TY - JOUR

T1 - Diffusion in axon guidance

AU - Goodhill, Geoffrey J.

PY - 1997

Y1 - 1997

N2 - Axon 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 several millimetres. The time it takes for this maximum guidance distance to fall to the asymptotic value depends on the diffusion constant. This time is a few hours for a small molecule but as much as a few days for a large molecule. The model therefore predicts that guidance over distances larger than 1000 μm is possible if the start of production of the factor is carefully matched to the time when guidance is required.

AB - Axon 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 several millimetres. The time it takes for this maximum guidance distance to fall to the asymptotic value depends on the diffusion constant. This time is a few hours for a small molecule but as much as a few days for a large molecule. The model therefore predicts that guidance over distances larger than 1000 μm is possible if the start of production of the factor is carefully matched to the time when guidance is required.

KW - Chemotaxis

KW - Chemotropism

KW - Diffusible factors

KW - Gradients

KW - Growth cone

UR - http://www.scopus.com/inward/record.url?scp=0030762758&partnerID=8YFLogxK

U2 - 10.1111/j.1460-9568.1997.tb01496.x

DO - 10.1111/j.1460-9568.1997.tb01496.x

M3 - Article

C2 - 9240399

AN - SCOPUS:0030762758

VL - 9

SP - 1414

EP - 1421

JO - European Journal of Neuroscience

JF - European Journal of Neuroscience

SN - 0953-816X

IS - 7

ER -