Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.Author Summary: Conserved moieties are transferred between metabolites in internal reactions of a metabolic network but are not synthesised, degraded or exchanged with the environment. The total amount of a conserved moiety in the metabolic network is therefore constant over time. Metabolites that share a conserved moiety have interdependent concentrations because their total amount is constant. Identification of conserved moieties results in a concise description of all concentration dependencies in a metabolic network. The problem of identifying conserved moieties has previously been formulated in terms of the stoichiometry of metabolic reactions. Methods based on this formulation are computationally intractable for large networks. We show that reaction stoichiometry alone gives insufficient information to identify conserved moieties. By first incorporating additional data on the fate of atoms in metabolic reactions, we developed and implemented a computationally tractable algorithm to identify conserved moieties and their atomic structure.