Computational modelling of cell chain migration reveals mechanisms that sustain follow-the-leader behaviour

A biased random walk approach for modeling the collective chemotaxis of neural crest cells

Collective cell migration is a multicellular phenomenon that arises in various biological contexts, including cancer and embryo development. 'Collectiveness' can be promoted by cell-cell interactions such as co-attraction and contact inhibition of locomotion. These mechanisms act on cell polarity, pivotal for directed cell motility, through influencing the intracellular dynamics of small GTPases such as Rac1. To model these dynamics we introduce a biased random walk model, where the bias depends on the internal state of Rac1, and the Rac1 state is influenced by cell-cell interactions and chemoattractive cues. In an extensive simulation study we demonstrate and explain the scope and applicability of the introduced model in various scenarios. The use of a biased random walk model allows for the derivation of a corresponding partial differential equation for the cell density while still maintaining a certain level of intracellular detail from the individual based setting.

Agent-based approach for elucidating the release from collective arrest of cell motion in corneal epithelial cell sheet

Changes in cell fluidity have been observed in various cellular tissues and are strongly linked to biological phenomena such as self-organization. Recent studies suggested variety of mechanisms and factors, which are still being investigated. This study aimed to investigate changes in cell fluidity in multi-layered cell sheets, by exploring the collective arrest of cell motion and its release in cultures of corneal epithelial cells. We constructed mathematical models to simulate the behaviors of individual cells, including cell differentiation and time-dependent changes in cell-cell connections, which are defined by stochastic or kinetic rules. Changes in cell fluidity and cell sheet structures were expressed by simulating autonomous cell behaviors and interactions in tissues using an agent-based model. A single-cell level spatiotemporal analysis of cell state transition between migratable and non-migratable states revealed that the release from collective arrest of cell motion was initially triggered by a decreased ability to form cell-cell connections in the suprabasal layers, and was propagated by chain migration. Notably, the disruption of cell-cell connections and stratification occurred in the region of migratable state cells. Hence, a modeling approach that considers time-dependent changes in cell properties and behavior, and spatiotemporal analysis at the single-cell level can effectively delineate emergent phenomena arising from the complex interplay of cells.

NetLogo agent-based models as tools for understanding the self-organization of cell fate, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium

Interactions between primordium cells and their environment determines the self-organization of the zebrafish posterior Lateral Line primordium as it migrates under the skin from the ear to the tip of the tail forming and depositing neuromasts to spearhead formation of the posterior Lateral Line sensory system. In this review we describe how the NetLogo agent-based programming environment has been used in our lab to visualize and explore how self-generated chemokine gradients determine collective migration, how the dynamics of Wnt signaling can be used to predict patterns of neuromast deposition, and how previously defined interactions between Wnt and Fgf signaling systems have the potential to determine the periodic formation of center-biased Fgf signaling centers in the wake of a shrinking Wnt system. We also describe how NetLogo was used as a database for storing and visualizing the results of in toto lineage analysis of all cells in the migrating primordium. Together, the models illustrate how this programming environment can be used in diverse ways to integrate what has been learnt from biological experiments about the nature of interactions between cells and their environment, and explore how these interactions could potentially determine emergent patterns of cell fate specification, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

Neural crest migration with continuous cell states

Models of cranial neural crest cell migration in cell-induced (or self-generated) gradients have included a division of labour into leader and follower migratory states, which undergo chemotaxis and contact guidance, respectively. Despite validated utility of these models through experimental perturbation of migration in the chick embryo and gene expression analysis showing relevant heterogeneity at the single cell level, an often raised question has been whether the discrete cell states are necessary, or if a continuum of cell behaviours offers a functionally equivalent description. Here we argue that this picture is supported by recent single-cell transcriptome data. Motivated by this, we implement two versions of a continuous-state model: (1) signal choice and (2) signal combination. We find that the cell population migrates further than in the discrete-state model and than in experimental observations. We further show that the signal combination model, but not the signal choice model, can be successfully adjusted to experimentally plausible regimes by reducing the chemoattractant consumption parameter. Thus we show an equivalently plausible, experimentally motivated, model of neural crest 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.

Leaders in collective migration: are front cells really endowed with a particular set of skills?

