The role played by interlayer connections in shaping local responses and their long-range coupling has not yet been fully elucidated. Here, we analyze a rate model of a canonic local circuit with realistic anatomy. We find that this circuit generates a rich repertoire of possible dynamical states, including an oscillatory regime in which gammaand beta-oscillations dominate in superficial and deep layers, respectively, in agreement with experimental observations. This regime stems from non-linear inter-layer interactions, independently from intrinsic resonance properties of distinct layers. Moreover, by connecting two local circuits via cortico-cortical projections, the emergent phase differences define a flexible and frequency-dependent inter-areal hierarchy. Such dynamic patterns generally do not arise in randomized circuits, and the compatible connectomes are rare, although not unique. Altogether, these results suggest that inter-layer connectivity is homeostatically regulated to make local circuits fit to integrate and multiplex signals from several sources in multiple frequency bands.
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