Mathematical and experimental insights into the development of the enteric nervous system and Hirschsprung's disease

The vertebrate enteric nervous system is formed by a rostro-caudally directed invasion of the embryonic gastrointestinal mesenchyme by neural crest cells. Failure to complete this invasion results in the distal intestine lacking intrinsic neurons. This potentially fatal condition is called Hirschsprung's Disease. A mathematical model of cell invasion incorporating cell motility and proliferation of neural crest cells to a carrying capacity predicted invasion outcomes to imagined manipulations, and these manipulations were tested experimentally. Mathematical and experimental results agreed. The results show that the directional invasion is chiefly driven by neural crest cell proliferation. Moreover, this proliferation occurs in a small region at the wavefront of the invading population. These results provide an understanding of why many genes implicated in Hirschsprung's Disease influence neural crest population size. In addition, during in vivo development the underlying gut tissues are growing simultaneously as the neural crest cell invasion proceeds. The interactions between proliferation, motility and gut growth dictate whether or not complete colonization is successful. Mathematical modeling provides insights into the conditions required for complete colonization or a Hirschsprung's-like deficiency. Experimental evidence supports the hypotheses suggested by the modeling.     

Looking inside an invasion wave of cells using continuum models: proliferation is the key

Recently, a suite of cell migration assays were conducted to investigate the migration of neural crest (NC) cells along the gut during the development of the enteric nervous system (ENS). The NC cells colonise the gastro-intestinal tract as a rostro-caudal wave. Local behaviour was shown to be controlled by position relative to the leading edge of the wavefront. The assays involved chick-quail grafting techniques allowing the total invading population to be considered as a two-species system. A two-species continuum model with logistic proliferation and a migration mechanism is developed here to simulate the chick-quail graft experiments and provide a means of looking at the processes occurring within the invasion wave. Five migration mechanisms are considered--linear diffusion, two cases of nonlinear diffusion, chemokinesis and chemotaxis. The model results agree with the experimental observations, regardless of the specific type of migration mechanism. The results show that NC cell invasion is driven by proliferation and cell motility at the leading edge of the wave. Furthermore, logistic proliferation exerts the dominant control on the system. This observation is confirmed by analysing some simplified invasion models. Once the basic experiments were mathematically replicated, the mathematical models were used in turn to make some predictions that were yet to be experimentally tested. This involved conducting a sensitivity analysis of the system by interrupting the proliferation and/or migration ability of the leading edge. Numerical results show that the system is stable against these changes. Of the three experiments suggested, one was carried out and the experimental results were concordant with the theoretical predictions. The outcome of two other suggested experiments are predicted and left for future experimental validation.     

In vivo analysis reveals a critical role for neuropilin-1 in cranial neural crest cell migration in chick

The neural crest provides an excellent model system to study invasive cell migration, however it is still unclear how molecular mechanisms direct cells to precise targets in a programmed manner. We investigate the role of a potential guidance factor, neuropilin-1, and use functional knockdown assays, tissue transplantation and in vivo confocal time-lapse imaging to analyze changes in chick cranial neural crest cell migratory patterns. When neuropilin-1 function is knocked down in ovo, neural crest cells fail to fully invade the branchial arches, especially the 2nd branchial arch. Time-lapse imaging shows that neuropilin-1 siRNA transfected neural crest cells stop and collapse filopodia at the 2nd branchial arch entrances, but do not die. This phenotype is cell autonomous. To test the influence of population pressure and local environmental cues in driving neural crest cells to the branchial arches, we isochronically transplanted small subpopulations of DiI-labeled neural crest cells into host embryos ablated of neighboring, premigratory neural crest cells. Time-lapse confocal analysis reveals that the transplanted cells migrate in narrow, directed streams. Interestingly, with the reduction of neuropilin-1 function, neural crest cells still form segmental migratory streams, suggesting that initial neural crest cell migration and invasion of the branchial arches are separable processes.     

A Traveling Wave Model for Invasion by Precursor and Differentiated Cells

We develop and investigate a continuum model for invasion of a domain by cells that migrate, proliferate and differentiate. The model is applicable to neural crest cell invasion in the developing enteric nervous system, but is presented in general terms and is of broader applicability. Two cell populations are identified and modeled explicitly; a population of precursor cells that migrate and proliferate, and a population of differentiated cells derived from the precursors which have impaired migration and proliferation. The equation describing the precursor cells is based on Fisher’s equation with the addition of a carrying-capacity limited differentiation term. Two variations of the proliferation term are considered and compared. For most parameter values, the model admits a traveling wave solution for each population, both traveling at the same speed. The traveling wave solutions are investigated using perturbation analysis, phase plane methods, and numerical techniques. Analytical and numerical results suggest the existence of two wavespeed selection regimes. Regions of the parameter space are characterized according to existence, shape, and speed of traveling wave solutions. Our observations may be used in conjunction with experimental results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, our results may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells.     

