To elucidate whether elementary modes can be considered as true functional biological units, the stress response of yeast was investigated in a large number of different conditions. Towards this goal, we used microarray data obtained from several experimental analyses 323334 (see the 'Expression data' section in Materials and methods) and a bioinformatics tool called BlastSets 27. BlastSets enabled us to find similarities between the composition of two sets of genes or proteins derived from two different types of information (here, metabolic pathways and expression data). The elementary modes EM1 and EM2 were stored independently as two BlastSets collections. Entire KEGG pathways were also stored as a BlastSets collection, to find out whether stress responses involve entire pathways, as defined in KEGG, or only parts of these pathways, as represented by elementary modes. In many stress conditions, induced/repressed elementary modes were found with higher P values than whole pathways (Table 2).

The numbers of detected induced/repressed elementary modes for each stress condition are shown in Table 3, as well as the number of different KEGG pathways these elementary modes belong to. The numbers obtained with EM1 and EM2 are relatively well correlated but there is no absolute relationship between them; in most cases, the number of induced/repressed elementary modes is increased when compared to EM2, but a few of them show higher numbers with EM1. The same observation can be made about the number of KEGG pathways to which these elementary modes belong. In a majority of cases, elementary modes detected with EM1 are concentrated in a relatively small number of pathways, and EM2 increases this number by adding modes from adjacent pathways. But in a few cases, for example Thiuram, the number of pathways detected with EM2 is smaller than with EM1, indicating that these elementary modes tend to be isolated and poorly connected to adjacent pathways.

Examples of elementary modes induced in particular stress conditions are shown in Figure 2, including an induced elementary mode in the citrate cycle during stationary phase, and another induced one in sulfur metabolism in response to tetrachloro-isophthalonitrile exposure. The sets of induced enzymes detected by BlastSets are indeed highly connected. Fewer elementary modes could be identified from the sets of repressed enzymes and they are usually less connected, meaning that repressed enzymes are more dispersed in the mode. This fact has already been mentioned by Wei et al. 35 for the genetic model plant Arabidopsis thaliana, who observed that induced genes in the same metabolic pathway tend to be close and well connected to each other, while repressed genes are more distant.

BlastSets applies a stringent threshold on P values (P value must be lower than 6.0 × 10^-5 for EM1 and 3.4 × 10^-6 for EM2; see 'Description of BlastSets' section in Materials and methods), which should already guarantee that identified elementary modes are statistically significant. Nevertheless, in order to further assess the reliability of our results, we created random gene expression values by random permutation of gene expression values in several stress responses. These random sets of induced/repressed genes were compared to elementary modes in BlastSets, in the same way as for stress-induced/repressed genes. No active elementary mode was identified using these random sets. The procedure was repeated for several conditions, always with the same result. This finding confirms that elementary modes found to be active in specific environmental stress conditions have a high statistical significance.

To identify complete metabolic routes that are spread over several KEGG pathway maps, we constructed the EM2 collection containing elementary modes grouped in pairs. Two elementary modes are grouped as a set in EM2 if they share a common boundary compound. These compounds act as bridges between individual pathway maps, enabling more extended induced/repressed routes to be identified by this approach.

In each stress situation, we could then infer a 'backbone' of induced/repressed metabolic routes. Backbones were constructed by selecting the pairs of elementary modes with the lowest P values and connecting them to each other, thanks to results from the EM2 collection (see 'Analysis of BlastSets results' section in Materials and methods). These backbones can be viewed as the main modules characterizing metabolic activity in terms of expression data in a given condition. They are provided for each individual condition in Additional data file 2.

To assess how the activity of elementary modes is distributed in response to a set of diverse environmental stresses, we computed the probability distribution P(k) to find a given induced/repressed elementary mode in k stress conditions (Figure 3a). This distribution reveals a highly heterogeneous behavior: on one hand, a relatively low number of 'multitask' elementary modes are transcriptionally active in a large number of different conditions, while on the other hand, many 'specialized' elementary modes are active in a small number of conditions (less than three). About 77% of detected elementary modes appear to be conducting specialized tasks while the remaining 23% are involved in the more general stress response. This observed metabolic organization is far from a random distribution, where each induced/repressed elementary mode would have the same chance to be active in the vicinity of the average value. The deviation from a random distribution suggests that elementary modes involved in the stress response are governed by a more complex organization 36, that is, that they are organized into complex modules across the metabolic network.

It is possible to reveal the various patterns of stress responses by drawing the 'activity map' of elementary modes. In Figure 3b, each line represents an elementary mode and each column a stress condition; induced elementary modes are shown in red and repressed modes in green in this representation, which is deliberately chosen to look similar to a microarray. Indeed, in the same way a microarray represents a map of the transcriptional activity of individual genes, we are here able to construct a map of genome-scale elementary mode activities, revealing the transcriptional activity of entire metabolic processes. It is particularly clear on this map that most of the identified elementary modes are either only induced or only repressed. While the three repressed patterns are very similar, induced patterns are more diverse and very few elementary modes are induced over all conditions, confirming the trend revealed by the distribution in Figure 3a.

Our approach is able to provide new insights about metabolic activity in terms of expression data in particular conditions. We analyzed the raw expression data obtained for each stress condition in order to see which stresses lead to similar responses; the clustering tree of stress conditions based on raw expression data is provided as Additional data file 3. Among the 31 different conditions we studied, 12 had a too weak transcriptional response for any induced or repressed elementary mode to be detected. We noticed that, among the remaining 19 conditions that produced a sufficiently strong response, stresses could be divided into two main classes, which we hence denote as 'toxic' and 'non-toxic'. The toxic stress class mostly includes exposure of cells to toxic chemicals and metals. The non-toxic class, on the contrary, mostly includes other types of stresses, such as temperature changes, osmotic shocks, nutrient starvation, and so on. The list of conditions assigned to each class is provided in Table 4.

