Triple isotopic labeling and kinetic isotope effects: exposing H-transfer steps in enzymatic systems

Kinetic isotope effect (KIE) studies can provide insight into the mechanism and kinetics of specific chemical steps in complex catalytic cascades. Recent results from hydrogen KIE measurements have examined correlations between enzyme dynamics and catalytic function, leading to a surge of studies in this area. Unfortunately, most enzymatic H-transfer reactions are not rate limiting, and the observed KIEs do not reliably reflect the intrinsic KIEs on the chemical step of interest. Given their importance to understanding the chemical step under study, accurate determination of the intrinsic KIE from the observed data is essential. In 1975, Northrop developed an elegant method to assess intrinsic KIEs from their observed values [Northrop, D. B. (1975) Steady-state analysis of kinetic isotope effects in enzymic reactions. Biochemistry 14, 2644-2651]. The Northrop method involves KIE measurements using all three hydrogen isotopes, where one of them serves as the reference isotope. This method has been successfully used with different combinations of observed KIEs over the years, but criteria for a rational choice of reference isotope have never before been experimentally determined. Here we compare different reference isotopes (and hence distinct experimental designs) using the reduction of dihydrofolate and dihydrobiopterin by two dissimilar enzymes as model reactions. A number of isotopic labeling patterns have been applied to facilitate the comparative study of reference isotopes. The results demonstrate the versatility of the Northrop method and that such experiments are limited only by synthetic techniques, availability of starting materials, and the experimental error associated with the use of distinct combinations of isotopologues.     

Vibrationally enhanced hydrogen tunneling in the Escherichia coli thymidylate synthase catalyzed reaction

The enzyme thymidylate synthase (TS) catalyzes a complex reaction that involves forming and breaking at least six covalent bonds. The physical nature of the hydride transfer step in this complex reaction cascade has been studied by means of isotope effects and their temperature dependence. Competitive kinetic isotope effects (KIEs) on the second-order rate constant (V/K) were measured over a temperature range of 5-45 degrees C. The observed H/T ((T)V/K(H)) and D/T ((T)V/K(D)) KIEs were used to calculate the intrinsic KIEs throughout the temperature range. The Swain-Schaad relationships between the H/T and D/T V/K KIEs revealed that the hydride transfer step is the rate-determining step at the physiological temperature of Escherichia coli (20-30 degrees C) but is only partly rate-determining at elevated and reduced temperatures. H/D KIE on the first-order rate constant k(cat) ((D)k = 3.72) has been previously reported [Spencer et al. (1997) Biochemistry 36, 4212-4222]. Additionally, the Swain-Schaad relationships between that (D)k and the V/K KIEs reported here suggested that at 20 degrees C the hydride transfer step is the rate-determining step for both rate constants. Intrinsic KIEs were calculated here and were found to be virtually temperature independent (DeltaE(a) = 0 within experimental error). The isotope effects on the preexponential Arrhenius factors for the intrinsic KIEs were A(H)/A(T) = 6.8 +/- 2.8 and A(D)/A(T) = 1.9 +/- 0.25. Both effects are significantly above the semiclassical (no-tunneling) predicted values and indicate a contribution of quantum mechanical tunneling to this hydride transfer reaction. Tunneling correction to transition state theory would predict that these isotope effects on activation parameters result from no energy of activation for all isotopes. Yet, initial velocity measurements over the same temperature range indicate cofactor inhibition and result in significant activation energy on k(cat) (4.0 +/- 0.1 kcal/mol). Taken together, the temperature-independent KIEs, the large isotope effects on the preexponential Arrhenius factors, and a significant energy of activation all suggest vibrationally enhanced hydride tunneling in the TS-catalyzed reaction.     

