Gene networks show associations with seed region connectivity

Abstract

Primary patterns in adult brain connectivity are established during development by coordinated networks of transiently expressed genes; however, neural networks remain malleable throughout life. The present study hypothesizes that structural connectivity from key seed regions may induce effects on their connected targets, which are reflected in gene expression at those targeted regions. To test this hypothesis, analyses were performed on data from two brains from the Allen Human Brain Atlas, for which both gene expression and DW‐MRI were available. Structural connectivity was estimated from the DW‐MRI data and an approach motivated by network topology, that is, weighted gene coexpression network analysis (WGCNA), was used to cluster genes with similar patterns of expression across the brain. Group exponential lasso models were then used to predict gene cluster expression summaries as a function of seed region structural connectivity patterns. In several gene clusters, brain regions located in the brain stem, diencephalon, and hippocampal formation were identified that have significant predictive power for these expression summaries. These connectivity‐associated clusters are enriched in genes associated with synaptic signaling and brain plasticity. Furthermore, using seed region based connectivity provides a novel perspective in understanding relationships between gene expression and connectivity. Hum Brain Mapp 38:3126–3140, 2017. © 2017 Wiley Periodicals, Inc.

INTRODUCTION

In the mature human brain, trillions of synapses connect the axons and dendrites of billions of neurons. These dense, functionally specialized local assemblies are concentrated at neural network hubs and enable communication through long‐range fiber bundles. Throughout the lifetime of an organism, activity coursing through neural circuits modulates gene expression, which in turn activates the microscopic processes responsible for the reorganization of neural connectivity [Hübener and Bonhoeffer, 2014]. Dynamic patterns of gene expression alter the molecular milieu within and between brain cells throughout life, and the effects of changes in gene expression propagate between intra‐cellular, inter‐cellular, and larger scales by cell signaling within neural networks [Goldman and Kennedy, 2011]. Activity‐dependent reorganization of neural connectivity is thought to underlie the formation, reconsolidation, and dissolution of behavioral memories [Kandel et al., 2014, Zovkic et al., 2013]. Furthermore, altered plasticity is a key feature of pathophysiology across a variety of neurological disorders and may serve as a common substrate for intervention [Nithianantharajah and Hannan, 2006]. Therefore, it is of great interest to understand how gene expression patterns across the brain are related to neural connectivity.

Early steps toward understanding connectomics in the context of genomics utilized simple organisms and reduced assays to identify genes involved in the regulation of neural connectivity [Burne et al., 2011]. Some of the first network‐based approaches to link genetics with connectomics used the worm Caenorhabditis elegans (C. elegans), the only species whose nervous system has been mapped entirely at a cellular level [White et al., 1986]. Several studies have combined expression data with single‐neuronal level information [Baruch et al., 2008; Kaufman et al., 2006; Varadan et al., 2006]. These studies have shown that connections can be well‐predicted by gene expression and have demonstrated the network nature of these relationships.

Similar results were obtained for rodent brains indicating that large gene networks are relatable to connectivity even in more complex nervous systems [Fakhry and Ji, 2015; French and Pavlidis, 2011; Ji et al., 2014; Wolf et al., 2011]. Using data from the Allen Mouse Brain Atlas [Oh et al., 2014], high correlations in gene expression between brain regions were recently found to be associated with highly connected regions [Fulcher and Fornito, 2016].

Advances in human neuroimaging [Zatorre et al., 2012], and analyses that consider network architecture in the human brain, have begun to provide key insights into the neurobiology of brain assemblies in both the healthy and diseased brain [Iturria‐Medina et al., 2014; Sporns, 2011]. Furthermore, the availability of new, high‐dimensional data collections such as those made available by the Allen Institute for Brain Science (http://alleninstitute.org/), are facilitating investigations in humans. This Institute has meticulously constructed a unique atlas using diffusion weighted magnetic resonance imaging (DW‐MRI) and microarray gene expression profiling in the human brain [Hawrylycz et al., 2012; Jones et al., 2009; http://human.brain-map.org). Analyzing two brains, the institute obtained comprehensive gene expression measures for most known human genes at a large set of anatomically referenced locations that can be aligned to the DW‐MRI data from the same brains.

The complexity of gene expression dynamics across the human brain makes it challenging to obtain a mechanistic understanding of its relationships with brain connectivity [Kotaleski and Blackwell, 2010; Lee et al., 2014]. This complexity, however, can be reduced through the concept of network modularity. A modular network is composed of small groups of nodes that are densely interconnected within‐group and sparsely connected between‐group. Indeed, there is substantial evidence of modularity in biological networks spanning microscopic to macroscopic scales, including protein‐protein interactions, gene regulatory networks, and brain structural networks [Barabasi and Oltvai, 2004; Bassett and Bullmore, 2009; Wagner et al., 2007]. Analyses that exploit the expectation of modular networks can simplify the interpretation of results. One such example is the Weighted Gene Co‐expression Network Analysis (WGCNA) [Spiers et al., 2015; Xue et al., 2014; Zhang and Horvath, 2005]. This method applies hierarchical clustering to a Topological Overlap Matrix (TOM), where “overlap” refers to the strength of the relationship between two genes measured via direct or indirect routes. Biological networks are also often assumed to follow a scale‐free behavior; that is, the distribution of the degree of connectivity of the nodes in the network follows a power law. This implies that there are likely to be a small number of “hub” nodes with a very large number of connections, and that the proportion of nodes with $k$ connections, $P\left(k\right)$, decreases as a power of $1/k$ (following $P\left(k\right)\sim k^{-\gamma }$ for a parameter $\gamma$). The use of the TOM transformation makes it possible to interpret the resulting clusters as network modules that possess the scale‐free property. In post‐mortem human brain tissue, analysis of gene expression data with WGCNA—reducing complexity through encouraging scale‐free network behavior of the gene expression relationships—has already been key to demonstrating alterations in patterns of gene expression associated with Alzheimer's disease [Sekar et al., 2015], bipolar disorder [Akula et al., 2016], and altered methylation patterns indicating neuronal differentiation in schizophrenia [Maschietto et al., 2015].

