  Current understanding of neuronal growth is mostly qualitative, as the
staggering number of physical and chemical guidance cues involved prohibit a
fully quantitative description of axonal dynamics. We report on a general
approach that describes axonal growth in vitro, on poly-D-lysine coated glass
substrates, as diffusion in an effective external potential, representing the
collective contribution of all causal influences on the growth cone. We use
this approach to obtain effective growth rules that reveal an emergent
regulatory mechanism for axonal pathfinding on these substrates.