Kinetic isotope effect studies on the de novo rate of chromophore formation in fast- and slow-maturing GFP variants

The maturation process of green fluorescent protein (GFP) entails a protein oxidation reaction triggered by spontaneous backbone condensation. The chromophore is generated by full conjugation of the Tyr66 phenolic group with the heterocycle, a process that requires C-H bond scission at the benzylic carbon. We have prepared isotope-enriched protein bearing tyrosine residues deuterated at the beta carbon, and have determined kinetic isotope effects (KIEs) on the GFP self-processing reaction. Progress curves for the production of H 2O 2 and the mature chromophore were analyzed by global curve fitting to a three-step mechanism describing preoxidation, oxidation and postoxidation events. Although a KIE for protein oxidation could not be discerned ( k H/ k D = 1.1 +/- 0.2), a full primary KIE of 5.9 (+/-2.8) was extracted for the postoxidation step. Therefore, the exocyclic carbon is not involved in the reduction of molecular oxygen. Rather, C-H bond cleavage proceeds from the oxidized cyclic imine form, and is the rate-limiting event of the final step. Substantial pH-dependence of maturation was observed upon substitution of the catalytic glutamate (E222Q), indicating an apparent p K a of 9.4 (+/-0.1) for the base catalyst. For this variant, a KIE of 5.8 (+/-0.4) was determined for the intrinsic time constant that is thought to describe the final step, as supported by ultra-high resolution mass spectrometric results. The data are consistent with general base catalysis of the postoxidation events yielding green color. Structural arguments suggest a mechanism in which the highly conserved Arg96 serves as catalytic base in proton abstraction from the Tyr66-derived beta carbon.     

Transition state analysis for human and Plasmodium falciparum purine nucleoside phosphorylases

Recent studies have shown that Plasmodium falciparum is sensitive to a purine salvage block at purine nucleoside phosphorylase (PNP) and that human PNP is a target for T-cell proliferative diseases. Specific tight-binding inhibitors might be designed on the basis of specific PNP transition state structures. Kinetic isotope effects (KIEs) were measured for arsenolysis of inosine catalyzed by P. falciparum and human purine nucleoside phosphorylases. Intrinsic KIEs from [1'-(3)H]-, [2'-(3)H]-, [1'-(14)C]-, [9-(15)N]-, and [5'-(3)H]inosines were 1.184 +/- 0.004, 1.031 +/- 0.004, 1.002 +/- 0.006, 1.029 +/- 0.006, and 1.062 +/- 0.002 for the human enzyme and 1.116 +/- 0.007, 1.036 +/- 0.003, 0.996 +/- 0.006, 1.019 +/- 0.005, and 1.064 +/- 0.003 for P. falciparum PNPs, respectively. Analysis of KIEs indicated a highly dissociative D(N)A(N) (S(N)1) stepwise mechanism with very little leaving group involvement. The near-unity 1'-(14)C KIEs for both human and P. falciparum PNP agree with the theoretical value for a 1'-(14)C equilibrium isotope effect for oxacarbenium ion formation when computed at the B1LYP/6-31G(d) level of theory. The 9-(15)N KIE for human PNP is also in agreement with theory for equilibrium formation of hypoxanthine and oxacarbenium ion at this level of theory. The 9-(15)N KIE for P. falciparum PNP shows a constrained vibrational environment around N9 at the transition state. A relatively small beta-secondary 2'-(3)H KIE for both enzymes indicates a 3'-endo conformation for ribose and relatively weak hyperconjugation at the transition state. The large 5'-(3)H KIE reveals substantial distortion at the 5'-hydroxymethyl group which causes loosening of the C5'-H5' bonds during the reaction coordinate.     

Determination of the chlorine kinetic isotope effect on the 4-chlorobenzoyl-CoA dehalogenase-catalyzed nucleophilic aromatic substitution

The chlorine kinetic isotope effect (KIE) on the dehalogenation of 4-chlorobenzoyl-CoA catalyzed by 4-chlorobenzoyl-CoA dehalogenase has been measured at room temperature and optimal pH. The measured value of (37)k = 1.0090 +/- 0.0006 is larger than the KIEs recently measured for haloalkane and fluoroacetate dehalogenase. This indicates that the transition state for dissociation of chloride ion from the Meisenheimer intermediate is sensitive to the chlorine isotopic substitution. Simple modeling suggests that this sensitivity originates in the high isotopic sensitivity of the C-Cl bond bending modes.     

