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    Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

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    Type
    Article
    Authors
    Woolley, Thomas E.
    Baker, Ruth E.
    Gaffney, Eamonn A.
    Maini, Philip K.
    Seirin-Lee, Sungrim
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2012-05-22
    Permanent link to this record
    http://hdl.handle.net/10754/598080
    
    Metadata
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    Abstract
    Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.
    Citation
    Woolley TE, Baker RE, Gaffney EA, Maini PK, Seirin-Lee S (2012) Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems. Phys Rev E 85. Available: http://dx.doi.org/10.1103/PhysRevE.85.051914.
    Sponsors
    T.E.W. would like to thank the EPSRC for support. P.K.M. was partially supported by a Royal Society-Wolfson Research Merit Award. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    American Physical Society (APS)
    Journal
    Physical Review E
    DOI
    10.1103/PhysRevE.85.051914
    PubMed ID
    23004794
    ae974a485f413a2113503eed53cd6c53
    10.1103/PhysRevE.85.051914
    Scopus Count
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