Inhibition kinetics of catabolic dehydrogenases by elevated moieties of ATP and ADP – implication for a new regulation mechanism in Lactococcus lactis


E. W. J. van Niel, Department of Applied Microbiology, Lund University, PO Box 124, SE-221 00 Lund, Sweden
Fax: +46 46 2224203
Tel: +46 46 2220619


ATP and ADP inhibit, in varying degrees, several dehydrogenases of the central carbon metabolism of Lactococcus lactis ATCC 19435 in vitro, i.e. glyceraldehyde-3-phosphate dehydrogenase (GAPDH), lactate dehydrogenase (LDH) and alcohol dehydrogenase (ADH). Here we demonstrate mixed inhibition for GAPDH and competitive inhibition for LDH and ADH by adenine nucleotides in single inhibition studies. The nonlinear negative co-operativity was best modelled with Hill-type kinetics, showing greater flexibility than the usual parabolic inhibition equation. Because these natural inhibitors are present simultaneously in the cytoplasm, multiple inhibition kinetics was determined for each dehydrogenase. For ADH and LDH, the inhibitor combinations ATP plus NAD and ADP plus NAD are indifferent to each other. Model discrimination suggested that the weak allosteric inhibition of GAPDH had no relevance when multiple inhibitors are present. Interestingly, with ADH and GAPDH the combination of ATP and ADP exhibits lower dissociation constants than with either inhibitor alone. Moreover, the concerted inhibition of ADH and GAPDH, but not of LDH, shows synergy between the two nucleotides. Similar kinetics, but without synergies, were found for horse liver and yeast ADHs, indicating that dehydrogenases can be modulated by these nucleotides in a nonlinear manner in many organisms. The action of an elevated pool of ATP and ADP may effectively inactivate lactococcal ADH, but not GAPDH and LDH, providing leverage for the observed metabolic shift to homolactic acid formation in lactococcal resting cells on maltose. Therefore, we interpret these results as a regulation mechanism contributing to readjusting the flux of ATP production in L. lactis.


alcohol dehydrogenase


glyceraldehyde-3-phosphate dehydrogenase


lactate dehydrogenase


pyruvate formate-lyase


root-mean-square error




The lactic acid bacterium, Lactococcus lactis, plays an essential role in the manufacture of a wide range of dairy products. In recent years, L. lactis has also been used in industrial lactic acid production, as it has a rather simple and well-characterized metabolism and converts sugars mainly into lactate via glycolysis [1]. However, under certain conditions, this homolactic fermentation is shifted to mixed-acid production, i.e. formate, acetate and ethanol, in addition to lactate [2].

In glycolysis, glyceraldehyde-3-phosphate dehydrogenase (GAPDH) converts NAD+ to NADH, which must be regenerated for continued carbon catabolism. Lactate dehydrogenase (LDH) regenerates NAD by converting the end product of glycolysis, pyruvate, to lactate. An alternative way for lactococci to regenerate NAD in anaerobic conditions is through alcohol dehydrogenase (ADH), which is part of the pyruvate formate-lyase (PFL) pathway. The first enzyme in the PFL pathway converts pyruvate to formate and acetyl coenzyme A, which is further metabolized to either ethanol or acetate. PFL is inactive in the presence of oxygen and at a low pH [3,4]. With an active PFL pathway, three molecules of ATP are produced per hexose molecule catabolized, compared with the two ATP molecules conserved per hexose molecule when LDH is used. The extra ATP is derived from the production of acetate catalysed by acetate kinase. NAD+ is then regenerated via reduction of acetyl coenzyme A, with ethanol as an end product.

Homolactic behaviour is seen only during rapid growth in the presence of excess glucose and in resting cells [1], whereas mixed-acid fermentation is observed in glucose-limited conditions [2], and with growth on maltose, galactose or trehalose [5–7]. Under various growth conditions, the shift from mixed-acid to homolactic formation in L. lactis has been ascribed to allosteric regulation of: (a) PFL by glyceraldehyde-3-phosphate and dihydroxyacetone phosphate [4]; (b) LDH by the ratio of fructose 1,6-diphosphate and orthophosphate [4,8,9]; and (c) GAPDH and LDH by the redox charge (or NADH/NAD ratio) [10,11]. The latter hypothesis has been disproved in other studies in which the enzymatic level of GAPDH has been altered [11,12]. However, all of these regulations probably work in concert.

