The reaction of trimethylamine dehydrogenase with electron transferring flavoprotein.

The kinetics of electron transfer between trimethylamine dehydrogenase (TMADH) and its physiological acceptor, electron transferring flavoprotein (ETF), has been studied by static and stopped-flow absorbance measurements. The results demonstrate that reducing equivalents are transferred from TMADH to ETF solely through the 4Fe/4S center of the former. The intrinsic limiting rate constant (klim) and dissociation constant (Kd) for electron transfer from the reduced 4Fe/4S center of TMADH to ETF are about 172 s−1 and 10 μM, respectively. The reoxidation of fully reduced TMADH with an excess of ETF is markedly biphasic, indicating that partial oxidation of the iron-sulfur center in 1-electron reduced enzyme significantly reduces the rate of electron transfer out of the enzyme in these forms. The interaction of the two unpaired electron spins of flavin semiquinone and reduced 4Fe/4S center in 2-electron reduced TMADH, on the other hand, does not significantly slow down the electron transfer from the 4Fe/4S center to ETF. From a comparison of the limiting rate constants for the oxidative and reductive half-reactions, we conclude that electron transfer from TMADH to ETF is not rate-limiting during steady-state turnover. The overall kinetics of the oxidative half-reaction are not significantly affected by high salt concentrations, indicating that electrostatic forces are not involved in the formation and decay of reduced TMADH-oxidized ETF complex.

The kinetics of electron transfer between trimethylamine dehydrogenase (TMADH) and its physiological acceptor, electron transferring flavoprotein (ETF), has been studied by static and stopped-flow absorbance measurements. The results demonstrate that reducing equivalents are transferred from TMADH to ETF solely through the 4Fe/4S center of the former. The intrinsic limiting rate constant (k lim ) and dissociation constant (K d ) for electron transfer from the reduced 4Fe/4S center of TMADH to ETF are about 172 s ؊1 and 10 M, respectively. The reoxidation of fully reduced TMADH with an excess of ETF is markedly biphasic, indicating that partial oxidation of the iron-sulfur center in 1-electron reduced enzyme significantly reduces the rate of electron transfer out of the enzyme in these forms. The interaction of the two unpaired electron spins of flavin semiquinone and reduced 4Fe/4S center in 2-electron reduced TMADH, on the other hand, does not significantly slow down the electron transfer from the 4Fe/4S center to ETF. From a comparison of the limiting rate constants for the oxidative and reductive half-reactions, we conclude that electron transfer from TMADH to ETF is not rate-limiting during steady-state turnover. The overall kinetics of the oxidative half-reaction are not significantly affected by high salt concentrations, indicating that electrostatic forces are not involved in the formation and decay of reduced TMADH-oxidized ETF complex.
Trimethylamine dehydrogenase (TMADH; 1 EC 1.5.99.7) isolated from the methylotrophic bacterium W 3 A 1 is a homodimer of molecular weight of 166,000, with each subunit containing a covalently bound 6-cysteinyl FMN coenzyme and a 4Fe/4S (ferredoxin-type) iron-sulfur center (1)(2)(3)(4). TMADH also possesses 1 equivalent of tightly bound ADP/monomer, although the function of this cofactor remains unknown (5). The enzyme catalyzes the oxidative demethylation of trimethylamine to dimethylamine and formaldehyde, passing the pair of reducing equivalents thus obtained individually to its physiological oxi-dant, an electron-transferring flavoprotein (ETF), which becomes reduced to the level of the (anionic) semiquinone (4, 6 -8). The ETF from W 3 A 1 has been shown to be an ␣␤ dimer with molecular weight of 77,000 and contains 1 mol of FAD and AMP/mol of protein; the role of AMP is unclear.
Complete reduction of TMADH requires 3 electrons/subunit, 2 for full reduction of the FMN, and a 3rd for reduction of the iron-sulfur center. When TMADH is reduced to the level of 2 electrons/subunit, there are two possible distributions of reducing equivalents: 1) fully reduced FMN with oxidized iron-sulfur and 2) flavin semiquinone with reduced iron-sulfur center. At pH 7.0, the former distribution is favored by a factor of approximately 2:1. Furthermore, although some TMADH 2eq possesses flavin semiquinone and reduced iron-sulfur center at pH 7.0, the magnetic moments of the unpaired spins do not interact as is the case when TMADH is reduced by excess substrate, or by sodium dithionite at high pH or in the presence of the inhibitor tetramethylammonium chloride (6, 9 -11). This spin-interacting form exhibits a unique EPR signal that includes half-field features and is not simply the sum of the signals for flavin semiquinone and reduced iron-sulfur center; we designate this spin-interacting form as TMADH 2eq *.
