Proceeding from publicly available annotations, different groups of taxa were selected for this study as representative of environments or lineages of particular evolutionary interest. Hence, the organization of the metabolism of taxa from the three kingdoms archaea, bacteria and eukarya was compared, with an additional comparison of the superkingdom prokarya and the kingdom eukarya. Unicellular eukarya were opposed to multicellular eukarya to reveal how the more stable environment and cellular differentiation that a multicellular body implies impacted the organization of metabolism. Free-living bacteria were compared to host-associated bacteria, as taxa from the latter group typically inhabit less demanding environments-the host providing most nutrients, while limiting competitors and predators. Immotile bacteria were compared to motile ones, motility being a key competitive advantage allowing an active search for nutrients and evasion from predators or harmful environments. Aerobic bacteria were compared to anaerobes and to facultative aerobic bacteria as a potential negative control; in Raymond et al. 22 , the authors demonstrated that aerobic metabolism had little impact on the rewiring of metabolic network structure during evolution, although network size was affected. Finally, bacteria living in environments of distinct salinity (halophiles versus halotolerants) and temperature (mesophiles versus psychrophiles and thermophiles) were compared, to assess any large-scale adaptation of their metabolic network to these environments. Each group of taxa was thus selected for being a result of evolutionary pressures, and opposed to other groups either lacking their most prominent characteristics, or subject to distinct evolutionary pressures.

Networks of interacting pathways (NIPs) were constructed to represent the high-level organization of cellular metabolism in all taxa as described in Mazurie et al. 23 , using the latest version of the KEGG metabolic reactions database 24 . Then, for all taxa group comparisons considered, classification models were built to assess the effectiveness of a comprehensive set of 52 quantitative descriptors of the structure and complexity of NIPs in distinguishing the groups. Briefly, classification models were trained to predict the group to which a taxon belongs solely from the values of its NIP descriptors. Good predictions, as assessed by the accuracy and Kappa statistics of 10-fold cross-validation, would indicate that a sufficiently large difference exists between the NIPs of the different taxa groups to allow an accurate classification. Results are shown on Table 1.

The high scores obtained for most of the taxa group comparisons confirm that distinct evolutionary pressures are reflected by distinct organizational principles of the metabolism of species. Our results confirm the finding from Raymond et al. 22 showing a lack of significant differences between metabolic networks of aerobic versus anaerobic species. We also show that no distinction could be made between bacteria living in an environment of distinct salinity or distinct temperature, based on the topology of their NIPs. In the first case, this could be explained by a lack of representative taxa for halotolerant bacteria (only 4, compared to 15 halophiles). In the second case, the large number of representative taxa suggests a genuine absence of significant differences in the structure and complexity of NIPs of psycrophilic, mesophilic and thermophilic bacteria.

We first investigated the differences in the structure and complexity of the NIPs of species from different lineages or environments. Among the 52 NIP descriptors used for this investigation, we identified using feature selection algorithms (see Methods) the smallest subsets of descriptors that best discriminate taxa. The scores obtained are reported in Table 1. A list of these best discriminating descriptors of metabolic organization, as well as the average value obtained for each group of taxa, is given in Figure 1; values for all descriptors are provided as Additional file 1.

We next asked the question of how the importance of pathways changed during the evolution of species. More specifically, we are interested in pathways that are acquired or lost, those evolving to be more (or less) connected to other pathways in the cell, and finally those evolving to be more (or less) centrally located in the NIPs.

Thus, we calculated a frequency score for each metabolic pathway together with five descriptors of pathway connectivity and pathway centrality. Frequency is the fraction of taxa in a given subset that possess this pathway. Connectivity is represented by the weighted and unweighted versions of vertex degree; i.e., the number of connections with other pathways, and the number of metabolites exchanged. Centrality is represented by the closeness centrality and the weighted and unweighted versions of betweenness centrality; i.e., distances to other pathways, and fraction of the pathways cross-talk passing through. Closeness centrality may be regarded as a measure of how long it will take in average for metabolites to spread (through successive enzymatic conversions) from a pathway to other reachable pathways in the NIP: the higher the value, the shorter time needed. Betweenness centrality is a measure of how much of the metabolite traffic in the cell goes through a given pathway. High values reveal more efficiently organized metabolic networks, with central pathways being reused in, and in control of, a multitude of metabolic processes.

We tested the null hypothesis that the values taken by these scores are not significantly different across subsets of taxa. For each score and pair of subsets a p-value was calculated (using the Fisher's exact test for the frequency score, and Mann-Whitney U-test for the scores of connectivity and centrality) together with the amplitude of variation of the score. Those p-values were corrected for multiple testing using the Benjamini-Hochberg method 31 . Finally, the median variation and p-value for pathways in the same functional category (as defined by KEGG) was extracted. The results are shown in Figure 2 and in Additional file 2. From those we made the following observations:

- Pathways related to lipid metabolism are better represented and integrated in the metabolism of multicellular eukarya than unicellular eukarya. In the case of vertebrates, this evolution certainly allowed the apparition of complex signal transduction systems based on products of lipid metabolism, like steroid hormones 32 .

- Pathways related to glycan metabolism are more frequent and more integrated in the metabolism of multicellular eukarya than unicellular eukarya. This can be explained by the importance of extra-cellular matrix, of which proteoglycans are an important structural component, for the formation of multicellular structures 33 . It also supports the importance of glycosylation as a key mechanism for cell-cell communications and interactions, as shown by the fact that nearly all membrane and extracellular proteins are glycosylated 34 . Finally, this result is consistent with some of the findings from Peregrin-Alvarez et al. 35 showing a higher conservation of glycan-related pathways in eukarya.

