Eigengene networks for studying the relationships between co-expression modules

Abstract

Background: There is evidence that genes and their protein products are organized into functional modules according to cellular processes and pathways. Gene co-expression networks have been used to describe the relationships between gene transcripts. Ample literature exists on how to detect biologically meaningful modules in networks but there is a need for methods that allow one to study the relationships between modules.

Results: We show that network methods can also be used to describe the relationships between co-expression modules and present the following methodology. First, we describe several methods for detecting modules that are shared by two or more networks (referred to as consensus modules). We represent the gene expression profiles of each module by an eigengene. Second, we propose a method for constructing an eigengene network, where the edges are undirected but maintain information on the sign of the co-expression information. Third, we propose methods for differential eigengene network analysis that allow one to assess the preservation of network properties across different data sets. We illustrate the value of eigengene networks in studying the relationships between consensus modules in human and chimpanzee brains; the relationships between consensus modules in brain, muscle, liver, and adipose mouse tissues; and the relationships between male-female mouse consensus modules and clinical traits. In some applications, we find that module eigengenes can be organized into higher level clusters which we refer to as meta-modules.

Conclusion: Eigengene networks can be effective and biologically meaningful tools for studying the relationships between modules of a gene co-expression network. The proposed methods may reveal a higher order organization of the transcriptome. R software tutorials, the data, and supplementary material can be found at the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/EigengeneNetwork.

Figure 1

Overview of eigengene networks. A. Flowchart of the construction and analysis of an eigengene network based on a single data set. B. Analogous flowchart for constructing and analyzing consensus eigengene networks based on multiple data sets. C.–E. Illustrating the notion of eigengene as a representative of an entire gene co-expression module. C. Expression levels (y-axis) of module genes (grey lines) and the eigengene (black line) across microarray samples (x-axis). The plot shows that an eigengene is highly correlated with the expression profiles of the genes in the module. D. Heatmap of the gene expressions (rows correspond to genes, columns to samples, red denotes over-expression, green under-expression). E. Expression levels (y-axis) of the corresponding eigengene across the samples (x-axis). Whenever the module gene expression are high (red), the module eigengene are high and similarly for low (green) gene expressions.

Figure 2

Differential eigengene network analysis in human and chimp brain samples. A. Hierarchical clustering dendrogram of genes for identifying consensus modules (see text). Branches of the dendrogram, cut at the red line, correspond to consensus modules. Genes in each module are assigned the same color, shown in the color band below the dendrogram. Genes not assigned to any of the modules are colored grey. B., C. Clustering dendrograms of consensus module eigengenes for identifying meta-modules. The same three meta-modules (major branches) are evident in both dendrograms. D. Heatmap of eigengene adjacencies in the consensus eigengene network in human samples. Each row and column corresponds to one eigengene (labeled by consensus module color). Within the heatmap, red indicates high adjacency (positive correlation) and green low adjacency (negative correlation) as shown by the color legend. G. Corresponding plot for the chimp samples. E. Preservation measure for each consensus eigengene. Each colored bar corresponds to the eigengene of the corresponding color. The height of the bar (y-axis) gives the eigengene preservation measure (16). D denotes the overall preservation of the eigengene networks, Eq. (17). F. Heatmap of adjacencies in the preservation network Preserv^human,chimp, Eq. (15). Each row and column corresponds to a consensus module; saturation of the red color encodes adjacency according to the color legend. H. Characterizing consensus modules by differential expression of their corresponding eigengenes in the various brain areas from which samples were taken. Red means over-expression, green under-expression; numbers in each cell give the corresponding t-test p-value. Each column corresponds to an eigengene and each row corresponds to a brain area. Caudacc, caudate nucleus and anterior cingulate cortex; cerebcort, cerebellum and cortex; caudate, caudate nucleus.

Figure 3

Differential eigengene network analysis across four tissues in female mice. A. Hierarchical clustering dendrogram of genes for identifying consensus modules (see text). Branches of the dendrogram, cut at the red line, correspond to consensus modules. Genes in each module are assigned the same color, shown in the color band below the dendrogram. Genes not assigned to any of the modules are colored grey. Biological significance of the found modules was assessed by functional enrichment analysis, presented in the main text and in Additional File 4. B.–E. Clustering dendrograms of consensus module eigengenes for identifying meta-modules. F.–U. Matrix of plots showing the consensus eigengene networks in the four tissues. Each row and column corresponds to one tissue as indicated on the diagonal plots. The diagonal plots F., K., P., U. show the heatmap plots of eigengene adjacencies in each eigengene network. Each row and column corresponds to one eigengene (labeled by consensus module color). Within each heatmap, red indicates hight adjacency (positive correlation) and green low adjacency (negative correlation) as shown by the color legend. Each of the upper triangle plots (G., H., I., L., M., Q.) shows a barplot of of preservation of relationships of consensus eigengenes, Eq. (16) between the two tissues (corresponding row and column) as well as the overall network preservation measure D for that pair of tissues, Eq. (17). The lower triangle plots (J., N., O., R., S., T.) show the adjacency heatmaps for the pairwise preservation networks of the tissues corresponding to the row and column, Eq. (15). In the heatmap, each row and column corresponds to a consensus module; saturation of the red color encodes adjacency according to the color legend.

Figure 4

Permutation test results for showing that the number of genes in consensus modules is highly significant. Here we use the brain and muscle tissues of female mice. The size of a consensus module depends on the height cut-off used for cutting branches off the dendrogram. Thus, the number of genes in a consensus module (y-axis) depends on the height cut-off (x-axis). The red horizontal lines represent the observed number of genes in consensus modules for the original (unpermuted) data set. The boxplots (black) summarize the number of genes assigned to consensus modules after the gene list has been permuted between the two data set (1000 random permutations). For height cut-offs less than 0.99, the observed number of consensus genes is highly significant (p = 0.001).

Figure 5

Differential eigengene network analysis across female and male mouse liver tissues. A. Hierarchical clustering dendrogram of genes for identifying consensus modules (see text). Branches of the dendrogram, cut at the red line, correspond to consensus modules. Genes in each module are assigned the same color, shown in the color band below the dendrogram. Genes not assigned to any of the modules are colored grey. B.–C. Clustering dendrograms of consensus module eigengenes for identifying meta-modules. D.–G. Matrix of plots showing the consensus eigengene networks. The diagonal plots D., G. show heatmap plots of eigengene adjacencies in each eigengene network. Each row and column corresponds to one eigengene (labeled by consensus module color). Within each heatmap, red indicates high adjacency (positive correlation) and green low adjacency (negative correlation) as shown by the color legend. E. Barplot of preservation of relationships of consensus eigengenes between the two data sets, Eq. (16), as well as the overall network preservation measure D, Eq. (17). Each colored bar corresponds to the eigengene of the corresponding color. The height of the bar (y-axis) gives the eigengene preservation measure (16). F. Adjacency heatmap for the preservation network between female and male consensus eigengene networks, Eq. (15). Each row and column corresponds to a consensus module; saturation of the red color encodes adjacency according to the color legend. H., I. Consensus module significance for clinical traits, given by the correlation of the corresponding module eigengene (row) with the clinical trait (column). Shown are correlations and p-values; cell color encodes correlation (red, positive correlation, green, negative correlation according to the color legend).