Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems

The last few years have brought tremendous progress in experimental methods for metabolic flux determination by carbon-labeling experiments. A significant enlargement of the available measurement data set has been achieved, especially when isotopomer fractions within intracellular metabolite pools are quantitated. This information can be used to improve the statistical quality of flux estimates. Furthermore, several assumptions on bidirectional intracellular reaction steps that were hitherto indispensable may now become obsolete. To make full use of the complete measurement information a general mathematical model for isotopomer systems is established in this contribution. Then, by introducing the important new concept of cumomers and cumomer fractions, it is shown that the arising nonlinear isotopomer balance equations can be solved analytically in all cases. In particular, the solution of the metabolite flux balances and the positional carbon-labeling balances presented in part I of this series turn out to be just the first two steps of the general solution procedure for isotopomer balances. A detailed analysis of the isotopomer network structure then opens up new insights into the intrinsic structure of isotopomer systems. In particular, it turns out that isotopomer systems are not as complex as they appear at first glance. This enables some far-reaching conclusions to be drawn on the information potential of isotopomer experiments with respect to flux identification. Finally, some illustrative examples are examined to show that an information increase is not guaranteed when isotopomer measurements are used in addition to positional enrichment data.