Collective cell migration is the coordinated movement emerging from the interaction of at least two cells. In multicellular organisms, collective cell migration is ubiquitous. During development, embryonic cells often travel in numbers, whereas in adults, epithelial cells close wounds collectively. There is often a division of labour and two categories of cells have been proposed: leaders and followers. These two terms imply that followers are subordinated to leaders whose proposed broad range of actions significantly biases the direction of the group of cells towards a specific target. These two terms are also tied to topology. Leaders are at the front while followers are located behind them. Here, we review recent work on some of the main experimental models for collective cell migration, concluding that leader-follower terminology may not be the most appropriate. It appears that not all collectively migrating groups are driven by cells located at the front. Moreover, the qualities that define leaders (pathfinding, traction forces and matrix remodelling) are not specific to front cells. These observations indicate that the terms leaders and followers are not suited to every case. We think that it would be more accurate to dissociate the function of a cell from its position in the group. The position of cells can be precisely defined with respect to the direction of movement by purely topological terms such as “front” or “rear” cells. In addition, we propose the more ample and strictly functional definition of “steering cells” which are able to determine the directionality of movement for the entire group. In this context, a leader cell represents only a specific case in which a steering cell is positioned at the front of the group.

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.

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.

Physiological electrical signals promote chain migration of neuroblasts by up-regulating P2Y1 purinergic receptors and enhancing cell adhesion

Neuroblasts migrate as directed chains of cells during development and following brain damage. A fuller understanding of the mechanisms driving this will help define its developmental significance and in the refinement of strategies for brain repair using transplanted stem cells. Recently, we reported that in adult mouse there are ionic gradients within the extracellular spaces that create an electrical field (EF) within the rostral migratory stream (RMS), and that this acts as a guidance cue for neuroblast migration. Here, we demonstrate an endogenous EF in brain slices and show that mimicking this by applying an EF of physiological strength, switches on chain migration in mouse neurospheres and in the SH-SY5Y neuroblastoma cell line. Firstly, we detected a substantial endogenous EF of 31.8 ± 4.5 mV/mm using microelectrode recordings from explants of the subventricular zone (SVZ). Pharmacological inhibition of this EF, effectively blocked chain migration in 3D cultures of SVZ explants. To mimic this EF, we applied a physiological EF and found that this increased the expression of N-cadherin and β-catenin, both of which promote cell-cell adhesion. Intriguingly, we found that the EF up-regulated P2Y purinoceptor 1 (P2Y1) to contribute to chain migration of neuroblasts through regulating the expression of N-cadherin, β-catenin and the activation of PKC. Our results indicate that the naturally occurring EF in brain serves as a novel stimulant and directional guidance cue for neuronal chain migration, via up-regulation of P2Y1.

Modeling perspectives on echolocation strategies inspired by bats flying in groups

Bats navigating with echolocation - which is a type of active sensing achieved by interpreting echoes resulting from self-generated ultrasonic pulses - exhibit unique behaviors during group flight. While bats may benefit from eavesdropping on their peers׳ echolocation, they also potentially suffer from confusion between their own and peers׳ pulses, caused by an effect called frequency jamming. This hardship of group flight is supported by experimental observations of bats simplifying their sound-scape by shifting their pulse frequencies or suppressing echolocation altogether. Here, we investigate eavesdropping and varying pulse emission rate from a modeling perspective to understand these behaviors׳ potential benefits and detriments. We define an agent-based model of echolocating bats avoiding collisions in a three-dimensional tunnel. Through simulation, we show that bats with reasonably accurate eavesdropping can reduce collisions compared to those neglecting information from peers. In large populations, bats minimize frequency jamming by decreasing pulse emission rate, while collision risk increases; conversely, increasing pulse emission rate minimizes collisions by allowing more sensing information generated per bat. These strategies offer benefits for both biological and engineered systems, since frequency jamming is a concern in systems using active sensing.

