Pre-steady state of reaction of nucleoside diphosphate kinase with anti-HIV nucleotides.

The pre-steady-state reaction of Dictyostelium nucleoside diphosphate (NDP) kinase with dideoxynucleotide triphosphates (ddNTP) and AZT triphosphate was studied by quenching of protein fluorescence after manual mixing or by stopped flow. The fluorescence signal, which is correlated with the phosphorylation state of the catalytic histidine in the enzyme active site, decreases upon ddNTP addition according to a monoexponential time course. The pseudo-first order rate constant was determined for different concentrations of the various ddNTPs and was found to be saturable. The data are compatible with a two-step reaction scheme, where fast association of the enzyme with the dideoxynucleotide is followed by a rate-limiting phosphorylation step. The rate constants and dissociation equilibrium constants determined for each dideoxynucleotide were correlated with the steady-state kinetic parameters measured in the enzymatic assay in the presence of the two substrates. It is shown that ddNTPs and AZT triphosphate are poor substrates for NDP kinase with a rate of phosphate transfer of 0.02 to 3.5 s-1 and a KS of 1-5 mM. The equilibrium dissociation constants for ADP, GDP, ddADP, and ddGDP were also determined by fluorescence titration of a mutant F64W NDP kinase, where the introduction of a tryptophan at the nucleotide binding site provides a direct spectroscopic probe. The lack of the 3'-OH in ddNTP causes a 10-fold increase in KD. Contrary to "natural" NTPs, NDP kinase discriminates between various ddNTPs, with ddGTP the more efficient and ddCTP the least efficient substrate within a range of 100 in kcat values.

Nucleoside analogues like 3Ј-deoxy-3Ј-azidothymidine (AZT) 1 and dideoxynucleosides (ddN) are widely used as antiviral drugs, particularly in the multitherapy protocols now used in the treatment of AIDS. These drugs are targeted at the HIV reverse transcriptase as the lack of the 3Ј-OH required for the 3Ј-5Ј phosphodiester bond formation during DNA elongation blocks viral DNA synthesis. To exert their antiviral activ-ity, the nucleoside analogues must be phosphorylated into triphosphates derivatives by cellular kinases. Although AZT, ddT, and ddC are structurally related, they show different patterns of intracellular phosphorylation (1). The synthesis of mono-and diphospho-derivatives involves kinases specific for either purines (for example deoxyguanosine kinase) or pyrimidines (for example deoxycytidine kinase or thymidine kinase). In all cases, the last step in the pathway leading to the triphospho-derivative is catalyzed by nucleoside diphosphate (NDP) kinase (EC 2.7.4.6), which has little specificity toward the nucleobase (2).
NDP kinase phosphorylates all nucleoside diphosphates into triphosphates using ATP as the major phosphate donor. The reaction involves the formation of a phosphorylated intermediate according to a ping-pong bi-bi mechanism following the scheme below, where E-P is the phosphorylated intermediate on the catalytic histidine (3).
EϳP ϩ N 2 DP 7 N 2 TP ϩ E (reaction B) SCHEME I In recent years, genes encoding NDP kinase have been cloned from a number of prokaryotic and eukaryotic organisms (4,5). NDP kinases are made up from 17-kDa subunits with highly conserved sequences. The x-ray structures of NDP kinases from several species have also been determined at high resolution (5)(6)(7)(8), and these studies have shown that both the subunit fold and the active site are remarkably conserved.
Solving the NDP kinase structure in the presence of dTDP (9), ADP (10), and GDP (11) was an important step toward an understanding of the phosphate transfer mechanism. The nucleotide binding site is very different from other known nucleotide-binding proteins, with the base stacking on a phenylalanine near the protein surface without polar interactions with the protein side chains. The ribose and phosphate moieties are located deeper inside the active site, forming numerous bonds with a Mg 2ϩ ion and protein side chains. The nucleotide conformation is original, with a hydrogen bond between the 3Ј-OH of the sugar and the ␤-phosphate. In addition, the 3Ј-OH accepts H-bonds from Lys 16 and Asn 119 (in this report, we use the numbering of Dictyostelium NDP kinase). The catalytic His 122 points its N␦ toward the phosphate, a well defined water molecule bridging it to the ␤-phosphate oxygen in the ADP complex, at the presumed position of ATP ␥-phosphate.
