Hierarchical modularity of nested bow-ties in metabolic networks

Abstract

Background: The exploration of the structural topology and the organizing principles of genome-based large-scale metabolic networks is essential for studying possible relations between structure and functionality of metabolic networks. Topological analysis of graph models has often been applied to study the structural characteristics of complex metabolic networks.

Results: In this work, metabolic networks of 75 organisms were investigated from a topological point of view. Network decomposition of three microbes (Escherichia coli, Aeropyrum pernix and Saccharomyces cerevisiae) shows that almost all of the sub-networks exhibit a highly modularized bow-tie topological pattern similar to that of the global metabolic networks. Moreover, these small bow-ties are hierarchically nested into larger ones and collectively integrated into a large metabolic network, and important features of this modularity are not observed in the random shuffled network. In addition, such a bow-tie pattern appears to be present in certain chemically isolated functional modules and spatially separated modules including carbohydrate metabolism, cytosol and mitochondrion respectively.

Conclusion: The highly modularized bow-tie pattern is present at different levels and scales, and in different chemical and spatial modules of metabolic networks, which is likely the result of the evolutionary process rather than a random accident. Identification and analysis of such a pattern is helpful for understanding the design principles and facilitate the modelling of metabolic networks.

Figure 1

The hierarchical clustering tree for the Core of the GSC for the E.coli network. See Additional file 2 for metabolite abbreviations of the E.coli network.

Figure 2

Decomposition of the Core for the GSC of the E.coli metabolic network. This graph is drawn with the graph analysis software Pajek [39]. The nodes included in the biggest strongly connected component of each cluster are shown in red colour.

Figure 3

Decomposition of the E.coli metabolic network by expanding the clustering of the Core. Triangles correspond to the nodes of the Core. The four parts (GSC, S, P, IS) of bow-tie structure for the modules are shown in distinct colours.

Figure 4

Cartographic representation of the metabolic network for E.coli. Each circle represents a module and is coloured according to the KEGG pathway classification of the reactions belonging to it, while the arcs reflect the connection between clusters. The area of each colour in one circle is proportional to the number of reactions that belong to the corresponding metabolism. The width of an arc is proportional to the number of reactions between the two corresponding modules. For simplicity, bi-directed arcs are presented by grey edges.

Figure 5

Bio-reactions in the 3^rd module and the connection to other modules. Each node represents a metabolite and is coloured according to the class of metabolism it participates in. This module contains the majority of metabolites from TCA cycle with glyoxylate bypass, in which the reactions are highlighted by red arcs. Nodes from other modules that link with module 3 are shown by triangles, with module serial number shown in the parentheses. The metabolite abbreviations are listed in Additional file 2.

Figure 6

Distribution of the 12 precursors in the 12 modules of the E.coli metabolic network. The three major pathways – Embden-Meyerhof-Parnas (EMP), tricarboxylic acid (TCA) and pentose phosphate pathway (PPP) for the generation of the 12 precursors are outlined.

Figure 7

Corresponding sub-tree and bow-tie structure of module 3. (A) Sub-tree of module 3 (B) Bow-tie structure ofmodule 3 Each branch of the sub-tree corresponds to a red node in module 3, while the pink node titled "OASUC" also has parallelism in the sub-tree because it is included in the Core of E.coli network. These nodes were resulted from the decomposition of the Core. Then by the "majority role" the Core clusters were expanded to the whole network, the pink (other than "OASUC"), green, and blue nodes were assigned to cluster 3. The metabolite abbreviations are listed in Additional file 2.

Figure 8

The connections among the GSC parts of the twelve bow-tie like modules. The width of an arc is proportional to the number of links between the GSC parts of the two corresponding modules. For simplicity, bi-directed arcs are presented by grey edges.

Figure 9

Comparison of the Core of E.coli network with that of a randomized network. (A) 12 clusters of the Core for E.coli network (B) 12 clusters of the Core for a randomized network Both of the Cores are decomposed by our algorithm. Different clusters are shown in different colours. These two networks include 163 and 227 nodes respectively. The network in (A) and the decomposition result is just the same as that in Figure 2. The network in (B) is the Core of the 51^st network in Table S4 of Additional file 1.