Phenomenological approaches to collective behavior in epithelial cell migration

Engineering tools for quantifying and manipulating forces in epithelia

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

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 rotational motion of freely expanding T84 epithelial cell colonies

Coordinated rotational motion is an intriguing, yet still elusive mode of collective cell migration, which is relevant in pathological and morphogenetic processes. Most of the studies on this topic have been carried out on epithelial cells plated on micropatterned substrates, where cell motion is confined in regions of well-defined shapes coated with extracellular matrix adhesive proteins. The driver of collective rotation in such conditions has not been clearly elucidated, although it has been speculated that spatial confinement can play an essential role in triggering cell rotation. Here, we study the growth of epithelial cell colonies freely expanding (i.e. with no physical constraints) on the surface of cell culture plates and focus on collective cell rotation in such conditions, a case which has received scarce attention in the literature. One of the main findings of our work is that coordinated cell rotation spontaneously occurs in cell clusters in the free growth regime, thus implying that cell confinement is not necessary to elicit collective rotation as previously suggested. The extent of collective rotation was size and shape dependent: a highly coordinated disc-like rotation was found in small cell clusters with a round shape, while collective rotation was suppressed in large irregular cell clusters generated by merging of different clusters in the course of their growth. The angular motion was persistent in the same direction, although clockwise and anticlockwise rotations were equally likely to occur among different cell clusters. Radial cell velocity was quite low as compared to the angular velocity, in agreement with the free expansion regime where cluster growth is essentially governed by cell proliferation. A clear difference in morphology was observed between cells at the periphery and the ones in the core of the clusters, the former being more elongated and spread out as compared to the latter. Overall, our results, to our knowledge, provide the first quantitative and systematic evidence that coordinated cell rotation does not require a spatial confinement and occurs spontaneously in freely expanding epithelial cell colonies, possibly as a mechanism for the system.

Spatio-temporal analysis of collective migrationin vivoby particle image velocimetry

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

Distinct Modes of Tissue Expansion in Free Versus Earlier-Confined Boundaries for More Physiological Modeling of Wound Healing, Cancer Metastasis, and Tissue Formation

Collective cell migration is often seen in many biological processes like embryogenesis, cancer metastasis, and wound healing. Despite extensive experimental and theoretical research, the unified mechanism responsible for collective cell migration is not well known. Most of the studies have investigated artificial model wound to study the collective cell migration in an epithelial monolayer. These artificial model wounds possess a high cell number density compared to the physiological scenarios like wound healing (cell damage due to applied cut) and cancer metastasis (smaller cell clusters). Therefore, both systems may not completely relate to each other, and further investigation is needed to understand the collective cell migration in physiological scenarios. In an effort to fill this existing knowledge gap, we investigated the freely expanding monolayer that closely represented the physiological scenarios and compared it with the artificially created model wound. In the present work, we report the effect of initial boundary conditions (free and confined) on the collective cell migration of the epithelial cell monolayer. The expansion and migration aspects of the freely expanding and earlier-confined monolayer were investigated at the tissue and cellular levels. The freely expanding monolayer showed significantly higher expansion and lower migration in comparison to the earlier-confined monolayer. The expansion and migration rate of the monolayer exhibited a strong negative correlation. The study highlights the importance of initial boundary conditions in the collective cell migration of the expanding tissue and provides useful insights that might be helpful in the future to tune the collective cell migration in wound healing, cancer metastasis, and tissue formation.

Azobenzene-based sinusoidal surface topography drives focal adhesion confinement and guides collective migration of epithelial cells

Surface topography is a key parameter in regulating the morphology and behavior of single cells. At multicellular level, coordinated cell displacements drive many biological events such as embryonic morphogenesis. However, the effect of surface topography on collective migration of epithelium has not been studied in detail. Mastering the connection between surface features and collective cellular behaviour is highly important for novel approaches in tissue engineering and repair. Herein, we used photopatterned microtopographies on azobenzene-containing materials and showed that smooth topographical cues with proper period and orientation can efficiently orchestrate cell alignment in growing epithelium. Furthermore, the experimental system allowed us to investigate how the orientation of the topographical features can alter the speed of wound closure in vitro. Our findings indicate that the extracellular microenvironment topography coordinates their focal adhesion distribution and alignment. These topographic cues are able to guide the collective migration of multicellular systems, even when cell-cell junctions are disrupted.

