Cargando…
A non-local evolution equation model of cell–cell adhesion in higher dimensional space
A model for cell–cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243 (2006), pp. 98–113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dim...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Taylor & Francis
2013
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3957472/ https://www.ncbi.nlm.nih.gov/pubmed/23289870 http://dx.doi.org/10.1080/17513758.2012.755572 |
_version_ | 1782307793321066496 |
---|---|
author | Dyson, Janet Gourley, Stephen A. Webb, Glenn F. |
author_facet | Dyson, Janet Gourley, Stephen A. Webb, Glenn F. |
author_sort | Dyson, Janet |
collection | PubMed |
description | A model for cell–cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243 (2006), pp. 98–113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments. |
format | Online Article Text |
id | pubmed-3957472 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2013 |
publisher | Taylor & Francis |
record_format | MEDLINE/PubMed |
spelling | pubmed-39574722014-03-28 A non-local evolution equation model of cell–cell adhesion in higher dimensional space Dyson, Janet Gourley, Stephen A. Webb, Glenn F. J Biol Dyn Research Article A model for cell–cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243 (2006), pp. 98–113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments. Taylor & Francis 2013-01-07 2013-12 /pmc/articles/PMC3957472/ /pubmed/23289870 http://dx.doi.org/10.1080/17513758.2012.755572 Text en © 2013 The Author(s). Published by Taylor & Francis. http://www.informaworld.com/mpp/uploads/iopenaccess_tcs.pdf This is an open access article distributed under the Supplemental Terms and Conditions for iOpenAccess articles published in Taylor & Francis journals (http://www.informaworld.com/mpp/uploads/iopenaccess_tcs.pdf) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Research Article Dyson, Janet Gourley, Stephen A. Webb, Glenn F. A non-local evolution equation model of cell–cell adhesion in higher dimensional space |
title | A non-local evolution equation model of cell–cell adhesion in higher dimensional space |
title_full | A non-local evolution equation model of cell–cell adhesion in higher dimensional space |
title_fullStr | A non-local evolution equation model of cell–cell adhesion in higher dimensional space |
title_full_unstemmed | A non-local evolution equation model of cell–cell adhesion in higher dimensional space |
title_short | A non-local evolution equation model of cell–cell adhesion in higher dimensional space |
title_sort | non-local evolution equation model of cell–cell adhesion in higher dimensional space |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3957472/ https://www.ncbi.nlm.nih.gov/pubmed/23289870 http://dx.doi.org/10.1080/17513758.2012.755572 |
work_keys_str_mv | AT dysonjanet anonlocalevolutionequationmodelofcellcelladhesioninhigherdimensionalspace AT gourleystephena anonlocalevolutionequationmodelofcellcelladhesioninhigherdimensionalspace AT webbglennf anonlocalevolutionequationmodelofcellcelladhesioninhigherdimensionalspace AT dysonjanet nonlocalevolutionequationmodelofcellcelladhesioninhigherdimensionalspace AT gourleystephena nonlocalevolutionequationmodelofcellcelladhesioninhigherdimensionalspace AT webbglennf nonlocalevolutionequationmodelofcellcelladhesioninhigherdimensionalspace |