Spontaneous pinwheel annihilation during visual development

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Abstract
Neurons in the visual cortex respond preferentially to edge-like stimuli of a particular orientation1. It is a long-standing hypothesis that orientation selectivity arises during development through the activity-dependent refinement of cortical circuitry2,3,4. Unambiguous evidence for such a process has, however, remained elusive5,6,7. Here we argue that, if orientation preferences arise through activity-dependent refinement of initially unselective patterns of synaptic connections, this process should leave distinct signatures in the emerging spatial pattern of preferred orientations. Preferred orientations typically change smoothly and progressively across the cortex1. This smooth progression is disrupted at the centres of so-called pinwheels8,9, where neurons exhibiting the whole range of orientation preferences are located in close vicinity10. Assuming that orientation selectivity develops through a set of rules that we do not specify, we demonstrate mathematically that the spatial density of pinwheels is rigidly constrained by basic symmetry principles. In particular, the spatial density of pinwheels, which emerge when orientation selectivity is first established, is larger than a model-independent minimal value. As a consequence, lower densities, if observed in adult animals, are predicted to develop through the motion and annihilation of pinwheel pairs.