Multi-cellular logistics of collective cell migration

Reentrant melting of lanes of rough circular disks

We consider binary suspension of rough, circular particles in two dimensions under athermal conditions. The suspension is subject to a time-independent external drive in response to which half of the particles are pulled along the field direction, whereas the other half is pushed in the opposite direction. Simulating the system with different magnitude of external drive in steady state, we obtain oppositely moving macroscopic lanes only for a moderate range of external drive. Below as well as above the range we obtain states with no lane. Hence we find that the no-lane state reenters along the axis of the external drive in the nonequilibrium phase diagram corresponding to the laning transition, with varying roughness of individual particles and external drive. Interparticle friction (contact dissipation) due to the roughness of the individual particle is the main player behind the reentrance of the no-lane state at high external drives.

Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

Collective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

Plasticity of cancer cell invasion: Patterns and mechanisms

Cancer cell migration and invasion are integral components of metastatic disease, which is the major cause of death in cancer patients. Cancer cells can disseminate and migrate via several alternative mechanisms including amoeboid cell migration, mesenchymal cell migration, and collective cell migration. These diverse movement strategies display certain specific and distinct hallmarks in cell-cell junctions, actin cytoskeleton, matrix adhesion, and protease activity. During tumor progression, cells pass through complex microenvironments and adapt their migration strategies by reversible mesenchymal-amoeboid and individual-collective transitions. This plasticity in motility patterns enables cancer cells disseminate further and thus limit the efficiency of anti-metastasis therapies. In this review, we discuss the modes and mechanisms of cancer cell migration and focus on the plasticity of tumor cell movement as well as potential emerging therapeutic options for reducing cancer cell invasion.

Agent-based modelling and parameter sensitivity analysis with a finite-element method for skin contraction

In this paper, we extend the model of wound healing by Boon et al. (J Biomech 49(8):1388–1401, 2016). In addition to explaining the model explicitly regarding every component, namely cells, signalling molecules and tissue bundles, we categorized fibroblasts as regular fibroblasts and myofibroblasts. We do so since it is widely documented that myofibroblasts play a significant role during wound healing and skin contraction and that they are the main phenotype of cells that is responsible for the permanent deformations. Furthermore, we carried out some sensitivity tests of the model by modifying certain parameter values, and we observe that the model shows some consistency with several biological phenomena. Using Monte Carlo simulations, we found that there is a significant strong positive correlation between the final wound area and the minimal wound area. The high correlation between the wound area after 4 days and the final/minimal wound area makes it possible for physicians to predict the most probable time evolution of the wound of the patient. However, the collagen density ratio at the time when the wound area reaches its equilibrium and minimum, cannot indicate the degree of wound contractions, whereas at the 4th day post-wounding, when the collagen is accumulating from null, there is a strong negative correlation between the area and the collagen density ratio. Further, under the circumstances that we modelled, the probability that patients will end up with 5% contraction is about 0.627.

A Camera Sensors-Based System to Study Drug Effects On In Vitro Motility: The Case of PC-3 Prostate Cancer Cells

Cell motility is the brilliant result of cell status and its interaction with close environments. Its detection is now possible, thanks to the synergy of high-resolution camera sensors, time-lapse microscopy devices, and dedicated software tools for video and data analysis. In this scenario, we formulated a novel paradigm in which we considered the individual cells as a sort of sensitive element of a sensor, which exploits the camera as a transducer returning the movement of the cell as an output signal. In this way, cell movement allows us to retrieve information about the chemical composition of the close environment. To optimally exploit this information, in this work, we introduce a new setting, in which a cell trajectory is divided into sub-tracks, each one characterized by a specific motion kind. Hence, we considered all the sub-tracks of the single-cell trajectory as the signals of a virtual array of cell motility-based sensors. The kinematics of each sub-track is quantified and used for a classification task. To investigate the potential of the proposed approach, we have compared the achieved performances with those obtained by using a single-trajectory paradigm with the scope to evaluate the chemotherapy treatment effects on prostate cancer cells. Novel pattern recognition algorithms have been applied to the descriptors extracted at a sub-track level by implementing features, as well as samples selection (a good teacher learning approach) for model construction. The experimental results have put in evidence that the performances are higher when a further cluster majority role has been considered, by emulating a sort of sensor fusion procedure. All of these results highlighted the high strength of the proposed approach, and straightforwardly prefigure its use in lab-on-chip or organ-on-chip applications, where the cell motility analysis can be massively applied using time-lapse microscopy images.

