A free boundary model for transport induced neurite growth

TL;DR

This paper presents a free boundary model that captures how vesicle transport influences neurite growth, incorporating drift-diffusion equations and numerical simulations to reproduce growth cycles.

Contribution

It introduces a novel free boundary model linking vesicle transport to neurite length changes, with proven existence, uniqueness, and numerical validation.

Findings

Model reproduces cycles of neurite extension and retraction

Establishes mathematical well-posedness of the model

Demonstrates biological relevance through numerical simulations

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.