Kinetic and thermodynamic characterizations of yeast guanylate kinase.

Yeast guanylate kinase was expressed at high level in Escherichia coli using pET-17b vector. It was purified to homogeneity by a simple two-column procedure with an average yield of ∼100 mg/liter. The steady-state kinetic parameters for both forward and reverse reactions were determined by initial velocity measurements. The turnover numbers (kcat) were 394 s−1 for the forward reaction (formation of ADP and GDP) and 90 s−1 for the reverse reaction (formation of ATP and GMP). Km values were 0.20, 0.091, 0.017, and 0.097 mM for MgATP, GMP, MgADP, and GDP, respectively. Analysis of the initial velocity patterns indicated a sequential mechanism. GMP was found to have partial substrate inhibition. The substrate inhibition was not competitive with MgATP and could be attributed to formation of the abortive complex guanylate kinase·MgADP·GMP. The equilibrium constant of the reaction was measured under various conditions by NMR and a radiometric assay. The results showed that the steady-state kinetic parameters were consistent with the thermodynamic constant. NMR titration and equilibrium dialysis showed that both substrates and products could bind to free guanylate kinase. The dissociation constants were 0.090, 0.18, 0.029, 0.084, and 0.12 mM for MgATP, ATP, GMP, MgADP, and GDP, respectively. Viscosity-dependent kinetics was used to identify the rate-limiting steps of the reaction. The results indicated that the reaction rate is largely controlled by the chemical step.

Guanylate kinase (GK) 1 catalyzes the reversible phosphoryl transfer from ATP to GMP in the presence of Mg 2ϩ (1). The enzyme is essential for converting GMP to GDP and therefore synthesis of GTP. It plays an important role in the cGMP cycle (2) and is also required for metabolic activation of the antiviral drugs acyclovir and gancyclovir (3,4).
GK has been purified to various degrees of purity from several sources (5 and references therein), but detailed characterization has been hampered by its low abundance. Mammalian GK has been characterized by steady-state kinetics (1, 2), but no further mechanistic studies have been reported. It was not until 1989 that yeast GK was purified to homogeneity, and its amino acid sequence was determined by peptide sequencing (6). The crystal structure of yeast GK in complex with GMP was solved and refined shortly afterwards at 2-Å resolution (7,8).
The genes for yeast GK, Escherichia coli GK, and bovine GK were recently cloned (9 -11). The amino acid sequence of porcine brain GK was determined by peptide sequencing (5). Yeast GK shares 44.8% identity with E. coli GK, 51% identity with porcine GK, and 55% identity with bovine GK. It is noteworthy that, unlike the yeast and mammalian GKs, which are monomeric, E. coli GK is tetrameric at low salt conditions and dimeric at high salt conditions (10). Interestingly, several proteins, including the protein encoded by Drosophila tumor suppresser gene dlg-A (12), a rat presynaptic density protein (SAP90) (13), a rat postsynaptic density protein (PSD-95) (14), and the major palmitoylated membrane protein p55 of human erythrocytes (15), share significant homology with the entire sequence of GK. It has been suggested that GK may be involved in guanine nucleotide-mediated signal transduction pathways by regulating the ratio of GTP and GDP (12).
In this paper we describe the heterologous expression, purification, and characterizations of the wild-type yeast GK. We report the complete steady-state kinetic parameters for both forward and reverse reactions catalyzed by GK. We show that GK catalyzes the phosphoryl transfer via a sequential mechanism, and the reaction rate is largely controlled by the chemical step.
Cloning and Expression-The gene for guanylate kinase was amplified by PCR from a yeast genomic library kindly provided by Dr. Richard Young. The primers for PCR were 5Ј-GGGGTACCCATATGTC-CCGTCCTATCGTAATTTC-3Ј (forward with KpnI and NdeI sites) and 5Ј-CGGGATCCTCATTTTTCTGCAAAGATAAAATC-3Ј (reverse with BamHI site). The PCR product was cloned into pUC19 plasmid. In order to ensure that the amplified gene is wild type, its nucleotide sequence was determined by double-stranded DNA sequencing from both forward and reverse directions. The wild-type gene was then subcloned into pET17b plasmid. The resulting expression construct was designated pET17b-YGK and transformed into the strain BL21(DE3) (16). The clones expressing GK were selected by SDS-PAGE.