Clustered cell migration: Modeling the model system of Drosophila border cells

In diverse developmental contexts, certain cells must migrate to fulfill their roles. Many questions remain unanswered about the genetic and physical properties that govern cell migration. While the simplest case of a single cell moving alone has been well-studied, additional complexities arise in considering how cohorts of cells move together. Significant differences exist between models of collectively migrating cells. We explore the experimental model of migratory border cell clusters in Drosophila melanogaster egg chambers, which are amenable to direct observation and precise genetic manipulations. This system involves two special characteristics that are worthy of attention: border cell clusters contain a limited number of both migratory and non-migratory cells that require coordination, and they navigate through a heterogeneous three-dimensional microenvironment. First, we review how clusters of motile border cells are specified and guided in their migration by chemical signals and the physical impact of adjacent tissue interactions. In the second part, we examine questions around the 3D structure of the motile cluster and surrounding microenvironment in understanding the limits to cluster size and speed of movement through the egg chamber. Mathematical models have identified sufficient gene regulatory networks for specification, the key forces that capture emergent behaviors observed in vivo, the minimal regulatory topologies for signaling, and the distribution of key signaling cues that direct cell behaviors. This interdisciplinary approach to studying border cells is likely to reveal governing principles that apply to different types of cell migration events.

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

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

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

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

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

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

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.

Cell Division Induces and Switches Coherent Angular Motion within Bounded Cellular Collectives

Collective cell migration underlies many biological processes, including embryonic development, wound healing, and cancer progression. In the embryo, cells have been observed to move collectively in vortices using a mode of collective migration known as coherent angular motion (CAM). To determine how CAM arises within a population and changes over time, here, we study the motion of mammary epithelial cells within engineered monolayers, in which the cells move collectively about a central axis in the tissue. Using quantitative image analysis, we find that CAM is significantly reduced when mitosis is suppressed. Particle-based simulations recreate the observed trends, suggesting that cell divisions drive the robust emergence of CAM and facilitate switches in the direction of collective rotation. Our simulations predict that the location of a dividing cell, rather than the orientation of the division axis, facilitates the onset of this motion. These predictions agree with experimental observations, thereby providing, to our knowledge, new insight into how cell divisions influence CAM within a tissue. Overall, these findings highlight the dynamic nature of CAM and suggest that regulating cell division is crucial for tuning emergent collective migratory behaviors, such as vortical motions observed in vivo.

The role of tumor microenvironment in collective tumor cell invasion

For many cancer types, cancer cells invade into surrounding tissues by collective movement of cell groups that remain connected via cell-cell junctions. This migration is completely distinguished from single-cell migration, in which cancer cells disrupt the tight intercellular junctions and gain a mesenchymal phenotype. Recently, emerging evidence has revealed that collective cell invasion depends on not only cell-intrinsic mechanisms but also on extracellular mechanisms by bidirectional interplay between the tumor cell and the tumor environment. Herein, in this review we discuss the role and underline mechanisms of tumor microenvironment in collective tumor cell invasion, particularly focusing on extracellular matrix remodeling and cross-talk between tumor and stromal cells.

