Optimality and saturation in axonal chemotaxis

Chemotaxis (detecting and following chemical gradients) plays a crucial role in the function of many biological systems. In particular, gradient following by neuronal growth cones is important for the correct wiring of the nervous system. There is increasing interest in the constraints that determine how small chemotacting devices respond to gradients, but little quantitative information is available in this regard for neuronal growth cones. Mortimer et al. ( 2009 ) and Mortimer, Dayan, Burrage, and Goodhill ( 2011 ) proposed a Bayesian ideal observer model that predicts chemotactic performance for shallow gradients. Here we investigated two important aspects of this model. First, we found by numerical simulation that although the analytical predictions of the model assume shallow gradients, these predictions remain remarkably robust to large deviations in gradient steepness. Second, we found experimentally that the chemotactic response increased linearly with gradient steepness for very shallow gradients as predicted by the model; however, the response saturated for steeper gradients. This saturation could be reproduced in simulations of a growth rate modulation response mechanism. Together these results illuminate the domain of validity of the Bayesian model and give further insight into the biological mechanisms of axonal chemotaxis.