Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

Handle URI:
http://hdl.handle.net/10754/598080
Title:
Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems
Authors:
Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim
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.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
22-May-2012
DOI:
10.1103/PhysRevE.85.051914
PubMed ID:
23004794
Type:
Article
ISSN:
1539-3755; 1550-2376
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorWoolley, Thomas E.en
dc.contributor.authorBaker, Ruth E.en
dc.contributor.authorGaffney, Eamonn A.en
dc.contributor.authorMaini, Philip K.en
dc.contributor.authorSeirin-Lee, Sungrimen
dc.date.accessioned2016-02-25T13:12:17Zen
dc.date.available2016-02-25T13:12:17Zen
dc.date.issued2012-05-22en
dc.identifier.citationWoolley 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.en
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.pmid23004794en
dc.identifier.doi10.1103/PhysRevE.85.051914en
dc.identifier.urihttp://hdl.handle.net/10754/598080en
dc.description.abstractCellular 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.en
dc.description.sponsorshipT.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).en
dc.publisherAmerican Physical Society (APS)en
dc.titleEffects of intrinsic stochasticity on delayed reaction-diffusion patterning systemsen
dc.typeArticleen
dc.identifier.journalPhysical Review Een
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionRiken, Wako, Japanen
kaust.grant.numberKUK-C1-013-04en

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