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C. Wittmann, Biochemical Engineering Institute, Saarland University, 66041 Saarbrücken, Germany; POB 151150. Fax: + 49 681 302 4572, Tel.: + 49 681 302 2205, E-mail: firstname.lastname@example.org
In the present work, a novel comprehensive approach of 13C-tracer studies with labeling measurements by MALDI-TOF MS, and metabolite balancing was developed to elucidate key fluxes in the central metabolism of lysine producing Corynebacterium glutamicum during batch culture. MALDI-TOF MS methods established allow the direct quantification of labeling patterns of low molecular mass Corynebacterium products from 1 µL of diluted culture supernatant. A mathematical model of the central Corynebacterium metabolism was developed, that describes the carbon transfer through the network via matrix calculations in a generally applicable way and calculates steady state mass isotopomer distributions of the involved metabolites. The model was applied for both experimental planning of tracer experiments and parameter estimation. Metabolic fluxes were calculated from stoichiometric data and from selected mass intensity ratios of lysine, alanine, and trehalose measured by MALDI-TOF MS in tracer experiments either with 1-13C glucose or with mixtures of 13C6/12C6 glucose. During the phase of maximum lysine production C. glutamicum ATCC 21253 exhibited high relative fluxes into the pentose phosphate pathway of 71%, a highly reversible glucose-6-phosphate isomerase, significant backfluxes from the tricarboxylic acid cycle to the pyruvate node consuming the lysine precursor oxaloacetate, 36% net flux of anaplerotic carboxylation and 63% contribution of the dehydrogenase branch in the lysine biosynthetic pathway. Due to the straightforward and simple measurements of selected labeling patterns by MALDI-TOF MS sensitively reflecting the flux parameters of interest, the presented approach has an excellent potential to extend metabolic flux analysis from single experiments with enormous experimental effort to a broadly applied technique.
intensity ratio of two mass isotopomer pools of masses m1 and m2. ν, reaction rate
flux partitioning ratio
diaminopimelate dehydrogenase branch in the lysine biosynthesis
lumped reaction of pyruvate and phosphoenolpyruvate carboxylase
lumped reaction of phosphoenolpyruvate carboxykinase, oxaloacetate decarboxylase, and malic enzyme
pentose phosphate pathway
succinylase branch in lysine biosynthesis.
Production of amino acids by Corynebacterium glutamicum belongs to the major processes in industrial biotechnology. The world market for amino acids amounts to about 3 billion US dollars, whereby lysine with a worldwide production of about 250 000 tonnes per annum is one of the most important products . Optimization of cultivation strategies and producer strains have led to increased yields and rates of amino-acid production by Corynebacteria. To a large extent, the strain improvement was based on random mutagenesis and subsequent selection [2,3]. In the last decade the powerful tools of genetic engineering allowed the targeted amplification and disruption of selected genes, which led to a number of mutants with increased capabilities of lysine secretion . However, practically achieved yields are still far from theoretical optima, leaving a significant potential for further improvement. To achieve such improvements in a targeted and efficient way, detailed knowledge of intracellular carbon flux distributions and their regulation is needed. Data on genome, transcriptome and proteome are nowadays generated with enormous efficiency, whereas the quantification of the metabolome including intracellular flux distributions is still difficult and time-consuming. Experimental developments in this area are therefore strongly desired.
So far, metabolite balancing and NMR techniques are the mainly applied techniques for metabolic flux analysis. The quantification of intracellular flux parameters by metabolite balancing usually leads to underdetermined systems. This requires assumptions on the energy metabolism [YATP, stoichiometry of oxidative phosphorylation (P/O) ratio, NADH balance, NADPH balance]. Stoichiometric parameters such as P/O ratios or ATP-yields, often originate from wild type strains and continuous cultures and may not hold true in cases of highly engineered strains . Moreover, such parameters may not stay constant during batch cultivations with changes of the physiological status of the cells. Therefore their consideration in flux analysis can cause errors or uncertainties in the obtained results. To circumvent this problem, additional information can be provided by tracer studies with 13C-labeled substrates. Recently, different research groups have quantified carbon fluxes in the central metabolism of Corynebacteria by isotopic tracer studies with NMR [6,7] which has provided valuable insights into the cellular metabolism. Due to the inherent low sensitivity of NMR, labeling patterns are mostly analyzed from amino acids obtained from hydrolyzed cellular proteins [8,9]. Mass spectrometry is regarded as valuable tool for metabolic flux analysis [10,11]. Several authors have demonstrated the potential of GC-MS for the analysis of protein hydrolysates or metabolites in 13C tracer experiments [12–16].
In the present work, a novel approach comprising 13C tracer studies with labeling measurements by MALDI-TOF MS, and metabolite balancing was applied to determine the entire carbon flux distribution in the central metabolism of lysine producing C. glutamicum during batch culture. MALDI-TOF MS was hereby applied for labeling measurements of the extracellular products lysine, alanine and trehalose. This technique requires minimal sample volumes in the range of microliters, minimal sample pretreatment, and allows fast and sensitive quantification of mass isotopomer distributions. Due to the information provided by the 13C labeling data additionally to the stoichiometric data, no assumptions on reduction equivalents or on energy formation had to be included in the flux calculation. A great advantage of the developed method is the straightforward measurement of only a few sensitive labelings, previously identified by computer based experimental design. These labelings provide the missing information to obtain the entire flux distribution map.
Materials and methods
Corynebacterium glutamicum ATCC 21253 was obtained from the American Type Strain and Culture Collection (Mannassas, VA, USA). The strain is homoserine and leucine auxotroph, exhibits a concerted aspartate kinase inhibition caused by threonine and lysine and accumulates lysine under the limitation of threonine.
LB5G and PMB media described by Vallino and Stephanopoulos  were used for precultures and main cultures, respectively. Cells inoculated from LB5G plates, grown overnight on LB5G medium in 25 mL flask cultures with 5 mL medium on a rotary shaker at 150 r.p.m. and 30 °C and washed twice with PMB medium were used as inoculation for the main cultures.
Tracer experiments for metabolic flux analysis of C. glutamicum ATCC 21253 were carried out in a 100-mL bioreactor (Meredos, Nörten-Hardenberg, Germany) either with 99% 1-13C glucose or with a mixture of nonlabeled and 99% 13C6 glucose (60 : 40) as carbon source. The applied bioreactor had a working volume of 75 mL. Temperature and pH were controlled at 30 ± 0.1 °C, and at 7.00 ± 0.05 with 0.5 m NH4OH, respectively. Aeration was adjusted to 75 mL·min−1 by a mass flow controller (Brooks, Veenendaal, the Netherlands) and stirrer speed was maintained at 600 r.p.m.
