Estimation of metabolic flux from dominant rate constants in vivo: application to brain and heart

In an earlier paper (Cohen and Bergman, Am. J. Physiol. 268 (1995) E397), we explored the relationship between the exponents in the exponential curve fit to isotopic enrichment versus time and the fractional turnover rate of the largest metabolic pool in the pathway. Here we present the analysis on a more rigorous footing and apply it to questions of cerebral and cardiac metabolism. Our emphasis in this paper is to describe and justify mathematically an approach for analysis of metabolic dynamics, not with the intention of replacing the use of numerical software for estimation of flux rates but for giving the scientist the opportunity to examine the system in an approximate manner, and thereby to check not only that the results of the numerical solution are the correct solutions to the equations but also that the equations portray the correct simplification of the metabolic pathway. We introduce the "dominant rate constant" as a tool for deriving algebraic formulas relating rates of metabolic flux, sizes of metabolic pools, and the dynamics of isotopic enrichment. Illustrations of such algebraic formulas are provided for the rates of the citric acid cycle (CAC), glycolysis and glutamine synthesis in brain, as well as the rate of the CAC in heart. In addition, we prove that formulas for estimation of rates of glycolysis and of the CAC depend critically on the fractional turnover rates of lactate and glutamate, respectively. The justification for analysis of simulated data is that we are studying the effects of simplifications of metabolic models on the accuracy of estimation of metabolic pathways. Our use of the dominant rate constant is an analytical convenience that allows us to assess proposed simplifications of metabolic pathways. (C) 2003 Elsevier Inc. All rights reserved.