Centrality, network capacity, and modularity as parameters to analyze the core-periphery structure in metabolic networks

Genome-scale metabolic networks of organisms are normally very large and complex. Previous studies have shown that they are organized in a hierarchical and modular manner. In particular, a core-periphery modular organization structure has been proposed for metabolic networks. However, no methods or parameters are available in the literature to quantitatively evaluate or find the hierarchical and modular structure of metabolic networks. in this paper, we propose a parameter called core coefficient to quantitatively evaluate the core-periphery structure of a metabolic network. This parameter is defined based on the concept of closeness centrality of metabolites and a newly defined parameter: network capacity. To find or define the core and the periphery modules of a metabolic network, we further developed a method to decompose metabolic networks based on a quantitative parameter of modularity and a procedure of core extraction. The method has been developed with genome-scale metabolic networks of five representative organisms, which include Aeropyrum pernix, Bacillus subtilis, Escherichia coli, Saccharomyces cerevisiae, and Homo sapiens. The results were compared with two artificially generated network models.