Contact inhibition of locomotion probabilities drive solitary versus collective cell migration

Limits on the accuracy of contact inhibition of locomotion

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor-much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false-positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Polarization and motility of one-dimensional multi-cellular trains

Collective cell migration, whereby cells adhere to form multi-cellular clusters that move as a single entity, play an important role in numerous biological processes, such as during development and cancer progression. Recent experimental work focused on migration of one-dimensional cellular clusters, confined to move along adhesive lanes, as a simple geometry in which to systematically study this complex system. One-dimensional migration also arises in the body when cells migrate along blood vessels, axonal projections, and narrow cavities between tissues. We explore here the modes of one-dimensional migration of cellular clusters ("trains") by implementing cell-cell interactions in a model of cell migration that contains a mechanism for spontaneous cell polarization. We go beyond simple phenomenological models of the cells as self-propelled particles by having the internal polarization of each cell depend on its interactions with the neighboring cells that directly affect the actin polymerization activity at the cell's leading edges. Both contact inhibition of locomotion and cryptic lamellipodia interactions between neighboring cells are introduced. We find that this model predicts multiple motility modes of the cell trains, which can have several different speeds for the same polarization pattern. Compared to experimental data, we find that Madin-Darby canine kidney cells are poised along the transition region where contact inhibition of locomotion and cryptic lamellipodia roughly balance each other, where collective migration speed is most sensitive to the values of the cell-cell interaction strength.

Tumour follower cells: A novel driver of leader cells in collective invasion (Review)

Collective cellular invasion in malignant tumours is typically characterized by the cooperative migration of multiple cells in close proximity to each other. Follower cells are led away from the tumour by specialized leader cells, and both cell populations play a crucial role in collective invasion. Follower cells form the main body of the migration system and depend on intercellular contact for migration, whereas leader cells indicate the direction for the entire cell population. Although collective invasion can occur in epithelial and non‑epithelial malignant neoplasms, such as medulloblastoma and rhabdomyosarcoma, the present review mainly provided an extensive analysis of epithelial tumours. In the present review, the cooperative mechanisms of contact inhibition locomotion between follower and leader cells, where follower cells coordinate and direct collective movement through physical (mechanical) and chemical (signalling) interactions, is summarised. In addition, the molecular mechanisms of follower cell invasion and metastasis during remodelling and degradation of the extracellular matrix and how chemotaxis and lateral inhibition mediate follower cell behaviour were analysed. It was also demonstrated that follower cells exhibit genetic and metabolic heterogeneity during invasion, unlike leader cells.

MACC1-induced migration in tumors: Current state and perspective

Malignant tumors are still a global, heavy health burden. Many tumor types cannot be treated curatively, underlining the need for new treatment targets. In recent years, metastasis associated in colon cancer 1 (MACC1) was identified as a promising biomarker and drug target, as it is promoting tumor migration, initiation, proliferation, and others in a multitude of solid cancers. Here, we will summarize the current knowledge about MACC1-induced tumor cell migration with a special focus on the cytoskeletal and adhesive systems. In addition, a brief overview of several in vitro models used for the analysis of cell migration is given. In this context, we will point to issues with the currently most prevalent models used to study MACC1-dependent migration. Lastly, open questions about MACC1-dependent effects on tumor cell migration will be addressed.

Nuclear export inhibition jumbles epithelial-mesenchymal states and gives rise to migratory disorder in healthy epithelia

Dynamic nucleocytoplasmic transport of E-M factors regulates cellular E-M states; yet, it remains unknown how simultaneously trapping these factors affects epithelia at the macroscale. To explore this question, we performed nuclear export inhibition (NEI) via leptomycin B and Selinexor treatment, which biases nuclear localization of CRM1-associated E-M factors. We examined changes in collective cellular phenotypes across a range of substrate stiffnesses. Following NEI, soft substrates elevate collective migration of MCF10A cells for up to 24 hr, while stiffer substrates reduce migration at all time points. Our results suggest that NEI disrupts migration through competition between intercellular adhesions and mechanoactivation, generally causing loss of cell-cell coordination. Specifically, across substrate stiffnesses, NEI fosters an atypical E-M state wherein MCF10A cells become both more epithelial and more mesenchymal. We observe that NEI fosters a range of these concurrent phenotypes, from more epithelial shYAP MCF10A cells to more mesenchymal MDCK II cells. α-Catenin emerges as a potential link between E-M states, where it maintains normal levels of intercellular adhesion and transmits mechanoactive characteristics to collective behavior. Ultimately, to accommodate the concurrent states observed here, we propose an expanded E-M model, which may help further understand fundamental biological phenomena and inform pathological treatments.

