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• W2019703377 abstract "The Michaelis constant (Km) and Vmas (E0kcat) values for two mutant sets of enzymes were studied from the viewpoint of their definition in a rapid equilibrium reaction model and in a steady state reaction model. The “AMP set enzyme” had a mutation at the AMP-binding site (Y95F, V67I, and V67I/L76V), and the “ATP set enzyme” had a mutation at a possible ATP-binding region (Y32F, Y34F, and Y32A/Y34A). Reaction rate constants obtained using steady state model analysis explained discrepancies found by the rapid equilibrium model analysis. (i) The unchanged number of bound AMPs for Y95F and the wild type despite the markedly increased Km values for AMP of the AMP set of enzymes was explained by alteration of the rate constants of the AMP step (k+2, k–2) to retain the ratio k+2/k–2. (ii) A 100 times weakened selectivity of ATP for Y34F in contrast to no marked changes in Km values for both ATP and AMP for the ATP set of enzymes was explained by the alteration of the rate constants of the ATP steps. A similar alteration of the Km and kcat values of these enzymes resulted from distinctive alterations of their rate constants. The pattern of alteration was highly suggestive. The most interesting finding was that the rate constants that decided the Km and kcat values were replaced by the mutation, and the simple relationships between Km, kcat, and the rate constants of Km1=k+1/k-1 and kcat = kf were not valid. The nature of the Km and kcat alterations was discussed. The Michaelis constant (Km) and Vmas (E0kcat) values for two mutant sets of enzymes were studied from the viewpoint of their definition in a rapid equilibrium reaction model and in a steady state reaction model. The “AMP set enzyme” had a mutation at the AMP-binding site (Y95F, V67I, and V67I/L76V), and the “ATP set enzyme” had a mutation at a possible ATP-binding region (Y32F, Y34F, and Y32A/Y34A). Reaction rate constants obtained using steady state model analysis explained discrepancies found by the rapid equilibrium model analysis. (i) The unchanged number of bound AMPs for Y95F and the wild type despite the markedly increased Km values for AMP of the AMP set of enzymes was explained by alteration of the rate constants of the AMP step (k+2, k–2) to retain the ratio k+2/k–2. (ii) A 100 times weakened selectivity of ATP for Y34F in contrast to no marked changes in Km values for both ATP and AMP for the ATP set of enzymes was explained by the alteration of the rate constants of the ATP steps. A similar alteration of the Km and kcat values of these enzymes resulted from distinctive alterations of their rate constants. The pattern of alteration was highly suggestive. The most interesting finding was that the rate constants that decided the Km and kcat values were replaced by the mutation, and the simple relationships between Km, kcat, and the rate constants of Km1=k+1/k-1 and kcat = kf were not valid. The nature of the Km and kcat alterations was discussed. Adenylate kinase (ADK) 1The abbreviation used is: ADK, adenylate kinase. 1The abbreviation used is: ADK, adenylate kinase. is a two-substrate enzyme, ATP and AMP, and acts by a random Bi Bi mechanism. One Vmax and four Km values can be determined for ADK reactions for many mutant enzyme reactions but do not give consistent explanations of the relationship between mutational cause and effects (1Yan H. Dahnke T. Zhou B. Nakazawa A. Tsai M.D. Biochemistry. 1990; 29: 10956-10964Crossref PubMed Scopus (37) Google Scholar, 2Tian G. Yan H. Jiang R.T. Kishi F. Nakazawa A. Tsai M.D. Biochemistry. 1990; 29: 4296-4304Crossref PubMed Scopus (57) Google Scholar, 3Tsai M.D. Yan H. Biochemistry. 