Tracer experiments for the estimation of the extent of re-utilization of secreted products by C. glutamicum ATCC 21253 were performed in shake flasks. The strain was grown on 99% 13C6 glucose as carbon source thus leading to the synthesis of completely labeled products. In three separate experiments, nonlabeled lysine, alanine, and trehalose were added after 8 h of cultivation time, respectively.
Amino acids were separated by HPLC (Kontron Instruments, Neufahrn, Germany) after precolumn derivatization (AccQ-Tag method, Millipore, Milford, USA) on a Novapac C18 column (Millipore, Milford, USA). Measurement conditions were as specified in the instruction manual. Concentrations of glucose, trehalose, citrate, α-ketoglutarate, acetate and lactate were measured by HPLC (Kontron Instruments, Neufahrn, Germany) with a Aminex HPX 87-H column (Biorad) and 0.025 m H2SO4 as isocratic eluent at 45 °C with a flow rate of 0.8 mL·min−1. Pyruvate and partly glucose were analyzed enzymatically (Sigma-Aldrich, Deisenhofen, Germany). Cell concentration was either measured gravimetrically as cell dry mass or with a spectrophotometer at 660 nm (Pharmacia). The correlation factor between dry biomass and D660 was determined as 0.294 g dry biomass per unit at D660.
Labeling patterns of metabolites were analyzed by MALDI-TOF MS using a Bruker Reflex III system equipped with a 384 Scout sample plate (Bruker-Daltonics, Bremen, Germany). The experimental protocol for sample preparation and MALDI analysis is described elsewhere . The mass distributions of the compounds of interest were obtained as mean values from 300 single laser pulses. For this purpose spectra were collected from six different sample spots, each analyzed by 5 × 10 shots on different coordinates. Due to the heterogeneous structure of matrix and analyte crystal, only selected positions within the sample spot led to useful spectra. Other did not show target signals and were therefore not included in further data processing. Mass calibration was performed with aqueous solutions of lysine, trehalose and alanine. The accuracy was ± 0.1 apparent mass units.
1-13C glucose (99%) and U-13C glucose (99%) applied as tracer substrates were purchased from Euriso-Top (Saarbruecken, Germany). All other chemicals were purchased from Sigma-Aldrich (Deisenhofen, Germany) and were of analytical grade.
The simulations performed for experimental design and parameter estimation were carried out on a personal computer applying the software matlab 5.3 and simulink 3.0 (Mathworks Inc., Nattick, MA, USA).
Recently we introduced a mathematical model programmed in matlab and simulink for obtaining mass distributions of intermediary metabolites from a given set of metabolic fluxes . This model was further extended and modified for predicting the influence of variations in metabolic fluxes and labeling positions and degrees in the tracer substrate glucose on labeling patterns of extracellular metabolites of C. glutamicum. Additionally an algorithm was now programmed in matlab allowing the estimation of flux parameters from experimental labeling data obtained by MALDI-TOF MS.
The following definitions for labeling patterns of molecules were used in the present paper. An ‘isotopomer’ is described by a specific number of 13C atoms in specific positions of the molecule. For a compound with n carbon atoms, 2n isotopomers are possible. A ‘mass isotopomer’ is specified by the number of 13C atoms in the molecule, but not by their positions. A compound with n carbons can have n + 1 different mass isotopomers. The relative molar fractions of different mass isotopomer pools can be determined by mass spectrometry. The sum of molar fractions of all mass isotopomer pools is equal to 1. The ratio between molar fractions of two mass isotopomer pools of masses m1 and m2 is identical with mass spectral intensity ratios and defined in the present work as ‘intensity ratio’Im1/m2. If more than two mass isotopomer pools are assessed their relative ratios are named ‘mass distribution’.
The biochemical network of the C. glutamicum metabolism comprising 37 different fluxes is shown in Fig. 1. The quantification of five key flux parameters was of special importance in the present work. These were the flux partitioning ratios (a) between glycolysis and pentose phosphate pathway (ΦPPP), (b) between the alternative pathways in the lysine biosynthesis (ΦDH), (c) at the pyruvate node (ΦPC), (d) the reversibility of glucose-6-phosphate isomerase (ζPGI), and (e) the reversibility of fluxes between C4 metabolites of the tricarboxylic acid cycle and C3 metabolites from the glycolysis (ζPC/PEPCK). The definition of these flux parameters is given in the appendix.
The pools of malate and oxaloacetate in the tricarboxylic acid cycle were lumped together. The same was performed for the pools of phosphoenolpyruvate and pyruvate in the glycolysis. It is known that a number of enzymes can potentially catalyze fluxes around the pyruvate node, and fluxes between C4 metabolites of the tricarboxylic acid cycle and C3 metabolites from the glycolysis. Anaplerotic oxaloacetate formation in Corynebacteria can be catalyzed by phosphoenolpyruvate carboxylase or by pyruvate carboxylase. Potentially, also malic enzyme can work as anaplerotic enzyme and produce malate from phosphoenolpyruvate. At least three different enzymes can catalyze the flux in the opposite direction: phosphoenolpyruvate carboxylase (oxaloacetate to phosphoenolpyruvate), malic enzyme (malate to phosphoenolpyruvate), and oxaloacetate decarboxylase (oxaloacetate to pyruvate). A differentiation between these enzymes by tracer experiments is not possible without specially elaborated conditions such as strains lacking pyruvate kinase activity  or cofeeding of labeled glucose and lactate and the measurement of single isotopomers . The tracer experiments of the present work cause identical labeling patterns for the two alternative anaplerotic reactions and for the three possible decarboxylating reactions, respectively. Therefore, the fluxes of anaplerotic pyruvate carboxylation and of oxaloacetate decarboxylation, as regarded in the network in Fig. 1, represent the overall fluxes by the concerted action of all potential enzymes, respectively. The corresponding flux parameter was defined as ζPC/PEPCK, as under in vivo conditions pyruvate carboxylase and phosphoenolpyruvate carboxykinase are the most important enzymes in C. glutamicum.
The transaldolase and transketolase reactions in the PPP were regarded as reversible. The values for the reversibilities of these reactions were taken from previous flux calculations for C. glutamicum. As the mass distributions of extracellular Corynebacterium metabolites are rather insensitive towards changes in the PPP reversibilities, these flux parameters practically did not significantly interfere with the performed measurements .
A metabolite pool for CO2 was implemented, reflecting its mass isotopomer distribution as a result of the CO2 producing and consuming reactions in the network. The integration of 13C labeling from CO2 into oxaloacetate/malate in the anaplerotic carboxylation was thus taken into account.