This study investigates the relationships between topologically inspired gene expression networks and DW‐MRI functional connectivity strengths, across brain regions, using data from two adult human post‐mortem brains from the Allen Human Brain Atlas. Specifically, the hypothesis investigated is that connectivity at some of the seed regions induces important effects on their connected targets, and that these effects are reflected in gene expression. Although several other groups have analyzed similar data to investigate connectivity‐expression relationships [Goel et al. 2014; Hawrylycz et al., 2015; Oldham et al., 2008; Richiardi et al., 2015], they have not analyzed seed region connectivity. The present analysis will provide a novel perspective on the relationship between gene expression and connectivity in the brain.

MATERIALS AND METHODS

Data

The Allen Human Brain Atlas [Hawrylycz et al., 2012; http://human.brain-map.org) is one of the projects hosted at the Allen Institute for Brain Science (http://alleninstitute.org). Gene expression data was derived from two post‐mortem, ex‐vivo, neurotypical male brains aged 39 and 24. DW‐MRI was performed in cranio, immediately following death, and at site of death for both brains. Neural connectivity data were obtained by T1‐weighted MPRAGE and DW‐MRI, acquired using a 3T Siemens Magnetom Trio scanner. T1 images were acquired with 1 mm isotropic voxels, three‐dimensional acquisition, three averages, TI = 900 ms, TR = 1,900 ms, TE = 2.63 ms, 9° flip angle, and image matrix = 256 × 192 × 256. DW‐MRI images were taken in 64 directions using an Echo Planar Imaging sequence, with 2 mm axial slices, 1.875 × 1.875 mm² in plane voxels, TR = 9,300 ms, TE = 94 ms, 90° flip angle, and image matrix = 128 × 128 × 68. Connectivity patterns estimated in the data from the Allen Human Brain Atlas were compared with a template connectivity matrix to examine the stability of connectivity patterns. The template connectivity matrix was created from 72 healthy subjects using the intravoxel fiber Orientational Distribution Functions (ODFs) of Turboprop DW‐MRI from the artifact‐free HARDI Illinois Institute of Technology (IIT) Human Brain Atlas (v.3) [Varentsova et al., 2014]. Final voxel dimensions of the template in the MNI152 stereotaxic space were 1 × 1 × 1 mm³.

Comprehensive measurement of gene transcriptional activity (gene expression), across most known human genes, can be obtained with many different experimental techniques and provide a snapshot of which genes are being actively transcribed in the sampled tissue. Here, gene expression profiling was performed using a custom‐designed Agilent microarray chip containing 60,000 probes for each sample, capturing 20,783 genes; 893 regions were sampled from brain 1 (H0351.2002) and 946 samples regions from brain 2 (H0351.2001). Data were normalized both within and between brains by the Allen Institute for Brain Science [see the technical white paper Microarray Data Normalization (March 2013) http://human.brain-map.org.

Validation of gene clusters obtained from H0351.2002 and H0351.2001 was performed by comparing results to gene expression data from four additional human brains also available from the Allen Human Brain Atlas. These brains from three male donors (age 31, 55, and 57 years old) and one female donor (aged 49) were measured for gene expression using the same microarray platform and passed the same quality control steps. However, the roughly 500 samples per brain were taken from only one hemisphere, and no DW‐MRI data were available.

Estimation of Inter‐Region Connectivity

First, each subject's T1 image was normalized to the MNI space (using SPM12 toolbox, http://www.fil.ion.ucl.ac.uk/spm/software/spm12/). Inverse normalization parameters were then applied to the template parcellation scheme [AAL atlas, see Tzourio‐Mazoyer et al., 2002]. After resampling to each individual's native space, we used an in‐house program to obtain the external/surface voxels of each brain region. Estimates of probabilistic anatomical connectivity values between each brain voxel and the surface of each gray matter region (voxel‐region connectivity from the previous calculations), using the DW‐MRI data and a fully automated fiber tractography algorithm [Iturria‐Medina et al., 2007], were obtained with tracking parameters of maximum trace length = 500 mm and curvature threshold = ±90°. Intravoxel white matter ODF maps were estimated using the Q‐ball approach [Tuch, 2004]. Based on the resulting voxel‐region connectivity maps, the anatomical connection density (ACD) between any pairs of regions i and j (ACD_ij ≡ ACD_ji) was calculated. The ACD measure [Iturria‐Medina et al., 2007, 2008] reflects the degree of evidence supporting the existence of each white matter connection, after controlling for region size. It is estimated by counting the “effective” number of voxels over the surface of both regions and weighting each voxel by its voxel‐region connectivity value with the connected region, relative to the total number of considered superficial voxels (see Fig. 1).

Figure 1.

The anatomical connection density. The ACD measure (Iturria‐Medina et al., 2007, 2008) reflects the degree of evidence supporting the existence of each white matter connection, after controlling for region size. It is estimated by counting the effective number of voxels over the surface of both regions and weighting each voxel by its voxel‐region connectivity value with the opposite zone, relative to the total number of considered superficial voxels.

It was not possible to estimate connectivity information for all of the 893 regions in brain 1 or the 946 regions in brain 2. Analyses were restricted to the 720 regions in brain 1 and 730 regions in brain 2 where both gene expression and connectivity data were obtained. Therefore, matrices (720 × 720, 730 × 730) of ACD measures were obtained for each of the two subjects from the Allen Human Brain Atlas. Elements of these matrices measure connection density between seed regions, located on the diagonal of the matrix, and the other brain regions.

Filtering of Probe and Gene Expression Data

A series of steps was taken to reduce the dimensionality of the gene profile data and to retain only a single probe per gene for analysis. Probes with no Entrez ID were discarded from analysis. When two probes were available for a gene, the most variable one was retained, as this probe presumably captures more transcriptional sensitivity. If more than two probes were available, the probe most correlated with the others, as per the collapseRows function in the WGCNA R package [Miller et al., 2011], was retained. This choice is expected to best represent the general pattern of expression of the gene. The number of genes for analysis was then reduced by excluding half the genes with lowest variability in both brains (see Supporting Information Text). It is well known that only a fraction of the genes is expressed in any particular cell type [Darmanis et al., 2015], and that the inclusion of non‐informative elements can compromise effective clustering [Tritchler et al. 2009]. After this triaging process, gene expression profiles for a total of $n=$10,395 genes at $b$ brain regions were used in the analyses; we denote such matrices by $G_{n\times b}=\left\{g_{i,j}\right\}$ (see Table 1 for key notation).

