Kinetic and thermodynamic control of ATP synthesis by sarcoplasmic reticulum adenosinetriphosphatase

Several experimental parameters, critical to the analysis of ATP synthesis by sarcoplasmic reticulum ATPase, were determined experimentally. 1) The phosphorylated enzyme intermediate obtained with acetylphosphate in the presence of a Ca2+ gradient was shown to be entirely ADP sensitive but quite stable in the absence of added ADP. On the contrary, the phosphoenzyme obtained with ATP is unstable due to the ADP formed during the phosphoryl transfer reaction. For this reason, addition of ADP to [32P]phosphoenzyme obtained with [32P]acetylphosphate provides the simplest conditions for kinetic studies on [gamma-32P]ATP synthesis. 2) The dissociation rate constant of newly synthesized ATP (in the reverse direction of the ATPase cycle) was measured experimentally and found to be 16 s-1. This value agrees well with the dissociation rate constant determined for adenyl-5'-yl imidodiphosphate bound to this enzyme. 3) ATP synthesis observed in the absence of a Ca2+ gradient was shown to be a kinetic overshoot due to ligand-induced perturbation of a limited number of partial reactions and occurring before equilibration of the entire system. Most of the ATP formed under these conditions was subsequently hydrolyzed as the overall equilibrium was reached. 4) Based on these and other (previously characterized) parameters, satisfactory simulations of single and multiple cycle ATP synthesis, in the presence and in the absence of a Ca2+ gradient, were obtained.     

Kinetics of interaction of adenosine diphosphate and adenosine triphosphate with adenosine triphosphatase of bovine heart submitochondrial particles.

The short preincubation of submitochondrial particles with low concentrations of ADP in the presence of Mg2+ results in a complete loss of their ATPase and inosine triphosphatase activities. Other nucleoside diphosphates (IDP and GDP) do not affect the ATPase activity. The ADP-inhibited ATPase can be activated in a time-dependent manner by treatment of submitochondrial particles with the enzyme converting ADP into ATP (phosphoenolpyruvate plus pyruvate kinase). The activaton is a first-order reaction with rate constant 0.2 min-1 at 25 degrees C. The rate constant of activation is increased in the presence of ATP up to 2 min-1, and this increase shows saturation kinetics with Km value equal to that for ATPase reaction itself (10(-4) M at 25 degrees C at pH 8.0). The experimental results obtained are consistent with the model where two alternative pathways of ADP dissociation from the inhibitory site of ATPase exist; one is spontaneous dissociation and the second is ATP-dependent dissociation through the formation of the ternary complex between ADP, the enzyme and ATP. ADP-induced inactivation and ATP-dependent activation of ATPase activity of submitochondrial particles is accompanied by the same directed change of their ability to catalyse the ATP-dependent reverse electron transport from succinate to NAD+. The possible implication of the model suggested is discussed in terms of functional role of the inhibitory high-affinity binding site for ADP in the mitochondrial ATPase.     

The kinetics of rabbit muscle pyruvate kinase. Initial-velocity, substrate- and product-inhibition and isotopic-exchange studies of the reverse reaction.

1. An assay, based on the transfer of label from [gamma-32P]ATP to [32P]phosphoenolpyruvate, suitable for a steady-state kinetic analysis of pyruvate kinase in the reverse direction (i.e. phosphoenolpyruvate synthesis), is described. 2. This assay was used in a kinetic investigation of the rabbit muscle enzyme including initial-rate and product-inhibition experiments, at a pH of 7.4 and constant concentrations of total K+ and free Mg2+. 3. These studies indicate that there is a random release of ADP and phosphoenolpyruvate from the enzyme and that there is a competitive substrate inhibition by ATP. Some of the results were suggestive that the rapid-equilibrium assumption, generally used for this enzyme was not valid. 4. Techniques were developed to measure the rate of isotopic exchange between all the substrate-product pairs. 5. By using these techniques the rates of isotopic exchange at chemical equilibrium were measured. The results indicate that this enzyme does not catalyse a truly rapid-equilibrium random mechanism, although in the forward reaction all initial-rate data obtained to date are consistent with this assumption.     

Mechanism of action of cAMP-dependent protein kinase. V. Free energy spectra

The catalytic subunit of cAMP-dependent protein kinase from pig brain was shown to catalyse an isotope exchange reaction ATP in equilibrium with ADP. The kinetic parameters of the exchange were determined. The enzyme can also use GTP as the donor substrate; phosphotransferase and "GTPase" reactions were investigated. Based on the kinetic data obtained in this and in the previous paper the free energy profiles of protein kinase catalysed reactions are discussed.     