Previous freeze-quench studies have demonstrated that when TMADH 2eq * is mixed with ETF ox , the EPR signal arising from the spin-interacting state is lost within a few milliseconds with no concomitant appearance of that for the reduced ironsulfur center, as would be expected if electrons are transferred from the flavosemiquinone of TMADH 2eq * to ETF ox to give enzyme possessing oxidized flavin and reduced 4Fe/4S center (11). On the basis of these results, it has been proposed that electrons are transferred from the iron-sulfur center of TMADH to ETF ox (11), but direct evidence has been lacking. The present work provides direct evidence that electron transfer to ETF takes place exclusively via the iron-sulfur center of TMADH and determines the intrinsic rate constant for electron transfer and dissociation constant using stopped-flow rapid mixing technique. The results are incorporated into a comprehensive kinetic mechanism for the reaction of TMADH.

MATERIALS AND METHODS
Enzyme Purification and Materials-Methylophilus methylotrophus W 3 A 1 was grown and trimethylamine dehydrogenase was purified as described by Steenkamp and Mallinson (4), with the exception that the gel filtration step of the purification was performed using Sephacryl S-200 instead of Sephadex G-200. Enzyme concentration was determined from the 442 nm absorbance of oxidized enzyme using an extinction coefficient of 27.3 mM Ϫ1 cm Ϫ1 (3). Enzyme assay was performed as described by McIntire (12). ETF from M. methylotrophus W 3 A 1 was obtained essentially as described by Steenkamp and Gallup (7) with the exception that again Sephacryl S-200 was used instead of Sephadex G-100. ETF as isolated was partially reduced, so it was oxidized with ferricenium hexafluorophosphate and then passed through a Sephadex G-25 column equilibrated with 50 mM, pH 7.0, phosphate buffer. The concentration of ETF was determined from the absorbance of the oxidized form at 438 nm, using a molar extinction coefficient of 11.3 mM Ϫ1 cm Ϫ1 (7). Phenylhydrazine-inactivated TMADH was prepared as de-* This work was supported by Grant MCB 9420185 from the National Science Foundation. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Static Experiments-Oxidized ETF was placed in an anaerobic cuvette, covered with a black cloth (to prevent incidental photoreduction), and made anaerobic by alternately evacuating and flushing with O 2free argon. Solutions of reduced TMADH were prepared by being made anaerobic as above, then titrated with either titanium citrate or sodium dithionite. Samples (1.0 ml) of reduced enzyme were removed through a serum stopper using a Hamilton syringe and placed in one side of an anaerobic split cell, which had been made anaerobic in advance by flushing with O 2 -free argon. Anaerobic oxidized ETF (1.0 ml) was placed in the other side of the split cell, and a spectrum was recorded using a Hewlett-Packard 8452A single beam diode array spectrophotometer. The two protein solutions were then mixed by tipping the split cell and a second spectrum recorded, the difference between the two representing the static spectral change associated with electron transfer from TMADH to ETF.
Kinetic Experiments-Kinetic experiments were carried out using a Kinetic Instrument Inc. stopped-flow apparatus equipped with an On Line Instruments Systems (OLIS) model 3920Z data collection system. Anaerobic TMADH was prepared as above in a tonometer equipped with a ground joint for the dithionite titration syringe, a side arm cuvette, and a three-way stopcock valve with a male Luer connector, and reduced by titration with sodium dithionite to the desired level. ETF was made anaerobic as above and transferred to a syringe fitted with a three-way valve so that anaerobic buffer could be added to the syringe to change the ETF concentration by serial dilution. The concentrations of ETF were at least 5 times larger than that of TMADH to ensure pseudo first-order conditions in the experiments described. Kinetic transients obtained after mixing reduced TMADH with ETF were monitored as transmittance voltage and collected by a high speed A/D converter, then converted to absorbance changes by OLIS software. Time courses thus obtained were fitted to sums of exponentials using an iterative nonlinear least squares Levenberg-Marquardt algorithm (18), using the expression ⌬A(t) ϭ ⌺⌬A n exp(Ϫk n t) (with the floating variables ⌬A n and k n representing the absorbance change and observed rate constant, respectively for the nth kinetic phase).