A force balance can explain local and global cell movements during early zebrafish development

Embryonic morphogenesis takes place via a series of dramatic collective cell movements. The mechanisms that coordinate these intricate structural transformations across an entire organism are not well understood. In this study, we used gentle mechanical deformation of developing zebrafish embryos to probe the role of physical forces in generating long-range intercellular coordination during epiboly, the process in which the blastoderm spreads over the yolk cell. Geometric distortion of the embryo resulted in nonuniform blastoderm migration and realignment of the anterior-posterior (AP) axis, as defined by the locations at which the head and tail form, toward the new long axis of the embryo and away from the initial animal-vegetal axis defined by the starting location of the blastoderm. We found that local alterations in the rate of blastoderm migration correlated with the local geometry of the embryo. Chemical disruption of the contractile ring of actin and myosin immediately vegetal to the blastoderm margin via Ca²⁺ reduction or treatment with blebbistatin restored uniform migration and eliminated AP axis reorientation in mechanically deformed embryos; it also resulted in cellular disorganization at the blastoderm margin. Our results support a model in which tension generated by the contractile actomyosin ring coordinates epiboly on both the organismal and cellular scales. Our observations likewise suggest that the AP axis is distinct from the initial animal-vegetal axis in zebrafish.

A mathematical model of collective cell migration in a three-dimensional, heterogeneous environment

Cell migration is essential in animal development, homeostasis, and disease progression, but many questions remain unanswered about how this process is controlled. While many kinds of individual cell movements have been characterized, less effort has been directed towards understanding how clusters of cells migrate collectively through heterogeneous, cellular environments. To explore this, we have focused on the migration of the border cells during Drosophila egg development. In this case, a cluster of different cell types coalesce and traverse as a group between large cells, called nurse cells, in the center of the egg chamber. We have developed a new model for this collective cell migration based on the forces of adhesion, repulsion, migration and stochastic fluctuation to generate the movement of discrete cells. We implement the model using Identical Math Cells, or IMCs. IMCs can each represent one biological cell of the system, or can be aggregated using increased adhesion forces to model the dynamics of larger biological cells. The domain of interest is filled with IMCs, each assigned specific biophysical properties to mimic a diversity of cell types. Using this system, we have successfully simulated the migration of the border cell cluster through an environment filled with larger cells, which represent nurse cells. Interestingly, our simulations suggest that the forces utilized in this model are sufficient to produce behaviors of the cluster that are observed in vivo, such as rotation. Our framework was developed to capture a heterogeneous cell population, and our implementation strategy allows for diverse, but precise, initial position specification over a three- dimensional domain. Therefore, we believe that this model will be useful for not only examining aspects of Drosophila oogenesis, but also for modeling other two or three-dimensional systems that have multiple cell types and where investigating the forces between cells is of interest.

Directional collective cell migration emerges as a property of cell interactions

Collective cell migration is a fundamental process, occurring during embryogenesis and cancer metastasis. Neural crest cells exhibit such coordinated migration, where aberrant motion can lead to fatality or dysfunction of the embryo. Migration involves at least two complementary mechanisms: contact inhibition of locomotion (a repulsive interaction corresponding to a directional change of migration upon contact with a reciprocating cell), and co-attraction (a mutual chemoattraction mechanism). Here, we develop and employ a parameterized discrete element model of neural crest cells, to investigate how these mechanisms contribute to long-range directional migration during development. Motion is characterized using a coherence parameter and the time taken to reach, collectively, a target location. The simulated cell group is shown to switch from a diffusive to a persistent state as the response-rate to co-attraction is increased. Furthermore, the model predicts that when co-attraction is inhibited, neural crest cells can migrate into restrictive regions. Indeed, inhibition of co-attraction in vivo and in vitro leads to cell invasion into restrictive areas, confirming the prediction of the model. This suggests that the interplay between the complementary mechanisms may contribute to guidance of the neural crest. We conclude that directional migration is a system property and does not require action of external chemoattractants.

