Enzymes transient state kinetics

Kinetic studies involving enzymes can principally be classified into steady and transient state kinetics. In tlie former, tlie enzyme concentration is much lower tlian that of tlie substrate in tlie latter much higher enzyme concentration is used to allow detection of reaction intennediates. In steady state kinetics, the high efficiency of enzymes as a catalyst implies that very low concentrations are adequate to enable reactions to proceed at measurable rates (i.e., reaction times of a few seconds or more). Typical enzyme concentrations are in the range of 10 M to 10 ], while substrate concentrations usually exceed lO M. Consequently, tlie concentrations of enzyme-substrate intermediates are low witli respect to tlie total substrate (reactant) concentrations, even when tlie enzyme is fully saturated. The reaction is considered to be in a steady state after a very short induction period, which greatly simplifies the rate laws. 

This scheme accounts for the steady-state and transient-state kinetics of the enzyme under normal conditions.1343,1371,1442... 

In disagreement with the above indications was the finding of Aldridge et al. (146) that for enzyme which was phosphorylated at pH 5.5 with inorganic phosphate and rapidly mixed with buffer at pH 8.4, the rate of dephosphorylation was twice as fast as the turnover of the enzyme at pH 8.0. Also, transient state kinetic studies by Femley and Walker (99, 110) showed a rapid release (burst) of phenol followed by a steady state release of phenol, only at pH < 7. Thus, these data would seem to indicate that at pH >7 the rate determining step is phosphorylation. 

EPSP synthase catalyzes the synthesis of EPSP by an addition-elimination reaction through the tetrahedral intermediate shown in Fig. 2a. This enzyme is on the shikimate pathway for synthesis of aromatic amino acids and is the target for the important herbicide, glyphosate, which is the active ingredient in Roundup (The Scotts Company EEC, Marysville, OH). Transient-state kinetic studies led to proof of this reaction mechanism by the observation and isolation of the tetrahedral intermediate. Moreover, quantification of the rates of formation and decay of the tetrahedral intermediate established that it was tmly an intermediate species on the pathway between the substrates (S3P and PEP) and products (EPSP and Pi) of the reaction. The chemistry of this reaction is interesting in that the enzyme must first catalyze the formation of the intermediate and then catalyze its breakdown, apparently with different requirements for catalysis. Quantification of the rates of each step of this reaction in the forward and reverse directions has afforded a complete description of the free-energy profile for the reaction and allows... 

Johnson KA. Transient-state kinetic analysis of enzyme reaction pathways. The Enzymes. 1992 XX 1-61. 

Carboxypeptidase A is one of the most intensely investigated zinc metalloenzymes. The enzyme as isolated contains 1 g-atom of zinc per protein molecular weight of 34,600. Removal of the metal atom either by dialysis at low pH or by treatment with chelating agents gives a totally inactive apoenzyme (46). Activity can be restored by readdition of zinc or one of a number of other di-valent metal ions (47). Through a combined use of chemical modification and transient state kinetic studies, it has been possible to determine the role of zinc in the catalysis of ester and peptide hydrolysis by this enzyme. 

Transient-State Kinetic Analysis of Enzyme Reaction Pathways... 

The kinetic analysis of an enzyme mechanism often begins by analysis in the steady state therefore, we first consider the conclusions that can be derived by steady-state analysis and examine how this information is used to design experiments to explore the enzyme reaction kinetics in the transient phase. It has often been stated that steady-state kinetic analysis cannot prove a reaction pathway, it can only eliminate alternate models from consideration (5). This is true because the data obtained in the steady state provide only indirect information to define the pathway. Because the steady-state parameters, kcat and K, are complex functions of all of the reactions occurring at the enzyme surface, individual reaction steps are buried within these terms and cannot be resolved. These limitations are overcome by examination of the reaction pathway by transient-state kinetic methods, wherein the enzyme is examined as a stoichiometric reactant, allowing individual steps in a pathway to be established by direct measurement. This is not to say that steady-state kinetic analysis is without merit rather, steady-state and transient-state kinetic studies complement one another and analysis in the steady state should be a prelude to the proper design and interpretation of experiments using transient-state kinetic methods. Two excellent chapters on steady-state methods have appeared in this series (6, 7) and they are highly recommended. 

Although steady-state kinetic methods cannot establish the complete enzyme reaction mechanism, they do provide the basis for designing the more direct experiments to establish the reaction sequence. The magnitude of kcm will establish the time over which a single enzyme turnover must be examined for example, a reaction occurring at 60 sec will complete a single turnover in approximately 70 msec (six half-lives). The term kcJKm allows calculation of the concentration of substrate (or enzyme if in excess over substrate) that is required to saturate the rate of substrate binding relative to the rate of the chemical reaction or product release. In addition, the steady-state kinetic parameters define the properties of the enzyme under multiple turnovers, and one must make sure that the kinetic properties measured in the first turnover mimic the steady-state kinetic parameters. Thus, steady-state and transient-state kinetic methods complement one another and both need to be applied to solve an enzyme reaction pathway. 

