To determine the extent to which the supply of the precursor 2-oxoglutarate (2-OG) controls the synthesis of lysine in Saccharomyces cerevisiae growing exponentially in high glucose, top-down elasticity analysis was used. Three groups of reactions linked by 2-OG were defined. The 2-OG supply group comprised all metabolic steps leading to its formation, and the two 2-OG consumer groups comprised the enzymes and transporters involved in 2-OG transformation into lysine and glutamate and their further utilization for protein synthesis and storage. Various 2-OG steady-state concentrations that produced different fluxes to lysine and glutamate were attained using yeast mutants with increasing activities of Krebs cycle enzymes and decreased activities of Lys synthesis enzymes. The elasticity coefficients of the three enzyme groups were determined from the dependence of the amino acid fluxes on the 2-OG concentration. The respective degrees of control on the flux towards lysine (flux control coefficients) were determined from their elasticities, and were 1.1, 0.41 and −0.52 for the 2-OG producer group and the Lys and Glu branches, respectively. Thus, the predominant control exerted by the 2-OG supply on the rate of lysine synthesis suggests that over-expression of 2-OG producer enzymes may be a highly effective strategy to enhance Lys production.
In fungi, the amino acid Lys is synthesized through the α-aminoadipate pathway (α-AAP) using 2-oxoglutarate (2-OG) and acetyl CoA as precursors. These metabolites are condensed into homocitrate by homocitrate synthase (HCS), the first enzyme of the pathway (Fig. 1). In Saccharomyces cerevisiae, 2-OG is at a sub-saturating concentration (0.46 mm), whereas cytosolic acetyl CoA is saturating (230 μm) for the two HCS isoforms present in this yeast, Lys20 and Lys21 (Km(2-OG) = 4.6 and 9 mm; Km(acetyl CoA) = 7.7 and 19 μm, respectively) [1-3]. Therefore, higher cellular 2-OG contents may increase the rate of the HCS isoforms and hence may increase the Lys synthesis flux.
The supply of precursors appears to have a significant influence on the fluxes towards amino acid biosynthetic pathways. For example, increases in precursor availability have positive effects on the synthesis of several commercially valuable amino acids such as tryptophan [4, 5], phenylalanine , lysine [7, 8] and glutamate  in Corynebacterium glutamicum and Escherichia coli, as well as in the synthesis of oil in Chlamydomonas reinhardtii  and antibiotics in Penicillium .
With regard to Lys synthesis in S. cerevisiae, previous reports have shown parallel changes in the intracellular concentrations of 2-OG and Lys [12, 13]. These observations have led to the suggestion that the flux towards Lys is highly influenced by the 2-OG pool content in this yeast [12, 13]; however, quantitative studies to evaluate this hypothesis have not yet been performed.
Recently, we reported that the Lys synthesis flux is mostly controlled by the activity of the Lys20 HCS isoform, whereas the control exerted by protein synthesis (Lys demand) is low as neither the cellular protein content nor the amount of Lys present in proteins varied when the Lys pool increased sevenfold . However, the contribution of the 2-OG supply to the flux of Lys synthesis was not determined, and the possibility remained that a proportion of the control by Lys20 may be accounted for by the 2-OG supply. Therefore, specific determination of the control exerted by the 2-OG supply on the Lys flux appears relevant to understanding the controlling mechanisms of this pathway.
Metabolic control analysis (MCA) provides a theoretical and experimental framework to quantify the degree of influence that a step (an enzyme, transporter or a combination of these) has on the flux and metabolite concentrations of a metabolic pathway. MCA also allows understanding of the mechanisms that determine why a step controls the metabolic pathway or not [14, 15]. In MCA, the distribution of control of a metabolic pathway is analyzed in terms of flux and concentration control coefficients. The flux control coefficient () is a systemic property that represents the degree of control that the activity (a) of a particular reaction step (i) exerts on the pathway flux (J). For example, the fact that an enzyme has a of 1 means that it is the only step controlling the pathway flux as long as there is no significant contribution to flux control by steps in branching reactions (with negative flux-control coefficients) or channeling (in which case, all participant steps may have close to 1). However, MCA studies have demonstrated that the control of a metabolic flux is distributed among all steps in the pathway, with two or three steps usually having higher values [14, 15].
