Sparse graphical Gaussian modeling of the isoprenoid gene network in Arabidopsis thaliana

Abstract

We present a novel graphical Gaussian modeling approach for reverse engineering of genetic regulatory networks with many genes and few observations. When applying our approach to infer a gene network for isoprenoid biosynthesis in Arabidopsis thaliana, we detect modules of closely connected genes and candidate genes for possible cross-talk between the isoprenoid pathways. Genes of downstream pathways also fit well into the network. We evaluate our approach in a simulation study and using the yeast galactose network.

Figure 1

Bootstrapped GGM of the isoprenoid pathway. (a) Comparison between absolute pairwise correlation coefficients and presence of edges. Dots at 0 and 1 denote absent and present edges respectively. (b) Histogram of the bootstrap edge probabilities. (c) Comparison between absolute pairwise correlation coefficients and bootstrap edge probabilities for all 780 possible edges.

Figure 2

Bootstrapped GGM of the isoprenoid pathway with a cutoff at 0.8. The solid undirected edges connecting individual genes (in boxes) represent the GGM. Dotted directed edges mark the metabolic network, and are not part of the GGM. The grey shading indicates metabolic links to downstream pathways.

Figure 3

Dependencies between genes of the isoprenoid pathways according to the frequentist modified GGM method. (a) Subgraph of the gene module in the MEP pathway; (b) subgraph of the gene module in the MVA pathway. For an explanation of what the edges and shading indicate see legend to Figure 2.

Figure 4

Comparison of the absolute pairwise correlation coefficients and the modified GGM approaches. (a) Selected edges in the frequentist modified GGM approach (0 and 1 denote absent and present edges respectively). (b) θ-values in the latent random graph approach. (c) θ-values after attaching 795 genes from other pathways.

Figure 5

Hierarchical clustering of 40 genes involved in the isoprenoid pathway and 795 genes from other pathways. Clustering is depicted as a heatmap, in which red and green represent high and low expression values, respectively. Rows depict genes and columns depict hybridizations. Positions of the genes from the MEV pathway (m) and the plastoquinone and phytosterol pathways (+) are indicated in the left-hand column of the heatmap axis on the right side of the figure. Positions of the genes from the MEP pathway (n) and the plastoquinone, carotenoid and chlorophyll pathways (+) are indicated in the right column of the axis.

Figure 6

Performance of different GGM approaches. (a) ROC curves and (b) the proportion of true-positive edges as a function of the number of selected edges for the different graphical modeling strategies. Black line, the standard GGM; red line, frequentist modified GGM approach; blue line, latent random graph modified GGM approach; green line, pairwise correlation. Sparse networks with fewer edges as nodes (γ = 2.5) are represented in the left column, networks with approximately as many edges as nodes (γ = 1.5) are represented in the middle column, and networks with approximately twice as many edges as nodes (γ = 0.5) are in the right column.