A method to determine 18 O kinetic isotope effects in the hydrolysis of nucleotide triphosphates

A method to determine 18 O kinetic isotope effects (KIEs) in the hydrolysis of GTP that is generally applicable to reactions involving other nucleotide triphosphates is described. Internal competition, where the substrate of the reaction is a mixture of 18 O-labeled and unlabeled nucleotides, is employed, and the change in relative abundance of the two species in the course of the reaction is used to calculate KIE. The nucleotide labeled with 18 O at sites of mechanistic interest also contains 13C at all carbon positions, whereas the 16 O-labeled nucleotide is depleted of 13C. The relative abundance of the labeled and unlabeled substrates or products is reflected in the carbon isotope ratio (13C/12C) in GTP or GDP, which is determined by the use of a liquid chromatography-coupled isotope ratio mass spectrometer (LC-coupled IRMS). The LC is coupled to the IRMS by an Isolink interface. Carbon isotope ratios can be determined with accuracy and precision greater than 0.04% and are consistent over an order of magnitude in sample amount. KIE values for Ras/NF1(333)-catalyzed hydrolysis of [beta18 O3,13C]GTP were determined by change in the isotope ratio of GTP or GDP or the ratio of the isotope ratio of GDP to that of GTP. KIE values computed in the three ways agree within 0.1%, although the method using the ratio of isotope ratios of GDP and GTP gives superior precision (<0.1%). A single KIE measurement can be conducted in 25 min with less than 5 microg nucleotide reaction product.     

Calculation of isotope effects from first principles

Various means of calculating the effect of changing the mass of a given atom upon a chemical process are reviewed. Of particular interest is the deuterium isotope effect comparing the normal protium nucleus with its heavier deuterium congener. The replacement of the bridging protium in a neutral hydrogen bond such as the water dimer by a deuterium strengthens the interaction by a small amount via effects upon the vibrational energy. In an ionic H-bond such as the protonated water dimer, on the other hand, the reverse trend is observed in that replacement of the bridging protium by dimer weakens the interaction. In addition to the stability of a given complex, the rate at which a proton transfers from one group to another is likewise affected by deuterium substitution, viz. kinetic isotope effects (KIEs). The KIE is enlarged as the temperature drops, particularly so if the calculation of KIE includes proton tunneling. The KIE is also sensitive to any angular distortions or stretches present in the H-bond of interest. KIEs can be computed either by the standard transition state theory which is derived via only two points on the potential energy surface, or by more complete formalisms which take account of larger swaths of the surface. While more time intensive, the latter can also be applied to provide insights important in interpretation of experimental data.     

Vibrationally enhanced tunneling as a mechanism for enzymatic hydrogen transfer.

We present a theory of enzymatic hydrogen transfer in which hydrogen tunneling is mediated by thermal fluctuations of the enzyme's active site. These fluctuations greatly increase the tunneling rate by shortening the distance the hydrogen must tunnel. The average tunneling distance is shown to decrease when heavier isotopes are substituted for the hydrogen or when the temperature is increased, leading to kinetic isotope effects (KIEs)--defined as the factor by which the reaction slows down when isotopically substituted substrates are used--that need be no larger than KIEs for nontunneling mechanisms. Within this theory we derive a simple KIE expression for vibrationally enhanced ground state tunneling that is able to fit the data for the bovine serum amine oxidase (BSAO) system, correctly predicting the large temperature dependence of the KIEs. Because the KIEs in this theory can resemble those for nontunneling dynamics, distinguishing the two possibilities requires careful measurements over a range of temperatures, as has been done for BSAO.     

Kinetic isotope effect studies of the reaction catalyzed by uracil DNA glycosylase: evidence for an oxocarbenium ion-uracil anion intermediate

