Stopped-flow reaction kinetics of recombinant components of proton-translocating transhydrogenase with physiological nucleotides.

New information on the high resolution structure of the membrane proton pump, transhydrogenase, now provides a framework for understanding kinetic descriptions of the enzyme. Here, we have studied redox reactions catalyzed by mixtures of the recombinant NAD(H)-binding component (dI) of Rhodospirillum rubrum transhydrogenase, and the recombinant NADP(H)-binding component (dIII) of either the R. rubrum enzyme or the human enzyme. By recording changes in the fluorescence emission of native and engineered Trp residues, the rates of the redox reaction with physiological nucleotides have been measured under stopped-flow conditions, for the first time. Rate constants for the binding reaction between NAD(+)/NADH and the R. rubrum dI.dIII complex are much greater than those between nucleotide and isolated dI. For the redox step between the physiological nucleotides on the R. rubrum dI. dIII complex, the rate constant in the forward direction, k(f) approximately 2900 s(-1), and that for the reverse reaction, k(r) approximately 110 s(-1). Comparisons with reactions involving an analogue of NAD(H) indicate that the rate constants at this step are strongly affected by the redox driving force.

membrane. Crystal structures of the dIII components of human and bovine transhydrogenases were recently described (4 -6), and the solution structure of the Rhodospirillum rubrum equivalent was determined by NMR. 1 The basic fold of dIII is similar to the classical, dinucleotide-binding domain of lactate dehydrogenase, but NADP ϩ is bound with an unusual, "reversed" orientation. The nicotinamide ring of the bound NADP ϩ is exposed on a ridge of dIII. A homology model of dI (8), based on the crystal structure of the sequence-related alanine dehydrogenase (9), suggests that the nicotinamide ring of NADH is located in a deep cleft. It was proposed that, in the complete transhydrogenase, the ridge of dIII inserts into the cleft of dI to bring the nicotinamide rings of the two nucleotides into apposition to effect direct hydride transfer (5,6). The protruding helix-D/loop-D of dIII is thought to interact with the membrane-spanning, dII and, together with the adjacent, lidlike loop E, which passes over the bound nucleotide, might be responsible for the energy transmission. The proton translocation steps during turnover are probably coupled specifically to changes in the mode of NADP(H) binding (1,5,10).
Kinetic studies of transhydrogenase have also developed, following discoveries that fragments of the protein retain their nucleotide binding and some catalytic capacity. Thus, recombinant dI and dIII proteins, which bind their cognate nucleotides, have now been isolated from a number of species (11)(12)(13)(14)(15)(16); mixtures of these proteins, even from different species, catalyze transhydrogenation reactions, albeit with properties that are modified relative to those of the complete enzyme. Transient state experiments, in particular, have revealed useful information on the hydride transfer step (17)(18)(19). Without exception, experiments with dI⅐dIII complexes have been carried out with nucleotide analogues having altered absorbance spectra to facilitate measurement of the rate of reaction. In this report we describe transient state experiments with the physiological nucleotides. A procedure is described, in which single-turnover hydride transfer between NAD(H), on dI, and NADP(H), on dIII, is monitored by following changes in protein fluorescence. We use a natural Trp residue in human recombinant dIII, and an engineered Trp in the equivalent R. rubrum protein (20). The oxidation/reduction step is faster than expected from studies with substrate analogues, and we can detect a driving force effect that arises from differences in the redox potentials of the natural and analogue substrates.
EXPERIMENTAL PROCEDURES DNA coding for the dI and dIII proteins of R. rubrum transhydrogenase (rrdI 2 and rrdIII, respectively), and the human dIII protein (hs-* This work was supported in part by the Biotechnology and Biological Sciences Research Council and the Wellcome Trust. 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. ‡ Recipient of a British Heart Foundation studentship. § To whom correspondence should be addressed.  (11,13,16). The proteins were expressed and purified in their NADP ϩ forms by column chromatography (11,13,16). R. rubrum dIII, in which Glu 155 had been mutated to a Trp residue, was derived by site-directed mutagenesis, as described (20) and purified as for wild-type protein. Samples were stored in 20% glycerol at Ϫ20°C before use. All protein preparations were checked for purity (Ͼ95%) by SDS-polyacrylamide gel electrophoresis (21), and for cyclic transhydrogenation activity (10,13,16). Protein concentrations were determined using the microtannin assay (22); they are expressed as monomeric values.