Protein Purification and Characterization-Five ml of LB medium containing 100 g/ml ampicillin was inoculated with a single colony of the expression strain BL21(DE3) containing pET17b-YGK. It was incubated overnight at 37°C with vigorous shaking (200 rpm). The overnight culture was used to inoculate 2-4 liters of LB medium containing 100 g/ml ampicillin. The culture was incubated at 37°C with vigorous shaking for 12-16 h. It was harvested by centrifugation. The bacterial paste was washed once with buffer A (30 mM Tris-HCl, 1 mM EDTA, pH 7.5) and kept at Ϫ70°C until use. The procedure for purification of yeast GK was modified from that of Berger et al. (6). Briefly, the frozen bacterial cells were thawed at room temperature and suspended in 100 ml of precooled buffer A. Dithiothreitol and phenylmethanesulfonyl fluoride were added to a final concentration of 1 mM. The bacterial suspension was then sonicated for 3 min in a pulse mode at 4°C. The resulting lysate was centrifuged for 30 min at 27,000 ϫ g. The supernatant was loaded onto an Affi-Gel Blue gel column equilibrated with buffer A. The column was washed with buffer A until A 280 of the effluent was Ͻ0.05. It was eluted with 5 mM GMP in buffer A. GK fractions were identified by SDS-PAGE and concentrated to ϳ15 ml by an Amicon concentrator using a YM10 membrane. The protein solution was then applied to a Sephadex G-75 column equilibrated with buffer A. The column was developed with the same buffer. Fractions from the gel filtration column were monitored by A 280 and SDS-PAGE. Pure GK fractions were pooled and concentrated to 10 -20 ml. The concentrated GK was dialyzed to remove buffer components and lyophilized. The N-terminal sequence of GK was determined by the Macromolecular Structure Facility at Michigan State University. The molecular weight was determined by MSU-NIH Mass Spectrometry Facility.
Steady-state Kinetics-The forward reaction kinetics was measured by a coupled assay as described by Agarwal et al. (1). Briefly, the reaction solution in 1 ml contained 100 mM Tris-HCl, pH 7.7, 100 mM KCl, 5 mM MgCl 2 , 1.5 mM phospho(enol)pyruvate, 0.2 mM NADH, 40 units of pyruvate kinase, 85 units of lactate dehydrogenase, 0.3 g of GK, and varied amount of ATP and GMP. The reaction was initiated by addition of GK at 25°C. The concentrations of ATP and GMP stock solutions were measured spectrophotometrically, using extinction coefficients of 15,400 M Ϫ1 cm Ϫ1 at 259 nm and 13,700 M Ϫ1 cm Ϫ1 at 253 nm for ATP and GMP, respectively. The concentration of the GK stock solution was quantified on the basis of 1 A 280 ϭ 1.35 mg/ml determined according to the method of Gill and von Hippel (17). The reverse reaction kinetics was measured by coupling to hexokinase and glucose-6phosphate dehydrogenase. The reaction solution in 1 ml contained 100 mM Tris-HCl, pH 7.7, 100 mM KCl, 5 mM MgCl 2 , 20 mM glucose, 1 mM NADP, 16 units of hexokinase, 4 units of glucose-6-phosphate dehydrogenase, 0.3 g of GK, and varied amount of ADP and GDP. Kinetic parameters were obtained by nonlinear least square fit of the data to Cleland's equation (18) where is the measured initial reaction rate, A and B represent the two substrates (MgATP and GMP or MgADP and GDP), respectively; V max is the maximum initial reaction rate; K a and K b are the Michaelis constants for A and B; K ia is the