REUBEN O'DEA REUBEN.ODEA@NOTTINGHAM.AC.UK
Associate Professor
Continuum limits of pattern formation in hexagonal-cell monolayers
O'Dea, Reuben D.; King, John R.
Authors
John R. King
Abstract
Intercellular signalling is key in determining cell fate. In closely packed tissues such as epithelia, juxtacrine signalling is thought to be a mechanism for the generation of fine-grained spatial patterns in cell differentiation commonly observed in early development.
Theoretical studies of such signalling processes have shown that negative feedback between receptor activation and ligand production is a robust mechanism for fine-grained pattern generation and that cell shape is an important factor in the resulting pattern type. It has previously been assumed that such patterns can be analysed only with discrete models since significant variation occurs over a lengthscale concomitant with an individual cell; however, considering a generic juxtacrine signalling model in square cells, in O'Dea \& King (\emph{Multiscale analysis of pattern formation via intercellular signalling}, Accepted in \emph{Math. Biosci.}), a systematic method for the derivation of a continuum model capturing such phenomena due to variations in a model parameter associated with signalling feedback strength was presented. Here, we extend this work to derive continuum models of the more complex fine-grained patterning in hexagonal cells, constructing individual models for the generation of patterns from the homogeneous state and for the transition between patterning modes. In addition, by considering patterning behaviour under the influence of simultaneous variation of feedback parameters, we construct a more general continuum representation, capturing the emergence of the patterning bifurcation structure. Comparison with the steady-state and dynamic behaviour of the underlying discrete system is made; {in particular, we consider pattern-generating travelling waves and the competition between various stable patterning modes, through which we highlight an important deficiency in the ability of continuum representations to accommodate certain dynamics associated with discrete systems.
Citation
O'Dea, R. D., & King, J. R. (2012). Continuum limits of pattern formation in hexagonal-cell monolayers. Journal of Mathematical Biology, 64(3), https://doi.org/10.1007/s00285-011-0427-3
Journal Article Type | Article |
---|---|
Publication Date | Feb 1, 2012 |
Deposit Date | Jun 10, 2015 |
Publicly Available Date | Jun 10, 2015 |
Journal | Journal of Mathematical Biology |
Print ISSN | 0303-6812 |
Electronic ISSN | 1432-1416 |
Publisher | Springer Verlag |
Peer Reviewed | Peer Reviewed |
Volume | 64 |
Issue | 3 |
DOI | https://doi.org/10.1007/s00285-011-0427-3 |
Keywords | Continuum limit, Multiscale analysis, Pattern formation, Juxtacrine cell signalling |
Public URL | https://nottingham-repository.worktribe.com/output/1008015 |
Publisher URL | http://link.springer.com/article/10.1007%2Fs00285-011-0427-3 |
Additional Information | The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-011-0427-3 |
Files
JMBdelta_hexagonsblank.pdf
(535 Kb)
PDF
You might also like
Spreading dynamics on spatially constrained complex brain networks
(2013)
Journal Article
A multiscale analysis of nutrient transport and biological tissue growth in vitro
(2014)
Journal Article
A geometric network model of intrinsic grey-matter connectivity of the human brain
(2015)
Journal Article
Pushed and pulled fronts in a discrete reaction-diffusion equation
(2015)
Journal Article
Price of anarchy on heterogeneous traffic-flow networks
(2016)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: discovery-access-systems@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search