Building stable chains with motile agents: Insights into the morphology of enteric neural crest cell migration

Abstract

A defining characteristic of the normal development of the enteric nervous system (ENS) is the existence of an enteric neural crest (ENC) cell colonization wave, where the ENC cells form stable chains often associated with axons and near the vascular network. However, within this evolving neural network, the individual ENC cell elements constantly move, change direction and appear to act independently of neighbors. Three possible hypotheses are investigated. The simplest of these postulates that the ENS follows the vascular network as a template. We present evidence which does not support this hypothesis. Two viable alternatives are either that (i) the axons muster the ENC cells, providing the pattern for the chain migration or (ii) ENC cells form chains and the axons follow these paths. These two hypotheses are explored by developing a stochastic cellular automata model, where ENC agents follow simple rules, which reflect the underlying biology of movement, proliferation and differentiation. By simulating ENC precursors and the associated neurons and axons, two models with different fundamental mechanisms are developed. From local rules, a mesoscale network pattern with lacunae emerges, which can be analyzed quantitatively. Simulation and analysis establishes the parameters that affect the morphology of the resulting network. This investigation into the axon/ENC and ENC/ENC interplay suggests possible explanations for observations in mouse and avian embryos in normal and abnormal ENS development, as well as further experimentation.

Introduction

Cell movement within multicellular systems is classified according to the morphology of the resulting migration patterns. These range from individual cells with varying cell shapes, to muticellular chain-like networks, to collective movement, such as two-dimensional sheets as in wound healing. There is considerable debate in the literature (Discher et al., 2009, Friedl et al., 2004, Wolf et al., 2007) discussing the existence and transitions to various modes of migration. Recent studies have also proposed the interaction between various independent parameters that “tune” the system from one migratory mode to another (Friedl and Wolf, 2009). The formation of networks in angiogenesis (Owen et al., 2009, Merks et al., 2006), as well as invasion and branching mechanisms in tumor growth (Cristini et al., 2009) has gained much of the modelling attention. Two recent studies considered the interplay between the invading cells and host tissue (extracellular matrix) to produce fingers or branches: Painter (2009) investigated matrix remodelling, while Cox (2011) hypothesized strain-cue as a mechanism for biological network formation. Here we consider the formation of a chain-like network in the development of the enteric nervous system (ENS). We present experimental observations and develop a model which provides biological insight and has biological implications.

The ENS is an extensive nervous network in the gastrointestinal tract. The ENS is derived from migratory neural crest (NC) cells which arise from a small region in the hindbrain termed the vagal level (Newgreen and Young, 2002b). These cells enter the foregut rostrally and then colonize the entire gastrointestinal tract as a rostro-caudally (oro-anally) directed invasion wave advancing within the gut mesoderm. If this cell migratory wave fails to reach the anal end, a relatively common birth defect results, called Hirschsprung's Disease. In this disease the distal gut is aneural and cannot generate peristaltic waves, leading to intractable constipation that can be fatal if it is not surgically treated (Newgreen and Young, 2002a).

Time lapse observations of enteric NC-derived (ENC) cells colonizing avian and murine gut have emphasized that the movement of individual cells is unpredictable in speed and direction, while the wave-like spread of the entire population is predictable (Young et al., 2004). The pattern of colonization is in the form of chains of cells that intertwine along the wall of the gut while extending caudally along the length of the gut. These chains intersect to form a network. The network evolves over time to become more densely interconnected, as illustrated in Fig. 1. Noteworthy is the observation that the cell chains, once established, are in general spatially stable over hours even though the individual cells that make up the chains are constantly changing over the time-scale of minutes, with cells capable of moving in any direction along any particular section of chain (Young et al., 2004, Druckenbrod and Epstein, 2005, Druckenbrod and Epstein, 2007).

