Application of Graph Theory to Evaluate Chemical Reactions in Cells

Chemical reactions occur in cells for survival and adaptation to various conditions. After these chemical reactions, the reactants and products are often sequentially modified through metabolic pathways. In this study, we defined new features to evaluate the possibility of such inferred metabolic pathways. We focused on the main chain structure of a compound as a non-directional graph, and developed a method to define the similarity between these main chain structure graphs. In this study, we defined four features: 1) the number of main chain graph nodes, 2) the graphical density of the main chain graph, 3) the chemical density of the main chain, and 4) the graph centrality of the reaction group in the main chain graph. We defined the main chain structures of about 16,000 chemical compounds, and calculated the values of the four features by the defined equations for each compound. Finally, we calculated the correlation coefficients between all chemical compound pairs from the four defined features. A comparison of the similarities of the main chain graphs between known chemical reactions revealed that our defined features are suitable for detecting the possible reactions.