A precise model for the reaction product and the transition state has been proposed, based on the crystal structures of the enzyme phosphorylated by phosphoramidate (12) and of the ternary complex with ADP and AlF 3 (13). This model is also supported by the results of a large series of substitutions of con-served residues of the active site (14). NDP kinase has a very high turnover with k cat around 1000 s Ϫ1 for "natural" ribo-or deoxyribonucleotides. Comparing the structures of free enzyme and enzyme complexed with nucleotide diphosphates demonstrates that the change of conformation upon nucleotide binding is minimal. The movement is limited to the ␣ A /␣ 2 helices hairpin, which forms one side of the nucleotide binding site (8 -10). Dictyostelium NDP kinase has a single tryptophan (Trp 137 ), located at the proximity of the active site. We have shown previously that its fluorescence could be used as a probe for the phosphorylation state of the catalytic histidine (15).
We have recently reported that the diphospho-derivatives of some nucleotide analogues used as antiviral drugs are poor substrates for NDP kinase, as measured by the global enzymatic assay (16). Thus, when the diphospho-and triphosphoderivatives of azidothymidine, dideoxyadenosine, or dideoxythymidine are used as substrates, the rate of phosphate transfer is 10 2 to 10 4 times less than for natural nucleotides.
In this study, we present pre-steady-state kinetic experiments to investigate the phosphorylation of the enzyme by antiviral ddNTPs. Both stopped-flow and conventional techniques were used to measure fluorescence changes on a time scale ranging from milliseconds to several minutes. Using a mutant NDP kinase (F64W) in which an additional tryptophan was placed near the nucleotide binding site, we also measured the affinity constants of nucleotides and their analogues.

EXPERIMENTAL PROCEDURES
Materials-ATP, ADP, CDP, GDP, dTDP, lactate dehydrogenase, and pyruvate kinase were from Boehringer Mannheim, and dideoxynucleotide triphosphates from Amersham Pharmacia Biotech or from Boehringer Mannheim. [ 14 C]ADP (57 mCi/mmol) was from NEN Life Science Products. The synthesis of phosphoderivatives of AZT and of ddNDP has been described previously (16).
Site-directed Mutagenesis-The mutation F64W in Dictyostelium NDP kinase was made by site-directed mutagenesis according to Kunkel (17), using the oligonucleotide 5Ј-GAAAGACCATGGTTCGGT-GGTT-3Ј. Altered bases as compared with the wild type sequence are bold and underlined. The mutation was verified by DNA sequencing.
Enzyme Purification-Wild type and mutant Dictyostelium NDP kinase were overexpressed in Escherichia coli (XL1-Blue) using plasmid pndk as described (4) with small modifications. The cell extract was loaded at pH 8.4 onto DEAE-Sephacel which retained only E. coli NDP kinase (14) and the flow-through was adsorbed on Blue-Sepharose (Amersham Pharmacia Biotech) at pH 7.5. After washing with Tris buffer, the enzyme was eluted by a NaCl gradient (0 -1.5 M) in 50 mM Tris-HCl, pH 7.5. After dialysis, the protein was concentrated with an Amicon ultrafiltration cell, equilibrated in 50 mM Tris-HCl, pH 7.5, and stored frozen at Ϫ20°C. Protein concentration was determined using an absorbance coefficient of ⌬A 280 ϭ 0.55 for a 1 mg/ml solution. Mutant F64W NDP kinase was purified according to the same procedure. The absorption coefficient of F64W mutated NDP kinase was estimated to ⌬A 280 ϭ 0.85 for a 1 mg/ml solution according to Gill equation for a folded protein in water (18). All proteins were purified to homogeneity as judged by SDS-polyacrylamide gel electrophoresis. Enzyme concentration was expressed as concentration of 17-kDa subunits.
