A Model for Axon Guidance: Sensing, Transduction and Movement

Axon guidance by graded diffusible ligands plays a crucial role in the developing nervous system. In this paper, we extend the mathematical description of the growth cone transduction cascade of [1] by adding a model of the gradient sensing process related to the theory of [2]. The resulting model is composed by a series of subsystems characterized by suitable input/output relations. The study of the transmission of the noise-to-signal ratio allows to predict the variability of the gradient assay as a function of experimental parameters as the ligand concentration, both in the single and in the multiple ligand tests. For this latter condition, we address the biologically relevant case of silencing in commissural axons. We also consider a phenomenological model which reproduces the results of the experiments of [3]. This simple model allows to test hypotheses on receptor functions and regulation in time