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To identify the rate-limiting step(s) of the 3-isopropylmalate dehydrogenase-catalysed reaction, time courses of NADH production were followed by stopped flow (SF) and quenched flow (QF). The steady state kcat and Km values did not vary between enzyme concentrations of 0.1 and 20 μm. A burst phase of NADH formation was shown by QF, indicating that the rate-limiting step occurs after the redox step. The kinetics of protein conformational change(s) induced by the complex of 3-isopropylmalate with Mg2+ were followed by using the fluorescence resonance energy transfer signal between protein tryptophan(s) and the bound NADH. A reaction scheme was proposed by incorporating the rate constant of a fast protein conformational change (possibly domain closure) derived from the separately recorded time-dependent formation of the fluorescence resonance energy transfer signal. The rate-limiting step seems to be another slower conformational change (domain opening) that allows product release.
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3-Isopropylmalate dehydrogenase (IPMDH; EC 220.127.116.11) is an essential enzyme in the leucine biosynthesis pathway of bacteria, yeast, and plants. Because this pathway, including IPMDH, is absent in humans and in other mammals, IPMDH may constitute a potential target for inhibition by specific new drugs against pathogenic bacteria. Thus, detailed knowledge of both the architecture of the active site and the catalytic mechanism of IPMDH, including enzyme kinetics, is required.
IPMDH catalyses the complex reaction of simultaneous oxidation and decarboxylation of 3-carboxy-2-hydroxy-4-methylpentanoate [threo-d-3-isopropylmalate (IPM)] in the presence of NAD+. Similarly to reactions catalysed by other pyridine dinucleotide-linked β-hydroxy acid oxidative decarboxylases , the catalytic reaction requires the presence of divalent metal ions (Mn2+ or Mg2+). All enzymes of this class show a steady-state random kinetic mechanism ( and references therein). Up to now, however, in spite of the detailed crystallographic structures of IPMDHs of various origins [3-10], enzyme kinetic studies have been very limited [11-13]. Transient kinetic studies with IPMDH are still lacking, although they have the potential to reveal the presence of reaction intermediates and/or to identify the rate-limiting step(s) within the short period between mixing of enzyme and substrate and steady state or equilibrium being reached. In the present study, we applied complementary rapid mixing techniques, stopped flow (SF) and quenched flow (QF) (reviews in [14, 15]) to study the reaction catalysed by Thermus thermophilus IPMDH (TtIPMDH).
Crystallographic analyses of various IPMDHs have revealed a characteristic homodimer structure, with each subunit consisting of two domains. The complex of IPM with Mn2+ or Mg2+ (Mn-IPM or Mg-IPM) binds at the interface between the domains. This site, however, is also located at the subunit–subunit interface. Thus, IPM binding requires special attention with respect to the regulation of both domain–domain and subunit–subunit interactions. In fact, only IPMDH that binds the metal-complex of IPM shows a domain-closed conformation [5, 10]. A detailed atomic-level description of the mechanism of domain closure, upon binding of Mn-IPM, has been suggested for TtIPMDH on the basis of structural analysis . Accordingly, domain closure may play an essential role in the catalytic cycle, similarly to the mechanisms proposed for other multidomain enzymes [16-18].
There is a remarkable spectral property of the nonfunctioning (abortive) Mn-IPM–NADH–IPMDH complex, a fluorescence resonance energy transfer (FRET) phenomenon. Namely, upon excitation of the protein in solution, the fluorescence emitted by the Trp side chain(s) (donor) at λ = 340 nm will excite the fluorescence of the bound NADH (acceptor), so an emission band at λ = 410 nm can be finally observed. Interestingly, this FRET signal occurs only if the metal (Mn2+ or Mg2+) complex of the substrate, IPM, is also bound [11, 19], indicating that it appears only in a well-defined conformational state of the protein. Formation of the FRET signal can be attributed to the Mn-IPM-induced or Mg-IPM-induced conformational change, including optimal positioning of the Trp side chain(s) and the reduced nicotinamide ring. It is also assumed that this conformational change may either be part of the domain closure or accompany it .
