Directional collective cell migration emerges as a property of cell interactions

Versatile system cores as a conceptual basis for generality in cell and developmental biology

The discovery of general principles underlying the complexity and diversity of cellular and developmental systems is a central and long-standing aim of biology. While new technologies collect data at an ever-accelerating rate, there is growing concern that conceptual progress is not keeping pace. We contend that this is due to a paucity of conceptual frameworks that support meaningful generalizations. This led us to develop the core and periphery (C&P) hypothesis, which posits that many biological systems can be decomposed into a highly versatile core with a large behavioral repertoire and a specific periphery that configures said core to perform one particular function. Versatile cores tend to be widely reused across biology, which confers generality to theories describing them. Here, we introduce this concept and describe examples at multiple scales, including Turing patterning, actomyosin dynamics, multi-cellular morphogenesis, and vertebrate gastrulation. We also sketch its evolutionary basis and discuss key implications and open questions. We propose that the C&P hypothesis could unlock new avenues of conceptual progress in mesoscale biology.

Colec12 and Trail signaling confine cranial neural crest cell trajectories and promote collective cell migration

BACKGROUND

Collective and discrete neural crest cell (NCC) migratory streams are crucial to vertebrate head patterning. However, the factors that confine NCC trajectories and promote collective cell migration remain unclear.

RESULTS

Computational simulations predicted that confinement is required only along the initial one-third of the cranial NCC migratory pathway. This guided our study of Colec12 (Collectin-12, a transmembrane scavenger receptor C-type lectin) and Trail (tumor necrosis factor-related apoptosis-inducing ligand, CD253) which we show expressed in chick cranial NCC-free zones. NCC trajectories are confined by Colec12 or Trail protein stripes in vitro and show significant and distinct changes in cell morphology and dynamic migratory characteristics when cocultured with either protein. Gain- or loss-of-function of either factor or in combination enhanced NCC confinement or diverted cell trajectories as observed in vivo with three-dimensional confocal microscopy, respectively, resulting in disrupted collective migration.

CONCLUSIONS

These data provide evidence for Colec12 and Trail as novel NCC microenvironmental factors playing a role to confine cranial NCC trajectories and promote collective cell migration.

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.

Directional Persistence of Cell Migration in Schizophrenia Patient-Derived Olfactory Cells

Cell migration is critical for brain development and linked to several neurodevelopmental disorders, including schizophrenia. We have shown previously that cell migration is dysregulated in olfactory neural stem cells from people with schizophrenia. Although they moved faster than control cells on plastic substrates, patient cells were insensitive to regulation by extracellular matrix proteins, which increase the speeds of control cells. As well as speed, cell migration is also described by directional persistence, the straightness of movement. The aim of this study was to determine whether directional persistence is dysregulated in schizophrenia patient cells and whether it is modified on extracellular matrix proteins. Directional persistence in patient-derived and control-derived olfactory cells was quantified from automated live-cell imaging of migrating cells. On plastic substrates, patient cells were more persistent than control cells, with straighter trajectories and smaller turn angles. On most extracellular matrix proteins, persistence increased in patient and control cells in a concentration-dependent manner, but patient cells remained more persistent. Patient cells therefore have a subtle but complex phenotype in migration speed and persistence on most extracellular matrix protein substrates compared to control cells. If present in the developing brain, this could lead to altered brain development in schizophrenia.

Contact inhibition of locomotion generates collective cell migration without chemoattractants in an open domain

Neural crest cells are embryonic stem cells that migrate throughout embryos and, at different target locations, give rise to the formation of a variety of tissues and organs. The directional migration of the neural crest cells is experimentally described using a process referred to as contact inhibition of locomotion, by which cells redirect their movement upon the cell-cell contacts. However, it is unclear how the migration alignment is affected by the motility properties of the cells. Here, we theoretically model the migration alignment as a function of the motility dynamics and interaction of the cells in an open domain with a channel geometry. The results indicate that by increasing the influx rate of the cells into the domain a transition takes place from random movement to an organized collective migration, where the migration alignment is maximized and the migration time is minimized. This phase transition demonstrates that the cells can migrate efficiently over long distances without any external chemoattractant information about the direction of migration just based on local interactions with each other. The analysis of the dependence of this transition on the characteristic properties of cellular motility shows that the cell density determines the coordination of collective migration whether the migration domain is open or closed. In the open domain, this density is determined by a feedback mechanism between the flux and order parameter, which characterises the alignment of collective migration. The model also demonstrates that the coattraction mechanism proposed earlier is not necessary for collective migration and a constant flux of cells moving into the channel is sufficient to produce directed movement over arbitrary long distances.

