CoGA: An R Package to Identify Differentially Co-Expressed Gene Sets by Analyzing the Graph Spectra

<div><p>Gene set analysis aims to identify predefined sets of functionally related genes that are differentially expressed between two conditions. Although gene set analysis has been very successful, by incorporating biological knowledge about the gene sets and enhancing statistical power over gene-by-gene analyses, it does not take into account the correlation (association) structure among the genes. In this work, we present CoGA (Co-expression Graph Analyzer), an R package for the identification of groups of differentially <i>associated</i> genes between two phenotypes. The analysis is based on concepts of Information Theory applied to the spectral distributions of the gene co-expression graphs, such as the spectral entropy to measure the randomness of a graph structure and the Jensen-Shannon divergence to discriminate classes of graphs. The package also includes common measures to compare gene co-expression networks in terms of their structural properties, such as centrality, degree distribution, shortest path length, and clustering coefficient. Besides the structural analyses, CoGA also includes graphical interfaces for visual inspection of the networks, ranking of genes according to their “importance” in the network, and the standard differential expression analysis. We show by both simulation experiments and analyses of real data that the statistical tests performed by CoGA indeed control the rate of false positives and is able to identify differentially co-expressed genes that other methods failed.</p></div

REACTOME ACTIVATED NOTCH1 TRANSMITS SIGNAL TO THE NUCLEUS (RANTSN) gene expression heatmap.

<p>Heatmap showing the expression levels of genes belonging to the REACTOME ACTIVATED NOTCH1 TRANSMITS SIGNAL TO THE NUCLEUS pathway in astrocytoma grade II (green label) and oligodendroglioma grade II (blue label) microarrays. The red, black, and green colors on the expression matrix represent, respectively, the highest, intermediate, and lowest expression levels.</p

Comparison of the method findings in a real dataset.

<p>Gene sets identified by only one of the three methods (CoGA, GSCA, and GSNCA) and the corresponding p-values. For each group of gene sets, the column in bold indicates the method that identified those sets. The last column shows the p-value obtained by a differential expression analysis tool (GSEA).</p

Venn diagrams of the gene sets co-identified by the methods.

<p>Each diagram shows the number of gene sets co-identified by the Spectral distribution test from the CoGA package, and the GSCA and GSNCA methods. In (A), (B), and (C) the significance level of the tests is set to 0.01, 0.05, and 0.1, respectively.</p

Evaluation of the statistical power of the tests.

<p>Areas below the ROC curves for different proportions of altered genes (<i>γ</i>), varying from 0.05 to 0.5. The ROC curves were constructed for the CoGA, GSCA, and GSNCA methods.</p

CoGA Overview: (A) input data, (B) CoGA differential network analysis, and (C) CoGA further analysis.

<p>The CoGA package receives as input data a gene expression matrix, the sample labels, and a collection of gene sets. Then, it constructs a gene co-expression sub-graph for each gene set, and tests the equality in the network structural features between two biological conditions (B). The software allows the user to further analyze each gene set (C) by visualizing the gene co-expression graphs, ranking the genes according to their “importance” in the gene set network, and performing standard single gene differential expression analysis.</p

Observed false positive rate.

<p>Proportion of incorrectly rejected null hypotheses for different significance levels (<i>α</i> = 0.01, 0.05, 0.1) and different gene set sizes (<i>n</i>_<i>V</i> = 20, 40, 100).</p