Handle URI:
http://hdl.handle.net/10754/600079
Title:
Travelling Waves in Hyperbolic Chemotaxis Equations
Authors:
Xue, Chuan; Hwang, Hyung Ju; Painter, Kevin J.; Erban, Radek
Abstract:
Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology.
Citation:
Xue C, Hwang HJ, Painter KJ, Erban R (2010) Travelling Waves in Hyperbolic Chemotaxis Equations. Bull Math Biol 73: 1695–1733. Available: http://dx.doi.org/10.1007/s11538-010-9586-4.
Publisher:
Springer Nature
Journal:
Bulletin of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
16-Oct-2010
DOI:
10.1007/s11538-010-9586-4
PubMed ID:
20953726
Type:
Article
ISSN:
0092-8240; 1522-9602
Sponsors:
CX is supported by the Mathematical Biosciences Institute under the US NSF Award 0635561. KJP would like to acknowledge support from the Mathematical Biosciences Institute and BBSRC grant BB/D019621/1 for the Center for Systems Biology at Edinburgh. HJH is supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (Grant 2009-0094068). 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 is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). RE would also like to thank Somerville College, University of Oxford, for Fulford Junior Research Fellowship.
Appears in Collections:
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Full metadata record

DC FieldValue Language
dc.contributor.authorXue, Chuanen
dc.contributor.authorHwang, Hyung Juen
dc.contributor.authorPainter, Kevin J.en
dc.contributor.authorErban, Radeken
dc.date.accessioned2016-02-28T06:35:37Zen
dc.date.available2016-02-28T06:35:37Zen
dc.date.issued2010-10-16en
dc.identifier.citationXue C, Hwang HJ, Painter KJ, Erban R (2010) Travelling Waves in Hyperbolic Chemotaxis Equations. Bull Math Biol 73: 1695–1733. Available: http://dx.doi.org/10.1007/s11538-010-9586-4.en
dc.identifier.issn0092-8240en
dc.identifier.issn1522-9602en
dc.identifier.pmid20953726en
dc.identifier.doi10.1007/s11538-010-9586-4en
dc.identifier.urihttp://hdl.handle.net/10754/600079en
dc.description.abstractMathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology.en
dc.description.sponsorshipCX is supported by the Mathematical Biosciences Institute under the US NSF Award 0635561. KJP would like to acknowledge support from the Mathematical Biosciences Institute and BBSRC grant BB/D019621/1 for the Center for Systems Biology at Edinburgh. HJH is supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (Grant 2009-0094068). 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 is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). RE would also like to thank Somerville College, University of Oxford, for Fulford Junior Research Fellowship.en
dc.publisherSpringer Natureen
dc.subjectChemotaxisen
dc.subjectTravelling waveen
dc.subjectVelocity jump processen
dc.titleTravelling Waves in Hyperbolic Chemotaxis Equationsen
dc.typeArticleen
dc.identifier.journalBulletin of Mathematical Biologyen
dc.contributor.institutionOhio State University, Columbus, United Statesen
dc.contributor.institutionPohang University of Science and Technology, Pohang, South Koreaen
dc.contributor.institutionHeriot-Watt University, Edinburgh, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

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