The sample solution (usually between 0.1 to 1 μL) is injected into the GC inlet where it is vaporized and directed onto the chromatographic column by the carrier gas (usually helium). The sample molecules are separated through different interactions between the carrier gas phase and the stationary phase. To obtain the highest resolution in GC-MS analysis, the capillary column should be carefully chosen. The best general purpose phases are dimethylsiloxane (DB-1 or equivalent) or 5 % phenyl/95%dimethlysiloxane (DB-5 or equivalent). These non-polar phases exhibit an excellent separation capability for many compounds and a generally low column bleeding. Polar columns (DB-Wax or equivalent) are useful for selected derivates such as more polar alkylated compounds. The high separation capacity of GC is illustrated in Figure 3 for a sample containing various amino acids and related compounds.

The outlet of the GC column is connected via a heated transfer line with the ion source of the MS where the compounds eluting from the column are ionized. The most frequently used ionization method is electron impact (EI) ionization (Figure 4). Hereby the interference of the sample stream with a crossing electron beam leads to the loss of an electron from the sample molecules. The resulting ions with one electron missing, i.e. the molecular ions, give the total mass of each analyte. Due to the large amount of energy imparted to the molecular ion it usually fragments, producing further smaller ions with characteristic relative abundances that provide a 'fingerprint' for that molecular structure (Figure 5A). Often the molecular ion itself is not observed. The different fragment ions may contain different parts of the carbon skeleton of the analyte. In the given example for TBDMS-derivatized alanine the ion cluster [M-57]⁺at m/z 260 results from loss of a C₄H₉ group from the derivatization residue and contains all three alanine carbon atoms, whereas the ion cluster [M-85]⁺ at m/z 232 only contains the carbon atoms C₂ and C₃ of alanine due to additional loss of a CO-group including the C₁ atom of alanine. Chemical ionization (CI) as alternative ionization method plays a minor role for flux analysis, but has proven valuable in selected cases such as labelling analysis of glucose aldonitrile pentaacetate in different medical flux studies 35363738.

Through a slit the positive ions from the ion source enter into the mass separation part. Figure 3 shows the most wide spread type of mass separator in GC-MS analysis, a quadrupole, composed of four parallel cylindrical rods (about 25 cm length each), whereby opposite rods are electrically connected. The mass separation is based on the motion of ions in an oscillating electric field created through voltage variation between the rods. At a certain voltage, only analyte molecules of a distinct mass to charge (m/z) ratio (resonance ions) can pass and enter the detector, whereas ions exhibiting a different m/z ratio (non-resonance ions) are subjected to oscillations causing their collision with the rods. Within a few seconds the whole mass range available (usually 50 – 850 m/z) can be fully scanned. This short time interval required for a full scan is important, due to the typically narrow peaks eluting from the GC column that have to be scanned several times each (Figure 3). The sensitivity of a quadrupole detector can be significantly enhanced by selected ion monitoring (SIM), whereby only selected masses are sequentially measured with frequencies of 0.1 to 2 seconds each. The number of collected ions for the selected masses is increased up to several thousand folds in comparison to the scan mode. Quadrupole MS spectra can be easily compared with commercial or laboratory databases facilitating the identification of novel compounds and the validation that a signal is not interfered through isobaric overlay. In most cases the nominal-mass information provided by such instruments is sufficient, since the compounds analyzed are a priori known.

