Mathematical Modelling of Polarizing GTPases in Developing Axons

TL;DR

This paper develops a reaction-diffusion mathematical model to understand neuronal polarization, highlighting the roles of GTPases and PI3 kinase, and demonstrating polarization emergence at a critical neurite length with active transport inclusion.

Contribution

It introduces a novel reaction-diffusion model incorporating feedback loops and active transport to explain neuronal polarization mechanisms.

Findings

Polarization occurs at a critical neurite length with ultrasensitive activation.

Active transport of PI3 kinase is essential for symmetry breaking.

The model aligns with experimental observations of neuronal polarization.

Abstract

The aim of this paper is to contribute to the basic understanding of neuronal polarization mechanisms by developing and studying a reaction-diffusion model for protein activation and inactivation. In particular we focus on a feedback loop between PI3 kinase and certain GTPases, and study its behaviour in dependence of neurite lengths. We find that if an ultrasensitive activation is included, the model can produce polarization at a critical length as observed in experiments. Symmetry breaking to polarization in the longer neurite is found only if active transport of a substance, in our case active PI3 kinase, is included into the model.