1991; 30: 6806-6818Crossref PubMed Scopus (108) Google Scholar, 4Ayabe T. Park S.K. Nagahama H. Maruyama H. Sumida M. Takenaka H. Takenaka O. Onitsuka T. Hamada M. Biochem. Mol. Biol. Int. 1998; 46: 673-680PubMed Google Scholar, 5Ayabe T. Park S.K. Takenaka H. Takenaka O. Maruyama H. Sumida M. Onitsuka T. Hamada M. J. Biochem. (Tokyo). 2000; 128: 181-187Crossref PubMed Scopus (6) Google Scholar).These analyses are based on rapid equilibrium assumptions of steady state kinetics, which equates Km and kcat values with a dissociation constant of a substrate-binding step and a rate constant of a rate-limiting step, respectively. By using this assumption, enzyme reactions must fulfill conditions that are markedly restrictive; the minimum condition is the presence of a rate-limiting step and a high value of a rate constant corresponding to Km values. Whether the required conditions by using a rapid equilibrium assumption are fulfilled is not clear. Therefore, by using an analysis based on the work by Briggs and Haldane (6Briggs G.E. Haldane J.B.S. Biochem. J. 1925; 19: 338-339Crossref PubMed Google Scholar), the assumption of the steady state condition is disputed. The analysis of this study has no restriction on rate constants and is more generally applicable, so the analysis of the ADK mutant reactions by the two methods and a comparison of the results will give a consistent view of Km and kcat values, and their alteration with mutations as far as the problem is with the rate constants.In this study, two groups of mutant enzymes were used for the following reasons. ADK catalyzes the transfer of the γ-phosphate group of ATP to α-phosphate of AMP or vice versa. Two nucleotide-binding sites, one for AMP and the other for ATP, have been assigned on the basis of three-dimensional structures found by using x-ray crystallography (7Schultz G.E. Elzinga M. Marx F. Schirmer R.H. Nature. 1974; 250: 120-123Crossref PubMed Scopus (218) Google Scholar, 8Dreusicke D. Karplus P.A. Schulz G.E. J. Mol. Biol. 1988; 199: 359-371Crossref PubMed Scopus (220) Google Scholar, 9Diederichs K. Schulz G.E. Biochemistry. 1990; 29: 8138-8144Crossref PubMed Scopus (46) Google Scholar, 10Stehle T. Schulz G.E. J. Mol. Biol. 1990; 211: 249-254Crossref PubMed Scopus (67) Google Scholar, 11Berry M.B. Meador B. Bilderback T. Liang P. Glaser M. Phillips Jr., G.N. Proteins Struct. Funct. Genet. 1994; 19: 183-198Crossref PubMed Scopus (135) Google Scholar), nuclear magnetic resonance studies (12Fry D.C. Kuby S.A. Mildvan A.S. Biochemistry. 1985; 24: 4680-4689Crossref PubMed Scopus (118) Google Scholar, 13Fry D.C. Kuby S.A. Mildvan A.S. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 907-911Crossref PubMed Scopus (386) Google Scholar), and by using other techniques (3Tsai M.D. Yan H. Biochemistry. 1991; 30: 6806-6818Crossref PubMed Scopus (108) Google Scholar, 14Kim H.J. Nishikawa S. Tokutomi Y. Tanaka H. Hamada M. Kuby S.A. Uesugi S. Biochemistry. 1990; 29: 1107-1111Crossref PubMed Scopus (38) Google Scholar, 15Liang P. Phillips G.N. Jr. & Glaser M. Proteins Struct. Funct. Genet. 1991; 9: 28-36Crossref PubMed Scopus (31) Google Scholar, 16Okajima T. Tanizawa K. Fukui T. J. Biochem. (Tokyo). 1993; 114: 627-633Crossref PubMed Scopus (16) Google Scholar). The assigned site for AMP is near Tyr-95, and the ATP site is assigned near Arg-128 of yeast ADK (17Müller C.W. Schulz G.E. J. Mol. Biol. 1992; 224: 159-177Crossref PubMed Scopus (427) Google Scholar, 18Abele U. Schulz G.E. Protein Sci. 1995; 4: 1262-1271Crossref PubMed Scopus (129) Google Scholar). Type I ADK, including porcine muscle-type enzymes, has no such site corresponding to Arg-128 in the yeast enzyme. Thus, the assignment of the ATP-binding site in type I ADK is an issue to be clarified. As with many enzymes (19Bedouelle H. Carter P. Waye M.M. Winter G. Lowe D.M. Wilkinson A.J. Fersht A.R. Biochimie (Paris). 