuromast. Local velocity fields obtained by PIV proved sensitive to estimate the migration speed and directionality of the pLLP in zebrafish, predicting protoneuromast separation at short time scales. Finally, the PIV approach may be suitable for analysing the dynamics of otherin vivomodels of collective migration.

Physics of liquid crystals in cell biology

The past decade has witnessed a rapid growth in understanding of the pivotal roles of mechanical stresses and physical forces in cell biology. As a result, an integrated view of cell biology is evolving, where genetic and molecular features are scrutinised hand in hand with physical and mechanical characteristics of cells. Physics of liquid crystals has emerged as a burgeoning new frontier in cell biology over the past few years, fuelled by an increasing identification of orientational order and topological defects in cell biology, spanning scales from subcellular filaments to individual cells and multicellular tissues. Here, we provide an account of the most recent findings and developments, together with future promises and challenges in this rapidly evolving interdisciplinary research direction.

Oncogenic RAS instructs morphological transformation of human epithelia via differential tissue mechanics

The loss of epithelial homeostasis and the disruption of normal tissue morphology are hallmarks of tumor development. Here, we ask how the uniform activation oncogene RAS affects the morphology and tissue mechanics in a normal epithelium. We found that inducible induction of HRAS in confined epithelial monolayers on soft substrates drives a morphological transformation of a 2D monolayer into a compact 3D cell aggregate. This transformation was initiated by the loss of monolayer integrity and formation of two distinct cell layers with differential cell-cell junctions, cell-substrate adhesion, and tensional states. Computational modeling revealed how adhesion and active peripheral tension induces inherent mechanical instability in the system, which drives the 2D-to-3D morphological transformation. Consistent with this, removal of epithelial tension through the inhibition of actomyosin contractility halted the process. These findings reveal the mechanisms by which oncogene activation within an epithelium can induce mechanical instability to drive morphological tissue transformation.

Tight Junction ZO Proteins Maintain Tissue Fluidity, Ensuring Efficient Collective Cell Migration

Tight junctions (TJs) are essential components of epithelial tissues connecting neighboring cells to provide protective barriers. While their general function to seal compartments is well understood, their role in collective cell migration is largely unexplored. Here, the importance of the TJ zonula occludens (ZO) proteins ZO1 and ZO2 for epithelial migration is investigated employing video microscopy in conjunction with velocimetry, segmentation, cell tracking, and atomic force microscopy/spectroscopy. The results indicate that ZO proteins are necessary for fast and coherent migration. In particular, ZO1 and 2 loss (dKD) induces actomyosin remodeling away from the central cortex towards the periphery of individual cells, resulting in altered viscoelastic properties. A tug-of-war emerges between two subpopulations of cells with distinct morphological and mechanical properties: 1) smaller and highly contractile cells with an outward bulging apical membrane, and 2) larger, flattened cells, which, due to tensile stress, display a higher proliferation rate. In response, the cell density increases, leading to crowding-induced jamming and more small cells over time. Co-cultures comprising wildtype and dKD cells migrate inefficiently due to phase separation based on differences in contractility rather than differential adhesion. This study shows that ZO proteins are necessary for efficient collective cell migration by maintaining tissue fluidity and controlling proliferation.

Active flows and deformable surfaces in development

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

Mechanical plasticity in collective cell migration

Collective cell migration is crucial to maintain epithelium integrity during developmental and repair processes. It requires a tight regulation of mechanical coordination between neighboring cells. This coordination embraces different features including mechanical self-propulsion of individual cells within cellular colonies and large-scale force transmission through cell-cell junctions. This review discusses how the plasticity of biomechanical interactions at cell-cell contacts could help cellular systems to perform coordinated motions and adapt to the properties of the external environment.

Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells

Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.

Multiscale nature of cell rearrangement caused by collective cell migration

Collective cell migration (CCM), a highly coordinated and fine-tuned migratory mode, is involved in a plethora of biological processes, such as embryogenesis, tissue repair and cancer invasion. Although a good comprehension of how cells collectively migrate by following molecular rules has been generated, the impact of cellular rearrangements on collective migration remains less understood. Thus, considering CCM from a multi-scale quantitative approach could result in a powerful tool to address the contribution of cellular rearrangements in CCM and help to understand this important but still controversial topic. In this work, a review of existing literature in CCM modeling at different scales is given along with assortment of published experimental findings, to invite experimentalists to test given theoretical considerations in multicellular systems. In addition, three different time and space scales (free or weakly connected cells, cluster of cells and collision fronts of different cells clusters) are considered and the multi-scale nature of those processes was discussed with special emphasis of jamming and unjamming states.