The impact of adhesion on cellular invasion processes in cancer and development

In this paper we consider a simple continuous model to describe cell invasion, incorporating the effects of both cell-cell adhesion and cell-matrix adhesion, along with cell growth and proteolysis by cells of the surrounding extracellular matrix (ECM). We demonstrate that the model is capable of supporting both noninvasive and invasive tumour growth according to the relative strength of cell-cell to cell-matrix adhesion. Specifically, for sufficiently strong cell-matrix adhesion and/or sufficiently weak cell-cell adhesion, degradation of the surrounding ECM accompanied by cell-matrix adhesion pulls the cells into the surrounding ECM. We investigate the criticality of matrix heterogeneity on shaping invasion, demonstrating that a highly heterogeneous ECM can result in a “fingering” of the invasive front, echoing observations in real-life invasion processes ranging from malignant tumour growth to neural crest migration during embryonic development.     

Plasminogen activator activity is associated with neural crest cell motility in tissue culture

We have examined the possibility that proteases such as plasminogen activator (PA) contribute to the extraordinary motile capability of neural crest cells. We show that trunk neural crest cells that migrate from isolated neural tubes in vitro produce PA and that the level of cell-associated PA increases dramatically after 8 days in culture. This increase is not the result of differentiation or time in culture, because neural crest cell clusters that form on top of the neural tube and differentiate into pigment cells but are immotile produce very low levels of PA. If these clusters are removed from the neural tube and replated on a plastic substratum where they migrate, the level of PA associated with the cells increases dramatically, suggesting that PA production is associated with motility. Inhibitors of PA/plasmin activity significantly reduce neural crest cell motility in vitro, further supporting the idea that proteases are important in neural crest cell migration.     

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.     

Dual function of Slit2 in repulsion and enhanced migration of trunk,but not vagal,neural crest cells

Neural crest precursors to the autonomic nervous system form different derivatives depending upon their axial level of origin; for example, vagal, but not trunk, neural crest cells form the enteric ganglia of the gut. Here, we show that Slit2 is expressed at the entrance of the gut, which is selectively invaded by vagal, but not trunk, neural crest. Accordingly, only trunk neural crest cells express Robo receptors. In vivo and in vitro experiments demonstrate that trunk, not vagal, crest cells avoid cells or cell membranes expressing Slit2, thereby contributing to the differential ability of neural crest populations to invade and innervate the gut. Conversely, exposure to soluble Slit2 significantly increases the distance traversed by trunk neural crest cells. These results suggest that Slit2 can act bifunctionally, both repulsing and stimulating the motility of trunk neural crest cells.     

The location and phenotype of proliferating neural-crest-derived cells in the developing mouse gut

Neural crest cells that originate in the caudal hindbrain migrate into and along the developing gastrointestinal tract to form the enteric nervous system. While they are migrating, neural-crest-derived cells are also proliferating. Previous studies have shown that the expression of glial-derived neurotrophic factor (GDNF) and endothelin-3 is highest in the embryonic caecum, and that GDNF alone or in combination with endothelin-3 promotes the proliferation of enteric neural-crest-derived cells in vitro. However, whether neural proliferative zones, like those in the central nervous system, are found along the developing gut is unknown. We used a fluorescent nucleic acid stain to identify dividing cells or BrdU labelling (2 h after administration of BrdU to the mother), combined with antibodies specific to neural crest cells to determine the percentage of proliferating crest-derived cells in various gut regions of embryonic day 11.5 (E11.5) and E12.5 mice. The rate of proliferation of crest-derived cells did not vary significantly in different regions of the gut (including the caecum) or at different distances from the migratory wavefront of vagal crest-derived cells. The phenotype of mitotic enteric crest-derived cells was also examined. Cells expressing the pan-neuronal markers, neurofilament-M and Hu, or the glial marker, S100b, were observed undergoing mitosis. However, no evidence was found for proliferation of cells expressing neuron-type-specific markers, such as nitric oxide synthase (at E12.5) or calcitonin gene-related peptide (at E18.5). Thus, for enteric neurons, exit from the cell cycle appears to occur after the expression of pan-neuronal proteins but prior to the expression of markers of terminally differentiated neurons.This work was supported by the Australian Research Council (DP0345298) and the National Health and Medical Research Council of Australia (Project grant 145628 and Senior Research Fellowship 170224).     

