Section: New Results
Markov Chain for Axon Growth Modeling
Participants : Alejandro Mottini, Xavier Descombes, Florence Besse.
In this work we have defined a 2D discrete stochastic model for the simulation of axonal biogenesis [8] . 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.
For the validation, we have fluorescently labeled single neurons within intact adult Drosophila fly brains, and have acquired 3D fluorescent confocal microscopy images of their axonal trees. Both normal neurons and neurons in which the function of the imp (mutant type 1) or profilin (mutant type 2) genes was inactivated were imaged. imp encodes a conserved RNA binding protein controlling subcellular mRNA transport and local protein synthesis, and is essential for axonal remodeling. profilin encodes a regulator of the actin cytoskeleton involved in axonal pathfinding. Mutations in these two conserved genes have been linked to neurological pathologies.
Each image stack has a resolution of
We then have estimated the model parameters to generate two fields for
each population, a scalar field that represents the axon flexibility and a vector field that represents the attraction field. Since we obtain some estimates on a sparse set of points in the