The phosphorylated enzyme was prepared as described previously (15); the enzyme that had been preincubated in T buffer (50 mM Tris-HCl, pH 7.5, containing 5 mM MgCl 2 and 75 mM KCl) with a saturating amount of ATP was made free of nucleotides by gel filtration on Sephadex G-25. The concentration of the phosphorylated enzyme as well as the absence of nucleotides were checked from the absorbance spectrum of the protein. The stoichiometry of phosphorylation was determined in a parallel experiment using [␥-32 P]ATP, as described in Ref. 15. The phosphorylated enzyme was then kept at 4°C and used within 3 h after synthesis.
Activity Assays-Two different assays were used to measure NDP kinase activity. In the first assay, activity of NDP kinase was measured at 20°C with ATP and dTDP as substrates using coupled enzymes (lactate dehydrogenase and pyruvate kinase) as described previously (19). The second assay was used when small reaction volumes (a few microliters) were needed, in particular with radioactive substrates (16). When ddNTPs were tested as phosphate donors, [ 14 C]ADP was used as an acceptor. The initial rate of the reaction was determined at 20°C in the presence of a constant amount of [ 14 C]ADP (0.1 mM) during 2, 4, and 6 min. After separation of the radioactive nucleotides by thin layer chromatography on PEI-cellulose (Macherey-Nagel, Germany), their radioactivity was quantified using a PhosphorImager (Molecular Dynamics).
The ratio of apparent k cat /apparent K m , measured at a constant concentration of the other substrate is equal to the true value of k cat /K m for a ping-pong enzyme. It is a useful parameter when comparing natural substrates to nucleotides analogs. The nonlinear least-squares fit of the data was performed using Kaleidagraph (Abelbeck Software). Unless otherwise indicated, this software was also used for all of the fittings described below.
Binding Studies-The affinity of NDP for NDP kinase was measured by following the variation of intrinsic fluorescence of the mutant F64W enzyme upon nucleotide binding. All fluorescence measurements were performed at 20°C in T buffer on a Photon Technology International (PTI) spectrofluorometer (Quantamaster™). Successive aliquots of the nucleotide were added to the enzyme solution (2 M), and the fluorescence was measured at 340 nm with excitation at 295 nm for ADP and ddADP (2-nm excitation slit and 2-nm emission slit), or at 304 nm in the case of the other nucleotides (emission slit was then 4 nm). Experimental binding curves were fitted to a hyperbolic ligand-protein curve after correction for dilution. The inner filter effect was found to be negligible.
Slow Kinetics Experiments-Slow kinetics experiments were performed at 20°C on a PTI spectrofluorometer (Quantamaster™), sampled with continuous stirring. The reaction of wild type NDP kinase with NTP analogues was initiated by addition of the nucleotide (less than 25 l) to 1 ml of a 0.85 M enzyme solution in buffer T in a Hellma cell with four optical windows. In a similar manner, the reaction of phosphorylated enzyme (1 M) with NDP analogues was monitored in a 1-ml optical cell after addition of the substrate in a volume less than 25 l. The time required for manual mixing was less than 15 s. The tryptophan fluorescence of NDP kinase was monitored for up to 10 min at 340 nm, with excitation at 295 nm or 304 nm as above. The fitted curves were found to correspond to a single exponential progress, either decreasing for phosphate transfer to the enzyme or increasing in the case of phosphate transfer to the NDP analogues. The pseudo first-order rate constants (k obs ) were determined as a function of substrate concentration (S), with [S] in excess to [E], the enzyme concentration.
Stopped-flow Kinetic Experiments-Stopped-flow kinetic experi- Fitting is shown as solid line for AZT-XP only. The value for K eq is 0.13 Ϯ 0.02 in both cases. The saturation curve appears here as a sigmoid due to the logarithmic representation of the x axis. ments were performed at 20°C in buffer T with an Applied Photophysics SX.18MV microvolume stopped-flow reaction analyzer equipped with a high intensity xenon lamp. The excitation wavelength was 296 nm (for ATP and ddATP measurements) or 305 nm (for all the other nucleotides), with a 2-mm excitation slit and a 320-nm cutoff filter at the emission. Mixing was achieved in less than 2 ms. After mixing NDP kinase (0.85 M, final concentration) and ddNTP or ddNDP (25-3000 M, final concentration), the intrinsic protein fluorescence was recorded for 10 to 50 s. In each experiment 400 pairs of data were recorded, and the data from three or four experiments under identical conditions were averaged and then fitted to a number of nonlinear analytical equations using the Pro/kineticist software provided by Applied Photophysics. The fitted curves correspond to a single exponential.

