Primary Steps of the Na+-translocating NADH:Ubiquinone Oxidoreductase Catalytic Cycle Resolved by the Ultrafast Freeze-Quench Approach*

The Na+-translocating NADH:ubiquinone oxidoreductase (Na+-NQR) is a component of respiratory chain of various bacteria, and it generates a redox-driven transmembrane electrochemical Na+ potential. Primary steps of the catalytic cycle of Na+-NQR from Vibrio harveyi were followed by the ultrafast freeze-quench approach in combination with conventional stopped-flow technique. The obtained sequence of events includes NADH binding (∼1.5 × 107 m–1 s–1), hydride ion transfer from NADH to FAD (∼3.5 × 103 s–1), and partial electron separation and formation of equivalent fractions of reduced 2Fe-2S cluster and neutral semiquinone of FAD (∼0.97 × 103 s–1). In the last step, a quasi-equilibrium is approached between the two states of FAD: two-electron reduced (50%) and one-electron reduced (the other 50%) species. The latter, neutral semiquinone of FAD, shares the second electron with the 2Fe-2S center. The transient midpoint redox potentials for the cofactors obtained during the fast kinetics measurements are very different from ones achieved during equilibrium redox titration and show that the functional states of the enzyme realized during its turning over cannot be modeled by the equilibrium approach.

The Na ϩ -translocating NADH:ubiquinone oxidoreductase (Na ϩ -NQR) 2 is a redox-driven sodium pump that generates a transmembrane electrochemical Na ϩ potential (1). This enzyme is shown to operate in the respiratory chain of various bacteria, including several pathogenic microorganisms (2,3). One of the best ways to investigate the molecular mechanism of the functioning of an enzyme is to determine the time-dependent evolution of the molecular species (intermediate states) involved. The typical turnover rate of Na ϩ -NQR under optimal conditions (k cat ) is ϳ300 enzyme turnovers per second (4). For one oxidized NADH molecule, it delivers two electrons to the ubiquinone molecule through at least five cofactors (5) and translocates two sodium ions across the membrane (6) in 3 ms. During this short time, such a complex molecular machine should pass through a rather large number of catalytic intermediates. To resolve these intermediates, fast transient kinetics approaches should be used.
Previously (10,14), using the fact that in the absence of sodium ions, part of the catalytic cycle is dramatically slowed down, we were able to distinguish three main phases in the reduction of the enzyme by NADH. The fast phase, which can be resolved by stopped-flow only under very acid conditions (pH 5.5) and low temperature (4°C), was assigned to the twoelectron reduction of FAD. The intermediate phase had the absorption spectrum of the reduction of a neutral flavosemiquinone radical (FlH ⅐ 3 FlH 2 ), and the slowest step was assigned to the formation of flavosemiquinone anion from the oxidized flavin (Fl3 Fl ⅐ Ϫ). Although the rate of the first phase was not dependent on Na ϩ concentration, the next two steps were significantly accelerated by sodium ions with an apparent activation constant close to the K m of the enzyme to sodium.
In those three phases, we did not resolve the reduction of the 2Fe-2S center. Also it remained completely unknown how twoelectron oxidation of NADH is coupled to the one-electron steps seen in the Na ϩ -dependent phases. In addition, the most important question concerns the nature of the fast phase under physiological conditions, which was not resolved because of the high speed of this sodium-independent phase at neutral pH. To answer all these questions, we set up an experiment to resolve the primary steps of NADH oxidation by an ultrafast freezequench approach (15)(16)(17)(18) in combination with conventional stopped-flow.
Stopped-flow Kinetic Measurements-Na ϩ -NQR (3-9 mg ml Ϫ1 ) in buffer A (100 mM KCl, 10 mM HEPES/Tris (pH 7.5), 0.1% n-dodecyl ␤-D-maltoside (DM)) was rapidly mixed (dead time 3 ms) with an equal volume of buffer A containing 70 M NADH (potassium salt). To study the Na ϩ -NQR reduction kinetics at pH 5.5, the enzyme in buffer A was rapidly mixed with buffer B (100 mM KCl, 200 mM MES/Tris (pH 5.5), 0.1% DM) containing 70 M NADH. Rapid mixing experiments were carried out using a stopped-flow spectrophotometer equipped with a diode array detector capable of recording spectra at a rate of up to one per millisecond (Unisoku Instruments or HR2000ϩ Ocean Optics). All the experiments were performed at 3.5°C. The background sodium concentration in the mixtures was 30 M. Spectrum of the formation of the FAD semiquinone from FADH 2 was obtained by the oxidation of the reduced NqrF subunit (containing only noncovalently bound FAD as flavin cofactor) by oxygen as described in Ref. 12.