A mathematical model of wound healing in bovine corneal endothelium

We developed a mathematical model to describe healing processes in bovine corneal endothelial (BCE) cells in culture, triggered by mechanical wounds with parallel edges. Previous findings from our laboratory show that, in these cases, BCE monolayers exhibit an approximately constant healing velocity. Also, that caspase-dependent apoptosis occurs, with the fraction of apoptotic cells increasing with the distance traveled by the healing edge. In addition, in this study we report the novel findings that, for wound scratch assays performed preserving the basal extracellular matrix: i) the healing cells increase their en face surface area in a characteristic fashion, and ii) the average length of the segments of the cell columns actively participating in the healing process increases linearly with time. These latter observations preclude the utilization of standard traveling wave formalisms to model wound healing in BCE cells. Instead, we developed and studied a simple phenomenological model based on a plausible formula for the spreading dynamics of the individual healing cells, that incorporates original evidence about the process in BCE cells. The model can be simulated to: i) obtain an approximately constant healing velocity; ii) reproduce the profile of the healing cell areas, and iii) obtain approximately linear time dependences of the mean cell area and average length of the front active segments per column. In view of its accuracy to account for the experimental observations, the model can also be acceptably employed to quantify the appearance of apoptotic cells during BCE wound healing. The strategy utilized here could offer a novel formal framework to represent modifications undergone by some epithelial cell lines during wound healing.

Collective chemotaxis in a Voronoi model for confluent clusters

Collective chemotaxis, where single cells cannot climb a biochemical signaling gradient but clusters of cells can, has been observed in different biological contexts, including confluent tissues where there are no gaps or overlaps between cells. Although particle-based models have been developed that predict important features of collective chemotaxis, the mechanisms in those models depend on particle overlaps, and so it remains unclear if they can explain behavior in confluent systems. Here, we develop an open-source code that couples a two-dimensional Voronoi simulation for confluent cell mechanics to a dynamic chemical signal that can diffuse, advect, and/or degrade and use the code to study potential mechanisms for collective chemotaxis in cellular monolayers. We first study the impact of advection on collective chemotaxis and delineate a regime where advective terms are important. Next, we investigate two possible chemotactic mechanisms, contact inhibition of locomotion and heterotypic interfacial tension, and demonstrate that both can drive collective chemotaxis in certain parameter regimes. We further demonstrate that the scaling behavior of cluster motion is well captured by simple analytic theories.

Picking winners in cell-cell collisions: Wetting, speed, and contact

Groups of eukaryotic cells can coordinate their crawling motion to follow cues more effectively, stay together, or invade new areas. This collective cell migration depends on cell-cell interactions, which are often studied by colliding pairs of cells together. Can the outcome of these collisions be predicted? Recent experiments on trains of colliding epithelial cells suggest that cells with a smaller contact angle to the surface or larger speeds are more likely to maintain their direction ("win") upon collision. When should we expect shape or speed to correlate with the outcome of a collision? To investigate this question, we build a model for two-cell collisions within the phase field framework, which allows for cell shape changes. We can reproduce the observation that cells with high speed and small contact angles are more likely to win with two different assumptions for how cells interact: (1) velocity aligning, in which we hypothesize that cells sense their own velocity and align to it over a finite timescale, and (2) front-front contact repolarization, where cells polarize away from cell-cell contact, akin to contact inhibition of locomotion. Surprisingly, though we simulate collisions between cells with widely varying properties, in each case, the probability of a cell winning is completely captured by a single summary variable: its relative speed (in the velocity-aligning model) or its relative contact angle (in the contact repolarization model). Both models are currently consistent with reported experimental results, but they can be distinguished by varying cell contact angle and speed through orthogonal perturbations.

Cell Repolarization: A Bifurcation Study of Spatio-Temporal Perturbations of Polar Cells

The intrinsic polarity of migrating cells is regulated by spatial distributions of protein activity. Those proteins (Rho-family GTPases, such as Rac and Rho) redistribute in response to stimuli, determining the cell front and back. Reaction-diffusion equations with mass conservation and positive feedback have been used to explain initial polarization of a cell. However, the sensitivity of a polar cell to a reversal stimulus has not yet been fully understood. We carry out a PDE bifurcation analysis of two polarity models to investigate routes to repolarization: (1) a single-GTPase ("wave-pinning") model and (2) a mutually antagonistic Rac-Rho model. We find distinct routes to reversal in (1) vs. (2). We show numerical simulations of full PDE solutions for the RD equations, demonstrating agreement with predictions of the bifurcation results. Finally, we show that simulations of the polarity models in deforming 1D model cells are consistent with biological experiments.

Dynamic self-organization of migrating cells under constraints by spatial confinement and epithelial integrity

Understanding how migrating cells can establish both dynamic structures and coherent dynamics may provide mechanistic insights to study how living systems acquire complex structures and functions. Recent studies revealed that intercellular contact communication plays a crucial role for establishing cellular dynamic self-organization (DSO) and provided a theoretical model of DSO for migrating solitary cells in a free space. However, to apply those understanding to situations in living organisms, we need to know the role of cell-cell communication for tissue dynamics under spatial confinements and epithelial integrity. Here, we expand the previous numerical studies on DSO to migrating cells subjected spatial confinement and/or epithelial integrity. An epithelial monolayer is simulated by combining the model of cellular DSO and the cellular vertex model in two dimensions for apical integrity. Under confinement to a small space, theoretical models of both solitary and epithelial cells exhibit characteristic coherent dynamics, including apparent swirling. We also find that such coherent dynamics can allow the cells to overcome the strong constraint due to spatial confinement and epithelial integrity. Furthermore, we demonstrate how epithelial cell clusters behave without spatial confinement and find various cluster dynamics, including spinning, migration and elongation.