RESULTS
Changes in Fluorescence Associated with Phosphorylation of NDP Kinase by Antiviral Nucleotide Analogues-We have shown previously that the fluorescence of the single tryptophan in Dictyostelium NDP kinase is quenched upon phosphorylation of the enzyme by ATP (15). To test whether the interaction with ddNTP also results in a change of fluorescence, steadystate emission spectra ( exc ϭ 295 nm) were collected in presence of ddATP or ddADP at saturating concentrations, and compared with the spectrum of the native enzyme. A strong decrease (20%) in fluorescence intensity near 320 -340 nm was observed in the presence of ddATP. In contrast, the fluorescence was insensitive (less than 3% decrease) to ddADP bind-ing, as reported previously for ADP. Quenching (at least 10%) was also observed with other natural NTPs or ddNTPs ( exc ϭ 304 nm) and was likely due to the phosphorylation of the catalytic histidine. Conversely, the fluorescence signal of the phosphorylated enzyme was enhanced upon ddADP addition as the phosphate was transferred from the protein back to the nucleotide. This provided a convenient method to monitor histidine phosphorylation at different ddNTP/ddNDP ratios and to derive the equilibrium constants. As shown in Fig. 1, the equilibrium constant was the same for the ddTTP/ddTDP pair (K eq ϭ 0.13 Ϯ 0.02) and for the AZTTP/AZTDP pair. It did not differ significantly from natural nucleotides. A value of K eq ϭ 0.19 Ϯ 0.02 was obtained previously for the ATP/ADP pair by fluorescence titration (15). Applying the Haldane relationship to steady-state kinetic parameters yielded the same value. We conclude that the absence of 3Ј-OH or its replacement with an azido group in the analogue has no significant effect on the phosphorylation equilibrium between the enzyme and the nucleotides.
Steady-state Kinetic Parameters of NDP Kinase with ddNTP-Steady-state kinetic parameters were first measured in the phosphate exchange reaction between ddNTP and [ 14 C]ADP (reactions A and B, shown in Scheme I). Fig. 2 shows initial rate data for the native enzyme for ddGTP at various concentrations and the inset shows the comparison of the four ddNTPs at a given concentration. A constant concentration of ADP (0.1 mM), corresponding to twice the K m ADP (20), was used. The data were adjusted with the Michaelis equation. Table I summarizes the kinetic constants (apparent K m and apparent V max ) determined for ddATP, ddGTP, ddTTP, and ddCTP used as phosphate donors.
The lack of the 3Ј-OH in ddNTP dramatically affected the catalytic activity. An increase by a factor of 10 in apparent K m and a decrease of 500 -10,000 in apparent k cat were observed when comparing kinetic parameters of ddNTPs with those of ATP (20). Under the conditions used, the kinetic parameters of natural nucleotides were very similar (results not shown). In contrast, the kinetic constants of dideoxynucleotides varied strongly with the ddNTP used. In particular, ddCTP showed a very low value of k cat /K m , with a drop of more than 10 4 as compared with CTP.