1985; 67: 737-743Crossref PubMed Scopus (2) Google Scholar, 20Fersht A.R. Leatherbarrow R.J. Oxender D.L. Fox C.F. Protein Engineering. Alan R. Liss, Inc., New York1986: 269-278Google Scholar, 21Fersht A. Leatherbarrow R.J. Wells T.N. Biochemistry. 1987; 26: 6030-6038Crossref PubMed Scopus (135) Google Scholar, 22Fersht A.R. Biochemistry. 1988; 27: 1577-1580Crossref PubMed Scopus (169) Google Scholar), a mutant enzyme in which residues are replaced by other residues is an effective tool to identify the role of a residue in enzymatic functions. To explore the binding processes of ATP and AMP, two sets of mutants for the two binding sites were chosen. 1) For an AMP site mutant set (Y95F, V67I, and V67I/L76V), Tyr-95 is replaced by Phe, because Tyr-95 has been assumed to participate in the binding of one of the substrates, and Leu-76 and Val-67 are near the active site Tyr-95. 2) For a possible ATP-binding region mutant set (Y32F, Y34F, and Y32A/Y34A), Tyr-32 and Tyr-34 are replaced by Phe or both by Ala, because these Tyr are in the cleft where the hydrophobic substance binds, such as the ATP analogue 1-anilino-8-naphthalene sulfonate (23Radda G.K. Samadi D.R. Current Topics in Bioenergetics. 4. Academic Press, New York1971: 81-126Google Scholar, 24Augustin J. Hasselbach W. Eur. J. Biochem. 1973; 39: 75-84Crossref PubMed Scopus (13) Google Scholar, 25Einarsson R. Eklund H. Zepperzauer E. Boiwe T. Branden C.-I. Eur. J. Biochem. 1974; 49: 41-47Crossref PubMed Scopus (51) Google Scholar). The ATP-binding site of this study is not the currently determined one but was chosen because the site was once suggested to be a binding site of AMP (26Pai E.F. Sachenheimer W. Schirmer R.H. Schulz G.E. J. Mol. Biol. 1977; 114: 37-45Crossref PubMed Scopus (240) Google Scholar) and also to be a site of ATP (12Fry D.C. Kuby S.A. Mildvan A.S. Biochemistry. 1985; 24: 4680-4689Crossref PubMed Scopus (118) Google Scholar, 13Fry D.C. Kuby S.A. Mildvan A.S. Proc. Natl. Acad. Sci. U. S. A. 1986; 83: 907-911Crossref PubMed Scopus (386) Google Scholar). If these residues participate in substrate binding, the kinetic behavior of the mutants would be different from the wild type enzyme and should be discriminated among kinetic parameters.The advantage of kinetic measurements is that the dynamic aspect of an enzyme molecule is given by kinetic parameters, and the events not included in its activity are automatically omitted. The importance of the linkage between dynamics and enzyme catalysis was indicated in a recent study of adenylate kinase (27Watz M.W. Thai V. Wildman K.H. Hadjipavlou G. Eisenmesser E.Z. Kern D. Nat. Struct. Mol. Biol. 2004; 11: 945-949Crossref PubMed Scopus (397) Google Scholar). Kinetic parameters should be those that can describe the dynamic aspects of the enzyme and not the static binding of substrates. The results of the analysis of the two mutant sets by using rapid equilibrium and steady state methods are discussed, and their comparison shows advantages and disadvantages of each method.EXPERIMENTAL PROCEDURESMaterials—The enzyme was ADK in porcine skeletal muscle obtained as a recombinant protein by expressing its cDNA. Enzymes for gene manipulation and deoxyribonucleotides were purchased from Toyobo Co. Ltd. and Takara Shuzo Co. Ltd. Substrate nucleotide species were purchased from Sigma and Roche Applied Science. All other chemicals were purchased from Wako Pure Chemicals Co. and Nacalai Tesque Inc.Preparation of Mutants—Site-directed mutagenesis was done by using the methods described previously (28Kunkel T.A. Proc. Natl. Acad. Sci. U. S. A. 1985; 82: 488-492Crossref PubMed Scopus (4886) Google Scholar, 29Roberts J.D. Zakour R.A. Methods Enzymol. 