Regulation of pyruvate dehydrogenase by fatty acid in isolated rat liver mitochondria.

The mechanism by which fatty acid addition leads to the inactivation of pyruvate dehydrogenase in intact rat liver mitochondria was investigated. In all cases the fatty acid octanoate was added to mitochondria oxidizing succinate. Addition of fatty acid caused an inactivation of pyruvate dehydrogenase in mitochondria incubated under State 3 conditions (glucose plus hexokinase), in uncoupled, oligomycin-treated mitochondria, and in rotenone-menadione-treated mitochondria, but not in uncoupled mitochondria or in mitochondria incubated under State 4 conditions. A number of metabolic conditions were found in which pyruvate dehydrogenase was inactivated concomitant with an elevation in the ATP/ADP ratio. This is consistent with the inverse relationship between the ATP/ADP ratio and the pyruvate dehydrogenase activity proposed by various laboratories. However, in several other metabolic conditions pyruvate dehydrogenase was inactivated while the ATP/ADP ratio either was unchanged or even decreased. This observation implies that there are likely other regulatory factors involved in the fatty acid-mediated inactivation of pyruvate dehydrogenase. Incubation conditions in State 3 were found in which the ATP/ADP and the acetyl-CoA/CoASH ratios remained constant and the pyruvate dehydrogenase activity was correlated inversely with the NADH/NAD+ ratio. Other State 3 conditions were found in which the ATP/ADP and the NADH/NAD+ ratios remained constant while the pyruvate dehydrogenase activity was correlated inversely with the acetyl-CoA/CoASH ratio. Further evidence supporting these experiments with intact mitochondria was the observation that the pyruvate dehydrogenase kinase activity of a mitochondrial extract was stimulated strongly by acetyl-CoA and was inhibited by NAD+ and CoASH. In contrast to acetyl-CoA, octanoyl-CoA inhibited the kinase activity. These results indicate that the inactivation of pyruvate dehydrogenase by fatty acid in isolated rat liver mitochondria may be mediated through effects of the NADH/NAD+ ratio and the acetyl-CoA/CoASH ratio on the interconversion of the active and inactive forms of the enzyme complex catalyzed by pyruvate dehydrogenase kinase and pyruvate dehydrogenase phosphatase.     

Steady-state kinetics of formaldehyde dehydrogenase and formate dehydrogenase from a methanol-utilizing yeast, Candida boidinii.

Initial velocity studies and product inhibition studies were conducted for the forward and reverse reactions of formaldehyde dehydrogenase (formaldehyde: NAD oxidoreductase, EC 1.2.1.1) isolated from a methanol-utilizing yeast Candida boidinii. The data were consistent with an ordered Bi-Bi mechanism for this reaction in which NAD+ is bound first to the enzyme and NADH released last. Kinetic studies indicated that the nucleoside phosphates ATP, ADP and AMP are competitive inhibitors with respect to NAD and noncompetitive inhibitors with respect to S-hydroxymethylglutathione. The inhibitions of the enzyme activity by ATP and ADP are greater at pH 6.0 and 6.5 than at neutral or alkaline pH values. The kinetic studies of formate dehydrogenase (formate:NAD oxidoreductase, EC 1.2.1.2) from the methanol grown C. boidinii suggested also an ordered Bi-Bi mechanism with NAD being the first substrate and NADH the last product. Formate dehydrogenase the last enzyme of the dissimilatory pathway of the methanol metabolism is also inhibited by adenosine phosphates. Since the intracellular concentrations of NADH and ATP are in the range of the Ki values for formaldehyde dehydrogenase and formate dehydrogenase the activities of these main enzymes of the dissimilatory pathway of methanol metabolism in this yeast may be regulated by these compounds.     

