Oxaloacetate

We reconstructed the metabolic network of lysine producing C. glutamicum based on published information [39 (link)] and additional modelling details kindly provided by the authors [see Additional file 2]. The input substrate used was [1-¹³C]-glucose (with 99% enrichment purity), and all fluxes were normalized with respect to the glucose uptake rate (i.e., fluxes are expressed in percentage of glucose uptake rate). As the published MIDs are uncorrected, all the simulated EMU variables were modified for mass interference from non-carbon backbone isotopes using the molecular formula of the amino acids fragments (i.e., parent ion cluster). The first n+1 signal elements were normalized (n indicates number of backbone carbon), and then truncated to the correct vector length (equivalent to the measured MIDs) before performing weighted least-square analysis. The inferred metabolic model consisted of a total of 71 reactions and 42 balanceable metabolites. The metabolite model yielded a total of 26 degrees-of-freedom and 18 fluxes were determined experimentally: anabolic precursor yields (11), biomass yield (1), secreted product yields (5), and glucose uptake rate (1). To reduce the number of unknown parameters, these 18 fluxes were chosen as free fluxes, and the associated flux values were used deterministically as no redundant data exist in the measurement set. Note that if one suspects gross measurement errors in the flux measurement set, then these fluxes should be set free and the flux values subjected to the least-square analysis together with the MIDs. Five (5) of the remaining 8 free fluxes are associated with the reversibility of non-oxidative pentose-phosphate pathway enzymes (3), glucose-6P isomerase (1) and intercellular CO₂ exchange (1). The other 3 free fluxes were assigned (by the software) to the irreversible fluxes of glucose-6P dehydrogenase, pyruvate carboxylase, and glycine synthesis via the serine route.
The MID of 9 amino acids and trehalose were reported. Three "S" type reactions were included in the metabolite network to directly map label distribution of alanine, aspartate and glutamate to pyruvate, oxaloacetate and α-ketoglutarate, respectively. This was not necessary for all other amino acids and trehalose because these metabolites were already described in the isotopomer balances.

Whole-body glucose turnover was measured by determining the specific activity of glucose in the steady-state plasma using a scintillation counter. Hepatic glucose production was assumed to represent ∼90% of the measured whole-body glucose turnover based on our previously published data (7 (link)). Liver-specific metabolic flux rates were calculated using a combined NMR-LC-MS/MS method. We corrected for the natural abundance of each metabolite included in the flux calculations, measuring all possible enrichments (for instance, m+0, m+1, m+2, m+3, and m+4 for malate) and correcting the measured peak areas to account for the fact that once a carbon is labeled it can no longer contribute to the natural abundance (10 (link)). Samples were prepared for NMR by homogenizing 2–3 g of liver in 5 volumes of 7% perchloric acid. The pH of the samples was adjusted to 6.8–7.3 using 30% potassium hydroxide and 7% perchloric acid as necessary, and the samples were centrifuged at 4000 × g for 10 min. The supernatant was frozen in liquid N₂ and lyophilized. ¹³C NMR analysis was performed as described by Befroy et al. (6 (link)). Total glucose and alanine enrichment was measured by GC/MS and glutamate by LC-MS/MS, with ¹³C NMR used to algebraically divide the total enrichment to determine the enrichment of each carbon of these metabolites.
We calculated the [2-¹³C]malate enrichment by relating the positional enrichments of malate to those measured in glutamate assuming (and validating) full equilibration across fumarase as shown in Equations 1 and 2.


For calculation of the liver-specific metabolic flux ratio V_Pyr-Cyc/V_Mito = (V_PK + V_{ME, out})/(V_PC + V_{ME, in}+ V_PDH), we used our previously published isotopic labeling model (6 (link), 7 (link)) extended using a mass isotopomer multiordinate spectral analysis approach to take into account V_PK and unlabeled mass entry from propionate at the succinyl-CoA step of the TCA cycle (10 (link)). Here, V_{ME, out} refers to ME flux in the direction of pyruvate synthesis; V_{ME, in} refers to the reverse reaction of pyruvate into malate, and V_LDH refers to pyruvate synthesis via LDH. With these fluxes taken into account, we can describe the steady-state mass balance at pyruvate with Equation 3,
and isotope balance at [2-¹³C]pyruvate with Equation 4,

Because the positional enrichments of pyruvate and PEP cannot be measured reliably using our NMR-LC-MS/MS techniques, we use the following label substitutions shown in Equations 5 and 6,


Substituting Equations 5 and 6 into Equation 4 and rearranging, we derive Equation 7,

By separating out like terms, we get Equation 8,
where V_PDH denotes flux through pyruvate dehydrogenase; V_CS denotes flux through citrate synthase; V_PK denotes flux through pyruvate kinase; V_{ME, out} denotes flux through malic enzyme from malate to pyruvate; V_{ME, in} denotes flux through malic enzyme from pyruvate to malate; and V_PC denotes flux through pyruvate carboxylase. Additional fluxes shown in the complete flux diagram in Fig. 1 are V_{GNG OAA} gluconeogenesis from oxaloacetate, V_GNG total gluconeogenesis, and V_prop the rate of propionate entry into the TCA cycle. V_PDH/V_CS was measured using the ratio [4-¹³C]glutamate/[3-¹³C]alanine, as described by Alves et al. (11 (link)).

Absolute values of intracellular fluxes were calculated with a flux model comprising all the major pathways of yeast central carbon metabolism (Additional data file 2). Deleted reactions were not omitted from the mutant models; thus the mutations were independently verified from the ¹³C data. The stoichiometric matrix of 34 linear equations and 30 metabolites has an infinite condition number [57 (link)]; it is thus underdetermined, and has a solution space with an infinite number of different flux vectors that fulfill the constraints from determined uptake and production rates. To uniquely solve the system for fluxes (ν), a set of linearly independent equations that quantify flux ratios (FlRs) were used to obtain eight constraints on the relative flux distribution from METAFoR analysis (see Additional data file 2).
The fraction of cytosolic oxaloacetate originating from cytosolic pyruvate is given by:
The fraction of mitochondrial oxaloacetate derived through anaplerosis is given by:
The fraction of PEP originating from cytosolic oxaloacetate is given by:
The fraction of serine derived through glycolysis is given by:
The upper and lower bounds for mitochondrial pyruvate derived through the malic enzyme (from mitochondrial malate) are given by:
The contribution of glycine to serine biosynthesis is given by:
and, finally, the contribution of serine to glycine biosynthesis is given by:
The stoichiometric matrix including Equations 3-10 has a condition number of 31, implying that the model is numerically robust [57 (link)]. Error minimization was carried out as described by Fischer et al. [10 (link)]. Balanced NADPH production and consumption were not added as additional constraints. In general, NADPH production was constrained by Equations 3 and 7/8, which estimate the relative use of the PP pathway and malic enzyme, respectively. As an additional source of NADPH, the flux through the NADPH-dependent acetaldehyde dehydrogenase [33 (link)] was estimated from the acetate production rate and the biomass requirement for cytosolic acetyl-CoA. Deviation of the NADPH production estimated in this way from the consumption for biosynthesis was generally below ± 20%, suggesting that the model assumptions and the experimental data are highly consistent. All extreme flux patterns were independently verified in 30-ml cultures (data not shown).