Mathematical analysis of isotope labeling in the citric acid cycle with applications to 13C NMR studies in perfused rat hearts.

Rat hearts have been perfused in vitro with 5 mM glucose and either 5 mM acetate or 1 mM pyruvate to achieve steady state conditions, followed by replacement of the acetate with 90% enriched [2-13C]acetate or pyruvate with 90% enriched [3-13C]pyruvate. The hearts were frozen different times after addition of 13C-substrate and neutralized perchloric acid extracts from three pooled hearts per time point were used to obtain high resolution proton-decoupled 13C NMR spectra at 90.55 MHz. The 13C fractional enrichment of individual carbons of different metabolites was calculated from the area of the resolved resonances after correction for nuclear Overhauser enhancement and saturation effects. A mathematical flux model of the citric acid cycle and ancillary transamination reactions was constructed with the FACSIMILE program, and used to solve unknown flux parameters with constant pool sizes by nonlinear least squares analysis of the approximately 200 simultaneous differential equations required to describe the reactions. With [2-13C] acetate as substrate, resonances and line splittings due to 13C-13C spin coupling of the C-2, C-3, and C-4 carbons of glutamate were well resolved. The half-times to reach maximum 13C enrichment were 2.6 min for glutamate C-4 and 8 min for glutamate C-2 and C-3. From these data, a well determined citric acid cycle flux of 8.3 mumol/g dry weight X min was calculated for an observed oxygen consumption of 31 mumol/g dry weight X min. With [3-13C]pyruvate as substrate, resonances of aspartate C-2 and C-3 and of alanine C-3 were well resolved in addition to those of glutamate C-2, C-3, and C-4. Nonlinear least squares fitting of these data to the model gave nonrandomly distributed residuals for the 13C fractional enrichments of glutamate C-4, suggesting an incomplete model, but a well determined cycle flux of 11.9 mumol/g dry weight X min for an oxygen uptake of 35 mumol/g dry weight X min. Our studies demonstrate the practicality of 13C NMR, used in conjunction with mathematical modeling, for the measurement of metabolic flux parameters in living systems.