Requirement of signalling by receptor tyrosine kinase RET for the directed migration of enteric nervous system progenitor cells during mammalian embryogenesis

The majority of neurones and glia of the enteric nervous system (ENS) are derived from the vagal neural crest. Shortly after emigration from the neural tube, ENS progenitors invade the anterior foregut and, migrating in a rostrocaudal direction, colonise in an orderly fashion the rest of the foregut, the midgut and the hindgut. We provide evidence that activation of the receptor tyrosine kinase RET by glial cell line-derived neurotrophic factor (GDNF) is required for the directional migration of ENS progenitors towards and within the gut wall. We find that neural crest-derived cells present within foetal small intestine explants migrate towards an exogenous source of GDNF in a RET-dependent fashion. Consistent with an in vivo role of GDNF in the migration of ENS progenitors, we demonstrate that Gdnf is expressed at high levels in the gut of mouse embryos in a spatially and temporally regulated manner. Thus, during invasion of the foregut by vagal-derived neural crest cells, expression of Gdnf was restricted to the mesenchyme of the stomach, ahead of the invading NC cells. Twenty-four hours later and as the ENS progenitors were colonising the midgut, Gdnf expression was upregulated in a more posterior region - the caecum anlage. In further support of a role of endogenous GDNF in enteric neural crest cell migration, we find that in explant cultures GDNF produced by caecum is sufficient to attract NC cells residing in more anterior gut segments. In addition, two independently generated loss-of-function alleles of murine Ret, Ret.k- and miRet51, result in characteristic defects of neural crest cell migration within the developing gut. Finally, we identify phosphatidylinositol-3 kinase and the mitogen-activated protein kinase signalling pathways as playing crucial roles in the migratory response of enteric neural crest cells to GDNF.     

Analysis of migratory behavior of neural crest and fibroblastic cells in embryonic tissues

The precise migration of neural crest cells is apparently controlled by their environment. We have examined whether the embryonic tissue spaces in which crest cells normally migrate are sufficient to account for the pattern of crest cell distribution and whether other migratory cells could also distribute themselves along these pathways. To this end, we grafted a variety of cell types into the initial crest cell migratory pathway in chicken embryos. These cell types included (a) undifferentiated neural crest cells isolated from cultured neural tubes, intact crest from cranial neural folds, and crest derivatives (pigment cells and spinal ganglia); (b) normal embryonic fibroblastic cells from somite, limb bud, lateral plate, and heart ventricle; and (c) a transformed fibroblastic cell line (Sarcoma 180). Crest cells or their derivatives grafted into the crest migratory pathway all distributed normally, although in contrast to the result when neural tubes were graftedin situ, fewer cells were observed in the epithelium and few or none were localized in the nascent spinal ganglia. Grafted quail somite cells contributed to normal somitic structures and did not migrate extensively in the chicken host. Other fibroblasts did not migrate along cranial or trunk crest pathways, or invade adjacent tissues, but remained intact at the graft site. Sarcoma 180 cells, however, distributed themselves along the normal trunk crest pathway. Cranial and trunk crest cells and crest derivatives grafted ectopically in the limb bud or somite also dispersed, and were found along the ventral migratory pathway. Fibroblastic cells grafted into ectopic sites again remained intact and did not invade host tissue. We conclude (1) that neural crest cells and their derivatives are highly motile and invasive in their normal pathway, as well as in unfamiliar embryonic environments; and (2) that the crest pathway does not act solely to direct neural crest cells, since at least one transformed cell can follow the crest migratory route.     

Spatial Analysis of Multi-species Exclusion Processes: Application to Neural Crest Cell Migration in the Embryonic Gut

Hindbrain (vagal) neural crest cells become relatively uniformly distributed along the embryonic intestine during the rostral to caudal colonization wave which forms the enteric nervous system (ENS). When vagal neural crest cells are labeled before migration in avian embryos by in ovo electroporation, the distribution of labeled neural crest cells in the ENS varies vastly. In some cases, the labeled neural crest cells appear evenly distributed and interspersed with unlabeled neural crest cells along the entire intestine. However, in most specimens, labeled cells occur in relatively discrete patches of varying position, area, and cell number. To determine reasons for these differences, we use a discrete cellular automata (CA) model incorporating the underlying cellular processes of neural crest cell movement and proliferation on a growing domain, representing the elongation of the intestine during development. We use multi-species CA agents corresponding to labeled and unlabeled neural crest cells. The spatial distributions of the CA agents are quantified in terms of an index. This investigation suggests that (i) the percentage of the initial neural crest cell population that is labeled and (ii) the ratio of cell proliferation to motility are the two key parameters producing the extreme differences in spatial distributions observed in avian embryos.     

