Quantifying and assessing the effect of chemical symmetry in metabolic pathways

Atom tracing provides valuable information in many analyses of metabolic networks including pathway inference and flux estimation. Symmetries-mapping operations that produce atom equivalencies-introduce alternative tracings when multiple atom mappings are aggregated. Although several attempts have been made to consider symmetry while curating atom mappings, a definition of the symmetry amenable to automated computation and a systematic quantification of the extent of symmetries in both compounds and reactions is still lacking. Moreover, the impact of symmetries on the calculation of the atom economy of pathways and the simulation of isotopomer distribution is yet to be assessed. In this study, we formulate the symmetries of both compounds and reactions as automorphic mappings of the corresponding graph representations. We investigate the extent of both compound and reaction symmetries in several metabolic systems. We find, through random walking in the metabolic network of E.coli , that alternative tracings originated from symmetries could give rise to considerable amount of differential conservation of atoms and distinct transition patterns of the isotopomer distribution.