Discrete stochastic model for the generation of axonal trees.

Abstract

In this work we propose a 2D discrete stochastic model for the simulation of axonal biogenesis. The model is defined by a third order Markov Chain. The model considers two main processes: the growth process that models the elongation and shape of the neurites and the bifurcation process that models the generation of branches. The growth process depends, among other variables, on the external attraction field generated by a chemoattractant molecule secreted by the target area. We propose an estimation scheme of the involved parameters from real fluorescent confocal microscopy images of single neurons within intact adult Drosophila fly brains. Both normal neurons and neurons in which certain genes were inactivated have been considered (two mutations). In total, 53 images (18 normal, 21 type 1 mutant and 14 type 2 mutant) were used. The model parameters allow us to describe pathological characteristics of the mutated populations.