The potential of an enzyme/step to control the pathway flux is directly related to its kinetic properties, which are evaluated by the elasticity coefficients in MCA. The elasticity coefficient () quantifies the degree of change in the local rate (v) of pathway step i when the concentration of one of its interacting pathway metabolites (m) varies within the cell; the metabolites are usually the enzyme's substrates or products. However, they may also be activators, inhibitors or co-factors. The formal relationship between and is established in the connectivity theorem of MCA [14, 15], and, together with the summation theorem, may be used to determine the for single or group pathway enzymes or steps [14, 15]. This approach, referred to as top-down elasticity analysis (TDEA) [14-16], has been used to determine the distribution of the control of the fluxes of glycolysis [15, 17, 18] and oxidative phosphorylation in isolated mitochondria, cells and tissues [19-21].
TDEA requires clustering of the metabolic pathway into at least two groups of reactions linked by a common metabolite, namely the producer and consumer branches, which catalyze the synthesis and consumption of the selected metabolite, respectively. The changes in the rate of each branch in response to changes in the local concentration of the linking metabolite () are reflected by changes in the pathway flux. Hence, the values may be calculated from the values of each branch .
In the present study, TDEA was applied using S. cerevisiae mutants of enzymes that synthesize either 2-OG or Lys to determine the flux-control coefficient of the 2-OG supply on the Lys flux. Our results indicated that the group of enzymes/transporters that produce 2-OG exerts most of the control of this pathway.
Reactions included in each branch
2-oxoglutarate is a precursor for both Lys and Glu syntheses; hence, the latter may represent a significant leak from that of Lys and should be included in analysis of the control of Lys biosynthesis. To that end, metabolic steps linked by 2-OG to the flux to Lys were clustered into three groups of enzymes/transporters (Fig. 2): a 2-OG supply branch and two 2-OG consumer branches for Lys and Glu synthesis and utilization, respectively. Details of reactions included in each branch are described below and in Fig. 1.
The supply branch of 2-OG included all enzymes and transporters involved in its formation in mitochondria and the cytosol, such as mitochondrial de novo synthesis by the first three enzymes of the Krebs cycle, several dicarboxylic acid transporters, anaplerotic processes, Glu deamination by Gdh2 (NAD+-dependent glutamate dehydrogenase)  and transamination reactions. It was assumed that the mitochondrial and cytosolic 2-OG pools are rapidly equilibrated by the activity of dicarboxylic acid transporters ; therefore, to determine the elasticity coefficients, the 2-OG pool was considered as the total intracellular concentration regardless of subcellular compartmentalization or source.
The Lys branch includes the enzymes and transporters involved in conversion of 2-OG and acetyl CoA into Lys through the α-AAP, and the consumption of this amino acid for protein synthesis and its storage in the vacuole (Figs 1 and 2). Hence, the total intracellular pool of Lys (Lystotal) is the sum of Lys incorporated into proteins (Lysprot) and Lys that did not form peptide bonds (Lysfree), which includes the cytosolic and vacuolar pools . Although the first step of Lys biosynthesis occurs in the nucleus , there is free diffusion of metabolites between cytosol and nucleus, and hence identical concentrations in both subcellular compartments were assumed .
The Glu branch includes the activities of Gdh1 (NADP+-dependent glutamate dehydrogenase) and GOGAT (NAD+-dependent glutamate synthase), enzymes that are involved in conversion of 2-OG into the total intracellular pool of Glu (Glutotal) (Fig. 1); the latter represents the sum of the free Glu (vacuolar and cytosolic) and the amount of Glu in proteins (Fig. 2).
The initial glucose concentration in the culture medium was 111 mm, a condition under which repression of the 2-OG consumer enzymes of the Krebs cycle occurs ; therefore, these mitochondrial reactions that consume 2-OG were not considered for the analysis..
Metabolic pathway characteristics
Correct application of TDEA requires that several experimental conditions be observed, as described below.
Unaltered active enzyme contents
When the activities (i.e. the Vmax values =kcat × [enzyme]total) of the enzymes of one branch are modulated by genetic or biochemical means, the Vmax of the enzymes and transporters of the other branches must remain constant. Only then may it be assumed that the changes in the local rates of the branches (i.e. the flux that runs through them) are caused only by variations in the 2-OG content.