Filopodia-based contact stimulation of cell migration drives tissue morphogenesis

Cells migrate collectively to form tissues and organs during morphogenesis. Contact inhibition of locomotion (CIL) drives collective migration by inhibiting lamellipodial protrusions at cell-cell contacts and promoting polarization at the leading edge. Here, we report a CIL-related collective cell behavior of myotubes that lack lamellipodial protrusions, but instead use filopodia to move as a cohesive cluster in a formin-dependent manner. We perform genetic, pharmacological and mechanical perturbation analyses to reveal the essential roles of Rac2, Cdc42 and Rho1 in myotube migration. These factors differentially control protrusion dynamics and cell-matrix adhesion formation. We also show that active Rho1 GTPase localizes at retracting free edge filopodia and that Rok-dependent actomyosin contractility does not mediate a contraction of protrusions at cell-cell contacts, but likely plays an important role in the constriction of supracellular actin cables. Based on these findings, we propose that contact-dependent asymmetry of cell-matrix adhesion drives directional movement, whereas contractile actin cables contribute to the integrity of the migrating cell cluster.

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'.

Modelling collective cell migration: neural crest as a model paradigm

A huge variety of mathematical models have been used to investigate collective cell migration. The aim of this brief review is twofold: to present a number of modelling approaches that incorporate the key factors affecting cell migration, including cell-cell and cell-tissue interactions, as well as domain growth, and to showcase their application to model the migration of neural crest cells. We discuss the complementary strengths of microscale and macroscale models, and identify why it can be important to understand how these modelling approaches are related. We consider neural crest cell migration as a model paradigm to illustrate how the application of different mathematical modelling techniques, combined with experimental results, can provide new biological insights. We conclude by highlighting a number of future challenges for the mathematical modelling of neural crest cell migration.

Modelling chase-and-run migration in heterogeneous populations

Cell migration is crucial for many physiological and pathological processes. During embryogenesis, neural crest cells undergo coordinated epithelial to mesenchymal transformations and migrate towards various forming organs. Here we develop a computational model to understand how mutual interactions between migrating neural crest cells (NCs) and the surrounding population of placode cells (PCs) generate coordinated migration. According to experimental findings, we implement a minimal set of hypotheses, based on a coupling between chemotactic movement of NCs in response to a placode-secreted chemoattractant (Sdf1) and repulsion induced from contact inhibition of locomotion (CIL), triggered by heterotypic NC–PC contacts. This basic set of assumptions is able to semi-quantitatively recapitulate experimental observations of the characteristic multispecies phenomenon of “chase-and-run”, where the colony of NCs chases an evasive PC aggregate. The model further reproduces a number of in vitro manipulations, including full or partial disruption of NC chemotactic migration and selected mechanisms coordinating the CIL phenomenon. Finally, we provide various predictions based on altering other key components of the model mechanisms.

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell-cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell-cell boundaries can buckle. In this paper, we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the Cellular Potts Model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell-cell shear or sliding, from which cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks.

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.