Myriads of previous studies have identified adenine nucleotides, i.e. ATP, ADP and AMP, as inhibitors for dehydrogenases [13–18]. Nakamura et al. [17] suggested that GAPDH, which plays a regulatory role in glycolysis in round spermatids, is strongly inhibited by AMP and ADP at physiological concentrations. In addition, the inhibition mechanism by ATP and the relationship of this inhibition to regulate glycolysis in resting and contracting muscle cells was hypothesized [18]. Palmfeldt et al. [1] indicated that the ATP plus ADP moiety might have a regulating function in nongrowing cells of L. lactis ATCC 19435 fermenting maltose. The conclusion was partly based on changes in this moiety and the in vitro-determined inhibition of GAPDH, LDH and ADH by ATP and ADP independently.

Herein we characterize the inhibition kinetics of these three dehydrogenases with their most important natural inhibitors, i.e. ATP, ADP and the product of their coenzyme, i.e. NAD or NADH. Our approach was to estimate the kinetic parameters of the enzymes in cell extracts, rather than of the purified enzymes, for mimicking the complete system [1]. Studies with purified enzymes may not reflect what is happening in the whole cell [19]. It is known that L. lactis possesses isozymes of each of these dehydrogenases, e.g. L. lactis IL1403 contains three genes for LDH, two for ADH and two for GAPDH [20], which all could have been affected one way or another by both ATP and ADP. However, the few studies related to the expression of the dominant isozymes [21–23], including our own unpublished results, are discussed. From the kinetics study, it was concluded that the inhibition action of the ADP plus ATP moiety is of a co-operative nature and mainly affects ADH such that it will contribute to inhibiting mixed-acid formation. A similar nonlinear inhibition was also observed with purified enzymes, i.e. commercial horse liver and yeast ADH, justifying the determinations carried out with cell extracts. Moreover, it also demonstrates that this type of inhibition can occur in eukaryotic ADHs, indicating that this type of inhibition might be widespread in nature.


Inhibition kinetics by a single inhibitor

The inhibition kinetics of lactococcal GAPDH, LDH and ADH were determined in vitro for each inhibitor, ATP, ADP, AMP and their corresponding coenzyme product, i.e. NAD or NADH. Cornish–Bowden plots revealed that the nature of inhibition for most of these cases was that of the parabolic competitive (LDH, Fig. 1B) or parabolic mixed (GAPDH) inhibition type, except for the inhibition of LDH by NAD (Fig. 1A). As an example, the parabolic competitive inhibition of LDH by ADP is shown in Fig. 1B (for all other cases, see Fig. S1). The Cornish–Bowden plot demonstrated inhibition of GAPDH by AMP as mixed inhibition (Fig. S1), but model fitting resulted in high confidence intervals for most of the parameters (Table 1). The competitive inhibition model (Eqn 2) also fitted well [adjusted R2 = 0.987, root-mean-square error (rmse) = 0.0016], but had parameter values with lower confidence intervals (e.g. Ki =0.47 ± 0.19, n = 1.15 ± 0.26). The inhibitory effect of NAD on ADH and that of NADH on GAPDH was more complex than according to Eqns (2) or (3) and was not investigated further.

Figure 1.

 Cornish–Bowden plots of single inhibition of LDH by NAD+ and ADP. (A) LDH competitive inhibition by NAD at different NADH concentrations (mm): 0.2 (□), 0.18 (bsl00001), 0.14 (Δ), 0.1 (bsl00066), 0.06 (o). (B) Parabolic competitive inhibition of LDH by ADP at different NADH concentrations (mm): 0.2 (□), 0.18 (bsl00001), 0.12 (Δ), 0.09 (bsl00066).