The flux through the 2-OG supply branch was manipulated using the idh2Δ, idp1Δ and mks1Δ strains of S. cerevisiae (Table 1). The first two have decreased activities of NAD+ and NADP+ isocitrate dehydrogenases (Idh and Idp, respectively) (Table 2). However, Mks1 (multicopy kinase suppresor) protein inhibits the function of the Rtg1/Rtg3 (retrograde regulation) complex which in turn increases transcription of the genes encoding enzymes of the early steps of the Krebs cycle to produce 2-OG for ammonia assimilation . Hence, the mks1Δ mutant displays increased activities of citrate synthase (Cit) and Idh (Table 2). In these three mutants, the activities of the enzymes of the Lys branch were fairly similar to those of the wild-type (WT) (Table 2), and so they may be reliably used for TDEA. Interestingly, the low Idh activity in the idh2Δ strain elicited a significant increase in the activities of the 2-OG-producing enzymes Idp, Gdh2 and Cit (Table 2). This behavior in the idh2Δ strain was probably a response to the low intracellular Glu levels (Table 3), which may activate signaling of the RTG target genes . The lower Glu content in this strain (Table 3) may be a consequence of the lower activity of Gdh1 (Table 2). In contrast, in the idp1Δ strain, a slight increase in Gdh1 activity (Table 2) did not bring about Glufree accumulation (Table 3), suggesting negligible control by Gdh1 on Glu concentration in this mutant.
Table 1. Strains of S. cerevisiae used in this study.
MATa his3Δ1 leu2Δ0 met15Δ0 ura3Δ0/pRS426
Low activity of NAD+-isocitrate dehydrogenase in the 2-OG supply branch
Low activity of NADP+-isocitrate dehydrogenase in the 2-OG supply branch
High activity of citrate synthase and NAD+-isocitrate dehydrogenase in the 2-OG supply branch due to lack of repression by the MKS protein on transcription of genes of the Krebs cycle
Low activity of HCS and Lys9 in the Lys branch due to decrease function of the Lys14 transcription factor
Low activity of the HCS isoforms in the Lys branch
Table 2. Key enzyme activities.
Enzyme activities are in nmol·min−1 × mg protein. Values are means ± SD from 15 (WT) or three (mutant strains) independent experiments. a P < 0.005, bP < 0.05, c P < 0.025, d P < 0.01 versus WT using Student's t test for non-paired samples.
The flux through the Lys branch was changed using the lys21Δ and lys14Δ strains (Table 1). As expected, both strains showed a specific decrease in HCS activity (Table 2), although the latter also showed pronounced lower saccharopine reductase (Lys9) activity, in agreement with previous reports [3, 30]. The lys21Δ strain showed similar activities of the other Lys pathway enzymes, as well as those of the 2-OG supply and Glu branches, compared to the WT (Table 2). However, the lys14Δ strain showed two surprising changes: (a) a slight increase in all enzyme activities of the 2-OG producer branch (Table 2), and (b) a pronounced decrease in Gdh1 activity (Table 2), which did not affect Glu production capacity as this strain showed the highest Glufree levels of all the analyzed strains (Table 3).
All the experimental determinations were performed in cells growing exponentially. Under this condition, the specific growth rate (μ) is constant (although different depending on the strain; see Table 3 for values); therefore, it was established that the cells were under steady-state conditions, i.e. the enzyme activities and intracellular metabolite contents were constant under exponential growth. The Lys, Glu and 2-OG intracellular contents normalized by biomass were constant between two and three duplications in the WT strain (data not shown); this 3–5 h time frame was also used for the determination of metabolites and fluxes in the other strains. It was assumed that the concentrations of other metabolites involved in the pathways, such as acetyl CoA, NAD(P)+, NAD(P)H and ATP (Fig. 1), did not change among the strains. However, the Glufree levels decreased in the idh2Δ and idp1Δ strains (Table 3), and this may influence Lystotal biosynthesis because Glu is required as an amino donor in two reactions of the α-AAP (Fig. 1) . Nevertheless, over-expression of Lys20 increased the intracellular Lysfree content in the first mutant by more than fourfold (Fig. 3A, closed versus open symbols). If Lys synthesis were limited by the availability of amino groups, higher Lys levels could not have occurred. Moreover, over-expression of Lys20 did not elicit significant changes in the Glu intracellular content (Fig. 3B), and, remarkably, the 2-OG pool was significantly decreased when Lys20 was over-expressed in the mks1Δ and lys21Δ strains (open versus closed symbols, Fig. 3B), with no significant variation in the Glu pool. Thus, these results indicate that Lystotal production was limited only by the 2-OG supply and not the availability of amino groups.