Throughout this report, sequences are numbered according to the isolated protein components. Thus, Met 1 of rrdI corresponds to Met 1 of PntAA (see Ref. 23), Met 1 of rrdIII corresponds to Met 262 of PntB (23), and Met 1 of hsdIII corresponds to Met 837 of the complete human protein (16,24).
When proteins were to be used for analysis by NMR, the host cells of E. coli were grown on minimal medium (M9) containing 1 g/liter 15 NH 4 Cl. They were purified as described above, and prepared for experiments as described (25). 1 H, 15 N HSQC spectra were acquired, at a protein concentration of 600 M, on a Bruker AMX 500 spectrometer, using the fast heteronuclear single quantum correlation (FHSQC) NMR spectroscopy pulse sequence (26).
Proteins to be used in rapid mixing experiments were concentrated, and washed by filtration, in 10 mM (NH 4 ) 2 SO 4 , 20 mM Hepes, pH 8.0. Where required, NADP ϩ on dIII was replaced with NADPH, as described (17,18). Stopped-flow spectroscopy was performed, under the conditions described in the figure legends, on an Applied Photophysics DX-17MV instrument operating either in its absorbance mode at 375 nm, with an optical path length of 2 mm, or in its fluorescence mode, with 280 nm excitation light and Ͼ305 nm emission, isolated using a WG305 cut-off filter. The slits were set to 9.3 nm. In all stopped-flow experiments, the proteins and nucleotides were loaded into the instrument drive syringes in a buffer comprising 10 mM (NH 4 ) 2 SO 4 , 20 mM Hepes, pH8.0. Recordings of steady-state spectra on a Spex FluoroMax showed that fluorescence changes in the stopped-flow instrument originate from the protein Trp residues; changes resulting from nucleotide emission were negligible in the conditions employed. The kinetic data were fitted as described previously (17)(18)(19), either to a single exponential, or to the sum of two exponentials, with the instrument software, which employs the Marquardt-Levenberg algorithm for nonlinear regression. The dead time of the instrument, measured as described (27), was 1.31 ms. In calculating the amplitudes of absorbance and fluorescence changes, due correction was made for the signal undetected in the dead time. Rate constants were fitted to the kinetic scheme (see Reaction 2) using the programs KINSIM (28) and FITSIM (29).

Single-turnover Transhydrogenation Revealed by Changes in
Trp Fluorescence-Stopped-flow analysis of transhydrogenation (with substrate combinations AcPdAD ϩ ϩ NADPH (Refs. 17 and 18) and AcPdADH ϩ NADP ϩ (Ref. 19)) in mixtures of dI and dIII proteins revealed a burst of reaction before onset of the very slow steady-state rate. The burst is limited to a single turnover of dIII by the slow release of product, either NADP ϩ or NADPH. In mixtures of rrdI ϩ rrdIII, the burst is biphasic. The fast phase (phase A), which is predominant at high concentrations of dI (relative to dIII), is thought to correspond to hydride transfer in dI⅐dIII complexes present at the instant of mixing. The slow phase (phase B), which is predominant at low concentrations of dI (relative to dIII), is thought to result from the multiple turnovers of dI that are required to complete the single turnover of dIII. Phase B is limited by the dissociation of dI⅐dIII complexes; the re-association of the proteins and the exchange of nucleotides on dI are both relatively fast. Fig. 1 shows that the stopped-flow kinetics of AcPdAD ϩ reduction by NADPH with mixtures of rrdI and rrdIII.E155W (trace b) were indistinguishable, within error, from those obtained with mixtures of rrdI and wild-type rrdIII (trace a). The reaction was measured from the absorbance change at 375 nm, which corresponds to formation of AcPdADH. The apparent first order rate constants for phase A (558 and 610 s Ϫ1 ) and for phase B (32 and 28 s Ϫ1 ) were similar for the wild-type and the mutant dIII proteins. We previously showed that the steady-state kinetics of transhydrogenation are not significantly affected by this amino acid substitution (20) and, furthermore, 1 H, 15 N HSQC NMR spectra of rrdIII.E155W (in the NADP ϩ and NADPH forms) differed from spectra of wild-type protein (25,30) only in those resonances that are assigned to residues close to the site of the mutation (data not shown).