The DNA repair enzyme uracil DNA glycosylase catalyzes the first step in the uracil base excision repair pathway, the hydrolytic cleavage of the N-glycosidic bond of deoxyuridine in DNA. Here we report kinetic isotope effect (KIE) measurements that have allowed the determination of the transition-state structure for this important reaction. The small primary (13)C KIE (=1.010 +/- 0.009) and the large secondary alpha-deuterium KIE (=1.201 +/- 0.021) indicate that (i) the glycosidic bond is essentially completely broken in the transition state and (ii) there is significant sp(2) character at the anomeric carbon. Large secondary beta-deuterium KIEs were observed when [2'R-(2)H] = 1.102 +/- 0.011 and [2'S-(2)H] = 1.106 +/- 0.010. The nearly equal and large magnitudes of the two stereospecific beta-deuterium KIEs indicate strong hyperconjugation between the elongated glycosidic bond and both of the C2'-H2' bonds. Geometric interpretation of these beta-deuterium KIEs indicates that the furanose ring adopts a mild 3'-exo sugar pucker in the transition state, as would be expected for maximal stabilization of an oxocarbenium ion. Taken together, these results strongly indicate that the reaction proceeds through a dissociative transition state, with complete dissociation of the uracil anion followed by addition of water. To our knowledge, this is the first transition-state structure determined for enzymatic cleavage of the glycosidic linkage in a pyrimidine deoxyribonucleotide.     

Pre-steady-state studies of phosphite dehydrogenase demonstrate that hydride transfer is fully rate limiting

Phosphite dehydrogenase (PTDH) is a unique NAD-dependent enzyme that catalyzes the oxidation of inorganic phosphite to phosphate. The enzyme has great potential for cofactor regeneration, and mechanistic studies have provided some insight into the residues that are important for catalysis. In this investigation, pre-steady-state studies were performed on the His6-tagged wild-type (WT) enzyme, several active site mutants, a thermostable mutant (12X-PTDH), and a thermostable mutant with dual cofactor specificity (NADP-12X-PTDH). Stopped-flow kinetic experiments indicate that slow steps after hydride transfer do not significantly limit the rate of reaction for the WT enzyme, the active site mutants, or the thermostable mutant. Pre-steady-state kinetic isotope effects (KIEs) and single-turnover experiments further confirm that slow steps after the chemical step do not significantly limit the rate of reaction for any of these proteins. Collectively, these results suggest that the hydride transfer step is fully rate determining in PTDH and that the observed KIE on kcat is the intrinsic effect in WT PTDH and the mutants examined. In contrast, a slow step after catalysis may partially limit the rate of phosphite oxidation by NADP-12X-PTDH with NADP as the cofactor. Finally, site-directed mutagenesis of Asp79 indicates that this residue is important in orienting Arg237 for proper interaction with phosphite.     

Role of Y94 in proton and hydride transfers catalyzed by thymidylate synthase

Thymidylate synthase (TS) catalyzes the substitution of a carbon-bound proton in a uracil base by a methyl group to yield thymine in the de novo biosynthesis of this DNA base. The enzymatic mechanism involves making and breaking several covalent bonds. Traditionally, a conserved tyrosine (Y94 in Escherichia coli, Y146 in Lactobacillus casei, and Y135 in humans) was assumed to serve as the general base catalyzing the proton abstraction. That assumption was examined here by comparing the nature of the proton abstraction using wild-type (wt) E. coli TS (ecTS) and its Y94F mutant (with a turnover rate reduced by 2 orders of magnitude). A subsequent hydride transfer was also studied using the wt and Y94F. The physical nature of both H-transfer steps was examined by determining intrinsic kinetic isotope effects (KIEs). Surprisingly, the findings did not suggest a direct role for Y94 in the proton abstraction step. The effect of this mutation on the subsequent hydride transfer was examined by a comparison of the temperature dependency of the intrinsic KIE on both the wt and the mutant. The intrinsic KIEs for Y94F at physiological temperatures were slightly smaller than those for wt but, otherwise, were as temperature-independent, suggesting a perfectly preorganized reaction coordinate for both enzymes. At reduced temperatures, however, the KIE for the mutant increased with a decrease in temperature, indicating a poorly preorganized reaction coordinate. Other kinetic and structural properties were also compared, and the findings suggested that Y94 is part of a H-bond network that plays a critical role at a step between the proton and the hydride transfers, presumably the dissociation of H4folate from the covalently bound intermediate. The possibility that no single residue serves as the general base in question but, rather, that the whole network of H-bonds at the active site catalyzes proton abstraction is discussed.     