Metabolite contents and fluxes
Various 2-OG steady-state levels were established below and above those of the WT strain using the six mutant strains (Fig. 3 and Table 3). Lack of one of the two isoforms of the NAD+-dependent isocitrate dehydrogenase in the idh2Δ strain, and lack of one of the three isoforms of the NADP+-dependent isocitrate dehydrogenase in the idp1Δ strain, produced significantly lower 2-OG contents [32, 33] (Fig. 3 and Table 3). In contrast, enhanced activities of the first steps of the Krebs cycle in the mks1Δ strain induced maximal 2-OG intracellular and Lysfree contents compared to WT (open diamond versus circle, Fig. 3A) [12, 28]. Remarkably, no significant differences in Lysprot were observed for all these mutants (Table 3), suggesting that demand for this amino acid for protein synthesis does not significantly control the pathway flux, as previously demonstrated for HCS mutants .
The decrease in the Lystotal biosynthetic capacity of the lys20Δ and lys21Δ strains did not significantly affect their growth rate or Lysprot (Table 3). However, they exhibited lower Lysfree contents than the WT strain, particularly the lys20Δ strain. This emphasizes the role of Lys20 HCS in controlling the flux of the α-AAP (Table 3). In contrast, in the lys14Δ strain, lack of the Lys14 transcriptional activator negatively affected its growth rate and intracellular Lys content (Table 3) as a consequence of lower HCS and Lys9 activities  (Fig. 1 and Table 2); consequently, this mutant showed a marked accumulation of 2-OG and Glufree contents (Table 3).
Determination of the elasticity and flux-control coefficients
The fluxes towards each metabolite (columns 2–6 of Table 3) were calculated by multiplying the values of metabolite levels by the specific growth rates (see Experimental procedures for details) . From these individual fluxes, the total fluxes of each branch were calculated. Thus, the total flux of the Lys branch (JLys total) is equal to the sum of the flux towards Lysprot (JLys prot) plus the expansion flux towards Lysfree (JLys free), as is typical of a growing system, in which the metabolite concentration is kept constant to balance the continuous change in volume and cell number . Hence, demand for the amino acid for protein synthesis is included in the total flux of the Lys branch. Similarly, JGlu total is equal to the sum of the fluxes of JGlu prot plus JGlu free. The flux of the 2-OG supply branch is equal to the sum of JLys total plus JGlu total plus the small 2-OG expansion flux (J2-OG).
The elasticity coefficient of the 2-OG supply branch towards 2-OG () was determined by plotting J2-OG supply versus the 2-OG content exhibited by the WT, lys21Δ and lys14Δ strains (Fig. 4A). The lys20Δ strain showed atypical 2-OG concentrations (Fig. 4A and Table 3), and hence this strain was not included in determination of the elasticity coefficient. The negative slope of the dashed line or the value of the derivative at the WT point of the fitted line in Fig. 4A corresponds to the value (Table 4); the elasticity of the 2-OG supply towards 2-OG was negative because this metabolite is a product of the supply branch.
Table 4. Elasticity and flux-control coefficients. v represents the branch indicated in the first column.
The elasticity coefficient of the Lys branch towards 2-OG () was similarly determined at the WT reference point from the plot of JLys total versus the 2-OG levels for the idh2Δ, idp1Δ, WT and mks1Δ strains (Fig. 4B). The expected positive relationship between 2-OG content and flux through this branch was obtained. A similar plot was constructed for the Glu branch (Fig. 4C). The elasticity coefficients determined from these plots are shown in Table 4.
Setting the Lys flux as the flux of interest and solving the three linear equations derived from the summation, connectivity and branch theorems of MCA [14, 15, 35, 36] (see Experimental procedures for details, and legend to Fig. 2), the values of each branch towards Lystotal flux were calculated (Table 4). was significantly higher than the and the . Therefore, the flux towards Lystotal was mainly controlled by the enzymes/transporters that supply 2-OG. Remarkably, the Glu branch exerted high negative control on the Lystotal flux because this branch competes with the Lys branch for 2-OG.