Table 1.

Notation

Notation	Description
$\mathit{n}$ = 10,395	Number of genes analyzed
$\mathit{b}$	Number of brain regions analyzed. $b=720$ for brain 1 and $b$ =730 for brain 2 in the full analysis.
${\mathit{G}}_{\mathit{n}\times \mathit{b},\mathit{k}}=\left\{{\mathit{g}}_{\mathit{i},\mathit{j},\mathit{k}}\right\}, \mathit{i}=1,\dots ,\mathit{n}; \mathit{j}=1,\dots ,\mathit{b};$ k = 1,2	Gene expression matrix; $g_{i,j}$ is the expression of gene $i$ in brain region $j$ for brain k.
${\mathit{E}}_{1\mathit{k}}, {\mathit{E}}_{2\mathit{k}},\dots , {\mathit{E}}_{11\mathit{k}}$	Eigengenes from the WGCNA clustering of gene expression, $\mathit{G}$ using the full set of regions, ( $b=720 \mathrm{o}\mathrm{r} 730)$, for brain $k=\mathrm{1,2}$.
${\mathit{C}}_1, {\mathit{C}}_2,\dots {\mathit{C}}_{18}$	From the full approach, 18 anatomical indices were used to group sampled regions into categories. These are consensus clusters defined in common for both brains.

Clustering Gene Expression Profiles

Following the WGCNA approach [Langfelder and Horvath, 2008; Zhang and Horvath, 2005], a weighted network of gene expression was constructed. Let $g_j$ denote the vector of expression for gene j across the brain regions. First, signed Pearson correlations were constructed between all pairs of genes, $(g_j, g_{j^{\text{'}}})$, thereby obtaining a symmetric matrix of dimension (10,395 × 10,395) that is location‐scale invariant. Secondly, to accentuate the differences between strongly correlated and weakly correlated pairs of genes, the elements of this matrix were raised to the power 16 (soft‐thresholding); this number was empirically‐determined on our data according to the scale‐free criterion recommended by Zhang and Horvath [2005]. Thirdly, this transformed matrix was converted to a topological overlap matrix (TOM) [Ravasz et al., 2002], whose elements measure the strength of the network connections between pairs of genes within the network. The TOM transformation is the most crucial step in these calculations, since it changes a matrix of pairwise similarities into a matrix that reflects global properties of a network. Finally, average linkage hierarchical clustering with dynamic cutting [Langfelder and Horvath, 2008] was applied to the dissimilarity matrix (1 – TOM) to cluster the genes. Zhang and Horvath [2005] motivated the choice of the power transformation and the definition of the TOM for gene expression data by considerations of biological network topologies [Barabasi and Oltvai, 2004; Ravasz et al., 2002]. See Supporting Information for additional details.

Since these analyses are based on two brains, a consensus network applicable to both brains was estimated, following the WGCNA definition of consensus. That is, the strength of connection between two genes in the consensus network is the lower of the weights in the two individual TOMs, such that two genes in the consensus network are as connected as the lesser of the two individual network connections [Langfelder and Horvath, 2007].

Dominant patterns of expression within each consensus gene cluster are then summarized by the “eigengene,” $E_{ik}$ for cluster $i$, brain $k$. The eigengene is defined as the first principal component of the standardized gene expression matrix of the cluster (i.e., the first singular vector of this matrix), and is the linear combination of expression of the genes in the cluster that explains the most variance. Note that the eigengenes were separately calculated for each brain for the sets of genes in the consensus clusters. Although co‐regulated clusters of gene expression have been shown to be reproducible [e.g., Lee et al., 2004], individual levels of expression can be quite variable across brains [e.g., Lee et al., 2002]. Therefore, $E_{i1}$ and $E_{i2}$ denote the first principal components of the submatrices $G_1^{\left(C_i\right)}, G_2^{\left(C_i\right)}$, which contain gene expression data for genes in consensus cluster $C_i$ in brains 1 and 2, respectively. For simplicity, subscripts indicating brain 1 or 2 are typically suppressed.

To study gene expression cluster stability, network preservation statistics were calculated as implemented in the WGCNA software package (modulePreservation function [Langfelder et al., 2011]). A comparison was made between the gene expression consensus networks obtained from the original two brains and the consensus network based on the gene expression profiles of the four additional brains with only left hemisphere data. A density measure derived from within‐node transformed correlations was utilized, as well as two connectivity measures that look at connections between nodes. Permutation analysis shuffling module labels was used to estimate whether clusters were similar between the original two brains and the additional brains (see Supporting Information Text).

Analysis of Relationships Between Gene Expression and Connectivity

Pearson correlations between each connectivity vector (measuring the strength of the connectivity between seed region $j$ and all other brain regions) and each eigengene or $E_i$ (summarizing the expression of genes in consensus cluster $i$ for each brain region) were calculated for each brain. This enabled identification of gene clusters that correlate strongly with the pattern of connectivity linked to a specific seed region.

Then, group exponential lasso regression models [Breheny, 2015] were fitted to predict eigengene expression as a function of the connectivity vectors. This model requires externally defined groups; and therefore, the seed region connectivity vectors were grouped based on anatomical indexing of the brain regions. These groups were chosen based on the Allen Human Brain Atlas ontology for the hierarchy of brain structures, with the goal of obtaining a similar number of sampled brain regions within each group and a reasonable number of groups. The group exponential lasso model includes two levels of penalization to reduce both the number of groups and the number of elements within groups. Hence, this model selects not only anatomical brain regions that are associated with gene expression patterns, but also the most relevant seed region vectors within the anatomical structure. The fitting process calibrates the penalization such that more important groups receive less internal penalization.

Both the predominant cell types and the amount of brain activity may vary across different brain structures, leading to differences in gene expression. To protect these model fits against confounding arising from such cell type and brain activity differences, adjustment for overall trends in gene expression across all brain regions was made. Principal components were calculated from the expression patterns across 10,395 genes and all sampled brain regions. Then, linear models were fit for each brain and gene cluster, predicting the eigengene as a function of two selected principal components. The residuals from these models were then used as the response variables in the group exponential lasso models. For each gene cluster, the penalty parameter was selected by 10‐fold cross‐validation and minimization of the cross‐validated error. Statistical significance of the final model for each gene cluster was estimated through permutation of the residuals and repeated fits of the group exponential lasso models; that is, the P‐value for each gene cluster was estimated by the proportion of 1,000 permutations that generated a model with higher $R^2$ than the original model.