RESULTS
The Spectral Change Associated with Reaction of Reduced TMADH with Oxidized ETF-The absorption spectra for oxidized, 2-and 3-electron reduced TMADH are shown in Fig. 1A, and the spectra for oxidized and semiquinone forms of ETF are shown in Fig. 1B. To determine the absorbance change associated with electron transfer from TMADH to ETF, the following experiments were performed. 1.0 ml of 8.2 M fully reduced TMADH (generated by titration with dithionite) was placed in one compartment of an anaerobic split cell, with 1.0 ml of 50 M ETF ox in the other compartment. A spectrum was recorded, after which the two solutions were thoroughly mixed and a second spectrum recorded. The observed difference spectrum exhibits an absorption increase in the 300 -410 nm and 462-600 nm ranges and a decrease in the 410 -462 nm range (Fig.  1C). To demonstrate that the spectral change is quantitatively consistent with the reduction of ETF ox and the reoxidation of TMADH 3eq in a 3:1 stoichiometry, the difference spectra for reoxidation of TMADH 3eq and reduction of 3 equivalents of ETF ox were generated from the spectra of Fig. 1 (A and B) and added. The difference spectrum thus obtained (Fig. 1E, dotted line) is very similar to the experimental difference spectrum (Fig. 1E, solid line), demonstrating that 1 equivalent of TMADH 3eq reduced 3 equivalents of ETF ox . To determine whether bisulfite (formed upon oxidation of dithionite) interferes with electron transfer between TMADH and ETF, TMADH was fully reduced with titanium citrate and mixed with ETF ox in a split cell. The same result as dithionite reduced TMADH was obtained (data not shown), indicating that bisulfite binding to the flavin of TMADH does not take place to an appreciable extent under the present experimental conditions and can be neglected.
Comparable results to those described above are obtained when only partially reduced enzyme was used. When 1.0 ml of 14 M TMADH 2eq in the non-spin-interacting state (generated by titration with Ti III ⅐citrate to the level of 2 reducing equivalents/subunit at pH 7.0) is mixed with 1.0 ml of 42 M ETF ox , the spectral change shown in Fig. 1D is observed and found to be quantitatively consistent with the reduction of ETF ox and the reoxidation of TMADH 2eq in the ratio of 2:1. When TMADH 2eq in the spin-interacting state (generated by reduction with 1 equivalent of trimethylamine in the presence of 3 mM tetramethyl ammonium chloride) is mixed anaerobically with ETF ox at pH 7.0 in a split cell, the spectral change is again consistent with the reduction of ETF ox and the reoxidation of the spin interacting state of TMADH 2eq in the ratio 2:1. These results demonstrate that ETF is able to fully reoxidize TMADH.
Spectral Changes Associated with the Reaction of Reduced Phenylhydrazine-inactivated and Ferricenium-treated TMADH with Oxidized ETF-In addition to the above studies with native TMADH, we have examined the reoxidation of two covalently modified forms of TMADH by ETF. Inactivation of TMADH by reaction with phenylhydrazine results in addition of the phenyl moiety at the C(4a) position of the flavin to form a stable adduct (14). The absorption spectrum of 4a-phen-ylFMN resembles that of reduced flavin and the modified cofactor is redox-inert, so that when phenylhydrazine-inactivated TMADH is reduced with sodium dithionite the spectral change ( Fig. 2A) is due entirely to reduction of the enzyme iron-sulfur center. When reduced, phenylhydrazine-inactivated enzyme is mixed anaerobically with ETF ox in a split cell experiment of the type described above, the absorbance change shown in Fig. 2B is observed, exhibiting an absorbance increase in the 300 -424 nm and 466 -600 nm regions and an absorbance decrease in the 424 -466 nm region. This spectral change is quantitatively consistent with the reduction of ETF ox and the reoxidation of the reduced, inactivated TMADH in a stoichiometry of 1:1 (Fig.  2C). It is conceivable that the phenyl group of the inactivated enzyme dissociates in the course of this experiment, complicating the interpretation of the results. To demonstrate that this is not the case, phenylhydrazine-inactivated TMADH was reduced with dithionite, mixed with ETF ox as above, and separated from the reaction mix by passage through a small Sephacryl S-200 column. It was found that the TMADH fraction consisted entirely of phenylhydrazine-inactivated enzyme, as determined both spectrophotometrically and by enzyme assay. We conclude that the reduced iron-sulfur center of phenylhydrazine-inactivated TMADH is able to reduce ETF even when the flavin center of the enzyme is rendered redox-inert by covalent modification. The difference spectrum for 4Fe/4S center obtained from phenylhydrazine-inactivated TMADH, in agreement with that determined electrochemically (19), permits deconvolution of the difference spectrum for oxidized and fully reduced TMADH (Fig. 3).