Measurement of microsomal ATPase activities: a comparison between the inorganic phosphate-release assay and the NADH-coupled enzyme assay

The specific activity of the Mg2+-ATPase and the (Ca2+ + Mg2+)-ATPase has been measured in a microsomal fraction from pig antral smooth muscle with the phosphate-release assay and the NADH-coupled enzyme assay, and the release of inorganic phosphate as a function of time is compared with the concomitant production of ADP. Both assays are found to overestimate the true Mg2+-ATPase activity. The adenylate kinase inhibitor P1,P5-di(adenosine-5'-)pentaphosphate (Ap5A) reduces the specific activity of the Mg2+-ATPase measured in the NADH-coupled enzyme assay to about half of its original value; however, it does not affect the specific activity of the Mg2+-ATPase in the Pi-release assay. The considerable overestimation of the Mg2+-ATPase activity in the NADH-coupled enzyme assay results from a combined action of an ATP pyrophosphatase (ATP in equilibrium AMP + PPi) and adenylate kinase activity contaminating the microsomes. The adenylate kinase activity in the microsomes catalyses the conversion of AMP formed by the ATP pyrophosphatase together with ATP into two ADP's. Also the phosphate-release assay is prone to an overestimation artefact because an inorganic pyrophosphatase will degrade the pyrophosphate and thus lead to additional Pi-production. Measurements of AMP and NAD+ production by HPLC confirmed our proposed reaction scheme. The same (Ca2+ + Mg2+)-ATPase activity is found in both assays, because the (Ca2+ + Mg2+)-ATPase activity is calculated from the difference in ATPase activity in the presence and absence of Ca2+, so that as a consequence the interfering activities are automatically subtracted.     

Negative modulation of Escherichia coli NAD kinase by NADPH and NADH.

NAD kinase was purified 93-fold from Escherichia coli. The enzyme was found to have a pH optimum of 7.2 and an apparent Km for NAD+, ATP, and Mg2+ of 1.9, 2.1, and 4.1 mM, respectively. Several compounds including quinolinic acid, nicotinic acid, nicotinamide, nicotinamide mononucleotide, AMP, ADP, and NADP+ did not affect NAD kinase activity. The enzyme was not affected by changes in the adenylate energy charge. In contrast, both NADH and NADPH were potent negative modulators of the enzyme, since their presence at micromolar concentrations resulted in a pronounced sigmoidal NAD+ saturation curve. In addition, the presence of a range of concentrations of the reduced nucleotides resulted in an increase of the Hill slope (nH) to 1.7 to 2.0 with NADH and to 1.8 to 2.1 with NADPH, suggesting that NAD kinase is an allosteric enzyme. These results indicate that NAD kinase activity is regulated by the availability of ATP, NAD+, and Mg2+ and, more significantly, by changes in the NADP+/NADPH and NAD+/NADH ratios. Thus, NAD kinase probably plays a role in the regulation of NADP turnover and pool size in E. coli.     

Purification and properties of squid mantle adenylate kinase. Role of NADH in control of the enzyme.

Adenylate kinase (ATP:AMP phosphotransferase, EC 2.7.4.3) from the mantle muscle of the squid, Loligo pealeii, was purified over 170-fold to homogeneity as judged by polyacrylamide and starch gel electrophoresis. The tissue contains a single isozyme of adenylate kinase, the enzyme from cytoplasmic and mitochondrial compartments (90 and 10% of total activity, respectively) being identical in physical and kinetic properties. Molecular weight was found to be 27,000 +/- 400. The enzyme shows a pH optimum of 8.2 in the forward (APD utilizing) and 7.4 in the reverse direction. Michaelis constants for ADP, ATP, and AMP are 0.70, 0.13, and 0.15 mM, respectively, with optimal Mg2+:adenylate ratios being 1:2 for ADP and 1:1 for ATP. A comparison of mass action ratios with the equilibrium constant indicated that squid adenylate kinase is held out of equilibrium in resting, but not active, muscle. A search for metabolic modulators of adenylate kinase revealed that NADH (Ki of 0.1 mM) was the only modulator which exerted a significant effect within its in vivo concentration range. The data presented indicate that NADH inhibition is the factor maintaining adenylate kinase in a nonequilibrium state in resting muscle and that release of this inhibition can serve to integrate adenylate kinase into the known scheme of intermediary metabolism in this tissue. A sharp drop in NADH levels at the onset on muscular work co-ordinates that activation of aerobic metabolism in this tissue and allows adenylate kinase to return to equilibrium function. At equilibrium, the enzyme can function to ampligy the concentration of AMP, a potent activator and deinhibitor of key glycolytic and Krebs cycle enzymes. The effect of modulators of adenylate kinase in preventing denaturation by heat or proteolysis revealed that NADH and substrates induced conformational changes in the enzyme which rendered it less susceptible to denaturation. The conformation state induced by NADH differed from that induced by substrate.     

