Résumé
In microarray experiments, the global and the specific gene expression in the two-way table of gene × treatments (or tissues) can be studied using linear-bilinear models that incorporate the main effects of genes (G), treatment (T), and gene × treatment interaction (G × T). The plot of the first two axes obtained from the singular value decomposition of the bilinear (multiplicative) term of these models (biplot) facilitates the interpretation of the gene expression patterns. In this study, two microarray datasets were used to illustrate how two linear-bilinear models, the additive main effect and multiplicative interaction (AMMI) and the treatment regression model (TREG) and their biplots can be used to determine the overall gene expression pattern across treatments (or tissues) and for specific treatments. Dataset 1 had 5,339 genes and the objective was to identify genes with modified expression during maize (Zea mays) seed development in response to different parental ploidy levels. In Dataset 2, the aim was to study gene expression in 15 tissue samples with different levels of development of breast cancer when compared with the expression of the genes in noninfected tissues. The results from the analyses of Dataset 1 showed that the biplots of the AMMI and TREG models allow identification of subsets of genes and treatments with noncrossover G× T interaction or with important levels of crossover G × T. Results from Dataset 2 showed that the TREG model and its biplot facilitates the identification of genes with high expression in all tumor cells. Also, the TREG biplots allowed identification of subsets of genes with a low level of gene × tissue crossover interaction.