title: Mathematical guidance for axons.
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.
authors.affiliation: Georgetown Institute for Cognitive and Computational Sciences Research Building, Georgetown University Medical Center, Washington, DC 20007, USA.
authors.forename: G J
authors.initials: GJ
authors.lastname: Goodhill
mesh_terms: D000818:Animals; D001369:Axons / Q000502:physiology*; D006801:Humans; D008433:Mathematics; D008959:Models, Neurological; D009420:Nervous System / Q000166:cytology* / Q000254:growth & development*