Weiss et al. (Circ. Res. 70: 392-408, 1992) proposed a model of the citric acid cycle (CAC) in myocytes and a system of 17 differential equations that can be used to describe the changes over time in enrichment of carbons C-2 and C-4 of glutamate under conditions of metabolic steady state. They also proposed an empirical measure (KT) of flux through the CAC, which has been shown to be correlated to O2 consumption in rat hearts perfused with acetate or a mixture of glucose and acetate. We report a new method for estimation of the absolute rate of the flux through the CAC in heart (vTCA), without the numerical solution of differential equations. Unlike KT, our estimate is equal to the rate of flux catalyzed by the alpha-ketoglutarate dehydrogenase complex (vTCA), not merely correlated with it. We also estimate the rate of flux catalyzed by aspartate aminotransferase (vTA) and by NADP(+)-dependent malic enzyme (an anaplerotic reaction). The formula for vTCA during administration of [2-13C]acetate is as follows: vTCA = M[(C-2ssLC-4)/[C-4ss(LC-4-LC-2)]], where C-2ss and C-4ss represent steady-state fractional enrichment, LC-2 and LC-4 represent dominant rate constants of C-2 and C-4 of glutamate, respectively, and M is the sum of concentrations of aspartate, glutamate, and intermediates of the CAC. The assumptions underlying our formula are as follows: 1) metabolic steady state is maintained, 2) exchange of molecules between cytosolic and mitochondrial compartments is rapid, 3) 13C enters pools of the CAC only from acetyl CoA via citrate synthase, 4) [citrate]/[glutamate] < 1 + (vTCA/vTA), and 5) (m-[glutamate])/M < C-2ss/C-4ss.
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