Mathematical guidance for axons

Trends Neurosci. 1998 Jun;21(6):226-31. doi: 10.1016/s0166-2236(97)01203-4.

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.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.
  • Review

MeSH terms

  • Animals
  • Axons / physiology*
  • Humans
  • Mathematics*
  • Models, Neurological*
  • Nervous System / cytology*
  • Nervous System / growth & development*