1987; 154: 367-382Crossref PubMed Scopus (4543) Google Scholar), with mutagenic primer DNAs TACGGCTTAACCCACC (16-mer) for the Y34F mutation, CAGAAGTTTGGCTACA (16-mer) for the Y32F mutation, and GTCCAGAAGGCCGGCGCCACCCACCT (26-mer) for the Y32A/Y34A mutations, and by using the method of Nakayama and Eckstein (30Nakayama K. Eckstein F. Nucleic Acids Res. 1986; 14: 9679-9698Crossref PubMed Scopus (420) Google Scholar) with primers GACGGCTTTCCCCGGG (16-mer), GCAGCTGATCCCACTGG (17-mer), and GGACATGGTTCGAGACG (17-mer) for Y95F, V67I, and L76V mutation, respectively. The primer DNAs were prepared by using high pressure liquid chromatography with a C18 reversed phase column on a 0.1–1 m KH2PO4 linear gradient system of 30% CH3CN solution and on 20% PAGE after 5′-phosphorylation.Alteration of the target nucleotide sequences was confirmed by DNA sequencing. Substitutions of amino acid residues were confirmed by amino acid composition analysis by using an automated amino acid analyzer (Beckman System 7300).Mutated ADK proteins were expressed in Escherichia coli JM109 using the pMK2 expression vector (31Hibino T. Misawa S. Wakiyama M. Maeda S. Yazaki K. Kumagai I. Ooi T. Miura K. J. Biotechnol. 1994; 32: 139-148Crossref PubMed Scopus (17) Google Scholar) at 37 °C for 36 h. For Y95F, V67I, and V67I/L76V mutants, preliminary cultivation was done at 20, 25, 30, and 37 °C at various cultivation periods from 18 to 72 h. The optimal temperature and period of cultivation were 25 °C and 36 h, respectively, for Y95F mutant ADK and 30 °C and 24 h, respectively, for V67I and V67I/L76V mutant ADKs. The expressed ADK was extracted, purified, and refolded as described previously (32Barzu O. Michelson S. FEBS Lett. 1983; 153: 280-284Crossref PubMed Scopus (59) Google Scholar). The expressed wild type and six mutant proteins, as inclusion bodies, were obtained as a single band protein by using SDS-PAGE (18%) analysis.CD and Protein Concentration Measurements—The CD of the enzyme solution having extinction A280 = 1.0 was recorded by using a CD spectrometer (Jasco J-100) with a 1-cm light path for 250–300 nm and a 0.2-mm light path for 200–250 nm wavelength region. The molar concentration of the enzyme solution was measured with the extinction coefficient of 1.16 × 104 m–1cm–1 for the wild type. Extinction coefficients for mutant enzymes were obtained as coefficients of the wild type value multiplied by the ratio of combined extinction coefficients of amino acid residues for mutant enzymes to that for the wild type.CD spectra of the 220 nm region of Y95F and the other mutant enzymes were the same as for the wild type (data not shown). CD spectra in the 280 nm region of Y95F and the other mutant proteins lacking Tyr were less negative than for the wild type, presumably due to the substitution of Tyr by Phe. Thus, conformations of mutants had no effect due to the replacement of every target amino acid residue in the mutant enzymes.Kinetic Measurements—Kinetic measurements were done as described previously (33Agarwal K.C. Miech R.P. Parks R.E. Methods Enzymol. 1979; 51: 483-490Crossref Scopus (98) Google Scholar) at pH 7.0 and 25 °C. Sets of concentrations of both ATP and AMP used as substrates were as follows: 100, 150, 200, 300, 500, 800, 1000, 2000, and 5000 (μm) for the reactions of wild type enzyme; 50, 100, 150, 250, 500, 1000, and 4000 (μm) for the reactions of Y34F, Y95F, V67I, and V67I/L76V; 50, 100, 150, 200, 300, 400, 500, 700, 1000, and 4000 (μm) for Y32A/Y34A; 50, 100, 200, 300, 500, 700, 1000, 2000, and 5000 (μm) for the reactions of Y95F. Fig. 1 shows initial reaction rates but omits data that showed inhibitory effects by ATP or AMP. These reaction rates were further analyzed by using the random Bi Bi model with rapid equilibrium or steady state assumptions. For measurements of substrate specificity, reactions of many kinds of nucleotide substrates, which are described under “Results,” were analyzed by high pressure liquid chromatography with a DEAE column (DEAE-2SW, TOSOH) in a 0.1-0.8 m NaH2PO4 (pH 3.0, 30% CH3CN) gradient buffer system. The experimental conditions and composition of the reaction mixture were the same as for the kinetic measurements above (34Hamada M. Kuby S.A. Arch. Biochem. Biophys. 