Treatment of TMADH with 3 mM ferricenium hexafluorophosphate at pH 10 for 4 h at room temperature has been found empirically to give an iron-sulfur center that is EPR-active. 2 The EPR spectrum of the enzyme thus generated is found to superficially resemble that given by the oxidized form of vari- ous high potential iron proteins (20). The integrated spin intensity of this signal indicates that the iron-sulfur center is quantitatively converted to this paramagnetic state. Since there was no loss of iron associated with generation of this EPR-active species (as one would expect if the signal arose from formation of a 3Fe/4S center), we tentatively conclude that the procedure results in the 1-electron oxidation of the iron-sulfur center to a level corresponding to that for oxidized high potential iron proteins. Regardless of the nature of this oxidation product, the significant aspect with regard to the present work is that the procedure renders the iron-sulfur center of TMADH redox-inert in that treatment with trimethylamine for 30 min does not reduce the intensity of the new EPR signal. 3 It is found, however, that trimethylamine is still able to react with and reduce the enzyme FMN, but the reduced enzyme thus generated was not able to reduce ETF ox , even after prolonged incubation. These results demonstrate the flavin center of ferricenium-treated TMADH remains catalytically competent, but that rendering the iron-sulfur center redox-inert prevents reoxidation of the reduced flavin by ETF.
Kinetics of the Reaction of Phenylhydrazine-inactivated and Native TMADH with ETF-In order to further characterize the oxidative half-reaction of TMADH, the kinetics of the reaction of ETF with various forms of TMADH have been examined. In an effort to establish the intrinsic rate constant for the reaction of ETF with the reduced iron-sulfur center of TMADH, its reaction with the reduced phenylhydrazine-inactivated enzyme was first investigated. This form of TMADH possesses fully reduced iron-sulfur center and a redox-inert FMN so that it gives only a single reducing equivalent (from the iron-sulfur center) upon reoxidation by ETF. The reaction of reduced phenylhydrazine-inactivated TMADH with ETF ox at pH 7.0 exhibits two kinetic phases (Fig. 4A). The fast phase of the reaction   3. Deconvolution of the difference spectrum for oxidized and fully reduced TMADH. The difference spectrum for oxidized and reduced 4Fe/4S center (solid line) is obtained by subtracting the spectrum for reduced phenylhydrazine-inactivated TMADH from that for oxidized inactivated TMADH. The difference spectrum for oxidized and reduced TMADH (dashed line) is obtained by subtracting the spectrum for fully reduced TMADH from that for oxidized TMADH. The difference spectrum for the enzyme FMN and FMNH 2 (dotted line) is obtained by subtracting the difference spectrum for 4Fe/4S center from that for TMADH. accounts for 80% of the total spectral change and the observed rate constant is ETF concentration-dependent, and under pseudo first-order conditions this phase is first-order. A doublereciprocal plot (21) of k obs versus ETF concentration is linear (Fig. 5, open squares), giving values of k lim and K d of 173 s Ϫ1 and 16 M, respectively. The wavelength dependence of ⌬A for the fast phase is consistent with it being due to electron transfer from the iron-sulfur center of inactivated TMADH to ETF, and this phase thus reflects the intrinsic kinetic parameters for the reaction of the fully reduced iron-sulfur center with oxidized ETF. The slow phase of the reaction, with an [ETF]independent rate constant of ϳ3 s Ϫ1 , and given its relatively minor contribution (20%) to the overall spectral change in all likelihood represents a side reaction, possibly the auto-reduction of ETF under the reaction conditions. 4 The absorbance changes obtained from the stopped-flow experiments are identical, within experimental error, to those calculated for the static difference spectra (Fig. 6), indicating that there is no absorbance loss in the dead time of the stopped-flow apparatus. To investigate the ionic strength effect on the intrinsic k lim and K d for the reaction of ETF with the fully reduced iron-sulfur center of TMADH, dithionite-reduced, phenylhydrazine-inactivated TMADH was mixed with ETF ox in 50 mM KP i , pH 7.0, buffer containing 0.2 M KCl in a stopped-flow apparatus. The double-reciprocal plot of k obs versus ETF concentration is linear (data not shown) and gives k lim ϭ 125 s Ϫ1 and K d ϭ 16 M, not much different from the values obtained in the absence of KCl. The fact that ionic strength has little effect on k lim and K d indicates that electrostatic forces do not play a particularly significant role in the formation and decay of E red ⅐ETF ox complex.
