A transcriptional signature of hub connectivity in the mouse connectome

Abstract

Connectivity is not distributed evenly throughout the brain. Instead, it is concentrated on a small number of highly connected neural elements that act as network hubs. Across different species and measurement scales, these hubs show dense interconnectivity, forming a core or "rich club" that integrates information across anatomically distributed neural systems. Here, we show that projections between connectivity hubs of the mouse brain are both central (i.e., they play an important role in neural communication) and costly (i.e., they extend over long anatomical distances) aspects of network organization that carry a distinctive genetic signature. Analyzing the neuronal connectivity of 213 brain regions and the transcriptional coupling, across 17,642 genes, between each pair of regions, we find that coupling is highest for pairs of connected hubs, intermediate for links between hubs and nonhubs, and lowest for connected pairs of nonhubs. The high transcriptional coupling associated with hub connectivity is driven by genes regulating the oxidative synthesis and metabolism of ATP--the primary energetic currency of neuronal communication. This genetic signature contrasts that identified for neuronal connectivity in general, which is driven by genes regulating neuronal, synaptic, and axonal structure and function. Our findings establish a direct link between molecular function and the large-scale topology of neuronal connectivity, showing that brain hubs display a tight coordination of gene expression, often over long anatomical distances, that is intimately related to the metabolic requirements of these highly active network elements.

Keywords: complex networks; connectome; hub; metabolism; rich club.

Fig. 1.

Mapping the transcriptional signature of large-scale brain network topology. (A) Defining highly connected hub regions with connectivity degree $k>44$, all neuronal connections between each of 213 brain regions were labeled as rich (hub $\to$ hub; red), feeder (hub $\to$ nonhub or nonhub $\to$ hub; green), or peripheral (nonhub $\to$ nonhub; blue). (B) Network schematic illustrating the different connection types in the mouse brain. (C) Normalized expression levels of 17,642 genes (columns) measured in each brain region (rows) visualized here using color from low (blue) to high (red) are used to compute the correlation in expression profiles or gene coexpression for each pair of brain regions. Missing data are shown as green, and columns of the matrix have been reordered using hierarchical clustering to place genes with correlated expression patterns close to one another.

Fig. 2.

The mouse connectome contains a costly and topologically central rich club of densely interconnected hub regions. (A) Degree distribution of the mouse connectome. (B) Normalized rich club coefficient, ${\text{Φ}}_{\text{norm}}$ (red), and mean connection distance, d, of hub–hub links (purple) as a function of the degree, k, at which hubs (regions with degree $>k$) are defined. Red circles indicate values of ${\mathrm{\Phi }}_{\text{norm}}$ that are significantly higher than an ensemble of 10,000 null networks (permutation test; $P<0.05$); purple circles indicate where the mean connection distance of hub–hub links is significantly increased relative to all other network links (one-sided Welch’s t test; $P<0.05$). The topological rich regime ($42\le k\le 54$) is shaded gray.

Fig. S1.

Hub connectivity is topologically central and costly. Each plot shows the variation of a network property as a function of the number of connections (or degree k) at which hubs (regions with degree $>k$) are defined. A, Upper, C, Upper, and E, Upper show the degree distribution of the mouse connectome for ease of comparison with each plot. (A) Normalized rich club coefficient, ${\mathrm{\Phi }}_{\text{norm}}$, as in Fig. 2B reproduced here for ease of comparison. Circles indicate values of ${\mathrm{\Phi }}_{\text{norm}}$ that are statistically higher than an ensemble of 10,000 null networks (permutation test; $P<0.05$). The topological rich regime ($42\le k\le 54$) is shaded gray in all figures. (B) The proportion of brain regions with degree $>k$ in each of 13 broad anatomical divisions from the Allen Mouse Brain Atlas (24, 26) as a function of k. (C–F) The remaining plots summarize other mean properties of links connecting regions with degree $>k$, with circles indicating statistically significant increases relative to values assigned to all other network links (Welch’s t test; $P<0.05$): (C) connection distance (millimeters), (D) reciprocal connectivity, (E) ${\log }_{10}$ connectivity weight, and (F) communicability (line) (47) and edge betweenness centrality (dashed line) (46). Each of these properties increases with k and is elevated across the topological rich club regime, indicating a high centrality and cost of connections between hub regions.

