The Influence of Gene Expression Time Delays on Gierer–Meinhardt Pattern Formation Systems

S. Seirin Lee, E. A. Gaffney, N. A. M. Monk

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer-Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer-Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens. © 2010 Society for Mathematical Biology.
Original languageEnglish (US)
Pages (from-to)2139-2160
Number of pages22
JournalBulletin of Mathematical Biology
Issue number8
StatePublished - Mar 23 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). SSL would like to thank Professor PK Maini and The Centre for Mathematical Biology for warm hospitality and a visiting position as well as gratefully acknowledging funding from the Japan Society for the Promotion of Science (JSPS Fellowship DC1).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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