apparent dissociation constant for the binary complex EA. Determination of the Reaction Equilibrium Constant by Proton NMR-The reaction equilibrium constant is defined as The reaction was carried out at 25°C in a 5-mm NMR tube on a Varian VXR 500 MHz NMR spectrometer. The buffer for the reaction was composed of 20 mM perdeuterated Tris and 100 mM KCl in D 2 O, pH 7.5 (pH meter reading without correction for deuterium isotope effects). The total nucleotide concentration was ϳ5 mM. The concentration of GK was 5 M. The concentration of Mg 2ϩ was as specified in Fig. 4 and Table II. The reaction was initiated by addition of GK. The spectral width was 6000 Hz with the carrier frequency at the HDO resonance. The solvent resonance was suppressed by presaturation. Each free induction decay was composed of 16,000 data points with 80 transients. The delay between successive transients was 20 s to allow full relaxation of proton magnetization. The time domain data were processed by zero-filling to 32,000 points, exponential multiplication (0.5 Hz) and Fourier transformation. Chemical shifts were referenced to internal sodium 3-(trimethylsilyl)-propionate-2,2,3,3-d 4 . The concentrations of the reactants and products were calculated based on the integrals of H 2 resonance and H 8 resonance for adenine and guanine nucleotides, respectively. Deconvolution was performed for the overlapping peaks. Determination of the Reaction Equilibrium Constant by Radiometry-The reaction mixture (200 l) contained 100 mM Tris-HCl, pH 7.7, 100 mM KCl, 0.4 mM ATP, 0.4 mM GMP, 0.6 mM ADP, 0.6 mM GDP, 2.5 Ci of [␣-32 P]ATP, 5 mM MgCl 2 , and 0.6 M GK. The reaction was allowed to proceed for 5, 10, 20, and 40 min at room temperature. To terminate the reaction, 50 l of the reaction mixture was mixed with 50 l of 1 N HCl followed by addition of 50 l of chloroform. After 2 min of centrifugation, 50 l of the upper layer solution was taken and neutralized with 16 l of 2 N NaOH. To separate the reaction products, 2 l of the neutralized reaction mixture was loaded on a 20 ϫ 20 cm TLC plate and developed with 0.8 M KH 2 PO 4 solution, pH 3.4, for 1 h. After the TLC plate was dried, the nucleotides were visualized under UV light at 254 nm, and the radioactivity of ATP and ADP was analyzed by a liquid scintillation counter.

Determination of the Dissociation Constants of Binary Complexes by
Proton NMR-Substrate titration experiments were carried out in a 5-mm NMR tube. GK was dissolved in the perdeuterated Tris buffer as described before. Proton NMR parameters were the same as for determination of the reaction equilibrium constant except those described below. The number of transients was 96 or 104. Relaxation delay was 2.8 s. The dissociation constants were obtained by nonlinear least square fit of the data to the equation where ␦ f and ␦ b are the chemical shifts of a protein resonance at the free and ligand bound states; ␦ is the chemical shift of the resonance for each titration; E t is the total concentration of GK; and L t is the total concentration of the ligand. E t and L t were varied in each titration according to the following expressions: where E 0 is the initial concentration of GK; V 0 is the initial volume of the titration; ⌬V is the total volume of the added ligand solution; and L 0 is the concentration of the ligand stock solution.