The aim of the present study was the quantification of the flux distribution in the central metabolism of C. glutamicum, comprising the three flux partitioning ratios between glycolysis and pentose phosphate pathway, between anaplerosis and the tricarboxylic acid cycle, and between the two alternative branches in the lysine biosynthetic pathway, the reversibility of glucose-6-phosphate isomerase and the reversibility of the bidirectional fluxes between oxaloacetate and pyruvate.
In order to develop a straightforward and cost-efficient experimental setup for this task, simulation based experimental design was carried out at first. Among the different commercially available 13C labeled glucose isotopomers, 1-13C glucose and 13C6 glucose are by far the cheapest compounds. Therefore, the experiments were planned such, that the flux parameters of interest could be identified by exclusive feeding of either 1-13C glucose, or by mixtures of naturally labeled and 13C6 glucose, respectively. The flux estimation was based on the measurement of labeling patterns of extracellular products formed by the tested organism. In cultivations of C. glutamicum ATCC 21253 different by-products besides lysine, such as alanine, valine, or trehalose are observed, that could serve as potential candidates for flux analysis [17,18].
1-13C glucose is the substrate of choice for quantifying the flux partitioning ratio between glycolysis and pentose phosphate pathway (ΦPPP) of Corynebacterium glutamicum. The intensity ratios between single labeled and nonlabeled lysine or alanine can be measured as sensitive indicators to quantify ΦPPP. An excellent target for the quantification of the reversibility of glucose-6-phosphate isomerase (ζPGI) is trehalose, which is often secreted by lysine producers . The optimal substrate labeling to quantify ζPGI is 1-13C glucose, as illustrated below. Due to the fact that all fructose 6-phosphate molecules formed via the PPP from 1-13C-glucose have lost their label, the 13C labeling of the glucose-6-phosphate pool is diluted by the backflux from fructose 6-phosphate, catalyzed by reversible glucose-6-phosphate isomerase. This results in the additional formation of single and nonlabeled trehalose besides the double-labeled form. Computer simulations of the Corynebacterium metabolism showed that the intensity ratio Im+1/m+2 of trehalose sensitively reflects ζPGI. As the relative flux into the PPP determines the fraction of nonlabeled fructose 6-phosphate and thus the pool dilution of glucose-6-phosphate, the two parameters ζPGI and ΦPPP should be estimated in parallel, which is the case in the presented approach.
The quantification of the reversibility of the cycling fluxes between oxaloacetate and pyruvate (ζPC/PEPCK) is based on the use of mixtures of naturally labeled and 13C6 glucose . Here, the labeling of alanine or other products originating from pyruvate sensitively reflects ζPC/PEPCK. Only small amounts of m + 1 and m + 2 mass isotopomers are formed besides the nonlabeled and the fully labeled alanine in case of no backfluxes from oxaloacetate to pyruvate. In contrast, the fractions of m + 1 and m + 2 mass isotopomers are significantly increased due to backfluxes from the tricarboxylic acid cycle and the intensity ratios Im+1/m, and Im+2/m+3 of alanine and related products can be used to quantify ζPC/PEPCK.
The flux partitioning ratio ΦPC can be determined with the same tracer substrate mixture . The intensity ratio Im+1/m of lysine changes markedly with variation of ΦPC and can be thus measured to quantify this flux parameter. A novel strategy was developed to additionally determine ΦDH from the lysine labeling in such experiments. These studies were performed, because 3-13C or 4-13C glucose, previously identified as a suitable substrates for the quantification of ΦDH are rather expensive and 1-13C glucose is not a suitable substrate for this purpose. Metabolic simulations revealed that the intensity ratio of double to single labeled lysine Im+2/m+1 is influenced significantly by the value of ΦDH (data not shown).
Summarizing, the following strategy was chosen for the flux analysis of the tested Corynebacterium: In tracer experiments with 1-13C -glucose, the intensity ratios Im+1/m of lysine, Im+1/m of alanine and Im+1/m+2 of trehalose were measured, and in tracer experiments with mixtures of naturally labeled and 13C6 glucose, the intensity ratios Im+1/m, and Im+2/m+1 of lysine, and Im+1/m and Im+2/m+3 of alanine were determined. Thus the different flux parameters at the glucose-6-phosphate node and at the pyruvate node, were determined from the same experiment, respectively. The number of measured labelings (seven) was higher than the number of parameters (five). The redundant information could be used to increase the accuracy of the results.
The information obtained from 13C tracer studies and from metabolite balancing was combined for the estimation of the flux distribution during the phase of lysine production. In total, 37 different fluxes had to be determined, whereby 32 experimental constraints resulted from stoichiometric balancing, stoichiometric measurements and assumptions on the PPP reversibilities as described in the Appendix. Additional constraints were obtained from 13C labeling data. The network was overdetermined by the measurement of seven intensity ratios of mass isotopomers to estimate the five flux parameters ΦPPP, ΦPC,ΦDH, ζPC/PEPCK, and ζPGI. A least square approach was therefore possible. The flux of lysine measured from extracellular lysine accumulation was not included as stoichiometric constraint for the parameter estimation. The lysine flux was calculated from the 13C labeling data. Comparison of this value with the lysine flux determined from extracellular accumulation was used to prove the consistency of the data.
The parameter estimation was based on the optimization function ‘fmincon’ implemented in matlab. The flux parameters were estimated by minimization of the sum of the squares of the relative deviations (S) between experimental (Iexp) and modeled (Imod) intensity ratios of mass isotopomers corresponding to the optimized set of fluxes [Eqn. (1)].
Two optimization strategies were carried out: (a) simultaneous estimation of all parameters from all measured labelings, and (b) cyclic-sequential estimation of the parameters, whereby each parameter was calculated from its corresponding most sensitive intensity ratio. The latter was possible due to previously performed sensitivity studies. In the cyclic-sequential parameter estimation mode, estimated parameter values were always handed over to the following optimization cycle. Optimization cycles comprising the sequential estimation of all five parameters were repeated until all parameter values stayed constant.
Cultivation of c. glutamicum atcc 21253
The cultivation profile of C. glutamicum ATCC 21253 is displayed in Fig. 2A–C. During 25 h of cultivation, 14 mm lysine and about 3.5 g·L−1 of biomass were produced from 80 mm of glucose. Obviously, the cultivation can be divided into different phases: (I) initial exponential growth phase from 0 to 6 h, (II) phase of maximum lysine production with simultaneous reduced growth from 6 to 15 h, and (III) phase of reduced lysine production by nongrowing cells from 15 to 25 h. The specific growth rate during the phase I was 0.53 h−1.