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

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

Longer collagen fibers trigger multicellular streaming on soft substrates via enhanced forces and cell-cell cooperation

Grouped cells often leave large cell colonies in the form of narrow multicellular streams. However, it remains unknown how collective cell streaming exploits specific matrix properties, like stiffness and fiber length. It is also unclear how cellular forces, cell-cell adhesion and velocities are coordinated within streams. To independently tune stiffness and collagen fiber length, we developed new hydrogels and discovered invasion-like streaming of normal epithelial cells on soft substrates coated with long collagen fibers. Here, streams arise owing to a surge in cell velocities, forces, YAP activity and expression of mesenchymal marker proteins in regions of high-stress anisotropy. Coordinated velocities and symmetric distribution of tensile and compressive stresses support persistent stream growth. Stiff matrices diminish cell-cell adhesions, disrupt front-rear velocity coordination and do not promote sustained fiber-dependent streaming. Rac inhibition reduces cell elongation and cell-cell cooperation, resulting in a complete loss of streaming in all matrix conditions. Our results reveal a stiffness-modulated effect of collagen fiber length on collective cell streaming and unveil a biophysical mechanism of streaming governed by a delicate balance of enhanced forces, monolayer cohesion and cell-cell cooperation.This article has an associated First Person interview with the first authors of the paper.

Biological active matter aggregates: Inspiration for smart colloidal materials

Aggregations of social organisms exhibit a remarkable range of properties and functionalities. Multiple examples, such as fire ants or slime mold, show how a population of individuals is able to overcome an existential threat by gathering into a solid-like aggregate with emergent functionality. Surprisingly, these aggregates are driven by simple rules, and their mechanisms show great parallelism among species. At the same time, great effort has been made by the scientific community to develop active colloidal materials, such as microbubbles or Janus particles, which exhibit similar behaviors. However, a direct connection between these two realms is still not evident, and it would greatly benefit future studies. In this review, we first discuss the current understanding of living aggregates, point out the mechanisms in their formation and explore the vast range of emergent properties. Second, we review the current knowledge in aggregated colloidal systems, the methods used to achieve the aggregations and their potential functionalities. Based on this knowledge, we finally identify a set of over-arching principles commonly found in biological aggregations, and further suggest potential future directions for the creation of bio-inspired colloid aggregations.

Dynamics phenotyping across length and time scales in collective cell migration

Processes in collective migration span many length and time scales. In this review, we focus on length scales ranging from tens of microns (single cells) to a few millimeters (cell clusters) and the motion of these cells and cell groups on time scales of minutes to hours. We focus on epithelial cell sheets and metrics of motion developed to measure migration phenotypes in this system. Comparisons between cell motion and fluid flows, facilitated by the popular image analysis technique particle image velocimetry, yield metrics that can be used to study migration across a range of length and time scales. Measuring collective cell migration across these scales provides a complex, quantitative phenotype useful for migration models, in particular those that compare and contrast collective cell migration to movement of particles near a transition to jamming. Contrasting the motion of epithelial cells and the jamming transition illustrates aspects of collective motion that can be attributed to the jammed character of cell clusters, and highlights aspects of collective behavior that likely involve active motility and cell-cell guidance. The application of multiple migration metrics, which span multiple scales of the system, thus allows us to link cell-scale signals and mechanics to collective behavior.

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.

Limits of Applicability of the Voronoi Tessellation Determined by Centers of Cell Nuclei to Epithelium Morphology

It is well accepted that cells in the tissue can be regarded as tiles tessellating space. A number of approaches were developed to find an appropriate mathematical description of such cell tiling. A particularly useful approach is the so called Voronoi tessellation, built from centers of mass of the cell nuclei (CMVT), which is commonly used for estimating the morphology of cells in epithelial tissues. However, a study providing a statistically sound analysis of this method's accuracy is not available in the literature. We addressed this issue here by comparing a number of morphological measures of the cells, including area, perimeter, and elongation obtained from such a tessellation with identical measures extracted from direct imaging acquired by staining the cell membranes. After analyzing the shapes of 15,000 MDCK II epithelial cells under several conditions, we find that CMVT reasonably well reproduces many of the morphological properties of the tissue with an error that is between 10 and 15%. Moreover, cross-correlations between different morphological measures are reproduced qualitatively correctly by this method. However, all of the properties including the cell perimeters, number of neighbors, and anisotropy measures often suffer from systematic or size dependent errors. These discrepancies originate from the polygonal nature of the tessellation which sets the limits of the applicability of CMVT.

