Robust structure measures of metabolic networks that predict prokaryotic optimal growth temperature.

BACKGROUND: Metabolic networks reflect the relationships between metabolites (biomolecules) and the enzymes (proteins), and are of particular interest since they describe all chemical reactions of an organism. The metabolic networks are constructed from the genome sequence of an organism, and the graphs can be used to study fluxes through the reactions, or to relate the graph structure to environmental characteristics and phenotypes. About ten years ago, Takemoto et al. (2007) stated that the structure of prokaryotic metabolic networks represented as undirected graphs, is correlated to their living environment. Although metabolic networks are naturally directed graphs, they are still usually analysed as undirected graphs. RESULTS: We implemented a pipeline to reconstruct metabolic networks from genome data and confirmed some of the results of Takemoto et al. (2007) with today data using up-to-date databases. However, Takemoto et al. (2007) used only a fraction of all available enzymes from the genome and taking into account all the enzymes we fail to reproduce the main results. Therefore, we introduce three robust measures on directed representations of graphs, which lead to similar results regardless of the method of network reconstruction. We show that the size of the largest strongly connected component, the flow hierarchy and the Laplacian spectrum are strongly correlated to the environmental conditions. CONCLUSIONS: We found a significant negative correlation between the size of the largest strongly connected component (a cycle) and the optimal growth temperature of the considered prokaryotes. This relationship holds true for the spectrum, high temperature being associated with lower eigenvalues. The hierarchy flow shows a negative correlation with optimal growth temperature. This suggests that the dynamical properties of the network are dependant on environmental factors.

Functional prediction of environmental variables using metabolic networks.

In this manuscript, we propose a novel approach to assess relationships between environment and metabolic networks. We used a comprehensive dataset of more than 5000 prokaryotic species from which we derived the metabolic networks. We compute the scope from the reconstructed graphs, which is the set of all metabolites and reactions that can potentially be synthesized when provided with external metabolites. We show using machine learning techniques that the scope is an excellent predictor of taxonomic and environmental variables, namely growth temperature, oxygen tolerance, and habitat. In the literature, metabolites and pathways are rarely used to discriminate species. We make use of the scope underlying structure-metabolites and pathways-to construct the predictive models, giving additional information on the important metabolic pathways needed to discriminate the species, which is often absent in other metabolic network properties. For example, in the particular case of growth temperature, glutathione biosynthesis pathways are specific to species growing in cold environments, whereas tungsten metabolism is specific to species in warm environments, as was hinted in current literature. From a machine learning perspective, the scope is able to reduce the dimension of our data, and can thus be considered as an interpretable graph embedding.