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Multiscale analysis of pattern formation via intercellular signalling

O'Dea, Reuben D.; King, John R.

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Authors

John R. King



Abstract

Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting states of differentiation), provided that there is sufficiently strong feedback. The fine-grained nature of these patterns poses problems for analysis via traditional continuum methods since these require that significant variation takes place only over lengthscales much larger than an individual cell and such systems have therefore been investigated primarily using discrete methods. Here, however, we apply a multiscale method to derive systematically a continuum model from the discrete Delta-Notch signalling model of Collier \emph{et al.} (Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling, \emph{J. Theor. Biol.}, 183, 1996, 429--446) under particular assumptions on the parameters, which we use to analyse the generation of fine-grained patterns. We show that, on the macroscale, the contact-dependent juxtacrine signalling interaction manifests itself as linear diffusion, motivating the use of reaction-diffusion-based models for such cell-signalling systems. We also analyse the travelling-wave behaviour of our system, obtaining good quantitative agreement with the discrete system.

Journal Article Type Article
Publication Date Jun 1, 2011
Deposit Date Jun 10, 2015
Publicly Available Date Jun 10, 2015
Journal Mathematical Biosciences
Print ISSN 0025-5564
Electronic ISSN 0025-5564
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 231
Issue 2
DOI https://doi.org/10.1016/j.mbs.2011.03.003
Keywords Multiscale, Homogenisation, Pattern formation, Cell signalling
Public URL https://nottingham-repository.worktribe.com/output/1009983
Publisher URL http://www.sciencedirect.com/science/article/pii/S0025556411000332

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