Here we present a novel framework for the modeling of isotopic tracer systems that significantly reduces the number of system variables without any loss of information. The EMU framework is based on a highly efficient decomposition method that identifies the minimum amount of information needed to simulate isotopic labeling within a reaction network using the knowledge of atomic transitions occurring in the network reactions. The functional units generated by the decomposition algorithm, called elementary metabolite units (EMUs), form the new basis for generating system equations that describe the relationship between fluxes and isotopomer abundances. The decomposition algorithm is completely unsupervised and converges within seconds even for very large network models. Isotopomer abundances simulated using the EMU framework are identical to those obtained using the isotopomer and cumomer frameworks, however, requiring significantly less computation time. For a typical carbon labeling system the total number of equations that needs to be solved is reduced by one order-of-magnitude (100s EMUs vs. 1000s cumomers). As such, the EMU framework is most efficient for the analysis of labeling by multiple isotopic tracers. For example, the analysis of gluconeogenesis network model with 2H and 13C tracers requires only 300 EMUs compared to >3e4 cumomers.
The power of the EMU framework will be illustrated by a detailed analysis of the gluconeogenesis pathway in cultured primary hepatocytes probed by 2H and 13C labeled substrates using measurements of mass isotopomer labeling patterns of glucose, the main product of gluconeogenesis. We show that 13C and 2H-tracers provide unique flux information about this metabolic network. Specifically, for the first time, we have estimated net and reversible fluxes in the gluconeogenesis pathways in vivo through the application of a novel, custom-synthesized isotopic tracer [U-13C3,2H5]glycerol. Our results indicate that (i) gluconeogenesis contributes 50+-2% to glucose production in hepatocytes isolated from fed mice, and 90+-2% in hepatocytes isolated from overnight fasted mice, (ii) PGI reaction is at 70+-5% equilibrium (commonly believed to be at 100% equilibrium), (iii) transketolase and transaldolase fluxes are small, i.e. <10% of gluconeogenesis flux, (iv) glycerol is a good gluconeogenic precursor, contributing ~30% to glucose production. It is important to note that these results could not have been obtained with the conventional isotopomer/cumomer methods, due to the very large number of cumomers (>3e4) which cannot be simulated efficiently.