Kinetics pre-steady-state

Enzyme reactions proceed, in general, via several intermediate states. A simple model incorporating multiple states is shown below enzyme and substrate assodate to form an enzyme-substrate complex, which undergoes a conformational change to ES before breaking down into enzyme and product 

Since the concentrations of all the intermediate states are constant under steady state conditions, all of these states can, at least formally, be incorporated into a single kinetic intermediate state. It follows that under steady state conditions, kinetic data can provide no information about the existence and kinetic properties of intermediate enzyme-substrate complexes. An understanding of the mechanism of an enzyme catalysed reaction needs information about these intermediate states, which is therefore usually obtained from kinetic studies before steady state has been established, usually by rapid reaction methods. Comprehensive coverage of the techniques and methods of analysis of pre-steady state kinetics is beyond the scope of this chapter, but we discuss here methods for analysing simple exponential processes. Two approaches are used. In the first, the observed signal S(t) is fitted to an exponential function of the following form  

A is the amplitude of the reaction and t the time constant, with the dimension of (time). If the kinetic mechanism of the observed process is known then rate constants can be derived from the time constant. For example, for a simple dissodation process, such as the back reaction in Eqn. 9.36 but without the forward assodation process, the rate constant (k2i) is given by 1/r. In this case, the value of r is independent of reactant concentration. 

If both forward and back reactions can take place, then 1/t depends on both k12 und k21. In the special case that the concentration of S is much greater than that of E, then the association rate constant is given by the equation l/r= k12cs + k21. Values of the two rate constants can be determined from the dependence of r on the substrate concentration cs a linear regression of 1/r vs. cs yields k12 as the slope of the plot and k21 as the Y intercept. For this analysis to be valid it is important to be sure that the observed reaction represents a single exponential process. If the reaction involves more than one exponential processes, then more complex models need to be considered, since the minimal number of reaction steps is given by the number of exponential processes. 

This method of analysis has several disadvantages, one of which is that intermediate parameters (r) are evaluated from the data which then form the basis for global fitting of the data consequently, the global fitting is not carried out on the raw data directly. A second drawback is that the predictive power of this analysis as regards mechanism is rather limited. 

The reaction rate depends cleanly on the concentration of only one chemical species and so is said to obey first order kinetics. In a similar way, if a reaction does depend upon 

Obviously Equations (8.82) and (8.83) apply to the reverse scenario in which pure B is allowed to convert to A starting from initial concentration [B]q and converging at hnal equilibrium concentration [B]eq, in other words the exact opposite of the scenario to which Equations (8.80) and (8.81) apply. Now let us return to pre-steady-state kinetic analysis  

The first information on the mechanism of catalysis in wild type pAPX was published in 1996 (Marquez et al., 1996). The kinetic data are consistent with a scheme in which the ferric enzyme is oxidized by two electrons to a so-called Compound I intermediate with eoncomitant release of one mole of water, followed by two successive single electron reductions of the intermediate by ascorbate (S) to regenerate ferric enzyme, Eqs. (3)n(5). 

1998a) (pH 7.0, 20 C)). Hence, reduction of Compound I is competitive with its formation, and Compound II reduction represents the rate-limiting step. In contrast, while the rate constant for reaction of CcP with H2O2 is also fast ( 1 = 4.5 10 (Erman, 1998)), the activity with ascorbate (Yone- 

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Fig. 9. The MoFe protein cycle of molybdenum nitrogenase. This cycle depicts a plausible sequence of events in the reduction of N2 to 2NH3 + H2. The scheme is based on well-characterized model chemistry (15, 105) and on the pre-steady-state kinetics of product formation by nitrogenase (102). The enzymic process has not been chsiracter-ized beyond M5 because the chemicals used to quench the reactions hydrolyze metal nitrides. As in Fig. 8, M represents an aji half of the MoFe protein. Subscripts 0-7 indicate the number of electrons trsmsferred to M from the Fe protein via the cycle of Fig. 8.

The mechanism of the first half-reaction has been studied by a combination of reductive titrations with CO and sodium dithionite and pre-steady-state kinetic studies by rapid freeze quench EPR spectroscopy (FQ-EPR) and stopped-flow kinetics 159). These combined studies have led to the following mechanism. The resting enzyme is assumed to have a metal-bound hydroxide nucleophile. Evidence for this species is based on the similarities between the pH dependence of the EPR spectrum of Cluster C and the for the for CO, deter-... 

Fig. 8. A model of bases on steady-state and pre-steady-state kinetic data. Ps indicate the two phosphorylation sites. Cl, CII and NIII refer to domains A, B, and C, respectively.