Transition state structure of 5'-methylthioadenosine/S-adenosylhomocysteine nucleosidase from Escherichia coli and its similarity to transition state analogues

Methylthioadenosine/S-adenosylhomocysteine nucleosidase (MTAN) catalyzes reactions linked to polyamine metabolism, quorum sensing pathways, methylation reactions, and adenine salvage. It is a candidate target for antimicrobial drug design. Kinetic isotope effects (KIEs) were measured on the MTAN-catalyzed hydrolysis of 5'-methylthioadenosine (MTA) to determine the transition state structure. KIEs measured at pH 7.5 were near unity due to the large forward commitment to catalysis. Intrinsic KIEs were expressed by increasing the pH to 8.5. Intrinsic KIEs from MTAs labeled at 1'-(3)H, 1'-(14)C, 2'-(3)H, 4'-(3)H, 5'-(3)H, 9-(15)N, and Me-(3)H(3) were 1.160 +/- 0.004, 1.004 +/- 0.003, 1.044 +/- 0.004, 1.015 +/- 0.002, 1.010 +/- 0.002, 1.018 +/- 0.006, and 1.051 +/- 0.002, respectively. The large 1'-(3)H and small 1'-(14)C KIEs indicate that the Escherichia coli MTAN reaction undergoes a dissociative (D(N)A(N)) (S(N)1) mechanism with little involvement of the leaving group or participation of the attacking nucleophile at the transition state, causing the transition state to have significant ribooxacarbenium ion character. A transition state constrained to match the intrinsic KIEs was located with density functional theory [B3LYP/6-31G(d,p)]. The leaving group (N9) is predicted to be 3.0 A from the anomeric carbon. The small beta-secondary 2'-(3)H KIE of 1.044 corresponds to a modest 3'-endo conformation for ribose and a H1'-C1'-C2'-H2' dihedral angle of 53 degrees at the transition state. Natural bond orbital analysis of the substrate and the transition state suggests that the 4'-(3)H KIE is due to hyperconjugation between the lone pair (n(p)) of O3' and the antibonding (sigma) orbital of the C4'-H4' group, and the methyl-(3)H(3) KIE is due to hyperconjugation between the n(p) of sulfur and the sigma of methyl C-H bonds. Transition state analogues that resemble this transition state structure are powerful inhibitors, and their molecular electrostatic potential maps closely resemble that of the transition state.     

Transition state analysis of the arsenolytic depyrimidination of thymidine by human thymidine phosphorylase

Human thymidine phosphorylase (hTP) is responsible for thymidine (dT) homeostasis, promotes angiogenesis, and is involved in metabolic inactivation of antiproliferative agents that inhibit thymidylate synthase. Understanding its transition state structure is on the path to design transition state analogues. Arsenolysis of dT by hTP permits kinetic isotope effect (KIE) analysis of the reaction by forming thymine and the chemically unstable 2-deoxyribose 1-arsenate. The transition state for the arsenolytic reaction was characterized using multiple KIEs and computational analysis. Transition state analysis revealed a concerted bimolecular (A(N)D(N)) mechanism. A transition state constrained to match the intrinsic KIE values was found using density functional theory (B3LYP/6-31G*). An active site histidine is implicated as the catalytic base responsible for activation of the arsenate nucleophile and stabilization of the thymine leaving group during the isotopically sensitive step. At the transition state, the deoxyribose ring exhibits significant oxocarbenium ion character with bond breaking (r(C-N) = 2.45 ?) nearly complete and minimal bond making to the attacking nucleophile (r(C-O) = 2.95 ?). The transition state model predicts a deoxyribose conformation with a 2'-endo ring geometry. Transition state structure for the slow hydrolytic reaction of hTP involves a stepwise mechanism [Schwartz, P. A., Vetticatt, M. J., and Schramm, V. L. (2010) J. Am. Chem. Soc. 132, 13425-13433], in contrast to the concerted mechanism described here for arsenolysis.     

Environmentally coupled hydrogen tunneling. Linking catalysis to dynamics.