- Similarly, pathways related to glycan metabolism are more integrated in the metabolism of motile compared to immotile bacteria. This supports the importance of glycans as a motility factor 36 37 . Motile bacteria also have a higher integration of pathways related to the biodegradation of xenobiotics than immotile bacteria. Xenobiotics are poisons in the surrounding or inside the bacteria cell. Such metabolic capability is certainly advantageous for the motile cell, allowing it to actively colonize polluted environments with few or no competitors.

- The increase of metabolic capabilities associated to the transition from an anaerobic to aerobic lifestyle 22 essentially benefited to pathways related to lipid, amino acids and xenobiotics degradation metabolism. These pathways are also more connected and more integrated, especially so for xenobiotic degradation. This better integration certainly results from the cross-talks between many pathways that oxidative processes provide. E.g., the oxidation of amino acids and lipids to produce energy or intermediary metabolites, or the oxidation of xenobiotics 38 as exemplified by the cytochrome oxidase family.

- The decrease of NIP density observed when transitioning from free living to host-associated bacteria appears to be due in part to a significant decrease in the frequency of pathways related to carbohydrate and energy metabolism. Also, there is a general decrease of connectivity and centrality of all pathways. This is consistent with results from Henrissat et al. 39 , showing that the lack of glycogen metabolism is a trait associated with parasitic behavior in bacteria.

Finally, we report two observations, which we leave open for possible interpretation. We observed a divergence between change of centrality and connectivity for pathways related to amino acid and carbohydrate metabolism when comparing unicellular and multicellular eukarya, and pathways related to the biosynthesis of secondary metabolites when comparing prokarya and eukarya. These pathways are less directly connected to the rest of the metabolic network in the latter groups, while being more central. It means that these pathways process metabolites from and to a smaller range of neighboring pathways, while tunneling more of the overall metabolic fluxes in the cell.

Metabolic reactions for 1143 species were retrieved from January 2010 release of the KEGG database 24 using the KEGG API. All currency metabolites (except water) were kept, based on the conclusion from Mazurie et al. 23 that those common metabolites improve the capability of metabolic networks to capture the phylogeny of species. Out of these 1143 species, 1042 were selected as having completely sequenced genomes according to GOLD 3.0 40 , and a consistent metabolic pathway annotation. Consistency of pathway annotation was evaluated by comparing the number of pathways for each species to the logarithm of its number of ORFs. The resulting correlation was significant (r² of 0.66, p-value below 2.2 × 10^-16). All species with a number of pathways below average (species in the lowest 5% residuals) were filtered out. Finally, these 1042 species were clustered into 743 taxa to account for strains of the same species, subspecies, pathovars and biovars. For each of these 743 taxa, Networks of Interacting Pathways (NIPs) were reconstructed by linking overlapping metabolic pathways sharing at least one metabolite. I.e., two pathways are connected if the enzymes in the first pathway consume or produce at least one metabolite that is produced or consumed in the second pathway. The resulting links between pathways were weighted by the number of metabolites exchanged 23 .

Based on the annotations from GOLD 3.0 40 the 743 taxa were separated into the following groups: 656 prokarya (56 archaea and 600 bacteria) and 87 eukarya, 44 unicellular and 43 multicellular eukarya, 253 aerobe, 126 anaerobe and 170 facultative aerobe bacteria, 322 motile and 202 immotile bacteria, 4 halotolerant and 15 halophile bacteria, 525 free-living and 61 host-associated bacteria, and 24 psychrophile, 508 mesophile, and 61 thermophile Bacteria. All annotations are available in the Additional file 3.

Four categories of quantitative descriptors of network structure and complexity, based on the notions of degree, centrality, distance and cliques, were used to characterize the NIPs constructed to represent taxa (see Additional file 4 and associated references for details on the 52 descriptors used-25 basic and 27 derivatives). This set includes descriptors that have been successfully used in other fields 41 42 43 44 45 46 , as well as others specifically developed for the needs of our study. The latter include several weighted descriptors characterizing the intensity of cross talk between the metabolic pathways; they present a more realistic picture of network connectivity, distances, paths, and centrality at the higher organizational level of NIPs. Complete subgraphs (cliques) and their distribution were another addition to the basic topological characteristics of metabolic networks. The extensive set of network descriptors devised for this study thus enables the covering of all potentially relevant features of intracellular networks when comparing taxa. The values of these descriptors were calculated for each NIP using the NetworkX library https://networkx.lanl.gov/.

For each taxa group comparison a training set was constructed by reporting for each taxa the values taken by all 52 descriptors of its NIP together with the group it belong to. These training sets are available as Additional file 5. Supervised learning algorithms implemented in the Weka toolbox (Witten et al. 47 and Additional file 6) were applied on the training sets to predict the taxa group membership from the NIP descriptors values. A score of accuracy and Kappa statistic of the 10-fold cross-validation and that of the whole training set were calculated by comparing known and predicted membership. For a given training set, the accuracy and Kappa statistic were then taken as the highest obtained among all classification models. A high accuracy and Kappa statistic would mean the taxa group membership could be predicted from the NIP's high-level organization of metabolic networks. The smallest subset of NIP descriptors that still performs as well as the complete set of 52 was identified using feature selection algorithms 48 49 and a heuristic evaluation of subsets of descriptors on the classification models identified earlier as the best ones. A tool, MetaClassify, was developed to automate the training of the classification models and to retrieve the results http://oenone.net/tools/.