Pre-steady-state Kinetics of NDP Kinase Phosphorylation by ddNTPs-The fluorescence signal allowed us to monitor the time course of the phosphate transfer reactions between NDP kinase and nucleotides. However, the time-dependent change of the fluorescence was too fast to be observed when 1 M enzyme was reacted with 100 M ATP. This is due to the fact that the time response of the stopped flow is slow compared with the k cat of the enzyme (ϳ600 s Ϫ1 at 20°C). In contrast, when the enzyme was reacted with ddATP under the same conditions, a time-dependent quenching of the enzyme fluores-   (1) cence was observed in the second-to-minute time scale (Fig.  3A), with no observable lag. For all concentrations of ddATP tested, a single exponential decay was observed, characterized by a pseudo-first order rate constant k obs . The signal amplitude was constant, corresponding to a complete phosphorylation of the enzyme. The pseudo-first order rate constant of the phosphorylation reaction is shown in Fig. 4A as a function of [ddATP] in the 0.1-3 mM range. The observed rate constant (k obs ) increased linearly for [ddATP] Ͻ 0.2 mM before reaching a plateau. These data were best adjusted to the equation of a saturation curve with a maximum rate constant of 1 s Ϫ1 at saturating ddATP and an apparent equilibrium dissociation constant K S of 0.75 mM ( Fig. 4A and Table I). Similar monoexponential decays were found when reacting the enzyme with ddGTP, ddTTP, and ddCTP. The pseudo-first order rate constants varied with [ddNTP]. The corresponding parameters (Table I) showed noticeable differences between nucleotides; thus, ddGTP appears to be the best substrate, ddATP and ddTTP being slightly less efficient. ddCTP is a very poor substrate for NDP kinase, which was nearly inactive with ddCTP in the 0.1-3 mM range. Therefore, the kinetic parameters for ddCTP could not be determined precisely. Fig. 4B shows a similar dependence of the pseudo-first order rate constant when the reaction was initiated by hand mixing. In this case, only the linear part of the previous saturation curves were measured. The slope had the dimension of a bimolecular association rate constant and was suf-ficient to characterize the interaction of NDP kinase with low concentrations of NTP analogues. The values for these slopes are given as k ϩ2 /K S (Table I). In all cases (stopped-flow or hand mixing experiments), the very low intercepts with the vertical axis (ϳ0.1 s Ϫ1 or less) indicate that the phosphorylated intermediate generated during the reaction was stable in the absence of a NDP acceptor substrate.
Pre-steady-state Kinetics of NDP Kinase Dephosphorylation with ddNDP-The dephosphorylation of the phosphorylated enzyme (EϳP) by ddTDP and by AZTDP (reaction B, Scheme I) also displayed a monoexponential time course in the minute range (Fig. 5). The apparent time constant (apparent k dephos ) . The pseudo-first order rate constant for the reaction is hyperbolically dependent on ddNTP concentration. The solid lines are best fits of the data to an hyperbolic saturation curve according to Reaction 1. The values of apparent equilibrium dissociation constants (K S ) and maximum pseudo first-order rateconstant are given on Table I. B, hand mixing experiments with ddGTP (E), ddTTP (q), ddATP (‚), ddCTP (‚), as well as AZTTP (). The linear fit indicates that data can be analyzed as a second order reaction, with an apparent constant given as k obs ϭ k ϩ2 /K S in Table I. for ddTDP was about 5 times that of the apparent k obs for phosphorylation by ddTTP (reaction A, Scheme I) at the same nucleotide concentration.
Affinity of NDP Kinase Kinase for Nucleotide Diphosphates-In order to follow the binding of the nucleotide, we designed a specific mutant protein with a tryptophan inserted in position 64, replacing Phe 64 , which stacks with the nucleobase in the crystal structure (9,10). Purified F64W mutant NDP kinase showed essentially identical kinetic parameters to the wild type enzyme (Table II) and was stable up to 4.5 M urea. The intrinsic fluorescence of F64W NDP kinase (at an excitation wavelength of 295 nm, at 20°C, pH ϭ 7.5) is primarily due to its two tryptophans in position 64 and 137. The fluorescence of the F64W mutant enzyme decreased by 10% upon addition of a saturating amount of ADP (Fig. 6, inset) whereas wild type enzyme fluorescence was not affected (15).
We took advantage of this variation in intrinsic fluorescence to determine the affinity of nucleotide diphosphates for NDP kinase under equilibrium conditions. Fig. 6 shows a typical binding curve, where the fluorescence decreases as a function of [ADP]. The values of the dissociation constant K D at equilibrium for various nucleotides calculated from such binding curves are shown in Table III.