Kacser  derived equations to calculate from for branching pathways as shown in Fig. 2 (see Experimental procedures for complete description of the equations). To calculate the towards Lystotal, parameter α was defined as the fraction of J2-OG supply going to Glu synthesis. Similar values of for the flux to Lystotal to those shown in Table 4 were obtained using this alternative procedure. Therefore, Kacser's method was applied to determine the control distribution of the flux towards Glutotal. In consequence, for calculation of the towards Glutotal, parameter α was defined as the fraction of J2-OG supply going to Lys synthesis. The flux control distribution of Glutotal synthesis obtained indicated that its control was shared to a similar extent by the 2-OG supply and by reactions/processes inside the Glu branch (Table 4).
Predominant flux control by the 2-OG producer branch on Lys and Glu synthesis
In previous studies, a correlation between 2-OG and Lys intracellular pools was reported [12, 13]. However, a quantitative analysis of the extent to which the 2-OG supply determines the flux towards Lys was lacking. Moreover, in the previous studies, only the Lysfree pool was analyzed without taking into account its consumption for protein synthesis; as shown here, most of the Lystotal content is accounted for by the pool of peptidic Lys. Therefore, to increase our understanding of the mechanisms controlling Lys biosynthesis in S. cerevisiae and to obtain a quantitative description of its flux-control distribution, the supply of precursors and Lys utilization must be included in the analysis.
In our previous work , it was demonstrated that, within the α-AAP, Lys20 activity was the main controlling step of the flux to Lysfree because its over-expression in the cells led to an increase in the intracellular Lysfree pool and flux. Such an effect was not observed by over-expressing other LYS genes, including LYS21 . The high control by Lys20 is in agreement with results found in the present work, in which disruption of the LYS20 gene (but not LYS21) elicited a substantial decrease in Lysfree content to 34% of the WT level. In contrast, an increased growth rate and Lysfree pool were observed in the mks1Δ strain, indicating that increased expression of Idh and Cit, by removing the transcriptional repressor Mks1, results in enhanced 2-OG supply for accelerated Lys synthesis, which in turn induced higher Lysfree levels with no significant change in Lysprot.
Using TDEA, we demonstrated that the fluxes of the processes that synthesize and consume Lys are mainly controlled by the 2-OG supply. The rest of the control was shared to similar extents between Lys and Glu synthesis.
The flux control exerted by the two HCS isoforms was previously determined by individual and gradual expression of Lys20 and Lys21 activities in the cell, and by assessing the corresponding changes in the pathway flux . A of 0.13 for Lys21 was determined, whereas a range of values of 0.6–3.1 was obtained for Lys20 . values higher than 1 suggest that other phenomena, such as an increase in the 2-OG content upon Lys20 over-expression or under-estimation of the Lysprot value, may have contributed to the high Lys20 flux-control coefficient values. The results of the present paper using TDEA indicate that the previous high value determined for Lys20 actually included the contribution of the 2-OG supply reactions. Therefore, a higher accuracy of Lysprot determination, direct assessment of the flux control exerted by the 2-OG supply branch, and inclusion of the 2-OG leak towards Glu allowed a more comprehensive and precise description of the flux-control distribution of Lys synthesis in S. cerevisiae (Table 4).
Physiological implications of the high control by 2-OG supply on Lys synthesis
It is generally accepted that the flux through central carbon metabolism is much higher than the flux towards the branches represented by the biosynthetic pathways [11, 13]. In yeast cultured in medium with high glucose concentrations, de novo synthesis of 2-OG is performed in mitochondria by the first enzymatic reactions of the Krebs cycle enzymes  (Fig. 1). Despite being produced by a central pathway, our data indicate that 2-OG was not at saturating concentrations for the α-AAP. Glu and Gln biosynthesis also directly depends on the 2-OG pool (Fig. 1); hence, Lys20, the main controlling step within the α-AAP and the first step of the pathway, competes for the available 2-OG with Gdh1, the predominant isoform in cells grown in medium with high glucose concentration that is responsible of Glu synthesis . In this scenario, Glu/Gln synthesis in S. cerevisiae is favored over Lys synthesis, due to the higher Gdh1 activity (Table 2) and higher affinity for 2-OG (S0.5 2-OG = 0.29 mm) in the Glu/Gln synthesis, compared to the low activities (Table 2) and affinities of the two HCS isoforms for 2-OG (Km(2-OG) = 4.6–9 mm) [1, 2, 37] in the Lys synthesis pathway. Moreover, the steady-state 2-OG intracellular concentration of 0.4–0.9 mm (this study and ) is well below the Km(2-OG) of both HCS isoforms. This non saturating 2-OG concentration contributes to the strong dependence of Lystotal synthesis on 2-OG supply.
