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

Abstract

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.

Visual exploration of isotope labeling networks in 3D

“…The generated network structure can be described by (hyper-)graphs or, alternatively, matrix structures [19,21,26]. On the basis of these data structures and given flux values, it can then be quantitatively simulated how the labeled material fed to cell is distributed over all isotopomer pools [19,30]. This simulation is the central computational step for the evaluation of experimental measurement data.…”

“…Cumomers as introduced in [19] constitute an alternative representation of labeled particles in metabolic networks.…”

“…The modeling, evaluation and design of ILEs based on a mathematical model of isotope labeling dynamics are a rather complicated and computationally intensive procedure [18][19][20]. Different approaches have been extensively described in several technical papers [21][22][23][24][25] and will not be discussed here in detail.…”

Use of network analysis of metabolic systems in bioengineering

“…One of the techniques in MFA is metabolite balancing or metabolic-flux balancing [1]; others are optimization approaches [8,10,38,40] (which are particularly useful for underdetermined systems) and isotope and isotopomer balancing [42,43]. As mentioned in Sect.…”

Large-scale prediction of phenotype: Concept

“…They have been used to investigate the physiology of Escherichia coli, Saccharomyces cerevisiae, and Hybridoma Keasling, 1997, 1998;Nissen et al, 1997;Schulze et al, 1996;Follstad et al, 1999), lysine production and the effect of mutations in Corynebacterium glutamicum Stephanopoulos, 1993, 1994;Park et al, 1997;Dominguez et al, 1998), riboflavin production in Bacillus subtilis (Sauer et al, 1996(Sauer et al, , 1998, penicillin production in Penicillium chrysogenum (Jorgensen et al, 1995), as well as peptide amino acid metabolism in Chinese hamster ovary (CHO) cells (Nyberg et al, 1999a,b), just to cite a few. Moreover, MFA in combination with NMR, MS, and/or GC-MS can yield hard to get information about futile cycles, the degree of reaction reversibility, as well as active pathways (Szyperski, 1995(Szyperski, , 1998Szyperski et al, 1997;Schmidt et al, 1998;Klapa et al, 1999;Mollney et al, 1999;Park et al, 1999;Wiechert et al, 1999;Wittmann and Heinzle, 1999). Schilling, Edwards, and Palsson have even extended the use of MFA to include the analysis of genomic data and the structural properties of cellular networks (Edwards and Palsson, 1998;Schilling et al, 1999a,b).…”