Pathway Analysis

Pathway analysis is a statistical method that assesses whether sets of genes identified through an experiment are aligned with gene sets grouped by empirical evidence accumulating in annotated public databases [Shannon et al. 2003]. Specifically, for each gene cluster investigated and for a series of known pathways and all the genes therein, pathway analysis assesses whether more elements of the pathway are included in the cluster in question than would be expected by chance sampling. There has been rapid improvement in software packages interacting with databases of gene functions [Bindea et al., 2009; Saito et al., 2012; Shannon et al., 2003]. Cytoscape [Saito et al., 2012; Shannon et al., 2003] with Cluego + Cluepedia packages [Bindea et al., 2013] was used to query public resources including KEGG, Reactome, GO molecular function, and GO biological function databases. Pathway analysis was performed separately on each cluster of genes identified by WGCNA, and was repeated twice, once using only the set of 10,395 genes included in our gene clustering, and a second time using all genes. Pathway interpretation was primarily focused on clusters that demonstrated associations with connectivity.

RESULTS

The regions sampled within the Allen Human Brain Institute were not exactly equivalent between the two brains with both structural connectivity and gene expression data. Therefore, an approach for alignment was necessary in order to make the results comparable across the two brains. Two different strategies were employed in this regard. Firstly, a physical grouping of the sampled brain regions into 117 larger aligned regions was implemented prior to analysis using the automatic anatomical labeling (ALL) brain parcellation scheme [Tzourio‐Mazoyer et al., 2002] with the addition of the brain stem (Supporting Information Table S1A). This strategy is referred to the reduced approach, and the results of these analyses are largely found in the Supporting Information Text. Subsequently, a model‐based grouping of the estimated associations between expression and structural connectivity was performed, incorporating anatomical brain region labels to achieve comparability across brains. Eighteen anatomically defined sub‐regions were selected; Supporting Information Table S1B shows how many sampled brain regions fall into each of the sub‐regions.

Clustering of Gene Expression Data

Through the use of WGCNA, clusters of genes were identified where the correlations in gene expression display network properties. This strategy reduced the dimensionality of the gene expression data to 10 consensus gene clusters and their profiles across 700 regions from each brain. Table 2 shows the number of genes assigned to each cluster and assigns a color label to each. The names of all genes assigned to each cluster and the correlations of each gene with its respective cluster eigengene can be found in Supporting Information Table S2.

Table 2.

Description of the gene clusters obtained from WGCNA consensus cluster building

Cluster	# Genes		# Genes enriched in neurons		# Genes enriched in oligodendrocytes		# Genes enriched in astrocytes
Coral	938	9.02%	59	24.89%	2	2.2%	9	7.20%
Cyan	2,109	20.29%	14	5.91%	65	72.22%	48	38.40%
Lavender	430	4.14%	0	0.00%	2	2.22%	2	1.60%
Navy	583	5.61%	3	1.27%	0	0.00%	1	0.80%
Orange	1,280	12.31%	89	37.55%	4	4.44%	24	19.20%
Orchid	517	4.97%	4	1.69%	3	3.33%	8	6.40%
Plum	524	5.04%	33	13.92%	1	1.11%	2	1.60%
Seagreen	969	9.32%	12	5.06%	2	2.22%	9	7.20%
Sienna	1,297	12.48%	16	6.75%	8	8.88%	15	12.00%
Steelblue	1,406	13.53%	6	2.53%	3	3.33%	5	4.00%
Gray	342	3.29%	1	0.42%	0	0.00%	2	1.60%
Total	10,395	100%	237	100%	90	100%	125	100%

The number and percentage of genes found in each cluster are shown in the second column. The three last columns represent the number and proportion of genes found in each cluster known to be enriched in neuron, oligodendrocyte and astrocyte cells (Tan et al., 2013). It should be noted that the gray cluster contains genes that did not get assigned to any other cluster.

To verify whether the gene expression clusters obtained with WGCNA are stable and reproducible, density and connectivity module preservation statistics [Langfelder et al., 2011] for the consensus network from the two brains were compared with the consensus network from the four additional brains without DW‐MRI data. Most clusters (9 of 10) showed good cluster preservation; only the lavender cluster did not have good preservation properties (Fig. 2). Many of the genes assigned to this poorly‐preserved cluster are likely to have low or transient levels of expression, such as genes associated with perception of stimuli, hence clusters may be inconsistent across brains (Supporting Information Table S2).

Figure 2.

Validation of the gene clusters. Cluster validation compared network properties of the consensus reference network (based on the gene expression measures of the two brains) to the consensus test network (based on the four additional brains where no DW‐MRI data were available). The Z summary score combines two other scores to summarize the stability of each cluster; see Supporting Information Text for details. A score higher than 10 (green dashed line) represents strong evidence of cluster preservation, and a score between 2 and 10 (blue and green dashed lines) represents low to moderate evidence of preservation.

The heatmaps in Figure 3A (brain 1) and B (brain 2) show that the eigengene intensities across brain regions in each of the gene expression clusters are quite similar in the two brains, although the patterns are somewhat noisier in brain 2 than in brain 1. A very notable aspect of Figure 3 is that many of the eigengenes (e.g., orange, cyan, and sienna) show distinct levels of expression (either very high or very low) in the brain regions situated in the cerebellum ( $C_{15}$), implying that this region is behaving very differently relative to the rest of the brain.

Figure 3.

Heatmap representations of the eigengene intensities in brain 1 (A) and brain 2 (B). In order to visualize results, the sampled brain regions were grouped by anatomical labels into 18 regions ${ (C}_1,\dots C_{18})$ (Supporting Information Table S1B).