Roles of leader and follower cells in collective cell migration

Collective cell migration is a widely observed phenomenon during animal development, tissue repair, and cancer metastasis. Considering its broad involvement in biological processes, it is essential to understand the basics behind the collective movement. Based on the topology of migrating populations, tissue-scale kinetics, called the “leader–follower” model, has been proposed for persistent directional collective movement. Extensive in vivo and in vitro studies reveal the characteristics of leader cells, as well as the special mechanisms leader cells employ for maintaining their positions in collective migration. However, follower cells have attracted increasing attention recently due to their important contributions to collective movement. In this Perspective, the current understanding of the molecular mechanisms behind the “leader–follower” model is reviewed with a special focus on the force transmission and diverse roles of leaders and followers during collective cell movement.

Rules of contact inhibition of locomotion for cells on suspended nanofibers

Contact inhibition of locomotion (CIL), in which cells repolarize and move away from contact, is now established as a fundamental driving force in development, repair, and disease biology. Much of what we know of CIL stems from studies on two-dimensional (2D) substrates that do not provide an essential biophysical cue-the curvature of extracellular matrix fibers. We discover rules controlling outcomes of cell-cell collisions on suspended nanofibers and show them to be profoundly different from the stereotyped CIL behavior on 2D substrates. Two approaching cells attached to a single fiber do not repolarize upon contact but rather usually migrate past one another. Fiber geometry modulates this behavior; when cells attach to two fibers, reducing their freedom to reorient, only one cell repolarizes on contact, leading to the cell pair migrating as a single unit. CIL outcomes also change when one cell has recently divided and moves with high speed-cells more frequently walk past each other. Our computational model of CIL in fiber geometries reproduces the core qualitative results of the experiments robustly to model parameters. Our model shows that the increased speed of postdivision cells may be sufficient to explain their increased walk-past rate. We also identify cell-cell adhesion as a key mediator of collision outcomes. Our results suggest that characterizing cell-cell interactions on flat substrates, channels, or micropatterns is not sufficient to predict interactions in a matrix-the geometry of the fiber can generate entirely new behaviors.

Intermediate adhesion maximizes migration velocity of multicellular clusters

Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller subclusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal description based on the lattice gas model of statistical physics and a more realistic framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. In both cases, we find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between maintaining cell-cell contact and maintaining configurational freedom, and we identify maximal variability in the cluster aspect ratio as a revealing signature. Our results suggest a collective benefit for intermediate cell-cell adhesion.

Learning the dynamics of cell-cell interactions in confined cell migration

The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of migrating cells. While data-driven physical formalisms for the stochastic migration dynamics of single cells have been developed, such a framework for the behavioral dynamics of interacting cells still remains elusive. Here, we monitor stochastic cell trajectories in a minimal experimental cell collider: a dumbbell-shaped micropattern on which pairs of cells perform repeated cellular collisions. We observe different characteristic behaviors, including cells reversing, following, and sliding past each other upon collision. Capitalizing on this large experimental dataset of coupled cell trajectories, we infer an interacting stochastic equation of motion that accurately predicts the observed interaction behaviors. Our approach reveals that interacting noncancerous MCF10A cells can be described by repulsion and friction interactions. In contrast, cancerous MDA-MB-231 cells exhibit attraction and antifriction interactions, promoting the predominant relative sliding behavior observed for these cells. Based on these experimentally inferred interactions, we show how this framework may generalize to provide a unifying theoretical description of the diverse cellular interaction behaviors of distinct cell types.

Dynamic Self-Organization of Idealized Migrating Cells by Contact Communication

This Letter investigates what forms of cellular dynamic self-organization are caused through intercellular contact communication based on a theoretical model in which migrating cells perform contact following and contact inhibition and attraction of locomotion. Tuning those strengths causes varieties of dynamic patterns. This further includes a novel form of collective migration, snakelike dynamic assembly. Scrutinizing this pattern reveals that cells in this state can accurately respond to an external directional cue but have no spontaneous global polar order.

Cell Migration Guided by Cell-Cell Contacts in Innate Immunity

The directed migration of leukocytes to sites of damage or infection is necessary for a productive immune response. There is substantial evidence supporting a key role for chemoattractants in directed migration, however, less is known about how cell-cell contacts affect the migratory behavior of leukocytes in innate immunity. Here, we explore how cell-cell contacts can affect the directed migration of innate immune cells, including their role in attracting, repelling, or stopping cell motility. Further investigation of cell contact dynamics as guidance cues may yield new insights into the regulation of innate immunity.

Bridging from single to collective cell migration: A review of models and links to experiments

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.

