Neuronal networks exhibit a rich dynamical repertoire, a consequence of both the intrinsic properties of neurons and the structure of the network. It has been hypothesized that inhibitory interneurons corral principal neurons into transiently synchronous ensembles that encode sensory information and subserve behavior. How does the structure of the inhibitory network facilitate such spatiotemporal patterning? We established a relationship between an important structural property of a network, its colorings, and the dynamics it constrains. Using a model of the insect antennal lobe, we show that our description allows the explicit identification of the groups of inhibitory interneurons that switch, during odor stimulation, between activity and quiescence in a coordinated manner determined by features of the network structure. This description optimally matches the perspective of the downstream neurons looking for synchrony in ensembles of presynaptic cells and allows a low-dimensional description of seemingly complex high-dimensional network activity.
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