Sustained Oscillations of Epithelial Cell Sheets

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

Neural crest streaming as an emergent property of tissue interactions during morphogenesis

A fundamental question in embryo morphogenesis is how a complex pattern is established in seemingly uniform tissues. During vertebrate development, neural crest cells differentiate as a continuous mass of tissue along the neural tube and subsequently split into spatially distinct migratory streams to invade the rest of the embryo. How these streams are established is not well understood. Inhibitory signals surrounding the migratory streams led to the idea that position and size of streams are determined by a pre-pattern of such signals. While clear evidence for a pre-pattern in the cranial region is still lacking, all computational models of neural crest migration published so far have assumed a pre-pattern of negative signals that channel the neural crest into streams. Here we test the hypothesis that instead of following a pre-existing pattern, the cranial neural crest creates their own migratory pathway by interacting with the surrounding tissue. By combining theoretical modeling with experimentation, we show that streams emerge from the interaction of the hindbrain neural crest and the neighboring epibranchial placodal tissues, without the need for a pre-existing guidance cue. Our model suggests that the initial collective neural crest invasion is based on short-range repulsion and asymmetric attraction between neighboring tissues. The model provides a coherent explanation for the formation of cranial neural crest streams in concert with previously reported findings and our new in vivo observations. Our results point to a general mechanism of inducing collective invasion patterns.

Cellular organization and boundary formation in craniofacial development

Craniofacial morphogenesis is a highly dynamic process that requires changes in the behaviors and physical properties of cells in order to achieve the proper organization of different craniofacial structures. Boundary formation is a critical process in cellular organization, patterning, and ultimately tissue separation. There are several recurring cellular mechanisms through which boundary formation and cellular organization occur including, transcriptional patterning, cell segregation, cell adhesion and migratory guidance. Disruption of normal boundary formation has dramatic morphological consequences, and can result in human craniofacial congenital anomalies. In this review we discuss boundary formation during craniofacial development, specifically focusing on the cellular behaviors and mechanisms underlying the self-organizing properties that are critical for craniofacial morphogenesis.

Non-local Parabolic and Hyperbolic Models for Cell Polarisation in Heterogeneous Cancer Cell Populations

Tumours consist of heterogeneous populations of cells. The sub-populations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell–cell interactions, i.e. attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell–cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.

Neural crest delamination and migration: Looking forward to the next 150 years

Neural crest (NC) cells were described for the first time in 1868 by Wilhelm His. Since then, this amazing population of migratory stem cells has been intensively studied. It took a century to fully unravel their incredible abilities to contribute to nearly every organ of the body. Yet, our understanding of the cell and molecular mechanisms controlling their migration is far from complete. In this review, we summarize the current knowledge on epithelial-mesenchymal transition and collective behavior of NC cells and propose further stops at which the NC train might be calling in the near future.

Dancing Styles of Collective Cell Migration: Image-Based Computational Analysis of JRAB/MICAL-L2

Collective cell migration is observed during morphogenesis, angiogenesis, and wound healing, and this type of cell migration also contributes to efficient metastasis in some kinds of cancers. Because collectively migrating cells are much better organized than a random assemblage of individual cells, there seems to be a kind of order in migrating clusters. Extensive research has identified a large number of molecules involved in collective cell migration, and these factors have been analyzed using dramatic advances in imaging technology. To date, however, it remains unclear how myriad cells are integrated as a single unit. Recently, we observed unbalanced collective cell migrations that can be likened to either precision dancing or awa-odori, Japanese traditional dancing similar to the style at Rio Carnival, caused by the impairment of the conformational change of JRAB/MICAL-L2. This review begins with a brief history of image-based computational analyses on cell migration, explains why quantitative analysis of the stylization of collective cell behavior is difficult, and finally introduces our recent work on JRAB/MICAL-L2 as a successful example of the multidisciplinary approach combining cell biology, live imaging, and computational biology. In combination, these methods have enabled quantitative evaluations of the “dancing style” of collective cell migration.

Propagating Wave of ERK Activation Orients Collective Cell Migration

The biophysical framework of collective cell migration has been extensively investigated in recent years; however, it remains elusive how chemical inputs from neighboring cells are integrated to coordinate the collective movement. Here, we provide evidence that propagation waves of extracellular signal-related kinase (ERK) mitogen-activated protein kinase activation determine the direction of the collective cell migration. A wound-healing assay of Mardin-Darby canine kidney (MDCK) epithelial cells revealed two distinct types of ERK activation wave, a "tidal wave" from the wound, and a self-organized "spontaneous wave" in regions distant from the wound. In both cases, MDCK cells collectively migrated against the direction of the ERK activation wave. The inhibition of ERK activation propagation suppressed collective cell migration. An ERK activation wave spatiotemporally controlled actomyosin contraction and cell density. Furthermore, an optogenetic ERK activation wave reproduced the collective cell migration. These data provide new mechanistic insight into how cells sense the direction of collective cell migration.

