What do developmental mapping rules optimize?

Convergence ratios between pre- and postsynaptic cells in the visual system vary widely between cell classes, areas of the visual field, between individuals and between species. Proper stabilization of the convergence and divergence of single visual neurons is critical for visual integration generally, and for specific functions such as those of rod and cone pathways, or the center and peripheral regions of the visual field. In early development, retinal ganglion cells, target cells and all their processes are produced in excess and stabilize at certain mature values. The intent of the investigations described here is to determine what features of cell connectivity are stabilized over normal variability by these developmental processes and how such stabilization is accomplished, using the developing mammalian retinotectal system as an example. Orderly compression of the retinotopic map into a half tectum was induced by a partial tectal ablation at birth in hamsters, increasing the ratio of retinal ganglion cells to superior colliculus target cells. The convergence problem is solved in this case by undersampling the spatial array with respect to normal, preserving local spatial resolution, but potentially reducing sensitivity or introducing aliasing artifacts. Receptive field sizes of single neurons are indistinguishable from normal, and reduction of branching of presynaptic axon arbors is the mechanism of the remapping. Behaviorally, though the entire visual field is still represented in the remaining colliculus, the solution has a cost in decreased probability and increased latency to orient to visual stimuli, particularly in the peripheral visual field. The generality of this solution for retinal and other central convergence regulation problems is evaluated.