Many biological C-H activation reactions exhibit nonclassical kinetic isotope effects (KIEs). These nonclassical KIEs are too large (kH/kD > 7) and/or exhibit unusual temperature dependence such that the Arrhenius prefactor KIEs (AH/AD) fall outside of the semiclassical range near unity. The focus of this minireview is to discuss such KIEs within the context of the environmentally coupled hydrogen tunneling model. Full tunneling models of hydrogen transfer assume that protein or solvent fluctuations generate a reactive configuration along the classical, heavy-atom coordinate, from which the hydrogen transfers via nuclear tunneling. Environmentally coupled tunneling also invokes an environmental vibration (gating) that modulates the tunneling barrier, leading to a temperature-dependent KIE. These properties directly link enzyme fluctuations to the reaction coordinate for hydrogen transfer, making a quantum view of hydrogen transfer necessarily a dynamic view of catalysis. The environmentally coupled hydrogen tunneling model leads to a range of magnitudes of KIEs, which reflect the tunneling barrier, and a range of AH/AD values, which reflect the extent to which gating modulates hydrogen transfer. Gating is the primary determinant of the temperature dependence of the KIE within this model, providing insight into the importance of this motion in modulating the reaction coordinate. The potential use of variable temperature KIEs as a direct probe of coupling between environmental dynamics and the reaction coordinate is described. The evolution from application of a tunneling correction to a full tunneling model in enzymatic H transfer reactions is discussed in the context of a thermophilic alcohol dehydrogenase and soybean lipoxygenase-1.     

Use of an altered sugar-nucleotide to unmask the transition state for alpha(2-->6) sialyltransferase

Rat liver alpha(2-->6) sialyltransferase catalyzes the formation of a glycosidic bond between N-acetylneuraminic acid and the 6-hydroxyl group of a galactose residue at the nonreducing terminus of an oligosaccharide. This reaction has been investigated through the use of the novel sugar-nucleotide donor substrate UMP-NeuAc. A series of UMP-NeuAc radioisotopomers were prepared by chemical deamination of the corresponding CMP-NeuAc precursors. Kinetic isotope effects (KIEs) on V/K were measured using mixtures of radiolabeled UMP-NeuAc's as the donor substrate and N-acetyllactosamine as the acceptor. The secondary beta-(2)H KIE was 1.218 +/- 0.010, and the primary (14)C KIE was 1.030 +/- 0.010. A large inverse (3)H binding isotope effect of 0.944 +/- 0.010 was measured at the terminal carbon of the NeuAc glycerol side chain. These KIEs observed using UMP-NeuAc are much larger than those previously measured with CMP-NeuAc [Bruner, M., and Horenstein, B. A. (1998) Biochemistry 37, 289-297]. Solvent deuterium isotope effects of 1.3 and 2.6 on V/K and V(max) were observed with CMP-NeuAc as the donor, and it is revealing that these isotope effects vanished with use of the slow donor substrate UMP-NeuAc. Bell-shaped pH versus rate profiles were observed for V(max) (pK(a) values = 5.5, 9.0) and V/K(UMP)(-)(NeuAc) (pK(a)values = 6.2, 9.0). The results are considered in terms of a mechanism involving an isotopically sensitive conformational change which is independent of the glycosyl transfer step. The isotope effects reveal that the enzyme-bound transition state bears considerable charge on the N-acetylneuraminic acid residue, and this and other features of this mechanism provide new directions for sialyltransferase inhibitor design.     

Second-sphere amino acids contribute to transition-state structure in bovine purine nucleoside phosphorylase

Transition-state structures of human and bovine of purine nucleoside phosphorylases differ, despite 87% homologous amino acid sequences. Human PNP (HsPNP) has a fully dissociated transition state, while that for bovine PNP (BtPNP) has early SN1 character. Crystal structures and sequence alignment indicate that the active sites of these enzymes are the same within crystallographic analysis, but residues in the second-sphere from the active sites differ significantly. Residues in BtPNP have been mutated toward HsPNP, resulting in double (Asn123Lys; Arg210Gln) and triple mutant PNPs (Val39Thr; Asn123Lys; Arg210Gln). Steady-state kinetic studies indicated unchanged catalytic activity, while pre-steady-state studies indicate that the chemical step is slower in the triple mutant. The mutant enzymes have higher affinity for inhibitors that are mimics of a late dissociative transition state. Kinetic isotope effects (KIEs) and computational chemistry were used to identify the transition-state structure of the triple mutant. Intrinsic KIEs from [1'-3H], [1'-14C], [2'-3H], [5'-3H], and [9-15N] inosines were 1.221, 1.035, 1.073, 1.062 and 1.025, respectively. The primary intrinsic [1'-14C] and [9-15N] KIEs indicate a highly dissociative SN1 transition state with low bond order to the leaving group, a transition state different from the native enzyme. The [1'-14C] KIE suggests significant nucleophilic participation at the transition state. The transition-state structure of triple mutant PNP is altered as a consequence of the amino acids in the second sphere from the catalytic site. These residues are implicated in linking the dynamic motion of the protein to formation of the transition state.     