Rules of collective migration: from the wildebeest to the neural crest

Collective migration, the movement of groups in which individuals affect the behaviour of one another, occurs at practically every scale, from bacteria up to whole species' populations. Universal principles of collective movement can be applied at all levels. In this review, we will describe the rules governing collective motility, with a specific focus on the neural crest, an embryonic stem cell population that undergoes extensive collective migration during development. We will discuss how the underlying principles of individual cell behaviour, and those that emerge from a supracellular scale, can explain collective migration. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

The role of single cell mechanical behavior and polarity in driving collective cell migration

The directed migration of cell collectives is essential in various physiological processes, such as epiboly, intestinal epithelial turnover, and convergent extension during morphogenesis as well as during pathological events like wound healing and cancer metastasis. Collective cell migration leads to the emergence of coordinated movements over multiple cells. Our current understanding emphasizes that these movements are mainly driven by large-scale transmission of signals through adherens junctions. In this study, we show that collective movements of epithelial cells can be triggered by polarity signals at the single cell level through the establishment of coordinated lamellipodial protrusions. We designed a minimalistic model system to generate one-dimensional epithelial trains confined in ring shaped patterns that recapitulate rotational movements observed in vitro in cellular monolayers and in vivo in genitalia or follicular cell rotation. Using our system, we demonstrated that cells follow coordinated rotational movements after the establishment of directed Rac1-dependent polarity over the entire monolayer. Our experimental and numerical approaches show that the maintenance of coordinated migration requires the acquisition of a front-back polarity within each single cell but does not require the maintenance of cell-cell junctions. Taken together, these unexpected findings demonstrate that collective cell dynamics in closed environments as observed in multiple in vitro and in vivo situations can arise from single cell behavior through a sustained memory of cell polarity.

Dynamics of fiberboids

Fiberboids are active filaments trapped at the interface of two phases, able of harnessing energy (and matter) fluxes across the interface in order to produce a rolling-like self-propulsion. We discuss several table-top examples and develop the physical framework for understanding their complex dynamics. In spite of some specific features in the examples studied we conclude that the phenomenon of fiberboids is highly generic and robust across different materials, types of fluxes and timescales. Fiberboid motility should play a role from the macroscopic realm down to the micro scale and, as recently hypothesized, possibly as a means of biological self-propulsion that has escaped previous attention.

Active gel segment behaving as an active particle

We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction-driven cell motility, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bistability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile, and periodically repolarizing regimes displayed by an active agent confined in a viscoelastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.

Mechanisms of Neural Crest Migration

Neural crest cells are a transient embryonic cell population that migrate collectively to various locations throughout the embryo to contribute a number of cell types to several organs. After induction, the neural crest delaminates and undergoes an epithelial-to-mesenchymal transition before migrating through intricate yet characteristic paths. The neural crest exhibits a variety of migratory behaviors ranging from sheet-like mass migration in the cephalic regions to chain migration in the trunk. During their journey, neural crest cells rely on a range of signals both from their environment and within the migrating population for navigating through the embryo as a collective. Here we review these interactions and mechanisms, including chemotactic cues of neural crest cells' migration.

Coordination of cell migration mediated by site-dependent cell-cell contact

Contact inhibition of locomotion (CIL), the repulsive response of cells upon cell-cell contact, has been the predominant paradigm for contact-mediated responses. However, it is difficult for CIL alone to account for the complex behavior of cells within a multicellular environment, where cells often migrate in cohorts such as sheets, clusters, and streams. Although cell-cell adhesion and mechanical interactions play a role, how individual cells coordinate their migration within a multicellular environment remains unclear. Using micropatterned substrates to guide cell migration and manipulate cell-cell contact, we show that contacts between different regions of cells elicit different responses. Repulsive responses were limited to interaction with the head of a migrating cell, while contact with the tail of a neighboring cell promoted migration toward the tail. The latter behavior, termed contact following of locomotion (CFL), required the Wnt signaling pathway. Inhibition of the Wnt pathway disrupted not only CFL but also collective migration of epithelial cells, without affecting the migration of individual cells. In contrast, inhibition of myosin II with blebbistatin disrupted the migration of both individual epithelial cells and collectives. We propose that CFL, in conjunction with CIL, plays a major role in guiding and coordinating cell migration within a multicellular environment.

Redistribution of Adhesive Forces through Src/FAK Drives Contact Inhibition of Locomotion in Neural Crest

Contact inhibition of locomotion is defined as the behavior of cells to cease migrating in their former direction after colliding with another cell. It has been implicated in multiple developmental processes and its absence has been linked to cancer invasion. Cellular forces are thought to govern this process; however, the exact role of traction through cell-matrix adhesions and tension through cell-cell adhesions during contact inhibition of locomotion remains unknown. Here we use neural crest cells to address this and show that cell-matrix adhesions are rapidly disassembled at the contact between two cells upon collision. This disassembly is dependent upon the formation of N-cadherin-based cell-cell adhesions and driven by Src and FAK activity. We demonstrate that the loss of cell-matrix adhesions near the contact leads to a buildup of tension across the cell-cell contact, a step that is essential to drive cell-cell separation after collision.

•

Focal adhesions disassemble at cell-cell contacts in contact inhibition of locomotion

•

FA disassembly at the cell contact during CIL requires N-cadherin/Src/FAK signaling

•

Cell separation during CIL involves a buildup of tension across the cell contact

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.

