Mathematical Model for Evaluating the Krebs Cycle Flux with Non‐Constant Glutamate‐Pool Size by 13C‐NMR Spectroscopy

A practical method using matrix operations is proposed for studying the isotopic transformation of glutamate, or any other metabolite isotopomers, in the Krebs cycle. Two mathematical models were constructed for evaluating the Krebs cycle flux where the enrichment of [2-13C]acetyl-CoA is not 100% and the total glutamate concentration remains constant or varies during incubation. A comparative study of [1-13C]glucose metabolism was subsequently carried out using Saccharumyces cerevisiae cells from two different strains (ATCC-9763 and NCYC-239) by 13C-NMR spectroscopy and biochemical techniques. The results show that there are two types of Krebs cycles in cells. The first is represented by the ATCC cells which contain a small amount of 2-oxoglutarate dehydrogenase and hence the flux in the Krebs cycle is negligible. With [1-13C]glucose as a carbon source, the 13C-NMR spectra of glutamate exhibit the C2 and C4 resonances that are almost equivalent and much greater than that of the C3. Labeled metabolites derived from [1-13C]glucose enter the Krebs cycle at two points: oxaloacetate and citrate. The second cell type is represented by NCYC-239. The C2 and C3 areas are equivalent and smaller than the C4 resonance. The results suggest that labeled metabolites enter the Krebs cycle only at the citrate level via acetyl-CoA, 2-oxoglutarate dehydrogenase is present but pyruvate carboxylase is virtually absent or inactivated. When both are incubated with glucose, the total concentration of glutamate was found to decrease with the incubation time. The fraction of glutamate in isotopic exchange with the Krebs cycle in NCYC-239 cells is about 2.6% and the reduction in glutamate concentration is about 0.5%/min. Using our model, with a variable glutamate pool size, good agreement between the theoretical and experimental data is obtained.