Data Analysis-Basic data matrix manipulations and presentation were done with MATLAB (The MathWorks, South Natick, MA) (20). The data obtained from the stopped flow instrument were analyzed in the form of a surface of absorbance values on the time/wavelength plane. Decomposition of these surfaces was done using a global fitting with the assumption that the kinetics at a given wavelength of the surface can be described by the same exponential processes as at all other wavelengths. We also assume that the catalytic cycle can be represented as a sequence of irreversible monomolecular reactions. With this algorithm, the data surface is described by the formula where A(,t) is the absorbance at a given time (t) and wavelength (); m is the number of sequential reactions; e(l) is the extinction coefficient of the absorbance changes during the reaction step; c is the concentration of the intermediate formed during this step; and k i is the rate constant of this intermediate formation. This formula would be the same for the kinetic data at any wavelength. The amplitudes of the exponential processes are different at different wavelengths, and the vectors ⑀ 1 ()ϫc 1 , ⑀ 2 ()ϫc 2 , ⑀ 3 ()ϫc 3 , etc. are the kinetic difference spectra of optical changes, which proceed in the corresponding exponential process. c 0 () is a "constant term" spectrum that corresponds to the final state, toward which the entire system is decaying.
Freeze-Quench Kinetic Measurements-Na ϩ -NQR (15 mg ml Ϫ1 ) in buffer A (100 mM KCl, 10 mM HEPES/Tris (pH 7.5), 0.1% DM) or buffer C (100 mM NaCl, 10 mM HEPES/Tris (pH 7.5), 0.1% DM) was rapidly mixed with an equal volume of buffer A or buffer C containing 7 or 100 mM NADH (potassium or sodium salt), frozen on the liquid nitrogen cold silver drums, and packed into an EPR tube immersed into the liquid nitrogen bath using an ultrafast freeze-quench apparatus described in Ref. 17. The samples frozen at times from 80 s to 3.2 ms after mixing the enzyme with NADH were incubated for 30 min at Ϫ80°C to remove traces of liquid oxygen and superoxide oxygen-centered free radicals and were further studied by EPR spectroscopy. It is noteworthy that after mixing, the final concentrations of NADH and the enzyme became 4-fold lower. This was caused by mixing (in 1:1 proportion) and also by two times dilution by the carrier buffer (17). The apparent concentration of the enzyme in the EPR tube was additionally smaller by a factor of two because the sample in the form of ice powder after packing into the tube occupies 2-fold larger volume than just frozen liquid.
EPR Spectroscopy-A Bruker ESP-300 X-band (9.4 GHz) EPR spectrometer was used. The field modulation frequency was 100 kHz. The temperature of the sample was controlled with an ESR 900 liquid helium cryostat with an ITC4 temperature controller (Oxford Instruments). The frequency was calibrated with an HP X532B microwave frequency meter. All EPR data were corrected by subtracting the blank (EPR signal of tube with buffer). EPR signals were quantified by double integration of the experimental spectra obtained under nonsaturated conditions.
Determination of Second-order Rate Constant of NADH Oxidation-NADH:hexaammineruthenium oxidoreductase activity of the Na ϩ -NQR was measured at 30°C in a buffer containing 100 mM KCl, 20 mM HEPES/Tris (pH 7.5), 0.1% DM, 150 M NADH, and 0.5 or 1 mM hexaammineruthenium. NADH oxidation was monitored by registering the decrease in optical density at 340 nm (⑀ 340 ϭ 6.22 mM Ϫ1 cm Ϫ1 ) using a Hitachi-557 spectrophotometer. The rates of NADH oxidation at different concentrations of this reduced pyridine dinucleotide were determined by analyzing the first derivative of the NADH oxidation progress curves. Briefly, the NADH concentration can be calculated from optical density values of a direct OD 340 versus time curve, whereas the values of the first derivative of the direct curve are proportional to the rates of NADH oxidation. The data were fitted to the Michaelis-Menten equation using nonlinear regression analysis. The bimolecular rate constant was defined as k cat /K m . The second-order rate constant was 1.5 ϫ 10 7 M Ϫ1 s Ϫ1 .