Nanomechanical Force Mapping of Restricted Cell-To-Cell Collisions Oscillating between Contraction and Relaxation

Contact-mediated cell migration strongly determines the invasiveness of the corresponding cells, collective migration, and morphogenesis. The quantitative study of cellular response upon contact relies on cell-to-cell collision, which rarely occurs in conventional cell culture. Herein, we developed a strategy to activate a robust cell-to-cell collision within smooth muscle cell pairs. Nanomechanical traction force mapping reveals that the collision process is promoted by the oscillatory modulations between contraction and relaxation and orientated by the filopodial bridge composed of nanosized contractile machinery. This strategy can enhance the occurrence of cell-to-cell collision, which renders it advantageous over traditional methods that utilize micropatterned coating to confine cell pairs. Furthermore, modulation of the balance between cell tugging force and traction force can determine the repolarization of cells and thus the direction of cell migration. Overall, our approach could help to reveal the mechanistic contribution in cell motility and provide insights in tissue engineering.

Chase-and-run dynamics in cell motility and the molecular rupture of interacting active elastic dimers

Cell migration in morphogenesis and cancer metastasis typically involves interplay between different cell types. We construct and study a minimal, one-dimensional model composed of two different motile cells with each cell represented as an active elastic dimer. The interaction between the two cells via cadherins is modeled as a spring that can rupture beyond a threshold force as it undergoes dynamic loading from the interacting motile cells. We obtain a phase diagram consisting of chase-and-run dynamics and clumping dynamics as a function of the stiffness of the interaction spring and the threshold force and, therefore, posit that active rupture, or rupture via active forces, is a mechanosensitive means to regulate dynamics between cells. Since the parameters in the model differentiate between N- and E-cadherins, we make predictions for the interactions between a placodelike cell and a neural crestlike cell in a microchannel as well as discuss how our results inform chase-and-run dynamics found in a group of placode cells interacting with a group of neural crest cells. In particular, an argument was made in the latter case that the feedback between cadherins and cell-substrate interaction via integrins was necessary to obtain the chase-and-run behavior. Based on our two-cell results, we argue that this feedback accentuates, but is not necessary for, the chase-and-run behavior.

Connecting individual to collective cell migration

Collective cell migration plays a pivotal role in the formation of organs, tissue regeneration, wound healing and many disease processes, including cancer. Despite the considerable existing knowledge on the molecular control of cell movements, it is unclear how the different observed modes of collective migration, especially for small groups of cells, emerge from the known behaviors of individual cells. Here we derive a physical description of collective cellular movements from first principles, while accounting for known phenomenological cell behaviors, such as contact inhibition of locomotion and force-induced cell repolarization. We show that this theoretical description successfully describes the motion of groups of cells of arbitrary numbers, connecting single cell behaviors and parameters (e.g., adhesion and traction forces) to the collective migration of small groups of cells and the expansion of large cell colonies. Specifically, using a common framework, we explain how cells characterized by contact inhibition of locomotion can display coherent collective behavior when in groups, even in the absence of biochemical signaling. We find an optimal group size leading to maximal group persistence and show that cell proliferation prevents the buildup of intercellular forces within cell colonies, enabling their expansion.

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.

Physical models of collective cell motility: from cell to tissue

In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

Emergent structures and dynamics of cell colonies by contact inhibition of locomotion

Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated either to tissue morphogenesis or to cancer progression. Here, we study the organization of cell colonies by means of simulations of self-propelled particles with generic cell-like interactions. The interplay between cell softness, cell-cell adhesion, and contact inhibition of locomotion (CIL) yields structures and collective dynamics observed in several existing tissue phenotypes. These include regular distributions of cells, dynamic cell clusters, gel-like networks, collectively migrating monolayers, and 3D aggregates. We give analytical predictions for transitions between noncohesive, cohesive, and 3D cell arrangements. We explicitly show how CIL yields an effective repulsion that promotes cell dispersal, thereby hindering the formation of cohesive tissues. Yet, in continuous monolayers, CIL leads to collective cell motion, ensures tensile intercellular stresses, and opposes cell extrusion. Thus, our work highlights the prominent role of CIL in determining the emergent structures and dynamics of cell colonies.

Modeling Contact Inhibition of Locomotion of Colliding Cells Migrating on Micropatterned Substrates

In cancer metastasis, embryonic development, and wound healing, cells can coordinate their motion, leading to collective motility. To characterize these cell-cell interactions, which include contact inhibition of locomotion (CIL), micropatterned substrates are often used to restrict cell migration to linear, quasi-one-dimensional paths. In these assays, collisions between polarized cells occur frequently with only a few possible outcomes, such as cells reversing direction, sticking to one another, or walking past one another. Using a computational phase field model of collective cell motility that includes the mechanics of cell shape and a minimal chemical model for CIL, we are able to reproduce all cases seen in two-cell collisions. A subtle balance between the internal cell polarization, CIL and cell-cell adhesion governs the collision outcome. We identify the parameters that control transitions between the different cases, including cell-cell adhesion, propulsion strength, and the rates of CIL. These parameters suggest hypotheses for why different cell types have different collision behavior and the effect of interventions that modulate collision outcomes. To reproduce the heterogeneity in cell-cell collision outcomes observed experimentally in neural crest cells, we must either carefully tune our parameters or assume that there is significant cell-to-cell variation in key parameters like cell-cell adhesion.