During the first 6 h (phase I), the amino acids threonine, leucine and methionine are consumed, allowing growth of the homoserine auxotrophic strain and suppressing lysine formation due to the feedback inhibition of aspartate kinase inhibition caused by threonine (Fig. 2B). Citrate, present in the medium to facilitate the uptake of iron by the cells, was the major carbon source in the initial 4 h (not shown). Glucose concentration only slightly decreased during this time. With the depletion of citrate, the metabolism switched to glucose consumption as the sole source of carbon and energy for the rest of the cultivation.
Threonine, leucine and methionine were completely consumed after about 6 h, linked to the beginning of lysine production, which lasted from 6 to 25 h (Fig. 2A,B). The biomass still increased about twofold after the depletion of the essential amino acids, which can be explained by the use of endogenous threonine and methionine for growth . From 6 to 15 h maximum lysine production was observed. Afterwards, the growth completely stopped, but the cells still maintained the production of lysine until 25 h, even though with a lower rate. After 25 h, the lysine concentration reached the maximum level, while still about 5 g·L−1 of glucose were present in the medium. The complete utilization of the glucose lasted from 25 to 37 h (data not shown). During this final stage of the cultivation the concentration of lysine remained constant, and the biomass concentration dropped.
In addition to lysine, various by-products such as other amino acids, organic acids, and the disaccharide trehalose were formed (Fig. 2B,C). The observed profiles varied for the different by-products. The accumulation of trehalose, alanine and valine began together with lysine formation. Acetate was secreted throughout the whole cultivation. Pyruvate and lactate were produced after about 10 h. After 25 h the concentrations of lysine, alanine, valine and trehalose remained constant, whereas the levels of the organic acids further increased until the glucose was completely consumed (data not shown). The ammonium concentration stayed constant throughout the cultivation at about 1 g·L−1 (Fig. 2A). This resulted from the nearly equimolar relation between ammonium uptake by the cells and the ammonium supply by the pH control (NH4OH).
The overall specific glucose consumption rate and the biomass yield during this phase were determined as 1.72 ± 0.06 mmol·(g biomass)−1·h−1 and as 0.060 ± 0.003 g·(mmol glucose)−1, respectively. The glucose uptake flux was set to 100%. All other fluxes in the network were then calculated as relative fluxes normalized to the glucose uptake flux. Table 1 shows the obtained yields for extracellular products during the phase of maximum lysine production, which was of central interest in the present work (phase II). They are identical to the secretion fluxes v2, v20, v21, v22, v23, v28, and v35 in Fig. 1. 21.3% of glucose were used for lysine production. In comparison, the other by-products listed in Table 1 summed up to 8.1% of the glucose carbon. From the experimentally determined biomass yield and from the biomass composition of C. glutamicum previously determined by Marx et al. , the demand for the 12 biomass precursors was calculated for the phase of maximum lysine production (Table 2). The values obtained correspond to the anabolic fluxes v4, v7, v9, v10, v18, v24, v25, v27, v32, and v34 in Fig. 1. In total, 36.8% of the glucose carbon was thus directed towards the anabolism during the phase of maximum lysine production. Among the different metabolites, the highest demand resulted for pyruvate, acetyl-CoA, and α-ketoglutarate. The major fraction of the biomass carbon originated from the glycolysis (34.8%) and from the tricarboxylic acid cycle (36.6%). The PPP contributed with only 14.9%. The rest of 13.6% came from AcCoA.
Table 1. Yield coefficients for extracellular products determined for C. glutamicum ATCC 21253 during lysine production in batch cultures as mean values from two cultivations. The values obtained correspond to the fluxes v2 (trehalose), v20 (pyruvate), v21 (lactate), v22 (alanine), v23 (valine), v28 (acetate), and v35 (lysine) in Fig. 1.
Yield coefficient (mol/mol)
Table 2. Precursor demand for biomass formation calculated from the experimentally determined yield coefficient YX/S = 0.0599 g·(mmol glucose)−1 and from biomass composition of C. glutamicum previously estimated  in batch cultures of C. glutamicum ATCC 21253 during lysine production. Values given are means of two cultivations. The values obtained correspond to the anabolic fluxes v4 (glucose-6-phosphate), v7 (fructose 6-phosphate), v9 (ribose 5-phosphate), v10 (erythrose 4-phosphate), v18 (glyceraldehyde 3-phosphate), v24 (3-phosphoglycerate), v25 (sum of phosphoenolpyruvate, and pyruvate), v27 (acetyl-CoA), v32 (α-ketoglutarate), and v34 (oxaloacetate) in Fig. 1.
Demand (mol/mol glucose)
Analysis of extracellular c. glutamicum products by maldi-tof ms
As shown previously MALDI-TOF MS can be applied for the detection of lysine and alanine in culture supernatants of C. glutamicum. Recent studies on quantification of lysine and alanine in cultivation samples of C. glutamicum, which are based on the measurement of relative peak intensities of the analyte and an internal standard, e.g. nonlabeled lysine and α-15N-lysine, respectively, revealed excellent correlation with conventional HPLC analysis indicating that the MALDI-TOF MS measured relative peak intensities were not disturbed by isobaric background overlay . The significance of potential chemical background noise interfering with the measured mass spectra of the analytes and influencing the obtained relative peak intensities was further examined as follows. The mass isotopomer distributions of lysine and alanine formed by C. glutamicum growing on nonlabeled glucose and analyzed by MALDI-TOF MS exhibited good correlation to theoretical values calculated from the occurrence of natural isotopes, providing additional evidence that isobaric background overlay is insignificant. The experimentally determined fractions of nonlabeled (m) single-labeled (m + 1), and double-labeled (m + 2) lysine as [M + H]+ adducts were 92.8%, 6.7%, and 0.5%, compared to theoretical values of 92.5%, 6.9%, and 0.6%, respectively. For the [M + H]+ ion of alanine the relative fractions were 95.7% (m), 3.5% (m + 1), and 0.8% (m + 2), whereas the corresponding calculated values were 95.8%, 3.8%, and 0.5%, respectively. In cultivations of C. glutamicum ATCC 21253 on U-13C glucose, only the signals of the fully labeled [M + H]+ adducts of lysine (m/z 153) and alanine (m/z 93) were obtained (data not shown).