Epithelial sheet folding induces lumen formation by Madin-Darby canine kidney cells in a collagen gel

Lumen formation is important for morphogenesis; however, an unanswered question is whether it involves the collective migration of epithelial cells. Here, using a collagen gel overlay culture method, we show that Madin-Darby canine kidney cells migrated collectively and formed a luminal structure in a collagen gel. Immediately after the collagen gel overlay, an epithelial sheet folded from the periphery, migrated inwardly, and formed a luminal structure. The inhibition of integrin-β1 or Rac1 activity decreased the migration rate of the peripheral cells after the sheets folded. Moreover, lumen formation was perturbed by disruption of apical-basolateral polarity induced by transforming growth factor-β1. These results indicate that cell migration and cell polarity play an important role in folding. To further explore epithelial sheet folding, we developed a computer-simulated mechanical model based on the rigidity of the extracellular matrix. It indicated a soft substrate is required for the folding movement.

Computational modelling of multi-cell migration in a multi-signalling substrate

Cell migration is a vital process in many biological phenomena ranging from wound healing to tissue regeneration. Over the past few years, it has been proven that in addition to cell-cell and cell-substrate mechanical interactions (mechanotaxis), cells can be driven by thermal, chemical and/or electrical stimuli. A numerical model was recently presented by the authors to analyse single cell migration in a multi-signalling substrate. That work is here extended to include multi-cell migration due to cell-cell interaction in a multi-signalling substrate under different conditions. This model is based on balancing the forces that act on the cell population in the presence of different guiding cues. Several numerical experiments are presented to illustrate the effect of different stimuli on the trajectory and final location of the cell population within a 3D heterogeneous multi-signalling substrate. Our findings indicate that although multi-cell migration is relatively similar to single cell migration in some aspects, the associated behaviour is very different. For instance, cell-cell interaction may delay single cell migration towards effective cues while increasing the magnitude of the average net cell traction force as well as the local velocity. Besides, the random movement of a cell within a cell population is slightly greater than that of single cell migration. Moreover, higher electrical field strength causes the cell slug to flatten near the cathode. On the other hand, as with single cell migration, the existence of electrotaxis dominates mechanotaxis, moving the cells to the cathode or anode pole located at the free surface. The numerical results here obtained are qualitatively consistent with related experimental works.

On the mechanical interplay between intra- and inter-synchronization during collective cell migration: a numerical investigation

Collective cell migration is a fundamental process that takes place during several biological phenomena such as embryogenesis, immunity response, and tumorogenesis, but the mechanisms that regulate it are still unclear. Similarly to collective animal behavior, cells receive feedbacks in space and time, which control the direction of the migration and the synergy between the cells of the population, respectively. While in single cell migration intra-synchronization (i.e. the synchronization between the protrusion-contraction movement of the cell and the adhesion forces exerted by the cell to move forward) is a sufficient condition for an efficient migration, in collective cell migration the cells must communicate and coordinate their movement between each other in order to be as efficient as possible (i.e. inter-synchronization). Here, we propose a 2D mechanical model of a cell population, which is described as a continuum with embedded discrete cells with or without motility phenotype. The decomposition of the deformation gradient is employed to reproduce the cyclic active strains of each single cell (i.e. protrusion and contraction). We explore different modes of collective migration to investigate the mechanical interplay between intra- and inter-synchronization. The main objective of the paper is to evaluate the efficiency of the cell population in terms of covered distance and how the stress distribution inside the cohort and the single cells may in turn provide insights regarding such efficiency.

Migration of cells in a social context

In multicellular organisms and complex ecosystems, cells migrate in a social context. Whereas this is essential for the basic processes of life, the influence of neighboring cells on the individual remains poorly understood. Previous work on isolated cells has observed a stereotypical migratory behavior characterized by short-time directional persistence with long-time random movement. We discovered a much richer dynamic in the social context, with significant variations in directionality, displacement, and speed, which are all modulated by local cell density. We developed a mathematical model based on the experimentally identified "cellular traffic rules" and basic physics that revealed that these emergent behaviors are caused by the interplay of single-cell properties and intercellular interactions, the latter being dominated by a pseudopod formation bias mediated by secreted chemicals and pseudopod collapse following collisions. The model demonstrates how aspects of complex biology can be explained by simple rules of physics and constitutes a rapid test bed for future studies of collective migration of individual cells.

The nature of the laning transition in two dimensions

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures ('lanes') characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262,144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.