Wild-type rrdI has a single Trp residue (at position 72), and binding) component; rrdIII.E155W, rrdIII with a Trp residue substituted for Glu 155 ; hsdIII, the dIII component of human transhydrogenase; AcPdAD ϩ , acetyl pyridine adenine dinucleotide (oxidized form); HSQC, heteronuclear single quantum correlation NMR spectroscopy. wild-type rrdIII has no Trp. The change in protein fluorescence that accompanies the burst of AcPdAD ϩ reduction by NADPH with a mixture of wild-type rrdI and rrdIII is also shown in Fig.  1 (trace c). There was a very small decrease in fluorescence with approximately similar kinetics to those of hydride transfer. It probably resulted from the quenching of dI-Trp 72 fluorescence by the weakly binding product, AcPdADH (Ref. 11), but the signal/noise ratio was too small for detailed analysis. The protein fluorescence of a mixture of rrdI and rrdIII.E155W under similar conditions substantially increased during the reduction of AcPdAD ϩ by NADPH (trace d). The signal/noise ratio was more than adequate to show that the kinetics of the fluorescence change were very similar in character to those of the 375-nm absorbance change. Both were distinctly biphasic. Within error, the k app values for phase A (603 Ϯ 71 s Ϫ1 and 571 Ϯ 58 s Ϫ1 in fluorescence and absorbance measurements, respectively), and for phase B (30.5 Ϯ 6.8 s Ϫ1 and 29.3 Ϯ 7.2 s Ϫ1 ) were similar. For reasons that will be discussed below, the amplitude of phase A of the fluorescence change was routinely a slightly greater fraction of the total amplitude of the burst, than was the amplitude of phase A of the absorbance change (e.g. 74 Ϯ 10% compared with 59 Ϯ 7%, for 37.5 M dI and 37.5 M dIII). The very slow, steady-state increase in the absorbance at 375 nm due to the reduction of AcPdAD ϩ during multiple turnovers (seen only on long time scales (Ref. 13)) was not evident in fluorescence measurements (data not shown). We propose that the fluorescence increase during the burst of hydride transfer results mainly from the change in occupancy of the dIII protein; bound NADP ϩ leads to greater Trp 155 fluorescence than bound NADPH (14,15,20).
Consistent with this interpretation, the replacement of phase A with phase B, as the concentration of the dI protein was increased (18), was also observed in fluorescence experiments (Fig. 2). The phenomenon was discussed in detail (18,19). Briefly, it results from an increase in the concentration of dI⅐dIII complex (and therefore in the fraction of phase A) at increasing dI concentrations, and a corresponding decrease in the concentration of free dIII.NADPH that, for oxidation, requires multiple turnover of dI (the fraction of phase B). In both absorbance and fluorescence experiments, the value of k app for phase A was independent of the dI concentration, as expected if it reflects intracomplex hydride transfer. The increase in the k app for phase B with dI concentration, in both sets of experiments, is a consequence of a lower rate of formation of dead end complex (18).
In a separate series of experiments, we monitored the burst of transhydrogenation from AcPdADH to NADP ϩ by following the absorbance decrease at 375 nm. The kinetics were similar in mixtures of rrdI plus rrdIII.E155W (results not shown), and in mixtures of rrdI plus rrdIII (see Ref. 19). With rrdI and rrdIII.E155W (but not with rrdI and rrdIII), a large decrease in protein fluorescence was observed, with similar kinetics to the 375 nm absorbance decrease. In contrast to the experiments with AcPdAD ϩ and NADPH (see above), the amplitude of phase A was a slightly smaller fraction of the total burst in the fluorescence measurements, although, again, there was no significant difference in the apparent rate constants.
Hydride Transfer between Physiological Nucleotides on Complexes of rrdI and rrdIII-The above experiments indicate that it should be possible to monitor transient-state hydride transfer between physiological nucleotides in dI⅐dIII complexes by recording changes in dIII tryptophan fluorescence. Previously, real-time observations were impossible because of the similar absorbance spectra of NAD(H) and NADP(H). Fig. 3 shows that a biphasic fluorescence decrease was observed upon mixing rrdI plus rrdIII.E155W loaded with NADP ϩ (syringe 1), and NADH (syringe 2) in the stopped-flow spectrophotometer, and a biphasic fluorescence increase was observed upon mixing rrdI plus rrdIII.E155W loaded with NADPH (syringe 1), and NAD ϩ (syringe 2). We attribute this, in the "forward" experiment, to reduction of NADP ϩ on dIII (decrease in Trp 155 fluorescence), and in the "reverse" experiment, to oxidation of NADPH on dIII (increase in Trp 155 fluorescence). The release of product NADP(H) is expected to be very slow (13).
