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Review
, 21 (6), 226-31

Mathematical Guidance for Axons

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Review

Mathematical Guidance for Axons

G J Goodhill. Trends Neurosci.

Abstract

Axon guidance by gradients plays an important role in wiring up the developing nervous system. Growth cones seem to sense a concentration difference across their spatial extent, and convert this into a signal to move up or down a gradient. In this article, a simple mathematical framework is developed to understand when and where gradient detection can occur as a function of gradient shape. This framework is applied to two examples:the guidance of axons by target-derived diffusible factors in vivo and in collagen gels, and guidance by substrate-bound gradients of optimal shape, as might be relevant in the retinotectal system.Two distinct spatial limits on guidance emerge: I mm for a target-derived diffusible gradient, and I cm for a substrate-bound gradient.

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