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

A bird's eye view of enteric nervous system development: lessons from the avian embryo

The avian embryo has been an important model system for studying enteric nervous system (ENS) development for over 50 y. Since the initial demonstration in chick embryos that the ENS is derived from the neural crest, investigators have used the avian model to reveal the cellular origins and migratory pathways of enteric neural crest-derived cells, with more recent work focusing on the molecular mechanisms regulating ENS development. Seminal contributions have been made in this field by researchers who have taken advantage of the strengths of the avian model system. These strengths include in vivo accessibility throughout development, ability to generate quail-chick chimeras, and the capacity to modulate gene expression in vivo in a spatially and temporally targeted manner. The recent availability of the chicken genome further enhances this model system, allowing investigators to combine classic embryologic methods with current genetic techniques. The strengths and versatility of the avian embryo continue to make it a valuable experimental system for studying the development of the ENS.

Modeling proliferative tissue growth: a general approach and an avian case study

During development, tissues often undergo rapid physical expansion due to cell proliferation. Continuous and discrete models of one- and two-dimensional tissue growth are developed and applied to observational data of the developing avian gut, where the gut tissue cells undergo dramatic proliferation. The discrete cellular automata model provides results at the level of individual cells that reflect a realistic stochasticity and nonuniformity expected in cellular systems. Averaging the discrete results predicts population-level properties of the system, which match those of the continuous model. This dual approach provides an understanding of the interaction between the individual-level and population-level aspects of a developmental growth process. Both models are applied to a case study involving the developing intestinal tract of a quail embryo. A nonuniform growth model accurately predicts the positions of measurable biological landmarks within the growing tissue. Furthermore, the discrete model provides a framework for modeling the interactions between growing tissues and other biological mechanisms, such as cell motility and proliferation on an expanding tissue.