Correlations Between Adult Gene Expression Patterns and Connectivity

Supporting Information Figure S2 displays P‐values corresponding to correlations between the eigengenes and connectivity vectors from each seed region to all other brain regions; well‐defined motifs indicate that several gene expression clusters—particularly orange, plum, orchid, and coral—are highly correlated with many of the connectivity vectors, particularly vectors with seed regions in the cerebellum( $C_{15}$) (orange and coral for brain 1), mesencephalon ( $C_{14}$) (plum and orchid for both brains), and pons ( $C_{16}$) (plum, orchid for brain 2). For these pairings, the P‐values are well below a conservative Bonferroni‐corrected threshold for multiple testing at 1%. Supporting Information Figure S3 shows that the orchid cluster displays positive statistically‐significant correlations with the connectivity clusters mentioned above, while the plum cluster displays negative statistically significant correlations with these connectivity clusters. Since a signed network was used to generate the gene clusters, this implies that coordinated coexpression of genes in the orchid module may promote or be promoted by neural connectivity, whereas an inverse relationship holds for the plum cluster.

Analyses Adjusted for Major Axes of Variation in Gene Expression

After noticing the consistent patterns in Figure 3, potential explanations were explored. A large proportion (80.2%) of all neurons in the brain are located in the cerebellum [Azevedo et al. 2009], and gene expression across the brain has been shown to depend significantly on the predominant cell types (neurons, oligodendrocytes, and astrocytes) in different regions in both adult mouse and human brains [Tan et al., 2013; Cahoy et al., 2008]. Therefore, the distribution across our clusters of genes with known cell‐type‐specific expression was examined. Tan et al. [2013] presented 519 genes with strong cell‐type specific gene expression; this list was derived from the mouse results of Cahoy et al. [2008] by keeping genes with a 10‐fold enrichment and human homologues. Among these 519 genes, 452 were included in our analyses, and Table 2 shows how these known cell‐type specific genes are partitioned across the 10 gene modules. A large proportion of genes that were identified as highly‐expressed in astrocytes are found in the cyan (38.40%), orange (19.20%), and sienna (12%) modules. In contrast, oligodendrocyte‐expressed genes are primarily found in the cyan (72.22%) module, and the genes with high expression in neurons tend to be in the orange (37.55%), coral (24.89%) and plum (13.92%) modules. Evidently, this distribution deviates markedly from a random distribution, and a Fisher's exact test shows very significant evidence for association (P < 1e‐5) between the gene clusters and the three cell types, based on a Monte–Carlo implementation of Fisher's exact test with 100,000 simulations. Hence, the primary motif captured by the WGCNA clusters is likely to be strongly related to variation in cell‐type mixtures across the brain.

Given that the differences in both eigengene intensities and neural connectivity may be associated with differences in cell types (Fig. 3) [Oldham et al. 2008; Richiardi et al., 2015], there is potential for confounding of their relationships. Figure 4A and B shows that the first (PC1) and second (PC2) principal components calculated from gene expression on all genes retained in the analyses clearly delineate the cerebellum, cortical and non‐cortical brain regions for brain 1, while PC1 and PC3 delineate the same brain regions in brain 2 (see Supporting Information Fig. S4 for PC1 vs. PC2 in brain 2). Hence, these selected two principal components (2PCs: PC1 and PC2 for brain 1 explaining 22.64% and 13.30% of variability; PC1 and PC3 for brain 2 explaining 19.52% and 7.43% of variability) were then included in subsequent analyses. In Supporting Information Figure S5C and D the correlations between the eigengenes are substantially reduced after adjusting for these 2PCs; therefore, through inclusion of these PCs, major axes of gene expression variation common across gene clusters are successfully removed.

Figure 4.

Principal component analysis of gene expression using all genes retained for analysis. The first two principal components are shown for brain 1 (A) while the first and third principal component are shown for brain 2 (B). The sampled brain regions are colored according to their location: cerebellum (red), cerebral cortex (green), vermis (purple), or other (turquoise).

Penalized regressions using the group exponential lasso model found that eigengene patterns in brain 1, (coral, lavender, navy, orange, orchid, plum, and seagreen clusters) were significantly associated (at a Bonferroni adjusted P < 0.05/20 for 10 gene clusters and 2 brains) with connectivity vectors from at least one of the anatomical index groupings (Table 3). Due to the noisier gene expression signals in brain 2, only 4 gene clusters (coral, orange, orchid, and plum) showed association with connectivity vectors. The orange and plum clusters are particularly interesting because highly statistically significant correlations with connectivity were seen in both brains (P < 1/1,000), explaining a proportion ranging between 0.0198 and 0.0658 of the eigengene variability (adjusted R ²). For the orange eigengene, the group exponential lasso model selected seed regions in the hippocampal formation and the pons for brain 1, while selecting seed regions in the mesencephalon and myelencephalon for brain 2. Here, the pathway analysis highlighted many pathways related to synaptic signaling (Supporting Information Table S3). For the plum eigengene, the group exponential model selected seed regions in the parietal and temporal lobes as associated for brain 1 and seed regions in the mesencephalon, pons, and myelencephalon for brain 2; pathway analysis of genes in the plum cluster also highlighted many pathways related to synaptic signaling and neuron development (Supporting Information Table S3).

Table 3.

Results of Group Lasso for the gene expression clusters

Gene cluster	Permuted P‐value from Brain 1	Brain 1 region groups retained in group lasso model (Adjusted $R^2$)	Permuted P‐value from Brain 2	Brain 2 region groups retained in group lasso model (Adjusted $R^2$)
Coral	0.041	Parietal lobe, diencephalon (0.002)	<1/1,000	Diencephalon (0.0476)
Cyan	1.00		0.058
Lavender	0.004	Frontal lobe, hippocampal formation (0.0168)	1.00
Navy	<1/1,000	Frontal lobe, hippocampal formation (0.0541)	1.00
Orange	<1/1,000	Hippocampal formation, pons (0.0658)	<1/1,000	Mesencephalon, myelencephalon (0.033)
Orchid	<1/1,000	Diencephalon, mesencephalon, myelencephalon (0.0332)	0.010	Diencephalon (0.00442)
Plum	<1/1,000	Parietal lobe, temporal lobe (0.0437)	<1/1,000	Mesencephalon, pons, myelencephalon (0.0198)
Seagreen	0.001	Basal ganglia, amygdala, mesencephalon (0.0119)	1.00
Sienna	1.00		1.00
Steelblue	0.033	Pons (0.00332)	1.00

Permutation P‐values are reported for all clusters, without adjustment for multiple testing. When this permutation P‐value is less than 0.05 the connectivity groups retained in the group lasso model are shown, together with the adjusted $R^2$. A Bonferroni correction for examination of 10 gene clusters in two brains would require significance at 0.0025.

