A mathematical model of axon guidance by diffusible factors

In the developing nervous system, gradients of target-derived diffusible factors play an important role in guiding axons to appropriate targets. In this paper, the shape that such a gradient might have is calculated as a function of distance from the target and the time since the start of factor production. Using estimates of the relevant parameter values from the experimental literature, the spatiotemporal domain in which a growth cone could detect such a gradient is derived. For large times, a value for the maximum guidance range of about 1 mm is obtained. This value fits well with experimental data. For smaller times, the analysis predicts that guidance over longer ranges may be possible. This prediction remains to be tested.