Modelling axon growing using CTRW

TL;DR

This paper introduces a probabilistic CTRW-based mathematical model to describe axon growth paths, capturing differences between normal and mutant axons and simulating environmental chemical signals influencing growth.

Contribution

It presents a novel CTRW model for axon growth that incorporates environmental chemical signals and distinguishes between normal and mutant axonal behaviors.

Findings

Different growth regimes identified in the model

Behavior of axons depends on specific model parameters

Simulation of chemical signal influence on axon guidance

Abstract

The main goal of this study is to propose a mathematical model describing paths of the axon growth cones and differences in the behavior of normal and mutant axons. We introduce a probabilistic model for axon growing, such that each family of axons is described as an ensemble of trajectories of a continuous time random walk (CTRW) model under different parameters in the case of normal and mutant axons. We describe different regimes in the model and conclude how the behavior of axons depends on the parameters of the model. Biological observations of the axonal growth process say us that the guiding development of axons to their targets is operated by chemical signals from the cellular environment. To simulate this control mechanism we propose the CTRW model, where a random waiting time reflects a reaction time of the growth cones on the neighboring chemical environment.