Abstract
The enteric nervous system (ENS) in our gastrointestinal tract is responsible for normal gut function and peristaltic contraction. Embryonic development of the ENS involves the colonisation of the gut wall from one end to the other by a growing population of motile neural crest cells. The colonisation wave is strictly timetabled and predictable, but individual neural crest cell movement is unpredictable in speed and direction. Failure of these cells to invade the whole gut results in the relatively common, potentially fatal birth defect. Continuum models of the population-level behaviour, based on the Fisher equation, are highly predictable. Discrete agent-based models, governed by agent probabilities, reproduce the population-level behaviour of the Fisher equation. However, individual agent contributions to the total population, measured by agent lineage, are highly variable. Both behaviours have been verified in a developmental invasion system. This work is the result of a rewarding long-standing and on-going collaboration between applied mathematicians and developmental biologists.
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Acknowledgments
This work is the result of collaborations with many people, including research fellows, students and other colleagues. We express our thanks to Ben Binder, Bevan Cheeseman, Barry Hughes, Anthony Fernando, Emily Hackett-Jones, Jack Hywood, Michael Mariani, Donald Newgreen, Catherine Penington, Mat Simpson and Dong Zhang. This work was supported by Australian Research Council and National Health and Medical Research Council grants.
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Landman, K.A. (2016). An Interaction with Biologists: Insights into Development and Disease. In: Anderssen, R., et al. Applications + Practical Conceptualization + Mathematics = fruitful Innovation. Mathematics for Industry, vol 11. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55342-7_5
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DOI: https://doi.org/10.1007/978-4-431-55342-7_5
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