1978; 190: 772-792Crossref PubMed Scopus (34) Google Scholar), except for omitting coupling enzymes and their substrates.Applied Reaction Models and Rate Equations—Fig. 1 shows a schematic representation of the random Bi Bi model of this enzyme reaction. In the case of the rapid equilibrium model based on the rapid equilibrium assumption (35King E.L. Altman C. J. Phys. Chem. 1956; 60: 1375-1387Crossref Scopus (746) Google Scholar), the ratio k–n/k+n of the rate constants of the same step n in Fig. 1 are replaced by one Michaelis constant, Knm, and the rate constant for the chemical step, kf, is replaced by kcat. Each step is discriminated by a single decimal number, n, at the suffix of rate constants or the superfix of Michaelis constants. The rate equation of the rapid equilibrium model at a steady state is described by Equation 1 with four Michaelis constants and one Vmax, where SM and ST are the concentrations of AMP and ATP, respectively, and Vmax is equal to kcat [E]0. [E]0 is omitted by making [E]0 unity. 1v=Km1Km3STSM+Km4ST+Km3SM+11Vm(Eq. 1) In the case of the steady state model based on the concept of steady state conditions (35King E.L. Altman C. J. Phys. Chem. 1956; 60: 1375-1387Crossref Scopus (746) Google Scholar), the enzyme species change to other species with rate constant k+n, k–n, or kf (Fig. 1). The condition of the steady state is written as shown in Equation 2, ∂e→/∂t=Ae→≡0→(Eq. 2) where e→ is an enzyme species vector t([E],[ET],[EM],[ETM]), 0→ is a zero vector, and A is the transformation matrix of the reaction described in Fig. 1. A≡-k+1-k+2k-1k-2kfk+1-k-1-k+3k-3k+2-k-2-k+4k-4k+3k+4-kf-k-3-k-4Parameter representation is the same as shown in Fig. 1. Because each element is a rate, the secondary rate constants, k+n, contain an appropriate substrate concentration to give a rate when multiplied by the enzyme concentration (i.e. k+1 ≡ k+1 × ST), but ST and SM are not described explicitly for simplicity of expression in this section.Each row of matrix A calculates a change in the amount of enzyme species during unit time, i.e. the top row calculates a change in free enzyme species as shown in Equation 3. ∂[E]/∂t=-(k+1+k+2)[E]+k-1[ET]+k-2[EM]+kf[ETM](Eq. 3) By replacing an arbitrary row of matrix A by a unit vector and replacing a corresponding element of the zero vector by [E]0, which establishes conservation of the enzyme molecules [E]0 = [E] + [ET] + [EM]+ [ETM], the equation is transformed into A'e→=E→0, where A′ is the matrix replaced by a kth (arbitrary) row, and E→0 is a modified zero vector of which the kth element is [E]0, and the other elements are zero. The enzyme species vector is calculated as e→=A'-1E→0 and the concentration of ternary complex species is obtained by the lth element of e→. So the reaction rate equation in the steady state model at a steady state (35King E.L. Altman C. J. Phys. Chem. 1956; 60: 1375-1387Crossref Scopus (746) Google Scholar, 36King E.L. J. Phys. Chem. 1956; 60: 1378-1384Crossref Scopus (27) Google Scholar) is derived as shown in Equation 4, v=kfdettAkl'¯detA'(Eq. 4) where detA′ is the determinant of matrix A′, and tA′kl is the cofactor matrix of (l,k) element of transposed A′; k is the number of the row replaced by a unit vector, and l is the number of enzyme species with which the reaction rate is expressed as kf[El]. (l is 4 in the model of this study.) [E]0 is omitted from the equation by making its value unity.The calculation of every kinetic constant was done as described previously (34Hamada M. Kuby S.A. Arch. Biochem. Biophys. 