Rate-limiting step: a quantitative definition. Application to steady-state enzymic reactions

The generality of the concept of a rate-limiting step in enzymic reactions recently has been questioned [Northrop, D. B. (1981) Biochemistry 20, 4056-4061] because, in simulated isotopic experiments, alterations of the step identified as rate limiting by current definitions do not consistently affect Vmax in the expected manner. In this paper a definition for a rate-limiting step is posed that eliminates such inconsistencies while the thrust of the original concept is retained. Thus, for any steady-state process involving a linear reaction sequence the rate-limiting step is taken as the "most sensitive" step, or the step which, if perturbed, causes the largest change in overall velocity, v. In both V and V/K enzymic systems the most sensitive step is identified by the relative magnitude of the sensitivity function, SFj, for the various forward steps. If forward steps are identified by kj, SFj is equal to delta(1/v)/[delta(1/kj)/(1/kj)], when the equilibrium constant for the step involving kj is maintained constant. The corresponding sensitivity index, SIj, is a normalized function of SFj (the normalizing factor is v) such that the sum of the values for SIj is equal to 1. In addition, there is an exact relationship between the sensitivity index for the isotopic step and the fraction of the intrinsic isotopic effect that is expressed in the overall rate of the reaction (when the intrinsic effect is taken as the fractional difference in reciprocal rate constant produced by the isotope). A procedure is described for approximating the sensitivity function for the various steps in a reaction sequence on the basis of the Gibbs energy profile for that reaction and thus identifying the most sensitive step. This approach also is used to consider the general question of whether a rate-limiting step should be specified for a multistep enzymic reaction. Identifying the rate-limiting step as the most sensitive step in a reaction sequence means that no aspect of the concept of minimal rate should be automatically considered as a property of a rate-limiting step.     

Catalytic reaction profile for alcohol oxidation by galactose oxidase

Galactose oxidase is a remarkable enzyme containing a metalloradical redox cofactor capable of oxidizing a variety of primary alcohols during enzyme turnover. Recent studies using 1-O-methyl alpha-D-galactopyranoside have revealed an unusually large kinetic isotope effect (KIE) for oxidation of the alpha-deuterated alcohol (kH/kD = 22), demonstrating that cleavage of the 6,6'-di[2H]hydroxymethylene C-H bond is fully rate-limiting for oxidation of the canonical substrate. This step is believed to involve hydrogen atom transfer to the tyrosyl phenoxyl in a radical redox mechanism for catalysis [Whittaker, M. M., Ballou, D. P., and Whittaker, J. W. (1998) Biochemistry 37, 8426-8436]. In the work presented here, the enzyme's unusually broad substrate specificity has allowed us to extend these investigations to a homologous series of benzyl alcohol derivatives, in which remote (meta or para) substituents are used to systematically perturb the properties of the hydroxyl group undergoing oxidation. Quantitative structure-activity relationship (QSAR) correlations over the steady state rate data reveal a shift in the character of the transition state for substrate oxidation over this series, reflected in a change in the magnitude of the observed KIE for these reactions. The observed KIE values have been shown to obey a log-linear correlation over the substituent parameter, Hammett sigma. For the relatively difficult to oxidize nitro derivative, the KIE is large (kH/kD = 12.3), implying rate-limiting C-H bond cleavage for the oxidation reaction. This contribution becomes less important for more easily oxidized substrates (e.g., methoxy derivatives) where a much smaller KIE is observed (kH/kD = 3.6). Conversely, the solvent deuterium KIE is vanishingly small for 4-nitrobenzyl alcohol, but becomes significant for the 4-methoxy derivative (kH2O/kD2O = 1.2). These experiments have allowed us to develop a reaction profile for substrate oxidation by galactose oxidase, consisting of three components (hydroxylic proton transfer, electron transfer, and hydrogen atom transfer) comprising a single-step proton-coupled electron transfer mechanism. Each component exhibits a distinct substituent and isotope sensitivity, allowing them to be identified kinetically. The proton transfer component is unique in being sensitive to the isotopic character of the solvent (H2O or D2O), while hydrogen atom transfer (C-H bond cleavage) is independent of solvent composition but is sensitive to substrate labeling. In contrast, electron transfer processes will in general be less sensitive to isotopic substitution. Our results support a mechanism in which initial proton abstraction from a coordinated substrate activates the alcohol toward inner sphere electron transfer to the Cu(II) metal center in an unfavorable redox equilibrium, forming an alkoxy radical which undergoes hydrogen atom abstraction by the tyrosine-cysteine phenoxyl free radical ligand to form the product aldehyde.     