Fig. S2.

Probability that (A) a connection exists, $p\left(d\right)$, and (B) an existing connection has a reciprocal match, $p_r\left(d\right)$, estimated in 25 equiprobable bins as a function of the separation distance, d, for all connected pairs of brain regions. The mean of each bin is shown with a circle, and its extent is shown with a horizontal line. Exponential fits are plotted as dotted lines and labeled.

Fig. S3.

Relationship between gene coexpression, connectivity, and separation distance in the mouse connectome. All pairs of brain regions i and j (excluding self-connections, $i\ne j$) were classed as (i) reciprocally connected pairs of brain regions if both $i\to j$ and $j\to i$ (orange), (ii) unidirectionally connected pairs of brain regions if either $i\to j$ or $j\to i$ (but not both; green), or (iii) unconnected pairs if neither connection is present (blue). (A) Distributions of gene coexpression for each of the above types of interregion pairs. (B) Gene coexpression, $G_{ij}$, as a function of Euclidean distance of separation, $d_{ij}$, for all interregion pairs, with a fitted exponential decay as labeled. (C) Distributions of gene coexpression for all classes of interregion pairs after correcting for the exponential distance relationship shown in B. Both before and after correcting for spatial correlation in the data, pairs of reciprocally connected brain regions have the highest gene coexpression followed by unidirectionally connected brain regions and unconnected brain regions; P values from Welch’s t tests are annotated to A and C.

Fig. 3.

Gene coexpression is elevated for connections involving brain network hubs. (A) Connectogram showing (spatially corrected) gene coexpression values across the mouse connectome. All neuronal connections (lines) between brain regions (circles) are colored according to the gene coexpression of the regions that they connect. Brain regions are organized by anatomical division and sorted by degree (shown as bars), with bars colored bright red for hubs ($k>44$). A larger version of this connectogram with all regions labeled is in Fig. S4. (B, Top) Degree distribution. (B, Middle) Proportion of links classified as rich, feeder, and peripheral, where hub nodes have degree $>k$. (B, Bottom) Mean (spatially corrected) gene coexpression for rich, feeder, and peripheral connections as a function of k, with the mean across all network links shown as a dashed black line and the topological rich club regime shaded. Circles indicate a statistically significant increase in gene coexpression in a given link type relative to the rest of the network (one-sided Welch’s t test; $P<0.05$).

Fig. S4.

A larger version of Fig. 3A with all regions labeled. All neuronal connections (lines) between brain regions (circles) are colored according to the gene coexpression of the regions that they connect. Brain regions are organized by anatomical division and sorted by degree (shown as bars), with bars colored bright red for hubs ($k>44$). Abbreviations of brain regions are from the Allen Mouse Brain Atlas (26).

Fig. S5.

Rich club organization and gene coexpression results are robust to the significance threshold used to retain connectome links. In our primary analyses, we retained connectome links with $P<0.05$ in the computational model of the mouse connectome (24), producing a link density of 6.9%. Here, the data are reanalyzed using the more lenient threshold of $P<0.5$, yielding a connectome with a link density of 12.9%. (A) Degree distribution. (B) Normalized rich club coefficient, ${\mathrm{\Phi }}_{\text{norm}}\left(k\right)$, computed relative to 10,000 randomized null networks. The topological rich regime from the point where ${\mathrm{\Phi }}_{\text{norm}}$ increases sharply (at $k=78$) to $k=110$ is shaded. (C) Proportion of each link type (rich, feeder, and peripheral) as a function of k. (D) Mean gene coexpression in each link type as a function of k, with statistically significant enrichment over other types of links indicated with circles (Welch’s t test; $P<0.05$) and an analogous topological rich club regime for this network shaded gray. The same qualitative results are reproduced with this denser connectome, including the coexpression increase for rich and feeder links across the topological rich club regime. The increase in gene coexpression for peripheral links at very low k is not meaningful for the hub connectivity analyzed here (at this k, 85% of nodes are labeled as hub, and less than 1% of links are labeled as peripheral). Qualitatively similar rich club curves and gene coexpression patterns were also found at link thresholds $P<0.25$ (link density, 9.7%) and $P<0.75$ (link density, 17.2%).

