Axon guidance by graded diffusible ligands plays an important role in the developing nervous system. Concentration gradients induce an asymmetric localization of molecules in the axon tip, the growth cone, and the consequent internal polarized signaling pathway leads to rearrangement of the growth cone cytoskeleton and, ultimately, to motility. In this work, we provide a mathematical description of the growth cone transduction chain as a series of functional boxes characterized by input/output

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... elations. The model relies on the assumption that the characteristic time of independent concentration measures by growth cone receptors, the characteristic time of growth cone internal reorganization preceding motion and the characteristic time needed for a discernible axon turning belong to separated scales. The results give insight into the deterministic vs. stochastic regime of internal growth cone functions that are not readily accessible from experimental observations, pointing out a substantial equilibrium of the two contributions. The mathematical model predicts the decrease of the coefficient of variation of the signal moving down the functional chain leading to motion. Moreover, possible mechanisms that allow for buffering against noise are highlighted. These results have an interest also for the more experimentally-minded reader, since they can be used to predict sample sizes for detecting significant differences in benchmark gradient assays.