Modelling axon growing using CTRW

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.