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A Mathematical Framework for Modeling Axon Guidance
In this paper, a simulation tool for modeling axon guidance is presented. A mathematical framework in which a wide range of models can been implemented has been developed together with efficient numerical algorithms. In our framework, models can be defined that consist of concentration fields of gui...
Autores principales: | , |
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Formato: | Texto |
Lenguaje: | English |
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Springer-Verlag
2006
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2806218/ https://www.ncbi.nlm.nih.gov/pubmed/17061055 http://dx.doi.org/10.1007/s11538-006-9142-4 |
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author | Krottje, Johannes K. Ooyen, Arjen van |
author_facet | Krottje, Johannes K. Ooyen, Arjen van |
author_sort | Krottje, Johannes K. |
collection | PubMed |
description | In this paper, a simulation tool for modeling axon guidance is presented. A mathematical framework in which a wide range of models can been implemented has been developed together with efficient numerical algorithms. In our framework, models can be defined that consist of concentration fields of guidance molecules in combination with finite-dimensional state vectors. These vectors can characterize migrating growth cones, target neurons that release guidance molecules, or other cells that act as sources of membrane-bound or diffusible guidance molecules. The underlying mathematical framework is presented as well as the numerical methods to solve them. The potential applications of our simulation tool are illustrated with a number of examples, including a model of topographic mapping. |
format | Text |
id | pubmed-2806218 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2006 |
publisher | Springer-Verlag |
record_format | MEDLINE/PubMed |
spelling | pubmed-28062182010-01-15 A Mathematical Framework for Modeling Axon Guidance Krottje, Johannes K. Ooyen, Arjen van Bull Math Biol Original Article In this paper, a simulation tool for modeling axon guidance is presented. A mathematical framework in which a wide range of models can been implemented has been developed together with efficient numerical algorithms. In our framework, models can be defined that consist of concentration fields of guidance molecules in combination with finite-dimensional state vectors. These vectors can characterize migrating growth cones, target neurons that release guidance molecules, or other cells that act as sources of membrane-bound or diffusible guidance molecules. The underlying mathematical framework is presented as well as the numerical methods to solve them. The potential applications of our simulation tool are illustrated with a number of examples, including a model of topographic mapping. Springer-Verlag 2006-10-24 2007-01 /pmc/articles/PMC2806218/ /pubmed/17061055 http://dx.doi.org/10.1007/s11538-006-9142-4 Text en © Society for Mathematical Biology 2006 |
spellingShingle | Original Article Krottje, Johannes K. Ooyen, Arjen van A Mathematical Framework for Modeling Axon Guidance |
title | A Mathematical Framework for Modeling Axon Guidance |
title_full | A Mathematical Framework for Modeling Axon Guidance |
title_fullStr | A Mathematical Framework for Modeling Axon Guidance |
title_full_unstemmed | A Mathematical Framework for Modeling Axon Guidance |
title_short | A Mathematical Framework for Modeling Axon Guidance |
title_sort | mathematical framework for modeling axon guidance |
topic | Original Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2806218/ https://www.ncbi.nlm.nih.gov/pubmed/17061055 http://dx.doi.org/10.1007/s11538-006-9142-4 |
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