Many cells cooperate with their neighbors to move as a group. However, the mechanisms of these cell-cell interactions are not well understood. One experimental tool to analyze interactions is to allow cells to collide with one another, and see what happens. In order to better understand what features these experiments measure, we develop a computational model of cell-cell collisions, and identify the biochemical and mechanical parameters that lead to different outcomes of collisions. We can recreate all known types of collisions seen in experiments, including cells reversing on contact, sticking, or walking past each other. Our model suggests that what happens in a collision may depend strongly on the mechanical forces between the two cells.

Epithelial self-healing is recapitulated by a 3D biomimetic E-cadherin junction

Epithelial monolayers undergo self-healing when wounded. During healing, cells collectively migrate into the wound site, and the converging tissue fronts collide and form a stable interface. To heal, migrating tissues must form cell-cell adhesions and reorganize from the front-rear polarity characteristic of cell migration to the apical-basal polarity of an epithelium. However, identifying the "stop signal" that induces colliding tissues to cease migrating and heal remains an open question. Epithelial cells form integrin-based adhesions to the basal extracellular matrix (ECM) and E-cadherin-mediated cell-cell adhesions on the orthogonal, lateral surfaces between cells. Current biological tools have been unable to probe this multicellular 3D interface to determine the stop signal. We addressed this problem by developing a unique biointerface that mimicked the 3D organization of epithelial cell adhesions. This "minimal tissue mimic" (MTM) comprised a basal ECM substrate and a vertical surface coated with purified extracellular domain of E-cadherin, and was designed for collision with the healing edge of an epithelial monolayer. Three-dimensional imaging showed that adhesions formed between cells, and the E-cadherin-coated MTM resembled the morphology and dynamics of native epithelial cell-cell junctions and induced the same polarity transition that occurs during epithelial self-healing. These results indicate that E-cadherin presented in the proper 3D context constitutes a minimum essential stop signal to induce self-healing. That the Ecad:Fc MTM stably integrated into an epithelial tissue and reduced migration at the interface suggests that this biointerface is a complimentary approach to existing tissue-material interfaces.

Mechanisms and in vivo functions of contact inhibition of locomotion

Contact inhibition of locomotion (CIL) is a process whereby a cell ceases motility or changes its trajectory upon collision with another cell. CIL was initially characterized more than half a century ago and became a widely studied model system to understand how cells migrate and dynamically interact. Although CIL fell from interest for several decades, the scientific community has recently rediscovered this process. We are now beginning to understand the precise steps of this complex behaviour and to elucidate its regulatory components, including receptors, polarity proteins and cytoskeletal elements. Furthermore, this process is no longer just in vitro phenomenology; we now know from several different in vivo models that CIL is essential for embryogenesis and in governing behaviours such as cell dispersion, boundary formation and collective cell migration. In addition, changes in CIL responses have been associated with other physiological processes, such as cancer cell dissemination during metastasis.

Cell density and actomyosin contractility control the organization of migrating collectives within an epithelium

The mechanisms underlying collective migration are important for understanding development, wound healing, and tumor invasion. Here we focus on cell density to determine its role in collective migration. Our findings show that increasing cell density, as might be seen in cancer, transforms groups from broad collectives to small, narrow streams. Conversely, diminishing cell density, as might occur at a wound front, leads to large, broad collectives with a distinct leader-follower structure. Simulations identify force-sensitive contractility as a mediator of how density affects collectives, and guided by this prediction, we find that the baseline state of contractility can enhance or reduce organization. Finally, we test predictions from these data in an in vivo epithelium by using genetic manipulations to drive collective motion between predicted migratory phases. This work demonstrates how commonly altered cellular properties can prime groups of cells to adopt migration patterns that may be harnessed in health or exploited in disease.

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of "collective guidance" computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster's size-clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.

Ring-Shaped Microlanes and Chemical Barriers as a Platform for Probing Single-Cell Migration

Quantification and discrimination of pharmaceutical and disease-related effects on cell migration requires detailed characterization of single-cell motility. In this context, micropatterned substrates that constrain cells within defined geometries facilitate quantitative readout of locomotion. Here, we study quasi-one-dimensional cell migration in ring-shaped microlanes. We observe bimodal behavior in form of alternating states of directional migration (run state) and reorientation (rest state). Both states show exponential lifetime distributions with characteristic persistence times, which, together with the cell velocity in the run state, provide a set of parameters that succinctly describe cell motion. By introducing PEGylated barriers of different widths into the lane, we extend this description by quantifying the effects of abrupt changes in substrate chemistry on migrating cells. The transit probability decreases exponentially as a function of barrier width, thus specifying a characteristic penetration depth of the leading lamellipodia. Applying this fingerprint-like characterization of cell motion, we compare different cell lines, and demonstrate that the cancer drug candidate salinomycin affects transit probability and resting time, but not run time or run velocity. Hence, the presented assay allows to assess multiple migration-related parameters, permits detailed characterization of cell motility, and has potential applications in cell biology and advanced drug screening.

