Uncovering structural regularities and architectural topologies of cortical circuitry is vital for understanding neural computations. Recently, an experimentally constrained algorithm generated a dense network reconstruction of a ∼0.3-mm3 volume from juvenile rat somatosensory neocortex, comprising ∼31,000 cells and ∼36 million synapses. Using this reconstruction, we found a small-world topology with an average of 2.5 synapses separating any two cells and multiple cell-type-specific wiring features. Amounts of excitatory and inhibitory innervations varied across cells, yet pyramidal neurons maintained relatively constant excitation/inhibition ratios. The circuit contained highly connected hub neurons belonging to a small subset of cell types and forming an interconnected cell-type-specific rich club. Certain three-neuron motifs were overrepresented, matching recent experimental results. Cell-type-specific network properties were even more striking when synaptic strength and sign were considered in generating a functional topology. Our systematic approach enables interpretation of microconnectomics 'big data' and provides several experimentally testable predictions.
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We thank the members of the Segev Lab for helpful discussions related to this project. We also thank I. Nadav for the image processing. This work was supported by the Gatsby Charitable Foundation and the EPFL-Hebrew University Collaborative Grant, the EPFL support to the Laboratory of Neural Microcircuitry (LNMC), the ETH Domain for the Blue Brain Project (BBP), the Human Brain Project through the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement no. 604102 (HBP) and from the European Union H2020 FET program through grant agreement no. 720270 (HBP SGA1), the Brain Science grant of the Sachs Family and by the ISF Centers of Excellence grants 1789/11 and 2180/15.
The authors declare no competing financial interests.
Integrated supplementary information
2D projection of m-types, obtained by overlaying multiple reconstructed morphologies, aligning somata to a single point, and summing the fiber length per μm3 (axon left, green; dendrite right, magenta). Density plots for 55 known inhibitory (cyan) and excitatory (red) m-types arranged horizontally by layer. Morphologies in L2 and L3 are not separated. Inhibitory neurons: DAC, Descending Axon Cell; LAC, Large Axon Cell; HAC, Horizontal Axon Cell; NGC-DA, Neurogliaform Cell with Dense Axonal arborization; NGC-SA, Neurogliaform Cell with Slender Axonal arborization; SAC, Small Axon Cell; BP, Bipolar Cell; BTC, Bitufted Cell; ChC, Chandelier Cell; DBC, Double Bouquet Cell; LBC, Large Basket Cell; MC, Martinotti Cell; NBC, Nest Basket Cell; NGC, Neurogliaform Cell; SBC, Small Basket Cell. Excitatory neurons: PC, Pyramidal Cell; SP & SS, Star Pyramidal and Spiny Stellate cells; TTPC1 & TTPC2, late (1) and early (2) bifurcating apical tufts; UTPC & STPC, Untufted and Slender-tufted; TPC, Tufted Pyramidal Cells; dendrites terminating in L4 (TPC-L4) and L1 (TPC-L1), UTPC, Untufted Pyramidal Cells; IPC, Pyramidal Cell with inverted apical-like dendrites; BPC, Pyramidal Cell with Bipolar apical-like dendrites. Inset, expanded L5-TTPC1 with an exemplar reconstruction superimposed.
Supplementary Figure 2 The probability of finding a connection between two neurons decays with their intersomatic distance
The probability is computed for each distance bin (50 bins were used for the whole distance domain 0 - 2,090 μm) by dividing the number of observed connections in this bin (inset) by the number of existing pairs in the bin. I-to-I (blue) connections are more confined than E-to-E (red). Black depicts the distance dependence profile of the entire microcircuit.
Both (a) in-degrees and (b) out-degrees of neurons in the central NMC show dependency on their distance from the center of the column (denoted by the crosses at left NMC images). Images at left depict 2D histograms of degrees across the horizontal plane of the column (322 bins). (c) and (d), when taking into account the external connections from (c) and to (d) the surrounding columns, the distance dependence of the neuron’s degrees disappears. Pearson correlations coefficients, r, and their respective P-values are depicted.
(a) In-degrees and (b) out-degrees show long tail distributions also when accounting for extrinsic connections from/to external neurons (gray lines depict internal degree distribution, as in Figure 3). (c) The top 157 (half-percentile) highly connected in-hubs (having 1313-1444 incoming connections) arise from only 4 cell types (pie chart). The top 157 highly connected out-hubs (having 1321-1467 outgoing connections) arise primarily from 3 cell-types. The tendency of intermediate and deep layers to possess in-hubs, whereas out-hubs tend to emerge from superficial and intermediate layers is depicted. (d,e) Highly connected hubs as in (c) but in terms of the number of contacts and synaptic conductance, respectively.
Entire network and E/I subnetworks, both at the network-wide level and within layers demonstrate: (a) A characteristic path length, l, that is comparable to that expected from the corresponding ER-random networks l(ER). (b) Clustering coefficient, c higher than expected from the corresponding random networks c(ER).
Supplementary Figure 6 Rich club analysis using two implementations for generating random networks with matching degree sequence
The open squares are as in Fig. 3i whereas the orange dots are computed using the algorithm provided in the Brain Connectivity Toolbox33. The ratio of the number of connections among NMC neurons whose total degree (in-degree + out-degree) > d to that expected from random networks with matching degree sequence (namely, each node maintained in-degree and out-degree similar to its original values) is plotted for all d (N=1,000, s.d. is depicted by gray). This ratio is above 1 for high degree neurons, reflecting the presence of rich-club phenomenon according both implementations.
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Gal, E., London, M., Globerson, A. et al. Rich cell-type-specific network topology in neocortical microcircuitry. Nat Neurosci 20, 1004–1013 (2017). https://doi.org/10.1038/nn.4576
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