Collective motion of cells: from experiments to models

Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems that have been extensively studied in recent years. A number of general principles have been established. The interactions at the level of cells are quite different from those among individual animals, therefore the study of collective motion of cells is likely to reveal some specific important features which we plan to overview in this paper. In addition to presenting the most appealing results from the quickly growing related literature we also deliver a critical discussion of the emerging picture and summarize our present understanding of collective motion at the cellular level. Collective motion of cells plays an essential role in a number of experimental and real-life situations. In most cases the coordinated motion is a helpful aspect of the given phenomenon and results in making a related process more efficient (e.g., embryogenesis or wound healing), while in the case of tumor cell invasion it appears to speed up the progression of the disease. In these mechanisms cells both have to be motile and adhere to one another, the adherence feature being the most specific to this sort of collective behavior. One of the central aims of this review is to present the related experimental observations and treat them in light of a few basic computational models so as to make an interpretation of the phenomena at a quantitative level as well.

The neural crest: a versatile organ system

The neural crest is the name given to the strip of cells at the junction between neural and epidermal ectoderm in neurula-stage vertebrate embryos, which is later brought to the dorsal neural tube as the neural folds elevate. The neural crest is a heterogeneous and multipotent progenitor cell population whose cells undergo EMT then extensively and accurately migrate throughout the embryo. Neural crest cells contribute to nearly every organ system in the body, with derivatives of neuronal, glial, neuroendocrine, pigment, and also mesodermal lineages. This breadth of developmental capacity has led to the neural crest being termed the fourth germ layer. The neural crest has occupied a prominent place in developmental biology, due to its exaggerated migratory morphogenesis and its remarkably wide developmental potential. As such, neural crest cells have become an attractive model for developmental biologists for studying these processes. Problems in neural crest development cause a number of human syndromes and birth defects known collectively as neurocristopathies; these include Treacher Collins syndrome, Hirschsprung disease, and 22q11.2 deletion syndromes. Tumors in the neural crest lineage are also of clinical importance, including the aggressive melanoma and neuroblastoma types. These clinical aspects have drawn attention to the selection or creation of neural crest progenitor cells, particularly of human origin, for studying pathologies of the neural crest at the cellular level, and also for possible cell therapeutics. The versatility of the neural crest lends itself to interlinked research, spanning basic developmental biology, birth defect research, oncology, and stem/progenitor cell biology and therapy.

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.

Interplay between intercellular signaling and cell movement in development

Cell movement and local intercellular signaling are crucial components of morphogenesis during animal development. Intercellular signaling regulates the collective movement of a cell population via direct cell-cell contact. Cell movement, conversely, can influence local intercellular signaling by rearranging neighboring cells. Here, we first discuss theoretical models that address how intercellular signaling regulates collective cell movement during development. Examples include neural crest cell migration, convergent extension, and cell movement during vertebrate axis elongation. Second, we review theoretical studies on how cell movement may affect intercellular signaling, using the segmentation clock in zebrafish as an example. We propose that interplay between cell movement and intercellular signaling must be considered when studying morphogenesis in embryonic development.

Simulating cancer growth with multiscale agent-based modeling

There have been many techniques developed in recent years to in silico model a variety of cancer behaviors. Agent-based modeling is a specific discrete-based hybrid modeling approach that allows simulating the role of diversity in cell populations as well as within each individual cell; it has therefore become a powerful modeling method widely used by computational cancer researchers. Many aspects of tumor morphology including phenotype-changing mutations, the adaptation to microenvironment, the process of angiogenesis, the influence of extracellular matrix, reactions to chemotherapy or surgical intervention, the effects of oxygen and nutrient availability, and metastasis and invasion of healthy tissues have been incorporated and investigated in agent-based models. In this review, we introduce some of the most recent agent-based models that have provided insight into the understanding of cancer growth and invasion, spanning multiple biological scales in time and space, and we further describe several experimentally testable hypotheses generated by those models. We also discuss some of the current challenges of multiscale agent-based cancer models.

Investigation of the essential role of platelet-tumor cell interactions in metastasis progression using an agent-based model

BACKGROUND

Metastatic tumors are a major source of morbidity and mortality for most cancers. Interaction of circulating tumor cells with endothelium, platelets and neutrophils play an important role in the early stages of metastasis formation. These complex dynamics have proven difficult to study in experimental models. Prior computational models of metastases have focused on tumor cell growth in a host environment, or prediction of metastasis formation from clinical data. We used agent-based modeling (ABM) to dynamically represent hypotheses of essential steps involved in circulating tumor cell adhesion and interaction with other circulating cells, examine their functional constraints, and predict effects of inhibiting specific mechanisms.