Modeling cell shape and dynamics on micropatterns

Adhesive micropatterns have become a standard tool to study cells under defined conditions. Applications range from controlling the differentiation and fate of single cells to guiding the collective migration of cell sheets. In long-term experiments, single cell normalization is challenged by cell division. For all of these setups, mathematical models predicting cell shape and dynamics can guide pattern design. Here we review recent advances in predicting and explaining cell shape, traction forces and dynamics on micropatterns. Starting with contour models as the simplest approach to explain concave cell shapes, we move on to network and continuum descriptions as examples for static models. To describe dynamic processes, cellular Potts, vertex and phase field models can be used. Different types of model are appropriate to address different biological questions and together, they provide a versatile tool box to predict cell behavior on micropatterns.

Collective cell migration over long time scales reveals distinct phenotypes

Introduction

Migratory phenotypes of metastasizing tumor cells include single and collective cell migration. While migration of tumor cells is generally less cooperative than that of normal epithelial cells, our understanding of precisely how they differ in long time behavior is incomplete.

Objectives

We measure in a model system how cancer progression affects collective migration on long time scales, and determine how perturbation of cell-cell adhesions, specifically reduced E-cadherin expression, affects the collective migration phenotype.

Methods

Time lapse imaging of cellular sheets and particle image velocimetry (PIV) are used to quantitatively study the dynamics of cell motion over ten hours. Long time dynamics are measured via finite time Lyapunov exponents (FTLE) and changes in FTLE with time.

Results

We find that non-malignant MCF10A cells are distinguished from malignant MCF10CA1a cells by both their short time (minutes) and long time (hours) dynamics. In addition, short time dynamics distinguish non-malignant E-cadherin knockdown cells from the control, but long time dynamics and increasing spatial correlations remain unchanged.

Discussion

Epithelial sheet collective behavior includes long time dynamics that cannot be captured by metrics that assess cooperativity based on short time dynamics, such as instantaneous speed or directionality. The use of metrics incorporating migration data over hours instead of minutes allows us to more precisely describe how E-cadherin, a clinically relevant adhesion molecule, affects collective migration. We predict that the long time scale metrics described here will be more robust and predictive of malignant behavior than analysis of instantaneous velocity fields alone.

Dynamics of Cell Ensembles on Adhesive Micropatterns: Bridging the Gap between Single Cell Spreading and Collective Cell Migration

The collective dynamics of multicellular systems arise from the interplay of a few fundamental elements: growth, division and apoptosis of single cells; their mechanical and adhesive interactions with neighboring cells and the extracellular matrix; and the tendency of polarized cells to move. Micropatterned substrates are increasingly used to dissect the relative roles of these fundamental processes and to control the resulting dynamics. Here we show that a unifying computational framework based on the cellular Potts model can describe the experimentally observed cell dynamics over all relevant length scales. For single cells, the model correctly predicts the statistical distribution of the orientation of the cell division axis as well as the final organisation of the two daughters on a large range of micropatterns, including those situations in which a stable configuration is not achieved and rotation ensues. Large ensembles migrating in heterogeneous environments form non-adhesive regions of inward-curved arcs like in epithelial bridge formation. Collective migration leads to swirl formation with variations in cell area as observed experimentally. In each case, we also use our model to predict cell dynamics on patterns that have not been studied before.

Front-Rear Polarization by Mechanical Cues: From Single Cells to Tissues

Directed cell migration is a complex process that involves front-rear polarization, characterized by cell adhesion and cytoskeleton-based protrusion, retraction, and contraction of either a single cell or a cell collective. Single cell polarization depends on a variety of mechanochemical signals including external adhesive cues, substrate stiffness, and confinement. In cell ensembles, coordinated polarization of migrating tissues results not only from the application of traction forces on the extracellular matrix but also from the transmission of mechanical stress through intercellular junctions. We focus here on the impact of mechanical cues on the establishment and maintenance of front-rear polarization from single cell to collective cell behaviors through local or large-scale mechanisms.

Optimizing micropattern geometries for cell shape and migration with genetic algorithms

Adhesive micropatterns have become a standard tool to control cell shape and function in cell culture.