Determination of the Dissociation Constant of GK⅐GDP Complex by Equilibrium Dialysis-
The experiments were carried out in a Spectrum equilibrium dialyzer. The buffer was composed of 100 mM Tris-HCl, pH 7.7, 100 mM KCl, and 5 mM dithiothreitol. GK concentration was 0.1 mM. The concentrations of GDP ranged from 0.02 to 0.64 mM. [8,5Ј-3 H]GDP was used as a tracer for measuring bound and free GDP. Dialysis was allowed to proceed for 2, 4, and 6 h with rotation at 10 rpm at room temperature. The radioactivity of each compartment of the dialysis cells was measured by liquid scintillation counting. The data were analyzed by nonlinear least square fit to the equation where P t is the GK concentration, L b and L f are the concentrations of bound and free GDP, respectively. Viscosity-dependent Kinetics-A concentrated sucrose stock solution was prepared in the assay buffer and then diluted to desired concentrations (10, 20, 30, and 40%). Relative viscosities of the reaction mixtures were measured by a Cannon-Fenske viscometer at 24°C. The viscosity of the assay buffer containing 0% sucrose was used as a reference. The basic assay procedure was the same as described for steady-state kinetics. However, 50% more pyruvate kinase and lactic dehydrogenase were used. It was checked that the reaction rate was not limited by the coupling enzymes. One substrate was kept at a saturating concentration, and the other substrate was varied. GK was preincubated with the fixed substrate. The reactions were initiated with the varied substrate.

RESULTS
Expression and Purification-The gene of yeast GK has been cloned and sequenced by Konrad (9). We cloned the gene into the expression vector pET-17b by PCR from a yeast genomic library. Since Taq DNA polymerase for PCR is prone to make errors, the nucleotide sequence of the cloned gene was determined from both 5Ј-and 3Ј-directions. No mutations in the gene were found in the selected clone designated pET17b-YGK. The expression construct was transformed into the E. coli strain BL21(DE3). Surprisingly, as shown in Fig. 1, GK is expressed at very high level without IPTG induction (lane 3), although it is expressed at somewhat higher level with IPTG induction (lane 4). GK was purified to homogeneity (Fig. 1, lane 5) by a simple two-column procedure modified from Berger et al. (6). The average yield is ϳ100 mg of pure GK per liter of E. coli culture. The specific activity is ϳ1,150 units/mg. The enzyme is stable at 37°C for at least 2 weeks. The N-terminal nine amino acid sequence was determined to be Ser-Arg-Pro-Ile-Val-Ile-Ser-Gly-Pro, in agreement with the amino acid sequence of GK purified from yeast (6). It indicates that the initiation methionine of the recombinant GK is removed in E. coli. The molecular weight determined by mass spectrometry is the same as calculated without the initiation methionine (data not shown).
Steady-state Kinetics-The kinetics of the forward reaction (formation of ADP and GDP) was measured by coupling the reaction to those of pyruvate kinase and lactate dehydrogenase (1). The rate of the reverse reaction (formation of ATP and GMP) was measured by a coupled assay using hexokinase and glucose-6-phosphate dehydrogenase as the coupling enzymes. Kinetic parameters were obtained by nonlinear least square analysis of the initial velocity data varying both substrates. It was found that GMP has partial substrate inhibition (Fig. 2). At concentrations above 0.22 mM, the initial velocity decreases with increasing GMP concentration and levels off at ϳ50% of the apparent maximum velocity. The partial substrate inhibition by GMP is not competitive with MgATP. Because of the substrate inhibition the highest concentration of GMP used for full kinetic analysis was 0.17 mM. At this concentration GMP shows negligible substrate inhibition, and the kinetic data follow Michaelis-Menten equation. Double-reciprocal plots of the kinetic data are linear as shown in Fig. 3. The intersecting patterns in the double-reciprocal plots indicate a sequential mechanism for the reaction. The kinetic parameters are summarized in Table I.
