Random connectivity generates inhibitory microcircuits that decorrelate adaptation in visual cortex

Inhibitory neurons are fundamental to sensory processing in the cortex but the rules governing their connections with excitatory neurons are unclear. Are pyramidal cells with different functions generated through specific or random connections? We used two-photon imaging, optogenetics and modelling to investigate opposing forms of adaptation in layer 2/3 of mouse visual cortex. We find that a slow modulatory drive acts differentially depending on the relative strength of inputs that individual pyramidal cells receive from parvalbumin-positive and somatostatin-positive interneurons. The number of depressing and sensitizing pyramidal cells could be explained quantitatively by the simplest connectivity rule - all inhbitory synapses made randomly. The functional heterogeneity of the pyramidal cell population therefore begins with general statistics of the connectome - interneurons are much sparser and connect with probabilities far less than one. The resulting "patchwork" of inhibitory microcircuits causes modulatory inputs to strongly decorrelate pyramidal cells on the behavioural time-scale of seconds.