The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation

Type
Article

Authors
Klika, Václav
Baker, Ruth E.
Headon, Denis
Gaffney, Eamonn A.

KAUST Grant Number
KUK-C1-013-04

Online Publication Date
2011-11-10

Print Publication Date
2012-04

Date
2011-11-10

Abstract
Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction. © 2011 Society for Mathematical Biology.

Citation
Klika V, Baker RE, Headon D, Gaffney EA (2011) The Influence of Receptor-Mediated Interactions on Reaction-Diffusion Mechanisms of Cellular Self-organisation. Bull Math Biol 74: 935–957. Available: http://dx.doi.org/10.1007/s11538-011-9699-4.

Acknowledgements
This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). One of the authors (V.K.) is grateful for the hospitality of the Oxford Centre for Collaborative Applied Mathematics and the Institute for Mathematics and Its Applications during work on this project, as well as for many helpful comments and collaborations from his colleagues.

Publisher
Springer Nature

Journal
Bulletin of Mathematical Biology

DOI
10.1007/s11538-011-9699-4

PubMed ID
22072186

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