Other mass separators available are time-of-flight (TOF) mass separators or ion traps. In TOF instruments, ions formed in the ion source are accelerated in a short electric field to a high kinetic energy, whereby ions with lower masses reach higher velocities and need a shorter time to reach the detector. The mass to charge ratio of each ion is determined from the time elapsed from ion formation to ion arrival at the detector. This type of mass separation in GC-TOF-MS systems offers a greater mass accuracy as compared to a conventional quadrupole. This, however, is normally not required for the labelling measurement and does therefore not compensate for the relatively high price of such instruments. Only the high scan speed possible allowing multiple scanning of single peaks during their elution and shortening of analysis time 39 could be beneficial for high-throughput applications or the analysis of rather complex samples. Alternatively, ion traps can be applied for mass separation. A drawback of ion traps to be used for flux analysis is the comparatively low accuracy for the labelling measurement resulting in a higher uncertainty of the determined fluxes. Relative errors of around 1 % for the most abundant mass peaks 40 are about two to tenfold higher as compared to that of quadrupole instruments 15. An advantage, however, is the possibility to use the ion trap as a multi stage MSn mass spectrometer which can provide more detailed information on the labelling pattern. This might be useful in cases, where a high degree of labelling information is needed to determine the fluxes of interest 41. Similarly triple-quadrupole instruments can be run as multistage mass spectrometers. A further variant, useful e.g. for isotope labelling studies in humans or animals, is isotope ratio (IR) GC-MS 4243. It is based on electron impact ionization with maximized ionization probability. IR GC-MS exhibits an extremely high precision of ± 0.00001 % for the isotope ratio measurement and is optimal to quantify low label enrichment 44. It is, however, limited to the analysis of gases of high volatility and low reactivity such as CO₂, N₂ or SO₂. The analytes of interest are transformed into one of these gases before introduction into the instrument. Usually this provides information only about the specific labelling enrichment, i.e. the relative abundance of ¹³C atoms in the entire molecule. More detailed information on number and position of ¹³C can be obtained, if all carbon atoms are isolated position specific prior to measurement as recently shown for position specific ¹³C analysis of methyl palmitate through pyrolytic fragmentation 45.

Depending on the experiment, the analytes of interest are cellular polymers (analysis of balanced growth in chemostat or batch processes), free intracellular metabolites (analysis of process dynamics) or extracellular metabolites in the medium (analysis of production phases with reduced growth or without growth). Exemplified for amino acids, the different experimental steps of sampling and sample pre-treatment for subsequent labelling analysis by GC-MS are given in Figure 6. Free intracellular amino acids are extracted from the cells, whereby immediate quenching is important to prevent changes in the labelling pattern during sampling. Due to the high sensitivity of GC-MS only 1 mg cell dry mass are required to obtain labelling patterns from free intracellular amino acids 52. Various quenching and fast sampling methods described in the literature for metabolome analysis can be applied here. For bacteria fast filtration with cellulose nitrate or polyamide filters (0.2 μm pore size) is suitable 53, whereas yeast cells can be efficiently quenched with cold buffered methanol 54. The quenched cells should be washed to prevent interference with compounds contained in the medium. Metabolite extraction can be performed by incubation in boiling ethanol or in boiling water. After separation from cell debris the extract is lyophilized to concentrate the metabolites and remove the water. For the analysis of amino acids from the cell protein cells are harvested by centrifugation or filtration, washed and subsequently hydrolyzed by 24 h incubation at 110°C in 6 M HCl. During hydrolysis asparagine and glutamine are deaminated to aspartate and glutamate. Cysteine, methionine and tryptophan are destroyed through oxidation. If the hydrolysis time is shortened to about 8 h, signals can be also obtained for e.g. cysteine or methionine, but at the cost of a generally low yield. The hydrolysate is neutralized by addition of 6 M NaOH, whereby often the required volume of NaOH is less than the volume of HCl due to HCl evaporation during the hydrolysis. The pH should be checked, because the subsequent derivatization is significantly disturbed by an alkaline pH. The neutralized hydrolysate is clarified by filtration, whereby a stable glycerol-free filter material has to be chosen. Glycerol would be leached out of the filter and interfere in the later derivatization and GC-MS analysis. Finally the clarified hydrolysate is lyophilized. Extracellular metabolites are harvested by centrifugation followed directly by lyophilization.

In order for a compound to be analyzed by GC-MS it must be volatile and thermally stable. Most of the metabolites utilized for flux analysis are polar or even charged and thus not sufficiently volatile to be directly analyzed, so that derivatization is typically required. This holds for amino acids 16212450, organic acids 3235 or sugars 1931375556. For this purpose a number of straightforward derivatization reactions involving silylation, alkylation or acetylation are available (Table 1). The reactions are mainly simple, one-pot conversions with high yield. More details on derivatization protocols are given in recent review articles 575859606162. For the analysis of amino acids, silylation with N-methyl-N-t-butyldimethylsilyl-trifluoro-acetamide (MBDSTFA) is especially useful, since it leads to derivates which exhibit high signal intensity for the [M-57] fragment ions. These originate from loss of a t-butyl group from the derivatization residue, contain the entire carbon skeleton of the analyte and are thus valuable for flux calculation 63. It should be noted that many reagents used are unstable in the presence of water, so that the aqueous samples, as described above, have to be dried and re-dissolved in organic solvent prior to derivatization. It is also possible to directly add the reagent to the lyophilized sample, using an additional solvent such as dimethylformamide, however, improves the conversion.