31P NMR studies of the arginine kinase reaction. Equilibrium constants and exchange rates at stoichiometric enzyme concentration.

The arginine kinase reaction, the reversible transfer of the terminal phosphoryl group of ATP to L-arginine, has been investigated by the technique of 31P NMR at catalytic and stoichiometric concentrations of the enzyme. Three of the four substrates, ATP, ADP, and P-arginine produce easily distinguishable resonances in the 31P NMR spectrum, thus permitting a determination of equilibrium constants from the integrated areas of the resonances. From the linewidths, the exchange rates between reactants and products may be evaluated. At pH 7.25 and a temperature of 12 degrees, the equilibrium constant at catalytic enzyme concentration: Keq = [MgADP] [P-arginine]/[MgATP] [L-arginine], is found to be 0.10 +/- 0.02 and that at stoichiometric enzyme concentration: K'eq = [E-MgADP] [E-P-arginine]/[E-MgATP] [E-arginine] to be 1.56 +/- 0.5. Thus, as the enzyme concentration increased, the production of P-arginine is increasingly favored. From the NMR line shapes in the presence of excess enzyme, the rate of the single step, the transfer of the phosphoryl group on the surface of the enzyme is found to be 192 +/- 15 s-1 in the forward direction, i.e. from E-MgATP, and 154 +/- 15 s-1 in the reverse direction from E-P-argine. At 12 degrees and pH 7.25, the rate of the overall reaction in the forward direction was determined from kinetic measurements to be 19 s-1, an order of magnitude slower than the rate measured by NMR. It can, therefore, be concluded that the interconversion of substrates on the surface of the enzyme is not the rate-determining step in the overal reaction. From the equilibrium constants and other known data the dissociation constant of P-arginine from its enzyme complex can be determined and is found to be 100 muM.     

Ion-pair reverse-phase high-performance liquid chromatography. Application to the study of chicken liver NAD+ kinase

An ion-pair, reverse-phase, high-performance liquid chromatography method of assay was developed and used in a series of rate studies carried out with the enzyme chicken liver NAD+ kinase (ATP:NAD+ 2'-phosphotransferase, EC 2.7.1.23). Complete separation of all products and reactants was achieved within 15 min. ATP, NAD+, ADP, and NADP+ were monitored at 260 nm as they eluted from a Zorbax (Dupont) ODS (4.6 X 250-mm) column using an acetonitrile and 0.01 mM NH4(H2PO4)/0.005 M tetrabutylammonium phosphate (pH 7.0) gradient. The enzyme shows a marked preference for ATP (and dATP) and Mg2+ (or Mn2+) relative to other trinucleotides and divalent metal ions. It exhibits residual adenylate kinase and ATPase activity, but no NADH kinase activity. When polyphosphate replaced ATP, NADP+ production dropped to 2.5%. The addition of Ca2+ and/or bovine brain calmodulin did not significantly enhance the rate of NADP+ production.     

A kinetic study of the rat liver adenosine kinase reverse reaction

Adenosine kinase is an enzyme catalyzing the reaction: adenosine + ATP --> AMP + ADP. We studied some biochemical properties not hitherto investigated and demonstrated that the reaction can be easily reversed when coupled with adenosine deaminase, which transforms adenosine into inosine and ammonia. The overall reaction is: AMP + ADP --> ATP + inosine + NH(3). The exoergonic ADA reaction shifts the equilibrium and fills the energy gap necessary for synthesis of ATP. This reaction could be used by cells under particular conditions of energy deficiency and, together with myokinase activity, may help to restore physiological ATP levels.     

A Kinetic Study of the Rat Liver Adenosine Kinase Reverse Reaction

Adenosine kinase is an enzyme catalyzing the reaction: adenosine + ATP → AMP + ADP. We studied some biochemical properties not hitherto investigated and demonstrated that the reaction can be easily reversed when coupled with adenosine deaminase, which transforms adenosine into inosine and ammonia. The overall reaction is: AMP + ADP → ATP + inosine + NH₃. The exoergonic ADA reaction shifts the equilibrium and fills the energy gap necessary for synthesis of ATP. This reaction could be used by cells under particular conditions of energy deficiency and, together with myokinase activity, may help to restore physiological ATP levels.     