The metabolic backbones inside each class show recurrent similarities, which allowed us to construct a common backbone for each class (Figure 4). The two classes show a clearly distinct global response and few elementary modes are induced in both backbones, with the exception of the citrate cycle and nucleotide sugar metabolism. In addition, we represented both classes by networks where each node corresponds to a metabolic pathway and each edge denotes that at least one pair of elementary modes spanning both pathways is present in a stress response (see 'Construction of toxic and non-toxic networks' section in Materials and methods). The toxic response network is shown in Figure 5a and exhibits two components. The inner component is composed of a group of strongly connected pathways centered on sulfur metabolism, pyruvate metabolism and lysine biosynthesis metabolism. These pathways thus have a strong tendency to be activated simultaneously. They constitute the core of the toxic stress response and cover most parts of the toxic backbone described previously. The external component, in contrast, is composed of a sparse network with thinner connections. In the non-toxic network this bi-component nature is less clear, but it is still possible to identify a more strongly connected central component containing starch and sucrose metabolism, the pentose phosphate pathway, glycolysis, and arginine and proline metabolism (Figure 5b).

In some cases, the observed transcriptional metabolic response confirms earlier findings. Vido et al. 37 reported that cadmium exposure increases the synthesis of cysteine and perhaps of glutathione, which is essential for cellular detoxification. The synthesis of these two compounds is possible through the activation of the sulfur amino acid pathway. We observe that, among the three elementary modes activated in response to cadmium exposure, two have cysteine as their final product, and among these two, one elementary mode is a part of cysteine metabolism and another is a part of sulfur metabolism. Cysteine is also one of the compounds produced in the general backbone of the response to toxic stresses (Figure 4a).

Amino acid starvation is known to activate the transcription factor Gcn4p, which induces genes involved in amino acid biosynthetic pathways, except the cysteine pathway 38, although the genes involved in the biosynthesis of cysteine precursors (homocysteine and serine) are induced. This is exactly what we observe in response to amino acid starvation: several elementary modes from amino acid biosynthetic pathways are activated but none from the cysteine pathway, even if some elementary modes from the cysteine pathway are linked to modes activated during amino acid starvation.

Genes induced in stationary-phase cultures of yeast are associated with mitochondrial functions, that is, aerobic respiration and the citrate cycle 39. ATP synthesis is thus very important for yeast in the stationary phase. In our results, the elementary modes activated during the stationary phase are part of metabolic pathways linked to aerobic respiration, including glycolysis, the citrate cycle, pyruvate metabolism and oxidative phosphorylation.

Trehalose and glycerol are produced in large amounts by cells in stress situations 40. Schade et al. 40 have shown that there is an overlap between the late cold response and the environmental stress response. This response corresponds to the production of glycerol and trehalose. This is what we observed in the general non-toxic backbone response (Figure 4b): glycerol is produced just a few reactions after glycerone phosphate, and trehalose is present one step before D-glucose in the starch and sucrose metabolism KEGG map (the only reason why it cannot appear as an end product in our study is that it is not a boundary compound in KEGG maps). These examples, confirming previously observed results, enable us to be confident in the identification of metabolic processes found to be induced/repressed in response to other stress conditions.

We have chosen experiments analyzing the gene expression responses of the yeast S. cerevisiae to various environmental stresses. Three sets of microarray experiments have been selected for our study. Causton et al. 32 described the transcriptional response to environmental changes using genome-wide expression experiments; data are available on the Young lab website 44. Gasch et al. 33 analyzed gene expression of yeast cells during the adaptation to stressful environments in order to identify the main patterns of response in these different conditions; data were downloaded from the Stanford MicroArray Database website 45. Iwahashi et al. 34 studied transcriptional responses of yeast to physical and chemical stresses using microarray; data are available from the Yeast Environmental Stress database 34.

These three datasets enabled us to study a total of 31 stress conditions. Some of these stresses involved environmental changes or nutrient depletion, while others involved exposure to toxic compounds such as pesticides or fungicides. The latter include: ash, which refers to exposure to burned ash from an industrial incinerator; maneb, which is a fungicide used in the control of several diseases of fruit, vegetable, field crops and ornamentals; pentachlorophenol (PCP), which is an effective fungicide, herbicide and algicide used as a wood preservative; tetrachloro-isophthalonitrile (TPN), which is a fungicide used to prevent biofouling on ships and in agriculture; thiuram, which is a compound used as fungicide to prevent crop damage and to protect harvested crops; and zineb, which was rated as a pesticide of low toxicity and may be a weak mutagen.

We plotted the distributions of the natural logarithm of fold-change values for the Causton, Gasch and Iwahashi datasets. For each of the three sets of data, the standard deviation was determined. A threshold was defined by multiplying the standard deviation by a constant, and this threshold was used to determine which genes were considered as significantly induced or repressed in each condition. Genes whose fold change was higher than the threshold were considered induced; genes whose fold change was lower than 1 divided by the threshold were considered repressed. For each condition, a set of induced genes and a set of repressed genes were constructed. Table 5 indicates the number of genes present in each set.

For three particular conditions (one from each dataset), we re-assigned gene expression values randomly to all genes of the experiment. We then processed these random expression data using the same procedures as described above. The resulting sets of random induced/repressed genes were compared to elementary modes using BlastSets in the same way as real expression data.