The fluorescence burst during transhydrogenation from NADPH to NAD ϩ was monitored in a set of experiments performed at a fixed concentration of rrdIII.E155W and variable rrdI (Fig. 4). The results were very similar to those obtained for hydride transfer between NADP(H) and AcPdAD(H), as observed in both absorbance measurements (18), and fluorescence measurements (Fig. 2). Notably, the fast phase (phase A) replaced the slow phase (phase B) as the dI concentration was increased, the k app for phase A was independent of dI concentration, and the k app for phase B increased with the dI concentration (see above). This clearly establishes the internal consistency of the proposed mechanisms.
Attempts to determine the k app values of phase A for forward and reverse transhydrogenation at saturating concentrations of NADH and NAD ϩ , respectively, are shown in Fig. 5; both sets of experiments were performed with protein concentrations that ensured dominance by phase A. Phase A of the forward reaction with physiological nucleotides was very fast. The maximum value of k app that can be measured by the spectrophotometer is approximately 800 -900 s Ϫ1 , and this was exceeded at concentrations of NADH in excess of 50 -100 M. Phase A of the fluorescence change during the reverse reaction was slower and, therefore, easier to resolve. At close-to-saturating concentrations of NAD ϩ , at 20.8°C, the value of k app was approximately 600 s Ϫ1 . For reasons that will be explained below, the dependence of the phase A k app for reverse transhydrogenation on the concentration of NAD ϩ was also determined at a lower temperature; at 7.8°C the k app value at saturating nucleotide was approximately 60% less than that at 20.8°C (Fig. 5).
The Binding of NAD(H) to rrdI-To provide a more complete description of the hydride transfer step in dI⅐dIII complexes with physiological nucleotides, we have determined the on and off rate constants for NAD(H) and isolated rrdI from changes in Trp 72 fluorescence (11). The kinetic profile of fluorescence quenching with NADH was too fast to measure accurately in the stopped-flow machine above 15°C, but at lower temperatures the reaction fitted to a single exponential (not shown). Assuming that binding is a simple, one-step reaction, and provided that the concentration of NADH is much greater (Ͼ10fold) than that of dI, it can be easily shown (e.g. Ref. 31) that k obs ϭ k on [NADH] ϩ k off . Thus, values of k on and k off are obtained from the gradient and intercept, respectively, of a plot of [NADH] versus k obs . The validity of the approach was supported by the linear dependence of k obs on NADH concentration (Fig. 6, upper panel). Between 8 and 15°C, k off exhibited a classical temperature dependence; Arrhenius plots (data not shown) yielded an activation energy of 135 kJ⅐mol Ϫ1 . Extrapolation to higher temperatures gave values that were within the range suggested by NMR experiments (32,33). Values of k on for NADH binding were less steeply dependent on temperature; the activation energy was 22 kJ⅐mol Ϫ1 . A low activation energy for k on and a large value for k off are not uncommon for ligandprotein interactions. Extrapolation to 20°C gave k on Ϸ 2 ϫ 10 7 M Ϫ1 s Ϫ1 , k off Ϸ 810 s Ϫ1 and K d (Ϸ40 M) in good agreement with the K d value obtained by equilibrium dialysis (30 Ϯ 2 M) (34).
The k off for NAD ϩ and rrdI was obtained from competition experiments. The protein was incubated with NAD ϩ , at a concentration high enough to ensure substantial occupation of the binding sites. Upon subsequent addition of NADH in the stopped-flow spectrophotometer, the emission from Trp 72 was quenched with approximately first-order kinetics as the reduced nucleotide replaced the bound NAD ϩ . At high concentrations of NADH, the rate of fluorescence quenching becomes limited by k off for NAD ϩ . Because of the rapid rate of NAD ϩ release, reliable data were only obtained at temperatures below 15°C. Fig. 6 (lower panel) shows the results of experiments with 1 mM NAD ϩ ; equivalent experiments (data not shown) were performed with 5 mM NAD ϩ and yielded similar values of k off . The internal consistency of the measured rate constants was checked by performing a simulation of each experimental trace using the measured values of k on and k off for NADH (see above) and K d Ϸ 300 M for NAD ϩ . Arrhenius plots of the measured values of k off for NAD ϩ were linear, and gave an activation energy of 54 kJ⅐mol Ϫ1 . Extrapolation to 20°C yielded k off Ϸ 1700 s Ϫ1 . Using the K d (Ϸ 300 M) obtained by equilibrium dialysis (34), k on Ϸ 6 ϫ 10 6 M Ϫ1 s Ϫ1 .
