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The C 3 -C 4 metabolite interconversion at the anaplerotic node in many microorganisms involves a complex set of reactions. C 3 carboxylation to oxaloacetate can originate from phosphoenolpyruvate and pyruvate, and at the same time multiple C 4 -decarboxylating enzymes may be present. The functions of such parallel reactions are not yet fully understood. Using a 13 C NMR-based strategy, we here quantify the individual fluxes at the anaplerotic node of Corynebacterium glutamicum, which is an example of a bacterium possessing multiple carboxylation and decarboxylation reactions. C. glutamicum was grown with a 13 C-labeled glucose isotopomer mixture as the main carbon source and 13 C-labeled lactate as a cosubstrate. 58 isotopomers as well as 15 positional labels of biomass compounds were quantified. Applying a generally applicable mathematical model to include metabolite mass and carbon labeling balances, it is shown that pyruvate carboxylase contributed 91 ؎ 7% to C 3 carboxylation. The total in vivo carboxylation rate of 1.28 ؎ 0.14 mmol/g dry weight/h exceeds the demand of carboxylated metabolites for biosyntheses 3-fold. Excess oxaloacetate was recycled to phosphoenolpyruvate by phosphoenolpyruvate carboxykinase. This shows that the reactions at the anaplerotic node might serve additional purposes other than only providing C 4 metabolites for biosynthesis.The interconversions between the C 3 metabolism and the C 4 metabolites of the tricarboxylic acid cycle function either as a replenishment of tricarboxylic acid cycle intermediates (anaplerosis) or as the initial steps of gluconeogenesis. These carboxylation and decarboxylation reactions are catalyzed by a number of enzymes (1, 2). Synthesis of oxaloacetate via carboxylation of C 3 metabolites may be catalyzed by phosphoenolpyruvate (PEP) 1 carboxylase, PEP carboxytransphosphorylase, or pyruvate carboxylase. The reverse reaction, decarboxylation of oxaloacetate, may analogously lead to PEP or pyruvate, catalyzed by PEP carboxykinase or oxaloacetate decarboxylase, respectively. NAD ϩ -or NADP ϩ -dependent malic enzyme catalyzes the reaction from malate to pyruvate. In some organisms, this enzyme is also thought to act in a pyruvate-carboxylating sense (3).To date, a full understanding of these enzymatic reactions and their functions has been hindered by a lack of knowledge about their activities in vivo. The occurrence of parallel reactions and the involvement of a set of metabolites in activity control of the enzymes prevents reliable estimations on the actual enzyme use. Moreover, it is not possible to derive quantitative data on in vivo flux rates by enzyme characterizations alone. Instead, carbon-13 labeling techniques, which employed NMR spectroscopy (for an overview, see e.g. Refs. 4 and 5) or mass spectrometry, as well as carbon-14 radiolabeling methods have been used to quantify in vivo intracellular fluxes in central metabolism including conversions between PEP, pyruvate, and oxaloacetate/malate. However, although these studies quantified the total C ...

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 13C nuclear magnetic resonance (13C 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. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 66: 86–103, 1999.

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. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 66: 69–85, 1999.

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.