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The topographic projection of retinal ganglion cell (RGC) axons to mouse superior colliculus (SC) or chick optic tectum (OT) is formed in three phases: RGC axons overshoot their termination zone (TZ); they exhibit interstitial branching along the axon that is topographically biased for the correct location of their future TZ; and branches arborize preferentially at the TZ and the initial exuberant projection refines through axon and branch elimination to generate a precise retinotopic map. We present a computational model of map development that demonstrates that the countergradients of EphAs and ephrinAs 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 a proposed repellent action of EphAs/ephrinAs present on RGC branches and arbors added to that of EphAs/ephrinAs expressed by OT/SC cells is required to progressively restrict branching and arborization to topographically correct locations and eliminate axon overshoot. Simulations show that this molecular framework alone can develop considerable topographic order and refinement, including axon elimination, a feature not programmed into the model. Generating a refined map with a condensed TZ as in vivo requires an additional parameter that enhances branch formation along an RGC axon near sites that it has a higher branch density, and resembles an assumed role for patterned neural activity. The same computational model generates the phenotypes reported in ephrinA deficient mice and Isl2-EphA3 knockin mice. This modeling suggests that gradients of counter-repellents 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. However, competitive interactions between RGC axons that enhance the probability of continued local branching are required to generate precise retinotopy.

Abstract

Probabilistic modelling of text data in the bagof-words representation has been dominated by directed graphical models such as pLSI, LDA, NMF, and discrete PCA. Recently, state of the art performance on visual object recognition has also been reported using variants of these models. We introduce an alternative undirected graphical model suitable for modelling count data. This "Rate Adapting Poisson" (RAP) model is shown to generate superior dimensionally reduced representations for subsequent retrieval or classification. Models are trained using contrastive divergence while inference of latent topical representations is efficiently achieved through a simple matrix multiplication.

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