Reaction Equilibrium Constants-In order to check whether the kinetic data are consistent with thermodynamic parameters, we determined the equilibrium constant of the reaction by NMR and a radiometric assay. We approached the reaction equilibrium from both forward and reverse directions. The proton NMR spectra of the forward and reverse reactions are shown in Fig. 4. It can be clearly seen from the spectra that there is a side reaction resulting the formation of GTP. The GTP resonances were assigned by comparing with those of authentic GTP from Sigma. Since GTP can act as a phosphate donor (albeit a poor one) with GMP as the phosphate acceptor (9), GTP is most likely generated by phosphoryl transfer between two GDP molecules. Because the side reaction is much slower than the main one, the reaction equilibrium is maintained throughout the time course once established. Thus the side reaction has no effect on the evaluation of the reaction equilibrium constant. The reaction equilibrium was reached within 10 min after addition of GK because the equilibrium constants calculated using spectra b and f are the same as those calculated based on spectra c, d, g, and h. The equilibrium constants determined under various conditions are listed in Table II. Since the equilibrium constant, as defined under "Experimental Procedures," does not take into account the metal ion coordination states of the nucleotides, it is of no surprise that Mg 2ϩ concentration affects the reaction equilibrium. Similar effects on the reactions catalyzed by adenylate kinase and other kinases have been observed (19,20). The equilibrium constant determined by the radiometric assay is 2.1, in close agreement with the NMR results considering the Mg 2ϩ effects. It is 2.2 by calculation using the kinetic parameters according to Haldane relationships. The results indicate that the kinetic parameters are consistent with the thermodynamic constant.
Dissociation Constants of Binary Complexes-Next we compared the kinetic parameters K i with the corresponding dissociation constants K d . Except GK⅐GDP complex, the dissociation constants of all binary complexes were determined by NMR titrations. The proton NMR spectra of free GK and various binary complexes are shown in Fig. 5. Some representative NMR titration curves are shown in Fig. 6 and Fig. 7A. The curves were obtained by nonlinear least square fit of the titration data to the 1:1 binding model as described under "Experimental Procedures." Fitting the GDP NMR titration data to the 1:1 model was not satisfactory presumably because of binding of GDP to the ATP site in addition to the GMP site. The dissociation constant of GK⅐GDP complex was determined by equilibrium dialysis at much lower GK and GDP concentrations to minimize binding of GDP to the ATP site. The data from the equilibrium dialysis experiments could be fitted well to the 1:1 binding model as shown in Fig. 7B. The dissociation constants of the various binary complexes are listed in Table II. The K d values of all the substrate complexes except GK⅐MgADP are very close to those of the corresponding kinetic constants (K i ). The K d value of GK⅐MgADP is somewhat higher than that of K i(MgADP) presumably because of the differences in experimental conditions such as Mg 2ϩ concentration.
Viscosity Effects-Viscosity-dependent kinetics was used to determine whether the chemical step is rate-limiting in the reaction catalyzed by GK. Increases in viscosity were achieved by addition of sucrose (0 -40%). The results are summarized in Table I and plotted in Fig. 8. With ATP and GMP as substrates, k cat of the wild-type GK decreases only slightly with addition of the viscogen. Addition of sucrose has a moderate effect on k cat /K m . Two control experiments were performed for appropriate interpretation of the viscosity effects, one with dGMP (a poor substrate) and the other with the site-directed mutant S80A (a sluggish enzyme). With dGMP as the phosphate acceptor, k cat of the wild-type GK is reduced to 51 s Ϫ1 . K m for dGMP is 0.38 mM. Addition of sucrose has no effect on k cat and only a small effect on k cat /K m . With GMP as the phosphate acceptor, k cat of S80A mutant is 15 s Ϫ1 . K m(GMP) and K m(MgATP) of S80A are 0.50 and 0.23 mM, respectively. Addition of sucrose causes a slight decrease in k cat /K m of S80A and a slight increase in k cat .

FIG. 4. Determination of reaction equilibrium constant by proton NMR.
A, the initial reaction components contained 2.5 mM ATP, 2.5 mM GMP, and 5.6 mM MgCl 2 . B, the initial reaction components contained 2.5 mM ADP, 2.5 mM GDP, and 5.6 mM MgCl 2 . Spectra a and e were acquired before addition of GK. Spectra b and f were acquired 10 min after addition of GK. Spectra c and g were acquired 30 min after addition of GK. Spectra d and h were acquired 60 min after addition of GK.

