A model of fasciculation and sorting in mixed populations of axons

TL;DR

This paper models axon fasciculation and sorting during neural development using interacting random walkers, exploring how fascicle sizes and sorting evolve with distance and interaction strength.

Contribution

It extends a previous model to include finite interaction strengths and multiple axon types, providing analytical insights into fascicle formation and sorting dynamics.

Findings

Mean fascicle size increases with distance

Sorting by axon type peaks at a finite distance

Slow time scales emerge from fascicle interactions

Abstract

We extend a recently proposed model (Chaudhuri et al., EPL 87, 20003 (2009)) aiming to describe the formation of fascicles of axons during neural development. The growing axons are represented as paths of interacting directed random walkers in two spatial dimensions. To mimic turnover of axons, whole paths are removed and new walkers are injected with specified rates. In the simplest version of the model, we use strongly adhesive short-range inter-axon interactions that are identical for all pairs of axons. We generalize the model to adhesive interactions of finite strengths and to multiple types of axons with type-specific interactions. The dynamic steady state is characterized by the position-dependent distribution of fascicle sizes. With distance in the direction of axon growth, the mean fascicle size and emergent time scales grow monotonically, while the degree of sorting of fascicles by axon type has a maximum at a finite distance. To understand the emergence of slow time scales, we develop an analytical framework to analyze the interaction between neighboring fascicles.