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

Handle URI:
http://hdl.handle.net/10754/599921
Title:
The Influence of Gene Expression Time Delays on Gierer–Meinhardt Pattern Formation Systems
Authors:
Seirin Lee, S.; Gaffney, E. A.; Monk, N. A. M.
Abstract:
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.
Citation:
Seirin Lee S, Gaffney EA, Monk NAM (2010) The Influence of Gene Expression Time Delays on Gierer–Meinhardt Pattern Formation Systems. Bull Math Biol 72: 2139–2160. Available: http://dx.doi.org/10.1007/s11538-010-9532-5.
Publisher:
Springer Nature
Journal:
Bulletin of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
23-Mar-2010
DOI:
10.1007/s11538-010-9532-5
PubMed ID:
20309645
Type:
Article
ISSN:
0092-8240; 1522-9602
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSeirin Lee, S.en
dc.contributor.authorGaffney, E. A.en
dc.contributor.authorMonk, N. A. M.en
dc.date.accessioned2016-02-28T06:32:29Zen
dc.date.available2016-02-28T06:32:29Zen
dc.date.issued2010-03-23en
dc.identifier.citationSeirin Lee S, Gaffney EA, Monk NAM (2010) The Influence of Gene Expression Time Delays on Gierer–Meinhardt Pattern Formation Systems. Bull Math Biol 72: 2139–2160. Available: http://dx.doi.org/10.1007/s11538-010-9532-5.en
dc.identifier.issn0092-8240en
dc.identifier.issn1522-9602en
dc.identifier.pmid20309645en
dc.identifier.doi10.1007/s11538-010-9532-5en
dc.identifier.urihttp://hdl.handle.net/10754/599921en
dc.description.abstractThere 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.en
dc.description.sponsorshipThis 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).en
dc.publisherSpringer Natureen
dc.subjectGene expressionen
dc.subjectGierer-Meinhardt systemen
dc.subjectTime delaysen
dc.subjectTuring pattern formationen
dc.titleThe Influence of Gene Expression Time Delays on Gierer–Meinhardt Pattern Formation Systemsen
dc.typeArticleen
dc.identifier.journalBulletin of Mathematical Biologyen
dc.contributor.institutionOkayama University, Okayama, Japanen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Nottingham, Nottingham, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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