Decrease in membrane fluidity and traction force induced by silica-coated magnetic nanoparticles

Background

Nanoparticles are being increasingly used in biomedical applications owing to their unique physical and chemical properties and small size. However, their biophysical assessment and evaluation of side-effects remain challenging. We addressed this issue by investigating the effects of silica-coated magnetic nanoparticles containing rhodamine B isothiocyanate [MNPs@SiO₂(RITC)] on biophysical aspects, such as membrane fluidity and traction force of human embryonic kidney 293 (HEK293) cells. We further extended our understanding on the biophysical effects of nanoparticles on cells using a combination of metabolic profiling and transcriptomic network analysis.

Results

Overdose (1.0 μg/µL) treatment with MNPs@SiO₂(RITC) induced lipid peroxidation and decreased membrane fluidity in HEK293 cells. In addition, HEK293 cells were morphologically shrunk, and their aspect ratio was significantly decreased. We found that each traction force (measured in micropillar) was increased, thereby increasing the total traction force in MNPs@SiO₂(RITC)-treated HEK293 cells. Due to the reduction in membrane fluidity and elevation of traction force, the velocity of cell movement was also significantly decreased. Moreover, intracellular level of adenosine triphosphate (ATP) was also decreased in a dose-dependent manner upon treatment with MNPs@SiO₂(RITC). To understand these biophysical changes in cells, we analysed the transcriptome and metabolic profiles and generated a metabotranscriptomics network, which revealed relationships among peroxidation of lipids, focal adhesion, cell movement, and related genes and metabolites. Furthermore, in silico prediction of the network showed increment in the peroxidation of lipids and suppression of focal adhesion and cell movement.

Conclusion

Taken together, our results demonstrated that overdose of MNPs@SiO₂(RITC) impairs cellular movement, followed by changes in the biophysical properties of cells, thus highlighting the need for biophysical assessment of nanoparticle-induced side-effects.

Tactics of cancer invasion: solitary and collective invasion

Much attention has been paid on the mechanism of cancer invasion from the viewpoint of the behaviour of individual cancer cells. On the other hand, histopathological analyses of specimens from cancer patients and of cancer invasion model animals have revealed that cancer cells often exhibit collective invasion, characterized by sustained cell-to-cell adhesion and polarized invasion as cell clusters. Interestingly, it has recently become evident that during collective invasion of cancer cells, the cells localized at invasion front (leader cells) and the cells following them (follower cells) exhibit distinct cellular characteristics, and that there exist the cells expressing representative proteins related to both epithelial and mesenchymal properties simultaneously, designated as hybrid epithelial-to-mesenchymal transition (EMT)-induced cells, in cancer tissue. Furthermore, the findings that cells adopted in hybrid EMT state form clusters and show collective invasion in vitro emphasize an importance of hybrid EMT-induced cells in collective cancer invasion. In this article, we overview recent findings of the mechanism underlying collective invasion of cancer cells and discuss the possibility of controlling cancer invasion and metastasis by targeting this process.

Cell-cell adhesion and 3D matrix confinement determine jamming transitions in breast cancer invasion

Plasticity of cancer invasion and metastasis depends on the ability of cancer cells to switch between collective and single-cell dissemination, controlled by cadherin-mediated cell-cell junctions. In clinical samples, E-cadherin-expressing and -deficient tumours both invade collectively and metastasize equally, implicating additional mechanisms controlling cell-cell cooperation and individualization. Here, using spatially defined organotypic culture, intravital microscopy of mammary tumours in mice and in silico modelling, we identify cell density regulation by three-dimensional tissue boundaries to physically control collective movement irrespective of the composition and stability of cell-cell junctions. Deregulation of adherens junctions by downregulation of E-cadherin and p120-catenin resulted in a transition from coordinated to uncoordinated collective movement along extracellular boundaries, whereas single-cell escape depended on locally free tissue space. These results indicate that cadherins and extracellular matrix confinement cooperate to determine unjamming transitions and stepwise epithelial fluidization towards, ultimately, cell individualization.

Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia

The coordination of cell proliferation and migration in growing tissues is crucial in development and regeneration but remains poorly understood. Here, we find that, while expanding with an edge speed independent of initial conditions, millimeter-scale epithelial monolayers exhibit internal patterns of proliferation and migration that depend not on the current but on the initial tissue size, indicating memory effects. Specifically, the core of large tissues becomes very dense, almost quiescent, and ceases cell-cycle progression. In contrast, initially-smaller tissues develop a local minimum of cell density and a tissue-spanning vortex. To explain vortex formation, we propose an active polar fluid model with a feedback between cell polarization and tissue flow. Taken together, our findings suggest that expanding epithelia decouple their internal and edge regions, which enables robust expansion dynamics despite the presence of size- and history-dependent patterns in the tissue interior.