The mass isotopomer distribution of a compound can be directly taken from an ion cluster containing the entire carbon backbone of the analyte. In many cases these mass isotopomer distributions sensitively reflect the flux parameters of interest. This can be illustrated for the problem of quantifying the flux partitioning at the glucose 6-phosphate node between the pentose phosphate pathway (PPP) and glycolysis, important pathways in many microorganisms. With [1-¹³C] glucose as tracer substrate the labelled carbon atom is completely released as CO₂ in the PPP, whereas the label is completely conserved through the different glycolytic reactions (Figure 7). The mass isotopomer distribution of pyruvate, receiving carbon from both pathways, thus significantly changes with a variation of the flux partitioning. As revealed by metabolic simulations an increase of the relative flux into the PPP is reflected by a decrease of the fraction of single labelled pyruvate and an increase of the fraction of non-labelled pyruvate. GC-MS measurement of the labelling of pyruvate or pyruvate derived metabolites such as alanine allows precise estimation of PPP and glycolytic flux. This becomes obvious from mass spectra of TBDMS-derivatized alanine from tracer experiments of a lysine producing Corynebacterium glutamicum mutant (Figure 5B) and Saccharomyces cerevisiae (Figure 4C) cultivated on 99 % [1-¹³C] glucose in batch culture. In both cases the heavier mass isotopomer fractions, e.g. at the ion cluster m/z 260, are increased due to the enrichment with ¹³C. In comparison with S. cerevisiae the fraction of single labelled alanine is markedly reduced in C. glutamicum revealing a significantly higher flux through the PPP in this organism, which is related to the increased NADPH demand for lysine production. Similarly mass isotopomer distributions of other metabolites give access to various other flux parameters, such as dual pathways in amino acid biosynthesis 64, bidirectional fluxes around the pyruvate node 64 or parallel pathways in different cellular compartments 18 and different flux ratios 24. In other studies, summed fractional labelling data have been utilized for the analysis of fluxes 6566. Hereby, the lower degree of information for each single compound was compensated by the consideration of different ion fragments containing different parts of the carbon skeleton for the analytes 67. More detailed information on the labelling of a compound can be obtained with GC-MS via additional analysis of fragment ions, which contain only specific parts of the carbon skeleton of the analyte. As example, the entire positional isotopomer distribution of pyruvate can be determined by GC-MS via analysis of four ion clusters of its methyl-ester derivate 17 or via GC-MS analysis of different ions of pyruvate derived amino acids valine and alanine 16. More complex protocols may be required for analytes containing more carbon atoms, thus exhibiting a substantially increased number of possible positional isotopomers. The determination of 24 out of 32 positional isotopomers of glutamate involves chemical and enzymatic synthesis of five different derivates of glutamate prior to GC-MS analysis 36. Also other protocols for resolution of positional isotopomer pools are rather laborious and include various steps for purification and chemical or enzymatic conversion of the analytes 35496869 which impedes the broad and routine use of such techniques. It should be noticed that the resolution of single positional isotopomer pools not necessarily leads to an increase in information for flux quantification 6770, but in selected cases single isotopomer pools might be required to calculate all fluxes of interest. A major tool to obtain additional fragments towards positional isotopomer analysis is targeted fragmentation using MS/MS, also called tandem MS, where selected ions can be isolated, subsequently fragmented and the fragments can be analyzed for their mass distribution. The potential of such approaches for flux analysis is underlined by recent studies 7172.

