Analysis of local and global topographic order in mouse retinocollicular maps

We introduce the Lattice Method for the quantitative assessment of the topographic order within the pattern of connections between two structures. We apply this method to published visuocollicular mapping data obtained by Fourier-based intrinsic imaging of mouse colliculus. We find that, in maps from wild types and β2 knock-outs, at least 150 points on the colliculus are represented in the visual field in the correct relative order. In maps from animals with knock-out of the three ephrinA ligands (TKO), thought to specify the rostrocaudal axis of the map, the projection on the colliculus of each small circular area of visual field is elongated approximately rostrocaudally. Of these projections, 9% are made up of two distinct regions lying along the direction of ingrowth of retinal fibers. These are similar to the ectopic projections found in other ephrinA knock-out data. Coexisting with the ectopic projections, each TKO map contains a submap where neighbor-neighbor relations are preserved, which is ordered along both rostrocaudal and mediolateral axes, in the orientation found in wild-type maps. The submaps vary in size with order well above chance level, which can approach the order in wild-type maps. Knock-out of both β2 and two of the three ephrinAs yields maps with some order. The ordered TKO maps cannot be produced by correlated neural activity acting alone, as this mechanism is unable to specify map orientation. These results invite reassessment of the role of molecular signaling, particularly that of ephrinAs, in the formation of ordered nerve connections.