Algebraic comparison of metabolic networks, phylogenetic inference, and metabolic innovation

Abstract

Background: Comparison of metabolic networks is typically performed based on the organisms' enzyme contents. This approach disregards functional replacements as well as orthologies that are misannotated. Direct comparison of the structure of metabolic networks can circumvent these problems.

Results: Metabolic networks are naturally represented as directed hypergraphs in such a way that metabolites are nodes and enzyme-catalyzed reactions form (hyper)edges. The familiar operations from set algebra (union, intersection, and difference) form a natural basis for both the pairwise comparison of networks and identification of distinct metabolic features of a set of algorithms. We report here on an implementation of this approach and its application to the procaryotes.

Conclusion: We demonstrate that metabolic networks contain valuable phylogenetic information by comparing phylogenies obtained from network comparisons with 16S RNA phylogenies. The algebraic approach to metabolic networks is suitable to study metabolic innovations in two sets of organisms, free living microbes and Pyrococci, as well as obligate intracellular pathogens.

Figure 1

Graphical representation of the basic binary operations of the network algebra. Diagrams (A) and (B) summarize the citric-acid cycle of P. horikoshii and H. pylori [31]. Hypergraphs can always be drawn as bipartite graphs with one class of vertices representing the hypergraph vertices (chemical species, ●), while the other class of vertices encodes the hyperedges (chemical reactions, ■). Each reaction is connected by (directed) arrows from its educts and to its products. For clarity of presentation we have omitted the direction of the arrows (most reactions are reversible) as well as small molecules such as CO₂ and H₂O here. Furthermore, two reactions are marked in color, namely the ones catalyzed by citrate synthase in red, and pyruvate dehydrogenase in green. The results of the basic operations are as follows: (a) Intersection A ∩ B; (b) Union A ∪ B; (c) Symmetric Difference A △ B; (d) Strict Symmetric Difference A ◊ B; (e) Difference A \ B; (f) Difference B \ A.

Figure 2

Unrooted phylogenies. (top) Maximum parsimony tree of 16S rRNA sequences. (center) Phy-logenetic tree calculated from metabolic network data using the Fitch algorithm for distance matrices. (bottom) Phylogenetic tree calculated from metabolic network data using Splits decomposition with the Fitch-Margoliash power 2 fit for distance matrices. Species abbreviations are collected in Table 1.

Figure 3

(top) The Pyrococcus spp. clade has been selected (dashed oval) for differential network analysis. (bottom) Differential metabolic network. Numbers in the ovals refer to reaction ids in the KEGG database.

Figure 4

Unrooted network phylogeny using PHYLIP with the Fitch-Margoliash algorithm. A set of obligatory intracellular pathogens has been selected (dashed oval) for differential network analysis (see text).

Figure 5

Differential network corresponding the split shown in Figure 4. These reactions are specializations of the intracellular parasites.