To calculate the ¹³C labelling of a molecule from a GC-MS measurement, the data have to be corrected for natural isotopes. Hereby, atoms of the analyte and of added derivatization residues have to be considered. Natural isotopes typically occurring in GC-MS are carbon, hydrogen, nitrogen, oxygen and silicium (Table 2). Mathematically, the presence of natural isotopes can be considered by correction matrices 17737475. Straightforward is the 'addition' of the natural isotopes to the simulated data during flux calculation and the direct comparison with the measurement data 17. Alternatively the natural isotopes can be 'subtracted' from the measurement signals to obtain the labelling of the carbon skeleton of the analyte and compare this value with the corresponding simulated data during flux calculation 76.

Quantitative accuracy of the measurement is crucial for mass isotopomer analysis. Several sources of error may potentially affect the measurement result and should therefore be taken into account. First the signals have to be checked for purity, i.e. that isobaric interference of the analytes with co-eluting compounds does not occur. For the consistency check of GC-MS mass isotopomer distributions several efficient software tools have been developed 257677. A check can also be done experimentally by an additional cultivation on naturally labelled substrate in parallel to the tracer experiment and comparison of the mass isotopomer distributions from this study with theoretically expected values, calculated from the natural abundance of isotopes or experimental values from pure standard compounds. Another potential cause of inaccuracy is incomplete resolution of adjacent ions due to ion scattering and peak tailing. Therefore the mass spectrometer (lens system, quadrupole pre-filter, quadrupole rods, detector) has to be tuned to enable optimum mass-resolving capacity 50. To obtain optimal signal intensity and avoid interference the signal for each mass isotopomer should be collected in SIM mode from the maximum of each mass peak. The m/z value at the peak maximum typically deviates from an integer value due to underlying atom masses contained in the ion. Nonlinearity of the detector response at different mass isotopomer ratios or different analyte amounts may further lead to false results 78. Whereas such effects are observed for fatty acid methyl esters, mass isotopomer ratios of naturally labelled TBDMS-amino acids were not affected over a concentration range of 3 orders of magnitude 50. Interference with background noise leads to false results for low abundance signals which therefore should not be considered for flux calculation. The same holds for signals above the saturation of the detector which underestimate the relative abundance of the most prominent mass isotopomer fractions. Such effects can be visualized by an inhomogeneous peak composition 50. Reduction of the electron multiplier voltage (EMV) at the detector or sample dilution may compensate for such effects. One should further consider that the efficiency of electron multipliers can significantly decrease with life time. This can lead to a drift of the measured labelling pattern, i.e. mass isotopomer ratio, with increasing EMV or sample amount (Figure 8A). In such cases the multiplier should be changed. The high separation capacity of GC leads to isotope discrimination, as shown by the elution behaviour of the different mass isotopomers of TBDMS₃-glutamate (Figure 8B). To adequately consider all mass isotopomers of a compound and obtain meaningful results, the average mass spectrum of the whole peak range has to be considered. This leads to a significantly reduced signal-to-noise ratio that excludes the use of labelling data from low abundance fragments 50.

Generally, metabolic flux analysis by isotope labelling experiments requires a known topology of the biochemical network. Topological phenomena, such as metabolite channelling, compartmentation or zonation, mainly observed in eukaryotic systems, may influence the fate and the labelling pattern of metabolites in the network and must be considered, when interpreting obtained labelling data 80. Metabolite channelling can prevent label scrambling of symmetric intermediates through orientation-conserved biocatalytic reactions as found for mitochondrial TCA cycle enzymes in mammalian cells 81 and yeast 82 and for pentose phosphate pathway (PPP) enzymes in yeast 83. The compartments in eukaryotic cells lead to spatially separated metabolite pools and reactions, which has significant impact on labelling patterns. As example amino acid metabolism in yeast may occur in the cytosol, the mitochondrium or in both compartments, whereby the pathway location may vary between different species 8485 or with cultivation conditions 18. In tissue cultures zonation of metabolic activities may lead to heterogeneous labelling patterns as described for triose phosphate pools in rat liver 86. The significant impact of metabolite channelling, compartmentation or zonation on labelling patterns, requesting their consideration in flux analysis, can be exploited by using isotope labelling studies to unravel these important features in biological systems 87. Evidence for isotope effects on rate and equilibrium of metabolic reactions has not been gained, so that it appears justified to neglect them 16.

