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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(More)
Midbrain, hindbrain and vagal neural crest (NC) produced abundant enteric nervous system (ENS) in co-grafted aneural hindgut and midgut, using chick-quail chorio-allantoic membrane grafts, forming complete myenteric and submucosal plexuses. This ability dropped suddenly in cervical and thoracic NC levels, furnishing an incomplete ENS in one or both(More)
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,(More)
A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion(More)
A non-traditional operator split (OS) scheme for the solution of the advection-diffusion-reaction (ADR) equation is proposed. The scheme is implemented with the recently published central scheme [A. Kurganov, E. Tadmor, New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000)(More)
A defining characteristic of the normal development of the enteric nervous system (ENS) is the existence of 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(More)
Although cell migration is an essential process in development, how cells reach their final destination is not well understood. Secreted molecules are known to have a migratory effect, but it remains unclear whether such molecules act as directional guidance cues or as motility regulators. There is potential to use signalling molecules in new medical(More)
BACKGROUND During embryonic development of segmented animals, body segments are thought to arise from the so-called "posterior growth zone" and the occurrence of this "zone" has been used to support the homology of segmentation between arthropods, annelids, and vertebrates. However, the term "posterior growth zone" is used ambiguously in the literature,(More)
Cell lineage tracing is a powerful tool for understanding how proliferation and differentiation of individual cells contribute to population behaviour. In the developing enteric nervous system (ENS), enteric neural crest (ENC) cells move and undergo massive population expansion by cell division within self-growing mesenchymal tissue. We show that single ENC(More)