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In vivo stationary flux analysis by 13C labeling experiments

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Metabolic Engineering

Part of the book series: Advances in Biochemical Engineering/Biotechnology ((ABE,volume 54))

Abstract

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.

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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

X:

vector of all absolute pool sizes in a metabolic network

v→, v←:

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

v:

overall flux vector comprising v → and v ←

vnet, vxch:

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

N:

stoichiometric matrix

Ncnstr, ccnstr:

linear constraint matrix and constraint value vector

Pi, P inpi :

carbon atom transition matrices corresponding to reaction step i

Q i :

bimolecular isotopomer transition tensor corresponding to reaction step i

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

ɛ w , ɛ y , ɛ Y :

measurement noise vectors for fluxes, labels and pool sizes

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  1. Institute of Biotechnology, Research Center Jülich, D-52425, Jülich, Germany

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H. Sahm (Volume Editor)C. Wandrey (Volume Editor)

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Wiechert, W., de Graaf, A.A. (1996). In vivo stationary flux analysis by 13C labeling experiments. In: Sahm, H., Wandrey, C. (eds) Metabolic Engineering. Advances in Biochemical Engineering/Biotechnology, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102334

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