Mathematical guidance for axons

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71 Scopus citations

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: 1 mm for a target-derived diffusible gradient, and 1 cm for a substrate-bound gradient.

Original languageEnglish
Pages (from-to)226-231
Number of pages6
JournalTrends in Neurosciences
Volume21
Issue number6
DOIs
StatePublished - Jun 1 1998

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