Aberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delays

Handle URI:
http://hdl.handle.net/10754/597441
Title:
Aberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delays
Authors:
Seirin Lee, S.; Gaffney, E. A.
Abstract:
Turing's pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing's model has received limited attention. Here, we novelly focus on the Gierer-Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing's mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99-130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing's model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing's mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing's mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning. © 2010 Society for Mathematical Biology.
Citation:
Seirin Lee S, Gaffney EA (2010) Aberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delays. Bull Math Biol 72: 2161–2179. Available: http://dx.doi.org/10.1007/s11538-010-9533-4.
Publisher:
Springer Nature
Journal:
Bulletin of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
23-Mar-2010
DOI:
10.1007/s11538-010-9533-4
PubMed ID:
20309644
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 gratefully acknowledges funding from The Japan Society for The Promotion of Science (JSPS Fellowship DC1).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSeirin Lee, S.en
dc.contributor.authorGaffney, E. A.en
dc.date.accessioned2016-02-25T12:33:18Zen
dc.date.available2016-02-25T12:33:18Zen
dc.date.issued2010-03-23en
dc.identifier.citationSeirin Lee S, Gaffney EA (2010) Aberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delays. Bull Math Biol 72: 2161–2179. Available: http://dx.doi.org/10.1007/s11538-010-9533-4.en
dc.identifier.issn0092-8240en
dc.identifier.issn1522-9602en
dc.identifier.pmid20309644en
dc.identifier.doi10.1007/s11538-010-9533-4en
dc.identifier.urihttp://hdl.handle.net/10754/597441en
dc.description.abstractTuring's pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing's model has received limited attention. Here, we novelly focus on the Gierer-Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing's mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99-130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing's model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing's mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing's mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning. © 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 gratefully acknowledges funding from The Japan Society for The Promotion of Science (JSPS Fellowship DC1).en
dc.publisherSpringer Natureen
dc.subjectGene expressionen
dc.subjectGrowing domainsen
dc.subjectTime delaysen
dc.subjectTuring pattern formationen
dc.titleAberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delaysen
dc.typeArticleen
dc.identifier.journalBulletin of Mathematical Biologyen
dc.contributor.institutionOkayama University, Okayama, Japanen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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