For reasons that will become clear under "Discussion," the possibility was considered that the nucleotide-binding parameters of dI might be altered when it is in complex with dIII. An important consideration, in the measurement of these parameters, is that isolated dI protein is dimeric; the species, (dI) 2 ⅐dIII, forms with high affinity (K d Ͻ 10 Ϫ6 M) and (dI) 2 ⅐(dIII) 2 forms only with low affinity (K d Ͼ Ͼ 10 Ϫ6 M) (13,18,25). Thus, because protein concentrations in the micromolar range are required for ligand binding experiments, the dI population is heterogeneous; we operate within the equilibrium, (dI) 2 ϩ dIII 7 (dI) 2 ⅐dIII. Another consideration is that it has not yet been possible to obtain stable preparations of apo-dIII; we must use either dIII.NADP ϩ or dIII.NADPH, and then design experiments to avoid hydride transfer. Direct measurement of the K d for NADH in mixtures of rrdI and rrdII-I.NADPH, using equilibrium dialysis, is difficult because of the elevated background fluorescence from the nucleotide on the dIII protein. However, experiments indicated that the binding constant is similar, within a factor of 3, in isolated dI (34), and in dI⅐dIII complexes. 3 Because the value is quite high, measurement of K d from the quenching of Trp 72 fluorescence suffers from significant error due to the inner-filtering effect of the added nucleotide (11,30). Nevertheless, results from this kind of experiment strongly supported the conclusion that the K d of dI for NADH is unaffected by complexation with dIII (data not shown).
Despite these findings, the kinetic experiments shown in Fig.  7 indicate that k on and k off for NADH might be substantially greater with dI⅐dIII complexes than with isolated dI. These were carried out at a temperature, and with an NADH concentration, that yielded clear, slow, monophasic kinetics of Trp 72 quenching when nucleotide was mixed with isolated rrdI in the stopped-flow machine (see Fig. 6, upper panel). However, when repeated with dI plus increasing concentrations of wild-type rrdIII.NADPH, the observable amplitude of the fluorescence quenching decreased, although the k app remained approximately constant. Control experiments (with NADPH in the absence of dIII) established that the amplitude loss was not the result of the higher background fluorescence (data not shown). Since the steady-state fluorescence spectra of dI and dIII were simply additive (data not shown), it is concluded that a component of Trp 72 fluorescence quenching takes place very rapidly, i.e. in the apparatus dead time, and is not directly observed. This would indicate that k on and k off for NADH are greater, by at least an order of magnitude, in dI⅐dIII than in dI. They must increase approximately in parallel, since the K d is not significantly altered (see above).
Hydride Transfer between Physiological Nucleotides on Hybrid Complexes of rrdI and hsdIII-Mixtures of rrdI and hsdIII also catalyze a single-turnover burst of hydride transfer between AcPdAD(H) and NADP(H) (16). Because of the relatively weak interactions between the two protein components of the hybrid system, the burst is monophasic. Wild-type hsdIII has a single, natural Trp residue at position 154; it is in an equivalent position to the engineered Trp 155 in rrdIII (20). Fig. 8  (upper panel) shows that there was a fluorescence increase upon mixing rrdI, and hsdIII loaded with NADPH, with AcP-3 T. Bizouarn, personal communication. dAD ϩ (trace b), which had similar monophasic kinetics to the burst of AcPdADH formation measured as the absorbance increase at 375 nm (trace a). It was previously established that, at a fixed hsdIII concentration, the k app for the burst of AcP-dAD ϩ reduction increases with the concentration of rrdI (16), reflecting the elevated concentration of dI⅐dIII complex in the mixture. In a series of experiments (data not shown), the k app values for AcPdAD ϩ reduction and for the protein fluorescence change increased together when the concentration of dI was increased from 6.25 to 37.5 M (dIII ϭ 25 M). As in the homologous R. rubrum system (see above), it is proposed that the fluorescence change mainly results from the quenching of Trp 154 emission during oxidation of NADPH on dIII.
