A free boundary model for transport induced neurite growth
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911284008583168 |
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| author | Marino, Greta Pietschmann, Jan-Frederik Winkler, Max |
| author_facet | Marino, Greta Pietschmann, Jan-Frederik Winkler, Max |
| contents | We introduce a free boundary model to example the effect of vesicle transport onto neurite growth. It consists of systems of drift-diffusion equations describing the evolution of the density of antero- and retrograde vesicles in each neurite coupled to reservoirs located at the soma and the growth cones of the neurites, respectively. The model allows for a change of neurite length depending on the vesicle concentration in the growth cones. After establishing existence and uniqueness for the time-dependent problem, we briefly comment on possible types of stationary solutions. Finally, we provide numerical studies on biologically relevant scales using a finite volume scheme. We illustrate the capability of the model to reproduce cycles of extension and retraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00527 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A free boundary model for transport induced neurite growth Marino, Greta Pietschmann, Jan-Frederik Winkler, Max Analysis of PDEs 92-08, 92C20, 35R35, 35K45, 35A05 We introduce a free boundary model to example the effect of vesicle transport onto neurite growth. It consists of systems of drift-diffusion equations describing the evolution of the density of antero- and retrograde vesicles in each neurite coupled to reservoirs located at the soma and the growth cones of the neurites, respectively. The model allows for a change of neurite length depending on the vesicle concentration in the growth cones. After establishing existence and uniqueness for the time-dependent problem, we briefly comment on possible types of stationary solutions. Finally, we provide numerical studies on biologically relevant scales using a finite volume scheme. We illustrate the capability of the model to reproduce cycles of extension and retraction. |
| title | A free boundary model for transport induced neurite growth |
| topic | Analysis of PDEs 92-08, 92C20, 35R35, 35K45, 35A05 |
| url | https://arxiv.org/abs/2302.00527 |