Fig. S6.

The relationship between gene coexpression and hub connectivity is robust to different processing methods. A and C are the same as in Fig. 3B but with different corrections applied. (A) When spatial correlations in gene coexpression values are not corrected for, gene coexpression remains increased for rich connections in the topological rich regime but does not remain increased for feeder links. (B) An alternative to the global spatial correction for gene coexpression values applied here is to correct the effect in each division separately. Exponential fits, $r_g\left(d\right)=\exp \left(-\text{η}d\right)$, are shown (where links $i\to j$ are labeled as division i), with every pair of regions shown as a point in the plot colored by their division (using the same color labels as in Fig. S1B). (C) Applying this division-based spatial correction shown in B yields similar results to that of the global spatial correction.

Fig. S7.

Mean gene coexpression in rich, feeder, and peripheral links for the five GO-annotated biological process categories showing a significant increase in gene coexpression for connections involving hubs computed as the mean GCC value (Table 1). Gene coexpression curves are highly consistent across these GO categories, despite containing different sets of genes. (A) Mean GCC score computed across genes in each category (labeled in the legend) for rich, feeder, and peripheral links as a function of the degree, k, at which hubs are defined (degree $>k$). (B) Table showing the membership of 70 unique genes (rows) annotated to five GO categories (columns); membership is indicated in black. The citrate metabolic process and tricarboxylic acid cycle categories contain many similar genes, which are completely different from the genes annotated to the other categories. The category energy-coupled proton transmembrane transport against electrochemical gradient contains the same annotations as the ATP hydrolysis-coupled proton transport category, and all genes annotated to these categories are also annotated to hydrogen ion transmembrane transport, which includes 26 additional genes.

Fig. 4.

Transcriptional coupling of metabolic genes is selectively increased for connections involving hubs. Mean GCC scores across 70 unique genes implicated in the transcriptional signature of hub connectivity (Table 1) in rich, feeder, and peripheral links as a function of the degree k at which hubs are defined. Circles indicate a significant enrichment in a given link type over all other links (one-sided Welch’s t test; $P<0.05$). There is a strikingly specific increase in the coexpression of these genes for rich connections in the topological rich club regime (shaded gray).

Fig. S8.

Interregional gene coexpression and regional gene expression of 20 exemplary metabolic genes related to hub connectivity. The 20 genes plotted here (of 70 unique genes annotated to the processes listed in Table 1) are those with the greatest increases in coexpression in rich and feeder connections relative to peripheral connections. Of the 70 genes annotated to these biological processes, 64 (or 91%) show increased expression in hubs over nonhubs [of which 12 are significantly increased: $P<0.05$; false discovery rate (FDR) -corrected across 70 genes; one-sided Welch’s t test; none showed significant decreases], and 57 (or 81%) show increased GCC scores in rich links over peripheral links (of which 46 are significantly increased: $P<0.05$; FDR-corrected; one-sided Welch’s t test). (A) Distributions (mean $\pm$ SD) of coexpression values for each individual gene across rich (red), feeder (green), and peripheral (blue) connections. (B) Distribution of normalized regional gene expression for hubs (orange) and nonhubs (blue). Genes related to citrate metabolism are shown italicized and underlined to distinguish them from genes related to proton transport. (C) Distributions of mean gene expression in nonhub regions and hub regions across all 70 genes. Mean gene expression is significantly increased in hubs (orange) over nonhubs (blue; $P=0.028$; Welch’s t test).

Fig. S9.

The association between topological connection type and mean GCC scores is robust to changes in significance threshold and gene annotation sets. Plots are the same as in Fig. 4, but use (A and B) all 112 genes annotated to 12 biological process GO categories showing increased gene coexpression in rich and feeder links over peripheral links at a false discovery rate (FDR) of 0.1 (Table S5) or (C and D) all 335 genes annotated to 25 biological process and cellular component categories showing increased gene coexpression in rich and feeder links over peripheral links at an FDR of 0.05 (Table S4).