Connection strength of the macaque connectome augments topological and functional network attributes

Abstract

Mammalian brains constitute complex organized networks of neural projections. On top of their binary topological organization, the strength (or weight) of these neural projections can be highly variable across connections and is thus likely of additional importance to the overall topological and functional organization of the network. Here we investigated the specific distribution pattern of connection strength in the macaque connectome. We performed weighted and binary network analysis on the cortico-cortical connectivity of the macaque provided by the unique tract-tracing dataset of Markov and colleagues (2014) and observed in both analyses a small-world, modular and rich club organization. Moreover, connectivity strength showed a distribution augmenting the architecture identified in the binary network version by enhancing both local network clustering and the central infrastructure for global topological communication and integration. Functional consequences of this topological distribution were further examined using the Kuramoto model for simulating interactions between brain regions and showed that the connectivity strength distribution across connections enhances synchronization within modules and between rich club hubs. Together, our results suggest that neural pathway strength promotes topological properties in the macaque connectome for local processing and global network integration.

Keywords: Connectome; Functional synchronization; Macaque; Network; Projection strength.

Figure 1.

The 29 injection sites of the macaque dataset. Injection sites were distributed along all six cortical lobes, that is, 4 in occipital (yellow), 6 in temporal (green), 6 in parietal (orange), 5 in frontal (light blue), 7 in prefrontal (red), 1 in limbic (dark blue) cortical structures. The 29 injection regions are highlighted. The layout is as presented by Markov et al. (2014) and made available at core-nets.org by Markov and colleagues.

Figure 2.

Clustering and characteristic path length per region. Clustering in binary (A) and weighted (B) macaque connectome reconstructions. Clustering coefficient of cortical regions in the binary network ranged from 0.67 (medium clustering) to 0.87 (high clustering). In the weighted reconstruction, clustering coefficients ranged from 0.54 (medium clustering) to 0.90 (high clustering). (C) Cortical regions showed characteristic path length ranging from 1.13 to 1.68 steps. (D) The path length of the weighted network ranged from 0.19 to 0.31 steps.

Figure 3.

Network configurations in the small-world morphospace. (A) Schematic representation of a morphospace. The clustering coefficient and average shortest path length are shown for networks generated by either a small-world organization maximizing or minimizing optimization procedure (orange arrows). The black square indicates the original macaque connectome. Yellow circles indicate the generated networks, and darker shades of yellow indicate networks generated in later iterations. Network variants in the final iteration, forming the Pareto front, are indicated by orange circles. Gray circles represent the population of generated randomized networks. (B) The binary macaque network shows an as low as possible shortest path length and as high as possible clustering coefficient. (C) The weighted network shows close to the Pareto front of networks with maximum small-world organization in the morphospace of networks with similar in- and out-degree and in-strength. (D) The weighted network shows not close to either Pareto front in the space of networks with similar binary topology.

Figure 4.

Detection of modules in the macaque dataset. (A) Modularity detection in the binary network showed the presence of two modules. (B) In the weighted network version, modularity detection revealed four modules. High overlap was observed between the modules found in the binary and weighted networks (Rand index = 0.70, p < 0.001, 10,000 permutations).

Figure 5.

Rich club coefficient as function of in-degree k_in. (A) Curves represent the rich club coefficient in the binary connectivity network of the macaque cerebral cortex (black), averaged rich club coefficient of randomized networks (gray; 10,000 permutations) and the normalized rich club coefficient (red). Shading of the region 36 <k_in < 56, indicates rich club presence where ϕ_unw significantly exceeded ϕ_norm (p < 0.05, FDR corrected). (B) For the weighted macaque network, the normalized rich club coefficient (red) increased with k_in and rich club organization was present for 25 <k_in < 64 and 65 <k_in < 75 (p < 0.05, FDR corrected).

Figure 6.

Comparison strength of connection groups. Average strength of inter- (A) and intramodular (B) connections, linking between rich club nodes (rich club connections, red), between rich club and the periphery (feeder connections, orange), or between peripheral regions (local connections, yellow). Among intermodular links, rich club connections exhibited on average strongest connections (rich club–feeder, p < 0.001; rich club–local, p < 0.004; feeder–local, p = 0.738; 10,000 permutations, FDR corrected), indicating the importance of rich club connections in communication between anatomical communities. Intramodular links showed similar strength between connection classes (all p > 0.05, FDR corrected).

Figure 7.

Synchrony of simulated function. (A) Computed average synchronization probability for binary, weighted, and weights-shuffled macaque networks showed a critical regime between 0.02 and 0.04. (B) Binary and weighted networks showed higher intramodular synchrony relative to intermodular synchrony, reflecting the structural organization. The intra-/intermodular synchrony ratio of the weighted network was also higher than in the weights-shuffled network, suggesting connectivity strength to increase local functional specialization. (C) The synchrony between rich club regions (RC-RC) was higher than between rich club regions and periphery (RC-P) or among peripheral regions (P-P) for the binary and weighted network. The synchrony ratio in the weighted network was higher compared with the ratio seen in the weights-shuffled network, indicating that the connectivity strength distribution increases network integration through rich club synchronization.

Figure 8.

Interaction of rich club and modular network organization on synchrony of simulated function. The ratio of synchrony between rich club regions (RC-RC) and the synchrony between rich club regions and periphery (RC-P) or among periphery (P-P) among intramodular (A) or intermodular (B) region pairs.