Determination of the Affinity of Na ϩ -NQR to NAD ϩ -Parameters of NAD ϩ binding to Na ϩ -NQR were determined by studying the inhibition of the enzyme activity in the presence of this compound. The rates of NADH oxidation by membrane vesicles from the Vibrio harveyi NDKm34 strain (⌬ndh) (21) at various NADH concentrations were determined as described above. These experiments were carried out in the presence of 0 -20 mM NAD ϩ . It was found that NAD ϩ is a competitive inhibitor of Na ϩ -NQR with k I value of 11 mM.
Protein content was determined by the bicinchoninic acid method using bovine serum albumin as a standard. The sodium concentration was measured by flame photometry.

Stopped-flow Recording of Na ϩ -NQR Reduction by NADH-
The primary steps of Na ϩ -NQR reduction by NADH are rather fast. Even in the absence of sodium ions, there are some fast catalytic steps, which probably occur in turnover earlier than Na ϩ is bound. However, in agreement with our previous results (10,14), at sufficiently acid conditions, the fast Na ϩ -independent phase became slow enough to be recorded by the stoppedflow technique. Our setup collects a data surface of optical changes during the course of the reaction with the time resolution of 1 ms between the individual spectra in the surface. The time course of the reaction followed at selected wavelength clearly shows the multicomponent behavior. To resolve these components, we applied the global analysis of the recorded surface (see "Experimental Procedures" for details). The fit reveals that such behavior can be best fitted as four sequential steps with time constants (at pH 7.5, 3.5°C) of 2.3 ms, 35 ms, 0.6 s, and 1.6 s, and the four corresponding kinetic difference spectra were obtained. Fig. 1 shows the kinetic spectrum of the fast phase of Na ϩ -NQR reduction by NADH at pH 5.5 and 3.5°C. This spectrum corresponds to the two-electron reduction of a flavin. Increase of pH resulted not only in increase of the apparent rate constant of this phase but also in a change of its spectrum. The amplitude of the fast phase obtained in the experiment became smaller because a large part of the reaction proceeds in the dead time of our setup, which is 3 ms. In Fig. 1, the spectra have amplitudes obtained by the fit, taking into account that the reaction starts 3 ms before the recording. As can be seen in Fig.  1, in addition to the troughs at 400 and 460 nm characteristic for the two-electron reduction of a flavin, the neutral pH spectrum also exhibits peaks at 527, 593, and 644 nm (the exact positions of the peaks were defined by the second derivative of the spectrum). This spectrum with three peaks is characteristic for the formation of the neutral flavosemiquinone radical (FlH ⅐ ) from the reduced flavin. Na ϩ -NQR as isolated, in oxidized form, already contains very stable neutral flavosemiquinone in the concentration of one electron spin per protein (4,14), which is detected in the enzyme even in the presence of such strong oxidant as ferricyanide (22). Lately it was shown that this neutral flavin radical is formed from noncovalently bound riboflavin (22). However, the positions of the maxima of its spectrum are different and significantly blue-shifted ( max ϭ 522, 578, and 629 nm (14)). Thus, the spectral changes for the fast kinetic phase cannot be attributed to riboflavin reduction (oxidation). It is noteworthy that the red shift of the long wavelength peaks is characteristic of the FAD radical in ferredoxin:NADP ϩ oxidoreductases of the FNR family (23,24), including FAD semiquinone in the NqrF subunit of Na ϩ -NQR (12).
Two spectra, one representing the formation of the FAD semiquinone in the NqrF subunit (Fig. 2, curve 2) and the other, which is the long wavelength region of the kinetic spectrum of the fastest phase (curve 1), are shown in Fig. 2. The stationary spectrum of the FAD neutral radical was obtained by NADHinduced reduction of the NqrF catalytic subunit in the presence of oxygen (see Ref. 12). It is absolutely clear that the two spectra are very similar and likely represent the redox transition of the same compound. This compound is FAD in the NqrF subunit, and we propose that at neutral pH, it can form a significant quantity of the radical state.
