Diffusion in Axon Guidance

AbstractAxon guidance by target‐derived diffusible factors plays an important role in the development of the nervous system. This paper considers the constraints imposed on this process by the mathematics of diffusion. A point source continuously producing a factor into an infinite three‐dimensional volume is considered as a model for both the in vivo and in vitro situation. Basic constraints for effective guidance are assumed to be that the concentration falls between certain maximum and minimum limits, and that the percentage change in concentration across the width of the growth cone exceeds a certain minimum value. The evolution of the shape of the gradient over time is analysed. Using biologically reasonable parameter values, it is shown that the maximum range over which growth cone guidance by a diffusible factor is possible for large times (several days) after the start of the production of the factor is 500–1000 μm. This maximum distance is independent of the diffusion constant of the diffusing molecule, applies to both chemoattractants and chemorepellents, and agrees with experimental data. At earlier times, however, the constraints may be satisfied for distances up to sev