Stochastic Turing Patterns: Analysis of Compartment-Based Approaches

Handle URI:
http://hdl.handle.net/10754/599739
Title:
Stochastic Turing Patterns: Analysis of Compartment-Based Approaches
Authors:
Cao, Yang; Erban, Radek
Abstract:
© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.
Citation:
Cao Y, Erban R (2014) Stochastic Turing Patterns: Analysis of Compartment-Based Approaches. Bull Math Biol 76: 3051–3069. Available: http://dx.doi.org/10.1007/s11538-014-0044-6.
Publisher:
Springer Science + Business Media
Journal:
Bulletin of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
25-Nov-2014
DOI:
10.1007/s11538-014-0044-6
PubMed ID:
25421150
Type:
Article
ISSN:
0092-8240; 1522-9602
Sponsors:
The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC Grant Agreement No. 239870. 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). Radek Erban would also like to thank the Royal Society for a University Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. Yang Cao's work was supported by the National Science Foundation under awards DMS-1225160 and CCF-0953590, and the National Institutes of Health under award GM078989.
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Full metadata record

DC FieldValue Language
dc.contributor.authorCao, Yangen
dc.contributor.authorErban, Radeken
dc.date.accessioned2016-02-28T06:08:43Zen
dc.date.available2016-02-28T06:08:43Zen
dc.date.issued2014-11-25en
dc.identifier.citationCao Y, Erban R (2014) Stochastic Turing Patterns: Analysis of Compartment-Based Approaches. Bull Math Biol 76: 3051–3069. Available: http://dx.doi.org/10.1007/s11538-014-0044-6.en
dc.identifier.issn0092-8240en
dc.identifier.issn1522-9602en
dc.identifier.pmid25421150en
dc.identifier.doi10.1007/s11538-014-0044-6en
dc.identifier.urihttp://hdl.handle.net/10754/599739en
dc.description.abstract© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.en
dc.description.sponsorshipThe research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC Grant Agreement No. 239870. 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). Radek Erban would also like to thank the Royal Society for a University Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. Yang Cao's work was supported by the National Science Foundation under awards DMS-1225160 and CCF-0953590, and the National Institutes of Health under award GM078989.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectCompartment-based modelsen
dc.subjectMultigrid discretizationen
dc.subjectStochastic reaction-diffusion systemsen
dc.subjectStochastic Turing patternsen
dc.titleStochastic Turing Patterns: Analysis of Compartment-Based Approachesen
dc.typeArticleen
dc.identifier.journalBulletin of Mathematical Biologyen
dc.contributor.institutionVirginia Polytechnic Institute and State University, Blacksburg, United Statesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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