Table 1.   The estimated VMAX and KM (mm) of the cofactor substrate (NADH or NAD) and estimated parameter values (KIC and KIU; mm) and Hill coefficient (n) with 95% confidence intervals for the competitive inhibition kinetics (Eqn 2) of LDH and ADH and the mixed inhibition kinetics (Eqn 3) of GAPDH with ATP, ADP, AMP and cofactor product (NAD for LDH and ADH, and NADH for GAPDH). rmse, root-mean-square error.
 InhibitorParameter values ± confidence intervalsGoodness of fit
KICKIUnKMVMAXR2Adjusted R2rmse
  1. Set as a fixed value as determined in one of the other assays.

LDHATP2.55 ± 0.541.15 ± 0.320.062a15.6 ± 0.50.99040.98970.3743
ADP1.90 ± 0.201.75 ± 0.230.062a24.4 ± 0.70.99090.99030.5449
AMP1.56 ± 1.480.94 ± 0.320.062a0.08 ± 0.020.98330.98140.0020
NAD1.64 ± 0.510.94 ± 0.130.06 ± 0.0227.7 ± 2.90.99100.99000.6533
ADHATP4.61 ± 0.344.02 ± 0.580.06 ± 0.037.0 ± 0.90.99070.98930.2227
ADP1.45 ± 0.201.42 ± 0.160.06a28.4 ± 1.00.98960.98910.6720
AMP3.43 ± 0.781.55 ± 0.300.06a23.1 ± 1.40.99720.97500.8892
GAPDHATP2.03 ± 0.364.16 ± 0.923.07 ± 0.690.14 ± 0.020.06 ± 0.000.99300.99200.0015
ADP0.96 ± 0.265.38 ± 2.761.70 ± 0.390.14a0.21 ± 0.010.98250.98080.0091
AMP0.27 ± 0.265.21 ± 5.690.79 ± 0.380.14a0.06 ± 0.010.99020.98880.0015

Mathematically, this parabolic inhibition could be described by introducing the Hill-type kinetics to the inhibition terms as described in Eqns (2, 3) and through statistical evaluation (Table 1) it was found to be superior and more flexible than the equation normally used for parabolic inhibition [24]:


containing γ as a factor by which the first inhibitor molecule changes the intrinsic dissociation constant of the vacant site.

Interestingly, only the complete and partial inhibition displayed the Hill-type of inhibition Eqns (2, 3). No good fits were obtained when a Hill-type inhibition was introduced to the uncompetitive part. In conclusion, the inhibitors bind to the active site of all three dehydrogenases, and in the case of GAPDH will also bind to an allosteric site.

The various parameter values were estimated using Eqn (2) for LDH and ADH and Eqn (3) for GAPDH (Table 1, Figs S2, S3). For LDH, ATP and NAD have nearly the same inhibitory strength with Hill coefficients close to 1, whereas ADP is a slightly stronger inhibitor, having a Hill coefficient higher than 1. For ADH, the dissociation constants and Hill coefficients are low for ADP, but high for ATP. Thus, separately each inhibitor affects ADH activity only moderately. ATP and ADP are strong competitive inhibitors for GAPDH due to their small dissociation constants and relatively high Hill coefficients. The uncompetitive inhibition of GAPDH by ATP and ADP, on the other hand, is weak, as illustrated by their high dissociation constants. However, it is still significantly present, as concluded from the data fitting: with Eqn (2) larger confidence intervals and rmse and lower adjusted R2 (0.950 and 0.968 for ATP and ADP, respectively) were obtained than with Eqn (3) (Table 1).