The observations of ENC cell dynamics described above have been obtained in organotypic cultures (Hearn et al., 1999), where gut growth is negligible. However, in vivo gut growth is dramatic (Binder et al., 2008) and this will have an impact on gut colonization by ENC cells (Newgreen et al., 1996). Nevertheless, the chain-like morphology of colonization is unchanged by the presence of gut growth.

Starting from at most 2000 vagal NC cells (in the avian model, Zhang et al., 2010), successful colonization involves a vast expansion of ENC cell numbers by cell division (Young et al., 2005). Surprisingly small numbers of initiating ENC cells can populate relatively large regions of gut: Sidebotham et al. (2002) estimated that around 70 cells or fewer could colonize the mouse hindgut in an organotypic culture where gut growth is limited, while Zhang et al. (2010) estimated that a similar number of ENC cells could colonize the avian midgut including the large cecal region in the more demanding circumstance of gut growth, in chorio-allantoic membrane grafts. Small numbers of highly proliferative vagal NC cells were more effective at colonization than less proliferative trunk NC cells, but this could be offset by higher starting numbers of less proliferative NC cells (Zhang et al., 2010). Conversely, reducing the initial numbers of vagal NC cells by ablation in avian models in vivo can lead to reduced lengths of neural gut, the distal region remaining aneural as in Hirschsprung's Disease (Barlow et al., 2008, Yntema and Hammond, 1954). Despite a decrease in the extent of colonization, the resulting ENS cell density at any colonized region is largely independent of the initial starting numbers (Allan and Newgreen, 1980). Therefore, the NC cell density increases, through proliferation, to reach a preferred density, which may be regarded as a local carrying capacity (Simpson et al., 2006). Such environment-limited growth is termed logistic growth. Consistent with this type of model is the variation in the final ENS cell density between mice with one or two copies of the Glial cell line-Derived Neurotrophic Factor (GDNF) gene (Flynn et al., 2007, Gianino et al., 2003), GDNF being a gut mitogen for early ENC produced by the gut mesodermal environment (Hearn et al., 1998).

Population-level models (partial differential equation models for cell density) (Simpson et al., 2006) and individual-level models (cellular automata models) (Simpson et al., 2007a) of the colonization of the gastrointestinal tract have been developed, either with or without gut growth. These models incorporate ENC cell movement as a random walk, leading to a diffusive term in the continuum models, and carrying-capacity limited proliferation. The models identify the crucial role of ENC cell proliferation in the colonization process (Simpson et al., 2007b), and in particular the importance of proliferation in the ENC cell wavefront (“frontal expansion model”). A wavefront phalanx of ENC cells is chiefly responsible for the colonization of essentially all the remaining uncolonized gut since, for the non-growing gut model, ENC cell proliferation is largely restricted to the wavefront (Simpson et al., 2007b). This is a result of proliferative opportunity relative to position within the colonizing wave—the wavefront cells are located adjacent to uncolonized tissue and are able to proliferate, whereas those behind the wavefront are at the carrying-capacity density. For a growing gut, frontal expansion still occurs, but now, since the entire gut field expands with time, ENC cell proliferation occurs throughout the colonized region, as observed (Young et al., 2005). A mismatch between gut growth and lower proliferation of ENC cells may lead to invasion failure (Hirschsprung's Disease) (Newgreen et al., 1996, Zhang et al., 2010, Landman et al., 2007).

These models have offered insights into ENC cell dynamics in the progress of a cellular wave and in the generation of Hirschsprung's Disease. However, they have provided no insights into the precise migratory ENC network morphology, that is, the emergence of chain migration.

Further biological properties are needed to generate a predictable colonizing wave of motile proliferative ENC cells in a realistic network where migrating cells form chains, which are relatively stable in position and over time, but in which the individual ENC cells move independently and unpredictably on the stable chains. After discussing these, we outline three alternative hypotheses for the emergence of chain migration. We use discrete mathematical models and simulation to explore these hypotheses and investigate their capacity to reproduce the full range of observed biological properties.