Quantification of Metabolic Fluxes

Abstract

The phenotype of an organism grown under defined environmental conditions may be characterized by the fluxes carried out at each individual reaction in the organism's metabolic network. Metabolic fluxes are nonmeasurable quantities, but they can be quantified using a combination of specific measurements and mathematical modelling.

Keywords: metabolic flux analysis; mathematical modelling of metabolism; labelling experiments; metabolic engineering

Figure 1.

Balanced growth conditions. An intracellular metabolite MA is in steady state if the sum of reactions rates (in molar units) v1 and v3,rev is equal to the sum of reaction rates v2, v3 and v4. Metabolite MA could be glucose 6‐phosphate, a central metabolite synthesized from glucose via glucokinase (or hexokinase, v1), and further metabolized through the Embden–Meyerhof–Parnas pathway via glucose‐6‐phosphate isomerase (v3, reversible), through the pentose phosphate pathway via glucose‐6‐phosphate dehydrogenase (v2), and through biosynthetic pathways via phosphoglucomutase (v4).

Figure 2.

Calculating the drain of a precursor metabolite for biomass formation.

Figure 3.

Application of linear metabolic flux analysis. A metabolic network, including the Embden–Meyerhof–Parnas pathway, the tricarboxylic acid cycle, the ethanol formation pathway, and the pyruvate carboxylase‐catalysed reaction. Reaction v8 represents the electron chain, with an assumed P/O ratio of 1.2. In order to include ATP and CO2 as intracellular metabolites that are balanced, reactions v9 and v10, representing the excess of ATP produced by the cells and the carbon dioxide evolution rate (CER), respectively, are included in the model.

For the sake of clarity, the chosen metabolic network contains a number of simplifications in relation to real metabolic networks. Thus, it is assumed that cell growth (biomass formation) is negligible, which means that there is no drain of precursor metabolites for biomass synthesis. Also, it is considered that ATP – instead of GTP – is the cofactor in the succinate thiokinase‐catalysed reaction, and that NADH – instead of FADH2 – is the cofactor in the succinate dehydrogenase‐catalysed reaction. Reactions around metabolites that are not part of any branch point in the network are lumped together. Squared metabolites are those considered as branch point metabolites.

AcCOA, acetyl‐coenzyme A; AKG, α‐ketoglutarate; ATP, adenosine triphosphate; CIT, citrate; ETH, ethanol; FADH2, flavin–adenine dinucleotide, reduced form; FUM, fumarate; GTP, guanosine triphosphate; G6P, glucose 6‐phosphate; ICIT, isocitrate; MAL, malate; NADH, nicotinamide–adenine dinucleotide, reduced form; OAA, oxaloacetate; PYR, pyruvate; P3G, 3‐phosphoglycerate; SUC, succinate; SucCOA, succinyl‐coenzyme A.

Figure 4.

Metabolic network structures for which linear MFA fails. (a) It is impossible to calculate the fluxes in the two branches of the network depicted on the left without measuring at least one flux between metabolite MA and metabolite MG. In some cases, there is a link between the two branches, via a cofactor such as NADH. In this case, as indicated in the figure for reactions converting MD into ME and MC into MG, it might be possible to calculate the fluxes v1 and v2 through the two parallel branches of the network. (b) In the case of reversible reactions or reactions carrying fluxes in opposite directions, it is only possible to calculate the net flux, i.e. the difference between the two opposite fluxes. The degree of reversibility or the flux carried out by each enzyme, in the case of fluxes in opposite directions, cannot be calculated.

Figure 5.

General idea of a labelling experiment. In a labelling experiment, a labelled substrate is fed to the organism. In this example, a three‐atom substrate is used (Sext) labelled in the first position. Fully labelled atoms are shaded in dark blue, whereas partially labelled positions are shaded in blue to light‐blue. The labelling pattern in the product (Pext), as well as in the intracellular metabolite A, directly reflects the relative magnitudes of the fluxes in the metabolic network. Thus, by measuring the amount of label in the product and/or in metabolite A, and employing the appropriate mathematical tools, it is possible to get qualitative and quantitative information on the relative utilization of pathways in a given metabolic network.

Figure 6.

Classification of 13C‐labelled molecules. In this example, a three‐carbon molecule is shown, but the principles can be extended to any molecule or molecule fragment obtained in the mass spectrometer. Filled circles correspond to 13C atoms, whereas nonfilled circles represent 12C atoms. The nomenclature Ii can be given with the index either on a decimal or on a binary basis (in the latter case, 0 corresponds to a 12C atom and 1 to a 13C atom).

Figure 7.