Experiments were then performed on hybrid dI⅐dIII complexes and physiological nucleotides (Fig. 8, lower panel). There was a monophasic decrease of protein fluorescence following the rapid mixing of rrdI, plus hsdIII loaded with NADP ϩ , and NADH (trace a), and a monophasic fluorescence increase upon mixing rrdI, plus hsdIII loaded with NADPH, and NAD ϩ (trace b). Again, it is proposed that the fluorescence change is a reflection of hydride transfer between the physiological substrates. Because the binding between rrdI and hsdIII is quite weak, it is difficult, under stopped-flow conditions, to saturate the latter with the former, and to measure meaningful rate constants for the reaction. However, it is evident from Fig. 8 that hydride transfer between physiological nucleotides, even in the hybrid complexes, is very fast.

DISCUSSION
The experiments described above, with the single species complex, rrdI⅐rrdIII.E155W, and the hybrid, rrdI⅐hsdIII, show that a transient-state burst of hydride transfer between physiological nucleotides (both forward and reverse reactions) can be monitored by observing changes in protein fluorescence. Human dIII has its own, single Trp residue, but because of the relatively low affinity between the protein components in the hybrid (16), the single-species complex is the system of choice for studies on the chemistry of the oxidation-reduction step. The mutation, E155W, in rrdIII had no significant effect on the hydride transfer rate (Fig. 1) and, as indicated by HSQC NMR spectra (data not shown; see Ref. 25), only minor effects on the protein structure, and on the conformational change that results from replacement of NADP ϩ with NADPH.
The changes in protein fluorescence that accompany hydride transfer in the dI⅐dIII complexes mainly arise from the single Trp residues in hsdIII and rrdIII.E155W. It is well documented that the Trp fluorescence of dIII is greater when NADP ϩ , rather than NADPH, occupies the nucleotide-binding site (14,15,20). There is also a small contribution (ϳ10%) to the fluorescence emission from Trp 72 of rrdI during the transhydrogenation burst; it probably results from changes in nucleotide occupation of dI (Fig. 1). This, and perhaps weak, secondary effects of NAD(H) bound to dI on Trp fluorescence in dIII, probably account for the small differences between the relative amplitudes of phase A in absorbance and fluorescence experi- In trace a, the dIII protein was pre-loaded with NADP ϩ and the second syringe contained 50 M NADH; in trace b, the dIII protein was preloaded with NADPH and the second syringe contained 1.2 mM NAD ϩ . Both traces represent the fluorescence changes after mixing equal volumes from the syringes, and they are both an average of seven repeats. A fluorescence increase is a downward deflection, and an absorbance increase is an upward deflection. Temperature was 20.7°C. ments (see Fig. 1). However, there was no significant difference between the k app values for phase A in measurements with AcPdAD(H), and we assume this to be the case also with physiological nucleotides.
There is good evidence (18,19), which is supported by experiments presented in this report (Figs. 2 and 4), that phase A of the reaction corresponds to the following kinetic components (Reaction 2).
Crucially, the rates of dissociation of the dI⅐dIII complex (k Ϸ 50 s Ϫ1 ), and of NADP ϩ (k Ϸ 0.03 s Ϫ1 ) and NADPH (k Ϸ 5 ϫ 10 Ϫ4 s Ϫ1 ) from dIII, are slow relative to the rates of hydride transfer; the products NADPH or NADP ϩ remain bound to the complex during the course of phase A. Therefore, when experiments are carried out at either high NADH concentrations (for forward transhydrogenation) or high NAD ϩ concentrations (for reverse), then the respective k app values are dominated by the hydride transfer step, and by either NAD ϩ release or NADH release. The k app value for the forward reaction at saturating NADH (k f(app) ) was too fast to measure, but the extrapolated value was Ն2000 s Ϫ1 (Fig. 5). The k app value for the reverse reaction at saturating NAD ϩ (k r(app) ) was ϳ600 s Ϫ1 . It was difficult to determine the values of on and off rate constants for NAD ϩ /NADH and the dI⅐dIII complex (see "Results"). However, even if we take values derived from experiments with isolated dI (Fig. 6), and these are almost certainly lower than those appropriate for the dI⅐dIII complex (see below), then the rate constants for the hydride transfer step are, k f Ն 2000 s Ϫ1 and k r Յ 500 s Ϫ1 ; precise values depend on the relative equilibrium positions of the hydride transfer and of product NAD(H) release steps. The minimal conclusion is that the equilibrium constant of the hydride transfer step with physiological nucleotides on the enzyme (K eq ϭ k f /k r ) is greater than unity. A similar conclusion was reached on the basis of measurements of the equilibrium K d values for NAD ϩ /NADH on dI and of the redox potential of bound NADP ϩ /NADPH on dIII (20,34), and on the basis of stopped-flow experiments with substrate analogues (19). It is probably an important feature of the complete enzyme. Because there is no isotopic exchange between the hydride equivalents transferred and the solvent (35), and because there seem to be no reaction intermediates on the hydride transfer pathway (17)(18)(19), it is unlikely that this step is directly linked to proton translocation. We have presented evidence that proton translocation by transhydrogenase is coupled to changes in the binding of NADP ϩ and NADPH, whereas NAD ϩ /NADH behave as passive hydride acceptor/donor (reviewed in Ref. 1). A specific suggestion (1,5,10,13) is that, during the forward reaction, H ϩ -binding from the p-phase prior to the hydride transfer step drives the enzyme into an occluded state from which bound NADP ϩ cannot be released. Following hydride transfer from NADH within the occluded state, H ϩrelease to the n-phase regenerates an open state from which NADPH can dissociate. The elevated equilibrium constant of the hydride transfer step ensures an intrinsic forward bias between the two power strokes in the reaction, and will have the effect of smoothing the ⌬G profile of the reaction path (36).