DISCUSSION
GK plays an essential role in the guanine nucleotide salvage and interconversion pathway (9,21). It has also been implicated in guanine nucleotide-mediated signal transduction pathways (12). It belongs to a family of enzymes that catalyze the phosphorylation of nucleoside monophosphates. These kinases are generally small monomeric enzymes with high substrate specificity. They are considered to be classical enzymes with substrate-induced motions. It has been suggested that the catalytic centers of these enzymes are assembled only upon substrate binding and dissembled after the products are released (22). Among the nucleoside monophosphate kinases, adenylate kinase (AK) is the most extensively studied one (23). Although the catalytic mechanism of AK is well investigated, very little is known about the catalytic mechanisms of other nucleoside monophosphate kinases. Furthermore, the structural basis of nucleotide specificity and substrate-induced fit mechanisms of these enzymes are largely unknown.
The reaction catalyzed by GK is very similar to that of AK, but the two enzymes are only distantly related and share 13% identity in the amino acid sequences. The putative ATP binding Dissociation constants of binary complexes domain of GK is very similar to that of AK; however, the GMP binding domain of GK and the AMP binding domain of AK are grossly different in structure (8). GK is rather specific with respect to nucleoside monophosphate substrate (1,9). The high substrate specificity of GK makes it a better model enzyme for studying the structural basis of nucleotide specificity. Moreover, GK is rather stable, in contrast to a previous report by Moriguchi (24). The high stability of GK makes it an excellent model enzyme for studying substrate-induced fit mechanisms by NMR.
Moriguchi et al. (24) have measured the K m values for MgATP and GMP (0.5 and 0.048 mM, respectively), but none of the kinetic parameters for the reverse reaction has been reported. We have determined the steady-state kinetic parameters for both forward and reverse reactions. The value for K m(GMP) determined by us is two times that reported by Moriguchi et al. (23), but our K m(MgATP) value is 40% of their measurement. It is noted that the specific activity of their enzyme preparation was rather low (ϳ1% of that of our preparation), and the activity was labile during storage. Thus the discrepancies could be due to the impurity in their enzyme preparation interfering with the kinetic assays and/or the possible differences in the assay procedures (no details have been given in their report). One way to check the consistency of the kinetic parameters is to measure the equilibrium constant of the reaction. The equilibrium constant calculated according to Haldane relationships is 2.2. It is in close agreement with those measured by NMR and the radiometric assay, indicating that the kinetic parameters are consistent with the thermodynamic constant.
Double-reciprocal plots of the initial velocity data show intersecting patterns for both forward and reverse reactions. The results are characteristic of a sequential mechanism. We have shown that all four nucleotides (ATP, GMP, ADP, and GDP) can bind to the free GK, and we have determined the dissociation constants of all binary enzyme substrate complexes. The results are in support of a random bi-bi mechanism. Since the dissociation constants measured by NMR and equilibrium dialysis are in line with the corresponding K i values, the kinetic mechanism is close to equilibrium random. Although an ordered mechanism can not be ruled out yet, a random bi-bi mechanism is consistent with those of mammalian GK (1).
Partial substrate inhibition by GMP has been observed. There are several possible causes for the substrate inhibition. (i) GMP binds to the MgATP site. (ii) There is a second GMP binding site separate from the active center for activity regulation. (iii) GMP combines with the product complex GK⅐MgADP to form the abortive complex GK⅐MgADP⅐GMP. Possibility i can be ruled out because the inhibition is not competitive with MgATP. Since the binding studies indicate that GK has only one GMP binding site, possibility ii can also be ruled out. Thus possibility iii is likely to be the cause of the partial substrate inhibition. However, formation of the abortive complex only slows down but does not arrest the release of MgADP. Formation of the abortive complex GK⅐MgADP⅐GMP has been demonstrated in porcine brain GK (1). Substrate inhibition has also been observed in E. coli AK and attributed to the formation of the abortive complex AK⅐MgADP⅐AMP (25).