The majority of GC-MS based flux approaches utilizes amino acid labelling patterns 165085888990. Knowing the precursor-amino acid relationships it is easy to deduce the labelling patterns of the precursor metabolites from labelling patterns of the amino acids. The relationship between precursor compounds from glycolysis, pentose phosphate pathway and TCA cycle and the amino acids for E. coli, C. glutamicum, B. subtilis, P. putida and S. cerevisiae is given in Figure 9. Except for lysine the synthesis of all amino acids is identical in all these microorganisms 91. In E. coli, B. subtilis and P. putida one lysine biosynthetic route is available each from oxaloacetate and pyruvate, respectively, which includes a symmetric intermediate that results in label scrambling. Bakers's yeast utilizes a-ketoglutarate and acetyl-CoA as lysine precursors. C. glutamicum possesses two alternative pathways for lysine biosynthesis, whereby the in vivo activity of the two branches can vary with cultivation conditions or genetic modifications 92. One should note that serine and glycine may not exclusively originate from their well known precursor 3-phosphoglycerate, but can also be formed from oxaloacetate via the threonine pathway and threonine aldolase 466.

The resolution of intracellular fluxes is strongly dependent on the ¹³C-labeling strategy. In GC-MS based approaches the use of [1-¹³C] glucose as well as the use of a mixture of [¹³C₆] glucose and unlabeled glucose has proven useful to resolve important fluxes throughout the central metabolism in different organisms. Concerning the central metabolic pathways, a mixture of [¹³C₆] glucose and unlabeled glucose is particularly useful to resolve fluxes downstream of PEP and some exchange fluxes that result in C-C bond cleavages, whereas the use of [1-¹³C] glucose is valuable for resolving the upper part of metabolism, in particular the oxidative PP pathway, glycolysis and the Entner-Doudoroff pathway 24. Combining [U-¹³C] glucose and [1-¹³C] glucose, either in two separate experiments 192124 or as a substrate mixture 20 may lead to an even better resolution of fluxes in the network. The resolution of a particular flux, however, depends on the network topology itself so general guidelines cannot be given. Questions concerning the determinability and the predicted accuracy of a certain flux together with an optimal experimental approach can be effectively answered by computer based experimental design 647093. One should note that the flux calculation is rather sensitive to the mixing ratio of two differently labelled compounds applied at the same time, e.g. [¹³C₆] glucose and naturally labelled glucose. This mixing ratio should be exactly known, considering the facts that during storage some labelled compounds are hygroscopic. For glucose this can be taken into account by 8 h drying at 80°C prior to weighting.

The flux parameters are usually estimated from the ¹³C tracer studies data by minimization of the deviation between experimental and simulated labelling data using numerical routines 15 Hereby, the free flux parameters of interest, such as flux partitioning ratios or reversibilities are varied by the optimization function starting from initial values until an acceptable agreement between experimental and simulated labelling patterns is achieved. Different optimization functions such as gradient or adaptive random search functions are available. To increase the probability of the identification of a global optimum for the solution, the convergence is usually tested for different initial guesses. As error criterion a weighted sum of least squares (SLS) is typically used (Equation 2).

S L S = ∑ i ( r i , exp ⁡ − r i , c a l c r i , exp ⁡ ) 2 s r , i 2       ( Eq .   2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@5FD3@