In brain 1 only, regions seeded in the frontal lobe and in the hippocampal formation were selected as predictive of the navy eigengene (adjusted R ² = 0.054). Many genes in the navy cluster are associated with chromatin modeling and may, therefore, be associated with large differences in cellular phenotypes (Supporting Information Table S3). In brain 2, the model with the highest R ², that is, where seed region connectivity was most predictive of gene expression patterns, was the coral eigengene and seed regions of the diencephalon (R ² = 0.0476); axon guidance was the top term in the pathway analysis of the coral gene cluster. (In brain 1, adjusted R ² was only 0.002 for the coral eigengene). The orchid gene model also showed interesting results, where seed region connectivity vectors from the diencephalon, mesencephalon, and myelencephalon explained 0.0332 of the variance in brain 1 (the diencephalon seed regions explained 0.0044 of the variance in brain 2). Pathway analysis of the orchid module highlights pathways related to nerve and embryonic development.

DISCUSSION

Earlier analyses linking connectivity and gene expression modules in mammals compared data from two different species: brain connectivity profiles from the rat, and gene expression patterns from the mouse [French and Pavlidis, 2011; Wolf et al., 2011]. Since then, the availability of data from the Allen Brain Institute has made studies in the same species, including human, much more accessible. This work and other more recent publications have been able to benefit from this resource.

The objective of this research was to examine the relationships between the variation in gene expression across regions in the brain and the patterns of neuronal connectivity emanating from or attracted to the same regions. The hypothesis was that relationships between gene expression and structural connectivity patterns starting from seed regions could identify molecular networks important for modulating adult brain connectivity. Using a network‐motivated approach, this work did identify several gene clusters expressed in the adult human brain that vary significantly with seed‐region‐based adult neural connectivity.

It is common to discard a large proportion of genes when analyzing microarray gene expression data [Cioli et al., 2014; Tan et al., 2013], thereby attaining more reliable results. There are several reasons for this: first, it is known that only a fraction of all genes is expressed in any particular cell type. For example, gene expression measurements in a series of single neurons from the temporal lobe have shown that at most 12,000 genes—about half of known transcripts—were expressed in 10% or more of neurons [Darmanis et al., 2015]. Even smaller numbers of genes were reliably detected in higher proportions of the cells. Hence, less than half of all genes are expressed in most neurons, as expected. Secondly, keeping unimportant genes (genes that show little variation) in cluster analysis can introduce bias in the results, even when these genes are discarded after the analysis [Tritchler et al., 2009]. However, Richiardi et al. [2015] and Fulcher and Fornito [2016] started their analysis using all genes, as did Goel et al. [2014], although they reduced the dimensionality of the expression data to five components obtained from a singular value decomposition. Although Hawrylycz et al. [2015] used the 50% of the genes that showed the most stability across brains to build their gene clusters, they then assigned all remaining genes to a cluster by examining the correlations of their expression profiles with the cluster eigengenes. In the present study, Supporting Information Figure S1 shows that the general patterns resulting from clustering of gene expression were little affected by changing the threshold from the most variable 50% of the genes to 40% or 60%. To further assess the sensitivity of our results to our choice of threshold, cluster assignments were compared between WGCNA using all genes versus 50% of the genes (Supporting Information Fig. S8). Although each of the original clusters was augmented by a large set of genes that had been discarded in our primary analysis, there was strong agreement in cluster assignments. Therefore, these WGCNA‐derived results are robust to alterations in the filtering threshold.

After selecting genes for analysis, the next step was to cluster the gene expression profiles across the brain through construction of a matrix of gene‐gene similarity of size $G$ by $G$ (for $G$ genes), followed by use of the TOM matrix to cluster genes. Goyal and Raichle [2013] and Hawrylycz et al. [2015] also used WGCNA‐motivated gene clustering. Despite many different analytic choices, there are similarities between Figure 3 and the figure in Hawrylycz et al. [2015] that shows eigengene results for WGCNA gene clusters based on six brains (their Fig. 4a). For example, our sienna cluster with large positive eigengene values in $C_{15}$ corresponds to their M17 and M22 clusters which also highlight the cerebellum.

However, others who also analyzed Allen Brain Institute gene expression data constructed correlations between $b$ brain regions across genes, thereby creating similarity matrices of size $b$ by $b$ [Fulcher and Fornito, 2016; Ji et al., 2014 (two studies of mouse transcriptome); Goel et al., 2014; Richiardi et al., 2015]. Earlier, French and Pavlidis [2011] had also constructed matrices of size $b$ by $b$ to look at agreement between a brain connectivity matrix from rat and a matrix of correlations of gene expression from mouse. This fundamental difference leads to different downstream analyses: studying correlations in gene expression between brain regions allows examination of spatial variation across the brain, whereas the approach used here enabled us to find variability between clusters of genes in their relationships with structural connectivity.

There are many ways of measuring the organization or activity of the brain. In the mouse, outgoing and incoming connection information is available from detailed experimentation [Fakhry and Ji, 2015; Fulcher and Fornito, 2016]. Hawrylycz et al. [2015] and Richiardi et al. [2015] examined resting state fMRI data from different individuals than those for which gene expression was measured; and Krienen et al. [2016] compared fMRI data from the Allen Institute with gene expression for 19 genes known to be enriched in human supragranular layers. Conclusions drawn here about relationships with DW‐MRI data cannot be expected to be fully comparable to those based on other data types; nevertheless, it is interesting to note that of the 19 genes studied by Krienen et al. [2016], which show associations with functional networks, 6 are found in the orange gene cluster.

Like us, Goel et al. [2014] based their analysis on structural connectivity estimated from DW‐MRI data but using a different sample of 14 adults. As in the reduced approach employed in the present study, they also aggregated brain regions and averaged the gene expression samples following their own brain atlas parcellation based on the AAL brain atlas (the same one we used). Romme et al. [2016] also used DW‐MRI data to create a measure of connectivity differences between schizophrenia patients and controls, evaluated at 57 cortical brain regions. They then summarized Allen Brain gene expression data for the same brain regions, and examined correlations between the DW‐MRI‐derived measure and gene expression. In contrast to the analyses in the present work, no correction for potential confounding was implemented, and hence the identified correlations may be capturing gradients in gene expression across rostrocaudal gradients [Krienen et al., 2016]. One might speculate whether such confounding could also affect analyses of measures such as cortical thickness: strong association between cortical thickness and Allen Institute‐derived expression at gene CNR1 was recently reported [French et al., 2015].