Multiple inhibition kinetics

The reduced and oxidized forms of the coenzyme [i.e. NAD(H)], ATP and ADP are all present in significant concentrations in the cytoplasm. Hence, they will inhibit the considered dehydrogenases simultaneously. The Yonitani–Theorell plots were used to determine the multiple inhibition kinetics and to evaluate any interactions between the inhibitors [25]. As an example, the plots for the inhibition by ATP and ADP of LDH, ADH and GAPDH are given (Fig. 2). Usually these plots show linear relationships between the inhibitor concentrations and V0/Vi (with V0 and Vi as the reaction velocities in the absence and presence of the inhibitor, respectively) (Fig. 2A). However, a parabolic plot emerged in the case of GAPDH, but with ADH the parabolic profile started only at higher ATP concentrations (Fig. 2B, C). Similar nonlinear plots were also obtained with other inhibitor combinations for LDH and ADH (Fig. S4). This nonlinearity was reflected in the multiple inhibition models through the values of the Hill coefficients and the interaction factor (α; Eqn 4). Thus, the multiple inhibition kinetics of all combinations could be adequately described by Eqn (4) for all three enzymes. Indeed, the multiple mixed inhibition model (Eqn 5) for GAPDH resulted in equal or slightly better fittings, but it also resulted in large confidence intervals for most of the parameters. Keeping a fixed value for the affinity constants of the substrate (KM) as determined in the single inhibitions, all remaining parameter values were estimated by nonlinear regression of Eqn (4) (Table 2, Figs S5, S6). For LDH, the relatively high values for α make it clear that the inhibitors are indifferent to each other at the active site. In addition, the dissociation constants for the inhibitors did not change dramatically (Table 2). Hence, the LDH activity was hardly influenced by any of the combinations of inhibitors. A similar conclusion can be drawn for the combination of ADP + NAD for ADH, whereas there was a slight increase in inhibition of ADH by the combination of ATP + NAD.

Figure 2.

 Multiple inhibition of LDH, ADH and GAPDH by ATP and ADP using Yonetani–Theorell plots. (A) Multiple inhibition of LDH by ATP and ADP at different ADP concentrations (mm): 8 (□), 6 (bsl00001), 4 (Δ), 2 (bsl00066), 0 (○). (B) Multiple inhibition of ADH by ATP and ADP at different ADP concentrations (mm): 4.5 (□), 4 (bsl00001), 3 (Δ), 1.5 (bsl00066), 0 (○). (C) Multiple inhibition of GAPDH by ATP and ADP at different ADP concentrations (mm): 2.5 (□), 2 (bsl00001), 1.5 (Δ), 1 (bsl00066), 0.5 (○), 0 (•).

Table 2.   Estimated parameter values with 95% confidence intervals for the multiple inhibition kinetics of LDH, ADH and GAPDH with ATP, ADP and the cofactor product (NAD for ADH and LDH, and NADH for GAPDH) as inhibitors. Similarly, for purified horse liver and yeast ADHs, with ATP and ADP as inhibitors.
I1 + I2EnzymeParameter values ± confidence intervalsGoodness of fit
KIC1 (mm)KIC2 (mm)n1n2αVMAXR2Adjusted R2rmse
  1. KM value for NADH (3.6 μm) taken from [26]. KM value for NADH (122 μm) taken from Brenda (

ATP + ADPLDH2.53 ± 0.431.26 ± 0.161.42 ± 0.151.40 ± 0.104.53 ± 1.770.50 ± 0.010.99600.99510.00669
ADH2.87 ± 0.300.72 ± 0.244.86 ± 1.251.28 ± 0.230.90 ± 0.480.04 ± 0.020.98690.98310.00119
GAPDH0.76 ± 0.101.25 ± 0.141.31 ± 0.141.65 ± 0.190.83 ± 0.270.65 ± 0.020.99270.99110.0107
ATP + NAD(H)LDH4.31 ± 0.400.65 ± 0.152.08 ± 0.230.95 ± 0.1614.6 ± 14.50.32 ± 0.010.98930.98750.00420
ADH3.20 ± 0.250.18 ± 0.054.79 ± 0.791.04 ± 0.143.16 ± 1.400.13 ± 0.000.98760.98500.00333
GAPDH1.19 ± 0.210.07 ± 0.021.30 ± 0.210.96 ± 0.191.80 ± 0.980.70 ± 0.030.98340.97970.0128
ADP + NAD(H)LDH2.23 ± 0.360.41 ± 0.121.66 ± 0.211.03 ± 0.1736.7 ± 61.20.22 ± 0.010.98550.98300.0038
ADH0.74 ± 0.370.02 ± 0.071.49 ± 0.410.57 ± 0.42120 ± 6560.10 ± 0.010.96860.95660.0036
GAPDH1.03 ± 0.160.04 ± 0.011.34 ± 0.221.17 ± 0.132.58 ± 1.130.63 ± 0.020.99220.99010.00898
ATP + ADPHorsea1.16 ± 0.230.04 ± 0.115.66 ± 1.070.86 ± 0.740.50 ± 0.020.99870.99790.00798
Yeastb1.91 ± 0.231.48 ± 0.635.93 ± 1.321.52 ± 1.270.77 ± 0.030.99900.99840.00837

