Handle URI:
http://hdl.handle.net/10754/600078
Title:
Travelling Waves in Hybrid Chemotaxis Models
Authors:
Franz, Benjamin; Xue, Chuan; Painter, Kevin J.; Erban, Radek
Abstract:
Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant), which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations. © 2013 Society for Mathematical Biology.
Citation:
Franz B, Xue C, Painter KJ, Erban R (2013) Travelling Waves in Hybrid Chemotaxis Models. Bull Math Biol 76: 377–400. Available: http://dx.doi.org/10.1007/s11538-013-9924-4.
Publisher:
Springer Science + Business Media
Journal:
Bulletin of Mathematical Biology
KAUST Grant Number:
KUK-C1- 013-04
Issue Date:
18-Dec-2013
DOI:
10.1007/s11538-013-9924-4
PubMed ID:
24347253
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. This prize money was used to support research visits of Chuan Xue and Kevin Painter in Oxford. Kevin Painter acknowledges a Leverhulme Trust Research Fellowship award (RF-2011-045). Chuan Xue is supported by the National Science Foundation in the United States through grant DMS-1312966 and the Mathematical Biosciences Institute at the Ohio State University as a long-term visitor.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorFranz, Benjaminen
dc.contributor.authorXue, Chuanen
dc.contributor.authorPainter, Kevin J.en
dc.contributor.authorErban, Radeken
dc.date.accessioned2016-02-28T06:35:36Zen
dc.date.available2016-02-28T06:35:36Zen
dc.date.issued2013-12-18en
dc.identifier.citationFranz B, Xue C, Painter KJ, Erban R (2013) Travelling Waves in Hybrid Chemotaxis Models. Bull Math Biol 76: 377–400. Available: http://dx.doi.org/10.1007/s11538-013-9924-4.en
dc.identifier.issn0092-8240en
dc.identifier.issn1522-9602en
dc.identifier.pmid24347253en
dc.identifier.doi10.1007/s11538-013-9924-4en
dc.identifier.urihttp://hdl.handle.net/10754/600078en
dc.description.abstractHybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant), which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations. © 2013 Society for Mathematical Biology.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. This prize money was used to support research visits of Chuan Xue and Kevin Painter in Oxford. Kevin Painter acknowledges a Leverhulme Trust Research Fellowship award (RF-2011-045). Chuan Xue is supported by the National Science Foundation in the United States through grant DMS-1312966 and the Mathematical Biosciences Institute at the Ohio State University as a long-term visitor.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectBacterial chemotaxisen
dc.subjectHybrid modelen
dc.subjectTravelling waveen
dc.titleTravelling Waves in Hybrid Chemotaxis Modelsen
dc.typeArticleen
dc.identifier.journalBulletin of Mathematical Biologyen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionOhio State University, Columbus, United Statesen
dc.contributor.institutionHeriot-Watt University, Edinburgh, United Kingdomen
kaust.grant.numberKUK-C1- 013-04en

Related articles on PubMed

All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.