Due to the lack of detailed whole brain connectivity information for the human brain, the present study utilized indirect measures of anatomical connectivity, based on water molecule restricted diffusion processes and approximate DW‐MRI fiber reconstruction techniques. These techniques still present limitations, including the complexity of dealing with fiber crossing, merging, and fanning fiber configurations, as well as the difficulty of differentiating spurious from real fiber pathways [Iturria‐Medina, 2013]. Such limitations could explain the low level of inter‐hemispheric connections in comparison with intra‐hemisphere connections seen in the reduced analysis (Supporting Information Text).

In order to make results as comparable as possible across the 2 brains, two different approaches were employed: one wherein over 700 brain regions were analyzed with a model that grouped the sampled brain regions into the same anatomical structures, and another wherein the resolution of the brain samplings was reduced to 117 larger and directly comparable regions. Despite the very different number of brain regions analyzed by the two approaches, there was substantial agreement in the defined gene clusters (see Supporting Information Table S4). By comparison (Fig. 3 and Supporting Information Fig. S6), eigengene patterns were more variable with the larger matrices, potentially allowing detection of more targeted associations between the eigengenes and the connectivity vectors. In fact, associations with seed‐region connectivity vectors were stronger than in the reduced analysis (Table 3 vs. Supporting Information Table S10), suggesting that there was more sensitivity when using the larger set of brain regions. When data from more brains become available, it would be more powerful yet to jointly analyze expression‐connectivity relationships for all brains simultaneously; however, this might require the development of analytic approaches that link parameter estimates from brain regions physically close to each other.

Some patterns of gene expression across the brain regions showed marked consistency across all gene clusters. This finding was consistent whether analyzing over 700 brain regions or using the reduced approach (Fig. 3 and Supporting Information Fig. S6 for the reduced approach). It is likely that these patterns are the consequence of differences in brain function and in cell type composition between cortex and non‐cortex regions. Since both connectivity and gene expression can be expected to vary substantially between these major subdivisions of the brain (cortex/non‐cortex/cerebellum), relationships between particular gene clusters and particular seed region connectivity vectors could be biased. To address this, subsequent analyses were adjusted using principal components of gene expression—based on all the genes analyzed—and only then were the associations with seed‐connectivity vectors estimated. Correlations between eigengene residuals were substantially reduced after adjusting for these two principal components (see Supporting Information Figs. S5C, D and S7C, D). Also, although the strengths of the relationships between gene expression and connectivity were reduced, many statistically significant seed region connectivity vectors that were predictive of eigengene residuals were identified. A similar concern about confounding has been raised by other authors. Richiardi et al. [2015] implemented a partial adjustment for distances between brain regions (although this was challenged by Pantazatos and Li [2016]), whereas Hawrylycz et al. [2015] restricted their analysis to only cortex regions to avoid the problem. Although the proportion of eigengene expression that is explained by the significantly associated connectivity vectors may appear small (1%–5% in Table 3), gene expression is known to be influenced by many factors such as genetics, circadian rhythms, cell cycle, etc. [Kaern et al., 2005], and in particular, different cell types will have very different patterns of expression. Hence the identified contributions of connectivity to the expression patterns, after correction for potential confounding, are noteworthy.

When implementing the adjustments for potential confounding, only 2 principal components were used to capture the clear clustering of brain regions visible in Figure 4A and B; notably, these 2 PCs were selected as they best captured this separation, and in particular, these PCs separate the cerebellum and cerebral cortex regions from the rest of the brain. It may be that the selected PCs may not capture all relevant nuances related to cell type differences, and hence that some confounding remains. However, since the genes used to calculate each eigengene are, of course, a subset of the 10,395 genes used to calculate the PCs, use of more than two components could reduce the ability to find associations between eigengenes and connectivity.

The TOM metric used in WGCNA is quite different from simple correlation‐based distance measures commonly used in clustering algorithms, since it is designed to reflect global properties of a network. It has been suggested that gene modules are more distinct when the TOM is used [Zhang and Horvath, 2005]. In a sensitivity analysis, fewer modules were obtained (8 compared with 10) when clustering using only correlations (without using the TOM). Although it was possible to find an equivalent module in the “no TOM” analysis for most gene clusters, many of the previously clustered genes (3,528) ended up in the “leftover” gray cluster which collects genes that cluster poorly. To compare clustering performance, relative strengths of connectivity were compared between genes in various clusters, by summing the connection strengths for all pairs of genes in a chosen set, and then calculating the ratio of this sum with and without the TOM metric (see Supporting Information Table S5). Over all analyzed genes, connectivity was 2.4 times stronger when using the TOM matrix compared with analysis without the TOM. Furthermore, the genes that moved into the leftover cluster in the “no TOM” analysis were 2.9–6.49 times more connected to genes in the clusters showing significant association with connectivity (orange, orchid, plum, and navy) when the TOM was used (see Supporting Information Table S5). Hence, a decision against use of the TOM metric would have excluded genes that show important evidence of connectivity, which would weaken the pathway analysis.

As an additional sensitivity analysis, simple Pearson correlations were calculated between gene expression levels and connectivity (Supporting Information Fig. S9). By comparison with Supporting Information Figure S2, it is visually apparent that use of the TOM matrix clarifies modularity. Hence, the use of WGCNA has allowed a clustering of genes in ways that would not have been captured in an analysis of correlations alone.

In the pathway analyses, the comparison set of genes was restricted to the 10,395 genes included in the designated clusters, that is, enrichment of specific pathways in the gene clusters was determined relative only to the 50% of the genes that demonstrated variability in gene expression across brain regions. However, pathway enrichment analyses were also performed comparing to all genes, and in general, all the conclusions were the same.