The combinations ATP + NADH and ADP + NADH had a severe inhibitory effect on GAPDH, but mainly because the dissociation constants of ATP and ADP were decreased by ∼ 50%, which more than compensates the concomitantly lower values of the Hill coefficients for the strength of inhibition (Tables 1, 2). In stark contrast, there is a synergy between ATP and ADP (α < 1) at the active site of ADH and GAPDH, and, in addition, the dissociation constants were lower in the presence of the other inhibitor (Table 2). In conclusion, when interpreted as the pool of ATP and ADP [using Eqn (6) and parameter values in Table 2], the two nucleotides affected ADH most strongly (> 95% inhibition), whereas most of the LDH activity was maintained (30–40% inhibition) (Fig. 3A).

Figure 3.

 Multiple inhibition of the lactococcal dehydrogenases and ADH of yeast and horse liver as a function of the ATP and ADP pool. Criterion for all data points chosen: [ATP] > [ADP]. (A) Dehydrogenases from Lactococcus lactis ATCC19435. LDH (Δ), GAPDH (□), ADH (bsl00001). (B) Comparison of eukaryotic ADHs. Baker’s yeast (•), horse liver (○). The lines represent the fitted model (Eqn 6).

Multiple inhibition kinetics of eukaryotic ADH

To investigate whether the nonlinear nature of the multiple inhibition by ATP and ADP is unique for L. lactis, two commercial eukaryotic ADHs, of horse liver and yeast, were tested. Indeed, when plotted as the rate versus the pool of ATP and ADP, a similar strong nonlinear profile was found (Fig. 3B). However, in this case there was no synergy between ATP and ADP (α >> 1, Eqn 6), but the combination of relatively low dissociation constants and high Hill coefficients accounted for the high nonlinearity (Table 2).


The inhibition kinetics of LDH, ADH and GAPDH of L. lactis ATCC 19435 investigated might be a result of various isozymes of each of these dehydrogenases because of the use of cell extracts. However, unpublished transcriptomics results with this strain have revealed that ldh, positioned in the las-operon (EC, gapB, coding for one of the NAD-dependent GAPDHs (EC, and adhE, coding for the alcohol-acetaldehyde dehydrogenase (EC, are those that are predominantly expressed (data not shown). ldh is expressed 37- and 14-fold higher than ldhX and ldhB, respectively; gapB is expressed seven-fold higher than gapA; and adhE is expressed 10-fold higher than adhA. These results are consistent with those obtained with other lactococcal strains [21–23]. For instance, the KM value of LDH of strain ATCC 19435 for NADH (Table 1) was identical to the LDH coded by ldh (KM = 0.06 mm), but not to the one coded by ldhB (KM = 0.2 mm), as found in L. lactis strain NZ9000 and strain NZ9015 [21], respectively. Therefore, we conclude that the kinetics determined herein for all three dehydrogenases pertain to only one of their isozymes, i.e. the ones mentioned above.

The analysis of the single inhibition with the Cornish–Bowden plots and model discrimination revealed that LDH and ADH of L. lactis ATCC 19435 are inhibited by all inhibitors studied in a different manner than GAPDH. Inhibition of LDH and ADH is competitive for ATP, ADP and AMP, whereas inhibition of GAPDH by ATP, ADP and AMP appeared to be mixed. However, the high dissociation constants for the uncompetitive part suggest the presence of only a weak allosteric binding site for ATP, ADP and AMP. Having such high confidence intervals, it is arguable whether in situ AMP inhibits GAPDH mainly in a competitive manner. The more complex inhibition of ADH and GAPDH by NADH and NAD, respectively, remains unclear and was not investigated further.

