Modelling Axon Growth Using Driven Diffusion

Axon growth has been studied at small scales using models based on diffusion.
An important part of the guidance of axons during their growth is following gradients of concentration of special chemicals called axonal guiders.
We show how a model of coupled random walkers in in a background potential derived from a the concentration guiders can lead to realistic paths for axons, exhibiting a high level of parallelism and following reasonably short paths.
We propose a simple mechanism by which using a handful of axonal guiders, a brain could accurately assign target addresses for hundreds of brain regions and grow axons from any brain region to any other using a small alphabet.
We also present some preliminary analysis of axon trajectories in the mouse brain.