In the present study, we followed separately the time courses of formation of the FRET signal and the transient kinetics of the catalytic reaction of TtIPMDH by using SF and QF methods, respectively. In this way we aimed: (a) to identify the nature of the elementary steps within a single transient; (b) to estimate the kinetic constants of the conformational process(es) represented by the FRET signal formation occurring in the unproductive Mg-IPM-NADH-IPMDH complex, which can be considered as a model of the functioning Mn-IPM–NAD+–IPMDH complex, as strongly supported by the current high-resolution crystal structure of the Mn-IPM–NADH–IPMDH complex (A. Palló, É. Gráczer, A. Merli, P. Závodszky, M. Weiss & M. Vas, unpublished); and (c) from comparison of the two different types of time course, to deduce the role of the conformational step(s) in the sequence of the possible elementary steps within a single transient. It became clear that neither the binding of substrates nor the redox step (NADH formation) is itself rate-limiting, as both of them are faster than the steady-state rate. It may be the chemical step of product formation itself or, most probably, a conformational transition that precedes the release of product.
Results and Discussion
Determination of the pre-steady-state rate of the IPMDH-catalysed reaction
In order to increase the spectral signal corresponding to formation of the products during the first catalytic cycle, high molar concentrations of enzyme subunits (at least 10–20 μm) are required. However, under these conditions, the rates of the catalytic reactions are much higher, and fast kinetic measurements are therefore required. The time courses of such measurements with TtIPMDH are shown in Fig. 1. In the SF experiments [curves (a)], direct SF traces of NADH formation were recorded at 340 nm upon mixing of the IPMDH–Mn2+–NAD+ complex with either subsaturating or saturating concentrations of IPM. Here, no apparent transient could be observed, although the dead time of the measurement was as low as 0.5 ms. The linear time-dependence at saturating concentrations of IPM could be fitted by a rate constant of 3.3 s−1, which satisfactorily corresponds to the steady-state kcat value determined at much lower (usually 0.1–0.3 μm subunit) enzyme concentrations. Thus, neither a burst nor a lag-phase could be apparently observed during these time courses. The SF experiments were also repeated at variable concentrations of both substrates, IPM and NAD+ (Fig. 2A,B). The derived Km values are also reported in Table 1, and agree well with the same values determined under multiturnover conditions at low enzyme concentrations.
Table 1. Summary of the pre-steady state and steady-state kinetic parameters of the TtIPMDH-catalysed reaction. Enzyme activity was determined in 25 mm Mops/KOH buffer (pH 7.6) at 20 °C with an ordinary spectrophotometric assay at 0.1 μm IPMDH , and by the SF or QF methods with a concentration range of 10–20 μm IPMDH. ss, steady state
Enzyme concentration (in subunits)
10 μm (SF)
20 μm (QF)
a Gráczer et al. . b É. Gráczer, A. Bacsó, L. Beinrohr, P. Závodszky, & M. Vas (unpublished). c Present SF experiments. d Present QF experiments.
However, under the conditions of the SF experiments (i.e. comparable molar concentrations of NADH formed and of the enzyme subunits), one should consider the possibility of a hypochromic decrease in the absorbance of enzyme-bound NADH as compared with that of the free NADH, as exemplified with other dehydrogenases [21-24]. Therefore, in a separate control experiment, we added increasing concentrations of IPMDH to a given concentration of NADH, and recorded the changes in the characteristic absorption band of NADH with λmax at 340 nm. We observed a significant decrease in the absorbance of NADH (without changing λmax) upon binding to the enzyme (Fig. 3A). This change in the absorbance of enzyme-bound NADH was used to estimate the Kd value of the enzyme-bound NADH. The binding curve shown in Fig. 3A yielded a value of 130 ± 30 μm. It is notable that this value is comparable (at least in its magnitude) not only to the Km value (240 ± 50 μm) of NAD+, but also to the separately determined Kd value (100 ± 20 μm) of NADH determined with isothermal titration calorimetry (ITC) (Fig. 3B).