Interestingly, a parabolic inhibition of each of the dehydrogenases was observed, which especially came to the fore at elevated concentrations of ATP and ADP (Fig. 2). Mathematically, this could be described through introducing a Hill coefficient for each inhibitor to the usual inhibition equations (Eqns 2, 3). In those forms, Eqns (2, 3) fitted the data more satisfactorily than the conventional parabolic model (Eqn 1), even though the same number of parameters had to be estimated. From the data analysis, it was understood that with Hill coefficients a higher flexibility was introduced and may be related to the multimeric nature of the enzymes involved. The outcome supports the view of a recently published theory that Hill-type kinetics can be used to describe allosteric inhibitor behaviour [27]. Model discrimination demonstrated that the Hill-type only worked for the complete and partial competitive inhibition, indicating a nonlinear negative co-operativity at the active site [24] as the means to ‘deactivate’ the dehydrogenases.

Inhibition of dehydrogenases by ATP or ADP is not novel, but their role as regulators of enzymes other than kinases remains underestimated. To compare the strength of inhibition of ATP and ADP, the single ‘inhibition term’ [defined as {1 + (I/KI)n}] was plotted against the inhibitor concentration (Fig. 4A) using the parameter values in Table 1. It revealed that GAPDH is most severely inhibited by each of these inhibitors, whereas LDH and ADH are only moderately inhibited.

Figure 4.

 Comparison between the effect of the single inhibitor and multiple inhibitors on the lactococcal dehydrogenases as expressed by the ‘inhibition term’. (A) Effect of the single inhibitors ATP (closed symbols) and ADP (open symbols) on LDH (bsl00001, □), ADH (bsl00066,Δ), GAPDH (•, ○). (B). Effect of the combined action of ATP and ADP on LDH (bsl00001), ADH (bsl00066), GAPDH (•).

In the case of multiple inhibition, the inhibitors act indifferently at the active site of LDH. Hence, the presence of all three inhibitors does not amplify the inhibition of LDH, leaving this enzyme only mildly inhibited. This can be illustrated by plotting the multiple inhibition term {defined as [1 + (I1/KI1)n1 + (I2/KI2)n2 + (I1I2KI1KI2)n]} against the concentration of the pool of ATP + ADP (Fig. 4B), displaying the same profile as for the single inhibition (Fig. 4A). For GAPDH in general, both the Hill coefficients and the dissociation constants were slightly lower than in the case of separate single inhibitions, resulting in the inhibition not being significantly different from the single inhibition (compare Fig. 4A, 4B). Again, multiple inhibition by ATP and ADP did not possess a stronger regulation of GAPDH activity. In contrast, for ADH, multiple inhibition revealed a drastic change to the single inhibition by ATP and ADP (Fig. 4). Especially through decreased values of the dissociation constants and a low value of α (Table 2), ADH became more strongly inhibited than GAPDH only at high levels of ATP + ADP, although this was not apparent at normal levels of the ATP + ADP moiety (Fig. 4B). Hence, only at elevated levels the regulating mechanism by this moiety becomes visible. In this way, strong inhibition of ADH, but low inhibition of LDH by the moiety guarantees a redirection of the catabolic metabolism from mixed-acid to homolactic acid formation, as observed by Palmfeldt et al. [1]. To our knowledge, this is the first time this phenomenon has been described. A strong regulation system by ATP has been described for GAPDH in rabbit muscle cells, but has not been studied in depth [18]. From simulations of in vivo conditions, the authors concluded that physiological concentrations of ATP and ADP regulate the glycolytic flux by inhibiting GAPDH by ∼ 90%.