Biotechnological implications of the flux-control distribution of Lys synthesis
Identification of the main controlling steps in a metabolic pathway enables the design of focused and rational strategies for modifying the rate of synthesis of an end-product or the concentration of a metabolite of interest [15, 38]. In this regard, our results indicated that the decrease in the 2-OG supply may be a suitable strategy for development of drugs that target the α-AAP in fungi, although this would be successful only for fungal pathogens that lack high-affinity Lys uptake systems . Our findings also suggested that enhancement of both the 2-OG supply and Lys20 activity may be appropriate strategies to increase the synthesis of Lysfree. A higher Lys content may be useful to increase tolerance to freezing and oxidative stresses [40-42]. Increased Lys production by over-expression of pyruvate carboxylase and/or biotin-synthesizing enzymes in Corynebacterium glutamicum [8, 43, 44] suggests that, in this bacterium, supply of the precursor also exerts significant flux control of Lys biosynthesis.
In the WT strain, only 3% of the intracellular Lys content is found in its free form (Table 3), and Lys excretion was not observed (this study and ); for these reasons, the yield in S. cerevisiae cannot compete commercially with the massive yields by bacteria that efficiently synthesize and excrete Lys . However, the analysis of the flux-control distribution in the present work provides understanding of the underlying mechanisms that control Lys biosynthesis in S. cerevisiae. In addition, the fact that distribution of the control of Lys biosynthesis flux is shared by several steps, as documented in the present study, indicates the requirement for multi-site strategies for efficient manipulation of this pathway [15, 38].
Strains and growth conditions
The BY4741 strain of S. cerevisiae was used as the reference strain (WT). This was isogenic for the lys14Δ, idh2Δ, idp1Δ, mks1Δ, lys20Δ and lys21Δ single mutants used in the present study (Table 1). The strains were obtained from the Euroscarf (European Saccharomyces cerevisiae archive for functional analysis; University of Frankfurt, Germany) collection (accession numbers Y03973, Y02392, Y03763, Y07222, Y03880 and Y03828, respectively). In the experiments in which the LYS20 gene was not over-expressed, the strains were transformed with the pRS426 (2 μ URA3) high copy-number plasmid ; alternatively, for the experiments in which the LYS20 gene was over-expressed, the strains were transformed with the pMUL20 (LYS20 2 μ URA3) plasmid . All transformants were obtained as previously described  and selected by uracil prototrophy.
The strains were grown in minimal medium based on the formulation of yeast nitrogen base (Difco, Franklin Lakes, NJ, USA), and supplemented with 40 mm ammonium sulfate as the nitrogen source and 2% filter-sterilized glucose as the carbon source. Histidine, leucine and methionine, which are required to satisfy auxotrophic requirements, were added at 20 mg·L−1 each. Fresh cells grown on solid minimal medium were used for pre-inoculum liquid cultures and were grown overnight in supplemented minimal medium. These cultures were used to inoculate fresh medium using one-fifth of the total volume of the flask. The cells were incubated at 30 °C under strong orbital shaking (250 r.p.m.), and cell growth was allowed to continue for only two or three duplications before harvesting; this protocol ensured that the cells were under exponential growth conditions. The cell number was estimated by turbidity, assuming that 1 unit of attenuance at 600 nm was equivalent to 18.4 × 106cells·mL−1.