As it is clear from the data in Fig. 1, the [Na ϩ ]-independent kinetic phase consists of more than one process. At pH 5.5, it is just two-electron reduction of the FAD, whereas at neutral pH, this two-electron reduction occurs in the dead time of the instrument and a subsequent step of electron separation is already seen. The time resolution of the stopped-flow device is not sufficient to resolve all fast events of the catalytic cycle. This is why we decided to apply the ultrafast freeze-quench approach.
Freeze-Quench Recording of Na ϩ -NQR Reduction by NADH-The ultrafast freeze-quench method makes possible the trapping of enzyme intermediates and consequent analysis of their chemical structure using different physical methods, particularly EPR, which is very informative in the case of Na ϩ -NQR. Our setup (17) can stop the reaction on the time scale from about 100 s to a few milliseconds after mixing. The fast stop in

Time-resolved Na ؉ -NQR Reduction
FEBRUARY 27, 2009 • VOLUME 284 • NUMBER 9 the approach is realized by freezing of a high speed (in our case ϳ100 m/s) 25-m-thick jet of mixed solution on the surface of rotating liquid-nitrogen cold silver cylinders. Fast mixing was achieved by the dramatic decrease of the mixing volumes (down to ϳ1 nl). The time of the reaction, defined by the jet fly time required for the sample leaving the mixing device to get to the freezing cylinders, and the increase of the reaction time were achieved by increasing the distance between mixer and silver cylinders.
Using this method, we studied the fast steps of the catalytic cycle, which cannot be resolved by optical spectroscopy using the stopped-flow approach. As we mentioned above, the oxidized Na ϩ -NQR contains neutral flavosemiquinone in the ratio 1:1 per enzyme molecule and therefore shows an EPR signal with the g ϭ 2.00 and 20 G line width (10). This is why at the zero time point obtained by the mixing of the enzyme with the buffer without NADH, there is a spectrum (Fig. 3A) of this radical. After the initiation of the reaction with NADH, the radical concentration increased with time. The additional rad-ical signal (3.5 ms minus 0 ms) has g ϭ 2.00 and is characterized by a slightly narrower bandwidth (ϳ18 G). Nevertheless, this shape of the appearing radical signal is characteristic for a neutral flavosemiquinone because it is significantly wider than the signal derived from the anionic form of the flavosemiquinone (ϳ14 G) (25). Such a conclusion is in good agreement with our optical spectroscopy data (see above). The reaction of the enzyme with NADH also resulted in the appearance of one more well characterized EPR signal belonging to the 2Fe-2S cluster with g xy ϭ 1.94 (Fig. 3B). This signal is absent at zero time and reaches about 50% at 3.2 ms after the start of the reaction. The relative amplitude of the signal was found by its comparison with the signal from the fully reduced enzyme, which was obtained from the same enzyme batch by mixing with dithionite and taking into account the ice powder packing factor (see "Experimental Procedures").
Having a radical signal from the enzyme in the concentration of one electron spin per protein before the start of the reaction (14) allows us to quantitatively determine the time course of the reaction. The integral of this signal corresponds to the microwave absorbance by one electron spin per enzyme. We can plot an additional signal appearing during the reaction as a fraction of the primary signal (Fig. 4) and have the kinetic curves of the reaction components development in time. As can be seen from Fig. 4, the flavosemiquinone radical signal (filled squares) develops absolutely synchronously with the reduction of 2Fe-2S cluster (filled circles). After the short lag, they both rose to about 50%. The solid line on the figure drawn through the data points represents the fit of those points with the kinetic model for the two-step sequential reaction with the parameters: k 1 ϭ 3200 s Ϫ1 and k 2 ϭ 970 s Ϫ1 . The experimental points were obtained in medium without sodium ions (background [Na ϩ ] ϳ30 M). The results of the same experiment conducted in the presence of 100 mM of Na ϩ were very similar (data not shown).

