PCA Modelling of Multi-species Cell Clusters: Ganglion Development in the Gastrointestinal Nervous System

  • Kerry A. LandmanEmail author
  • Donald F. Newgreen
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)


A defining characteristic of the enteric nervous system (ENS) is mesoscale patterned entities called ganglia. Ganglia are clusters of neurons with associated enteric neural crest (ENC) cells, which form in the simultaneously growing gut wall. At first, the precursor ENC cells proliferate and gradually differentiate to produce the enteric neurons; these neurons form clusters with ENC scattered around and later lying on the periphery of neuronal clusters. By immunolabelling neural cell–cell adhesion molecules, the adhesive capacity of neurons is determined to be greater than that of ENC cells. Using a probabilistic cellular automata (PCA) model, we test the hypothesis that local rules governing differential adhesion of neuronal agents and ENC agents will produce clusters that emulate ganglia. The clusters are relatively stable, relatively uniform and small in size, of fairly uniform spacing, with a balance between the number of neuronal and ENC agents. These features are attained in both fixed and growing domains, reproducing, respectively, organotypic in vitro and in vivo observations. Various threshold criteria governing ENC agent proliferation and differentiation and neuronal agent inhibition of differentiation are important for sustaining these characteristics. This investigation suggests possible explanations for observations in normal and abnormal ENS development.


Aggregation and clusters Differential adhesion 



This work was supported by Australian Research Council and National Health and Medical Research Council grants. Thanks are given to Emily Hackett-Jones and Dongcheng Zhang. MCRI facilities are supported by the Victorian Government’s Operational Infrastructure Support Program.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, University of MelbourneParkvilleAustralia
  2. 2.Murdoch Children’s Research Institute, Royal Children’s HospitalParkvilleAustralia

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