METHODS

We developed an ABM of Early Metastasis (ABMEM), a descriptive semi-mechanistic model that replicates experimentally observed behaviors of populations of circulating tumor cells, neutrophils, platelets and endothelial cells while incorporating representations of known surface receptor, autocrine and paracrine interactions. Essential downstream cellular processes were incorporated to simulate activation in response to stimuli, and calibrated with experimental data. The ABMEM was used to identify potential points of interdiction through examination of dynamic outcomes such as rate of tumor cell binding after inhibition of specific platelet or tumor receptors.

RESULTS

The ABMEM reproduced experimental data concerning neutrophil rolling over endothelial cells, inflammation-induced binding between neutrophils and platelets, and tumor cell interactions with these cells. Simulated platelet inhibition with anti-platelet drugs produced unstable aggregates with frequent detachment and re-binding. The ABMEM replicates findings from experimental models of circulating tumor cell adhesion, and suggests platelets play a critical role in this pre-requisite for metastasis formation. Similar effects were observed with inhibition of tumor integrin αV/β3. These findings suggest that anti-platelet or anti-integrin therapies may decrease metastasis by preventing stable circulating tumor cell adhesion.

CONCLUSION

Circulating tumor cell adhesion is a complex, dynamic process involving multiple cell-cell interactions. The ABMEM successfully captures the essential interactions necessary for this process, and allows for in-silico iterative characterization and invalidation of proposed hypotheses regarding this process in conjunction with in-vitro and in-vivo models. Our results suggest that anti-platelet therapies and anti-integrin therapies may play a promising role in inhibiting metastasis formation.

Colonizing while migrating: how do individual enteric neural crest cells behave?

Background

Directed cell migration is essential for normal development. In most of the migratory cell populations that have been analyzed in detail to date, all of the cells migrate as a collective from one location to another. However, there are also migratory cell populations that must populate the areas through which they migrate, and thus some cells get left behind while others advance. Very little is known about how individual cells behave to achieve concomitant directional migration and population of the migratory route. We examined the behavior of enteric neural crest-derived cells (ENCCs), which must both advance caudally to reach the anal end and populate each gut region.

Results

The behavior of individual ENCCs was examined using live imaging and mice in which ENCCs express a photoconvertible protein. We show that individual ENCCs exhibit very variable directionalities and speed; as the migratory wavefront of ENCCs advances caudally, each gut region is populated primarily by some ENCCs migrating non-directionally. After populating each region, ENCCs remain migratory for at least 24 hours. Endothelin receptor type B (EDNRB) signaling is known to be essential for the normal advance of the ENCC population. We now show that perturbation of EDNRB principally affects individual ENCC speed rather than directionality. The trajectories of solitary ENCCs, which occur transiently at the wavefront, were consistent with an unbiased random walk and so cell-cell contact is essential for directional migration. ENCCs migrate in close association with neurites. We showed that although ENCCs often use neurites as substrates, ENCCs lead the way, neurites are not required for chain formation and neurite growth is more directional than the migration of ENCCs as a whole.

Conclusions

Each gut region is initially populated by sub-populations of ENCCs migrating non-directionally, rather than stopping. This might provide a mechanism for ensuring a uniform density of ENCCs along the growing gut.

Unraveling intestinal stem cell behavior with models of crypt dynamics

The definition, regulation and function of intestinal stem cells (ISCs) has been hotly debated. Recent discoveries have started to clarify the nature of ISCs, but many questions remain. This review discusses the current advances and controversies of ISC biology as well as theoretical compartmental models that have been coupled with in vivo experimentation to investigate the mechanisms of ISC dynamics during homeostasis, tumorigenesis, repair and development. We conclude our review by discussing the key lingering questions in the field and proposing how many of these questions can be addressed using both compartmental models and experimental techniques.

Do pioneer cells exist?