Mass spectrum of alanine. In a mass spectrum, the abundance of the detected ions is represented as a function of the mass‐to‐charge ratio (m/z). In this example, two (N, N)‐dimethylformamide dimethyl acetal‐derivatized alanine fragments are shown: one containing all three carbon atoms of the amino acid, the molecular ion (cluster starting at m/z 158), and one containing only carbon atoms 2 and 3 (cluster starting at m/z 99). In each cluster, the peak corresponding to the lowest mass is that representing the fraction of all molecules that do not contain any 13C atoms (m). The other peaks represent the fraction of molecules containing one, two or three 13C atoms (m+1, m+2, and m+3, respectively), the mass isotopomers.

Figure 8.

Absorption spectrum of a three‐carbon‐atom fragment. In an NMR spectrum, the absorption intensity of a central 13C atom in a three‐carbon‐atom fragment is represented as a function of the chemical shift in the 13C dimension. The multiplet signal will present nine peaks: the area of the singlet peak S is proportional to the amount of 13C atoms that have only 12C neighbouring atoms; the area of the doublet peaks D1 are proportional to the amount of 13C atoms that have a 13C neighbouring atom to the right; the area of the doublet peaks D2 are proportional to the amount of 13C atoms that have a 13C neighbouring atom to the left; and the area of the double doublet peaks DD are proportional to the amount of 13C atoms that have 13C neighbouring atoms to the right and to the left. J1 is the scalar coupling constant between the central 13C atom and its neighbouring atom to the left, whereas J2 is the scalar coupling constant between the central 13C atom and its neighbouring atom to the right. The coupling constants J1 and J2 are usually different, as the chemical environment of the neighbouring atoms are different owing to the different atoms to which they are bound. When the analysed 13C atom is at the extremity of a fragment, only three peaks appear in the spectrum: one singlet peak and two doublet peaks, as the analysed 13C atom only has one neighbour atom in this case. From the measurements, it is possible to calculate the fractional labelling of the two neighbouring atoms according to eqns [i] and [ii].

Figure 9.

Principles of fractional labelling and isotopomer models.

Figure 10.

Principles of the calculation of metabolic fluxes in nonlinear MFA. A labelling experiment is carried out, from which some of the fluxes can be measured (e.g. extracellular fluxes and fluxes to formation of biomass), as well as the labelling in some intracellular metabolites. Flux calculation is an iterative process that starts with an initial guess on a subset of all fluxes, which are called free fluxes. From the set of free fluxes, the remaining fluxes can be calculated using the metabolic model, and with the complete set of fluxes the labelling of all the intracellular metabolites can be calculated using a model describing the carbon transitions in the individual biochemical reactions (either a fractional labelling or an isotopomer model). The calculated labelling of intracellular metabolites and the set of fluxes for which the corresponding measurements are available are used as input for a minimization routine that aims at minimizing the differences between measured and calculated data. These differences are divided by the standard deviation of the corresponding measurement, so that they become dimensionless and normalized. If the calculated error at the end of the minimization routine is appropriately small, and the metabolic model is physiologically adequate, the corresponding set of fluxes is the one that best describes the metabolism under investigation.

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References

Christensen B, Gombert AK and Nielsen J (2002) Analysis of flux estimates based on 13C‐labelling experiments. European Journal of Biochemistry 269: 2795–2800.

Nielsen J (2001) Metabolic engineering. Applied Microbiology and Biotechnology 55: 263–283.

Nielsen J, Villadsen J and Liden G (2002) Bioreaction Engineering Principles, 2nd edn. New York: Kluwer Academic/Plenum Press.

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Wiechert W, Siefke C, de‐Graaf AA and Marx A (1997) Bidirectional reaction steps in metabolic networks. II. Flux estimation and statistical analysis. Biotechnology and Bioengineering 55: 118–135.

Further Reading

Christensen B and Nielsen J (1999) Metabolic network analysis: a powerful tool in metabolic engineering. Advances in Biochemical Engineering/Biotechnology 66: 209–231.

Gombert AK and Nielsen J (2000) Mathematical modelling of metabolism. Current Opinion in Biotechnology 11: 180–186.

Szyperski T (1998) 13C‐NMR, MS and metabolic flux balancing in biotechnology research. Quarterly Reviews in Biophysics 31: 41–106.

Wiechert W (2001) 13C metabolic flux analysis. Metabolic Engineering 3: 195–206.

Wiechert W, Möllney M, Petersen S and de‐Graaf AA (2001) A universal framework for 13C metabolic flux analysis. Metabolic Engineering 3: 265–283.

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Gombert, Andreas Karoly, and Nielsen, Jens(May 2003) Quantification of Metabolic Fluxes. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1038/npg.els.0000622]