DISCUSSION
Rate of NADH Binding-In our fast kinetic measurements, we should be sure that the reaction rate is not limited by the rate of NADH binding. For that purpose, we determined the bimolecular rate constant of NADH oxidation by the enzyme using a  simple steady-state approach. For example, at a hexaammineruthenium concentration of 1 mM, the apparent K m of NADH oxidation was defined as 80 M. The k cat obtained in the same experiments was 1200 s Ϫ1 . Thus, the ratio of k cat /K M app should give the bimolecular rate constant, which was determined as 1.5 ϫ 10 7 M Ϫ1 s Ϫ1 . Such a bimolecular rate constant defines the time constant of NADH binding in our freeze-quench experiments at the minimal used NADH concentration 1/(1.75 ϫ 10 Ϫ3 M ϫ 1.5 ϫ 10 7 M Ϫ1 s Ϫ1 ) ϭ 38 s. This means that under our conditions, the Na ϩ -NQR reduction was not limited by the rate of NADH binding. In agreement with this conclusion, it was found that the parameters of the studied reaction were almost the same even after 15-fold increase in the NADH concentration used (data not shown).
Another important parameter of the system was defined by the steady-state approach. It is the time of the release of the product of the reaction, NAD ϩ , from the enzyme. Using the competitive inhibition methodology, we found that the binding constant for NAD ϩ is very poor and has a value of about 11 mM. Because the diffusion properties of such similar molecules as NAD ϩ and NADH are very similar, we can assume that the bimolecular rate constant that we found for NADH binding is also valid for NAD ϩ (this assumption could be incorrect if, for example, charge of the cofactor is important for its delivery to the binding site). Knowledge of these two numbers gives us the lifetime of the NAD ϩ -enzyme complex: 1/(11 ϫ 10 Ϫ3 M ϫ 1.5 ϫ 10 7 M Ϫ1 s Ϫ1 ) ϭ 6 s. This very low value means that the release of NAD ϩ from Na ϩ -NQR cannot limit the rate of any step of the enzyme catalytic cycle.
Primary Steps of the Reaction-The kinetic traces of 2Fe-2S cluster reduction and formation of FADH ⅐ has a lag phase during which the preceding reactions occur. The time constant for these EPR silent reactions is 320 s. Because the binding of NADH did not take more than 38 s, it is clear that there is at least one more process. By optical spectroscopy, we have seen that it should be two-electron reduction of FAD, which is a very common mechanism of NADH oxidation by direct hydride ion transfer from NADH to the flavin (17). Thus, we conclude that the concerted transfer of two electrons and the proton from NADH to FAD in the active site of Na ϩ -NQR takes about 300 s. As can be seen from Fig. 4, in the next step of the reaction, FAD shares its electron with the 2Fe-2S cluster forming 50% of reduced FAD and 50% of flavosemiquinone, which indicates establishing of quasi-equilibrium with the time constant of 1 ms. The equilibrium constant of this reaction dramatically depends on pH, and acid conditions stabilize the two-electron form of FAD (Fig. 1). The overall scheme of the primary events developing in the NqrF subunit can be seen in Fig. 5.
Comparison of Kinetic Quasi-equilibrium with Thermodynamic Equilibrium-The equilibrium redox titration at pH 7.5 showed that the midpoint redox potential of FAD is Ϫ200 mV and that the titration curve has a slope characteristic for a twoelectron reduction (19), which itself would argue against stable semiquinone formation. Even more surprising is the movement of an electron from FADH 2 to the 2Fe-2S center because it has midpoint redox potential more negative than the flavin (Ϫ270 mV) (10). Thus, the formation of the semiquinone from FADH 2 and the reduction of the 2Fe-2S cluster by FADH 2 are both endergonic reactions, and according to the values of the midpoint redox potentials, the reduced FAD should not give electrons to the 2Fe-2S cluster, and at neutral pH, the redox equilibrium depicted in Reaction 1 should be shifted to the left as we observe it under acid conditions. The most likely scenario is that during fast kinetics, the system passes transient states that cannot be accessed during equilibrium titration. There is also a possibility that in the presence of NADH during the fast phase, not only two electrons and a proton are transferred to the enzyme, but also the next molecule of NADH is bound (see scheme in Fig. 5). If NADH binding changes the redox properties of the FAD, then such unusual quasi-equilibrium can be explained by the formation of this complex.