Rich club organization of macaque cerebral cortex and its role in network communication

Abstract

Graph-theoretical analysis of brain connectivity data has revealed significant features of brain network organization across a range of species. Consistently, large-scale anatomical networks exhibit highly nonrandom attributes including an efficient small world modular architecture, with distinct network communities that are interlinked by hub regions. The functional importance of hubs motivates a closer examination of their mutual interconnections, specifically to examine the hypothesis that hub regions are more densely linked than expected based on their degree alone, i.e. forming a central rich club. Extending recent findings of rich club topology in the cat and human brain, this report presents evidence for the existence of rich club organization in the cerebral cortex of a non-human primate, the macaque monkey, based on a connectivity data set representing a collation of numerous tract tracing studies. Rich club regions comprise portions of prefrontal, parietal, temporal and insular cortex and are widely distributed across network communities. An analysis of network motifs reveals that rich club regions tend to form star-like configurations, indicative of their central embedding within sets of nodes. In addition, rich club nodes and edges participate in a large number of short paths across the network, and thus contribute disproportionately to global communication. As rich club regions tend to attract and disperse communication paths, many of the paths follow a characteristic pattern of first increasing and then decreasing node degree. Finally, the existence of non-reciprocal projections imposes a net directional flow of paths into and out of the rich club, with some regions preferentially attracting and others dispersing signals. Overall, the demonstration of rich club organization in a non-human primate contributes to our understanding of the network principles underlying neural connectivity in the mammalian brain, and further supports the hypothesis that rich club regions and connections have a central role in global brain communication.

Figure 1. Rich club detection and node/edge classification.

(A) Example networks, each composed of 48 nodes and 123 undirected edges, and displayed using a spring-embedding layout algorithm. Both networks contain a set of high-degree nodes (red). In the network at the top, these nodes are interconnected with a density (rich-club coefficient) of 0.711. The network below was derived by randomizing the original network, preserving all node degrees. High-degree nodes are again shown in red, and their connection density is 0.578. Comparison of the network at the top to a population of 10,000 randomized networks indicates the presence of a rich club, with p = 0.0004. Note that due to constraints imposed by the degree sequence high-degree nodes in the randomized network remain linked with an edge density that exceeds that of the network as a whole. (B) Identification of rich club nodes allows the classification of edges into rich club, feeder and local edges.

Figure 2. Connection matrix and network communities (modules).

(A) Binary connection matrix comprising 242 regions and 4090 directed projections. Regions are arranged by module assignment, and within each module they are ranked by their degree (sum of in-degree and out-degree). The node ordering and module assignments are reported in the Supplementary Information. (B) Surface rendering of the inflated right hemisphere of macaque cortex, with surface regions color-coded by to their module assignments. Some points on the surface corresponded to multiple cortical regions since multiple schemes for regional parcellations were used for surface mapping. This could lead to multiple module assignment for a given surface point. In case of multiple assignments, regions were colored according to a majority rule, choosing the mode of the distribution of module assignments. In the case of a tie, a module was chosen at random from the tied set, resulting in a mottled appearance. Surface plots at left and right show lateral (L) and medial (M) views; plots at top and bottom show ventral (V) and dorsal (D) views.

Figure 3. Centrality and hub regions.

(A) Regional scores for node betweenness, closeness, vulnerability and dynamic importance. Regions are arranged in the same order as shown in Figure 2A. Module assignments (see Figure 2) are indicated by the color bar at the right. (B) Surface rendering of the global centrality score.

Figure 4. Rich club regions and their spatial distribution.

(A) List of rich club member regions across all 14 rich club levels. Member regions of RC1 and RC2 are indicated, as are connector hubs (listed in blue). (B) Surface map of RC levels. (C) Surface maps of RC1 and RC2 member regions.

Figure 5. Comparison of core subshells and rich club members.

In both plots, the nodes are arranged along a circle, in the same order (by module and degree) used for displaying the connection matrix in Figure 2A, starting counterclockwise at the top. (A) Core subshell levels are displayed as concentric rings, with the innermost subshell nearest to the center of the circle. Regions are marked as black dots according to their subshell level. (B) Rich club levels are displayed as concentric rings, with the tightest rich club (RC1) corresponding to rich club level 1. Regions are marked as black dots according to their rich club level.

Figure 6. Motif contributions of rich club regions.

(A) Apex motifs 4, 6 and 9 are statistically overrepresented as compared to both randomized and latticized null models (z-scores 13.1, 12.3, and 59.5 against randomized controls; 15.1, 16.9 and 2.2 against latticized controls). All 13 3-node motifs are shown at the bottom. (B) Scatter plot of apex ratio (for all three apex motifs) and clustering coefficient for all 242 regions, with RC1 and RC2 color coded. (C) Examples of star-like motifs centered on rich club regions 46, 13a, and LIP. All surrounding regions are reciprocally connected to the center and unconnected otherwise. Regions are color coded by their module assignment.

Figure 7. Communication cost and path structure.

(A) Bar plots display the proportions of rich club (“R”, red), feeder (“F”, orange) and local (“L”, yellow) connections to network density and communication cost, shown for RC1 and RC2. (B) Heatmap (gray scale) of node degrees encountered along paths of path length (pl) 2, 3, 4, and 5. The median degrees are indicated in blue, and minimum degrees for nodes that are members of RC1 and RC2 are shown in red. The plot aggregates data on all paths starting and ending on non-rich club (non-RC2) nodes. Similar plots are obtained for paths starting and ending on non-RC1 nodes (not shown). (C) Proportion (probability) of touching an RC2 node plotted along all paths of lengths 2 to 5 steps. (D) Proportion (probability) of traveling along an RC2 edge plotted along all paths of lengths 3 to 5 steps. In panels (C) and (D), black symbols represent data from the macaque network, gray symbols represent means from 200 randomized networks preserving node degree sequence. Asterisks indicate that macaque data exceed the values from the empirical null distributions at p<0.05 (one-sided, uncorrected).

Figure 8. Directionality of paths and rich club.

The figure presents distributions of short communication paths leading into (“in-paths”) and emerging from (“out-paths”) rich club nodes. Plots at the top are for RC1 regions, and plots at the bottom are for RC2 regions. Data shown are for paths that begin and end on non-RC nodes. (A) Scatter plot of degree imbalance (in-degree minus out-degree) and path imbalance (in-paths minus out-paths) for the macaque cortex (red markers) and for averages obtained from 200 randomized networks preserving degree sequence (gray markers). Note that node degree imbalances are identical for randomized networks. Region names in large black font mark regions for which the difference between macaque and random population is significant (p<0.01, uncorrected). (B) The in-out paths ratio, shown here for the macaque cortex, is computed as (in-paths−out-paths)/(in-paths+out-paths). Black bars indicate regions for which the in-out paths ratio is significantly different (p<0.01, uncorrected) compared to that of a population of 200 randomized networks.