In the formation of projections that map one area of the nervous system onto another, guidance of axonal growth cones by directional cues encoded in target tissues is well established by observations on misrouted fibres, though other mechanisms contribute to the precision of connectivity patterns. General physical principles indicate that, if there is directional guidance of normally as well as misrouted axons, leading them toward their appropriate target positions, the inference for a role of graded distributions of molecules is a strong one. As explained in this paper, curving, meandering, branching and shifting connections are fully consistent with a crucial role of directional cues encoded by graded molecular distributions. A model is proposed according to which slight directional cues are strongly enhanced within the axonal growth cone; if the proximal part of the growth cone is activated indicating that the growth cone points in an entirely wrong direction, then a discontinuous directional change such as branching is elicited. Pathways are corrected in this way, and near the appropriate target position the terminal arbour is formed because from there all routes point towards less optimal positions, leading to multiple branching.

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