In the present work, a protocol for the analysis of trehalose, another C. glutamicum product, was developed. The trehalose labeling can be used to calculate the reversibility of glucose-6-phosphate isomerase in the C. glutamicum network (see above). Initial MALDI-TOF MS measurements with aqueous solutions of 10 mm trehalose and 2,5-DHB as matrix revealed, that it can be detected in the positive reflector mode as adduct with sodium (m/z 365), and with potassium (m/z 381) (data not shown). Proton adducts of trehalose were not observed. This was comparable to previous measurements of mono- and disaccharides by MALDI-TOF MS . Suitable signals were obtained over a broad range of the crystallized sample spot when using pure trehalose, whereby optimum signal intensities were observed in the center of the spot. Among different matrices tested, 2,5-DHB was found optimal. In principle, the developed protocol can be also applied to analyze trehalose in culture supernatants of C. glutamicum. Successful analysis of trehalose in cultivation samples however, required further optimization. This was due to its low concentration of about 1 mm and to the fact that additional compounds in the sample such as salts caused a strong suppression of the signal efficiency, when compared to the pure trehalose spectra. A 1 : 5 dilution of the culture supernatant, previously found to substantially increase the signal efficiency , was also chosen for the trehalose analysis. Over a broad range of the spot of a diluted cultivation sample, the trehalose signals were rather low or completely missing, but were significantly increased at distinct positions, where trehalose seemed to be concentrated by the crystallization. These hot spots were picked out by searching the sample spot with the laser. They were mainly located in the sample spot center. After identification of such a hot spot, optimal spectra were collected after initial ablation of the uppermost layer by the laser and subsequent series of five shots. Interference of the mass spectrum of trehalose by chemical background noise could be excluded from additional experiments of C. glutamicum ATCC 21253 as described below. In a first cultivation on nonlabeled glucose, the labeling of trehalose formed by the strain was quantified by MALDI-TOF MS (Fig. 3A). The measured relative fractions of nonlabeled, single-labeled and double-labeled trehalose as [M + K]+ adduct of 80.8, 11.1 and 8.1% agreed well with theoretical values of 80.3, 11.4 and 8.3%, respectively. The MALDI-TOF MS measurement of trehalose formed in a cultivation of C. glutamicum ATCC 21253 on U-13C labeled glucose gave the signals of the fully labeled mass isotopomer at m/z 377 (Na adduct) and m/z 393 (K adduct), but no peaks at m/z 365–367 and 381–383, respectively (Fig. 3B). It should be noticed that the small signals at m/z 376 and 391 result from the fact that the labeling degree of the substrate was only 99%.
Elucidation of in vivo uptake of secreted c. glutamicum products into the metabolism
A crucial question, when applying the labeling pattern of an extracellular product for flux analysis under batch conditions is, wether the labeling pattern of this compound reflects the actual flux distribution of the culture or the complete history of its production. The extent of the re-utilization of excreted metabolites by C. glutamicum was therefore assessed in separate tracer experiments for lysine, alanine and trehalose. For this purpose, cultures grown on 13C6-glucose and thus forming fully 13C labeled products were spiked with naturally labeled mass isotopomers of the studied metabolites. The time point of spiking was the beginning of secretion of the corresponding product after about 8 h. The relative amounts of internally produced and externally added lysine, alanine and trehalose were obtained by concentration measurements, performed directly before and after the spiking and at the end of the experiment.
At the end of the production phase, the labeling of the external pools was analyzed by MALDI-TOF MS and compared to the relative amounts of internally produced and externally added lysine, alanine and trehalose. In the case, where a secreted product is not re-utilized, the externally added naturally labeled mass isotopomers will remain in the medium. Formation of fully labeled product by the cells will cause an overlay of the two differently labeled pools, resulting in a labeling proportional to the concentration ratio of externally added to internally produced mass isotopomers. In the case, where a product is continuously exchanged between the interior of the cell and the medium, the externally added nonlabeled mass isotopomers would be replaced by internally produced labeled mass isotopomers and would thus disappear throughout the further cultivation. Mass spectra of lysine and trehalose in culture supernatants after 24 h of cultivation are shown in Fig. 3D. In both cases significant amounts of the nonlabeled mass isotopomers, which had been added to the culture already after 8 h of cultivation, were detected. For lysine the nonlabeled fraction (m/z 147) was about twofold higher than the fraction of internally produced 13C6 lysine (m/z 153). The smaller lysine signals at m/z 148 and m/z 152 originate from naturally occurring isotopes in the externally added lysine, and from the fact that the applied carbon source was only labeled with a degree of 99% in every carbon atom, thus leading to a minor production of lysine, which was only partially 13C labeled. The two trehalose fractions at m/z 381 and m/z 393 reflect the externally added nonlabeled and the internally produced fully labeled mass isotopomers. Both fractions were about equal.
The measured concentration ratios and the labeling ratios between naturally labeled and 13C enriched isotopomers obtained from the experiments are given in Table 3. At the end of the cultivation the concentration ratio of U-12C to U-13C mass isotopomers was 2.32, 0.52 and 0.79 for lysine, alanine and trehalose, respectively. These values agreed very well with the corresponding pool labelings at the end of the cultivations, indicating that the externally added pool was practically completely conserved during the cultivation. It can be concluded, that under the given conditions lysine, alanine and trehalose are not re-utilized by the strain after their secretion into the medium. In case of lysine, the active transport mechanism for lysine excretion recently identified in C. glutamicum supports this conclusion . Additional experiments showed, that the strain is not capable to use trehalose as a carbon source, which underlines the finding that no re-utilization was observed. Extracellular pools of lysine, alanine and trehalose were regarded as integral pools reflecting the process history of their formation.
Table 3. Quantification of in vivo fluxes of lysine, alanine and trehalose across the cell membrane of C. glutamicum ATCC 21253 in batch cultures. The cultures were grown on U-13C glucose thus synthesizing fully labeled products and spiked with non labeled products after 8 h. The ratio of non labeled to labeled product after 24 h of cultivation was measured by MALDI-TOF MS. The concentration ratio between externally added and internally produced products was measured by HPLC.
Mass intensity ratio (IU12C/U13C)
Concentration ratio (CU12C/U13C)
0.52 ± 0.03
0.56 ± 0.02
2.32 ± 0.21
2.29 ± 0.09
0.79 ± 0.06
0.71 ± 0.02
Analysis of 13C labeled products in tracer experiments of C. glutamicum by MALDI-TOF MS
In the performed tracer experiments, the mass isotopomer distributions of lysine, alanine and trehalose were quantified by MALDI-TOF MS at the end of the maximum lysine production phase at 15 h of cultivation.