1978; 190: 772-792Crossref PubMed Scopus (34) Google Scholar) for a rapid equilibrium model, and by the least square minimization of the function F = Σ(vo – vc)2 for a steady flow model, where vo is an experimentally observed reaction rate; vc is a rate calculated by Equation 4, and F is a summation of the square of the differences between them for all experimental points (36King E.L. J. Phys. Chem. 1956; 60: 1378-1384Crossref Scopus (27) Google Scholar). For the minimization, the hybrid method of Powell (37Powell M.J.D. Computer J. 1964; 7: 155-162Crossref Google Scholar, 38Powell M.J.D. Rabinowitz P. A Hybrid Method for Nonlinear Equations, Numerical Methods for Nonlinear Algebraic Equations. 115–161, Gordon and Breach Science Publishers, Inc., New York1970: 87-114Google Scholar) was used. Correction vectors for the Gauss-Newton algorithm and for the steepest direction were calculated by using the Jacobian matrix derived from the analytically coded δ(detA)/δk. The program was allowed to run until the correction vector decreased to a threshold value. A weighting function that decreases with increasing reaction rate was also used for the function F and the Jacobian matrix.Equilibrium Dialysis—Experiments of equilibrium binding for the Y95F mutant and wild type enzymes were done by using a handmade equilibrium dialysis instrument with 200-μl chambers. Each chamber was divided into two 100-μl parts by a dialysis membrane (Spectrum Pore 6, cut-off molecular weight 10,000; Spectrum Medical Industries, Inc.) and was rotated at 10 rpm. Chambers on one side contained weak radiolabeled ATP or AMP (370 MBq/mmol) at one of the following concentrations: 50, 100, 200, 300, 400, and 500 (μm); the chambers on the other side contained the nucleotide and enzyme (100 nmol in each chamber). Substrate binding to the Y34F mutant was checked at 300 μm ATP and AMP. The amount of enzymes in the chambers was estimated as for the CD measurement. The equilibration was established by overnight dialysis at 25 °C. The difference in radioactivity between the two sides was calculated by using a liquid scintillation counter (LKB model 2000), and the number of bound nucleotides was estimated without including the enzyme volume in the calculation.RESULTSPreparation of Enzymes—The amino acid compositions of purified enzymes indicated a corresponding alteration to every amino acid residue in the mutant proteins.Enzymatic Reactions—Profiles of the reaction rates for fixed AMP concentrations and increasing ATP concentrations were divided into two regions based on critical ATP concentrations at which concentration the reaction rate was largest for the fixed AMP concentration. In the ATP concentration range lower than the critical value, 1/v increased with 1/[ATP] linearly (Fig. 2b), but in the concentration range higher than the critical value, 1/v increased with increase in [ATP], indicating inhibition effects. An apparent Ki was calculated for this inhibition as the ATP concentration at which the reaction rate was half the largest value. The same profiles were obtained for all enzymes used in this study. Table I lists the critical ATP concentration and apparent values of Ki for the wild type and other mutant enzymes; these values were several hundred μm and a few mm, respectively. The reaction rates for the wild type and six other mutant enzymes in the lower concentration range than these critical values were plotted