Bidirectional reaction steps in metabolic networks: IV. Optimal design of isotopomer labeling experiments.

This article generalizes the statistical tools for the evaluation of carbon-labeling experiments that have been developed for the case of positional enrichment systems in part II of this series to the general case of isotopomer systems. For this purpose, a new generalized measurement equation is introduced that can describe all kinds of measured data, like positional enrichments, relative (13)C nuclear magnetic resonance ((13)C NMR) multiplet intensities, or mass isotopomer fractions produced with mass spectroscopy (MS) instruments. Then, to facilitate the specification of the various measurement procedures available, a new flexible textual notation is introduced from which the complicated generalized measurement equations are generated automatically. Based on these measurement equations, a statistically optimal flux estimator is established and parameter covariance matrices for the flux estimation are computed. Having implemented these tools, different kinds of labeling experiments can be compared by using statistical quality measures. A general framework for the optimal design of carbon-labeling experiments is established on the basis of this method. As an example it is applied to the Corynebacterium network from part II extended by various NMR and MS measurements. In particular, the positional enrichment, multiplet, or mass isotopomer measurements with the greatest information content for flux estimation are computed (measurement design) and various differently labeled input substrates are compared with respect to flux estimation (input design). It is examined in detail how the measurement procedure influences the estimation quality of specific fluxes like the pentose phosphate pathway influx.