Getting into shape: Optimal ligand gradients for axonal guidance

During neural development, neurons from downstream, presynaptic regions of the nervous system (such as the retina) send spatially patterned axonal projections to upstream, target regions (the tectum or superior colliculus). A servomechanism model has been proposed to explain the pattern and time-course of axonal growth between these two regions [Honda, H., 1998. Topographic mapping in the retinotectal projection by means of complementary ligand and receptor gradients: a computer simulation study. J. Theor. Biol., 192, 235-246]. Here, we show that a modification of this model incorporating a different criterion for axonal decision-making, called the local optimum rule, is guaranteed to converge to a topographic map under a wide range of conditions encountered during neural development. A theoretical investigation of these conditions leads to new hypotheses regarding map formation.