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

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.

Nonlinear diffusion and exclusion processes with contact interactions.

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.