**Date Published:** April 13, 2018

**Publisher:** Springer Berlin Heidelberg

**Author(s):** Teresa Mairinger, Wolfhard Wegscheider, David Alejandro Peña, Matthias G. Steiger, Gunda Koellensperger, Jürgen Zanghellini, Stephan Hann.

http://doi.org/10.1007/s00216-018-1017-7

**Abstract**

**In the field of metabolic engineering 13C-based metabolic flux analysis experiments have proven successful in indicating points of action. As every step of this approach is affected by an inherent error, the aim of the present work is the comprehensive evaluation of factors contributing to the uncertainty of nonnaturally distributed C-isotopologue abundances as well as to the absolute flux value calculation. For this purpose, a previously published data set, analyzed in the course of a 13C labeling experiment studying glycolysis and the pentose phosphate pathway in a yeast cell factory, was used. Here, for isotopologue pattern analysis of these highly polar metabolites that occur in multiple isomeric forms, a gas chromatographic separation approach with preceding derivatization was used. This rendered a natural isotope interference correction step essential. Uncertainty estimation of the resulting C-isotopologue distribution was performed according to the EURACHEM guidelines with Monte Carlo simulation. It revealed a significant increase for low-abundance isotopologue fractions after application of the necessary correction step. For absolute flux value estimation, isotopologue fractions of various sugar phosphates, together with the assessed uncertainties, were used in a metabolic model describing the upper part of the central carbon metabolism. The findings pinpointed the influence of small isotopologue fractions as sources of error and highlight the need for improved model curation.**

**Partial Text**

The assessment of absolute intracellular fluxes (i.e., reaction rates per unit cell volume or mass) found its way into metabolic engineering several decades ago. In metabolic engineering, possibilities to influence metabolic reaction rates are of special interest, since the quantitative understanding of metabolic flux regulation mechanisms allows a more precise reengineering of cell factories [1–3]. This technique can be used to engineer organisms such as bacteria or fungi to improve the industrial production of, for example, organic acids [4], lipids [5], or proteins [6]. The estimation of metabolic fluxes relies on stable isotope labeling experiments, where an isotope tracer (e.g., specifically 13C labeled glucose) is fed to an organism of interest. The resulting incorporation of the stable label into downstream metabolites is most commonly measured by mass spectrometry (MS)-based methods [3, 7]. Before the detection of these nonnaturally distributed 13C labeling patterns of free intracellular metabolites, separation of the analytes of interest is indispensable. For this purpose, either liquid chromatographic or gas chromatographic techniques are applied. Although the latter require a laborious derivatization step before analysis, the application of gas chromatography (GC)-based methods is convincing because of the excellent separation efficiency and broad metabolite coverage. This includes the separation of amino acids, organic acids, and metabolites with multiple structural isomeric forms, such as sugars and sugar phosphates, in one analytical run [8–11]. Sugar phosphates are of particular interest since many metabolites of the central carbon metabolism are phosphorylated, and the reaction involved therein often represents points of action in metabolic engineering [12].

After the measurand has been specified, in the next step of the uncertainty estimation process different uncertainty sources contributing to the total uncertainty of absolute flux values need to be identified, and can be visualized in a cause-and-effect diagram, as shown in Fig. 1 [24].Fig. 1Ishikawa diagram (also known as a “cause-and-effect diagram”) for identification of possible sources of measurement uncertainty of absolute flux values showing the most critical contributors to the uncertainty of absolute fluxes

As an example, for the measurement uncertainty of the C-isotopologue distribution, the model equation for the isotope-interference-corrected IF M+1 documentclass[12pt]{minimal}

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begin{document}$$ left({mathrm{IF}}_{mathrm{M}+{1}_{mathrm{corr}}}right) $$end{document}IFM+1corr of a metabolite, namely, Rl5P, is described in Eq. 1.1documentclass[12pt]{minimal}

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begin{document}$$ {mathrm{IF}}_{M+{1}_{mathrm{corr}}}=frac{A_{1_{mathrm{corr}}}times {F}_1}{A_0+{A}_{1_{mathrm{corr}}}times {F}_1+{A}_{2_{mathrm{corr}}}times {F}_2+{A}_{3_{mathrm{corr}}}times {F}_3+{A}_{4_{mathrm{corr}}}times {F}_4+{A}_{5_{mathrm{corr}}}times {F}_5} $$end{document}IFM+1corr=A1corr×F1A0+A1corr×F1+A2corr×F2+A3corr×F3+A4corr×F4+A5corr×F5