Neural crest and cancer: Divergent travelers on similar paths

Neural crest cells are multipotent progenitors that dynamically interpret diverse microenvironments to migrate significant distances as a loosely associated collective and contribute to many tissues in the developing vertebrate embryo. Uncovering details of neural crest migration has helped to inform a general understanding of collective cell migration, including that which occurs during cancer metastasis. Here, we discuss several commonalities and differences of neural crest and cancer cell migration and behavior. First, we focus on some of the molecular pathways required for the initial specification and potency of neural crest cells and the roles of many of these pathways in cancer progression. We also describe epithelial-to-mesenchymal transition, which plays a critical role in initiating both neural crest migration and cancer metastasis. Finally, we evaluate studies that demonstrate myriad forms of cell-cell and cell-environment communication during neural crest and cancer collective migration to highlight the remarkable similarities in their molecular and cell biological regulation.

Multidisciplinary approaches to understanding collective cell migration in developmental biology

Mathematical models are becoming increasingly integrated with experimental efforts in the study of biological systems. Collective cell migration in developmental biology is a particularly fruitful application area for the development of theoretical models to predict the behaviour of complex multicellular systems with many interacting parts. In this context, mathematical models provide a tool to assess the consistency of experimental observations with testable mechanistic hypotheses. In this review, we showcase examples from recent years of multidisciplinary investigations of neural crest cell migration. The neural crest model system has been used to study how collective migration of cell populations is shaped by cell–cell interactions, cell–environmental interactions and heterogeneity between cells. The wide range of emergent behaviours exhibited by neural crest cells in different embryonal locations and in different organisms helps us chart out the spectrum of collective cell migration. At the same time, this diversity in migratory characteristics highlights the need to reconcile or unify the array of currently hypothesized mechanisms through the next generation of experimental data and generalized theoretical descriptions.

Modelling the collective response of heterogeneous cell populations to stationary gradients and chemical signal relay

The directed motion of cell aggregates toward a chemical source occurs in many relevant biological processes. Understanding the mechanisms that control this complex behavior is of great relevance for our understanding of developmental biological processes and many diseases. In this paper, we consider a self-propelled particle model for the movement of heterogeneous subpopulations of chemically interacting cells towards an imposed stable chemical gradient. Our simulations show explicitly how self-organisation of cell populations (which could lead to engulfment or complete cell segregation) can arise from the heterogeneity of chemotactic responses alone. This new result complements current theoretical and experimental studies that emphasise the role of differential cell-cell adhesion on self-organisation and spatial structure of cellular aggregates. We also investigate how the speed of individual cell aggregations increases with the chemotactic sensitivity of the cells, and decreases with the number of cells inside the aggregates.

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.

Semblance of Heterogeneity in Collective Cell Migration

Cell population heterogeneity is increasingly a focus of inquiry in biological research. For example, cell migration studies have investigated the heterogeneity of invasiveness and taxis in development, wound healing, and cancer. However, relatively little effort has been devoted to exploring when heterogeneity is mechanistically relevant and how to reliably measure it. Statistical methods from the animal movement literature offer the potential to analyze heterogeneity in collections of cell tracking data. A popular measure of heterogeneity, which we use here as an example, is the distribution of delays in directional cross-correlation. Employing a suitably generic, yet minimal, model of collective cell movement in three dimensions, we show how using such measures to quantify heterogeneity in tracking data can result in the inference of heterogeneity where there is none. Our study highlights a potential pitfall in the statistical analysis of cell population heterogeneity, and we argue that this can be mitigated by the appropriate choice of null models.

