Circuits in visual cortex integrate the information derived from separate ON and OFF pathways to construct orderly columnar representations of orientation and visual space1–7. How this transformation is achieved to meet the specific topographic constraints of each representation remains unclear. Here we report several novel features of ON/OFF convergence visualized by mapping the receptive fields of layer 2/3 neurons in tree shrew visual cortex using two-photon imaging of GCaMP6 calcium signals. The spatially separate ON and OFF subfields of simple cells in layer 2/3 were found to exhibit topologically distinct relationships with the maps of visual space and orientation preference. The centers of OFF subfields for neurons in a given region of cortex were confined to a compact region of visual space and displayed a smooth visuotopic progression. In contrast, the centers of the ON subfields were distributed over a wider region of visual space, displayed significant visuotopic scatter, and an orientation-specific displacement consistent with orientation preference map structure. As a result, cortical columns exhibit an invariant aggregate receptive field structure: an OFF-dominated central region flanked by ON-dominated subfields. This distinct arrangement of ON- and OFF- inputs enables continuity in the mapping of both orientation and visual space and the generation of a columnar map of absolute spatial phase.

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The retinotopic maps of many visual cortical areas are thought to follow the fundamental principles that have been described for primary visual cortex (V1) where nearby points on the retina map to nearby points on the surface of V1, and orthogonal axes of the retinal surface are represented along orthogonal axes of the cortical surface. Here we demonstrate a striking departure from this conventional mapping in the secondary visual area (V2) of the tree shrew. Although local retinotopy is preserved, orthogonal axes of the retina are represented along the same axis of the cortical surface, an unexpected geometry explained by an orderly sinusoidal transform of the retinal surface. This sinusoidal topography is ideally suited for achieving uniform coverage in an elongated area like V2, is predicted by mathematical models designed to achieve wiring minimization, and provides a novel explanation for stripe-like patterns of intra-cortical connections and stimulus response properties in V2. Our findings suggest that cortical circuits flexibly implement solutions to sensory surface representation, with dramatic consequences for the large-scale layout of topographic maps.