As demonstrated in the previous section, low-abundance IFs result in high relative uncertainty. Thus, it is interesting to investigate the impact of these small fractions on the flux estimation. For this purpose, confidence intervals were calculated with use of only IFs with abundance greater than 2%, as well as with the complete set of isotope-interference-corrected IFs. As observed in Fig. 3, the resulting confidence intervals are essentially identical, which indicates that small IFs have a negligible effect on fluxes. Given that [1,6-13C2]glucose was used as tracer in the experiment, isotopologues with a higher mass increment were not expected to be generated for the reactions that were the focus of the present study (e.g., IFs of R5P from M+2 to M+5; see Fig. 2 part A). These IFs lead artificially to an improper weighting of the residuals and could bias parameter estimation during the subsequent fitting procedure [27]. The latter was observed from the improved sum of squared residuals that is obtained after removal of the small IFs, as well as from the normal probability plot of the standard-deviation-weighted residuals (compare Fig. 4a and b). Also, removal of IFs smaller than 2% shifted the distribution of weighted residuals toward the expected normal distribution (Fig. 4b), which then passed a Shapiro–Wilk test for normal distribution. However, the mean and standard deviation of this distribution still deviated from the expected values of 0 and 1, respectively. Moreover, statistical tests on the goodness of fit revealed bad fitting, since the variance-weighted sum of squared residuals did not pass the critical value of the X2 distribution for a confidence level of 95%.Fig. 3Effect of isotopologue fraction (IF) uncertainties on flux confidence intervals. Estimated fluxes (dots) along with their confidence intervals (bars) in different scenarios are depicted in the small figures associated with each reaction. Removal of IFs with an abundance of less than 2% has no effect on confidence intervals (compare the blue and red bars). Flux estimation, when the biological variance (three times the standard deviation) was included, yields threefold larger confidence intervals (yellow bars). Increasing the precision of critical analytes [IFs M+1and M+2 from fructose 6-phosphate (F6P) and glucose 6-phosphate (G6P)] has the largest impact on reducing flux uncertainty (purple bars). For reversible reactions, forward, reverse, and net fluxes are shown. Fluxes are given in millimoles per gram dry cell weight per hour. SD standard deviation. ADP adenosine diphosphate, ATP adenosine triphosphate, DHAP dihydroxyacetone phosphate, E4P erythrose 4-phosphate, FBA fructose bisphosphate aldolase, FBP fructose 1,6-bisphosphate, GAPDH glyceraldehyde 3-phosphate dehydrogenase, GLC glucose, G3P glyceraldehyde 3-phosphate, G6PDH glucose 6-phosphate dehydrogenase, HEX hexokinase, NADP nicotinamide adenine dinucleotide phosphate, NADPH reduced nicotinamide adenine dinucleotide phosphate, PI phosphate, PFK phosphofructokinase, PG3 3-phosphoglyceric acid, PGI glucose 6-phosphate isomerase, RIB5P ribose 5-phosphate, RPE ribulose 5-phosphate epimerase, RPI ribose 5-phosphate isomerase, RUL5P ribulose 5-phosphate, SED7P sedoheptulose 7-phosphate , TALA transaldolase, TKT1 transketolase 1, TKT2 transketolase 2, TPI triosephosphate isomerase, XYL5P xylulose-5-phosphateFig. 4Normal probability plots for the standard-deviation-weighted residuals after flux estimation. Deviation of a normal distribution (=0, =1) indicates errors in the metabolic model or in the measurement uncertainties of isotopologue fractions (IFs). Fluxes were estimated with use of a all IFs with their modeled standard uncertainty, b only IFs with abundance greater than 2%, c only IFs with abundance greater than 2% with three times their standard uncertainty to account for biological variability, and d only IFs with abundance greater than 2% with three times their standard deviation except for the isotopologues M+1 and M+2 from fructose 6-phosphate and glucose 6-phosphate. SSR sum of squared residuals

Although the isotopologue distribution of free intracellular metabolites is determined with high precision, the true value of IFs within a 13C-based MFA experiment remains poorly characterized because of the lack of a suitable certified matrix reference material for isotopologue analysis. The value of such a reference material was recently demonstrated by Heuillet et al. [42]. Besides, our analysis also pointed out the underlying metabolic model as a structural source of error, as also suggested in other studies [40, 41]. Thus, substantial efforts should focus on improved model curation by capturing all reactions affecting measured metabolites. As a further conclusion, we recommend a priori identification of metabolites involved in the metabolic fluxes of interest and to specifically focus on these with, for example, dedicated preconcentration steps for certain low-abundance metabolites and thereby potentially increase accuracy.

Source:

http://doi.org/10.1007/s00216-018-1017-7