Potential connectivity of neuron types. A, Partial matrix showing axonal and dendritic locations for selected DG, CA3, and CA2 types within certain parcels of the hippocampal formation (full matrix available online at Hippocampome.org/morphology). Bold, glutamatergic; gray, GABAergic; red boxes with horizontal lines, axons; blue boxes with vertical lines, dendrites; purple boxes with horizontal and vertical lines, both axons and dendrites; black circles, soma locations; red arrows, potential connections of granule cells. Parcel abbreviations for DG: SMo, outer stratum moleculare; SMi, inner stratum moleculare; SG, stratum granulosum; H, hilus; for CA3/CA2: SLM, stratum lacunosum-moleculare; SR, stratum radiatum; SL, stratum lucidum; SP, stratum pyramidale; SO, stratum oriens. B, Representative illustration of the overlapping spatial distribution (indicative of potential connectivity) of granule cell axons (right) and MFA ORDEN cell dendrites (left) in CA3 SL and SP (for both neurons: axons in red; dendrites in black). Morphological reconstruction of the granule cell downloaded from NeuroMorpho.Org (Ascoli et al., 2007), with layers drawn in, from a tracing originally presented in Bausch et al. (2006). Permission to reprint the MFA ORDEN cell (Vida and Frotscher, 2000) granted by Proceedings of the National Academy of Sciences of the United States of America (Copyright 2000 National Academy of Sciences, U.S.A.). C, Screenshot from the novel online toolbox (Hippocampome.org/connectivity) illustrating all information potentially received (arrows in) and sent (arrows out) by granule cells (black connections excitatory; orange inhibitory).
Comparison of the HC to well-known types of equivalently sized random networks. A, Broad categorizations, indicated by background shading from the four corners, aid in grouping and analyzing network topology along two dimensions of interest: CC and CPL. Data points for six types of random networks are averaged from 1000-network datasets; standard deviations are illustrated by the diameter. B, The combination of high CC and low CPL in the HC results in an optimally low overall communication cost in the network. BA, Barabasi–Albert; ER, Erdös–Rényi; KE, Klemm–Eguílez; Latt, square lattice; WS, Watts–Strogatz.
Modular structure of the potential hippocampal connectome. A, Chord diagram of the potential connectivity among all 122 types (produced with Circos software: Krzywinski et al., 2009). Thick chords with arrows emphasize the trisynaptic loop (dark green, perforant pathway lines; light green, temporoammonic path; red, mossy fibers; blue, Schaffer collaterals; orange, projection from CA1 to EC layer V); other connections are colored randomly to optimize visibility. Types are identifiable by both numbers in brackets (names provided in Table 1) and axon-dendrite patterning within the subregion of their soma location (colored box convention and layer ordering from inside-out as in Fig. 1; layers for CA1: SLM, SR, SP, SO; for subiculum: stratum moleculare, SP, polymorphic layer; for EC: I–VI). Shaded bars in the innermost ring show the total number of (signed) connections made by that type; excitatory types have outward-facing black bars and inhibitory types inward-facing gray bars. B, Modularity scores (Q) for the entire network and for the four detected modules. C, The communities correspond closely to the DG (module connection density 75.9%), CA3 (59.3%), CA1 (64.6%), and EC (70.1%; not shown). Numbered types and colored arrows as in A.
Breakdown of degree distribution to isolate neuron types with unusual connectivity. A, Difference in the axonal and dendritic architecture is evident in the OD (red data series) and ID (blue) distributions. B, The two OD tails are respectively attributable to highly connected hubs within the subset of neuron types that project to another subregion (green series; positive skewness) and to certain local neuron types with highly specific connectivity (gray; negative skewness).
Nested rich clubs within the HC. A, Top, distribution of nodes by TD; bottom, nodes with TD ≥55 are members of a densely interconnected rich club. Eight members of this club are also members of a second “ultra-rich” club level (dark purple shading; light purple shading indicates members of RC I but not RC II). B, Connection densities of RC I and RC II are elevated compared with the rest of the network. C, Modular analysis of each RC tier. D, The 56 neuron types of RC I (top) and the subset constituting RC II (bottom).
Alternate pathways between nodes afford resilience to the network. A, Length of the shortest directed route between each pair of neuron types. Presynaptic types are in rows, postsynaptic types in columns; see Table 1 for type names and ordering. Color gradient key: yellow, direct connection; orange, red, and dark red, two, three, and four steps, respectively; black, highest pathlength (five steps). B, Orange labels indicate the percentage of type pairs that can be bridged by a path of a given length, k (shown for k ≤ 5). In addition, at each k, blue columns show the average number of available conduits across all pairs of types. C, For k = 2, peak height in a three-dimensional plot indicates the number of two-step paths between types. D, Absorption measures the average length of all routes from (rows) and to (columns) other types. E, Driftness is relatively low for most type pairs, pointing to the availability of multiple pathways between nodes that are similar in length to the shortest path. Color gradient for D and E as in A.
Superpatterns and HC usage. A, Connectivity superpattern trimers are unweighted subgraphs of three nodes (disconnected superpatterns outlined in gray). B, Counts of disconnected and connected superpatterns. C, Percentage of connected superpatterns localized to a given module or found between modules. D, Within CA1, superpattern usage also varies by cell type, as indicated by ratios of pyramidal cells to interneurons (blue line) and perisomatic interneurons to dendritic-targeting neurons (dotted red line).
Weighted trimers analysis based on excitatory/inhibitory neuron type distinction. A, The eight patterns that constitute superpattern F, the single uplinked mutual dyad. Black lines and nodes are excitatory, gray lines and nodes are inhibitory, and blue lines indicate reciprocal connections that are excitatory in one direction and inhibitory in the other. ES values are shown in boxes in which background shading indicates strongly and mildly excitatory and inhibitory patterns; key shown in B. B, Relative importance of each ES to the DG, CA3, and CA1 modules. C, Pattern F4 is heavily utilized by CA3 and CA3c pyramidal cells; relatively light usage of this pattern by CA1 pyramidal cells and CA3 interneurons is shown for comparison. D, The CA3 pyramidal cell connected pattern fingerprint (brown) is plotted on top of the overall HC fingerprint (light blue) using a logarithmic scale.
Three-node feedback loops (superpattern G) are generally avoided in HC in favor of other two-step chains, such as feedforward loops (superpattern E). The excitatory/inhibitory combinations of these patterns are displayed in the right and left columns along with representative neuron type groupings and a computational interpretation. Black dots and arrows indicate excitatory types and connections; gray signifies inhibitory types and connections; and blue dots, located at the output of the loop, are excitatory in one pattern combination and inhibitory in the other. Total network occurrences for each pattern are shown in square brackets.
A, Motifs and antimotifs are largely determined by HC superpattern topology. Although some superpatterns are neutral, most superpatterns are strong motifs. Only superpatterns D, G, and I are severely underutilized relative to the population of random networks. A–D, The motif/anti-motif balance of individual superpatterns in the network does not necessarily hold for individual modules (e.g., superpatterns C and J).