The experimental data used to calculate values of k on and k off for NAD ϩ /NADH and isolated dI were reproducible, and the procedures should be reliable. The values obtained are in the range found commonly for soluble dehydrogenases (31), and are consistent with K d values determined by equilibrium procedures (11,33,34). We assumed that these values would be similar to the on and off rate constants for NAD ϩ /NADH and the dI⅐dIII complex. However, they are too small to be compatible with a minimal kinetic scheme (such as that shown in Reaction 2), in which a rapid-equilibrium hydride-transfer step is followed by NAD ϩ release (in forward transhydrogenation) or NADH release (in reverse transhydrogenation). The same conclusion is reached from experiments performed at 20°C (using extrapolated values of k on and k off ) and at 7°C (using measured values). It emerges that k on and k off for NAD ϩ /NADH and the dI⅐dIII complex must be at least 5 times greater than values measured for the isolated dI protein to provide a reasonable fit to the measured k f(app) and k r(app) . Although it proved difficult to measure the binding constants for NAD ϩ / NADH to dI⅐dIII (see "Results"), there was good evidence (Fig.  7) that k on and k off , at least for NADH, are indeed more than an order of magnitude larger in the complex. We envisage that in the dI⅐dIII complex (and in the complete enzyme), where the ridge of dIII inserts into the putative cleft of dI, there is a channel between the two protein components for the passage of nucleotide. In isolated dI, the cleft closes up slightly to restrict the nucleotide access to its binding site. This idea receives some support from the finding that the second order rate constants for nucleotide binding to isolated dI are considerably lower than that set by diffusional limitation (see Ref. 37). A difference in the NAD ϩ /NADH binding properties of dI in its isolated form and in the complete, membrane-bound protein was also inferred from a steady-state kinetic analysis (7). We previously showed that dissociation of the dI⅐dIII complex is unnecessary for NAD ϩ /NADH exchange between the dI binding site and the solvent (18). If we assume that the release of the product nucleotide (NAD ϩ or NADH) from the dI⅐dIII complex is fast enough to reach equilibrium during phase A, and if we take the K eq for the hydride transfer step from earlier experiments (19,20), then for the measured k f(app) and k r(app) (see above), k f and k r for the physiological substrates converge on values of 2900 and 110 s Ϫ1 , respectively. A similar exercise using experimental data for transhydrogenation between AcPdAD(H) and NADP(H) (18), yields 40 s Ϫ1 for k f and 500 s Ϫ1 for k r . It is clear that the rate constant for the reaction NADH 3 NADP ϩ is greater than that for AcPdADH 3 NADP ϩ , but that for NADPH 3 NAD ϩ is less than that for NADPH 3 AcPdAD ϩ . The E 0/ for AcPdAD ϩ / AcPdADH in aqueous solution (Ϫ0.248 V) is larger than that for NAD ϩ /NADH (Ϫ0.32 V) (38). It is suggested, therefore, that the differences in rates between the two sets of reactions are primarily the result of a different driving force; differences in transition state geometry, such as the distance of transfer of the hydride equivalent (whether H Ϫ , [2e Ϫ ϩ H ϩ ] or [e Ϫ ϩ H ⅐ ]) are probably less important.