Dynamics of path aggregation in the presence of turnover

TL;DR

This paper explores how aging and turnover affect the formation and size distribution of axon fascicles through simulations of directed random walks, revealing multiple time scales and scaling laws.

Contribution

It introduces a model combining axonal aging and turnover to study fascicle dynamics, providing new insights into the time scales and size distributions involved.

Findings

Multiple distinct time scales emerge, exceeding axonal lifetime.

Fascicle size distribution follows a scaling law in steady state.

Turnover influences the dynamics and size distribution of fascicles.

Abstract

We investigate the slow time scales that arise from aging of the paths during the process of path aggregation. This is studied using Monte-Carlo simulations of a model aiming to describe the formation of fascicles of axons mediated by contact axon-axon interactions. The growing axons are represented as interacting directed random walks in two spatial dimensions. To mimic axonal turnover, random walkers are injected and whole paths of individual walkers are removed at specified rates. We identify several distinct time scales that emerge from the system dynamics and can exceed the average axonal lifetime by orders of magnitude. In the dynamical steady state, the position-dependent distribution of fascicle sizes obeys a scaling law. We discuss our findings in terms of an analytically tractable, effective model of fascicle dynamics.