Atomic elementary flux modes explain the steady state flow of metabolites in large-scale flux networks

Steady state fluxes are a measure of cellular activity under homeostatic conditions, but understanding how individual substrates are metabolized remains a challenge in large-scale networks. Pathway-based approaches such as elementary flux mode (EFM) analysis are limited to small networks due to the combinatorial explosion of pathways and ambiguity of decomposing fluxes onto EFMs. Here, we present an alternative approach explaining metabolic fluxes in terms of the steady state flow of their atomic constituents. We refer to these pathways as atomic elementary flux modes (AEFMs) and show that computations involving AEFMs are orders of magnitude faster than standard EFMs. Using our approach, we enumerate carbon and nitrogen AEFMs in five genome-scale metabolic models and compute the AEFM decomposition of fluxes estimated in a HepG2 liver cancer cell line. Our results systematically characterize carbon and nitrogen remodeling and, on the HepG2 network, predict glutamine metabolism through a recently discovered non-canonical tricarboxylic acid (TCA) cycle.