3.2. Triclustering Identifies Gene Clusters in Three-Dimensional Datasets 
EMOA-δ-TRIMAX identified three gene clusters in the mouse lung profile of Thomas et al., 2009 [20] and 14 gene clusters in the mouse liver profiles of Thomas et al., 2011 [19]. The complete set of clusters is provided in Supplementary Table ST1. For defining the clusters, we first neglected the sign of the gene activity changes (whether up- or down-regulated) and clustered genes with a similar shape of their absolute dose response curves. The rationale behind this is that nearly all regulators (TFs), when put in the appropriate context, can act as transcriptional activators or repressors, either directly or indirectly. It is therefore conceivable that the same regulatory mechanisms are responsible for stimulating the expression of one gene set, but for the repression of another set. Just as a secondary measure, we subdivided the clusters into gene sets that are either up- or down-regulated.
We selected cluster 3 from the liver data and cluster 4 from the lung data (gene lists in Supplementary Table ST1) for further analysis, because only these two gene clusters showed similar expression trends in both tissues at the same doses, which were 20 ppm to 30 ppm. The set of up-regulated genes in liver (cluster 3) and lung (cluster 4) comprised 70 and 372 genes of the down-regulated genes in lung and liver comprised 21 and 566 genes, respectively. However, the up- and down-regulated gene sets overlapped in only 4 (up, Fisher test p-value: 0.036) and 2 (down, Fisher test p-value: 0.11) genes (Figure 4), suggesting that in spite of the observed overlaps, which may be moderately significant for the up-regulated, but hardly significant for the down-regulated genes, naphthalene induces rather specific responses in the two tissues.
Figure 4  Summary of regulated genes from cluster 3 (red, liver) and cluster 4 (blue, lung) and cluster overlaps. (a) Up-regulated genes. (b) Down-regulated genes.   The commonly up-regulated genes of both clusters (see Table 1) comprise one alcohol dehydrogenase (Aldh1a3), two proteins involved in GTP-dependent signal transduction (Trio and Gngt1) and one transport protein (Stx6), which may be involved in the metabolism of the toxic compound and its regulation. One of the two commonly down-regulated genes is Vcam1, which is involved in cell-cell adhesion and inflammatory processes. However, all these six common genes show only modest up- or down-regulation, resp.
microarrays-04-00270-t001_Table 1 Table 1  Table of common up- or down-regulated genes. Differential expression was quantified in comparison to control replicates.

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