Active inter-cellular forces in collective cell motility

The collective behaviour of confluent cell sheets is strongly influenced both by polar forces, arising through cytoskeletal propulsion, and by active inter-cellular forces, which are mediated by interactions across cell-cell junctions. We use a phase-field model to explore the interplay between these two contributions and compare the dynamics of a cell sheet when the polarity of the cells aligns to (i) their main axis of elongation, (ii) their velocity and (iii) when the polarity direction executes a persistent random walk. In all three cases, we observe a sharp transition from a jammed state (where cell rearrangements are strongly suppressed) to a liquid state (where the cells can move freely relative to each other) when either the polar or the inter-cellular forces are increased. In addition, for case (ii) only, we observe an additional dynamical state, flocking (solid or liquid), where the majority of the cells move in the same direction. The flocking state is seen for strong polar forces, but is destroyed as the strength of the inter-cellular activity is increased.

Collective cell migration and residual stress accumulation: Rheological consideration

Stress generation during collective cell migration represents one of the key factors which influence the configuration of migrating cells, viscoelasticity of multicellular systems and their inter-relation. Local generation of stress (normal and shear) is significant even in 2D. Normal stress is primarily accumulated within a core region of migrating cell clusters during their movement through the dense environment and during the collisions of migrating cell clusters caused by uncorrelated motility. Shear stress can be significant within perturbed boundary layers around migrating clusters. Cells are more sensitive to the action of shear stress compared with normal stress. Shear stress of a few Pa significantly influences cell state. Prior studies have shown that collectively migrating cells move in such a way to minimize this stress, but it has not yet been determined how cells effectively minimize it. Deeper insight into possible cell mechanisms for minimizing undesirable shear stress would be of great importance because it may help to direct morphogenesis, accelerate wound healing or prevent cancer invasion. In the proposed model three primary mechanisms in which cells may reduce shear are given: decreasing speed, tissue thickening, and/or reducing slip effects. Suggestions obtained from the proposed model indicate a need for further experimental studies that will reveal whether the heterogeneity in the cell-cell adhesion types correlates well with the stiffness inhomogeneity, or changes in the adhesion clustering, cytoskeletal linkage or some other modification to the adhesion complex (adherens junctions or tight junctions) are occurring to influence overall adhesive strength.

Spatiotemporal force and motion in collective cell migration

Cells move in collective groups in biological processes such as wound healing, morphogenesis, and cancer metastasis. How active cell forces produce the motion in collective cell migration is still unclear. Many theoretical models have been introduced to elucidate the relationship between the cell's active forces and different observations about the collective motion such as collective swirls, oscillations, and rearrangements. Though many models share the common feature of balancing forces in the cell layer, the specific relationships between force and motion vary among the different models, which can lead to different conclusions. Simultaneous experimental measurements of force and motion can aid in testing assumptions and predictions of the theoretical models. Here, we provide time-lapse images of cells in 1 mm circular islands, which are used to compute cell velocities, cell-substrate tractions, and monolayer stresses. Additional data are included from experiments that perturbed cell number density and actomyosin contractility. We expect this data set to be useful to researchers interested in force and motion in collective cell migration.

ERK-Mediated Mechanochemical Waves Direct Collective Cell Polarization

During collective migration of epithelial cells, the migration direction is aligned over a tissue-scale expanse. Although the collective cell migration is known to be directed by mechanical forces transmitted via cell-cell junctions, it remains elusive how the intercellular force transmission is coordinated with intracellular biochemical signaling to achieve collective movements. Here, we show that intercellular coupling of extracellular signal-regulated kinase (ERK)-mediated mechanochemical feedback yields long-distance transmission of guidance cues. Mechanical stretch activates ERK through epidermal growth factor receptor (EGFR) activation, and ERK activation triggers cell contraction. The contraction of the activated cell pulls neighboring cells, evoking another round of ERK activation and contraction in the neighbors. Furthermore, anisotropic contraction based on front-rear polarization guarantees unidirectional propagation of ERK activation, and in turn, the ERK activation waves direct multicellular alignment of the polarity, leading to long-range ordered migration. Our findings reveal that mechanical forces mediate intercellular signaling underlying sustained transmission of guidance cues for collective cell migration.

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.