Substance graphs are optimal simple-graph representations of metabolism

One approach to study the system-wide organization of biochemistry is to use statistical graph theory. In such heavily simplified methods, which disregard most of the dynamic aspects of biochemistry, one is faced with fundamental questions. One such question is how the chemical reaction systems should be reduced to a graph retaining as much functional information as possible from the original reaction system. In these graph representations, should the edges go between substrates and products, or substrates and substrates, or both? Should vertices represent substances or reactions? Different representations encode different information about the reaction system and affect network measures in different ways. This paper investigates which representation reflects the functional organization of the metabolic system in the best way, according to the defined criteria. Four different graph representations of metabolism (three where the vertices are metabolites, one where the vertices are reactions) are evaluated using data from different organisms and databases. The graph representations are evaluated by comparing the overlap between clusters (network modules) and annotated functions, and also by comparing the set of identified currency metabolites with those that other authors have identified using qualitative biological arguments. It is found that a “substance network”, where all metabolites participating in a reaction are connected, is better than others, evaluated with respect to both the functional overlap between modules and functions and to the number and identity of the identified currency metabolites.