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Trends Neurosci. 1998 Jun;21(6):226-31.

Mathematical guidance for axons.

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Georgetown Institute for Cognitive and Computational Sciences Research Building, Georgetown University Medical Center, Washington, DC 20007, USA.


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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