Properties of the thiamin triphosphate-synthesizing activity catalyzed by adenylate kinase (isoenzyme 1)

Adenylate kinase isozyme 1 (AK1) catalyzes thiamin triphosphate (TTP) formation from thiamin diphosphate (TDP) and ADP. The properties of the TTP-synthesizing activity of purified AK1 from porcine skeletal muscle were studied. The activity was found to require TDP, ADP, and Mg2+, and ATP was only 14.4% as active as ADP. Thiamin monophosphate (TMP) and thiamin were not utilized as substrates. ADP was specific as a phosphate donor; and CDP, UDP, and GDP supported TTP formation at rates less than 1% of that with ADP. Optimal pH and temperature for the TTP-synthesizing activity were 10.0 and 37 degrees C, respectively. The activity showed saturation kinetics for both substrates, and the Km values for TDP and ADP were calculated to be 0.83 mM and 43 microM, respectively. The enzyme catalyzed the reverse reaction (TTP + AMP----TDP + ADP) and stoichiometry between TTP and TDP was demonstrated in the forward and reverse reactions.     

Steady-state kinetics of skeletal muscle myosin light chain kinase indicate a strong down regulation by products

The kinetic behaviour of myosin light chain kinase isolated from skeletal muscle was studied under steady-state conditions using highly purified phosphorylatable light chains 2 (LC2). Forward reaction, product inhibition, and reverse reaction data indicate a sequential mechanism which can be interpreted best by a rapid-equilibrium random bi-bi reaction model. The forward reaction parameters are KATP = 150 microM, KLC2 = 5.3 microM, and Ki LC2 = 7.6 microM. The enzyme forms a dead-end complex with ADP and light chain 2; Kd, ADP of this complex is 50 microM. The forward reaction is also strongly inhibited by the phosphorylated light chain 2, Ki, LC2P is 1.5 microM. An equilibrium constant Keq of about 70 can be calculated from the kinetic parameters which agrees with the directly measured value of about 60. The role of the two inhibitory mechanisms in the regulation of the enzyme and of the high energy of the light chain phosphate bond as deducible from Keq are discussed.     

Kinetic control of mitochondrial ATP synthesis

In order to gain a clearer understanding of the kinetic control of ATP synthesis, rat liver and rat heart mitochondria were incubated under conditions that resulted in various rates of net ATP synthesis or ATP hydrolysis. Radiolabeled phosphate was included in the incubation media, and exchange rates between phosphate and ATP were determined as a function of rates of net ATP synthesis. Since ATP synthase is a highly reversible enzyme, the catalyzed reaction was expected to approach equilibrium especially at low rates of respiration and net ATP synthesis. Thus ADP + Pi V1 in equilibrium V2 ATP. If V1 is the rate of incorporation of radiolabeled phosphate into ATP, then net ATP synthesis (or hydrolysis) is V1 - V2. Since V1 and V1 - V2 could be measured, it was possible to calculate V2. V1 doubled in the transition from zero to maximal net ATP synthesis, whereas V2 decreased by over 90% when the rate of ATP synthesis was high due to high-media ADP. In heart mitochondria at 37 degrees C when respiration increased from 104 +/- 10 to 842 +/- 51 nanoatoms of O2/(min X mg), incorporation of [33P]phosphate into ATP (V1) increased from 1,100 +/- 60 to 1,978 +/- 121 and V2 decreased from 1,100 to near zero. These data demonstrate that mitochondrial ATP synthesis does not occur near equilibrium under physiological conditions and relatively high rates of ATP synthesis. A reaction with a high ratio of forward to reverse flux is obviously not near equilibrium. The important most sensitively controlled reaction appears to be V2, ATP hydrolysis. Possible mechanisms of kinetic control of V2 are discussed.(ABSTRACT TRUNCATED AT 250 WORDS)     

Requirement of medium ADP for the steady-state hydrolysis of ATP by the proton-translocating Paracoccus denitrificans Fo.F1-ATP synthase

Fo.F1-ATP synthase in inside-out coupled vesicles derived from Paracoccus denitrificans catalyzes Pi-dependent proton-translocating ATPase reaction if exposed to prior energization that relieves ADP.Mg2+ -induced inhibition (Zharova, T.V. and Vinogradov, A.D. (2004) J. Biol. Chem.,279, 12319-12324). Here we present evidence that the presence of medium ADP is required for the steady-state energetically self-sustained coupled ATP hydrolysis. The initial rapid ATPase activity is declined to a certain level if the reaction proceeds in the presence of the ADP-consuming, ATP-regenerating system (pyruvate kinase/phosphoenol pyruvate). The rate and extent of the enzyme de-activation are inversely proportional to the steady-state ADP concentration, which is altered by various amounts of pyruvate kinase at constant ATPase level. The half-maximal rate of stationary ATP hydrolysis is reached at an ADP concentration of 8 x 10(-6) M. The kinetic scheme is proposed explaining the requirement of the reaction products (ADP and Pi), the substrates of ATP synthesis, in the medium for proton-translocating ATP hydrolysis by P. denitrificans Fo.F1-ATP synthase.     