Cell extract preparation and enzyme activity assays
Cells at the mid-exponential growth phase (6–9 h after inoculation) were harvested by centrifugation at 4500 g for 5 min at 4 °C, and washed twice with cold distilled water with centrifugation as indicated. Cytosol-enriched extracts were prepared, and enzyme activity assays for Lys1 (saccharopine dehydrogenase), Lys2 (α-aminoadipate reductase), Lys9 and the combined activity of Lys20 and Lys21 (HCS) were performed as previously described . To determine the activities of the NAD+-dependent isocitrate dehydrogenase (the combined activities of Idh1 and Idh2, here abbreviated as Idh), NADP+-dependent isocitrate dehydrogenase (the combined activities of Idp1, Idp2 and Idp3, here abbreviated as Idp), the NAD+-dependent glutamate dehydrogenase (here abbreviated as Gdh2), the NADP+-dependent glutamate dehydrogenase (Gdh1), citrate synthase (the combined activities of Cit1 and Cit2, here abbreviated as Cit) and glutamate synthase (the activity of Glt1, here referred to as GOGAT), cytosolic extracts were obtained by disrupting the cells with glass beads and vigorous mixing with a vortex (five cycles of 1 min vortexing at maximal speed followed by 1 min rest on ice) in 50 mm HEPES buffer, pH 7.0, containing 1 mm phenylmethanesulfonyl fluoride, 1 mm EDTA and 1 mm dithiothreitol as protease inhibitors. After centrifugation at 16 873 g for 10 min at 4 °C, glycerol at a final concentration of 10% v/v was added to the supernatants and used immediately.
Enzyme activities were determined from the change in the NAD(P)H absorbance monitored at 340 nm in a spectrophotometer (Agilent, Santa Clara, CA, USA). All enzymatic assays were performed at 30 °C in a reaction volume of 1 mL in assay buffer that consisted of 50 mm HEPES buffer pH 7.0, 140 mm KCl and 4 mm MgCl2. The amount of protein used was adjusted to ensure that the initial reaction rate was linear within the range of protein concentrations used. A period of 5 min for thermal equilibration and baseline stabilization of the assay buffer with substrates was used before starting the reaction by adding the cytosolic extract.
The Idh activity was determined in the direction of 2-OG formation as previously described  using 2 mm AMP, 1 mm MnCl2, 1 mm NAD+ and 4 mm d,l-isocitrate (assuming a 50% concentration of d-isocitrate, which is the actual substrate); the reaction was started by addition of 0.06–0.18 mg protein of cytosolic cell fraction. The Idp activity was determined in the direction of 2-OG formation as previously described  using 1 mm NADP+ and 4 mm d,l-isocitrate (with the same assumption as above). The reaction was started by addition of 0.04–0.12 mg protein of cytosolic cell fraction. Gdh2 activity was determined in the direction of Glu formation as previously described  using 5 mm 2-OG, 200 mm (NH4)2SO4, 1 mm ADP and 0.2 mm NADH; the reaction was started by addition of 0.04–0.12 mg protein of cytosolic cell fraction. Gdh1 activity was determined in the direction of Glu formation as previously described  using 5 mm 2-OG, 200 mm (NH4)2SO4 and 0.2 mm NADPH; the reaction was started by addition of 0.02–0.10 mg protein of cytosolic cell fraction. Cit activity was determined in the direction of citrate formation  in an assay buffer that contained 20 mm HEPES pH 7.5, 540 mm glycerol, 0.1 mm 5,5′-dithiobis-(2-nitrobenzoic acid), 0.1 mm acetyl CoA, 5 mm freshly prepared oxaloacetate and 1.6 mm ADP, and the reaction was started by addition of 0.04–0.08 mg protein of cytosolic cell fraction. GOGAT activity was determined in the direction of Glu formation  in the Cit activity assay buffer plus 0.2 mm NADH, 10 mm freshly prepared glutamine and 0.05–0.15 mg protein of cytosolic cell fraction; the reaction was started by addition of 2 mm 2-OG. Protein content was determined by the Lowry method  using bovine serum albumin as standard.
Metabolite determination and analysis
Intracellular free Lys and Glu were extracted and determined by HPLC as previously reported . For 2-OG extraction and intracellular content determination, 100 mL of cell culture at an attenuance at 600 nm of 2.0 were harvested by rapid centrifugation and extracted in boiling water as previously described .
