Graph-based analysis of volumetric image data reveals predominant layer Va-to-II/III feedback in mouse motor cortex

How precise 3D interactions among cortical neurons underlie layer-specific computations remains elusive. We develop a graph-framework to infer functional connectivity from fast volumetric two-photon Ca2+ imaging of spontaneous activity in the awake mouse primary motor cortex. By converting deconvolved traces into binary spike trains, removing population bursts, and applying an adaptive, layer-specific threshold, we reconstruct a directed, weighted network of ∼1,000 neurons. Decomposition into strongly connected components reveals ∼30 sub-networks of ∼10 neurons, predominantly in layer II/III and often bridging to layer Va. Across six 20-min recordings, we find that (1) layer II/III dominates connectivity, (2) feedback (Va → II/III) links exceed and outweigh feedforward (II/III → Va) ones, and (3) information flows in ≤6 synapses. We uncover seven geometrical and dynamical motifs with characteristic event sizes and durations, revealing diverse column-like microcircuits in M1 with a net ascending flow, suggesting that such sub-networks form elemental processing modules for motor control.