Tracer experiment with 1-13C glucose
Lysine was detected in the positive reflector mode as [M + H]+, [M + Na]+, and [M + K]+ adduct, whereby the proton adducts gave the highest signals. The mass isotopomer distribution of lysine produced by C. glutamicum ATCC 21253 from 1 to 13C-glucose as tracer substrate is shown in Fig. 3E. The displayed spectrum resulted from five single laser shots on a sample spot with a laser attenuation of 60. Obviously the applied labeling resulted in significant formation of higher labeled mass isotopomers of lysine in addition to the nonlabeled mass isotopomer. The four peaks of lysine at m/z 147.0 (nonlabeled), m/z 148.0 (singly labeled), m/z 149.0 (double labeled) and 150.0 (triple labeled) are completely resolved. Suitable lysine spectra could be obtained from the majority of sample spot coordinates. Lysine was detected in different depths of the crystal. Up to 50 shots performed on the same coordinate yielded lysine ions in the spectrum. In addition to 2,5-dihydroxybenzoic acid, also sinapinic acid was a suitable matrix for the lysine measurement. No isobaric overlays of lysine mass isotopomer ions with matrix ions were observed with both matrices.
The analysis of trehalose was performed in the positive reflector mode with 2,5-DHB as matrix. Trehalose was detected as adducts [M + Na]+ and [M + K]+. The mass isotopomer distribution of the [M + K]+ adduct produced by the studied strain from 1 to 13C-glucose is shown in Fig. 3F. Besides the nonlabeled form of mass m (m/z 380.8), trehalose mass isotopomers up to the mass m + 5 (m/z 385.8) were detected. Double labeled trehalose was the dominating fraction. The obtained spectrum already clearly indicates that the glucose-6-phosphate isomerase is a reversible enzyme. In case of an irreversible glucose-6-phosphate isomerase, glucose-6-phosphate would originate exclusively from glucose taken up. Thus, the labeling of glucose-6-phosphate would be identical to the labeling of the applied tracer substrate. Pure 1-13C-glucose as tracer substrate would therefore lead to the sole formation of double labeled trehalose. The substantial occurrence of nonlabeled and single labeled trehalose in Fig. 3F denotes the presence of nonlabeled glucose-6-phosphate. This requires a backflux of nonlabeled fructose 6-phosphate originating from the PPP, via the reversible action of glucose-6-phosphate isomerase. The formation of fructose 6-phosphate via the PPP is linked to a release of the label as 13CO2 with the applied tracer substrate.
Tracer experiment with U-13C glucose
The mass spectrum of lysine from the tracer experiment with 40% 13C6-glucose is presented in Fig. 3G. All seven mass isotopomers of lysine from the 12C6 to the 13C6 labeled molecule were detected. Due to the fact that a slight excess of nonlabeled glucose was used in the tracer substrate mixture, the mass fractions of lower masses are a little bit higher compared to those of higher masses. If an equimolar mixture of fully labeled and nonlabeled glucose would be applied, the spectrum would be symmetric.
Alanine mass distributions were determined in the positive reflector mode with 2,5 DHB. A spectrum of the proton adduct of alanine from a cultivation with 40% 13C6 glucose is displayed in Fig. 3H. In comparison to lysine, higher laser energies were necessary to ionize this amino acid. A reason for this can be the less effective ionization due to the presence of only one positively charged amino group. Moreover, the concentration of alanine was smaller compared to lysine. The main fractions are the nonlabeled and the fully labeled alanine mass isotopomers, which result from the cleavage of the C6 substrates into the corresponding C3 metabolites within the glycolysis (Fig. 3H). Besides these two fractions, also the m + 1 and m + 2 mass isotopomers can be seen. These labelings mainly originate from reversible backfluxes of carbon from the tricarboxylic acid cycle to the glycolysis. The different reactions in the tricarboxylic acid cycle comprise (a) the release of carbon from the metabolite skeletons by decarboxylation, (b) the integration of carbon into the metabolite skeleton by carboxylation, (c) the combination of metabolite skeletons in the addition of oxaloacetate and acetyl CoA, and (d) the scrambling of label at the point of the symmetric molecule succinate. The concerted action of these reactions causes a significant regrouping of the carbon skeleton. In case of backfluxes from the tricarboxylic acid cycle to the glycolysis, the regrouped labelings of the tricarboxylic acid cycle are mixed in the pool of pyruvate with the labelings originating from glycolysis and PPP. This leads to the formation of single-labeled and doubled-labeled pyruvate and the subsequent product alanine. To a much smaller extent also the reversibilities of transaldolase and transketolase in the PPP may lead to m + 1 and m + 2 mass isotopomers of alanine. The m + 1 and m + 2 mass isotopomers of alanine thus clearly indicate the presence of a cycling flux between the tricarboxylic acid cycle and the glycolysis.
Metabolic flux distribution of c. glutamicum
The intensity ratios of lysine, alanine and trehalose measured by MALDI MS in the tracer experiments are summarized as mean values from 300 laser shots in Table 4. These labeling data together with the obtained stoichiometric data in Tables 1 and 2 were applied for calculating the entire flux map of the central metabolism of C. glutamicum during the phase of lysine production. Alternatively, the flux parameters were estimated (a) simultaneously from all measured intensity ratios, or (b) cyclic-sequentially from the respective sensitive labelings as described above. With both strategies, and for various different initial guesses for the parameters, identical results were obtained, which makes the identification of a global optimum very likely. The flux parameters were determined as follows: ΦPPP 0.74, ζPGI = 11.70, ΦPC = 0.35, ΦDH = 0.63, and ζPC/PEPCK = 0.49. With both strategies, and for various different initial guesses for the parameters, identical results were obtained, which makes the identification of a global optimum very likely.
Table 4. 13C tracer experiments of C. glutamicum ATCC 21253 in batch cultures with 1-13C glucose and mixtures of nonlabeled and fully labeled glucose. Mass intensity ratios measured by MALDI-TOF MS from culture supernatants after 16 h of cultivation (Iexp) and calculated from the obtained flux distribution after parameter estimation (Ical). The measured results reflect 300 laser shots in the positive reflector mode for each intensity ratio.
Mass intensity ratio
99% 1-13C glucose
Im+1/m of lysine
Im+1/m of alanine
Im+1/m+2 of trehalose
40% 13C6 glucose
Im+1/m of lysine
Im+3/m+1 of lysine
Im+1/m of alanine
Im+2/m+3 of alanine
The cyclic-sequential estimation of single parameters (considering three optimization cycles) was faster in comparison to the simultaneous determination. The values for ΦPPP, ΦPC, ζPC/PEPCK, and ζPGI obtained after the first estimation cycle were within a range of 98–102% compared to the corresponding final values. The value determined for ΦDH differed slightly more. Within three optimization cycles, all flux parameters reached their final values. Throughout further iteration no change of any of the parameters was observed, indicating that all labeling patterns calculated from the obtained flux distribution matched with the experimental data. The calculated intensity ratios reflecting the corresponding flux distribution are given in Table 4. Clearly an excellent agreement between experimentally determined and calculated intensity ratios was achieved. The sum of the squares of the relative deviations between experimental and calculated intensity ratios was 8.8 × 10−4.
