Theoretical analysis of gradient detection by growth cones

Gradients of diffusible and substrate-hound molecules play an important rol e in guiding axons to appropriate targets in the developing nervous system, Although some of the molecules involved have recently been identified, lit tle is known about the physical mechanisms by which growth cones sense grad ients, This article applies the seminal Berg and Purcell (1977) model of gr adient sensing to this problem. The model provides estimates for the statis tical fluctuations in the measurement of concentration by a small sensing d evice. By assuming that gradient detection consists of the comparison of co ncentrations at two spatially or temporally separated points, the model the refore provides an estimate for the steepness of gradient that can be detec ted as a function of physiological parameters. The model makes the followin g specific predictions. (a) It is more likely that growth cones use a spati al rather than temporal sensing strategy, (b) Growth cone sensitivity incre ases with the concentration of ligand, the speed of ligand diffusion, the s ize of the growth cone, and the time over which it averages the gradient si gnal. (c) The minimum detectable gradient steepness for growth cones is rou ghly in the range 1-10%, (d) This value varies depending on whether a bound or freely diffusing ligand is being sensed, and on whether the sensing occ urs in three or two dimensions. The model also makes predictions concerning the role of filopodia in gradient detection. (C) 1999 John Wiley & Sons, I nc.