against the ATP concentration (Fig. 2, a and c–h); these reaction rates were used for further analysis.Fig. 2Linear part of catalytic reactions for wild type (a and b), Y32F(c), Y34F(d), Y32A/Y34A(e), Y95F(f), V67I(g), and V67I/L76V (h). AMP concentrations used were 100, 150, 200, 300, 500, 800, 1000, 2000, and 5000 μm from the bottom to the top, respectively, for the wild type-catalyzed reaction; 50, 100, 200, 300, 500, 1000, 2000, and 5000 μm for Y32F; 50, 100, 150, 250, 500, 1000, and 4000 μm for Y34F, Y95F, and V67I, V67I/L76V; 50, 100, 150, 200, 300, 500, 700, and 1000 μm for Y32A/Y34A. Solid rate lines on the rate plots were calculated by Equation 4 with the obtained rate constants as described in the text following Equation 4 and Fig. 1 for each enzyme reaction. The rates of 5000 μm for AMP of the Y32F reaction are plotted with rectangles because they cross the rate line for AMP 2000 μm. b, double-reciprocal plots of the wild type reactions are shown in the same concentration range used in a. Linear dependence of inversed rates, slopes, and ordinate sections of their rate lines for inversed ATP, inversed AMP, and inversed AMP concentrations, respectively, shows that the random Bi Bi mechanism on rapid equilibrium assumption is applicable to this enzyme reaction.View Large Image Figure ViewerDownload Hi-res image Download (PPT)Table IKinetic parameters determined by the rapid equilibrium modelEnzymeKm1Km2Km3Km4kcat/s-1ATPaATP is a critical ATP concentration above which the inhibition dominates in the ADK reaction. Ki is the inhibition constant obtained as a value that gives the half of the observed maximum catalytic rate above the critical ATP concentration at 200 μm AMP.KiμmμmμmμmμmμmWild type1002504001501.83E + 03500800Y32F704007001201.17E + 025001000Y34F1805405001706.00E + 015001000Y32A/Y34A1404708002001.55E + 008001500Y95F290500bThe value cannot be calculated exactly because the ordinate intersections of α(M) and β(M) were negative or zero within experimental error. Thus, values of α and β are estimated for 1/[AMP] first, and then slope and intersections of α and β as a function of 1/[ATP] are determined.>6500bThe value cannot be calculated exactly because the ordinate intersections of α(M) and β(M) were negative or zero within experimental error. Thus, values of α and β are estimated for 1/[AMP] first, and then slope and intersections of α and β as a function of 1/[ATP] are determined.800bThe value cannot be calculated exactly because the ordinate intersections of α(M) and β(M) were negative or zero within experimental error. Thus, values of α and β are estimated for 1/[AMP] first, and then slope and intersections of α and β as a function of 1/[ATP] are determined.8.47E + 0110002000V67I250120016001406.18E + 0010002200V67I/L76V13068048009003.11E + 0110001800a ATP is a critical ATP concentration above which the inhibition dominates in the ADK reaction. Ki is the inhibition constant obtained as a value that gives the half of the observed maximum catalytic rate above the critical ATP concentration at 200 μm AMP.b The value cannot be calculated exactly because the ordinate intersections of α(M) and β(M) were negative or zero within experimental error. Thus, values of α and β are estimated for 1/[AMP] first, and then slope and intersections of α and β as a function of 1/[ATP] are determined. Open table in a new tab Kinetic Behavior with the Random Bi-Bi Model Using the Rapid Equilibrium Assumption—The rate equation by the rapid equilibrium model (Equation 1) was simplified as shown in Equation 5. 