Adenylate kinase of plants. Properties of adenylate kinase of pea leaves]

The properties of adenylate kinase in 2 ADP in equilibrium ATP + AMP reaction have been studied. The dependence of the enzyme activity on medium pH, protein concentration, substrates, Mg++ ions, AMP, adenine and adenosine has been also investigated. pH optimum is found to be 8.5 for forward reaction and 8-9--for the reverse one. The Michaelis constants are as follows: for ADP--1.17-10(-4) M, for ATP--3.33-10(-4) M at 24 degrees C, in 50 mM tris-HCl pH 7.6. The optimal ratio, Mg++ ions/substrates (ADP, ATP + AMP), is 1:2. The chelates of adenine nucleotides with Mg++ ions are proved to be "true" reaction substrates. Unlike adenine and adenosine, the product of AMP reaction inhibits adenylate kinase activity. It is concluded that the properties of adenylate kinase in plants are similar to those of animals and humans (moikinase).     

A two-step synthesis of new water-soluble polymers of NAD+ and ADP. The biological properties of these polymers

Alkylation at the N-1 position of the adenine moiety of NAD+, ADP or ATP with 2,3-epoxypropyl acrylate, followed by polymerization with or without acrylamide at pH 8, gave water-soluble polymers of NAD+ and ADP where the alkyl chain was located at the exocyclic adenine C-6 amino group. Cofactor incorporations were good to high: 145-447 mumol NAD+/g polymer and 667 mumol ADP/g polymer. About 30% of the bound NAD+ could be reduced with rabbit muscle lactae dehydrogenase, yeast alcohol dehydrogenase and Bacillus subtilis alanine dehydrogenase; 84% of the bound ADP was phosphorylated with rabbit muscle creatine kinase. High cofactor activities were obtained with polymerized NAD+ with alcohol dehydrogenase as enzyme: the initial rate of NAD+ polymer reduction was 35-81% that of free NAD+. These values remained substantially high with agarose-immobilized alcohol dehydrogenase (15-36%) and should eventually allow their use in continuous enzymatic reactors. Enzymatic phosphorylation of ADP polymer by creatine kinase gave an ATP polymer with high biological activity: 480 mumol ATP/g polymer were transformed with yeast hexokinase.     

Kinetic mechanism of the type II calmodulin-dependent protein kinase: studies of the forward and reverse reactions and observation of apparent rapid-equilibrium ordered binding

The kinetic reaction mechanism of the type II calmodulin-dependent protein kinase was studied by using its constitutively active kinase domain. Lacking regulatory features, the catalytic domain simplified data collection, analysis, and interpretation. To further facilitate this study, a synthetic peptide was used as the kinase substrate. Initial velocity measurements of the forward reaction were consistent with a sequential mechanism. The patterns of product and dead-end inhibition studies best fit an ordered Bi Bi kinetic mechanism with ATP binding first to the enzyme, followed by binding of the peptide substrate. Initial-rate patterns of the reverse reaction of the kinase suggested a rapid-equilibrium mechanism with obligatory ordered binding of ADP prior to the phosphopeptide substrate; however, this apparent rapid-equilibrium ordered mechanism was contrary to the observed inhibition by the phosphopeptide which is not supposed to bind to the kinase in the absence of ADP. Inspection of product inhibition patterns of the phosphopeptide with both ATP and peptide revealed that an ordered Bi Bi mechanism can show initial-rate patterns of a rapid-equilibrium ordered system when a Michaelis constant for phosphopeptide, Kip, is large relative to the concentration of phosphopeptide used. Thus, the results of this study show an ordered Bi Bi mechanism with nucleotide binding first in both directions of the kinase reaction. All the kinetic constants in the forward and reverse directions and the Keq of the kinase reaction are reported herein. To provide theoretical bases and diagnostic aid for mechanisms that can give rise to typical rapid-equilibrium ordered kinetic patterns, a discussion on various sequential cases is presented in the Appendix.