The entire flux distribution of C. glutamicum ATCC 21253 for the phase of lysine production in batch culture is given in Fig. 4. From the 100% influx of carbon into the cells, 24.4% were directed into the glycolysis, whereas the major fraction of 71.0% entered the PPP. This is equal to a flux partitioning ratio between glycolysis and PPP ΦPPP = 0.74. Clearly the strain supplied substantial amounts of NADPH by the high influx into the oxidative part of the PPP. The rest of carbon at the glucose-6-phosphate node was used for synthesis of extracellular trehalose (3.4%), and growth (1.2%). Flux through the glycolysis arriving at the pyruvate node was 146.9%, indicating that 26.6% of the total carbon are withdrawn from the metabolism in the glycolytic and the PPP reactions for the formation of biomass precursors, and extracellular products such trehalose or CO2. At the pyruvate node a high net flux of 36.6% was observed for the anaplerotic carboxylation of pyruvate, while 68.8% was directed towards the tricarboxylic acid cycle. The resulting flux partitioning ratio was ΦPC = 0.35. Besides these two major routes of carbon flux at the pyruvate node, 18.8% were channeled into the lysine biosynthetic pathways, 14.0% were used for growth and 8.6% were excreted into the medium as different amino acids and organic acids. The tricarboxylic acid cycle exhibited a significant activity with a flux of 51.1% for citrate synthase. With the consumption of α-ketoglutarate for growth, the remaining flux through the rest of the tricarboxylic acid cycle to the pool of oxaloacetate was 40.9%. Significant bidirectional fluxes between the pools of pyruvate and oxaloacetate were observed. Whereas a forward flux of 54.6% was found for the formation of oxaloacetate/malate, a backward flux of 18.0% continuously depleted these C4 units from the tricarboxylic acid cycle. The superposition of both fluxes resulted in the observed net flux of 36.6% for the anaplerotic carboxylation. The net flux was thus about twofold higher then the backflux, leading to a reversibility of the fluxes between pyruvate and oxaloacetate of ζPC/PEPCK = 0.49. Both alternative pathways of lysine biosynthesis were active in vivo. The major fraction of lysine was formed via the dehydrogenase branch with a relative flux of 11.9%, whereas 6.9% of the carbon was directed through the succinylase pathway. The corresponding flux partitioning ratio thus was ΦDH = 0.63. Glucose-6-phosphate isomerase was found to be a highly reversible enzyme. The estimated reversibility of the enzyme was ζPGI = 11.7, indicating that the exchange flux between glucose-6-phosphate and fructose 6-phosphate was much higher than the net flux.
Concerning the overall carbon flux into catabolism, anabolism and product formation from the uptaken glucose, 36.9% of carbon were consumed for biomass formation, 18.8% for lysine synthesis and 8.1% for by-product formation. 36.2% of the input carbon was released as CO2. It comprised a consumption flux of 9.1% through the anaplerotic carboxylation of pyruvate, plus CO2 formation in the PPP (11.8%), at the entry into the tricarboxylic acid cycle (11.5%), in the tricarboxylic acid cycle decarboxylation reactions (15.3%), in the lysine biosynthesis (3.1%), from phosphoenolpyruvate carboxykinase activity (3.0%), and linked to the formation of valine (0.5%).
As can be seen from Fig. 2A growth is reduced during the lysine production phase, which is linked to a reduced ATP demand. Nonetheless, the tricarboxylic acid cycle still exhibits significant activity during this phase. In this light, the observed in vivo activity of enzymes catalyzing the transformation of C4 units of the tricarboxylic acid cycle into C3 units of the glycolysis, may be involved in the waste of excess ATP.
The obtained information on the intracellular flux distribution can be used to set up a balance for NADPH. As previously shown for C. glutamicum, glucose-6-phosphate dehydrogenase , 6-phosphogluconate dehydrogenase , and isocitrate dehydrogenase  use NADPH as cofactor. This leads to a formation flux for NADPH of 71.0 + 71.0 + 51.1 = 193.1%. On the other hand, NADPH is required for growth and for the synthesis of lysine. Four NADPH are needed for one lysine, resulting in a consumption flux for NADPH of 75.2%. With a demand of 14.849 mmol NADPH·(g biomass)−1 for growth  and a biomass yield of 0.0599 g·(mmol Glc)−1 (this paper), an additional flux of 88.9% of NADPH is required for growth. This leads to an overall consumption flux of 164.1%. Considering the NADPH formation flux of 193.1%, lysine formation by C. glutamicum ATCC 21253 seemed no to be limited by NADPH, but the cells have to deal in fact with an excess flux of 29.0% NADPH. This implies the in vivo activity of NADPH consuming reactions. Similar findings were reported for the lysine producing strain C. glutamicum MH 20–22 B . Possible candidates pointed out by the authors were in vivo NADPH regeneration by an oxidase, malic enzyme or alternative reactions, which have not been identified yet.
The substantial activity of the tricarboxylic acid cycle provides a high production rate of succinyl-CoA, which is required as cofactor in the biosynthesis of lysine, methionine, and diaminopimelic acid. The total demand of succinyl-CoA of 8.6% comprises relative fluxes for the production of extracellular lysine (6.9%), lysine (0.5%) and methionine (0.9%) contained in cell proteins, and diaminopimelate as a cell wall building block (0.3%). The supply of succinyl-CoA of 40.9% is much higher than the total demand of 8.6%. This underlines, that the reactions requiring succinyl-CoA are not limited due to a shortage of this cofactor. The relatively low activity of the succinylase pathway for lysine formation is therefore due to other reasons. Succinyl-CoA is used to a large extent of almost 80% for energy formation.
The relative flux into the product lysine obtained from the 13C labeling data was 18.8%. It showed good agreement with the relative flux calculated independently from extracellular rates for lysine formation and glucose consumption, which was 21.3%. This underlines the consistency of the presented data.
