Isotopomer subspaces as indicators of metabolic-pathway structure

The relative abundances and rates of formation of particular isotopic isomers (isotopomers) of metabolic intermediates from (13)C-labelled substrates in living cells provide information on the routes taken by the initial (13)C-atoms. When a primary substrate such as [U,(13)C] d-glucose is added to human erythrocytes, the pattern of labels in terminal metabolites is determined by a set of carbon-group exchange reactions in both glycolysis and the pentose phosphate pathway (PPP). Of a given terminal metabolite, not all possible isotopomers will be produced from each possible primary substrate isotopomer. There are only 8 different (13)C-isotopomers of lactate but not all of these are produced when one of the 64 possible (13)C-isotopomers of glucose is used as the input substrate; thus a subset of all 63 glucose isotopomers x 8 lactate isotopomers+1 unlabelled glucose x 1 unlabelled lactate=505 pattern associations, would be produced if a complete experimental analysis were performed with all the glucose variants. The pattern of labelling in this isotopomer subspace reflects the nature of the re-ordering reactions that 'direct' the metabolism. Predicting the combinatorial rearrangements for particular sets of reactions and comparing these with real data should enable conclusions to be drawn about which enzymes are involved in the real metabolic system. An example of the glycolysis-PPP system is discussed in the context of a debate that occurred around the F- and L-type PPPs and which one actually operates in the human RBC. As part of this discussion we introduce the term 'combinatorial deficit' of all possible isotopomers and we show that this deficit is less for the F- than the L-type pathway.