Non-steady state model applicable to NMR studies for calculating flux rates in glycolysis, gluconeogenesis, and citric acid cycle

We present a mathematical model for calculating most reaction rates of glycolysis, gluconeogenesis and citric acid cycle in mammalian cells. The model also includes cycles such as the "phosphoenolpyruvate (PEP)-->pyruvate-->oxaloacetate-->PEP" cycle and the "pyruvate-->acetyl-CoA-->citrate-->citric acid cycle-->oxaloacetate-->PEP--> pyruvate" cycle. The model, which does not require steady state conditions, is based on a set of equations, each one describing the fates of a given carbon of a selected intermediate. These fates are expressed as ratios of integrated transfer of this carbon to corresponding carbons in subsequent metabolites. At each bifurcation, the sum of all proportions adds up to 1. Among several calculation routes to determine a proportion value, we chose the one that was based on the most reliable parameter determined experimentally. The data introduced in the model are the micrograms of atom of traced carbon measured on each carbon of a number of products (corrected for natural tracer abundance). These incorporations can be measured by 13C NMR, gas chromatography-mass spectroscopy, or 14C counting. Thanks to its flexibility, this model can be applied to data obtained with substrates other than glucose under many experimental conditions.