A free boundary model for transport induced neurite growth
- 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.
| Author: | Greta MarinoGND, Jan-Frederik PietschmannORCiDGND, Max Winkler |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/102110 |
| Parent Title (English): | arXiv |
| Publisher: | arXiv |
| Type: | Preprint |
| Language: | English |
| Year of first Publication: | 2023 |
| Release Date: | 2023/02/20 |
| Issue: | arXiv:2302.00527 |
| DOI: | https://doi.org/10.48550/arXiv.2302.00527 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme | |
| Latest Publications (not yet published in print): | Aktuelle Publikationen (noch nicht gedruckt erschienen) |
