Modular co-evolution of metabolic networks

Abstract

Background: The architecture of biological networks has been reported to exhibit high level of modularity, and to some extent, topological modules of networks overlap with known functional modules. However, how the modular topology of the molecular network affects the evolution of its member proteins remains unclear.

Results: In this work, the functional and evolutionary modularity of Homo sapiens (H. sapiens) metabolic network were investigated from a topological point of view. Network decomposition shows that the metabolic network is organized in a highly modular core-periphery way, in which the core modules are tightly linked together and perform basic metabolism functions, whereas the periphery modules only interact with few modules and accomplish relatively independent and specialized functions. Moreover, over half of the modules exhibit co-evolutionary feature and belong to specific evolutionary ages. Peripheral modules tend to evolve more cohesively and faster than core modules do.

Conclusion: The correlation between functional, evolutionary and topological modularity suggests that the evolutionary history and functional requirements of metabolic systems have been imprinted in the architecture of metabolic networks. Such systems level analysis could demonstrate how the evolution of genes may be placed in a genome-scale network context, giving a novel perspective on molecular evolution.

Figure 1

Cartographic representation of the metabolic network for H. sapiens. 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. The modularity metric of this decomposition is 0.8868.

Figure 2

The distribution of Jaccard coefficient (JC) for enzyme pairs in the global metabolic network and its modules. (A) The distribution of JC for all pairwise enzymes in the H. sapiens metabolic network. (B) The relationship between the average JC for enzyme pairs in modules and the inter-module degree of module.

Figure 3

Comparison of the similar extent of phylogenetic profiles for enzyme pairs within each module with that within the global metabolic network of H. sapiens. (A) Average JC of enzyme pairs within modules. The red column represents the global network. The modules are ordered according to their average JC in a decreasing way. (B) Percentage of enzyme pairs within modules with JC ≥ 0.66 (threshold definition). The red column represents the global network. The modules are drawn in the same order as in (A).

Figure 4

Relationship between evolutionary age of modules and average inter-module degrees.

Figure 5

Relationship between average evolutionary rate of enzyme genes within modules and inter-module degrees. (A) The average evolutionary rate of module is negative correlation with the inter-module degree. (B) Core modules (inter-module degree > 5) are evolutionarily constrained at higher extent than periphery modules (inter-module degree ≤ 5) do.

Figure 6

Decomposition of one randomized network of the H. sapiens network, shown as a network of modules. Each circle represents a module, while the arcs reflect the connection between clusters. The width of an arc is proportional to the number of links between the two corresponding modules. For simplicity, bi-directed arcs are presented by grey edges. The modularity metric of this decomposition is 0.7845.

Figure 7

Accuracy of simulated annealing algorithm to identify topological modules. We obtain 30 independent decompositions of the H. sapiens metabolic network and plot the fraction of times that each pair of nodes is clustered into the same module.