Dideoxynucleotide diphosphates displayed lower affinity for NDP kinase than the natural substrates (Fig. 6). The K D values were, respectively, 25 M and 220 M for ADP and ddADP and 14 M and 120 M for GDP and ddGDP (Table III). The absence of a 3Ј-OH resulted in the loss of affinity equivalent to 1.3 kcal/mol of binding free energy. However, stopped-flow experiments performed with 1 M of F64W NDP kinase and 100 M ddADP failed to detect a time-dependent variation in fluorescence, indicating that the association reaction was completed within the mixing time and, therefore, that the bimolecular rate constant was at least 2 ϫ 10 6 M Ϫ1 ϫ s Ϫ1 .

DISCUSSION
In this work, we have conducted steady-state and pre-steadystate experiments to study the interaction of NDP kinase with antiviral dideoxynucleotide triphosphates as substrates. The enzyme from the slime mold Dictyostelium discoideum is a 102-kDa hexamer. It is highly homologous to both isoforms of the human enzyme (57% sequence identity), and has a very similar three-dimensional structure, especially at the active site (8 -10) (Fig. 7). Conclusions drawn from this study should therefore be applicable to the human enzymes. The structure of AZT-DP complexed with a point mutant of Dictyostelium NDP kinase was recently resolved (21). It shows that the analogue binds at the same site and in the same orientation as the natural substrate dTDP. As could be expected, the phosphorylation equilibrium between the enzyme and its substrates is unaffected by the absence of the 3Ј-OH in dideoxynucleotides or its substitution in AZT derivatives. However, the analogues are very poor substrates (16), and we have found in the present study that the rate of phosphate transfer was strongly reduced in pre-steady-state experiments when either the histidine phosphorylation or the dephosphorylation step was followed as a function of time and substrate concentration. In Dictyostelium NDP kinase, the fluorescence of Trp 137 is the signal which we use to monitor the phosphate transfer step in the kinetics,  (Table III). Inset, fluorescence emission spectra of F64W NDP kinase in the absence and in the presence of ADP. The emission spectra of F64W NDP kinase (2 M in subunits) in buffer T is modified by the addition of 0.5 mM ADP. Spectra are corrected by the PTI procedure. as it is sensitive to the state of histidine phosphorylation, but not to substrate binding. Our kinetic data are compatible with the following reaction.
When studying the forward reaction, the concentration of the ddNDP product remains very low and the product binding reaction can be neglected. Under these circumstances, the [E-P⅐ddNDP]/[E-P] ratio must be less than k ϩ2 /kЈ Ϫ1 and therefore much smaller than 1, given the very low rate of phosphorylation observed with the analogues. Then, the mechanism of phosphorylation by ddNTP simplifies to Reaction 2.
When studying dephosphorylation by ddNDP in the absence of ddNTP, the same argument leads to writing the reaction mechanism as shown in Reaction 3.
The bimolecular steps are expected to be fast in both directions, and in neither type of experiment are they directly observable in the kinetics. For Reaction 2, and in large excess of the ddNTP ligand, the rate of the single step that is observed should be as shown below (22,23).
The observed rate of phosphorylation should increase with [ddNTP] to reach a plateau value equal to k ϩ2 , the true rate of histidine phosphorylation, with half-saturation occurring for [ddNTP] ϭ k Ϫ1 /k ϩ1 ϭK S , the equilibrium dissociation constant of the nucleotide substrate. At low [ddNTP], k obs is expected to increase linearly with [ddNTP] with an apparent bimolecular rate constant that is k ϩ2 /K S . Equation 1 was used to fit the curves in Fig. 4 (A and B), yielding rate and dissociation constants listed in Table I. Whereas the two purine dideoxynucleotides have similar dissociation constants K S Ϸ 1 mM, the rate of phosphorylation is larger for ddGTP (k ϩ2 ϭ 3.5 s Ϫ1 ) than for ddATP (1 s Ϫ1 ). On the other hand, pyrimidine dideoxynucleotides are relatively poorer substrates for NDP kinase phosphorylation. ddTDP has k ϩ2 Ϸ 2.5 s Ϫ1 and K S Ϸ 5 mM, too large a value for saturation to be reached under our experimental concentrations. With ddCTP, the catalytic efficiency is so poor that neither K S nor the rate of phosphate transfer could safely be determined in stopped-flow experiments at nucleotide concentrations up to 3 mM.