The temperature dependence of the rate of electron transfer from the 4Fe/4S center of TMADH to ETF was studied by reacting dithionite-reduced phenylhydrazine-inactivated TMADH with ETF ox at 5, 15, 25, and 35°C. The observed rate constants were temperature dependent and the Arrhenius plot is linear (not shown), giving activation energy of 12.8 kcal/mol.
The reaction of fully reduced native TMADH with ETF also exhibits two kinetic phases, although in this case the extent of the spectral change associated with the slow phase (approxi- 4 Anaerobic ETF is slowly reduced by light in the absence of any reagent. The slow phase of the reaction of reduced phenylhydrazineinactivated TMADH with ETF accounts for only 20% of the total spectral change; in addition, reduced phenylhydrazine-inactivated TMADH possesses only 1 electron/subunit and its reaction with ETF should not be biphasic. When reduced phenylhydrazine-inactivated TMADH reacts with ETF under aerobic conditions, the transients show only one phase. Thus, the slow phase in all likelihood represents a side reaction, probably the auto-reduction of ETF. By contrast, for the reaction of fully reduced native TMADH with ETF, the slow phase contributes 67% of the total spectral change, corresponding to approximately 2 equivalents removed from the enzyme, and can not be disregarded. mately 67%) appears to be kinetically significant. Fig. 4B shows kinetic transients obtained on mixing TMADH 3eq with excess ETF ox at pH 7.0 in a stopped-flow spectrophotometer. The transient observed at 370 nm consists of both phases, while that observed at 440 nm contains only the slow phase. The observed rate constants for each kinetic phase at a given set of reaction conditions are found to be independent of observation wavelength over the range of 300 -600 nm. At 370 nm, the fast phase accounts for about one third of the total absorbance change and the observed rate constant is dependent on the ETF concentration; a double-reciprocal plot of k obs for the fast phase versus ETF concentration is linear (Fig. 5, open circles) and the fit of the data gives k lim ϭ 172 s Ϫ1 and K d ϭ 10 M, in good agreement with the results using phenylhydrazine-inactivated enzyme. The observed rate constant for the slow phase is also ETF concentration dependent and the double-reciprocal plot of k obs versus ETF concentration is linear (not shown), giving k lim ϭ 16 s Ϫ1 and K d ϭ 9.9 M. The overall kinetics are consistent with the rapid removal of the first reducing equivalents from fully reduced TMADH, followed by the much slower removal of the second and third equivalents from the 2-electron reduced enzyme thus generated (owing to an unfavorable distribution of the reducing equivalents in TMADH 2eq and TMADH 1eq , see "Discussion").
It is of interest to determine whether the rate constant for the reaction of reduced iron-sulfur center in TMADH 2eq with ETF ox is dependent on whether the iron-sulfur center existed in a strong magnetic interaction with the flavin site. As in the case of fully reduced enzyme, the reaction of TMADH 2eq in the non-spin-interacting state with ETF ox is biphasic (data not shown). The fast phase accounts for about 30% of the total absorbance change, and the observed rate constant is dependent on the ETF concentration; a double-reciprocal plot of k obs for the fast phase versus ETF concentration is linear (Fig. 5,  filled squares), and the fit of the data gives k lim ϭ 157 s Ϫ1 and K d ϭ 24 M. The observed rate constant for the slow phase is approximately 10 s Ϫ1 and is independent of [ETF] under pseudo first-order conditions. In this experiment, approximately 40% of the TMADH 2eq exists initially with an electron distribution possessing flavin semiquinone and reduced ironsulfur center, but in which the two unpaired spins are not interacting to any detectable extent (22). When the experiment is repeated using TMADH 2eq in the spin-interacting state (generated by reduction of the enzyme with 1 equivalent of trimethylamine in the presence of 3 mM tetramethyl ammonium chloride), the reaction again exhibits two kinetic phases (data not shown). The fast phase accounts for about 70% of the total absorbance change and the observed rate constant is ETF concentration dependent, with k lim and K d of 149 s Ϫ1 and 39 M, respectively (Fig. 5, filled circles). The rate constant for the slow phase, which accounts for approximately 30% of the total absorbance change, is about 4 s Ϫ1 and independent of ETF concentration.