ATP and ADP function as energy carriers, metabolites in RNA synthesis and as allosteric regulators of key enzymes in various pathways, and are thus ubiquitous within the metabolic network [28]. Usually, ATP and ADP are antagonistic in regulation, i.e. one functions as a positive, whereas the other functions as a negative regulator. In general, intracellular concentrations of ATP and ADP in proliferating prokaryotes and yeast are in the order of 2–5 and 1–2 mm, respectively [29,30]. Most studies with respect to ATP and ADP are carried out in exponential growing cells, e.g. in steady-state situations of continuous cultures. Few studies have looked into changing levels of ATP and ADP under stress conditions, such as growth in the presence of high sugar concentrations [31,32]. Fewer studies have been dedicated to nongrowing cells, i.e. stationary phase and resting cells. Those studies have focused on ATP concentrations alone [10] or on both ATP and ADP concentrations in, for example, L. lactis [1,32], Escherichia coli (E. M. Lohmeier-Vogel, personal communication) and yeast [30]. These studies have revealed elevated levels of both compounds, giving moieties up to 12–21 mm [1,32]. The reason for this could be that the nucleotide metabolic network in active nongrowing cells is less wide than in growing cells, for instance because of a lack of high RNA turnover. In such a case, completely different mechanisms of enzyme regulation may emerge, not normally operating in (rapidly) growing cells. The inhibition kinetics of the dehydrogenases as described in this study could be an example.

We would therefore like to propose the negative co-operative regulation of ADH by the ATP–ADP moiety as a new regulation mechanism in L. lactis, and it remains to be seen whether it is more widespread in nature. In L. lactis, this system is most probably adapted to regulate the flux of ATP production through strong nonlinear inhibition of ADH: by obtaining two instead of three ATPs per sugar unit in excess concentrations of ATP and ADP [1].

Materials and methods

Organism and cultivation conditions

Lactococcus lactis subspecies lactis (Lister) [33] deposited as Streptococcus lactis sp. ATCC19435 was obtained from the American Type Culture Collection (Manassas, VA, USA). It was cultivated at 30 °C in a 1 L fermenter with a working volume of 0.7 L. The medium consisted of (g·L−1): yeast extract 5, MgSO4 0.5, K2HPO4 2.5, KH2PO4 2.5 and maltose 10. The pH was maintained at 6.5 by controlled addition of 5 m sodium hydroxide. The cultures were stirred with a magnetic stirrer at a speed of 100 r.p.m. and were kept anaerobic by flushing N2 gas through the headspace. The biomass was monitored by measuring the optical density at 620 nm. At the end of the log phase, the cells were harvested by centrifugation (6300 g, 10 min, 4 °C), washed twice in triethanolamine (TEA) buffer (50 mm TEA, 5 mm MgCl2.6H2O, pH 7.2) and subsequently stored at −20 °C until further use.

Enzyme assays

The cell suspensions were mixed with glass beads (1 : 1, v/v). Cell extracts were prepared by disintegrating the cells using the glass bead method (6 × 30 s of vortex with 30 s intervals of cooling on ice). Cell debris was removed by centrifugation (15 800 g, 10 min, 4 °C). The supernatant was collected and liberated from interfering metabolites below 10 kDa using a PD10-desalting column (Sigma Aldrich, St Louis, MO, USA), which was equilibrated with 25 mL TEA buffer before use. Cell extract (2.5 mL) was added to the column and eluted with 2 mL TEA buffer, and subsequently kept on ice during analysis. All assays were carried out with an Ultrospec 2100 pro spectrophotometer (Amersham Biosciences, Little Chalfont, UK). The buffer pH was set at 7.2 to mimic the intracellular pH conditions of L. lactis cells [34].