Arsenate and phosphate as nucleophiles at the transition states of human purine nucleoside phosphorylase

Purine nucleoside phosphorylase (PNP) catalyzes the reversible phosphorolysis of 6-oxypurine (2'-deoxy)ribonucleosides, generating (2-deoxy)ribose 1-phosphate and the purine base. Transition-state models for inosine cleavage have been proposed with bovine, human, and malarial PNPs using arsenate as the nucleophile, since kinetic isotope effects (KIEs) are obscured on phosphorolysis due to high commitment factors. The Phe200Gly mutant of human PNP has low forward and reverse commitment factors in the phosphorolytic reaction, permitting the measurement of competitive intrinsic KIEs on both arsenolysis and phosphorolysis of inosine. The intrinsic 1'-(14)C, 1'-(3)H, 2'-(2)H, 9-(15)N, and 5'-(3)H(2) KIEs for inosine were measured for arsenolysis and phosphorolysis. Except for the remote 5'-(3)H(2), and some slight difference between the 2'-(2)H KIEs, all isotope effects originating in the reaction coordinate are the same within experimental error. Hence, arsenolysis and phosphorolysis proceed through closely related transition states. Although electrostatically similar, the volume of arsenate is greater than phosphate and supports a steric influence to explain the differences in the 5'-(3)H(2) KIEs. Density functional theory calculations provide quantitative models of the transition states for Phe200Gly human PNP-catalyzed arsenolysis and phosphorolysis, selected upon matching calculated and experimental KIEs. The models confirm the striking resemblance between the transition states for the two reactions.     

Cyclooxygenase reaction mechanism of prostaglandin H synthase from deuterium kinetic isotope effects

Cyclooxygenase catalysis by prostaglandin H synthase (PGHS) is thought to involve a multistep mechanism with several radical intermediates. The proposed mechanism begins with the transfer of the C13 pro-(S) hydrogen atom from the substrate arachidonic acid (AA) to the Tyr385 radical in PGHS, followed by oxygen insertion and several bond rearrangements. The importance of the hydrogen-transfer step to controlling the overall kinetics of cyclooxygenase catalysis has not been directly examined. We quantified the non-competitive primary kinetic isotope effect (KIE) for both PGHS-1 and -2 using several deuterated AAs, including 13-pro-(S) d-AA, 13,13-d₂-AA and 10, 10, 13,13-d₄-AA. The primary KIE for steady-state cyclooxygenase catalysis, ^Dk_cat, ranged between 1.8 and 2.3 in oxygen electrode measurements. The intrinsic KIE of AA radical formation by C13 pro-(S) hydrogen abstraction in PGHS-1 was estimated to be 1.9-2.3 using rapid freeze-quench EPR kinetic analysis of anaerobic reactions and computer modeling to a mechanism that includes a slow formation of a pentadienyl AA radical and a rapid equilibration of the AA radical with a tyrosyl radical, NS1c. The observation of similar values for steady-state and pre-steady state KIEs suggests that hydrogen abstraction is a rate-limiting step in cyclooxygenase catalysis. The large difference of the observed KIE from that of plant lipoxygenases indicates that PGHS and lipoxygenases have very different mechanisms of hydrogen transfer.