Optogenetic activation of Plexin-B1 reveals contact repulsion between osteoclasts and osteoblasts

During bone remodelling, osteoclasts induce chemotaxis of osteoblasts and yet maintain spatial segregation. We show that osteoclasts express the repulsive guidance factor Semaphorin 4D and induce contact inhibition of locomotion (CIL) in osteoblasts through its receptor Plexin-B1. To examine causality and elucidate how localized Plexin-B1 stimulation may spatiotemporally coordinate its downstream targets in guiding cell migration, we develop an optogenetic tool for Plexin-B1 designated optoPlexin. Precise optoPlexin activation at the leading edge of migrating osteoblasts readily induces local retraction and, unexpectedly, distal protrusions to steer cells away. These morphological changes are accompanied by reorganization of Myosin II, PIP₃, adhesion and active Cdc42. We attribute the resultant repolarization to RhoA/ROCK-mediated redistribution of β-Pix, which activates Cdc42 and promotes protrusion. Thus, our data demonstrate a causal role of Plexin-B1 for CIL in osteoblasts and reveals a previously unknown effect of Semaphorin signalling on spatial distribution of an activator of cell migration.

The Molecular Basis of Radial Intercalation during Tissue Spreading in Early Development

Radial intercalation is a fundamental process responsible for the thinning of multilayered tissues during large-scale morphogenesis; however, its molecular mechanism has remained elusive. Using amphibian epiboly, the thinning and spreading of the animal hemisphere during gastrulation, here we provide evidence that radial intercalation is driven by chemotaxis of cells toward the external layer of the tissue. This role of chemotaxis in tissue spreading and thinning is unlike its typical role associated with large-distance directional movement of cells. We identify the chemoattractant as the complement component C3a, a factor normally linked with the immune system. The mechanism is explored by computational modeling and tested in vivo, ex vivo, and in vitro. This mechanism is robust against fluctuations of chemoattractant levels and expression patterns and explains expansion during epiboly. This study provides insight into the fundamental process of radial intercalation and could be applied to a wide range of morphogenetic events.

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.

Review on experiment-based two- and three-dimensional models for wound healing

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.

Modelling collective cell migration of neural crest

Collective cell migration has emerged in the recent decade as an important phenomenon in cell and developmental biology and can be defined as the coordinated and cooperative movement of groups of cells. Most studies concentrate on tightly connected epithelial tissues, even though collective migration does not require a constant physical contact. Movement of mesenchymal cells is more independent, making their emergent collective behaviour less intuitive and therefore lending importance to computational modelling. Here we focus on such modelling efforts that aim to understand the collective migration of neural crest cells, a mesenchymal embryonic population that migrates large distances as a group during early vertebrate development. By comparing different models of neural crest migration, we emphasize the similarity and complementary nature of these approaches and suggest a future direction for the field. The principles derived from neural crest modelling could aid understanding the collective migration of other mesenchymal cell types.

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.

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.

In vivo confinement promotes collective migration of neural crest cells

Collective cell migration is fundamental throughout development and in many diseases. Spatial confinement using micropatterns has been shown to promote collective cell migration in vitro, but its effect in vivo remains unclear. Combining computational and experimental approaches, we show that the in vivo collective migration of neural crest cells (NCCs) depends on such confinement. We demonstrate that confinement may be imposed by the spatiotemporal distribution of a nonpermissive substrate provided by versican, an extracellular matrix molecule previously proposed to have contrasting roles: barrier or promoter of NCC migration. We resolve the controversy by demonstrating that versican works as an inhibitor of NCC migration and also acts as a guiding cue by forming exclusionary boundaries. Our model predicts an optimal number of cells in a given confinement width to allow for directional migration. This optimum coincides with the width of neural crest migratory streams analyzed across different species, proposing an explanation for the highly conserved nature of NCC streams during development.

Phase-field model for collective cell migration

We construct a phase-field model for collective cell migration based on a Ginzburg-Landau free-energy formulation. We model adhesion, surface tension, repulsion, coattraction, and polarization, enabling us to follow the cells' morphologies and the effect of their membranes fluctuations on collective motion. We were able to measure the tissue surface tension as a function of the individual cell cortical tension and adhesion and identify a density threshold for cell-sheet formation.

