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arXiv · 2302.00527

A free boundary model for transport induced neurite growth

Greta Marino·Jan-Frederik Pietschmann·Max Winkler
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Abstract

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.

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Greta Marino, Jan-Frederik Pietschmann, Max Winkler. 2023-02-01. A free boundary model for transport induced neurite growth. https://arxiv.org/abs/2302.00527

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