By this, the differences between experimental (r_exp) and calculated (r_calc) labelling data, e. g. molar fractions of mass isotopomers ratios, are normalized and the resulting relative experimental errors of the corresponding MS measurements (s_r,i) are used for weighting. As a result, data with relatively small error contribute to a higher extent, whereas the influence of data with a relatively high error and uncertainty has only a minor influence on the overall optimization result. Statistical analysis is of great importance in order to identify whether differences observed for intracellular flux distributions between different experiments can be really attributed to strain or condition specific differences. Such analysis can be performed by a Monte-Carlo approach including multiple parameter estimation runs with statistical variation of the experimental data 9495. The statistical variation is done such that random errors are added to the data sets, assuming a normal distribution of measurement errors around previously obtained mean values. Subsequently, multiple parameter estimations are carried out for each scenario, yielding multiple flux distributions with a corresponding mean value and a standard deviation for each intracellular flux parameter, from which confidence limits for the single parameters can be calculated. The high accuracy of intracellular fluxes determined by GC-MS based flux analysis is illustrated by a phase plane plot for different mutant strains of C. glutamicum (Figure 10). Based on previous experimental data 21 250 independent estimates for the PPP and the TCA cycle flux with statistically varied experimental data for each strain show that, despite the strains differ only gradually in the corresponding fluxes, clear differentiation is possible. This is a great advantage as compared to NMR based flux approaches resulting in much higher uncertainty of intracellular fluxes 21. Flux analysis using GC-MS allows a high goodness of fit, if all critical steps of the comprehensive approach are carefully addressed 192122. High deviation in selected mass isotopomer distributions leaves the estimated fluxes questionable. Such deviations may point at underlying errors in the performed study. Potential sources of errors include the labelling measurement itself, assumptions in the network topology, e.g. on available pathways, or carbon transfer in the underlying reactions, or simply errors in the complex metabolic model. Simulated and experimental labelling data as well as statistics on the calculated fluxes display important information that should always be included in the presentation of flux studies.

GC-MS based metabolic flux analysis has been applied to various microorganisms. This includes several flux studies of E. coli, one of the most prominent model organisms. As example, different mutants were studied at miniaturized scale providing information on gene function 23. Metabolic flux analysis utilizing GC-MS was used also to investigate the adaptation of E. coli to the loss of key metabolic enzymes 96, the function of soluble and membrane bound transhydrogenase 97 or growth on different substrates 26. Additionally, the effect of single gene deletion on metabolic fluxes has been studied applying a combination of GC-MS and NMR for labelling analysis 269899100101102. A number of studies have been carried out for the industrial amino acid producer C. glutamicum, providing important knowledge for rational strain improvement. This microorganism has been investigated with respect to the influence of different substrates in batch culture 1922, fluxes in chemostat culture under substrate limitation 41, the comparison of different lysine producing mutants 421103 and different phases of a production process 20. Further prokaryotes studied on the level of intracellular carbon flux using GC-MS based approaches are Bacillus subtilis 79104, Bacillus clausii 105or Streptomyces noursei 106. In another study flux ratio analysis was applied to compare fluxes in Pseudomonas putida, Zymononas mobilis, Sinorhizobium meliloti, Rhodobacter sphaeroides and Lactococcus versutus 107. Among yeasts studied on the level of intracellular fluxes by GC-MS are Saccharomyces cerevisiae with studies on the influence of growth rate 1827, or the comparison of different mutants 66, several members of the genus Pichia 8488108, Phaffia rhodozyma 28 or different other species 109. Flux studies with fungi comprise e. g. biotechnologically relevant species such as Penicillium chrysogenum 29, Aspergillus nidulans 65 or Aspergillus niger 95.

Isotopic tracer experiments with GC-MS labelling analysis are utilized in the biomedical area field since many years 1213. Flux studies in this field significantly contributed to our current understanding on metabolic function in mammalian cell lines or organs or on the underlying metabolism related to diseases 110. The inherent complexity of the networks with different compartments or tissue zones, metabolite channelling and complex dilution effects of the labelling often restricts the determination by a tracer experiment to selected flux parameters 15. Flux studies of mammalian cell cultures comprise e.g. the comparison of different cell lines 30, the influence of butyrate on differentiation of adenocarcinoma cells 55, or the response of fasted rat hepatocytes to different substrates 31. Extensive work has been carried out on quantifying fluxes in the central metabolism of tissue cultures. This involves studies on the pentose phosphate pathway in human hepatoma cells 111, or on anaplerosis, cataplerosis and the TCA cycle in perfused rat liver 3536112, and rat heart 32113114. Another important application of stable isotopes and GC-MS is the in vivo quantification of polymer biosynthesis as exemplified by studies on DNA synthesis in rats 51115116, protein turn-over in humans 117 or lipidogenesis in humans 118. Hereby, a mathematical approach is applied that allows the calculation of the labelling of the actual precursor molecules of a particular polymer 119120121.