In vivo stationary flux analysis by 13C labeling experiments

  • W. Wiechert
  • A. A. de Graaf
Part of the Advances in Biochemical Engineering/Biotechnology book series (ABE, volume 54)


Stationary flux analysis is an invaluable tool for metabolic engineering. In the last years the metabolite balancing technique has become well established in the bioengineering community. On the other hand metabolic tracer experiments using 13C isotopes have long been used for intracellular flux determination. Only recently have both techniques been fully combined to form a considerably more powerful flux analysis method. This paper concentrates on modeling and data analysis for the evaluation of such stationary 13C labeling experiments. After reviewing recent experimental developments, the basic equations for modeling carbon labeling in metabolic systems, i.e. metabolite, carbon label and isotopomer balances, are introduced and discussed in some detail. Then the basics of flux estimation from measured extracellular fluxes combined with carbon labeling data are presented and, finally, this method is illustrated by using an example from C. glutamicum. The main emphasis is on the investigation of the extra information that can be obtained with tracer experiments compared with the metabolite balancing technique alone. As a principal result it is shown that the combined flux analysis method can dispense with some rather doubtful assumptions on energy balancing and that the forward and backward flux rates of bidirectional reaction steps can be simultaneously determined in certain situations. Finally, it is demonstrated that the variant of fractional isotopomer measurement is even more powerful than fractional labeling measurement but requires much higher numerical effort to solve the balance equations.


Reaction Step Citric Acid Cycle Tracer Experiment Corynebacterium Glutamicum Label State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols and Abbreviations

A, B, C, D, E, S, P, …

metabolite names

A, B, C, D, E, S, P, …

absolute molar pool size of metabolites

b1, b2

positional fractional carbon labeling of metabolite B with 2 carbon atoms

b00, b01, b10, b11

isotopomer fractions of metabolite B with 2 carbon atoms

\(v_1^ \to ,v_1^ \leftarrow ,v_2^ \to ,v_2^ \leftarrow \)

forward and backward fluxes corresponding to biochemical reaction steps

x, xinp

vectors of all fractional carbon labels in a metabolic network and all input labels from substrates fed into the system


vector of all absolute pool sizes in a metabolic network

v, v

vectors of all forward and backward fluxes corresponding to metabolic reaction steps


overall flux vector comprising v and v

vnet, vxch

vectors of all net and exchange fluxes corresponding to metabolic reaction steps


stoichiometric matrix

Ncnstr, ccnstr

linear constraint matrix and constraint value vector

Pi, Piinp

carbon atom transition matrices corresponding to reaction step i


bimolecular isotopomer transition tensor corresponding to reaction step i


pool size to fractional labeling state mapping matrix

w, y, Y

measured fluxes, labels and pool sizes

Mw, My, My

measurement matrices for fluxes, labels and pool sizes

ɛw, ɛy, ɛY

measurement noise vectors for fluxes, labels and pool sizes


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • W. Wiechert
    • 1
  • A. A. de Graaf
    • 1
  1. 1.Institute of BiotechnologyResearch Center JülichJülichGermany

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