The determination of bisubstrate reaction mechanism is based on a combination of steady state and, possibly, pre-steady state kinetic studies. This can include determination of apparent substrate cooperativity, as described in Chapter 2, study of product and dead-end inhibiton patterns (Chapter 2), and attempts to identify... 

Happe, R. P., Roseboom, W. and Albracht, S. P. (1999) Pre-steady-state kinetics of the reactions of [NiFe]-hydrogenase from Chromatium vinosum with H2 and CO. Eur. J. Biochem., 259, 602-8. 

It has been known for some time that two molecules of 6,7-dimethyl-8-D-ribityllumazine dismute to form riboflavin. An intermediate pentacyclic compound has now been detected by pre-steady-state kinetic studies <2003JBC47700>. 

Pre-Steady State Kinetics Can Provide Evidence for Specific Reaction Steps... 

We have introduced kinetics as the primary method for studying the steps in an enzymatic reaction, and we have also outlined the limitations of the most common kinetic parameters in providing such information. The two most important experimental parameters obtained from steady-state kinetics are kcat and kcat/Km. Variation in kcat and kcat/Km with changes in pH or temperature can provide additional information about steps in a reaction pathway. In the case of bisubstrate reactions, steady-state kinetics can help determine whether a ternary complex is formed during the reaction (Fig. 6-14). A more complete picture generally requires more sophisticated kinetic methods that go beyond the scope of an introductory text. Here, we briefly introduce one of the most important kinetic approaches for studying reaction mechanisms, pre-steady state kinetics. 

The first evidence for a covalent acyl-enzyme intermediate came from a classic application of pre-steady state kinetics. In addition to its action on polypeptides,... 

FIGURE 6-19 Pre-steady state kinetic evidence for an acyl-enzyme intermediate. The hydrolysis of p-nitrophenylacetate by chymotrypsin is measured by release of p-nitrophenoi (a colored product). Initially, the reaction releases a rapid burst of p-nitrophenol nearly stoichiometric with the amount of enzyme present. This reflects the fast acylation phase of the reaction. The subsequent rate is slower, because enzyme turnover is limited by the rate of the slower deacylation phase. 

Methods for measurement An introduction to pre - steady state kinetics... 

As we discussed in Chapter 3, the KM for an enzymatic reaction is not always equal to the dissociation constant of the enzyme-substrate complex, but may be lower or higher depending on whether or not intermediates accumulate or Briggs-Haldane kinetics hold. Enzyme-substrate dissociation constants cannot be derived from steady state kinetics unless mechanistic assumptions are made or there is corroborative evidence. Pre-steady state kinetics are more powerful, since the chemical steps may often be separated from those for binding. 

It is often said that kinetics can never prove mechanisms but can only rule out alternatives. Although this is certainly true of steady state kinetics, in which the only measurements made are those of the rate of appearance of products or disappearance of reagents, it is not true of pre-steady state kinetics. If the intermediates on a reaction pathway are directly observed and their rates of formation and decay are measured, kinetics can prove a particular mechanism. This is the... 

The so-called Klenow fragment of DNA polymerase 1 of E. coli (Chapter 14, section Al) contains the 5 -3 -polymerization and the 3 -5 -exonuclease domains. Detailed pre-steady state kinetics have been made of the polymerization and exonuclease activities.39-43 The editing site is 35 A away from the polymerization site.32 The mechanism of the polymerization activity (Figure 13.7) is very similar to that for hydrolysis (Figure 13.8). The key to both is the presence of two metal ions, 3.9 A apart, that stabilize the developing charges on the transition state and metal-bound HO- or RO ions (see Chapter 2, section B7).44,45... 

An even better way to determine absolute rate constants is to use pre - steady state kinetics to measure the rate constants for the formation or decay of enzyme-bound intermediates (Chapter 4). The rate constants for first-order exponential time courses are independent of enzyme concentration and so are unaffected by the presence of denatured enzyme. The impurity just lowers the amplitude of the trace. Pre-steady state kinetics are also less prone to artifacts, discussed next, that are caused by the presence of small amounts of contaminants that have a much higher activity than the mutant being analyzed. The steady state kinetics of a weakly active mutant could be dominated by a fraction of a percent of wild type. In pre-steady state kinetics, however, that contaminant would contribute only a fraction of a percent of the amplitude of the trace. This would be either lost in the noise or observed as a minor fast phase. 

