Extracting gene networks for low-dose radiation using graph theoretical algorithms

Abstract

Genes with common functions often exhibit correlated expression levels, which can be used to identify sets of interacting genes from microarray data. Microarrays typically measure expression across genomic space, creating a massive matrix of co-expression that must be mined to extract only the most relevant gene interactions. We describe a graph theoretical approach to extracting co-expressed sets of genes, based on the computation of cliques. Unlike the results of traditional clustering algorithms, cliques are not disjoint and allow genes to be assigned to multiple sets of interacting partners, consistent with biological reality. A graph is created by thresholding the correlation matrix to include only the correlations most likely to signify functional relationships. Cliques computed from the graph correspond to sets of genes for which significant edges are present between all members of the set, representing potential members of common or interacting pathways. Clique membership can be used to infer function about poorly annotated genes, based on the known functions of better-annotated genes with which they share clique membership (i.e., "guilt-by-association"). We illustrate our method by applying it to microarray data collected from the spleens of mice exposed to low-dose ionizing radiation. Differential analysis is used to identify sets of genes whose interactions are impacted by radiation exposure. The correlation graph is also queried independently of clique to extract edges that are impacted by radiation. We present several examples of multiple gene interactions that are altered by radiation exposure and thus represent potential molecular pathways that mediate the radiation response.

Figure 1. Comparison of Pearson's and Spearman's Correlation Coefficients

Figure 2. Impact of Normalization on the Correlation Distributions

Normalization results in a distribution approximately centered around zero.

Figure 3. The Distributions of Correlations in Control and IR Are Highly Similar

Control (blue dashed) and IR (red solid) lines overlay each other across the entire distribution. The vertical lines in each tail of the distribution delineate the edges that were included in the graph after applying the threshold of |0.875| to the correlation matrix.

Figure 4. Distribution of Clique Sizes in Control and IR

Maximum clique and average clique sizes were larger in IR (red bars) than control (blue bars).

Figure 5. Scale Free Properties of Gene Connectivity

Gene lists were sorted in order of abundance for each condition, and the 400 genes most abundant in control (blue bars) and IR (red bars) were plotted against clique membership (A) and vertex degree (B). Although average vertex degree and clique membership were not markedly different between control and IR, the genes most abundant in IR cliques were more highly connected and present in more cliques than in control.

Figure 6. Genes Co-Expressed with Tulp4 in HSCs

Gene expression data from HSCs [43] were used in WebQTL (webqtl.org) to identify genes most highly correlated with Tulp4. The majority of genes encode proteins involved in immune function (e.g., immunoglobulins).

Figure 7. Differential Correlation Identifies Edges Impacted by IR

The graph was filtered to identify edges that exceeded r = |0.875| in one condition but were less than |0.25| in the other. Vertices with > 8 differential correlations are represented in (A). Red indicates edges that are present only in IR, while blue edges are only found in control. Dark edges for each color represent the subset of edges that are differentially correlated and of opposite direction (+ vs. −) in the two conditions, while bright edges are of the same direction. The portion of the graph containing three connected sub-graphs centered around Top3a, Notch3, and an unannotated gene is shown in (B).

Figure 8. Overall Schema of Our Approach