Intrinsic differences among spatially distinct neural crest stem cells in terms of migratory properties, fate determination, and ability to colonize the enteric nervous system

We have systematically examined the developmental potential of neural crest stem cells from the enteric nervous system (gut NCSCs) in vivo to evaluate their potential use in cellular therapy for Hirschsprung disease and to assess differences in the properties of postmigratory NCSCs from different regions of the developing peripheral nervous system (PNS). When transplanted into developing chicks, flow-cytometrically purified gut NCSCs and sciatic nerve NCSCs exhibited intrinsic differences in migratory potential and neurogenic capacity throughout the developing PNS. Most strikingly, gut NCSCs migrated into the developing gut and formed enteric neurons, while sciatic nerve NCSCs failed to migrate into the gut or to make enteric neurons, even when transplanted into the gut wall. Enteric potential is therefore not a general property of NCSCs. Gut NCSCs also formed cholinergic neurons in parasympathetic ganglia, but rarely formed noradrenergic sympathetic neurons or sensory neurons. Supporting the potential for autologous transplants in Hirschsprung disease, we observed that Endothelin receptor B (Ednrb)-deficient gut NCSCs engrafted and formed neurons as efficiently in the Ednrb-deficient hindgut as did wild-type NCSCs. These results demonstrate intrinsic differences in the migratory properties and developmental potentials of regionally distinct NCSCs, indicating that it is critical to match the physiological properties of neural stem cells to the goals of proposed cell therapies.     

Annexin A6 Modulates Chick Cranial Neural Crest Cell Emigration

The vertebrate neural crest is a population of migratory cells that originates in the dorsal aspect of the embryonic neural tube. These cells undergo an epithelial-to-mesencyhmal transition (EMT), delaminate from the neural tube and migrate extensively to generate an array of differentiated cell types. Elucidating the gene regulatory networks involved in neural crest cell induction, migration and differentiation are thus crucial to understanding vertebrate development. To this end, we have identified Annexin A6 as an important regulator of chick midbrain neural crest cell emigration. Annexin proteins comprise a family of calcium-dependent, membrane-binding molecules that mediate a variety of cellular and physiological processes including cell adhesion, migration and invasion. Our data indicate that Annexin A6 is expressed in the proper spatio-temporal pattern in the chick midbrain to play a potential role in neural crest cell ontogeny. To investigate Annexin A6 function, we have depleted or overexpressed Annexin A6 in the developing midbrain neural crest cell population. Our results show that knock-down or overexpression of Annexin A6 reduces or expands the migratory neural crest cell domain, respectively. Importantly, this phenotype is not due to any change in cell proliferation or cell death but can be correlated with changes in the size of the premigratory neural crest cell population and with markers associated with EMT. Taken together, our data indicate that Annexin A6 plays a pivotal role in modulating the formation of cranial migratory neural crest cells during vertebrate development.     

Coalescence of interacting cell populations

We analyse the coalescence of invasive cell populations by studying both the temporal and steady behaviour of a system of coupled reaction-diffusion equations. This problem is relevant to recent experimental observations of the dynamics of opposingly directed invasion waves of cells. Two cell types, u and v, are considered with the cell motility governed by linear or nonlinear diffusion. The cells proliferate logistically so that the long-term total cell density, u+v approaches a carrying capacity. The steady-state solutions for u and v are denoted u(s) and v(s). The steady solutions are spatially invariant and satisfy u(s)+v(s)=1. However, this expression is underdetermined so the relative proportion of each cell type u(s) and v(s) cannot be determined a priori. Various properties of this model are studied, such as how the relative proportion of u(s) and v(s) depends on the relative motility and relative proliferation rates. The model is analysed using a combination of numerical simulations and a comparison principle. This investigation unearths some novel outcomes regarding the role of overcrowding and cell death in this type of cell migration assay. These observations have relevance to experimental design and interpretation regarding the identification and parameterisation of mechanisms involved in cell invasion.     

Enteric neuroblasts require the phosphatidylinositol 3‐kinase pathway for GDNF‐stimulated proliferation

The enteric nervous system (ENS) develops from neural crest cells that enter the gut, migrate, proliferate, and differentiate into neurons and glia. The growth factor glial‐derived neurotrophic factor (GDNF) stimulates the proliferation and survival of enteric crest‐derived cells. We investigated the intracellular signaling pathways activated by GDNF and their involvement in proliferation. We found that GDNF stimulates the phosphorylation of both the PI 3‐kinase downstream substrate Akt and the MAP kinase substrate ERK in cultures of immunoaffinity‐purified embryonic avian enteric crest‐derived cells. The selective PI 3‐kinase inhibitor LY‐294002 blocked GDNF‐stimulated Akt phosphorylation in purified crest cells, and reduced proliferation in cultures of dissociated quail gut. The ERK kinase (MEK) inhibitors PD 98059 and UO126 did not reduce GDNF‐stimulated proliferation, although PD 98059 blocked GDNF‐stimulated phosphorylation of ERK. We conclude that the PI 3‐kinase pathway is necessary for the GDNF‐stimulated proliferation of enteric neuroblasts. © 2001 John Wiley & Sons, Inc. J Neurobiol 47: 306–317, 2001