In order to avoid the problem of reduction of absorbance of the enzyme-bound NADH in the SF experiment of Fig. 1 [curves (a)], we carried out QF experiments, indicated by curve (b) in Fig. 1. In these experiments, the reaction mixture of enzyme and substrates was quenched after various time intervals by addition of a high concentration of EDTA (see 'Determination of the pre-steady-state rate of the IPMDH-catalysed reaction'). Through complex formation with the essential metal ion, Mn2+, EDTA prevents the occurrence of any further enzyme reaction (i.e. immediately stops the reaction), and this process is also accompanied by immediate release of the enzyme-bound product, NADH. This was shown by detection of a larger amount of NADH being produced than in the SF experiments, where the hypochromic effect of the bound NADH largely distorted the spectral signal. The time-dependence of NADH formation detected in this way is shown by the experimental points of curve (b) in Fig. 1. This curve represents a complex time course fitted to the experimental points: a single exponential fast pre-steady-state phase, plus a slower, linear steady-state phase. It is clear that, under the same experimental conditions, the steady-state phase provides the same rate as was obtained in the SF experiment. It is worth mentioning that, despite the dispersion of the data points in QF experiments, other time courses obtained at different concentrations (not shown) also suggest the presence of a burst preceding the steady state. Importantly, the amplitude of this burst is proportional to the enzyme concentration. Table 1 summarizes the rate constants derived from both the SF and QF experiments shown in Fig. 1, compared with the previously determined steady-state rate constants from multiturnover experiments.
Two independent conclusions can be drawn from the data of Table 1. First, the catalytic activity of IPMDH does not vary with the protein concentration within a range of at least two orders of magnitudes. This finding is in agreement with the previous assumption that the dimeric form of IPMDH is the only active and stable form; under native conditions, it is not able to dissociate into its subunits . Second, transient kinetic measurements have revealed burst formation of NADH; that is, the redox step occurs much faster than the steady-state rate of the catalysis. It follows, therefore, that: (a) all of the elementary steps before the redox step [i.e. substrate binding (k1 and k2) and the accompanying conformational changes, possibly including domain closure] occur faster than the redox step itself (k3); and (b) any elementary step after the redox step, i.e. decarboxylation (k4), enol–keto tautomerization (k5), or dissociation of the product (k6) with the accompanying domain opening (Scheme 1), can limit the steady-state rate of the IPMDH-catalysed reaction. It has to be noted that Scheme 1 does not preclude the random binding of the two substrates, NAD+ and IPM, as the same kinetic time courses were obtained independently of the order of addition of the substrates.
Time-dependent formation of the FRET signal as followed by fluorescence SF
As mentioned above, fluorescence resonance energy is transferred from the Trp indole rings (mainly from Trp195 of TtIPMDH ) to the nicotinamide ring of NADH bound to the enzyme. This is accompanied by a characteristic spectral change, FRET (illustrated in Fig. 4A), which appears exclusively if the metal–IPM complex is also bound to the enzyme. Thus, it may be reasonably attributed to the occurrence of IPM-induced domain closure. Here we tested the time courses of formation of this FRET signal at various enzyme and substrate (IPM) concentrations. Some of the typical kinetic curves recorded are shown in Fig. 4B. The approximate half-times of all of these curves are ~ 0.1 s, independently of the substrate and enzyme concentrations. Thus, the first-order character of this process is immediately indicated from these measurements, in accordance with the assumption of a conformational change. In the course of more accurate kinetic analysis, however, it became evident that the curves could not be fitted by single exponentials. This is demonstrated by the dashed line in Fig. 4B, when we attempted to fit the kinetic curve obtained at 1000 μm IPM. Indeed, the residuals between the fitted and the measured curves are not satisfactory (Fig. 4C, dataset 1). This finding suggested that the time course of FRET signal formation may represent a composite signal of at least two first-order processes. Thus, fitting of the experimental time courses was further probed with three different models, each of them composed of two simple first-order processes occurring: (a) simultaneously; (b) sequentially; and (c) in two reversible directions, i.e. leading to an equilibrium. The kinetic curves could be satisfactorily fitted by either of the first two models, but the obtained kinetic constants were somewhat different (Table 2). Accordingly, the residuals of the fitting trials using the first two models (i.e. composite of two parallel or two sequential first-order processes) were almost zero (Fig. 4C, datasets 2 and 3, respectively). It has to be noted, however, that fitting trials with a model of two reversible first-order reactions (not shown) led to results with huge values of the statistical errors. Furthermore, this model would yield very much smaller values of the rate constants than those shown in Table 2. Such small values of the rate constants, however, would be irrelevant in light of the results of the transition kinetic SF and QF measurements of the catalysed reaction. However, it is not easy to decide between the first two models, as the rate constants obtained were not very different from each other. Indeed, considering that any global protein conformational process (such as domain closure) certainly represents the sum of several first-order (simultaneous or sequential) steps, each of them possessing its characteristic rate constant and amplitude, both models may have equal validity.