The in vivo flux distribution of C. glutamicum ATCC 21253 during lysine production in batch culture obtained in the present work, revealed both similarities and differences compared to a metabolite balancing approach in batch cultivations of the same strain  and 13C tracer experiments in continuous culture with C. glutamicum MH 20–22B by NMR . The relative flux into lysine of 18.8% (this work), was almost identical with 18.6% of Marx et al. , whereas Vallino and Stephanopoulos found 24% . In accordance to our work, the above mentioned authors observed, that the major carbon flux at the glucose-6-phosphate node is directed towards the pentose phosphate pathway during the production of lysine. The relatively high activity of the pentose phosphate pathway was also observed for glutamate producing Corynebacteria. A good agreement was found for the anaplerotic carboxylation of pyruvate, which was 36.6% in the present paper, 38% for MH 20–22B  and 41% for ATCC 21253 .
A shown, C. glutamicum ATCC 21253 produced 63% of the lysine via the dehydrogenase pathway. In contrast, only 26% of lysine were synthesized through the dehydrogenase branch in continuous culture by C. glutamicum MH 20–22B . This might be caused by the different growth conditions. It is known that the flux partitioning ratio between dehydrogenase and succinylase pathway responds to parameters such as ammonium concentration or cultivation stage .
An interesting result is the obvious correlation between tricarboxylic acid cycle activity and backflux from oxaloacetate and malate to glycolysis. Both, cycling fluxes between C3 units of the glycolysis and C4 units of the tricarboxylic acid cycle (ζPC/PEPCK = 0.49) and relative flux through the tricarboxylic acid cycle (51.1%) were lower in the present work, compared to Marx et al. , ζPC/PEPCK = 0.8 and 62.1%. The backflux from the tricarboxylic acid cycle to the glycolysis is related to a waste of ATP, which is formed mainly via the tricarboxylic acid. The correlation between the two flux values may therefore correspond to a certain energy level that is adjusted in the cells during the production of lysine. A reduced tricarboxylic acid cycle activity may require less active ATP wasting reactions, whereas a higher activity of the ‘futile’ cycle could be caused by the higher tricarboxylic acid cycle activity.
As shown the developed approach gives a detailed picture with the determination of 37 metabolic fluxes, providing interesting insights into the functioning of the metabolism of C. glutamicum at a low experimental effort. 13C tracer experiments with MALDI-TOF MS (this paper), NMR , and metabolite balancing  lead to similar conclusions concerning the metabolism of C. glutamicum during lysine production. This supports the consistency of the applied techniques. Differences in the fine structure of the flux distribution may be attributed to the different strains and growth conditions applied.
It has to be stated, that metabolite balancing could resolve the examined flux distribution only to a limited extent. Important fluxes such as the flux partitioning in the lysine biosynthesis, the bidirectional fluxes at the pyruvate node or the reversibility of the glucose-6-phosphate isomerase cannot be resolved with this technique. Moreover, assumptions on the stoichiometry of the energy metabolism would have to be included. Comparing the presented approach with NMR techniques leads to several conclusions. The analysis of the 13C labeling of the proteinogenic amino acids from cell hydrolysates by NMR as described by Marx et al. , provides a high information content for the calculation of the flux distribution, which can be used to identify topological aspects of metabolic networks. With only selected labelings measured in the approach of the present paper, the number of experimental flux constraints is comparably lower. Preliminary information on the network of active biochemical reactions is therefore required. This potential drawback of the described MS technique could be overcome by increasing the number of measured labelings . With regard to a maximized information content from labeling experiments a combination of both, NMR and MS techniques, providing orthogonal information on labeling patterns, may be optimal .
A disadvantage of the NMR approach by Marx et al.  is the enormous experimental effort, the insensitivity of NMR and the requirement of steady-state continuous cultures, which impedes its use as a broadly applied method for metabolic flux analysis. Moreover, nongrowing batch cultures cannot be analyzed by such a technique. The method proposed in the present paper is characterized by straightforward and simple measurement of a few selected labeling patterns by mass spectrometry, sensitively reflecting the flux parameters of interest. This reduces the experimental effort substantially. As shown, MALDI-TOF MS can be applied to quantify the labeling of low molecular mass products such as lysine, alanine or trehalose in cultivation samples. Due to the high sensitivity of MALDI-TOF MS, only minimal sample amounts are needed. The sample preparation, which comprises only cell separation and dilution, is rather simple and fast. Moreover, this technique is also applicable to batch or fed-batch cultures, which are of much higher industrial relevance than continuous processes. Flux analysis under batch conditions is faster and less expensive compared to continuous cultures, which can take several residence times with labeled substrate for each flux situation to be examined.
The implementation of a rational experimental design procedure before the actual experimental work provides valuable information on key labelings that sensitively reflect the flux parameters of interest. Thus only a few selected label measurements have to be performed, which significantly reduces the experimental effort. Moreover, this knowledge can be used for efficient parameter estimation, characterized by cyclic-sequential determination of single parameters from the respective sensitive intensity ratios.
Summarizing, the presented approach has an excellent potential to extend metabolic flux analysis from single experiments with enormous experimental effort to a broadly applied technique. It seems especially useful for organisms, for which information on the network topology is already available. Hereby, the generality of the developed metabolic model allows a straightforward application of the presented technique to other biological systems. An interesting future development is the analysis of labeling patterns of intracellular metabolites by MALDI-TOF MS, which may provide valuable information for the analysis of metabolic flux dynamics.
Flux partitioning ratios (Φ), and reversibilities (ζ) were defined as relative fluxes into one of the two branches, and as ratio of backward or exchange flux to the net flux in the forward direction, respectively. Fluxes are denoted by v, the indexing refers to Fig. 1.
The following 12 balance equations of intracellular metabolites were formulated for the examined network using the numbering of the fluxes of Fig. 1.
The rank of the stoichiometric matrix corresponding to Eqns. (7–18) was determined with the software matlab as 12, indicating that the equations were linearly independent. Additional constraints resulted from the fixation of the reversibilities of transaldolase and transketolases, from experimental determination of substrate uptake (v1) and product secretion fluxes (v2, v20, v21, v22, v23, v28) (Table 1) and from experimental data on precursor demand for biomass formation (v4, v7, v9, v10, v18, v24, v25, v27, v32, v34) (Table 2). All fluxes were normalized to the glucose uptake flux, which was set to 1. In total, 32 experimental constraints were obtained from stoichiometric balancing (12 constraints), from the fixation of the PPP reversibilities (three constraints), and stoichiometric measurements on product secretion (seven constraints), and biomass formation (10 constraints). At least five additional informations were therefore required from the labeling measurements to calculate the entire distribution of 37 intracellular fluxes.
We acknowledge the financial support of BASF AG, Ludwigshafen, Germany.