Dynamics of path aggregation in the presence of turnover

¹  Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Strasse 38, 01187 Dresden, Germany, EU
²  Department of Mathematics, University of British Columbia - Vancouver, BC, Canada V6T 1Z2
³  TCMP Division, Saha Institute of Nuclear Physics - 1/AF Bidhan Nagar, Kolkata 700064, India
⁴  Institute of Physiology, Academy of Sciences of the Czech Republic - Videnska 1083, 14220 Praha 4, Czech Republic, EU

Corresponding author: zapotocky@biomed.cas.cz

Received: 16 April 2009
Accepted: 8 July 2009

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.