Modeling the molecular control of retinotopic map development and refinement

Abstract

Abstract: : Purpose: The topographic projection of retinal ganglion cell (RGC) axons to mouse superior colliculus (SC) or chick optic tectum (OT) is formed in three phases: (1) RGC axons overshoot their termination zone(TZ), (2) they exhibit interstitial branching along the axon that is topographically biased for the correct location of their future TZ, and (3) branches arborize preferentially at the TZ and the initial exuberant projection refines through axon elimination to generate a precise map. The purpose of this study was to develop a computational model of this map formation process to determine the molecular mechanisms that control the refinement of topographic axonal connections. Methods: A computational model of map formation was developed based on the known countergradients of EphAs and ephrin–As repellents in the retina and OT / SC. The model hypothesized that EphA/ephrin–A repellents present on RGC branches and arbors adds to the EphA/ephrin–A repellents expressed by OT/SC cells and progressively restrict branching to more topographically correct locations and eliminate axon overshoot. Branching was simulated along 300 retinal axons for a total of 200 iterations using a custom program written for Matlab 6.0. Results: We present a computational model of map development that demonstrates that the countergradients of EphAs and ephrin–As in retina and the OT/SC and bidirectional repellent signaling between RGC axons and OT/SC cells are sufficient to direct an initial topographic bias in RGC axon branching. Our model also suggests that co–repulsion amongst arbors through EphA/ephrin–A signaling is required and cooperates with OT/SC expressed EphAs/ephrin–As to determine the location of the TZ for each RGC axon. Simulations show that this molecular framework acting alone can develop a considerable topographic order and subsequent refinement. By adding an additional parameter that enhances branch formation along an RGC axon near areas of higher branch density, and resembles an assumed role for patterned neural activity, the computational model simulates normal retinotopic map development in chick OT and rodent SC. The same computational model generates the phenotypes reported in ephrin–A deficient mice and Isl2–EphA3 knockin mice. Conclusions: These simulations suggest that sigmoidal gradients of counterrepellents can establish a substantial degree of topographic order in the OT/SC, and that repellents present on RGC axon branches and arbors make a substantial contribution to map refinement.

Keywords: plasticity • visual development • superior colliculus/optic tectum