Perhaps the most difficult aspect of learning transient-state kinetic methods is that it is not possible to lay down a prescribed set of experiments to be performed in a given sequence to solve any mechanism. Rather, the sequence of experiments will be dictated by the details of the enzyme pathway, the relative rates of sequential steps, and the availability of signals for measurement of rates of reaction. The latter constraint applies mainly to stopped-flow methods, and less so for chemical-quench-flow methods provided that radiolabeled substrates can be synthesized. Therefore, 1 will describe the kinetic methods used to establish an enzyme reaction mechanism with emphasis on the direct measurement of the chemical reactions by rapid quenching methods. Stopped-flow methods are useful in instances in which optical signals provide an easy means to measure the rates of individual steps of the reaction. 

The use of pH variation and isotope effects in transient kinetics can be illustrated with a recent study on dihydrofolate reductase. Analysis by steady-state methods had indicated an apparent p/fa of 8.5 that was assigned to an active site aspartate residue required to stabilize the protonated state of the substrate (59). In addition, it was shown that there was an isotope effect on substitution of NADPD (the deuterated analog) for NADPH at high pH but not at low pH, below the apparent p/fa This somewhat puzzling finding was explained by transient-state kinetic analysis. Hydride transfer, the chemical reaction converting enzyme-bound NADPH and dihydrofolate to NAD+ and tetrahydrofolate, was shown to occur at a rate of approximately 1000 sec at low pH. The rate of reaction decreased with increasing pH with a of 6.5, a value more in line with expectations for an active site aspartate residue. As shown in Fig. 14, there was a threefold reduction in the rate of the chemical reaction with NADPD relative to NADPH. Thus direct measurement of the chemical reaction revealed the full isotope effect. 

This study has important lessons for enzyme kinetic analysis. The use of pH variation and examination of isotope elfects can be a powerful combination to explore the chemistry of enzyme-catalyzed reactions and to dissect the contributions of individual reaction steps to the net steady-state turnover (27). Examination of the effects of pH on each step of the reaction pathway could resolve the contributions of ionizable groups toward ground-state binding energy and transition-state stabilization. The use of isotope effects by transient-state kinetic methods is more limited than in the steady state due to the errors involved in comparing two rate measurements. In the steady state, the ratio method has allowed isotope effects of less than 1% to be measured accurately (8a, 58). By transient-state kinetics, one would require at least a 10-20% change in rate to demonstrate a convincing difference between two rate measurements in most instances. 

The application of transient kinetic methods to the solution of enzyme mechanisms has increased dramatically due to recent advances in instrumentation and in the overexpression and purification of new enzymes. Transient kinetics are becoming the method of choice for evaluation of site-directed enzyme mutants and for detailed questions regarding the relationships between protein structure and observable function. In conjunction with advances in methods of structural and genetic analyses, transient-state kinetic analysis forms the basis for what might be called the new enzymology. ... 

Duggleby, R. G. (1994). Analysis of progress curves for enzyme-catalyzed reactions application to unstable enzymes, coupled reactions, and transient state kinetics. Bkdhimica et Biophyska Acta (BBA) - General subjects, vol. 1205, no.2, (April 1994), pp. 268-274, ISSN 0304-4165... 

Pettersson, G. (1976). The transient-state kinetics of two substate enzyme systems operating by an ordered ternary complex mechanism. European Journal of Biochemistry, 69,273-8. 

Steady state kinetic measurements on an enzyme usually give only two pieces of kinetic data, the KM value, which may or may not be the dissociation constant of the enzyme-substrate complex, and the kcM value, which may be a microscopic rate constant but may also be a combination of the rate constants for several steps. The kineticist does have a few tricks that may be used on occasion to detect intermediates and even measure individual rate constants, but these are not general and depend on mechanistic interpretations. (Some examples of these methods will be discussed in Chapter 7.) In order to measure the rate constants of the individual steps on the reaction pathway and detect transient intermediates, it is necessary to measure the rate of approach to the steady state. It is during the time period in which the steady state is set up that the individual rate constants may be observed. 

Later, we shall discuss several examples of the successful application of transient kinetics to the solution of enzyme mechanisms (Chapter 7) and to protein folding (Chapters 18 and 19). Here, we briefly describe some of the strategies and tactics used by the kineticist to initiate a transient kinetic study. On many occasions, steady state kinetics and other studies have set kineticists a well-defined and specific question to answer. At other times, they just wish to study a particular system to gather information. In both cases there is no substitute for... 

The steady state and stopped-flow kinetic studies on the horse liver enzyme are now considered classic experiments. They have shown that the oxidation of alcohols is an ordered mechanism, with the coenzyme binding first and the dissociation of the enzyme-NADH complex being rate-determining.15,26,27 Both the transient state and steady state methods have detected that the initially formed enzyme-NAD+ complex isomerizes to a second complex 27,28 In the reverse reaction, the reduction of aromatic aldehydes involves rate-determining dissociation of the enzyme-alcohol complex,27,29 whereas the reduction of acetaldehyde is... 

The initial rate enzyme kinetics uses very low enzyme concentrations (e.g., 0.1 juM to 0.1 pM) to investigate the steady-state region of enzyme-catalyzed reactions. To investigate an enzymatic reaction before the steady state (i.e., transient state), special techniques known as transient kinetics (Eigen and Hammes, 1963) are employed. The student should consult chapters of kinetic texts (Hammes, 1982 Robert, 1977) on the topics. KinTekSim (http //www.kintek-corp.com/kintek-sim.htm) is the Windows version of KINSIM/FITSIM (Frieden, 1993) which analyzes and simulate enzyme-catalyzed reactions. 

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