Viscosity-dependent kinetics has been used to identify the rate-limiting steps of quite a few enzyme-catalyzed reactions (26 -32). Since one substrate was kept at a saturating concentration and preincubated with GK in the viscosity studies, the kinetics can be described by Scheme I: where A is the fixed substrate preincubated with the enzyme; B is the varied substrate used to initiate the reaction; P and Q are the corresponding products; k 7 is a combined rate constant for product release; and all other constants are the rate constants for individual steps. The steady-state kinetic parameters k cat and k cat /K m (B) for the above scheme can be easily derived by Cleland's net rate method (33), as shown in Equations 7 and 8: For viscosity sensitive steps, k ϭ k 0 / rel , where rel is the relative viscosity, k 0 and k are the rate constants in the absence and presence of viscogen, respectively (34). By combining the Kramers' relationship with Equations 7 and 8, one can obtain the following normalized equations: Both k cat 0 /k cat versus rel and (k cat /K m 0 /(k cat /K m ) versus rel plots are linear. The slopes and intercepts of the plots vary between 0 and 1 depending on the relative rates of the diffusion and chemical steps. For k cat 0 /k cat versus rel plot, the slope and intercept are determined by the relative rates of the chemical and product release steps. If the chemical step is much faster than product release (k 5 ϩ k 6 Ͼ Ͼ k 7 ), then the slope is 1 and the intercept is 0. When the chemical step is rate-limiting (k 5 ϩ k 6 Ͻ Ͻ k 7 ), then the slope is 0 and the intercept is 1. The ratio of the slope and intercept is equal to (k 5 ϩ k 6 )/k 7 . On the other hand, the slope and intercept of (k cat /K m 0 )/(k cat /K m ) versus rel plot are dependent on the relative rates of the chemical step and the steps both before and after the chemical step (substrate dissociation and product release). If the chemical step is much faster than substrate dissociation (k 5 Ͼ Ͼ k 4 ) or product release (k 6 Ͼ Ͼ k 7 ), the slope is 1 and the intercept is 0. When the chemical step is fully rate-limiting (k 5 Ͻ Ͻ k 4 and k 6 Ͻ Ͻ k 7 ), the slope is 0 and the intercept is 1. The ratio of the slope and intercept is (k 5 /k 4 ϩ k 6 /k 7 ). In the case of the wild-type GK with GMP as the phosphate acceptor, addition of the viscogen has very small effects on k cat (the slope and intercept of the k cat 0 /k cat versus rel plot are 0.09 and 1, respectively). It has essentially no effects on k cat when dGMP (a poor substrate) is used as the phosphate acceptor (slope ϭ 0.01 and intercept ϭ 1). It causes a small increase in k cat in the case of the site-directed mutant S80A (a sluggish enzyme, slope ϭ Ϫ0.1). A small increase in k cat with addition of a viscogen has been observed in a number of cases (27,28,32). It could be due to an increase in either k 5 or k 7 in the presence of the viscogen. The results suggest that product release is unlikely to be the rate-limiting step. The slope and intercept of the (k cat /K m 0 /(k cat /K m ) versus rel plot is 0.3 and 0.7 for the wild-type GK with GMP as the phosphate acceptor. The moderate decrease in k cat /K m is significant because addition of the viscogen has only very small effects on k cat /K m in both control experiments. Furthermore, addition of the viscogen has a greater effect on k cat /K m than on k cat . The results indicate that the steps before the chemical step are likely to be ratelimiting to some degree. However, the reaction rate is largely controlled by the chemical step.
In summary, a complete set of kinetic parameters has been determined for both forward and reverse reactions catalyzed by GK. The steady-state kinetic parameters are consistent with the measured thermodynamic constants. The substrate inhibition by GMP may be attributed to the formation of an abortive complex. GK catalyzes the phosphoryl transfer via a sequential mechanism. The chemical step is the major rate-limiting step in the GK-catalyzed reaction.