Determination of Lys incorporated into proteins (Lysprot) was performed as follows. Cellular protein was obtained from 9.2 × 108 cells grown at the exponential phase, which were washed twice with cold distilled water as described above. The cells disrupted with glass beads and vigorous vortexing for 5 min in 10 mm Tris/HCl buffer, pH 8, containing 1% Triton X-100, 1% SDS, 1 mm EDTA, 25% phenol, 24% chloroform and 1% isoamyl alcohol. The protein-containing middle phase was separated by centrifugation at 16 873 g for 10 min at 4 °C in a microcentrifuge and de-lipidated three times using 1 mL chloroform and vortexing for 5 min, followed by centrifugation. The last pellet was resuspended in 2 mL of 1% SDS, 2% Na2CO3 and 0.4% NaOH. After centrifugation (10 min at 16 873 g), the polysaccharide-rich pellet was discarded and the supernatant was used for protein determination. The equivalent to 1.5 mg cellular protein was precipitated using trichloroacetic acid, and the pellet was washed twice with cold acetone. The protein was hydrolyzed by incubation with 6 M HCl at 110 °C for 24 h in vacuum-sealed glass tubes. The samples were derivatized using phthaldialdehyde, and the Lys content was determined by HPLC using a C18 reversed-phase column . Lysprot (nmol Lys in proteins per 108 cells) was calculated multiplying the cellular protein content (mg protein/108 cells) by the nmol Lys in proteins per mg cellular protein.
Determination of steady-state metabolic fluxes
The net flux through the Lys biosynthetic pathway (JLys total) was the sum of the metabolic flux of Lys incorporated into proteins (JLys prot) plus the free Lys expansion flux (vacuolar and cytosolic free Lys; JLys free).
The JLys free and JGlu free values were calculated by multiplication of intracellular free Lys (Lysfree) or Glu (Glufree) (nmol/108 cells) by the specific growth rate (μ). Similarly, JLys prot and JGlu prot values were calculated by multiplication of Lys or Glu incorporated into proteins (nmol·mg protein−1) by the cellular protein content (mg protein/108 cells) and the specific growth rate [3, 34]. The cellular protein contents (mg protein/108 cells) were 1.1 ± 0.03, 1 ± 0.02, 1 ± 0.03, 1.2 ± 0.02, 0.9 ± 0.01, 0.9 ± 0.03 and 1.1 ± 0.02 for the WT, idh2Δ, idp1Δ, lys20Δ, lys21Δ, lys14Δ and mks1Δ strains, respectively. Lys and Glu were not detected in the cell-free culture medium of any of the strains used (data not shown), thus fluxes towards extracellular Lys or Glu were not included in the analysis. The net flux towards 2-OG production (J2-OG supply) was the sum of JLys total plus JGlu total plus the J2-OG expansion flux. This last flux was calculated as the product of the 2-OG intracellular pool (nmol/108 cells) multiplied by the specific growth rate.
Determination of the elasticity and flux-control coefficients
Metabolic steps leading to Lys and Glu production were clustered into three groups of reactions linked by 2-OG (Figs 1 and 2). To estimate the elasticity coefficient of the two 2-OG consumer branches ( and ), increasing steady-state 2-OG intracellular concentrations were established by using cultures of the idh2Δ, idp1Δ, WT and mks1Δ strains (Table 3). Data for JLys total versus 2-OG were plotted, and was calculated by multiplying the slope of the tangent to the fitted curve at the 2-OG concentration point of the WT strain (circle in Fig. 3B) by the scalar factor ([2-OG]WT/JLys total0) which correspond to the values of the WT strain  or by determining the derivative at the WT point of the fitted line. Similarly, was calculated from the plot of JGlu total versus 2-OG (Fig. 3C). The elasticity of the 2-OG supply branch () was determined by using the values of 2-OG concentration and the total flux towards 2-OG (J2-OG supply) for the WT, lys21Δ and lys14Δ strains. was calculated by multiplying the value of the negative slope of the tangent at the WT point in Fig. 3A by the same scalar factor.
The values were used to calculate the towards Lystotal by solving Eqns (1)-(3) derived from the summation, connectivity and branching theorems of MCA, respectively [35, 36]:
in which , and are the flux-control coefficients towards Lystotal synthesis of the 2-OG supply branch, the Lys branch and the Glu branch, respectively. The flux-control coefficient values were obtained solving the following inverse matrix:
Calculation of towards Lystotal was also performed using Eqns (4)-(6) developed by Kacser :
using α = 0.47, which represents the fraction of the J2-OG supply leaking to JGlu total in the WT strain. The results obtained with this procedure were identical to those obtained by solving the inverse matrix. Thereafter, Kacser's equations were used to calculate the distribution of control of the flux to Glu total (total in subindexl) synthesis. In this case, the value for α was 0.53.
The present work was partially supported by grants from the Consejo Nacional de Ciencia y Tecnología (CONACyT) (numbers 80534, 178638, 106583 and 123636) and the Instituto de Ciencia y Tecnologia del Distrito Federal (number PICS08-5).