Because the affinity of NDP kinase for its natural nucleotide substrates could not be determined in the same way, we resorted to designing a mutant where a tryptophan replaces Phe 64 at the base binding site (Fig. 7). The substitution provides a spectroscopic signal that monitors ligand binding. The stability and steady-state catalytic properties of the F64W NDP kinase given in Table II are very similar to those of the wild type enzyme. Equilibrium dissociation constants for E⅐NDP dead-end complexes were determined by fluorescence  titration for the natural nucleotides and their analogues. Values listed in Table III show that the absence of the 3Ј-OH in the dideoxy analogues raises the dissociation constant by a factor of about 10 in purine nucleotides. This same ratio is also seen in steady-state parameters, K m values being Ϸ10 times larger for ddNTP than for NTP substrates (16). Differences between natural nucleotides are apparent in Table III, with ADP and GDP having similar affinities that are significantly better than for dTDP and especially CDP. The trends are the same for K S values obtained for the ddNTPs from the analysis of presteady-state kinetics above. Although the dephosphorylation reaction was not studied in the same details, our data suggest that it obeys similar rules. Phosphate transfer from the phospho-enzyme to a dideoxynucleoside diphosphate substrate is slow and rate-limiting compared with substrate binding. Because saturation of the observed rate of dephosphorylation was not achieved at substrate concentrations used for manual mixing experiments (Fig. 5), only the apparent bimolecular rate constant k Ϫ2 /K S can be derived from these data. For ddTTP, k Ϫ2 /K S ϭ 4500 M Ϫ1 s Ϫ1 , which exceeds by a ratio of Ϸ5 the corresponding value of k ϩ2 /K S values found for ddTTP in Table I. According to the Haldane equation, this ratio should be equal to the equilibrium constant K eq for phosphorylation, which we find to be 1/0.13 Ϸ 7 by direct measurement (Fig. 1). The two determinations of K eq are completely independent, and their agreement strongly supports our interpretation of the kinetic data.
An early study by Wä linder et al., in 1969, investigated the phosphorylation of bovine NDP kinase by [␥-32 P]ATP using a rapid mixing technique (24). The pseudo-first order rate constants for phosphorylation by ATP and for dephosphorylation by dGDP exceeded the turnover number of the overall reaction, indicating that the phosphoenzyme could be an intermediate in the NDP kinase reaction. With these substrates, both steps are fast and, in the case of the Dictyostelium enzyme where k cat is on the order of 1000 s Ϫ1 , they are completed in less than a millisecond, too fast for stopped-flow studies. With less efficient substrates such as the antiviral analogues studied here, the turnover rate constant drops to 1-2 s Ϫ1 . Phosphorylation by ddNTP in one direction and dephosphorylation by ddNDP in the other direction are slow and rate-limiting in the overall reaction. Accordingly, the rates of phosphorylation k ϩ2 derived from the analysis of pre-steady-state data are in very good agreement with steady-state k cat values measured with the same nucleotide analogues as substrates (Table I).
Our results indicate that the absence of the 3Ј-OH in the analogues result in a 10-fold increase in the dissociation constant and in a 300 -5000 decrease in the rate of phosphate transfer, resulting in a factor 3 ϫ 10 3 to 5 ϫ 10 4 in catalytic efficiency. The 3Ј-OH of the nucleotide sugar is involved in a hydrogen bond network with Asn 119 , Lys 16 on the protein, and also with the oxygen that bridges the ␤and ␥-phosphates of the nucleotide itself (Fig. 7). Removing the Asn 119 or Lys 16 side chains results in mutant NDP kinases that display a much less dramatic decrease in catalytic efficiency than when the 3Ј-OH is removed; k cat /K m drops by a factor of 10 in the N119A mutant (21) and by a factor of 200 in the K16A mutant. 2 The loss of the internal hydrogen bond between the 3Ј-OH and the bridging phosphate oxygen in ddNTP is likely to be the major reason for the low activity of the enzyme on dideoxy-or AZT derivative substrates. Additional differences are observed between the nucleotide analogues themselves, with ddCTP being the poorest substrate of all, but these differences have no obvious interpretation at present.