Table 2. The limiting values of the amplitudes and the kinetic constants derived from the fluorescence SF data of FRET signal formation at infinite IPM concentrations. The time-dependence of FRET signal formation was followed under the conditions given in the legend to Fig. 4. The kinetic curves shown in Fig. 4B, as well as other similar experiments, were fitted by the sum of two first-order reactions. The dependencies of the rate constants on IPM concentration are shown in Fig. 4D. The Kd values of IPM binding were determined by fitting the dependences of the rate constants of FRET signal formation and the FRET amplitudes on the concentration of IPM to a single binding hyperbola. The Kd values obtained from the whole FRET signal (A1 + A2) agree well with the value determined earlier . ND, not determined
Fluorescence amplitudes (a.u.)
Rate constants (s−1)
A1 + A2
180 ± 15
205 ± 26
385 ± 30
17.8 ± 2.0
5.35 ± 0.3
168 ± 15
216 ± 26
384 ± 30
25.6 ± 3.0
5.90 ± 0.4
Kd (μm) of IPM binding
25.1 ± 3.7
10.4 ± 2.8
37.8 ± 7.0
14.3 ± 2.0
Interpretation of the kinetic scheme of the IPMDH-catalysed reaction
Taking together the above results, we assume that the complex kinetic character of the time courses most possibly has to be attributed to a kinetic scheme (Scheme 1) including several steps, as follows.
Step 1: binding of NADH to the enzyme, which is assumed to reach equilibrium rapidly (with a K1 equilibrium constant) in the time scale of the experiment.
Step 2: binding of IPM to the enzyme, which may be too slow as compared with a diffusion-controlled process; that is, it may represent two-step binding – formation of a collision complex, and an induced conformational change, possibly the closure of the two domains.
Step 3: occurrence of the first chemical step (hydride transfer from the C2 atom of IPM to the nicotinamide ring of NAD+), which produces NADH. Crystal structural data , however, suggest that only the domain-closed conformation brings the reacting atoms of the two substrates into appropriate proximity for occurrence of the hydride transfer. Thus, domain closure is a prerequisite for occurrence of the redox step. Indeed, we have shown here that this step occurs during the pre-steady state, with a rate constant of 24 ± 7 s−1, which is very similar to both of the rate constants (17.8 ± 2 s−1 or 25.6 ± 3.0 s−1) derived from the FRET measurements. The latter process or processes is or are most probably representative of the IPM-induced conformational change, in line with the fact that this rate constant is independent of the concentration of IPM (Fig. 4D; Table 2). Thus, it is conceivable that this IPM-induced first-order conformational transition, represented by the domain closure, may determine the rate of NADH formation during the pre-steady state. It is also notable that, at low IPM concentrations (below 100 μm), the fitted k1 values depend on the IPM concentrations (Fig. 4D), possibly because of the initially weaker (Kd = 37.8 ± 7.0 μm; Table 2) interaction with IPM under these conditions.
Steps 4 and 5: these include the occurrence of the further chemical steps, i.e. decarboxylation and tautomerization, respectively, which may not require domain opening.
Step 6: dissociation of the product, which may be limited by the rate of domain opening (the step characterized by k6 in Scheme 1). It is very probable that the steady-state rate of the catalytic turnover is limited by this process. If it is so, domain opening is certainly slower than domain closure, as the steady-state rate of the catalysis is approximately 5- to 10-fold lower than the pre-steady-state rate (Table 1). Although the slower phase of FRET signal formation yielded rate constants (5.35 ± 0.3 s−1 or 5.90 ± 0.4 s−1; Table 2) very similar to the catalytic turnovers (3.4 ± 0.5 s−1; Table 1), this probably has nothing to do with the domain opening, as the opening process should be accompanied by the disappearance (and not the formation) of the FRET signal. Indeed, various types of simultaneous elementary conformational steps (only few of which are relevant to the main domain closure) are represented by FRET signal formation. However, our attempt to measure the rate of disappearance of the FRET signal by substituting the bound substrate IPM with the product 2-oxo-isocaproate failed.