Repulsive cues combined with physical barriers and cell-cell adhesion determine progenitor cell positioning during organogenesis

The precise positioning of organ progenitor cells constitutes an essential, yet poorly understood step during organogenesis. Using primordial germ cells that participate in gonad formation, we present the developmental mechanisms maintaining a motile progenitor cell population at the site where the organ develops. Employing high-resolution live-cell microscopy, we find that repulsive cues coupled with physical barriers confine the cells to the correct bilateral positions. This analysis revealed that cell polarity changes on interaction with the physical barrier and that the establishment of compact clusters involves increased cell–cell interaction time. Using particle-based simulations, we demonstrate the role of reflecting barriers, from which cells turn away on contact, and the importance of proper cell–cell adhesion level for maintaining the tight cell clusters and their correct positioning at the target region. The combination of these developmental and cellular mechanisms prevents organ fusion, controls organ positioning and is thus critical for its proper function.

The precise positioning of organ progenitor cells is essential for organ development and function. Here the authors use live imaging and mathematical modelling to show that the confinement of a motile progenitor cell population results from coupled physical barriers and cell-cell interactions.

Mathematical modelling of angiogenesis using continuous cell-based models

In this work, we develop a mathematical formalism based on a 3D in vitro model that is used to simulate the early stages of angiogenesis. The model treats cells as individual entities that are migrating as a result of chemotaxis and durotaxis. The phenotypes used here are endothelial cells that can be distinguished into stalk and tip (leading) cells. The model takes into account the dynamic interaction and interchange between both phenotypes. Next to the cells, the model takes into account several proteins such as vascular endothelial growth factor, delta-like ligand 4, urokinase plasminogen activator and matrix metalloproteinase, which are computed through the solution of a system of reaction–diffusion equations. The method used in the present study is classified into the hybrid approaches. The present study, implemented in three spatial dimensions, demonstrates the feasibility of the approach that is qualitatively confirmed by experimental results.

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.

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.

Cells as strain-cued automata

We argue in favor of representing living cells as automata and review demonstrations that autonomous cells can form patterns by responding to local variations in the strain fields that arise from their individual or collective motions. An autonomous cell's response to strain stimuli is assumed to be effected by internally-generated, internally-powered forces, which generally move the cell in directions other than those implied by external energy gradients. Evidence of cells acting as strain-cued automata have been inferred from patterns observed in nature and from experiments conducted in vitro. Simulations that mimic particular cases of pattern forming share the idealization that cells are assumed to pass information among themselves solely via mechanical boundary conditions, i.e., the tractions and displacements present at their membranes. This assumption opens three mechanisms for pattern formation in large cell populations: wavelike behavior, kinematic feedback in cell motility that can lead to sliding and rotational patterns, and directed migration during invasions. Wavelike behavior among ameloblast cells during amelogenesis (the formation of dental enamel) has been inferred from enamel microstructure, while strain waves in populations of epithelial cells have been observed in vitro. One hypothesized kinematic feedback mechanism, "enhanced shear motility", accounts successfully for the spontaneous formation of layered patterns during amelogenesis in the mouse incisor. Directed migration is exemplified by a theory of invader cells that sense and respond to the strains they themselves create in the host population as they invade it: analysis shows that the strain fields contain positional information that could aid the formation of cell network structures, stabilizing the slender geometry of branches and helping govern the frequency of branch bifurcation and branch coalescence (the formation of closed networks). In simulations of pattern formation in homogeneous populations and network formation by invaders, morphological outcomes are governed by the ratio of the rates of two competing time dependent processes, one a migration velocity and the other a relaxation velocity related to the propagation of strain information. Relaxation velocities are approximately constant for different species and organs, whereas cell migration rates vary by three orders of magnitude. We conjecture that developmental processes use rapid cell migration to achieve certain outcomes, and slow migration to achieve others. We infer from analysis of host relaxation during network formation that a transition exists in the mechanical response of a host cell from animate to inanimate behavior when its strain changes at a rate that exceeds 10-4-10-3s-1. The transition has previously been observed in experiments conducted in vitro.

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.