The orange and plum clusters showed highly significant associations with seed region connectivity vectors in both brains, particularly with seed regions in pons, hippocampal formation, mesencephalon, myelencephalon, and parietal and temporal lobes. Pathways associated with synaptic signaling were significantly enriched in both the orange and plum clusters (Supporting Information Table S3); in fact, the most significantly enriched pathways across all the gene clusters were found in the orange cluster. There is substantial overlap between the genes in the orange cluster and the blue cluster from the reduced analysis (Supporting Information Table S4), which also displayed very highly significant pathway enrichment for synaptic signaling pathways. However, in the reduced analysis, no seed region connectivity vectors were retained in the elastic net models. Therefore, it appears that orange cluster gene expression varies with fine‐scale seed region connectivity, and this relationship was hidden when the brain regions were aggregated. In fact, pons, myelencephalon, and mesencephalon were all grouped into the brain stem region in the reduced analysis.

The orange and plum clusters each contain many genes involved in glutamatergic activity, calcium signaling, and kinases involved in synaptic signaling. Glutamatergic transmission is a fundamental mechanism of neural network communication and is also necessary for the induction and expression of activity‐dependent changes in network connectivity [Bliss and Lomo, 1973; Malenka and Bear, 2004]. While calcium is relevant to diverse biological processes, functions relating to calcium are important contributors to neural connectivity in health and disease [Kandel et al., 2013; Mattson et al., 2000]. Several genes in these clusters regulate cAMP levels and cyclic nucleotides, known regulators of cell state. In addition to various synaptic effects, cyclic nucleotides regulate the cellular perception of a multitude of extracellular molecules with important implications for brain morphology [Guidotti et al., 1974; Kandel et al., 2013; Zufall et al., 1997]. For example, modulation of cyclic nucleotides can switch neural cells from interpreting the same extracellular molecule as a growth signal to a signal for structural collapse, often in collaboration with calcium dynamics [Hardingham et al., 2002; Ming et al., 1997; Song et al., 1997]. Collectively, it would seem that many of these genes and enriched pathways are related to brain plasticity.

The present analysis was restricted to the two brains where both expression and DW‐MRI data were available in the same brains. Although others have looked at larger series of brains for either connectivity or gene expression, this decision allows the capture of individual aspects of the relationships between expression and connectivity common between the two brains. Certainly, differences between brain 1 and brain 2 in the clarity of the eigengene patterns and the results of the penalized models were apparent. Hence, it will be extremely informative to perform similar analyses on a larger series of brains to better understand which patterns are common across all brains. Furthermore, these two brains are from individuals without known disease. To explore how these associations might be altered by disease, the results of this study would need to be replicated with a larger set of healthy and diseased adult human neural samples with data on both gene expression and connectivity by brain region.

Although many authors have noted strong relationships between connectivity and gene expression, the analysis methods chosen here—that is, the network‐motivated gene clustering, adjustment for major axes of variation in gene expression, and the penalized models with seed region connectivity vectors—may help identify associations not simply due to differences in cell type composition or brain activity. Furthermore, through the use of WGCNA, a dimension reduction step has been effectively implemented while simultaneously obtaining an informative partitioning of the genes. The consequent gain in interpretability at the pathway level comes with some loss of interpretability for the contributions of individual genes; however, the importance of individual gene contributions can be assessed by looking at their contribution to eigengene summaries.

CONCLUSIONS

This study has identified seed‐region DW‐MRI connectivity vectors that explain gene expression variation in several network‐defined clusters of gene expression in adult human brains. Analyses of association between the connectivity vectors and the expression cluster summaries were adjusted for the major axes of gene expression variation across the brain by including two principal components of gene expression in penalized regression models; they therefore captured more than just variation due to brain activity or predominant cell type differences. Pathway analysis of two gene clusters with the most statistically significant links to seed region connectivity revealed pathways related to synaptic signaling and neuron development, thereby strongly suggesting activity related to brain plasticity.

Our analytic approach is an example of data integration, in that the extraction of eigengenes from consensus clusters of gene expression data condensed the gene‐level information into a form directly comparable with connectivity information. This strategy, combined with group‐penalized regression models, enabled comparability of results across brains, and could be useful in further studies of brain architecture.

COMPETING INTERESTS

The authors declare that no competing interests exist.

AUTHOR CONTRIBUTIONS

Conceptualization, Y.I.‐M., M.F., C.G., A.La. and A.C.; Methodology, M.F., Y.I.‐M., C.G., A.La., A.C., and J.G.; Validation, M.F. and J.G.; Formal Analysis, M.F., Y.I.‐M., J.G., and A.Lo.; Resources, A.E., Y.I.‐M., K.O.K. and C.G.; Writing‐Original Draft, M.F. and J.G.; Writing‐Review & Editing, C.G., A.C., J.G., M.F., Y.I.‐M., C.K., A.E., and A.La.; Visualization, M.F. and J.G.; Supervision, C.G., A.La., A.C., and A.E.; Project Administration, C.G.; Funding Acquisition, C.G. and A.E.

URLS

Allen Institute for Brain Science: http://alleninstitute.org/

Allen Human Brain Atlas: http://human.brain-map.org

Cytoscape: http://www.cytoscape.org/

Cytoscape Cluego: http://apps.cytoscape.org/apps/cluego

Cytoscape CluePedia: http://apps.cytoscape.org/apps/cluepedia

Glmnet: https://cran.r-project.org/web/packages/glmnet/index.html

GO database (Gene Ontology Consortium): http://geneontology.org/page/go-database

ITT Human Brain Atlas: http://www.iit.edu/~mri/Home.html

KEEG (Kyoto Encyclopedia of Genes and Genomes): http://www.genome.jp/kegg/

Reactome: http://www.reactome.org/

SMP12 toolbox: http://www.fil.ion.ucl.ac.uk/spm/software/spm12/

Table S1: https://www.mcgill.ca/statisticalgenetics/files/statisticalgenetics/forest_et_al_2017_table_s1ab.docx

Table S2: https://www.mcgill.ca/statisticalgenetics/files/statisticalgenetics/forest_et_al_2017_table_s2.xlsx

Table S3: https://www.mcgill.ca/statisticalgenetics/files/statisticalgenetics/forest_et_al_2017_table_s3.xlsx

Table S8:

https://www.mcgill.ca/statisticalgenetics/files/statisticalgenetics/forest_et_al_2017_table_s8.xlsx

WGCNA:

https://labs.genetics.ucla.edu/horvath/CoexpressionNetwork/Rpackages/WGCNA/

Supporting information

Supporting Information