1/v=αSMST+βSM(Eq. 5) By comparing Equation 5 with Equation 1, slope αSM (apparent Km/Vmax) and intercept βSM (apparent 1/Vmax) of the rate equation were written as shown in Equation 6 and Equation 7, respectively. αSM=(Km1Km3/SM+Km4)/Vmax(Eq. 6) βSM=(Km3/SM+1)/Vmax(Eq. 7) For the rapid equilibrium model, these two parameters were calculated by using the reaction rates of increasing ATP concentration from 50 μm to 1 mm ATP and fixed AMP concentrations for wild type, Y32F, Y34F, Y32A/Y34A, Y95F, V67I, and V67I/L76V mutant enzyme reactions. Then αSM and βSM for increasing ATP were plotted against 1/[AMP] for these seven enzyme reactions (data not shown). Because all plots, including the wild type, lie on linear lines, the rapid equilibrium model was applicable in the concentration ranges used here despite modification of the respective sites, and Kmn and Vmax values were calculated from the slopes and intercepts of αSM and βSM plots by using Equations 6 and 7. Km2, which is not in Equations 6 and 7, was calculated using the relation Km1Km3=Km2Km4, which represents an identity of two states of enzyme species bound by ATP and AMP produced by two different reaction pathways.Table I lists the calculated kinetic parameters. Km values of Y32F, Y34F, and Y32A/Y34A mutant enzymes for ATP ( Km1 and Km4) were about one, two, and two times, respectively, larger than for the wild type. The Km values for AMP ( Km2 and Km3) of these ATP site mutant enzymes were about one to two times larger than for the wild type. Among them Km3 of 800 μm for the Y32A/Y34A mutant was the largest. The catalytic rates were from 1.8 × 10–3 s–1 for the wild type to 1.6 × 100 s–1 for the Y32A/Y34A mutant enzyme, i.e. the rate constant of Y32A/Y34A was about 10–3 times that of the wild type enzyme. For Y95F, only a few parameters were derived because the intersections of the plots of αSM against 1/[AMP] were negative or zero within experimental error, and therefore no reasonable values were obtained for Km2. The intercept of βSM against 1/[AMP] was positive but very small for the Y95F mutant enzyme and was therefore assigned as zero. Accordingly, Km2 for Y95F was estimated as 6.5 mm from the slope of αST and the intercept of βST, using the rate equation of the rapid equilibrium model. Y95F, V67I, and V67I/L76V, the mutant enzymes near the AMP site, had markedly larger values of Km for AMP ( Km2 and Km3) (Table I), but values of Km for ATP did not change appreciably. In particular, Y95F showed the most marked change in Km values for AMP, indicating that Tyr-95 participates directly in the AMP site in ADK. These results, together with the increase in Ki for ATP, imply that Tyr-95, Val-67, and Leu-76 have inhibitory roles in addition to being a binding site for AMP.Specificity of Substrates—To analyze the specificity of the enzyme reaction for several kinds of substrate nucleotides, double-reciprocal plots of initial velocities against the inverse of a substrate concentration were made for the wild type, Y32F, Y34F and Y32A/Y34A (Fig. 3, a–d, respectively). These plots were linear for many kinds of nucleotide species and for all applied enzyme reactions, except for CMP of the wild type (Fig. 3a). The inverse of the reaction rate for the wild type enzyme with a substrate set of ATP and CMP depended on the square of 1/[CMP], but for other mutant enzymes on the same substrate set it was linearly dependent on 1/[CMP]. Nucleotide species (UTP, GTP, and CTP for Y34F and CMP for Y32A/Y34A) showed an inhibitory effect (i.e" @default.
• W2019703377 created "2016-06-24" @default.
• W2019703377 creator A5016127967 @default.
• W2019703377 date "2005-09-01" @default.
• W2019703377 modified "2023-09-30" @default.
• W2019703377 title "Nonfixed Relationship of the Michaelis Constant and Maximum Velocity with Their Corresponding Rate Constants" @default.
• W2019703377 cites W1499075537 @default.
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