Travelling waves in hybrid chemotaxis models.

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-bas...

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Main Authors: Franz, B, Xue, C, Painter, K, Erban, R
Formato: Journal article
Idioma:English
Publicado: 2014
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author Franz, B
Xue, C
Painter, K
Erban, R
author_facet Franz, B
Xue, C
Painter, K
Erban, R
author_sort Franz, B
collection OXFORD
description 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.
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spelling oxford-uuid:05b2b087-8fe2-4cd9-b35c-e676556a5e0a2022-03-26T08:58:34ZTravelling waves in hybrid chemotaxis models.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:05b2b087-8fe2-4cd9-b35c-e676556a5e0aEnglishSymplectic Elements at Oxford2014Franz, BXue, CPainter, KErban, RHybrid 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.
spellingShingle Franz, B
Xue, C
Painter, K
Erban, R
Travelling waves in hybrid chemotaxis models.
title Travelling waves in hybrid chemotaxis models.
title_full Travelling waves in hybrid chemotaxis models.
title_fullStr Travelling waves in hybrid chemotaxis models.
title_full_unstemmed Travelling waves in hybrid chemotaxis models.
title_short Travelling waves in hybrid chemotaxis models.
title_sort travelling waves in hybrid chemotaxis models
work_keys_str_mv AT franzb travellingwavesinhybridchemotaxismodels
AT xuec travellingwavesinhybridchemotaxismodels
AT painterk travellingwavesinhybridchemotaxismodels
AT erbanr travellingwavesinhybridchemotaxismodels