Control of the collective migration of enteric neural crest cells by the Complement anaphylatoxin C3a and N-cadherin

We analyzed the cellular and molecular mechanisms governing the adhesive and migratory behavior of enteric neural crest cells (ENCCs) during their collective migration within the developing mouse gut. We aimed to decipher the role of the complement anaphylatoxin C3a during this process, because this well-known immune system attractant has been implicated in cephalic NCC co-attraction, a process controlling directional migration.

We used the conditional Ht-PA-cre transgenic mouse model allowing a specific ablation of the N-cadherin gene and the expression of a fluorescent reporter in migratory ENCCs without affecting the central nervous system. We performed time-lapse videomicroscopy of ENCCs from control and N-cad-herin mutant gut explants cultured on fibronectin (FN) and micropatterned FN-stripes with C3a or C3aR antagonist, and studied cell migration behavior with the use of triangulation analysis to quantify cell dispersion. We performed ex vivo gut cultures with or without C3aR antagonist to determine the effect on ENCC behavior. Confocal microscopy was used to analyze the cell-matrix adhesion properties. We provide the first demonstration of the localization of the complement anaphylatoxin C3a and its receptor on ENCCs during their migration in the embryonic gut. C3aR receptor inhibition alters ENCC adhesion and migration, perturbing directionality and increasing cell dispersion both in vitro and ex vivo. N-cad-herin-null ENCCs do not respond to C3a co-attraction. These findings indicate that C3a regulates cell migration in a N-cadherin-dependent process. Our results shed light on the role of C3a in regulating collective and directional cell migration, and in ganglia network organization during enteric nervous system ontogenesis. The detection of an immune system chemokine in ENCCs during ENS development may also shed light on new mechanisms for gastrointestinal disorders.

Emergent Collective Chemotaxis without Single-Cell Gradient Sensing

Many eukaryotic cells chemotax, sensing and following chemical gradients. However, experiments show that even under conditions when single cells cannot chemotax, small clusters may still follow a gradient. This behavior is observed in neural crest cells, in lymphocytes, and during border cell migration in Drosophila, but its origin remains puzzling. Here, we propose a new mechanism underlying this "collective guidance," and study a model based on this mechanism both analytically and computationally. Our approach posits that contact inhibition of locomotion, where cells polarize away from cell-cell contact, is regulated by the chemoattractant. Individual cells must measure the mean attractant value, but need not measure its gradient, to give rise to directional motility for a cell cluster. We present analytic formulas for how the cluster velocity and chemotactic index depend on the number and organization of cells in the cluster. The presence of strong orientation effects provides a simple test for our theory of collective guidance.

Molecular basis of contact inhibition of locomotion

Contact inhibition of locomotion (CIL) is a complex process, whereby cells undergoing a collision with another cell cease their migration towards the colliding cell. CIL has been identified in numerous cells during development including embryonic fibroblasts, neural crest cells and haemocytes and is the driving force behind a range of phenomenon including collective cell migration and dispersion. The loss of normal CIL behaviour towards healthy tissue has long been implicated in the invasion of cancer cells. CIL is a multi-step process that is driven by the tight coordination of molecular machinery. In this review, we shall breakdown CIL into distinct steps and highlight the key molecular mechanisms and components that are involved in driving each step of this process.

The front and rear of collective cell migration

Collective cell migration has a key role during morphogenesis and during wound healing and tissue renewal in the adult, and it is involved in cancer spreading. In addition to displaying a coordinated migratory behaviour, collectively migrating cells move more efficiently than if they migrated separately, which indicates that a cellular interplay occurs during collective cell migration. In recent years, evidence has accumulated confirming the importance of such intercellular communication and exploring the molecular mechanisms involved. These mechanisms are based both on direct physical interactions, which coordinate the cellular responses, and on the collective cell behaviour that generates an optimal environment for efficient directed migration. The recent studies have described how leader cells at the front of cell groups drive migration and have highlighted the importance of follower cells and cell-cell communication, both between followers and between follower and leader cells, to improve the efficiency of collective movement.

Mechanobiology of cell migration in the context of dynamic two-way cell-matrix interactions

Migration of cells is integral in various physiological processes in all facets of life. These range from embryonic development, morphogenesis, and wound healing, to disease pathology such as cancer metastasis. While cell migratory behavior has been traditionally studied using simple assays on culture dishes, in recent years it has been increasingly realized that the physical, mechanical, and chemical aspects of the matrix are key determinants of the migration mechanism. In this paper, we will describe the mechanobiological changes that accompany the dynamic cell-matrix interactions during cell migration. Furthermore, we will review what is to date known about how these changes feed back to the dynamics and biomechanical properties of the cell and the matrix. Elucidating the role of these intimate cell-matrix interactions will provide not only a better multi-scale understanding of cell motility in its physiological context, but also a more holistic perspective for designing approaches to regulate cell behavior.

