Bidirectional reaction steps in metabolic networks: III. Explicit solutionand 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 signifi cant enlargement of the available measurement data set has been achieved, e specially when isotopomer fractions within intracellular metabolite pools a re quantitated. This information can be used to improve the statistical qua lity of flux estimates. Furthermore, several assumptions on bidirectional i ntracellular reaction steps that were hitherto indispensable may now become obsolete. To make full use of the complete measurement information a gener al mathematical model for isotopomer systems is established in this contrib ution. Then, by introducing the important new concept of cumomers and cumom er fractions, it is shown that the arising nonlinear isotopomer balance equ ations can be solved analytically in all cases. In particular, the solution of the metabolite flux balances and the positional carbon-labeling balance s presented in part I of this series turn out to be just the first two step s of the general solution procedure for isotopomer balances. A detailed ana lysis of the isotopomer network structure then opens up new insights into t he intrinsic structure of isotopomer systems. In particular, it turns out t hat isotopomer systems are not as complex as they appear at first glance. T his enables some far-reaching conclusions to be drawn on the information po tential of isotopomer experiments with respect to flux identification. Fina lly, some illustrative examples are examined to show that an information in crease is not guaranteed when isotopomer measurements are used in addition to positional enrichment data. (C) 1999 John Wiley & Sons, Inc.