DISCUSSION
The present results indicate that when TMADH is treated with phenylhydrazine, rendering the FMN redox-inert (13), the iron-sulfur center can be reduced by dithionite and reoxidized by ETF. Similarly, when TMADH is treated with ferricenium hexafluorophosphate at high pH, oxidizing the iron-sulfur center to a paramagnetic but redox-inert state, the FMN can be reduced by trimethylamine but cannot be reoxidized by ETF. These results strongly suggest that reducing equivalents introduced into TMADH at the flavin site in the course of turnover are transferred to ETF exclusively via the iron-sulfur center. This is consistent with the interpretation of previous kinetic results, which have also implicated the iron-sulfur center as the site of the oxidative half-reaction of TMADH (11).
The reaction of ETF with reduced, phenylhydrazine-inactivated enzyme gives the intrinsic kinetic parameters for the reaction of ETF with the fully reduced iron-sulfur center without the complication of subsequent electron transfer from the flavin and further reduction of ETF. The limiting rate constant of 173 s Ϫ1 for electron transfer from the reduced iron-sulfur center to ETF is much faster than the rate-limiting step in the reductive half-reaction (product dissociation, with a rate constant of 3.5 s Ϫ1 ; Ref. 9), so electron transfer from the iron-sulfur center of TMADH to ETF is not rate-limiting during steadystate turnover. The fact that both k lim and K d (16 M) are insensitive to high salt concentration indicates that electrostatic forces are not involved in the formation and decay of E red ⅐ETF ox complex. The good agreement between both k lim and K d for the reoxidation of reduced, phenylhydrazine-inactivated TMADH with ETF ox and the fast phase of the reoxidation of FIG. 6. Static and kinetic difference spectra. Panel A, the solid line is the static difference spectrum calculated from the spectrum taken after mixing of TMADH 2eq (14 M) with ETF ox (42 M) at pH 7.0 minus the spectrum recorded before mixing (see Fig. 1D). The closed circles represent the kinetic data obtained by mixing TMADH 2eq (14 M) with ETF ox (37 M) in 50 mM phosphate buffer, pH 7.0, at 25°C in a stopped-flow apparatus. Panel B, the solid line is the static difference spectrum calculated from the spectrum taken after mixing of dithionitereduced phenylhydrazine-inactivated TMADH (12 M) with ETF ox (34 M) in 50 mM phosphate buffer, pH 7.0, minus the spectrum recorded before mixing (see Fig. 2B). The closed circles represent the kinetic data obtained by mixing reduced phenylhydrazine-inactivated TMADH (12 M) with ETF ox (36 M) in 50 mM phosphate buffer, pH 7.0, in a stopped-flow apparatus at 25°C. fully reduced enzyme support the conclusion that the former reaction accurately represents the intrinsic reaction of enzyme possessing fully reduced iron-sulfur center with ETF, and that reaction of the enzyme flavin with phenylhydrazine does not significantly perturb the iron-sulfur center.
The fast phase of the reaction of TMADH 3eq with ETF accounts for one third of the total absorbance change, and k lim is the same as that for the reaction of phenylhydrazine-inactivated TMADH with ETF, indicating the fast phase represents the removal of the first reducing equivalent from the reduced 4Fe/4S center to give TMADH 2eq . Because the slow phase accounts for two thirds of the total absorbance change, it most likely represents removal of the second and third equivalents from the FMNH 2 of TMADH 2eq, steps which are not kinetically resolved. Consistent with this interpretation is the good agreement between the rate constants for the slow phases of the reactions of ETF with TMADH 3eq and TMADH 2eq (16 s Ϫ1 and 10 s Ϫ1 , respectively). The small rate constants for both slow phases are owing to the unfavorable distribution of the reducing equivalents in TMADH 2eq and TMADH 1eq . The distribution of the reducing equivalents favors the enzyme form with FMNH 2 and oxidized 4Fe/4S in TMADH 2eq and with FMNH⅐ and oxidized 4Fe/4S in TMADH 1eq . The reoxidation of fully reduced TMADH by ETF can thus be summarized as shown in Scheme 1.
