Visualization of Metabolic Networks as Networks of Atoms by Pajek: An Application of Connectivity Matrix Method

Many studies have been conducted about the global topological nature of metabolic networks since the report by Barabasi's group [3]. Topological nature of networks depends on the definition of nodes and edges/arcs. In most of such studies, metabolites are assumed as nodes either in the studies conducted with or without the care of atomic tracing [1,3,4,5]. This is acceptable because the main function of metabolism is consumption and production of metabolites. However, it should be noted that the definition of the edges varied depending on the researches. On the other hand, instead of metabolites, atoms can be assumed as nodes, where metabolic networks are defined by inter-metabolite atom-level connectivity through enzymatic reactions and by intra-metabolite atom-level connectivity through chemical bonds without variation of the edge definition [6,7]. Understanding metabolic networks as networks of atoms seems to have certain value because it provides an insight about evolution of metabolic networks, that is, co-evolution of interand intra-metabolite atom-level connectivities corresponding to evolutional emergences of new compounds associated with those of new reactions. Possible correlation between 2 types of connectivities seems to deserve investigation. Connectivity matrix method [6] has been proposed for analyses of biological networks, where all the connectivities of interest in a given network are expressed in a matrix, connectivity matrix, and then a variety of analyses can be conducted on Octave or Matlab using functions or script files written by researchers. Whereas calculation of topological indices based on connectivity matrix would produce valuable information about network structure, graphical representation of the network makes it easy to understand the nature of the network. In the present study, both interand intra-metabolite connectivities in a model network of carbohydrate metabolism were expressed in a connectivity matrix. Then, based on this matrix, the file for Pajek [9] was generated and the atom network structure was visualized.