Precise connections in the brain result from elaborate processes during development. In the visual system, axonal projections from retinal ganglion cells (RGCs) onto the superior colliculus form a precise retinotopic map. Studies have revealed that the development of retinocollicular maps involves three main factors: graded expression of molecular guidance cues such as EphAs and ephrin-As, activity dependent processes driven by spontaneous activity in RGCs, and different forms of axonal competition. In this study, we developed a new, versatile model including these factors. We first modeled the selective arborization of RGC axons, mediated by EphA/ephrin-A signaling, without assuming that this initial process instructed the map's final topology. We also derived an integro-differential equation modeling a second, dynamic phase in which activity-dependent plasticity of axonal arbors combined with their competition for collicular resources can deeply remodel the topology of immature maps. Our model hence challenges the view that retinotopic maps are instructed by matching molecular gradients and then merely refined by activity-dependent processes. We reproduce fine features of retinotopic map development in wild-type and various transgenic mice, allowing a new understanding of the underlying mechanisms. Our model predicts that competition is not based on comparisons of axonal EphA receptor levels but rather relies on the optimization of collicular resources mediated by neurotrophic receptors such as p75 NTR. Our model finally clarifies the elusive role of reverse signaling between retinal ephrin-As and collicular EphAs by reproducing for the first time the phenotypes of two mouse genotypes in which this function is altered.
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