In conclusion, the present complex transient kinetic study of the IPMDH-catalysed reaction and of the substrate-induced conformational change (as reflected by the FRET signal) provides a typical example of the investigation of complex enzyme mechanisms. It is quite possible that the fast part of the isomerization process represented by FRET signal formation can be considered as a time-dependent characteristic of the domain closure. As such, this rate may determine the pre-steady-state rate of NADH formation, which requires the domain-closed enzyme conformation. The steady-state rate of catalysis, however, is possibly limited by the much slower domain opening. This may also mean that, at equilibrium, the active (closed) conformation predominates over the inactive (open) one, at least in the complex with both NAD+ and Mn-IPM. The available data for various proteins, however, exhibit great variation in the equilibrium/energetic parameters of domain motions (e.g. [27-32]).
Reagents and enzyme
IPM was from Wako Biochemicals (Osaka, Japan); NADH was from Boehringer Mannheim (Mannheim, Germany). All other chemicals (high purity grade) were from Merck (Darmstadt, Germany) and Sigma (St. Louis, MO, USA).
Wild-type TtIPMDH was expressed in the Escherichia coli BL21 DE3 pLysS strain, and purified and stored as described previously [26, 33]. The molar activities of TtIPMDH subunits were 238 ± 30 min−1 when assayed in the presence of 0.5 mm IPM, 0.5 mm MnCl2 and 2 mm NAD+ in 25 mm Mops/KOH buffer (pH 7.6) at 20 °C . When MnCl2 was replaced by MgCl2 (2 mm), the molar activities of TtIPMDHs were 135 ± 20 min−1.
Control kinetic experiments with EDTA indicated that EDTA does not compete with binding of IPM; that is, inhibition by EDTA is solely attributable to withdrawal of the metal ion from the IPMDH active site .
ITC binding studies
ITC was performed with a MicroCal ITC-200 microcalorimeter (MicroCal Incorporate, Northampton, MA, USA) at 20 °C. Temperature equilibration prior to the experiment was performed for 1–2 h. All solutions were thoroughly degassed before use by stirring under vacuum. The sample of IPMDH solution (in the range of 1–2 mm subunit concentration) was prepared in 25 mm Mops/KOH buffer (pH 7.6). A typical titration experiment consisted of consecutive injections of 2 μL of the titrating ligand of 20 mm NADH (in approximately 20 steps) at 3 min intervals into the protein solution in a cell with a volume of 200 μL. The titration data were corrected for the small heat changes observed in control titrations of ligands into the buffer. The data were analysed with microcalorigin 7.0, assuming a 1 : 1 binding stoichiometry.
Experiments were carried out in a thermostatically controlled (20 °C) SF apparatus (SF-61 DX2; TgK Scientific, Bradford on Avon, UK). The dead time of the apparatus is 0.5 ms. For fluorescence measurements, excitation and emission slits were adjusted to 2 nm. Two types of experiment were carried out. In the first type of experiment, the formation of NADH from IPM and NAD+ in the presence of IPMDH was monitored by absorption at 340 nm. In the second, the kinetics of formation of the ternary complex IPM–NADH–IPMDH were followed using the FRET signal formed upon excitation of bound NADH by the fluorescence emission of protein Trp-s. In both cases, before being mixed with IPM, the enzyme was preincubated with the metal ion (MnCl2 or MgCl2) and with either NAD+ or NADH, respectively. The exact compositions of each initial solution in the syringes and in the reaction chamber of the SF apparatus are indicated in Figs 1 and 4. The excitation wavelength was 295 nm and the emission wavelength was > 400 nm; a cut-off filter was used. The fluorescence traces were biphasic, and were fitted by using equations of either the sum of two exponentials or two sequential first-order processes.
This is essentially a chemical sampling technique. Enzyme and substrates were mixed in a thermostatically controlled apparatus (QFM-400; Bio-Logic, Claix, France), the reaction mixtures were allowed to age for different times, and then quenched in 10 mm EDTA, and the NADH produced was assayed by absorption at 340 nm in a spectrophotometer (UV mc2; Safas, Monaco). It is a point-by-point method, and the time course of NADH formation was obtained from several experiments. The dead time of the apparatus is 6 ms. Time courses consisted of a burst and a steady state, and were fitted with an exponential and a linear equation with grafit 7.0.2 (Erithacus Software Limited, Staines, UK).
This work was supported by grant OTKA (NK 77978) from the Hungarian National Research Fund. Travel support by NKTH/OMFB (No. F-31/2009) and Egide (PHC Balaton No. 22295 QE) is gratefully acknowledged.