Conserved moiety fluxomics

Fluxomics seeks to infer reaction fluxes at genome-scale by introducing isotopically labelled metabolites into a living system and measuring the enrichment of isotopic tracers in downstream metabolites. This approach has the potential to quantify fluxes at genome-scale but current approaches to infer steady-state metabolic reaction fluxes are either not tractable or not efficient at genome-scale as the corresponding computational models are high-dimensional, involve nonlinear constraints and lack mathematical guarantees of convergence to a global optimum. Herein, we introduce conserved moiety fluxomics, which is a novel, efficient, mathematically transparent, and computationally efficient method to infer metabolic reaction flux at genome-scale. We demonstrate how identification of the set of conserved moieties for a given metabolic network leads to a novel moiety graph decomposition of a stoichiometric matrix that can be used to linearly relate metabolic reaction fluxes to the rate at which conserved moieties transition between metabolites. This linear formulation avoids combinatorial explosion because the number of conserved moieties is bounded, most reactions correspond to a small number of conserved moiety transitions, it is sufficient to represent the flow of moieties that have the potential to be labelled, and it is sufficient to represent constraints from those isotopologues that are actually measured. A non-linear yet strictly convex objective is used to ensure that inferred fluxes satisfy energy conservation and the second law of thermodynamics. Numerical results demonstrate the computational tractability of conserved moiety fluxomics at genome-scale, given liquid chromatography-mass spectrometry derived stationary mass isotopologue distribution data from an in vitro dopaminergic neuronal culture fed 13 C labelled glucose. Conserved moiety fluxomics unites the strengths of constraint-based modelling and metabolic flux analysis and has the potential to be further enhanced to enable inference of fluxes in whole-body metabolic models, including from non-stationary isotopic labelling data.