A three dimensional micropatterned tumor model for breast cancer cell migration studies

Breast cancer cell invasion is a highly orchestrated process driven by a myriad of complex microenvironmental stimuli, making it difficult to isolate and assess the effects of biochemical or biophysical cues (i.e. tumor architecture, matrix stiffness) on disease progression. In this regard, physiologically relevant tumor models are becoming instrumental to perform studies of cancer cell invasion within well-controlled conditions. Herein, we explored the use of photocrosslinkable hydrogels and a novel, two-step photolithography technique to microengineer a 3D breast tumor model. The microfabrication process enabled precise localization of cell-encapsulated circular constructs adjacent to a low stiffness matrix. To validate the model, breast cancer cell lines (MDA-MB-231, MCF7) and non-tumorigenic mammary epithelial cells (MCF10A) were embedded separately within the tumor model, all of which maintained high viability throughout the experiments. MDA-MB-231 cells exhibited extensive migratory behavior and invaded the surrounding matrix, whereas MCF7 or MCF10A cells formed clusters that stayed confined within the circular tumor regions. Additionally, real-time cell tracking indicated that the speed and persistence of MDA-MB-231 cells were substantially higher within the surrounding matrix compared to the circular constructs. Z-stack imaging of F-actin/α-tubulin cytoskeletal organization revealed unique 3D protrusions in MDA-MB-231 cells and an abundance of 3D clusters formed by MCF7 and MCF10A cells. Our results indicate that gelatin methacrylate (GelMA) hydrogel, integrated with the two-step photolithography technique, has great promise in the development of 3D tumor models with well-defined architecture and tunable stiffness.

SrGAP2-Dependent Integration of Membrane Geometry and Slit-Robo-Repulsive Cues Regulates Fibroblast Contact Inhibition of Locomotion

Migrating fibroblasts undergo contact inhibition of locomotion (CIL), a process that was discovered five decades ago and still is not fully understood at the molecular level. We identify the Slit2-Robo4-srGAP2 signaling network as a key regulator of CIL in fibroblasts. CIL involves highly dynamic contact protrusions with a specialized actin cytoskeleton that stochastically explore cell-cell overlaps between colliding fibroblasts. A membrane curvature-sensing F-BAR domain pre-localizes srGAP2 to protruding edges and terminates their extension phase in response to cell collision. A FRET-based biosensor reveals that Rac1 activity is focused in a band at the tip of contact protrusions, in contrast to the broad activation gradient in contact-free protrusions. SrGAP2 specifically controls the duration of Rac1 activity in contact protrusions, but not in contact-free protrusions. We propose that srGAP2 integrates cell edge curvature and Slit-Robo-mediated repulsive cues to fine-tune Rac1 activation dynamics in contact protrusions to spatiotemporally coordinate CIL.

Phenomenological approaches to collective behavior in epithelial cell migration

Collective cell migration in epithelial tissues resembles fluid-like behavior in time-lapse recordings. In the last years, hydrodynamic velocity fields in living matter have been studied intensely. The emergent properties were remarkably similar to phenomena known from active soft matter systems. Here, we review migration experiments of large cellular ensembles as well as of mesoscopic cohorts in micro-structured environments. Concepts such as diffusion, velocity correlations, swirl strength and polarization are metrics to quantify the cellular dynamics both in experiments as well as in computational simulations. We discuss challenges relating collective migration to single cell and oligocellular behavior as well as linking the phenotypic parameters to the underlying cytoskeleton dynamics and signaling networks. This article is part of a Special Issue entitled: Mechanobiology.

Microfabrication of Custom Collagen Structures Capable of Guiding Cell Morphology and Alignment

The patterning of biological components into structural analogues of native tissues to simulate an environment for directing cell growth is one important strategy in biomaterials fabrication. It is widely accepted that chemical, mechanical, and topological cues from the extracellular matrix (ECM) provide important signals for guiding cells to exhibit characteristic polarity, orientation, and morphology. To fully understand the delicate relationship between cell behavior and ECM features, biomaterials fabrication requires improved techniques for tailoring nano/microstructured patterns from relevant biological building blocks rather than using nonbiological materials. Here we reveal a unique approach for the nano/microfabrication of custom patterned biomaterials using collagen as the sole building material. With this new fabrication technique, we further revealed that custom collagen patterns could direct the orientation and morphology of fibroblast growth as a function of vertex density and pattern spacing. Our findings suggest that this technique may be readily adopted for the free form fabrication of custom cell scaffolds purely from natural biological molecules including collagen, among other relevant ECM components.

Interplay between chemotaxis and contact inhibition of locomotion determines exploratory cell migration

Directed cell migration in native environments is influenced by multiple migratory cues. These cues may include simultaneously occurring attractive soluble growth factor gradients and repulsive effects arising from cell-cell contact, termed contact inhibition of locomotion (CIL). How single cells reconcile potentially conflicting cues remains poorly understood. Here we show that a dynamic crosstalk between epidermal growth factor (EGF)-mediated chemotaxis and CIL guides metastatic breast cancer cell motility, whereby cells become progressively insensitive to CIL in a chemotactic input-dependent manner. This balance is determined via integration of protrusion-enhancing signalling from EGF gradients and protrusion-suppressing signalling induced by CIL, mediated in part through EphB. Our results further suggest that EphB and EGF signalling inputs control protrusion formation by converging onto regulation of phosphatidylinositol 3-kinase (PI3K). We propose that this intricate interplay may enhance the spread of loose cell ensembles in pathophysiological conditions such as cancer, and possibly other physiological settings.