Chemotaxis guidance of random walkers modeling self-wiring of neural networks

TL;DR

This paper introduces a stochastic model for neural growth cone guidance based on chemotaxis, coupling movement dynamics with chemical concentration reactions, and validates it through numerical experiments.

Contribution

It presents a novel coupled stochastic differential equation and reaction-diffusion system for modeling neural self-wiring processes.

Findings

Model accurately describes chemotactic guidance of neural growth cones.

Sensitivity analysis reveals key biological parameters affecting growth.

Nonlocal regularization impacts chemical concentration dynamics.

Abstract

A stochastic walker model is proposed to describe the chemotactic guidance of growth cones, i.e. the tips of developing neurites. The model accounts for the influence of both attractive and repulsive chemical cues, which are emitted by the growth cones and the somas. The system couples stochastic differential equations governing the motion of the growth cones with reaction-diffusion equations that describe the dynamics of the chemical concentrations. The existence of a unique solution to this coupled system is proved. Numerical experiments are performed to investigate the sensitivity of the model to key biological parameters. The impact of the nonlocal regularization of point sources in the reaction-diffusion equations is analyzed in a simplified deterministic setting.