ADH activity was measured spectrophotometrically by following the oxidation of NADH at 340 nm at 30 °C. The standard assay mixture contained (in total volume of 1 mL): TEA (50 mm, 5 mm MgCl2.6H2O, pH 7.2), glutathione (0.5 mm); NADH (0.06–0.25 mm), cell extract and one of the four inhibitors: NAD (0–4 mm), ATP (0–10 mm), ADP (0–8 mm), AMP (0–16 mm). The reaction was started by adding acetaldehyde (10 mm). LDH activity was measured spectrophotometrically at 340 nm by monitoring the oxidation of NADH at 30 °C [4,11]. The standard assay mixture contained (total volume of 1 mL): TEA (50 mm, 5 mm MgCl2.6H2O, pH 7.2), NADH (0.06–0.2 mm), cell extract and one of the four inhibitors: NAD (0–10 mm), ATP (0–6 mm), ADP (0–5 mm), AMP (0–10 mm). The reaction was started by adding sodium pyruvate (10 mm). GAPDH activity was measured at 340 nm by monitoring the reduction of NAD at 30 °C using a spectrophotometer. One millilitre of the reaction mixture contained: TEA (50 mm, 5 mm MgCl2.6H2O, pH 7.2), sodium arsenate (1 m), cysteine/HCl (1 m), cell extract and one of the following inhibitors: NADH (0–0.3 mm), ATP (0–4 mm), ADP (0–4 mm), AMP (0–2 mm). The reaction was started by adding the glyceraldehyde-3-phosphate (10 mm) [35]. The assays for yeast and horse liver ADH (EC and multiple inhibition analysis were performed similarly as above. Three concentrations of cell extract were used for each assay to test the linearity of the initial enzyme activities with the protein concentration. All assays were based on determining the initial conversion rates. The baseline was corrected for any background activity, measured for several minutes before adding the substrate to start the assay. The linearity of the assay was monitored over time by applying the standard assay (= complete assay without inhibitors) every 0.5 h. Any activity loss of the cell extract was corrected for. The majority of the inhibition datasets were carried out in duplicate, resulting in the same inhibition trends. The most elaborate datasets were chosen for fitting the models, the remaining duplicate datasets were used to validate the model (data not shown). Datasets for each case of single and multiple inhibition therefore consisted of measured inhibition trends instead of duplicates. All chemicals and enzymes were obtained from Sigma Aldrich.

Data analysis

To visualize the effect of the competitive inhibitor concentration on the conversion rate, the data were plotted as rate (v) versus substrate concentration (S) for each inhibitor concentration (I) to which, for this study, a Hill-type inhibition has been introduced:


in which VMAX is the maximum rate of the reaction, KIC is the dissociation constant for inhibitor I, KM is the affinity constant for NADH and n is the Hill coefficient. Similarly, the mixed inhibition kinetics can be expressed as:


with KIC as the dissociation constant at the active site (competitive inhibition) and KIU as the dissociation constant at the allosteric site (uncompetitive inhibition).

Multiple competitive inhibition could best be expressed by:


with the competitive inhibitors I1 and I2, their respective dissociation constants KIC1 and KIC2 and their respective Hill coefficients n1 and n2, and α as an interaction constant. In this way, the model describes the concomitant inhibition kinetics of each inhibitor plus the synergy (0 < α < 1), or indifference (α > 1) (Fig. S7) between the inhibition actions of both inhibitors at the active site.

When dealing with mixed inhibition, Eqn (4) becomes:


with KIU1 and KIU2 as the dissociation constants at the allosteric site (uncompetitive inhibition) and β as the mutual influence of the two inhibitors on the binding of each other at the allosteric site.

Plotting the multiple competitive inhibition kinetics as the normalized rates (Vi/V0) versus inhibitor concentration is the inverse of the Yonetani–Theorell equation [25]:


in which Vi and V0 are the actual rates with and without the inhibitor, respectively, and KAC1 [= KIC1n1 (1 + S/KM)) and KAC2 (= KIC2n2 (1 + S/KM)] are the apparent dissociation constants for the competitive inhibitors I1 and I2, respectively.

Data fitting and statistical analysis

Parameter estimation and statistical analysis were carried out using the Surface Fitting Tool (sftool) in matlab (R2009a). The parametric data fitting was based on nonlinear regression and the method of least squares. Model discrimination and choice was based on the goodness of fit. The goodness of fit was evaluated by visual examination of the fitted curves, 95% confidence bounds for the fitted coefficients and statistical analysis for determining the square of the multiple correlation coefficient (R2), the degrees of freedom adjusted R2 (adjusted R2) and rmse. The combination of smaller confidence bounds, values of R2 and adjusted R2 closer to 1 and an rmse value closer to 0 was used as the criterion for indicating a better fit.


This study was financially supported by the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning.