Aberrant Behaviours of Reaction Diffusion Self-organisation Models on Growing Domains in the Presence of Gene Expression Time Delays
KAUST Grant NumberKUK-C1-013-04
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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.
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.
SponsorsThis 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).
JournalBulletin of Mathematical Biology
CollectionsPublications Acknowledging KAUST Support
- The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems.
- Authors: Seirin Lee S, Gaffney EA, Monk NA
- Issue date: 2010 Nov
- The dynamics of Turing patterns for morphogen-regulated growing domains with cellular response delays.
- Authors: Seirin Lee S, Gaffney EA, Baker RE
- Issue date: 2011 Nov
- Gene expression time delays and Turing pattern formation systems.
- Authors: Gaffney EA, Monk NA
- Issue date: 2006 Jan
- Pattern formation in a Turing's type model with minimal reactional complexity
- Authors: Almirantis Y
- Issue date: 2000 Mar
- The sensitivity of Turing self-organization to biological feedback delays: 2D models of fish pigmentation.
- Authors: Gaffney EA, Lee SS
- Issue date: 2015 Mar