Establishing correlations in the en-mass migration of dermal fibroblasts on oriented fibrillar scaffolds

Wound healing proceeds via fibroblast migration along three dimensional fibrillar substrates with multiple angles between fibers. We have developed a technique for preparation of three dimensional fibrillar scaffolds with where the fiber diameters and the angles between adjacent fiber layers could be precisely controlled. Using the agarose droplet method we were able to make accurate determinations of the dependence of the migration speed, focal adhesion distribution, and nuclear deformation on the fiber diameter, fiber spacing, and angle between adjacent fiber layers. We found that on oriented single fiber layers, whose diameters exceeded 1 μm, large focal adhesion complexes formed in a linear arrangement along the fiber axis and cell motion was highly correlated. On multi layered scaffolds most of the focal adhesion sites reformed at the junction points and the migration speed was determined by the angle between adjacent fiber layers, which followed a parabolic function with a minimum at 30°. On these surfaces we observed a 25% increase in the number of focal adhesion points and a similar decrease in the degree of nuclear deformation, both phenomena associated with decreased mobility. These results underscore the importance of substrate morphology on the en-mass migration dynamics.

STATEMENT OF SIGNIFICANCE

En-mass fibroblast migration is an essential component of the wound healing process which can determine rate and scar formation. Yet, most publications on this topic have focused on single cell functions. Here we describe a new apparatus where we designed three dimensional fibrillar scaffolds with well controlled angles between junction points and highly oriented fiber geometries. We show that the motion of fibroblasts undergoing en-mass migration on these scaffolds can be controlled by the substrate topography. Significant differences in cell morphology and focal adhesions was found to exist between cells migrating on flat versus fibrillar scaffolds where the migration speed was found to be a function of the angle between fibers, the fiber diameter, and the distance between fibers.

VEGF signals induce trailblazer cell identity that drives neural crest migration

Embryonic neural crest cells travel in discrete streams to precise locations throughout the head and body. We previously showed that cranial neural crest cells respond chemotactically to vascular endothelial growth factor (VEGF) and that cells within the migratory front have distinct behaviors and gene expression. We proposed a cell-induced gradient model in which lead neural crest cells read out directional information from a chemoattractant profile and instruct trailers to follow. In this study, we show that migrating chick neural crest cells do not display distinct lead and trailer gene expression profiles in culture. However, exposure to VEGF in vitro results in the upregulation of a small subset of genes associated with an in vivo lead cell signature. Timed addition and removal of VEGF in culture reveals the changes in neural crest cell gene expression are rapid. A computational model incorporating an integrate-and-switch mechanism between cellular phenotypes predicts migration efficiency is influenced by the timescale of cell behavior switching. To test the model hypothesis that neural crest cellular phenotypes respond to changes in the VEGF chemoattractant profile, we presented ectopic sources of VEGF to the trailer neural crest cell subpopulation and show diverted cell trajectories and stream alterations consistent with model predictions. Gene profiling of trailer cells that diverted and encountered VEGF revealed upregulation of a subset of 'lead' genes. Injection of neuropilin1 (Np1)-Fc into the trailer subpopulation or electroporation of VEGF morpholino to reduce VEGF signaling failed to alter trailer neural crest cell trajectories, suggesting trailers do not require VEGF to maintain coordinated migration. These results indicate that VEGF is one of the signals that establishes lead cell identity and its chemoattractant profile is critical to neural crest cell migration.

Cell traction in collective cell migration and morphogenesis: the chase and run mechanism

Directional collective cell migration plays an important role in development, physiology, and disease. An increasing number of studies revealed key aspects of how cells coordinate their movement through distances surpassing several cell diameters. While physical modeling and measurements of forces during collective cell movements helped to reveal key mechanisms, most of these studies focus on tightly connected epithelial cultures. Less is known about collective migration of mesenchymal cells. A typical example of such behavior is the migration of the neural crest cells, which migrate large distances as a group. A recent study revealed that this persistent migration is aided by the interaction between the neural crest and the neighboring placode cells, whereby neural crest chase the placodes via chemotaxis, but upon contact both populations undergo contact inhibition of locomotion and a rapid reorganization of cellular traction. The resulting asymmetric traction field of the placodes forces them to run away from the chasers. We argue that this chase and run interaction may not be specific only to the neural crest system, but could serve as the underlying mechanism for several morphogenetic processes involving collective cell migration.