Most mathematical models of collective cell spreading make the standard assumption that the cell diffusivity and cell proliferation rate are constants that do not vary across the cell population. Here we present a combined experimental and mathematical modeling study which aims to investigate how differences in the cell diffusivity and cell proliferation rate amongst a population of cells can impact the collective behavior of the population. We present data from a three-dimensional transwell migration assay that suggests that the cell diffusivity of some groups of cells within the population can be as much as three times higher than the cell diffusivity of other groups of cells within the population. Using this information, we explore the consequences of explicitly representing this variability in a mathematical model of a scratch assay where we treat the total population of cells as two, possibly distinct, subpopulations. Our results show that when we make the standard assumption that all cells within the population behave identically we observe the formation of moving fronts of cells where both subpopulations are well-mixed and indistinguishable. In contrast, when we consider the same system where the two subpopulations are distinct, we observe a very different outcome where the spreading population becomes spatially organized with the more motile subpopulation dominating at the leading edge while the less motile subpopulation is practically absent from the leading edge. These modeling predictions are consistent with previous experimental observations and suggest that standard mathematical approaches, where we treat the cell diffusivity and cell proliferation rate as constants, might not be appropriate.

Simple rules for a "simple" nervous system? Molecular and biomathematical approaches to enteric nervous system formation and malformation

We review morphogenesis of the enteric nervous system from migratory neural crest cells, and defects of this process such as Hirschsprung disease, centering on cell motility and assembly, and cell adhesion and extracellular matrix molecules, along with cell proliferation and growth factors. We then review continuum and agent-based (cellular automata) models with rules of cell movement and logistical proliferation. Both movement and proliferation at the individual cell level are modeled with stochastic components from which stereotyped outcomes emerge at the population level. These models reproduced the wave-like colonization of the intestine by enteric neural crest cells, and several new properties emerged, such as colonization by frontal expansion, which were later confirmed biologically. These models predict a surprising level of clonal heterogeneity both in terms of number and distribution of daughter cells. Biologically, migrating cells form stable chains made up of unstable cells, but this is not seen in the initial model. We outline additional rules for cell differentiation into neurons, axon extension, cell-axon and cell-cell adhesions, chemotaxis and repulsion which can reproduce chain migration. After the migration stage, the cells re-arrange as a network of ganglia. Changes in cell adhesion molecules parallel this, and we describe additional rules based on Steinberg's Differential Adhesion Hypothesis, reflecting changing levels of adhesion in neural crest cells and neurons. This was able to reproduce enteric ganglionation in a model. Mouse mutants with disturbances of enteric nervous system morphogenesis are discussed, and these suggest future refinement of the models. The modeling suggests a relatively simple set of cell behavioral rules could account for complex patterns of morphogenesis. The model has allowed the proposal that Hirschsprung disease is mostly an enteric neural crest cell proliferation defect, not a defect of cell migration. In addition, the model suggests an explanations for zonal and skip segment variants of Hirschsprung disease, and also gives a novel stochastic explanation for the observed discordancy of Hirschsprung disease in identical twins.

Follow-the-leader cell migration requires biased cell-cell contact and local microenvironmental signals

Directed cell migration often involves at least two types of cell motility that include multicellular streaming and chain migration. However, what is unclear is how cell contact dynamics and the distinct microenvironments through which cells travel influence the selection of one migratory mode or the other. The embryonic and highly invasive neural crest (NC) are an excellent model system to study this question since NC cells have been observed in vivo to display both of these types of cell motility. Here, we present data from tissue transplantation experiments in chick and in silico modeling that test our hypothesis that cell contact dynamics with each other and the microenvironment promote and sustain either multicellular stream or chain migration. We show that when premigratory cranial NC cells (at the pre-otic level) are transplanted into a more caudal region in the head (at the post-otic level), cells alter their characteristic stream behavior and migrate in chains. Similarly, post-otic NC cells migrate in streams after transplantation into the pre-otic hindbrain, suggesting that local microenvironmental signals dictate the mode of NC cell migration. Simulations of an agent-based model (ABM) that integrates the NC cell behavioral data predict that chain migration critically depends on the interplay of biased cell-cell contact and local microenvironment signals. Together, this integrated modeling and experimental approach suggests new experiments and offers a powerful tool to examine mechanisms that underlie complex cell migration patterns.