The enzyme-product complexes of the yeast enzyme dissociate rapidly so that the chemical steps are rate-determining.31 This permits the measurement of kinetic isotope effects on the chemical steps of this reaction from the steady state kinetics. It is found that the oxidation of deuterated alcohols RCD2OH and the reduction of benzaldehydes by deuterated NADH (i.e., NADD) are significantly slower than the reactions with the normal isotope (kn/kD = 3 to 5).21,31 This shows that hydride (or deuteride) transfer occurs in the rate-determining step of the reaction. The rate constants of the hydride transfer steps for the horse liver enzyme have been measured from pre-steady state kinetics and found to give the same isotope effects.32,33 Kinetic and kinetic isotope effect data are reviewed in reference 34 and the effects of quantum mechanical tunneling in reference 35. 

Although the use of pre-steady state kinetics is undoubtedly superior as a means of analyzing the chemical mechanisms of enzyme catalysis (Chapters 4 and 7), steady state kinetics is more important for the understanding of metabolism, since it measures the catalytic activity of an enzyme in the steady state conditions in the cell. 

Chapter Njjgludes examples of parallel reactions, e.g., the attack of various nucleophiles on acylchymotrypsins, measured by steady state and pre-steady state kinetics. 

The calculation of rate constants from steady state kinetics and the determination of binding stoichiometries requires a knowledge of the concentration of active sites in the enzyme. It is not sufficient to calculate this specific concentration value from the relative molecular mass of the protein and its concentration, since isolated enzymes are not always 100% pure. This problem has been overcome by the introduction of the technique of active-site titration, a combination of steady state and pre-steady state kinetics whereby the concentration of active enzyme is related to an initial burst of product formation. This type of situation occurs when an enzyme-bound intermediate accumulates during the reaction. The first mole of substrate rapidly reacts with the enzyme to form stoichiometric amounts of the enzyme-bound intermediate and product, but then the subsequent reaction is slow since it depends on the slow breakdown of the intermediate to release free enzyme. 

Pre-steady state kinetics involves direct measurements, and direct measurements are always preferable, especially considering the tendency of enzymes to misbehave (section B5). 

The intermediate reacts sufficiently rapidly to be on the reaction pathway. These criteria require that pre-steady state kinetics be used at some stage in order to measure the relevant formation and decomposition rate constants of the intermediate. But the rapid reaction measurements are not sufficient by themselves, since the rate constants must be shown to be consistent with the activity of the enzyme under steady state conditions. Hence the power, and the necessity, of combining the two approaches. 

Proof of formation of an intermediate from pre-steady state kinetics under single-turnover conditions... 

The strategy is to measure the rate constants k2 and k3 of the acylenzyme mechanism (equation 7.1) and to show that each of these is either greater than or equal to the value of kCM for the overall reaction in the steady state (i.e., apply rules 2 and 3 of section Al). This requires (1) choosing a substrate (e.g., an ester of phenylalanine, tyrosine, or tryptophan) that leads to accumulation of the acylenzyme, (2) choosing reaction conditions under which the acylation and deacylation steps may be studied separately, and (3) finding an assay that is convenient for use in pre-steady state kinetics. The experiments chosen here illustrate stopped-flow spectrophotometry and chromopboric procedures. 

In the last section we saw that stopped-flow kinetics can detect intermediates that accumulate. Detection of these intermediates by steady state kinetics is of necessity indirect and relies on inference. Proof depends ultimately on relating the results to the direct observations of the pre-steady state kinetics. But steady state kinetics can also detect intermediates that do not accumulate, and, by extrapolation from the cases in which accumulation occurs, can prove their existence and nature. 

One experimental point worth noting in regard to Figure 7.8 is that the rate constant for the deacylation of the mischarged tRNA can be measured by the pre-steady state kinetics even in the presence of a large fraction of uncharged tRNA. This is not easily done by steady state kinetics, because of the competi-... 

A related phenomenon is half-of-the-sites or half-site reactivity, by which an enzyme containing 2n sites reacts (rapidly) at only n of them (Table 10.2). This can be detected only by pre-steady state kinetics. The tyrosyl-tRNA synthetase provides a good example, in that it forms 1 mol of enzyme-bound tyrosyl adenylate with a rate constant of 18 s1, but the second site reacts 104 times more slowly.13 However, as will be seen in Chapter 15, section J2b, protein engineering studies on the tyrosyl-tRNA synthetase unmasked a pre-existing asymmetry of the enzyme in solution. 

The accumulation of E-Tyr-AMP in the absence of tRNA and the stability of the complex were crucial for the initial success of protein engineering. These factors allow active-site titration and pre- steady state kinetics. Further, the longterm stability of E Tyr-AMP enables the direct solution of its structure by x-ray crystallography. 

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