Fig. 1. Experimental design of the transcriptome analysis on Bacillus subtilis ([Sekowska et al., 2001]).

Table 1. Quantification of false positives

For the definition of false positives we exploit the fact that each gene spot had been duplicated on the microarrays and any difference measured for two spots belonging to the same gene cannot have a biological cause. We ranked the genes according to this “duplicate factor”, as a function of the differences in their expressions, then identified “detected operons” and calculated the MSI (see Section 2 for details). As there is no biological cause for this detection, we find ourselves with false positives; they are characterized by a large MSI; this leads us to conclude that a “detected operon” is a false positive when MSI≥700. One exception is the operon YonRSTUVXyopAB, detected by all four tools, with small MSIs. As we cannot give a biological reason, we suspect that its detection is due to a default on the microarray used in the experiments.

Table 2. Comparison of the statistical tools when the experimental factor is identified and fully controlled

The identified and controlled experimental factor is the sulphur source (either methionine, or methylthioribose). Genes were ranked as a function of the differences in their expressions, false positives (MSI≥700) and “relevant detected operons”(MSI<700) were identified (see Section 2 for details). The bold entry for PLS, with MSI=635 is estimated to be a borderline case for a false positive; it has been included for PLS’s total of “relevant detected operons”. Note that only PCA detects a false positive (shaded entry). ICA is the most sensitive tool under these experimental conditions, identifying the largest number of “relevant detected operons”. ANOVA and PLS are the least sensitive.

Table 3. Comparison of the statistical tools when the experimental factor is identified but not under control

The experiments were carried out twice, on different days, using the same protocol; however, parameters like “room temperature” were not necessarily the same on the 2 days, introducing an identified but not controlled factor. PCA and ICA are the most sensitive tools, whilst ANOVA is the least sensitive (please refer to the legend of Table 2 for details about the classification procedure).

Table 4. Comparison of the statistical tools to detect possible interactions between the experimental factors

The expression of certain genes may be under the control of more than one factor, leading to an interaction between experimental factors. Only ICA and PCA are well adapted to cope with possible interactions; these interactions are identified because more than one factor plays a major role in the definition of an axis. ICA is more sensitive than PCA (please refer to the legend of Table 3 for details about the classification procedure).

Table 5. Overview of the results

The table sums up the results obtained in this study. The first part of the table relates to the number of “relevant detected operons” identified and thus to the tools’ relative sensitivities. “Table 2, Table 3 and Table 4”: adding the results from Table 2, Table 3 and Table 4, the total of “relevant detected operons” has been calculated for each tool. The entries for “ Table 2 and Table 3” have been obtained accordingly. Note that in both cases, ICA has the highest overall sensitivity, identifying the largest number of “relevant detected operons”, whilst ANOVA is the least sensitive. The second part of the tables relates to the tools’ accuracies: the percentage of “relevant detected operons” identified with a “good accuracy” (MSI<150) has been calculated for each tool, adding the results from Table 2, Table 3 and Table 4 (“ Table 2, Table 3 and Table 4”), etc. (see above). Overall, ICA has the highest accuracy, very closely followed by PCA, whilst ANOVA has the lowest accuracy.