Synaptic Development of Fine Spatial Scale Organization of Neuronal Orientation Tuning in Mouse Primary Visual Cortex

Primary sensory cortices often organize neurons with similar stimulus preference into spatially functional maps. Recent work in mouse primary visual cortex (V1) has established that neuronal tuning to the orientation of visual grating stimuli is organized into `micro-clusters', where physically close neuron pairs (~ 20$ um) share highly similar orientation preferences, but the organization is unstructured beyond this narrow range. This fine-scale organization is seemingly at odds with the underlying intracortical circuitry in mouse V1 whose spatial extent is an order of magnitude broader (100 ~ 200 um). In this study, we explore an activity-dependent synaptic plasticity model of spatially structured thalamo-cortical connectivity. We develop theory under asymptotic conditions specific for mouse V1, and derive concrete circuit conditions under which `micro-clusters' naturally develop. In particular, the recurrent interaction among V1 neurons requires an additional component over a `micro'-spatial scale, while the spatial profiles of balanced excitation and inhibition support an effective `micro'-scale interaction. Together, our results provide a developmental mechanism and analytical framework linking thalamo-cortical development, recurrent circuit structure, and the emergence of functional organization in primary visual cortex.