Transient kinetics, enzyme reactions

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. 

There is almost no biochemical reaction in a cell that is not catalyzed by an enzyme. (An enzyme is a specialized protein that increases the flux of a biochemical reaction by facilitating a mechanism [or mechanisms] for the reaction to proceed more rapidly than it would without the enzyme.) While the concept of an enzyme-mediated kinetic mechanism for a biochemical reaction was introduced in the previous chapter, this chapter explores the action of enzymes in greater detail than we have seen so far. Specifically, catalytic cycles associated with enzyme mechanisms are examined non-equilibrium steady state and transient kinetics of enzyme-mediated reactions are studied an asymptotic analysis of the fast and slow timescales of the Michaelis-Menten mechanism is presented and the concepts of cooperativity and hysteresis in enzyme kinetics are introduced. 

Identification of radical 3 as a species that is present in the steady-state phase of the reaction does not prove that it is an intermediate—it could be a species that is peripheral to the real reaction mechanism. Proof that a species is an intermediate requires a demonstration that it is kinetically competent to participate in the mechanism. In the case of a metastable radical, the usual procedure is to conduct transient kinetic studies using a rapid mixing apparatus equipped to quench samples by spraying them into liquid isopentane. The frozen aqueous samples (snows) from the timed cold quenches are then packed into EPR tubes and analyzed spectroscopically. Simple mixing of enzyme with SAM and lysine followed by freeze-quenching on the millisecond time scale does not work because the activation by SAM takes about 5 s. However, a preliminary mix of enzyme with SAM and [2- C]lysine, aging of the solution for 5 s within the apparatus. 

Comprehensive kinetic analysis defines the mechanistic basis for enzyme specificity and efficiency in ways that can be directly related to enzyme structure. In this article, the rationale will be described for design and interpretation of experiments to define the pathway of enzyme-catalyzed reactions using transient kinetic methods. These principles will be illustrated with three examples of biologically important reactions, none of which could have been solved with steady-state kinetics alone. This article is by no means a comprehensive survey of this extensive field, but rather, selected examples from the author s laboratory will be used to illustrate the methods to provide a flavor for what is possible. 

Transient-kinetic techniques most often rely on the rapid mixing of reactants with enzyme to initiate the reaction. This mixing is essential so that all enzyme molecules start reaction in synchrony with one another therefore, the time dependence of the observable reactions dehnes the kinetics of interconversion of enzyme intermediate states. Because mixing requires a hnite amount of time, conventional methods are limited in their ability to measure very fast reactions. For example, a typical value for the dead time of a stopped-flow instrument is approximately 1 ms, which is because of the time it takes to hll the observation cell. Thus, reactions with a half-life of less than 1 ms (rate > 700 s ) are difficult to observe depending on the signal to noise... 

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

Even in systems where chemical stabilization is used, radicals detected in solution are usually transient. This makes quantitation more difficult in these systems than in ones where the paramagnetic species are kinetically stable. Of course, quantitation is extremely important in all radical systems. It will distinguish between situations in which a radical is an obligate intermediate in an enzyme reaction and one in which the radical is formed in a secondary reaction or side reaction of low efficiency. However, in most biological ESR to date few attempts have been made to distinguish between such possibilities. 

There are several reasons to work with dilute solutions of enzyme. First, there is the obvious practical issue of conserving what is often a precious supply of enzyme that has been obtained with some labor and cost. Second, dilution can aid in eliminating unwanted interactions, thereby linearizing the rate vs enzyme curve as described above. Finally, it may be difficult to make measurements of initial rates in steady state unless the enzyme preparation is sufficiently dilute. If too much substrate is converted in the time required to make the measurement, then one must slow the reaction, and this is typically done by reducing the amount of enzyme in the assay. Transient kinetic methods typically require the use of concentrated enzyme solutions. Hence, these methods are seldom used until after basic understanding of the reaction mechanism has been obtained through steady-state kinetic methods, and critical tests can be designed to elucidate further the mechanism by transient kinetic methods. 

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 effect of pH variation and isotope (or elemental) substitution on reaction kinetics has been used in the steady state to explore the roles of active site acid/base catalysts and to attempt to define the nature of the transition state (8a, 8b, 58). Each of these methods also depends on the extent to which the rate of the chemical reaction is rate limiting in the steady state. If some other step limits the rate of steady-state turnover, then changes in the rate of the chemical reaction will be obscured. Use of pH variation or isotope effects in transient kinetic experiments has been useful in a number of cases (27), especially where it has been possible to examine directly the rate of the chemical reaction at the enzyme active site. In these cases, the effect of pH or isotope substitution can be interpreted directly in terms of the effect on a single 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. 

The model for a—j3 intersubunit communication indicates that it is the formation of the aminoacrylate species that leads to activation of the a reaction. When both serine and IGP are added simultaneously to the enzyme in a single enzyme turnover experiment, there is a lag in the cleavage of IGP that is a function of the reaction of serine to form the aminoacrylate species. Accordingly, amino acids other than serine that can undergo dehydration to form the aminoacrylate such as cysteine should serve as alternate substrates but should lead to a longer lag for the a subunit activation as determined by transient kinetic analysis. Cysteine does... 

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