The fast phases of the reactions of ETF with TMADH 2eq in non-spin-interacting state and in spin-interacting state account for 30% and 70% of the total absorbance change, respectively, presumably because only 40% of the 4Fe/4S center in TMADH 2eq in non-spin-interacting state and all the 4Fe/4S center in TMADH 2eq in spin-interacting state are reduced. k lim for the fast phases of the two reactions are within experimental error (15)(16)(17)(18)(19)(20)Ref. 23) of the value for the reaction of phenylhydrazine-inactivated TMADH with ETF. Thus, both fast phases of the reaction of ETF with TMADH 2eq in non-spininteracting state and in spin-interacting state represent the electron transfer from the reduced 4Fe/4S center in TMADH 2eq to ETF and the rate of the electron transfer is independent of the reduction state of the FMN. k lim (149 s Ϫ1 ) for the fast phase of the reaction of TMADH 2eq in the spin-interacting state with ETF is identical, within experimental error, to that for the fast phase of the reaction of TMADH 2eq in non-spin-interacting state with ETF (157 s Ϫ1 ). This indicates that formation of the spin-interacting state does not significantly slow down the electron transfer from the 4Fe/4S center to ETF and that binding of tetramethylammonium chloride has little effect on the rate of electron transfer from the iron-sulfur center of TMADH to ETF. As in the absence of tetramethylammonium chloride, the slow phase represents the oxidation of TMADH 1eq , in which the sole reducing equivalent resides primarily on the FMN center. The somewhat slower rate constant for the slow phase of the reaction in the presence of tetramethylammonium chloride (4 s Ϫ1 versus 10 s Ϫ1 in its absence) is consistent with the observation that binding of tetramethylammonium chloride raises the FMN/FMNH ⅐ half-potential (19), thereby further shifting the oxidation-reduction equilibrium within TMADH 1eq even further toward flavin reduction and iron-sulfur oxidation and slowing the rate of reaction with ETF.
Our kinetic results concerning the reaction of the various reduced forms of TMADH with ETF can be incorporated into a comprehensive kinetic mechanism for the turnover of TMADH with trimethylamine and ETF. Because of the unusual situation where reducing equivalents are introduced into the enzyme in pairs (at the FMN) and removed one at a time (at the iron-sulfur center), coupled with the ability of the enzyme to take up a total of 3 equivalents, the general mechanism shown in Scheme 2 must be considered. Two alternate paths exist in which the enzyme alternates between: 1) oxidized and 2-electron reduced forms (the "0/2 Cycle" shown on the left of Scheme 2, prevailing at low concentrations of trimethylamine) and 2) between 1-and 3-electron reduced forms (the "1/3 Cycle" shown on the right, prevailing at high concentrations of trimethylamine). The cycle in which the enzyme operates depends on the fate of TMADH 2eq formed after reaction of oxidized enzyme with 1 equivalent of trimethylamine. This species can react either with ETF to give oxidized enzyme, or with substrate to give the spin-interacting state, which subsequently leads to formation of fully reduced enzyme. Ultimately which branch is favored under a given set of experimental conditions depends on the relative concentrations of ETF and TMA and their relative rates of reaction with enzyme.
The reductive half-reaction of TMADH has been studied by using both substrate trimethylamine and nonphysiological substrate, diethylmethylamine (9 -11, 23, 24). Initial reduction of the enzyme by trimethylamine occurs at the flavin site and is very rapid (t1 ⁄2 Յ 2 ms, [TMA] ϭ 500 M). Following this initial rapid reduction, two slower kinetic phases (t1 ⁄2 are approximately 80 and 200 ms, respectively) are observed. The rate constant for the slowest phase is approximately equal to k cat (9 -11, 24). By using the non-physiological substrate, diethylmethylamine, it has been demonstrated that product release and the binding of the second substrate molecule to the 2-electron reduced enzyme is the rate-limiting step (23). Intramolecular electron transfer within TMADH 2eq has been studied using a pH jump technique and intramolecular equilibration of reducing equivalents is fast (k obs Ն 200 s Ϫ1 ) (25).